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abstract: 'We derive the non-equilibrium single-particle momentum distribution function of a hadron resonance gas. We then study the effects that this newly derived expression can have in the freeze-out description of fluid-dynamical models of heavy ion collisions and compare it with the method traditionally employed, the 14-moment approximation.'
address:
- '$^{a}$Department of Physics, McGill University, 3600 University Street, Montreal, Quebec, H3A2T8, Canada'
- '$^{b}$Institut für Theoretische Physik, Johann Wolfgang Goethe-Universität, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany'
- '$^{c}$Department of Physics, P.O.Box 35, FI-40014 University of Jyväskylä, Finland'
author:
- 'G. S. Denicol${}^{a,b}$ and H. Niemi${}^{c}$'
title: 'Derivation of transient relativistic fluid dynamics from the Boltzmann equation for a multi-component system'
---
Introduction
============
Fluid-dynamical models have been able to successfully describe the transverse momentum spectra and azimuthal transverse momentum anisotropies of particles observed in ultrarelativistic heavy ion collisions. One of the main ingredients of fluid-dynamical models is the so-called freeze-out procedure in which the fluid degrees of freedom are matched to kinetic or particle degrees of freedom. Since experiments at RHIC and LHC measure particles and not fluid elements, the freeze-out is an essential step towards the comparison with experimental data.
The Cooper-Frye formalism, usually applied to describe this matching process, demands the knowledge of microscopic information: the (single-particle) momentum distribution function of hadrons on the hypersurface in which freeze-out is performed (usually a constant temperature hypersurface). While this is well known for ideal fluids (Bose-Einstein or Fermi-Dirac distributions in the local rest frame of the fluid), it has remained an open problem for viscous fluids. We remark that, so far, Israel and Stewart’s (IS) simple ansatz for *single* component systems is still being employed in most fluid-dynamical calculations.
In this case, the non-equilibrium correction to the momentum distribution of the $i$–th hadronic species , $\delta f_{\mathbf{k}}^{\left( i\right) }$, is assumed to be [@Teaney:2003kp] $$\delta f_{\mathbf{k}}^{\left( i\right) }=\varepsilon _{\mu \nu }k_{i}^{\mu
}k_{i}^{\nu },$$where $k_{i}^{\mu }$ is the four-momentum of the corresponding hadron and $\varepsilon _{\mu \nu }$ is an expansion coefficient that should be matched to the fluid-dynamical variables.
The above expression has two distinct approximations: 1) the momentum dependence was assumed to be quadratic and 2) the coefficient $\varepsilon
_{\mu \nu }$ was assumed to be the same for all hadronic species, being matched to the shear stress tensor, $\pi ^{\mu \nu }$, as $\varepsilon _{\mu
\nu }=\pi ^{\mu \nu }/\left[2 \left( \varepsilon +P\right) T^{2}\right] $. Here, $\varepsilon $, $P$, and $T$ are the energy density, thermodynamic pressure, and temperature of the fluid. In principle, both these assumptions are incorrect. The limitations of the first assumption were already investigated in some works [@Schenke]. On the other hand, the second assumption and its domain of validity were just investigated in Ref. [@Molnar:2011kx]. The purpose of this work is to further elaborate the studies regarding how $\delta f_{\mathbf{k}}^{\left( i\right) }$ actually depends on the different particle species.
Method of moments
=================
We use the method of moments, as developed in Ref. [@Denicol:2012cn], to compute the $\delta f_{\mathbf{k}}^{\left( i\right) }$ of a multi-component system without making any *a priori* assumption regarding its momentum dependence and the particle dependence of the expansion coefficients. First we factorize $\delta f_{\mathbf{k}}^{\left( i\right) }$ in the following way $\delta f_{\mathbf{k}}^{(i)}=f_{0\mathbf{k}}^{(i)}\tilde{f}_{0\mathbf{k}}^{(i)}\phi _{\mathbf{k}}^{(i)}$, where $f_{0\mathbf{k}}^{(i)}$ is the local equilibrium distribution function, $\tilde{f}_{0\mathbf{k}}^{(i)}=1+a\tilde{f}_{0\mathbf{k}}^{(i)}$ ($a=-1$/$1$ for fermions/bosons), and $\phi _{\mathbf{k}}^{(i)}$ is an out-of-equilibrium contribution. Next, we expand $\phi _{\mathbf{k}}^{(i)}$ in terms of its moments using a complete and orthogonal basis constructed from particle four-momentum, $k_{i}^{\mu }$, and fluid four-velocity, $u^{\mu }$. As done in Ref. [@Denicol:2012cn], we use an expansion basis with two basic ingredients: 1) the irreducible tensors $1,k_{i}^{\left\langle \mu \right\rangle },k_{i}^{\left\langle \mu \right. }k_{i}^{\left.
\nu \right\rangle },k_{i}^{\left\langle \mu \right. }k_{i}^{\nu
}k_{i}^{\left. \lambda \right\rangle },\cdots \ $, analogous to the well-known set of spherical harmonics and constructed by the symmetrized traceless projection of $k_{i}^{\mu _{1}}\cdots k_{i}^{\mu _{m}}$, i.e., $k_{i}^{\left\langle \mu _{1}\right. }\cdots k_{i}^{\left. \mu
_{m}\right\rangle }\equiv \Delta _{\nu _{1}\cdots \nu _{m}}^{\mu _{1}\cdots
\mu _{m}}k_{i}^{\nu _{1}}\cdots k_{i}^{\nu _{m}}$, and 2) the orthonormal polynomials $P_{i\mathbf{k}}^{\left( n\ell \right)
}=\sum_{r=0}^{n}a_{nr}^{(\ell )i}\left( u_{\mu }k_{i}^{\mu }\right) ^{r}$, which are equivalent to the associated Laguerre polynomials in the limit of massless, classical particles [@Denicol:2012cn].
Then, the distribution function becomes,
$$f_{\mathbf{k}}^{(i)}=f_{0\mathbf{k}}^{(i)}+f_{0\mathbf{k}}^{(i)}\tilde{f}_{0\mathbf{k}}^{(i)}\sum_{\ell =0}^{\infty }\sum_{n=0}^{\infty }\mathcal{H}_{i\mathbf{k}}^{\left( n\ell \right) }\rho _{i,n}^{\mu _{1}\cdots \mu _{\ell
}}k_{i,\mu _{1}}\cdots k_{i,\mu _{\ell }}, \label{expansion}$$
where we introduced the energy-dependent coefficients, $\mathcal{H}_{i\mathbf{p}}^{\left( n\ell \right) }\equiv \left[ N_{i}^{\left( \ell \right)
}/\ell !\right] \sum_{m=n}^{\infty }a_{mn}^{(\ell )i}P_{i\mathbf{k}}^{\left(
m\ell \right) }\left( u_{\mu }k_{i}^{\mu }\right) $. The fields $\rho _{i,n}^{\mu _{1}\cdots \mu _{\ell }}$ can be determined exactly using the orthogonality relations satisfied by the expansion basis and can be shown to correspond to the irreducible moments of $\delta
f_{\mathbf{k}}^{(i)}$,$$\rho _{i,r}^{\mu _{1}\ldots \mu _{\ell }}\equiv \left\langle E_{i\mathbf{k}}^{r}k_{i}^{\left\langle \mu _{1}\right. }\ldots k_{i}^{\left. \mu _{\ell
}\right\rangle }\right\rangle _{\delta }\text{, \ \ \ }\left\langle \ldots
\right\rangle _{\delta }=\int dK_{i}\text{ }\left( \ldots \right) \delta f_{\mathbf{k}}^{(i)}, \label{Hk}$$where $g_{i}$ is the degeneracy factor of the $i$–th hadron species and $dK_{i}=g_{i}d^{3}\mathbf{k/}\left[ \left( 2\pi \right) ^{3}k_{i}^{0}\right] $. As long as this basis is complete, the above expansion fully describes $f_{\mathbf{k}}^{(i)}$, no matter how far from equilibrium the system is.
Here, we are interested only on the effects arising from the shear-stress tensor. For this case, it is enough to fix $\ell =2$ (take only irreducible second-rank tensors) in the expansion above, i.e., neglect all scalar terms, e.g. bulk viscous pressure, irreducible first-rank tensors, e.g. heat flow, and tensors with rank higher than two (that never appear in fluid dynamics). The next approximation is the truncation of the expansion in momentum space, keeping only the term with $n=0$ (with $\ell =2$ already fixed). Then, we obtain (for classical particles)$$f_{\mathbf{k}}^{(i)}=f_{0\mathbf{k}}^{(i)}+\frac{f_{0\mathbf{k}}^{(i)}}{2\left( \varepsilon _{i}+P_{i}\right) T^{2}}\pi _{i}^{\mu \nu }k_{i,\mu
}k_{i,\nu }\;.$$Above, $\pi _{i}^{\mu \nu }=\rho _{i,0}^{\mu \nu }$, $\varepsilon _{i}$, and $P_{i}$ are the shear-stress tensor, the energy density, and the thermodynamic pressure *of the* $i$*–th particle species*, respectively. Note that by keeping only the term with $n=0$ (for $\ell =2$) we have the same momentum dependence obtained in the IS formula. However, our expansion coefficients are not independent of the particle type. In this formalism, this did not have to be assumed, but appeared naturally as a consequence of the orthogonality relations satisfied by the basis.
In order to apply this expression to describe freeze-out, further approximations are required. This happens because in fluid dynamics we only evolve the total shear-stress tensor of the system ($\pi ^{\mu \nu
}=\sum_{i}\pi _{i}^{\mu \nu }$) and do not know, from fluid dynamics itself, how it divides into the individual shear-stress tensors of each hadron species ($\pi _{i}^{\mu \nu }$). In order to extract this information, it is mandatory to know how transient relativistic fluid dynamics emerges from the underlying microscopic theory.
Basically, transient relativistic fluid dynamics is derived as the long, but not asymptotically long, time limit of the Boltzmann equation. In this limit, it is possible to relate the shear-stress tensor of individual particle species with the total shear stress tensor, $\pi ^{\mu \nu }$, and the shear tensor, $\sigma ^{\mu \nu }=\partial ^{\left\langle \mu \right.
}u^{\left. \nu \right\rangle }$, of the system. This was done in Ref. [@Denicol:2012cn], for single component systems, and can be easily extended to multi-component systems. Here, we just write down the solution and leave the detailed derivation of this relation to a future work. The solution is, $$\pi _{i}^{\mu \nu }=\frac{\Omega ^{i0}}{\sum_{j}\Omega ^{j0}}\pi ^{\mu \nu
}+2\left[ \eta _{i}-\eta \frac{\Omega ^{i0}}{\sum_{j}\Omega ^{j0}}\right]
\sigma ^{\mu \nu }\equiv \alpha _{i}\pi ^{\mu \nu }+\beta _{i}\sigma ^{\mu
\nu }, \label{EquationN}$$where $\eta _{i}$ is the shear viscosity of the $i$–th species, while $\eta
=\sum_{i}\eta _{i}$ is the total shear viscosity. The matrices $\Omega $ are defined in such a way as to diagonalize the collision integral $\mathcal{M}$, $\Omega ^{-1}\mathcal{M}\Omega =\mathrm{diag}(\chi _{1},\cdots ,\chi _{N})$, with $\chi _{i}$ being the eigenvalues of $\mathcal{M}$. With the truncation in momentum assumed above and considering only elastic 2-to-2 collisions between *classical* particles, $\mathcal{M}$ has the following simple form $$\begin{gathered}
\mathcal{M}^{ij}=\mathcal{A}^{i}\delta ^{ij}+\mathcal{C}^{ij}, \\
\mathcal{A}^{i}=\frac{1}{5}\sum_{j=1}^{N_{\mathrm{hadr.}}}\int
dK_{i}dK_{j}^{\prime }dP_{i}dP_{j}^{\prime }\gamma _{ij}W_{\mathbf{pp}^{\prime }-\mathbf{kk}^{\prime }}^{ij}f_{i\mathbf{k}}^{\left( 0\right) }f_{j\mathbf{k}^{\prime }}^{\left( 0\right) }\left( u_{\lambda }k_{i}^{\lambda
}\right) ^{-1}k_{i}^{\left\langle \mu \right. }k_{i}^{\left. \nu
\right\rangle }\left[ p_{i\left\langle \mu \right. }p_{i\left. \nu
\right\rangle }-k_{i\left\langle \mu \right. }k_{i\left. \nu \right\rangle }\right] , \\
\mathcal{C}^{ij}=\frac{1}{5}\int dK_{i}dK_{j}^{\prime }dP_{i}dP_{j}^{\prime
}\gamma _{ij}W_{\mathbf{pp}^{\prime }-\mathbf{kk}^{\prime }}^{ij}f_{i\mathbf{k}}^{\left( 0\right) }f_{j\mathbf{k}^{\prime }}^{\left( 0\right) }\left(
u_{\lambda }k_{i}^{\lambda }\right) ^{-1}k_{i}^{\left\langle \mu \right.
}k_{i}^{\left. \nu \right\rangle }\left[ p_{j\left\langle \mu \right.
}^{\prime }p_{j\left. \nu \right\rangle }^{\prime }-k_{j\left\langle \mu
\right. }^{\prime }k_{j\left. \nu \right\rangle }^{\prime }\right] ,\end{gathered}$$where $\gamma ^{ij}=1-\left( 1/2\right) \delta ^{ij}$ and $W_{\mathbf{pp}^{\prime }-\mathbf{kk}^{\prime }}^{ij}$ is the transition rate.
Simple model of hadrons
=======================
In order to compute the coefficients $\alpha _{i}$ and $\beta _{i}$ appearing in Eq. \[EquationN\] we must provide a set of hadronic cross sections. In this work, we estimate these coefficients for the first time using a simple hadronic model, in which all hadrons have the same constant cross section, $\sigma _{ij}=$ $30$ mb. We consider only elastic collisions between the hadrons and include all hadrons up to a mass of $1.8$ GeV. In this case, $\alpha _{i}$ and $\beta _{i}$ are actually independent of the value chosen for the cross section and all the difference between the various hadrons species originate solely from their different masses. In this simple scheme, we computed $\alpha _{i}$ and $\beta _{i}$ for all hadron species up to $1.8$ GeV and included all the decays of unstable resonances.
In order to probe the effect this more sophisticated $\delta f_{\mathbf{k}}^{(i)}$ can have on heavy-ion observables, we computed the elliptic flow of pions, kaons, and protons using the fluid-dynamical model applied in Ref. [@Niemi:2012ry], with exactly the same parameters (GLmix initialization, HH-HQ shear viscosity parametrization), but considering several choices of $\delta
f_{\mathbf{k}}^{(i)}$. The resutls are shown in Figs.1. The different lines correspond to the following cases: 1) solid line uses Israel-Stewart’s ansatz, 2) dotted line uses the $\delta f_{\mathbf{k}}^{(i)}$ derived in this paper, and 3) dashed line uses the $\delta f_{\mathbf{k}}^{(i)}$ derived in this paper in the Navier-Stokes limit ($\pi ^{\mu \nu }=2\eta
\sigma ^{\mu \nu }$).
3.4cm 3.4cm 3.4cm
We see that the particle dependence of the coefficients do not have a strong effect on the differential elliptic flow, which looks very similar to the one computed using Israel-Stewart’s ansatz. At very non-central collisions, the difference is larger, but even then, cannot be considered as a crucial effect. Note that one of the reasons that makes this difference small is that we are not in the Navier-Stokes limit at freeze-out: the elliptic flow computed assuming the Navier-Stokes limit actually deviates more strongly from the one computed using Israel-Stewart’s ansatz. Furthermore, note that there is a qualitative particle dependence in our result, the elliptic flow of pions is below the one computed with Israel-Stewart’s ansatz while the elliptic flow of kaons and protons are always above.
We remark that these results arise from an over simplified hadronic description and this insensitivity to the particle species might be coming just from the simple choice of hadronic cross sections assumed. In future calculations, we will come back to this discussion using more realistic cross sections for the hadrons and also including inelastic collisions between the hadrons as well.
The work of H.N. was supported by the Academy of Finland, Project No. 133005. G.S.D thanks D. Molnar for helpful discussions.
[9]{}
W. Israel and J. Stewart, Annals Phys. [**118**]{}, 341-372 (1979); D. Teaney, Phys. Rev. C [**68**]{}, 034913 (2003).
K. Dusling, G. D. Moore and D. Teaney, Phys. Rev. C [**81**]{}, 034907 (2010); B. Schenke, S. Jeon, and C. Gale, Phys. Rev. C [**85**]{}, 024901 (2012).
D. Molnar, J. Phys. G [**38**]{}, 124173 (2011).
G. S. Denicol, H. Niemi, E. Molnar and D. H. Rischke, Phys. Rev. D [**85**]{}, 114047 (2012). H. Niemi, G. S. Denicol, P. Huovinen, E. Molnar and D. H. Rischke, Phys. Rev. C [**86**]{}, 014909 (2012); Phys. Rev. Lett. [**106**]{}, 212302 (2011).
|
Homer Alaska - News
Story last updated at
4:32 PM on
Wednesday, February 13, 2013
Begich focuses on healthy state economy
Neither rain nor snow could deter Homer area residents from attending a town hall meeting with Sen. Mark Begich on Sunday. More than 100 people crowded into the commons of Kachemak Bay Campus, Kenai Peninsula College-University of Alaska Anchorage, to listen to the senator's comments and to ask questions.
Photographer: McKibben Jackinsky, Homer News
U.S. Sen. Mark Begich speaks to a crowd of more than 100 area residents on Sunday at the Kachemak Bay Campus, Kenai Peninsula College-University of Alaska Anchorage.
Homer Mayor Beth Wythe introduced Begich, noting his five years of service to the state and his focus on "building a strong economy for Alaska." Begich serves on the U.S. Senate committees on Appropriations; Veterans' Affairs; Indian Affairs; Commerce, Science and Transportation; Homeland Security and Governmental Affairs; and the U.S. Senate Subcommittee on Oceans, Atmosphere, Fisheries and Coast Guard.
Although newly elected members of the Senate are still getting adjusted, Begich assured the audience that "we are fully engaged in a lot of issues."
One of those issues is passage of the Violence Against Women Act.
"The Senate passed it last year with bi-partisan support. It sat in the House and died at the end of the session, but we brought it back," said Begich.
"It's important for Alaska and for the rest of the country and I hope the House will move forward on it."
Begich is a co-sponsor of the VAWA, which seeks to strengthen protections for victims of domestic and sexual abuse and expand programs in support of those victims. On Tuesday, following his visit to Homer, Begich announced the bill had passed in the Senate with a vote of 78-22 and will now proceed to the House.
The need for a Postal Reform Bill that also passed the Senate last year but not the House was addressed by the senator. His comments followed a Feb. 6 announcement of changes to the postal service delivery schedule, namely of weekly five-day mail delivery and six-day package delivery beginning August 2013.
The bigger, over-riding issue, however, is how to deal with the nation's budget and its $16 trillion debt, said Begich.
"People think the debt occurred overnight, magically. No, this is 50 years of lack of people watching the bottom line, to be frank with you," he said.
Begich noted the importance of March 1, when automatic budget cuts occur, and March 27, when a continuing resolution allows Congress to fund government agencies if formal appropriations have not been signed into law.
"The problem is you can't modify a continuing resolution," said Begich, using the State Department as an example. Under a continuing resolution, "they will still receive dollars for work that they're doing in the Iraq war. There is no war in Iraq that we're engaged in, but we'll still spend the money because the continuing resolution does that. ... So, we're trying to figure out a regular appropriation bill so we can get the junk out and move forward."
Other topics needing attention are education and immigration reform and energy, "but we can't get to those issues when we're buried by budget issues," said Begich.
Around the state, Begich said Alaska's "economy is generally pretty good." With oil and gas revenues declining, however, the state will be challenged "to figure out how to manage the budget with or without tax changes," he said.
Compared to fishing on the East Coast, fishing in Alaska is in "good" shape. Begich credited Alaska's Legislature for funding ocean acidification research, he vowed to continue fighting against "Frankenfish," genetically engineered fish, and said the state's congressional delegation stands firm in "doing everything we can to take that product off the market."
In terms of oil and gas development on the outer continental shelf, Begich said the question isn't if it will happen but how it will be managed for the benefit of Alaska and with the necessary security and safety.
"One thing we're pushing is a revenue-sharing bill. Any development that goes on out there, we believe Alaska should get a share," he said. The benefit would go to tribes, local governments, village corporations, "people on the ground that are dealing with the impacts," with a small percent going to the state.
Before taking questions from the audience, Begich noted the importance of developing Alaska's ports and harbors and expanding educational opportunities.
"We'll fund roads and bike trials, but when it comes to ports, they kind of have to fend for themselves," he said. "That's a problem because they are a huge part of our economic engine."
He emphasized the need for vocational education and broadening a "STEM" approach (science, technology, engineering and math) to "STEAM" (science, technology, engineering, art and math).
Asked if he saw an end to the delay of President Obama's court and committee nominations, Begich described filibustering and changes he supports that would streamline the process.
"To not have judges in positions because of political fighting is ridiculous," he said.
With regard to the possibility of national funding for tsunami cleanup, Begich noted the bill providing assistance for areas struck by Super Storm Sandy.
"That bill should have been called the disaster relief bill, not the Sandy bill," said Begich, referencing disasters that occur elsewhere. "Climate change is happening. Anyone who doesn't think it's happening is on another planet. That means we'll have more disasters. ... Something's happening and we need to prepare for it."
He characterized marine debris it as a "slow disaster."
"We're used to earthquakes and storms. They end and you deal with it. ... This is one we want to deal with now. If we wait, the accumulation that will occur will be beyond management," he said.
Asked about the future of the proposed Pebble mine, Begich said he supported the review by the Environmental Protection Agency.
"I think Pebble has huge challenges ahead of them. I don't know how they'll ever meet (those challenges), to be frank with you, but we have to let EPA finish with (the review), and then the great debate will begin," he said.
The question-and-answer period was an opportunity for Begich to announce his intent to sponsor a bill safeguarding the right to vote, progress in the state for veterans to receive health care in their home communities, his support of balancing oil and gas development and environmental concerns, providing the U.S. Coast Guard with the resources it needs and the importance of looking ahead.
"Elected officials think about today, but this state, this community didn't get built on those ideas. We built thinking about the next 20 years, the next 30 years," said Begich. "I would challenge you to ask any legislator from any area, 'Where do you see Alaska in the next 20 years?' I'd be curious to know what they say. That's the question we're not facing in this state."
In terms of gun control, Begich doesn't foresee legislation being passed to ban weapons, but he has co-sponsored a bill that would provide teachers with the skills to quickly analyze the mental health of individuals in intervention scenarios. He spoke of the need for an improved background check system and said the Senate will be addressing the trafficking of guns.
Given the current economy, Begich was asked where he saw the nation in 20 years.
"As Americans, for us to believe that we're going over the cliff and that we'll be gone as a society, I will never believe that. This country has gone through worse conditions," said Begich. "This is about money. This is manageable. It does require people to make decisions. That's the difficult piece. But I'm not afraid to make these decisions."
Pointing to a negative "everything is falling apart" attitude he has observed in Washington, D.C, Begich said, "You can think that or you can do something about it. ... We have had plenty of ups and downs, but that doesn't get us to move to the next state. There will be some big bumps coming, but we'll be better for it."
Additional information about Sen. Begich can be found at www.begich.senate.gov.
McKibben Jackinsky can be reached at mckibben.jackinsky@homernews.com. |
/* $NetBSD: tsig_test.c,v 1.5 2020/05/24 19:46:25 christos Exp $ */
/*
* Copyright (C) Internet Systems Consortium, Inc. ("ISC")
*
* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/.
*
* See the COPYRIGHT file distributed with this work for additional
* information regarding copyright ownership.
*/
#if HAVE_CMOCKA
#include <sched.h> /* IWYU pragma: keep */
#include <setjmp.h>
#include <stdarg.h>
#include <stdbool.h>
#include <stddef.h>
#include <stdlib.h>
#include <unistd.h>
#define UNIT_TESTING
#include <cmocka.h>
#include <isc/mem.h>
#include <isc/print.h>
#include <isc/util.h>
#include <dns/rdatalist.h>
#include <dns/rdataset.h>
#include <dns/tsig.h>
#include "../tsig_p.h"
#include "dnstest.h"
#define CHECK(r) \
do { \
result = (r); \
if (result != ISC_R_SUCCESS) { \
goto cleanup; \
} \
} while (/*CONSTCOND*/0)
#define TEST_ORIGIN "test"
static int
_setup(void **state) {
isc_result_t result;
UNUSED(state);
result = dns_test_begin(NULL, false);
assert_int_equal(result, ISC_R_SUCCESS);
return (0);
}
static int
_teardown(void **state) {
UNUSED(state);
dns_test_end();
return (0);
}
static int debug = 0;
static isc_result_t
add_mac(dst_context_t *tsigctx, isc_buffer_t *buf) {
dns_rdata_any_tsig_t tsig;
dns_rdata_t rdata = DNS_RDATA_INIT;
isc_buffer_t databuf;
isc_region_t r;
isc_result_t result;
unsigned char tsigbuf[1024];
isc_buffer_usedregion(buf, &r);
dns_rdata_fromregion(&rdata, dns_rdataclass_any, dns_rdatatype_tsig,
&r);
isc_buffer_init(&databuf, tsigbuf, sizeof(tsigbuf));
CHECK(dns_rdata_tostruct(&rdata, &tsig, NULL));
isc_buffer_putuint16(&databuf, tsig.siglen);
isc_buffer_putmem(&databuf, tsig.signature, tsig.siglen);
isc_buffer_usedregion(&databuf, &r);
result = dst_context_adddata(tsigctx, &r);
dns_rdata_freestruct(&tsig);
cleanup:
return (result);
}
static isc_result_t
add_tsig(dst_context_t *tsigctx, dns_tsigkey_t *key, isc_buffer_t *target) {
dns_compress_t cctx;
dns_rdata_any_tsig_t tsig;
dns_rdata_t rdata = DNS_RDATA_INIT;
dns_rdatalist_t rdatalist;
dns_rdataset_t rdataset;
isc_buffer_t *dynbuf = NULL;
isc_buffer_t databuf;
isc_buffer_t sigbuf;
isc_region_t r;
isc_result_t result = ISC_R_SUCCESS;
isc_stdtime_t now;
unsigned char tsigbuf[1024];
unsigned int count;
unsigned int sigsize = 0;
bool invalidate_ctx = false;
memset(&tsig, 0, sizeof(tsig));
CHECK(dns_compress_init(&cctx, -1, dt_mctx));
invalidate_ctx = true;
tsig.common.rdclass = dns_rdataclass_any;
tsig.common.rdtype = dns_rdatatype_tsig;
ISC_LINK_INIT(&tsig.common, link);
dns_name_init(&tsig.algorithm, NULL);
dns_name_clone(key->algorithm, &tsig.algorithm);
isc_stdtime_get(&now);
tsig.timesigned = now;
tsig.fudge = DNS_TSIG_FUDGE;
tsig.originalid = 50;
tsig.error = dns_rcode_noerror;
tsig.otherlen = 0;
tsig.other = NULL;
isc_buffer_init(&databuf, tsigbuf, sizeof(tsigbuf));
isc_buffer_putuint48(&databuf, tsig.timesigned);
isc_buffer_putuint16(&databuf, tsig.fudge);
isc_buffer_usedregion(&databuf, &r);
CHECK(dst_context_adddata(tsigctx, &r));
CHECK(dst_key_sigsize(key->key, &sigsize));
tsig.signature = isc_mem_get(dt_mctx, sigsize);
isc_buffer_init(&sigbuf, tsig.signature, sigsize);
CHECK(dst_context_sign(tsigctx, &sigbuf));
tsig.siglen = isc_buffer_usedlength(&sigbuf);
assert_int_equal(sigsize, tsig.siglen);
isc_buffer_allocate(dt_mctx, &dynbuf, 512);
CHECK(dns_rdata_fromstruct(&rdata, dns_rdataclass_any,
dns_rdatatype_tsig, &tsig, dynbuf));
dns_rdatalist_init(&rdatalist);
rdatalist.rdclass = dns_rdataclass_any;
rdatalist.type = dns_rdatatype_tsig;
ISC_LIST_APPEND(rdatalist.rdata, &rdata, link);
dns_rdataset_init(&rdataset);
CHECK(dns_rdatalist_tordataset(&rdatalist, &rdataset));
CHECK(dns_rdataset_towire(&rdataset, &key->name, &cctx, target, 0,
&count));
/*
* Fixup additional record count.
*/
((unsigned char *)target->base)[11]++;
if (((unsigned char *)target->base)[11] == 0) {
((unsigned char *)target->base)[10]++;
}
cleanup:
if (tsig.signature != NULL) {
isc_mem_put(dt_mctx, tsig.signature, sigsize);
}
if (dynbuf != NULL) {
isc_buffer_free(&dynbuf);
}
if (invalidate_ctx) {
dns_compress_invalidate(&cctx);
}
return (result);
}
static void
printmessage(dns_message_t *msg) {
isc_buffer_t b;
char *buf = NULL;
int len = 1024;
isc_result_t result = ISC_R_SUCCESS;
if (!debug) {
return;
}
do {
buf = isc_mem_get(dt_mctx, len);
isc_buffer_init(&b, buf, len);
result = dns_message_totext(msg, &dns_master_style_debug, 0,
&b);
if (result == ISC_R_NOSPACE) {
isc_mem_put(dt_mctx, buf, len);
len *= 2;
} else if (result == ISC_R_SUCCESS) {
printf("%.*s\n", (int)isc_buffer_usedlength(&b), buf);
}
} while (result == ISC_R_NOSPACE);
if (buf != NULL) {
isc_mem_put(dt_mctx, buf, len);
}
}
static void
render(isc_buffer_t *buf, unsigned flags, dns_tsigkey_t *key,
isc_buffer_t **tsigin, isc_buffer_t **tsigout, dst_context_t *tsigctx) {
dns_message_t *msg = NULL;
dns_compress_t cctx;
isc_result_t result;
result = dns_message_create(dt_mctx, DNS_MESSAGE_INTENTRENDER, &msg);
assert_int_equal(result, ISC_R_SUCCESS);
assert_non_null(msg);
msg->id = 50;
msg->rcode = dns_rcode_noerror;
msg->flags = flags;
/*
* XXXMPA: this hack needs to be replaced with use of
* dns_message_reply() at some point.
*/
if ((flags & DNS_MESSAGEFLAG_QR) != 0) {
msg->verified_sig = 1;
}
if (tsigin == tsigout) {
msg->tcp_continuation = 1;
}
if (tsigctx == NULL) {
result = dns_message_settsigkey(msg, key);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_message_setquerytsig(msg, *tsigin);
assert_int_equal(result, ISC_R_SUCCESS);
}
result = dns_compress_init(&cctx, -1, dt_mctx);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_message_renderbegin(msg, &cctx, buf);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_message_renderend(msg);
assert_int_equal(result, ISC_R_SUCCESS);
if (tsigctx != NULL) {
isc_region_t r;
isc_buffer_usedregion(buf, &r);
result = dst_context_adddata(tsigctx, &r);
assert_int_equal(result, ISC_R_SUCCESS);
} else {
if (tsigin == tsigout && *tsigin != NULL) {
isc_buffer_free(tsigin);
}
result = dns_message_getquerytsig(msg, dt_mctx, tsigout);
assert_int_equal(result, ISC_R_SUCCESS);
}
dns_compress_invalidate(&cctx);
dns_message_destroy(&msg);
}
/*
* Test tsig tcp-continuation validation:
* Check that a simulated three message TCP sequence where the first
* and last messages contain TSIGs but the intermediate message doesn't
* correctly verifies.
*/
static void
tsig_tcp_test(void **state) {
const dns_name_t *tsigowner = NULL;
dns_fixedname_t fkeyname;
dns_message_t *msg = NULL;
dns_name_t *keyname;
dns_tsig_keyring_t *ring = NULL;
dns_tsigkey_t *key = NULL;
isc_buffer_t *buf = NULL;
isc_buffer_t *querytsig = NULL;
isc_buffer_t *tsigin = NULL;
isc_buffer_t *tsigout = NULL;
isc_result_t result;
unsigned char secret[16] = { 0 };
dst_context_t *tsigctx = NULL;
dst_context_t *outctx = NULL;
UNUSED(state);
/* isc_log_setdebuglevel(lctx, 99); */
keyname = dns_fixedname_initname(&fkeyname);
result = dns_name_fromstring(keyname, "test", 0, NULL);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_tsigkeyring_create(dt_mctx, &ring);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_tsigkey_create(keyname, dns_tsig_hmacsha256_name, secret,
sizeof(secret), false, NULL, 0, 0, dt_mctx,
ring, &key);
assert_int_equal(result, ISC_R_SUCCESS);
assert_non_null(key);
/*
* Create request.
*/
isc_buffer_allocate(dt_mctx, &buf, 65535);
render(buf, 0, key, &tsigout, &querytsig, NULL);
isc_buffer_free(&buf);
/*
* Create response message 1.
*/
isc_buffer_allocate(dt_mctx, &buf, 65535);
render(buf, DNS_MESSAGEFLAG_QR, key, &querytsig, &tsigout, NULL);
/*
* Process response message 1.
*/
result = dns_message_create(dt_mctx, DNS_MESSAGE_INTENTPARSE, &msg);
assert_int_equal(result, ISC_R_SUCCESS);
assert_non_null(msg);
result = dns_message_settsigkey(msg, key);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_message_parse(msg, buf, 0);
assert_int_equal(result, ISC_R_SUCCESS);
printmessage(msg);
result = dns_message_setquerytsig(msg, querytsig);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_tsig_verify(buf, msg, NULL, NULL);
assert_int_equal(result, ISC_R_SUCCESS);
assert_int_equal(msg->verified_sig, 1);
assert_int_equal(msg->tsigstatus, dns_rcode_noerror);
/*
* Check that we have a TSIG in the first message.
*/
assert_non_null(dns_message_gettsig(msg, &tsigowner));
result = dns_message_getquerytsig(msg, dt_mctx, &tsigin);
assert_int_equal(result, ISC_R_SUCCESS);
tsigctx = msg->tsigctx;
msg->tsigctx = NULL;
isc_buffer_free(&buf);
dns_message_destroy(&msg);
result = dst_context_create(key->key, dt_mctx, DNS_LOGCATEGORY_DNSSEC,
false, 0, &outctx);
assert_int_equal(result, ISC_R_SUCCESS);
assert_non_null(outctx);
/*
* Start digesting.
*/
result = add_mac(outctx, tsigout);
assert_int_equal(result, ISC_R_SUCCESS);
/*
* Create response message 2.
*/
isc_buffer_allocate(dt_mctx, &buf, 65535);
assert_int_equal(result, ISC_R_SUCCESS);
render(buf, DNS_MESSAGEFLAG_QR, key, &tsigout, &tsigout, outctx);
/*
* Process response message 2.
*/
result = dns_message_create(dt_mctx, DNS_MESSAGE_INTENTPARSE, &msg);
assert_int_equal(result, ISC_R_SUCCESS);
assert_non_null(msg);
msg->tcp_continuation = 1;
msg->tsigctx = tsigctx;
tsigctx = NULL;
result = dns_message_settsigkey(msg, key);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_message_parse(msg, buf, 0);
assert_int_equal(result, ISC_R_SUCCESS);
printmessage(msg);
result = dns_message_setquerytsig(msg, tsigin);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_tsig_verify(buf, msg, NULL, NULL);
assert_int_equal(result, ISC_R_SUCCESS);
assert_int_equal(msg->verified_sig, 0);
assert_int_equal(msg->tsigstatus, dns_rcode_noerror);
/*
* Check that we don't have a TSIG in the second message.
*/
tsigowner = NULL;
assert_true(dns_message_gettsig(msg, &tsigowner) == NULL);
tsigctx = msg->tsigctx;
msg->tsigctx = NULL;
isc_buffer_free(&buf);
dns_message_destroy(&msg);
/*
* Create response message 3.
*/
isc_buffer_allocate(dt_mctx, &buf, 65535);
render(buf, DNS_MESSAGEFLAG_QR, key, &tsigout, &tsigout, outctx);
result = add_tsig(outctx, key, buf);
assert_int_equal(result, ISC_R_SUCCESS);
/*
* Process response message 3.
*/
result = dns_message_create(dt_mctx, DNS_MESSAGE_INTENTPARSE, &msg);
assert_int_equal(result, ISC_R_SUCCESS);
assert_non_null(msg);
msg->tcp_continuation = 1;
msg->tsigctx = tsigctx;
tsigctx = NULL;
result = dns_message_settsigkey(msg, key);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_message_parse(msg, buf, 0);
assert_int_equal(result, ISC_R_SUCCESS);
printmessage(msg);
/*
* Check that we had a TSIG in the third message.
*/
assert_non_null(dns_message_gettsig(msg, &tsigowner));
result = dns_message_setquerytsig(msg, tsigin);
assert_int_equal(result, ISC_R_SUCCESS);
result = dns_tsig_verify(buf, msg, NULL, NULL);
assert_int_equal(result, ISC_R_SUCCESS);
assert_int_equal(msg->verified_sig, 1);
assert_int_equal(msg->tsigstatus, dns_rcode_noerror);
if (tsigin != NULL) {
isc_buffer_free(&tsigin);
}
result = dns_message_getquerytsig(msg, dt_mctx, &tsigin);
assert_int_equal(result, ISC_R_SUCCESS);
isc_buffer_free(&buf);
dns_message_destroy(&msg);
if (outctx != NULL) {
dst_context_destroy(&outctx);
}
if (querytsig != NULL) {
isc_buffer_free(&querytsig);
}
if (tsigin != NULL) {
isc_buffer_free(&tsigin);
}
if (tsigout != NULL) {
isc_buffer_free(&tsigout);
}
dns_tsigkey_detach(&key);
if (ring != NULL) {
dns_tsigkeyring_detach(&ring);
}
}
/* Tests the dns__tsig_algvalid function */
static void
algvalid_test(void **state) {
UNUSED(state);
assert_true(dns__tsig_algvalid(DST_ALG_HMACMD5));
assert_true(dns__tsig_algvalid(DST_ALG_HMACSHA1));
assert_true(dns__tsig_algvalid(DST_ALG_HMACSHA224));
assert_true(dns__tsig_algvalid(DST_ALG_HMACSHA256));
assert_true(dns__tsig_algvalid(DST_ALG_HMACSHA384));
assert_true(dns__tsig_algvalid(DST_ALG_HMACSHA512));
assert_false(dns__tsig_algvalid(DST_ALG_GSSAPI));
}
/* Tests the dns__tsig_algfromname function */
static void
algfromname_test(void **state) {
UNUSED(state);
assert_int_equal(dns__tsig_algfromname(DNS_TSIG_HMACMD5_NAME),
DST_ALG_HMACMD5);
assert_int_equal(dns__tsig_algfromname(DNS_TSIG_HMACSHA1_NAME),
DST_ALG_HMACSHA1);
assert_int_equal(dns__tsig_algfromname(DNS_TSIG_HMACSHA224_NAME),
DST_ALG_HMACSHA224);
assert_int_equal(dns__tsig_algfromname(DNS_TSIG_HMACSHA256_NAME),
DST_ALG_HMACSHA256);
assert_int_equal(dns__tsig_algfromname(DNS_TSIG_HMACSHA384_NAME),
DST_ALG_HMACSHA384);
assert_int_equal(dns__tsig_algfromname(DNS_TSIG_HMACSHA512_NAME),
DST_ALG_HMACSHA512);
assert_int_equal(dns__tsig_algfromname(DNS_TSIG_GSSAPI_NAME),
DST_ALG_GSSAPI);
assert_int_equal(dns__tsig_algfromname(DNS_TSIG_GSSAPIMS_NAME),
DST_ALG_GSSAPI);
assert_int_equal(dns__tsig_algfromname(dns_rootname), 0);
}
/* Tests the dns__tsig_algnamefromname function */
/*
* Helper function to create a dns_name_t from a string and see if
* the dns__tsig_algnamefromname function can correctly match it against the
* static table of known algorithms.
*/
static void
test_name(const char *name_string, const dns_name_t *expected) {
dns_name_t name;
dns_name_init(&name, NULL);
assert_int_equal(dns_name_fromstring(&name, name_string, 0, dt_mctx),
ISC_R_SUCCESS);
assert_int_equal(dns__tsig_algnamefromname(&name), expected);
dns_name_free(&name, dt_mctx);
}
static void
algnamefromname_test(void **state) {
UNUSED(state);
/* test the standard algorithms */
test_name("hmac-md5.sig-alg.reg.int", DNS_TSIG_HMACMD5_NAME);
test_name("hmac-sha1", DNS_TSIG_HMACSHA1_NAME);
test_name("hmac-sha224", DNS_TSIG_HMACSHA224_NAME);
test_name("hmac-sha256", DNS_TSIG_HMACSHA256_NAME);
test_name("hmac-sha384", DNS_TSIG_HMACSHA384_NAME);
test_name("hmac-sha512", DNS_TSIG_HMACSHA512_NAME);
test_name("gss-tsig", DNS_TSIG_GSSAPI_NAME);
test_name("gss.microsoft.com", DNS_TSIG_GSSAPIMS_NAME);
/* try another name that isn't a standard algorithm name */
assert_int_equal(dns__tsig_algnamefromname(dns_rootname), NULL);
}
/* Tests the dns__tsig_algallocated function */
static void
algallocated_test(void **state) {
UNUSED(state);
/* test the standard algorithms */
assert_false(dns__tsig_algallocated(DNS_TSIG_HMACMD5_NAME));
assert_false(dns__tsig_algallocated(DNS_TSIG_HMACSHA1_NAME));
assert_false(dns__tsig_algallocated(DNS_TSIG_HMACSHA224_NAME));
assert_false(dns__tsig_algallocated(DNS_TSIG_HMACSHA256_NAME));
assert_false(dns__tsig_algallocated(DNS_TSIG_HMACSHA384_NAME));
assert_false(dns__tsig_algallocated(DNS_TSIG_HMACSHA512_NAME));
assert_false(dns__tsig_algallocated(DNS_TSIG_HMACSHA512_NAME));
assert_false(dns__tsig_algallocated(DNS_TSIG_HMACSHA512_NAME));
/* try another name that isn't a standard algorithm name */
assert_true(dns__tsig_algallocated(dns_rootname));
}
int
main(void) {
const struct CMUnitTest tests[] = {
cmocka_unit_test_setup_teardown(tsig_tcp_test, _setup,
_teardown),
cmocka_unit_test(algvalid_test),
cmocka_unit_test(algfromname_test),
cmocka_unit_test_setup_teardown(algnamefromname_test, _setup,
_teardown),
cmocka_unit_test(algallocated_test),
};
return (cmocka_run_group_tests(tests, NULL, NULL));
}
#else /* HAVE_CMOCKA */
#include <stdio.h>
int
main(void) {
printf("1..0 # Skipped: cmocka not available\n");
return (0);
}
#endif /* if HAVE_CMOCKA */
|
"(Heavy breathing)" "And the fourth angel poured out his vial upon the sun and power was given unto him to scorch men with fire." "And the fifth angel poured out his vial upon the seat of the beast and his kingdom was full of darkness..." "(Breathing unevenly) No..." "The enemy is closer than you think." "(Heavy breathing) No!" "No!" " No!" "No!" "No!" "No!" "No!" " (Bird shrieks)" "(Whimpering)" "The King's doctor at once!" "(Heavy breathing)" "(Thunder)" "(Intro music)" "♪ I'm the King of my own land ♪" "♪ Facing tempests of dust ♪" "♪ I'll fight until the end ♪" "♪ Creatures of my dreams rise up and dance with me ♪" "♪ Now and forever ♪" "♪ I'm your King ♪" "His humors are out of balance." "(Masson) (Sighing)" "(Masson) Majesty, drink this to help you sleep." "(Masson) It's a herbal cordial to allay your pain and procure your rest." "Laudanum, saffron and bruised cloves." "(Masson) I beg you, heed the counsel of your medical advisers." "(Louis breathes heavily)" "What do you say?" "Have you ever had a fever?" "I have, Your Majesty." "What measures did you take?" "To permit my body to cure itself, it was necessary to purge." "There's a herb, sagewort." "Known as sweet wormword." "Fetch your remedy, but quickly and with a calm air." " No one must know of his condition." " (Masson) Sire." "(Breathing)" "(Chuckling)" "(Chuckling)" "(Music)" "Love is in your future." "Twice as much as you might think." "(Scoffing) I'm off to water the garden." "(Grunting)" "I think that's a no." "(Grunting)" "(Yawning)" "(Coughs)" "(Yawning)" "You did not respond to my last message." "(Grunting) Well, to be perfectly honest it didn't seem pressing." "It was a busy week." "Fail me again and your next piss will be sitting down!" "You have my full attention." "(Heavy breathing)" "Read and follow... to the letter." "Don't breathe." "(Gasping)" "(signing)" "Were you raised in a cattle shed?" "Why are you here?" "Come at once." "The King's Circle." "Wake my wife." "Do it now." "(Tense music)" "(Panting and moaning)" "(Grunting)" "(Sighing, panting)" "What will you see just before the end?" "(Panting)" "The face of my enemy." "(signing)" "I've always dreamed the same dream." "I'm in a great avenue of evergreens, sitting in wet grass," "gazing through the pine cones at a canopy of sky." "Then if I were you." "I would stay indoors." "(Laughing)" "(Knocking)" "(Knocking)" " Speak." " (Man) The King's Circle." "(Knocking)" "(Tense music)" "(Tense music) (Footsteps)" "I must speak to you in private." "You're still drunk." "It can wait." "But the gravity of my need..." "All needs of yours weigh the same." "(Panting, stammering)" "A great tide is stirring." "It pertains to your future, your place at its center." "Go to bed." "Please." "Philippa..." "Philippe!" "In the King's book of names, you'll find a circle of trust, a list of those he believes in his heart are the most loyal, faithful and true." "(Colbert) Your names are on that list." "(Colbert) An unbroken circle of trust." "(Colbert) We all know here what is at stake." "How is my King?" "The fever is consuming him." "Protocol now demands we begin work on the issue of succession." "I will not hear it." "He is stronger than a malady, stronger than a hundred fevers." "Not this one clearly." "Your words are comforting." "My King values expediency over sympathy." "(Colbert) As we hope for the best, we must nevertheless plan for the worst." "(Rohan) Where did this distemper come from?" "Is it poison?" "(Fabien) I'll root out the cause." "I hope you have more success." "More?" "If a sick man gets to the King I don't call it victory." "The Dauphin is direct successor but would require a regent." "I would argue a young King requires a council of elders, with experience of government." "(Colbert) Protocol's clear." "If the King..." "Do not say it." "Dies, or if he is incapable of exercising his duties, a regent shall be appointed." "Who?" "That is the choice before us." "What is the news?" "We did not see the King at mass and you know people gossip." "Hunting accident, broke his leg." "It will take weeks." "Your Majesty, please!" "Rumors are flying around court." "The truth might stop them." "Why such secrecy?" "So that rumors do not start." " What would happen if..." " No "if"." "He will be well." "Yes, of course." "Jezebel!" "(Smashing of glass)" " Delilah!" " Stop it!" "You may have shaved my seven locks and sold me to the Philistines but I'm not yet on my knees." "If the King's hair hurts perhaps it was the wine." "Eat the beast's fur that bit you." "But who wants fluff for breakfast?" "(Jacket hits him)" "Was I out of turn?" "Come now!" "How is our King?" "(Sighing) Please speak." "Why all the secrecy?" "Speak!" "You must vow to me." " On my father's life." " He's dead." " My mother's?" " Forget it." "(Sighing) I cannot help my tongue." "Please!" "I see your distress and it pains me." "(Sighing) Allow me to share your burden." "Speak!" "My brother is very sick." "I always said you'd make a marvelous King!" "(inhales) Stop!" "So you're serious." "Goodness!" "He is gravely ill." "And if he were to die, it might be possible that I will be regent." "God in heaven!" "I had no idea." "Not a word to anyone." "This is a testing time but I know with you by my side," " I can overcome anything." " Hmm, yes, of course." "Now, I must have air." "Come with me, please." "I cannot." "I have to, um, think." "Very well." "He is in my prayers as are YOU." "(Clicking fingers)" "(Clicking fingers)" "What did you mean when you said "a great tide is stirring?"" "Did I say that?" "Hmm!" "I must have been drunk." "(Shouting in distance)" "(Coughing)" "(Gurgling) (Coughing, spluttering)" "(Horse galloping)" "Father?" "Father!" "(crying)" "Help me!" "Please, he's dying." " What happened?" " I don't know." "(Groaning)" "You must come." "The King." "He will perish." "As will your King." "Save your father or save France." "The choice is yours." " The King?" " He ordered my eyes to the door but he's not ordered them back." "Stay here." "(Whispering indistinctly)" "(Bontemps) Move." "Move!" "(Whispering indistinctly)" "Shut the doors." "Close all the shutters." "Door!" "Door!" "Ah, there you are." "I can't decide if this will be a courante a sarabande or a passacaille." "You must return to bed." "(Bontemps) Your doctor is here." "I've created a new dance, Bontemps, and I wish my court to perform it." "Very well, Sire." "Everyone must learn it now." "Bring me a pen and paper and a gardener." " A gardener?" " Yes, my gardener Jacques." "He lost his hand in Malines." "Bring him here." "I see this dance unfolding in a garden, an orangerie full of blossom." "I didn't see you at our recent ballet." "I dance as commanded by you." "Then do so now." "Dance for me now." "Follow me." "First, a balancé." "Twice going forward and then a pas de bourrée." "Then another balancé going backwards, then another pas de bourée." "(Humming)" "If these are your steps, Sire, then your dance is a passacaille." "You're a man of quality Bontemps." "But I do not trust you," "I do not trust you at all." " Sire..." " I do not know him!" "Your Majesty, please!" "Where is my gardener?" "I need him." "Bring me Jacques!" "Guards!" "Please, bring me Jacques!" "Guards, bring me Jacques!" "They mean to kill me!" "They mean to kill me!" "Bring me Jacques!" "Water for the King!" "(Whimpering)" "My gardener will know what to do... (Bontemps) Shh..." "Shh... (Heavy breathing)" "His fever grows stronger." "(Bontemps) Your Majesty, the gardener." "(Footsteps)" "Tell me a story about my father." "Your mother suckled him young before you, which makes you milk brothers, does it not?" "A story, then." "Many years ago, an emissary from Japan visited our shores." "(Jacques) He brought a gift from China for your father, an ancient text that he said that every general in the emperor's army had read." "(Breathing)" "The text was called the Art of War." "(Jacques) So the story went around the palace of this most vital maxim:" ""Appear weak when you are strong and strong when you are weak."" "(Coughing)" "Out." "(Coughing)" "Out!" "Out!" "(Coughing)" "(Praying in Latin)" "(signing)" "Yes, Madame de Clermont!" "Forgive me." "I'd always assumed your office was in the east wing." "It is." "As promised Monsieur Colbert, our proof of noble heritage." "Ah!" " Good." "I will review it in due course." " Good day." "(Retching)" "(Coughing)" "We can't put his life in a child's hands." "Hardly a child." "My brother should be in Paris." "I have readied my own carriage." " I'll take him." " He can't travel." " An hour at most." " (Marie) It may kill him." "It is this palace that is killing him." "(Grunting)" "(Breathing)" "I was just in the laundry, I found this in one of the pockets." "The same shapes as you have in your book." "Don't go anywhere." "A meeting is planned for today. ls my horse ready?" " Fed and watered this morning!" " You've done well." " There's no one here!" " (Fabien) Yes, I noticed that myself." "(signing)" "Cassel, we are risking our lives being here." "I had to conceal my horse half a mile away." "You're one to talk." "Why the urgency?" "You didn't write it?" "It appears we are not the only ones bound by our intent." "Which is what, exactly?" "Revolution." "This is a monumental risk." "What if these were intercepted or deciphered?" "They have been deciphered." "Then our location is known?" "(Beatrice) Once a codex is broken it offers opportunity." "I wrote a new note, made sure it was found." "It proposes a rendezvous today on the other side of Paris, so we are quite safe here." "Cousin?" "(Beatrice) A great moment is upon us:" "the King has a fever and his sickness grows." "(Beatrice) We must plan quickly now for our future." "We have powerful and wealthy friends, some already at court." "Others, abroad, are watching very closely, all of them standing, ready to help." "A support message from the Dutch Republic." "A new captain general is rising in power." "William of Orange will be stadtholder commander of armies, sea admiral." "And he vows here to support whoever moves against King Louis, not just with words, but with money, materials, influence and arms." "I've heard enough." "Thank you for the puppet show." "Chevalier de Lorraine!" "Do not confuse the woman you have known with the woman you see now." "A gathering in Paris awaits you." "Canvas your supporters there." "(Beatrice) We know there are many." "(Coughing)" "The fever has broken." "The court mustn't know about my condition." "But surely your brother must be informed." "Close all the doors." "Do it now." "The issue of regent remains." "We know your position, of course." "Will no one vouch for me?" "It is not you who lacks merit, Your Highness." "Our concerns lie instead on those who would be around you." "Ah!" "Why not just say his name?" "We need someone whose behaviour is more suited to a King, someone who is his own man." "I hope I make myself clear." "Perfectly." "Her Majesty and Monsieur Colbert would, to my mind, ensure a resilient transition." "(signing)" "(Tense music)" "Then it is settled." "What are you doing?" "(Chevalier) Rumors make me giddy." "I'm going to Paris for a few days to un-giddy myself." "(Clicks)" "You said I'd make a great King." "And you would." "This is not idle chat." "What is this?" " You made a vow to me!" " And I kept it." "Then be truthful in return." "Have you been under a rock?" "We are on the verge of change." "There are whispers growing louder every day." "People are tired of how it is." "They wish to see change, one that would not deny the monarchy but share in its burden." "You can see it in your brother now." "One man cannot rule the land." "He's drowning in it," " (Chevalier) and you can save him." " You tread a dangerous path." "The only danger is smelling smoke and not acknowledging a fire." " You side with the nobles?" " I side with you just as the soldiers do." "Would you side with me?" " You cannot know what you're asking." " I know what I'm asking." "Until death forces my hand," "I cannot answer." "Very well." "But know this:" "Our future has changed, no matter what happens now." "My trunk!" "Sire, we rejoice at your recovery." "(Louis) Send tailors I want clothes." "As for my court, this is the message I want to convey." "(Bontemps) I am saddened to report the King's health has not improved." "He awakened before breakfast and passed on instructions that government continue under his word." "How can he make decisions in such a condition?" "The King wishes France to be informed immediately of his condition so they might offer their prayers." "Has he said anything?" "He has..." "The court should learn a new dance." "A dance?" "It is one he has composed himself in his moments of peace... to raise our spirits" "in anticipation of his recovery." "Colbert, tell Monsieur Lully to create a melody." "(Sniffling) (Whimpering)" "Your sacrifice won't be forgotten." "(Louis) My deep sympathy for your loss." "I know now my replacement for your father." "What is his name?" "I know that he stands before me now." "Many will oppose you, who would rather I chose one of my physicians." "(Louis) Be deaf to their judgements." "Will you accept the job?" "(Louis) If the answer is yes there is no going back." "Your life as you know it will be changed forever." "I accept." "Then it is yours." "Medicine is a fine career." "(Louis) Get Mlle de la Vallière." "(Whispering indistinctly)" "Where's Chevalier?" "I haven't seen him today." "He rides to Paris." "A gathering of nobles." "Does he indeed?" "What are you doing?" "Did you not hear?" "The King has a dance and expects us to know it." " Why are you here?" " Getting Mme Rochefoucauld's letter." " This is her chamber?" " No, this is Mme de Clermont." "Mme de la Rochefoucauld is down the hallway." "Oh my goodness, I'm so sorry!" "Excuse me." "Wait!" "I hoped you might stay here, you might think of this as home." "I cannot." "Not even for your children?" "For their sakes and for mine," "I must show contrition for my life." "You may go." "Thank you," "Majesty." "Thank you with all my heart." "Arrangements will be made." "(Giggling)" "Mother, I have missed you." "Every time I look for you, I am rushed back to my lady." "Your duty to me is to do well with her." "Do not think of me at all." "I found a chambermaid in your room." " Chambermaid?" " Yes." "Looking for Mme Rochefoucauld's letter but ended up in your room." "I went to the chapel." "Cassel was in conversation with new nobles, Anjou, Poitier..." " Who else?" " Mme de Clermont." "(Sighing) Since the court knew of the King's condition, conversations between these individuals increased markedly." "Anjou and Poitiers... too you say, both to Cassel." "I asked the stables, Potters, Anjou are riding to Paris." "(Fabien) Not the only ones." "Chevalier de Lorraine also reached Paris this morning." " About Clermont..." " (Fabien) Later." "Where are you going?" "Christ Jesus, life eternal in the bosom of the Father... life of souls made of your own likeness," "protect my brother in his time of need." "My God!" "(Laughs)" "I was told you were dying!" "I was but then I recovered." " You didn't tell me?" " I told no one." "(Philippe) Why?" "So I might see upon who I can depend." " You did not include me." " I did not." " You do not trust your own brother?" " Not the company he keeps." "(Deep breath)" "Chevalier may seem blithe and glib, but he has a backbone." "I wish you saw what I do:" "He's a man of honor." "You are blind to his failings and dumb to his faults." "Do not say such things." "A conspiracy was uncovered, nobles plotting against me as I am ill in bed." "(Louis) Chevalier is a ring leader." "All of them will be arrested." "Impossible." " He's no conspirator." " Very true." "He's a traitor and will be treated as such." "(Sobbing)" "To Versailles!" "(Fabien) Good idea." "(Grunting)" "The Duc d'Orléans will have your head for this for sure." "(Chevalier) When your neck's on the block you know what he will say?" "(Fabien) No." "(Spluttering)" "In any case," "I hope you're fond of horses." "(Breathing unevenly)" "(Gasping, choking, grunting)" "(Panting)" "Burn in hell you Catholic cunt." "(Spitting)" "(Coughing)" "I found a little something to aid us." "(Fabien) Aid us with what?" "(Beatrice) Endurance." "A love potion." "When I look at you I need nothing else." "Oh, I'm the same." "But I think it might be fun." "Come." "(Moaning)" "(Retching)" "(signing)" "(Whispering indistinctly)" "(Classical music)" "(Courtiers exclaim)" "(Classical music)" "(Coughing)" "(Coughing)" "(Choral music)" "Thank you." "(Choral music)" " (Man) Ha!" "Ha!" " (Nobleman) (Screaming)" " (Nobleman) (Shouting indistinctly) - (Priest) (Praying in Latin)" "(Screaming)" "(Screaming)" "(Whimpering)" "(Music)" "(Music)" |
/* -*- Mode: C++; tab-width: 8; indent-tabs-mode: nil; c-basic-offset: 2 -*- */
/* vim: set ts=8 sts=2 et sw=2 tw=80: */
/* This Source Code Form is subject to the terms of the Mozilla Public
* License, v. 2.0. If a copy of the MPL was not distributed with this
* file, You can obtain one at http://mozilla.org/MPL/2.0/. */
/* Macros to emulate C++11 typed enums and enum classes. */
#ifndef mozilla_TypedEnum_h
#define mozilla_TypedEnum_h
#include "mozilla/Attributes.h"
#if defined(__cplusplus)
#if defined(__clang__)
/*
* Per Clang documentation, "Note that marketing version numbers should not
* be used to check for language features, as different vendors use different
* numbering schemes. Instead, use the feature checking macros."
*/
# ifndef __has_extension
# define __has_extension __has_feature /* compatibility, for older versions of clang */
# endif
# if __has_extension(cxx_strong_enums)
# define MOZ_HAVE_CXX11_ENUM_TYPE
# define MOZ_HAVE_CXX11_STRONG_ENUMS
# endif
#elif defined(__GNUC__)
# if defined(__GXX_EXPERIMENTAL_CXX0X__) || __cplusplus >= 201103L
# if MOZ_GCC_VERSION_AT_LEAST(4, 5, 1)
# define MOZ_HAVE_CXX11_ENUM_TYPE
# define MOZ_HAVE_CXX11_STRONG_ENUMS
# endif
# endif
#elif defined(_MSC_VER)
# if _MSC_VER >= 1400
# define MOZ_HAVE_CXX11_ENUM_TYPE
# endif
# if _MSC_VER >= 1700
# define MOZ_HAVE_CXX11_STRONG_ENUMS
# endif
#endif
/**
* MOZ_ENUM_TYPE specifies the underlying numeric type for an enum. It's
* specified by placing MOZ_ENUM_TYPE(type) immediately after the enum name in
* its declaration, and before the opening curly brace, like
*
* enum MyEnum MOZ_ENUM_TYPE(uint16_t)
* {
* A,
* B = 7,
* C
* };
*
* In supporting compilers, the macro will expand to ": uint16_t". The
* compiler will allocate exactly two bytes for MyEnum and will require all
* enumerators to have values between 0 and 65535. (Thus specifying "B =
* 100000" instead of "B = 7" would fail to compile.) In old compilers the
* macro expands to the empty string, and the underlying type is generally
* undefined.
*/
#ifdef MOZ_HAVE_CXX11_ENUM_TYPE
# define MOZ_ENUM_TYPE(type) : type
#else
# define MOZ_ENUM_TYPE(type) /* no support */
#endif
/**
* MOZ_BEGIN_ENUM_CLASS and MOZ_END_ENUM_CLASS provide access to the
* strongly-typed enumeration feature of C++11 ("enum class"). If supported
* by the compiler, an enum defined using these macros will not be implicitly
* converted to any other type, and its enumerators will be scoped using the
* enumeration name. Place MOZ_BEGIN_ENUM_CLASS(EnumName, type) in place of
* "enum EnumName {", and MOZ_END_ENUM_CLASS(EnumName) in place of the closing
* "};". For example,
*
* MOZ_BEGIN_ENUM_CLASS(Enum, int32_t)
* A,
* B = 6
* MOZ_END_ENUM_CLASS(Enum)
*
* This will make "Enum::A" and "Enum::B" appear in the global scope, but "A"
* and "B" will not. In compilers that support C++11 strongly-typed
* enumerations, implicit conversions of Enum values to numeric types will
* fail. In other compilers, Enum itself will actually be defined as a class,
* and some implicit conversions will fail while others will succeed.
*
* The type argument specifies the underlying type for the enum where
* supported, as with MOZ_ENUM_TYPE(). For simplicity, it is currently
* mandatory. As with MOZ_ENUM_TYPE(), it will do nothing on compilers that do
* not support it.
*
* MOZ_{BEGIN,END}_ENUM_CLASS doesn't work for defining enum classes nested
* inside classes. To define an enum class nested inside another class, use
* MOZ_{BEGIN,END}_NESTED_ENUM_CLASS, and place a MOZ_FINISH_NESTED_ENUM_CLASS
* in namespace scope to handle bits that can only be implemented with
* namespace-scoped code. For example:
*
* class FooBar {
*
* MOZ_BEGIN_NESTED_ENUM_CLASS(Enum, int32_t)
* A,
* B = 6
* MOZ_END_NESTED_ENUM_CLASS(Enum)
*
* };
*
* MOZ_FINISH_NESTED_ENUM_CLASS(FooBar::Enum)
*/
#if defined(MOZ_HAVE_CXX11_STRONG_ENUMS)
/*
* All compilers that support strong enums also support an explicit
* underlying type, so no extra check is needed.
*/
# define MOZ_BEGIN_NESTED_ENUM_CLASS(Name, type) \
enum class Name : type {
# define MOZ_END_NESTED_ENUM_CLASS(Name) \
};
# define MOZ_FINISH_NESTED_ENUM_CLASS(Name) /* nothing */
#else
/**
* We need Name to both name a type, and scope the provided enumerator
* names. Namespaces and classes both provide scoping, but namespaces
* aren't types, so we need to use a class that wraps the enum values. We
* have an implicit conversion from the inner enum type to the class, so
* statements like
*
* Enum x = Enum::A;
*
* will still work. We need to define an implicit conversion from the class
* to the inner enum as well, so that (for instance) switch statements will
* work. This means that the class can be implicitly converted to a numeric
* value as well via the enum type, since C++ allows an implicit
* user-defined conversion followed by a standard conversion to still be
* implicit.
*
* We have an explicit constructor from int defined, so that casts like
* (Enum)7 will still work. We also have a zero-argument constructor with
* no arguments, so declaration without initialization (like "Enum foo;")
* will work.
*
* Additionally, we'll delete as many operators as possible for the inner
* enum type, so statements like this will still fail:
*
* f(5 + Enum::B); // deleted operator+
*
* But we can't prevent things like this, because C++ doesn't allow
* overriding conversions or assignment operators for enums:
*
* int x = Enum::A;
* int f()
* {
* return Enum::A;
* }
*/\
# define MOZ_BEGIN_NESTED_ENUM_CLASS(Name, type) \
class Name \
{ \
public: \
enum Enum MOZ_ENUM_TYPE(type) \
{
# define MOZ_END_NESTED_ENUM_CLASS(Name) \
}; \
Name() {} \
Name(Enum aEnum) : mEnum(aEnum) {} \
explicit Name(int num) : mEnum((Enum)num) {} \
operator Enum() const { return mEnum; } \
private: \
Enum mEnum; \
};
# define MOZ_FINISH_NESTED_ENUM_CLASS(Name) \
inline int operator+(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator+(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator-(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator-(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator*(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator*(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator/(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator/(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator%(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator%(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator+(const Name::Enum&) MOZ_DELETE; \
inline int operator-(const Name::Enum&) MOZ_DELETE; \
inline int& operator++(Name::Enum&) MOZ_DELETE; \
inline int operator++(Name::Enum&, int) MOZ_DELETE; \
inline int& operator--(Name::Enum&) MOZ_DELETE; \
inline int operator--(Name::Enum&, int) MOZ_DELETE; \
inline bool operator==(const int&, const Name::Enum&) MOZ_DELETE; \
inline bool operator==(const Name::Enum&, const int&) MOZ_DELETE; \
inline bool operator!=(const int&, const Name::Enum&) MOZ_DELETE; \
inline bool operator!=(const Name::Enum&, const int&) MOZ_DELETE; \
inline bool operator>(const int&, const Name::Enum&) MOZ_DELETE; \
inline bool operator>(const Name::Enum&, const int&) MOZ_DELETE; \
inline bool operator<(const int&, const Name::Enum&) MOZ_DELETE; \
inline bool operator<(const Name::Enum&, const int&) MOZ_DELETE; \
inline bool operator>=(const int&, const Name::Enum&) MOZ_DELETE; \
inline bool operator>=(const Name::Enum&, const int&) MOZ_DELETE; \
inline bool operator<=(const int&, const Name::Enum&) MOZ_DELETE; \
inline bool operator<=(const Name::Enum&, const int&) MOZ_DELETE; \
inline bool operator!(const Name::Enum&) MOZ_DELETE; \
inline bool operator&&(const bool&, const Name::Enum&) MOZ_DELETE; \
inline bool operator&&(const Name::Enum&, const bool&) MOZ_DELETE; \
inline bool operator||(const bool&, const Name::Enum&) MOZ_DELETE; \
inline bool operator||(const Name::Enum&, const bool&) MOZ_DELETE; \
inline int operator~(const Name::Enum&) MOZ_DELETE; \
inline int operator&(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator&(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator|(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator|(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator^(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator^(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator<<(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator<<(const Name::Enum&, const int&) MOZ_DELETE; \
inline int operator>>(const int&, const Name::Enum&) MOZ_DELETE; \
inline int operator>>(const Name::Enum&, const int&) MOZ_DELETE; \
inline int& operator+=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator-=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator*=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator/=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator%=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator&=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator|=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator^=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator<<=(int&, const Name::Enum&) MOZ_DELETE; \
inline int& operator>>=(int&, const Name::Enum&) MOZ_DELETE;
#endif
# define MOZ_BEGIN_ENUM_CLASS(Name, type) MOZ_BEGIN_NESTED_ENUM_CLASS(Name, type)
# define MOZ_END_ENUM_CLASS(Name) \
MOZ_END_NESTED_ENUM_CLASS(Name) \
MOZ_FINISH_NESTED_ENUM_CLASS(Name)
#endif /* __cplusplus */
#endif /* mozilla_TypedEnum_h */
|
Introduction {#S0001}
============
La prise en charge des patients hémodialysés s\'est nettement améliorée mais avec une augmentation des complications cardiovasculaires qui constituent la principale cause de morbidité et de mortalité \[[@CIT0001]\]. Le taux de mortalité dû aux maladies cardiovasculaires chez les patients dialysés est de 10 à 30 fois plus élevé que dans la population générale \[[@CIT0002]\]. Toutes les tuniques cardiaques peuvent être intéressées par ces complications \[[@CIT0001], [@CIT0003], [@CIT0004]\]. Dans le but de mieux caractériser ces atteintes, nous avons conduit cette étude afin de déterminer la prévalence des différentes complications cardiaques.
Méthodes {#S0002}
========
Il s\'agissait d\'une étude rétrospective, transversale. Elle s\'est déroulée sur une période de 4 ans allant de 2005 à 2009 au CHU Aristide le Dantec de Dakar. Tous les dossiers des patients en hémodialyse périodique pendant au moins 6 mois et ayant un bilan cardiologique ont été inclus. Ces dossiers contenaient l'âge, le sexe, le tabagisme, la néphropathie initiale, le diabète, la pression artérielle pré dialytique, la prise de poids inter dialytique (PPID) et la dose de dialyse ou Kt/V. Ce dernier permet d\'apprécier l\'efficacité de la dialyse et une valeur supérieure ou égale à 1,3 a été retenue comme normale. L\'hypertrophie ventriculaire gauche était définie par une masse ventriculaire gauche indexée à la surface corporelle supérieure à 131g/m^2^ chez l\'homme et 100g/m^2^ chez la femme. L\'hypertension artérielle pulmonaire était définie par une pression artérielle pulmonaire systolique supérieure à 35 mm Hg. Tous les patients ont bénéficié d\'une radiographie du thorax de face, d\'un électrocardiogramme et d\'une échographie cardiaque. Les dossiers des patients incomplets ont été exclus de l'étude. Les données ont été analysées à l\'aide du logiciel SPSS version 16.0, 2007. Les variables quantitatives ont été exprimées en moyennes ± écart type et les variables qualitatives en effectif et en pourcentage. Le test t de Student a été utilisé pour la comparaison des variables quantitatives et le test Chi 2 ou celui de Fisher exact pour la comparaison des variables qualitatives. L\'analyse multivariée a fait appel à la régression logistique multiple. Une valeur p \< 0,05 a été considérée comme significative.
Résultats {#S0003}
=========
Au total, 38 dossiers de patients hémodialysés étaient retenus pour l'étude. L'âge moyen était de 52 ans ± 12,85 et le sex-ratio H/F de 1,53. La néphropathie initiale était dominée par la néphroangiosclérose et la néphropathie diabétique respectivement chez 20 et 4 patients ([Tableau 1](#T0001){ref-type="table"}). Les signes physiques sont représentés respectivement sur le [Tableau 1](#T0001){ref-type="table"}. Quant aux signes radiologiques, l\'index cardiothoracique moyen (ICT) était de 0,53±0,06 (extrêmes: 0,42-0,76). Vingt-quatre patients avaient une cardiomégalie aux dépends du ventricule gauche (63,16%), tandis que 14 (36,84%) avaient un ICT inférieur à 0,5, et un seul patient avait un arc moyen gauche convexe évocateur d\'une hypertension artérielle pulmonaire (HTAP). Les anomalies électriques portaient respectivement sur: l\'hypertrophie ventriculaire gauche, l\'hypertrophie auriculaire gauche et les troubles de la repolarisation respectivement chez 27 (71,05%), 10 (26,32%) et 13 (34,21%) patients ([Tableau 2](#T0002){ref-type="table"}). Le [Tableau 3](#T0003){ref-type="table"} résume les moyennes des différents paramètres biologiques retenus pour l'étude. Les anomalies écho cardiographiques sont représentées sur la [Figure 1](#F0001){ref-type="fig"}. Sur le total des patients, la durée moyenne en hémodialyse était de 35,39 ± 13,71 mois (extrêmes: 9-48 mois). Huit patients étaient hémodialysés 12 heures par semaine, contre 30 qui bénéficiaient de 10 heures de séance par semaine. Vingt neuf patients (76%) avaient une prise de poids interdialytique (PPID) entre 3 et 4 Kg tandis que 9 (24%) avaient une PPID de plus de 5 Kg. L\'abord vasculaire pour l\'hémodialyse était une fistule artérioveineuse (FAV) chez tous les patients (100%). Le siège était distal chez 30 patients (78,95%) et proximal chez 7 (21,05%) dont 4 avaient une complication à type d\'hyperdébit. Le KT/V a été mesurée chez 19 patients. La moyenne était de 1,85 + /-0,44(extrêmes: 1,19-2,98). Dix-huit patients avaient un taux normal et 1 avait un taux bas. En analyse multivariée, l'âge, le sexe, la prise de poids interdialytique, le siège de la fistule artério-veineuse, l\'hyperparathyroïdie, l\'hypoalbuminémie, le nombre d\'heures de dialyse par semaine et le KT/V n'étaient pas associés à l\'HVG. En revanche, l\'HTA et l\'anémie ont été identifiés comme déterminants majeurs de la survenue de l\'HVG chez les patients hémodialysés (différence significative avec respectivement p \< 0,036 et 0,019). Il n\'existait pas de différence statistiquement significative entre la survenue des troubles de la repolarisation et l\'anémie (p= 0,06), la dyslipidémie (p = 0,5), l\'HTA (p = 0,17), le diabète (p= 0,64) et le taux de CRP (p = 0,4). Concernant les calcifications valvulaires cardiaques, il n\'y a pas de facteurs qui ont été décelés dans leur survenue notamment l'âge (p= 0,61) et l\'ancienneté en hémodialyse (p= 0,61). Ceci peut s\'expliquer aussi par la faible taille de notre échantillon et les écarts d'âge peu importants. Onze patients étaient décédés (29%) dont la cause de décès était dans 6 cas liée à une atteinte cardiovasculaire (54,55%). Les décès étaient liés à un infarctus du myocarde (2cas: 18,18%) et à un accident vasculaire cérébral (2 cas: 18,18%). Dans 2 cas (18,18%), la cause du décès était indéterminée.
{#F0001}
######
Néphropathies initiales et signes physiques
---------------------------------------------- --------
**Néphropathies initiales**
Glomérulonéphrite chronique 52,63%
Néphropathie indéterminée 10,53%
Néphropathie bilharzienne 2,63%
Néphropathie diabétique 10,53%
Néphroangiosclérose 7,89%
Néphropathie tubulo-interstitielle chronique 5,26%
Polykystose rénale autosomique dominante 7,89%
Cancer du rein 2,63%
**Signes physiques**
HTA 27 cas
Anémie clinique 29 cas
Arythmie cardiaque 3 cas
Frottement péricardique 1 cas
Insuffisance cardiaque 10 cas
---------------------------------------------- --------
######
Anomalies électriques
------------------------------------------------ --------
Tachycardie sinusale 4 cas
Bradycardie sinusale 2 cas
Hypertrophie ventriculaire gauche 27 cas
Hypertrophie auriculaire gauche 10cas
Hypertrophie biauriculaire 1 cas
Extrasystole ventriculaire monomorphes isolées 2 cas
Flutter atrial 1 cas
Troubles de la conduction 6 cas
Bloc de branche droit complet 1cas
Bloc de branche gauche complet 1cas
Hémibloc antérieur 3cas
Bloc auriculoventriculaire du 1^er^ degré 1 cas
------------------------------------------------ --------
######
Différents paramètres biologiques étudiés
Biologie Nombre moyenne Ecart type Min Max
------------------------- -------- --------- ------------ ----- ------
**Taux d\'hémoglobine** 38 8,89 1,81 6,2 13,1
**Ferritinémie** 34 760,66 1225,36 16 7113
**Protides** 31 75,75 5,41 67 91
**Albumine** 31 40,50 6,23 25 51
**Calcium** 37 92,18 10,52 63 119
**Phosphore** 37 51,78 21,67 23 113
**PTHi** 30 307,21 281,44 14 994
Discussion {#S0004}
==========
Dans notre étude, le taux moyen de l\'HVG (71,05%). C\'est le cas de Bah A. O. et al. en 2006 en République de Guinée (72,95%) \[[@CIT0003]\] et tout récemment de A. Aldlouni et al. en 2011 au Maroc (87%) \[[@CIT0001]\]. Ce taux élevé d\'HVG s\'explique par la fréquence de l\'anémie, de l\'HTA et de la prise de poids excessive chez ces patients. Une attention particulière sera accordée au suivi de l\'anémie et de l\'HTA d\'autant plus qu\'ils ont été identifiés comme déterminants majeurs de la survenue de l\'HVG. Ce fait a été aussi rapporté par Eba A., Aghrabat M.S. en 2006 en Mauritanie \[[@CIT0004]\]. Il en est de même de la FAV proximale à haut débit qui est reconnue comme un facteur favorisant l\'HVG \[[@CIT0005], [@CIT0006]\]. Statistiquement ceci conforte les résultats de notre étude. Parmi nos 8 patients qui avaient une FAV proximale, 4 avaient un hyperdébit. Au cours du suivi, la proportion des troubles de la repolarisation étaient retrouvés chez 13 patients soit 34,21% avec un âge moyen de 50,4 ans. Ce résultat est similaire à ceux retrouvés par SABOURI \[[@CIT0007]\] où l'âge moyen était de 55,7 ans. Dans la littérature comme le rapporte l'étude de B. CHARRA \[[@CIT0008]\], la prévalence élevée de l\'hypertrophie ventriculaire gauche, de l\'hypertension artérielle et du diabète chez les hémodialysés est à l\'origine d\'une maladie coronaire souvent silencieuse et associée à des troubles de la repolarisation non spécifiques sur l\'ECG de repos. Ceci conforte notre étude où nous avons établi une corrélation significative entre l\'HVG et la survenue des troubles de la repolarisation. Cependant, il n\'y avait pas de corrélation entre les troubles de la repolarisation et le diabète ainsi qu\'avec l\'HTA avec une différence non significative dans les 2 cas ce qui s\'explique entre autres par la faible taille de l'échantillon. Ce constat va à l\'encontre des résultats d\'autres études qui ont recherché les facteurs de risque cardio-vasculaires chez l\'hémodialysé. Notamment TAKEDA et Al. \[[@CIT0009]\] au Japon, qui ont démontré que le risque de survenue de nouveaux évènements cardio-vasculaires était fortement lié à l\'HTA (p\< 0,0005).
La prévalence des troubles de la conduction dans notre série était de 15,79%. Le même résultat a été noté par GERGAUD \[[@CIT0010]\] avec 15,3% des troubles de la conduction chez les hémodialysés. Chez 71,05%, des patients l'échographie cardiaque avait mis en évidence une HVG, qui pourrait être à l\'origine de ces troubles de la conduction. Cette théorie est réconfortée par JUNGERS P. \[[@CIT0011]\] qui avait montré dans sa série que l\'HVG et les calcifications de la jonction auriculo-ventriculaire étaient les principaux facteurs responsables des troubles de la conduction. Trois patients (7,89%) avaient des troubles du rythme. Ils avaient à la fois une HVG, une prise excessive du poids interdialytique et des troubles de la repolarisation. Des résultats similaires ont été retrouvés par JUNGERS P. \[[@CIT0009]\] et EBA A \[[@CIT0012]\] dans respectivement 12% et 3,5%. Nous avons retrouvé l\'HTAP chez 8 patients (21,05%). JUNGERS \[[@CIT0011]\] avait retrouvé dans sa série une HTAP dans 20%. L\'HVG, la FAV à haut débit, les troubles métaboliques et hormonaux associés à l\'IRCT et le tabagisme ont été évoqués comme les facteurs étiologiques possibles d\'HTAP chez les hémodialysés. Dans notre série, les calcifications des valves mitrales ont été retrouvées dans 5,26% et aortiques dans 10,52% des cas. Ce qui est similaire aux résultats retrouvés en Mauritanie où les calcifications des valves mitrales étaient mises en évidence respectivement dans 12% et 3% des cas sans calcifications des valves aortiques \[[@CIT0004]\]. Une corrélation a été retrouvée entre l'âge, la durée d\'hémodialyse et la présence des calcifications valvulaires dans la littérature \[[@CIT0013]\]. Aucune corrélation n\'a été retrouvée entre les calcifications valvulaires chez nos patients et l\'ancienneté en dialyse. Ce pendant dans une étude japonaise chez les hémodialysés (1290) patients suivis pendant 10ans (2000-2010) publiée en Févier 2013, il a été rapporté que les patients atteints de calcification de la valve étaient plus âgés et CRP sérique et de l\'hormone parathyroïdienne intacte étaient plus élevés; inversement, l\'indice de masse corporelle et le taux d\'albumine et de la créatinine sériques étaient plus faibles chez les patients présentant une calcification de la valve que chez ceux sans \[[@CIT0002]\]. Ceci pourrait être expliqué par la durée courte de nos patients en dialyse (moyenne inférieure à 2 ans) par rapport à celle décrite dans la littérature. Les décès dans notre étude étaient liés à une atteinte cardiovasculaire dans 54,55%. Les IDM et les AVC venaient au premier plan avec chacun un pourcentage de 18,18% des cas. En Afrique, EBA en Mauritanie avait retrouvé que 62% de décès étaient d\'origine cardiovasculaire chez les hémodialysés \[[@CIT0003]\] de même qu\'aux USA et au Japon où les causes cardiovasculaires de décès chez les hémodialysés étaient notées respectivement dans 52% et 58% des cas \[[@CIT0012], [@CIT0014]\].
Conclusion {#S0005}
==========
Les complications cardiaques sont fréquentes chez les patients sénégalais hémodialysés à Dakar. Leur prévention passe par un bon contrôle des principaux facteurs de risque à savoir l\'HTA et l\'anémie. La réalisation régulière d'échocardiographies permettrait leur dépistage précoce afin de pouvoir proposer un traitement optimal.
Etat des connaissance sur le sujet {#S20006}
----------------------------------
Les complications cardiovasculaires constituent la première cause de morbimortalité chez les patients hémodialysés chroniques.Elles sont dominées par l\'hypertrophie ventriculaire gauche, mais peuvent affecter toutes les tuniques cardiaques et vasculaires.
Contribution de notre étude a la connaissance {#S20007}
---------------------------------------------
Notre étude est venue confirmée encore que l\'hypertrophie ventriculaire gauche est la principale complication cardiaque chez les hémodialysés chroniques.Ce travail montre en plus que les calcifications cardiaques ne sont pas corrélées à l\'ancienneté en hémodialyse.
Conflits d\'intérêts {#S0008}
====================
Les auteurs ne déclarent aucun conflit d\'intérêts.
Contributions des auteurs {#S0009}
=========================
Tous les auteurs on lu et approuvé la version finale du manuscrit.
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No heating in the middle of a particularly nasty winter can be problematic, too - although it's mostly a matter of comfort, not survival. In most places, with robust shelter and adequate clothing, bedding, and food, it's fairly hard to freeze to death at home (but note that the cold may make some infections or medical conditions worse; you may have to worry about frozen water pipes, too). The situation can become a lot more dire if you are on foot in the middle of nowhere, so truly hardcore, wilderness-minded preppers may have something to ponder about; but hauling a sufficient amount of fuel is typically impractical to begin with, so their best bet would be warm clothing, improvised shelter, and the ability to build a fire. We'll talk about that in the section that deals with camping supplies.
Nail your studs together in lengthwise pairs at a 90-degree angle to form braces. This makes them stronger. Then run three or four braces horizontally across every door, hammering the nails from above and below directly into the frame at a 45-degree angle. If you drive them straight in, they're easier to pop out when somebody kicks the door. Use more braces to secure the drywall over the windows. Try to use longer nails and leave a couple inches of each nailhead sticking out for easy removal. — Clint Carter
It used to be that dashcams were prohibitively expensive; but today, the prices start at $50, so it makes sense to give the devices a try. I can recommend Rexing V1 ($100), but there are countless other options to choose from. The bottom line is, if you own a car, it's probably the most affordable and meaningful liability insurance policy you can get.
These are people who believe a thousand-year-old prophecy is about to come true. People who believe most of their loved ones will be dead within a year. People who are preparing for the possibility of killing their neighbors, who presumably will become feral and desperate. People who just might buy 3D printers and extra fancy new UV handheld water purifiers to help ride out the collapse of civilization, but who are probably more likely to spend $10 on PDF downloads of guides with names like Urban Chicken Farming After the Dollar Collapses. These are people who expect they themselves may only have a year left on this planet.
The 66-year-old tried starting his own spinoff meetup. Ozarks Resilience Group was to be a pragmatic organization that ran drills on real-life scenarios like hiking out of town with a bug-out bag. After six months of nonparticipation, he gave up. Allen estimates there are several hundred “hardcore preppers” in Springfield, but at most, there’s two dozen whom he would trust in an emergency.
To cope with a true emergency, it's not enough to know the risks and sit on a pile of overpriced survival gear: you need to plan ahead. If your house is on fire, there may be no time to rifle through folders to gather all your vital documents; if the floodwaters are rising or a chemical tanker overturns on a nearby highway, it may a bit late to start thinking about refueling your car. And if you're stranded on a rural road in a broken-down vehicle, you may sorely regret not putting any drinking water in the trunk.
In fact, the influx had begun well before Trump’s victory. In the first ten months of 2016, foreigners bought nearly fourteen hundred square miles of land in New Zealand, more than quadruple what they bought in the same period the previous year, according to the government. American buyers were second only to Australians. The U.S. government does not keep a tally of Americans who own second or third homes overseas. Much as Switzerland once drew Americans with the promise of secrecy, and Uruguay tempted them with private banks, New Zealand offers security and distance. In the past six years, nearly a thousand foreigners have acquired residency there under programs that mandate certain types of investment of at least a million dollars.
The next area of the book is on water. Every good prepper knows you can only last about 3 days without water. I promise you, you won’t want to go that long. Jim has some great information on finding water sources as well as filtering, purifying, and properly storing it. The next rule of 3 is “3 weeks without food”, so aptly enough, chapter 3 is on food, and how to avoid a starvation diet. Of course food storage is covered, but Jim also talks about the importance of diversification. If water is not in large supply, you’ll need foods that are easily eaten without having to add any water. He also talks a little about gardening, foraging, fishing, hunting and trapping, and how to preserve what food you find. It does you no good to get a deer if you can’t preserve some of that meat to eat at a later time.
To manage that fear, Dugger said, he has seen two very different responses. “People know the only real answer is, Fix the problem,” he said. “It’s a reason most of them give a lot of money to good causes.” At the same time, though, they invest in the mechanics of escape. He recalled a dinner in New York City after 9/11 and the bursting of the dot-com bubble: “A group of centi-millionaires and a couple of billionaires were working through end-of-America scenarios and talking about what they’d do. Most said they’ll fire up their planes and take their families to Western ranches or homes in other countries.” One of the guests was skeptical, Dugger said. “He leaned forward and asked, ‘Are you taking your pilot’s family, too? And what about the maintenance guys? If revolutionaries are kicking in doors, how many of the people in your life will you have to take with you?’ The questioning continued. In the end, most agreed they couldn’t run.”
As Huffman, of Reddit, observed, our technologies have made us more alert to risk, but have also made us more panicky; they facilitate the tribal temptation to cocoon, to seclude ourselves from opponents, and to fortify ourselves against our fears, instead of attacking the sources of them. Justin Kan, the technology investor who had made a halfhearted effort to stock up on food, recalled a recent phone call from a friend at a hedge fund. “He was telling me we should buy land in New Zealand as a backup. He’s, like, ‘What’s the percentage chance that Trump is actually a fascist dictator? Maybe it’s low, but the expected value of having an escape hatch is pretty high.’ ”
The funny thing about disasters is that they seldom unfold precisely as planned. Perhaps you will lose a job and get robbed the same week. Perhaps in the middle of a prolonged outage, you will find out that some of your emergency supplies have been misplaced, damaged, or spoiled. Maybe your plan to walk a mile to get drinking water from a river will get foiled by a broken limb. And maybe a brilliant home defense strategy will prove worthless when standing eye to eye with an angry mob of rioters armed with rocks.
When I am going through a grocery store gathering survival food, I get some strange looks from people close enough to hear me muttering under my breath as I discount items. Phrases like “not enough calories”, “needs more fat”, not enough carbs”, and the like roll off my tongue frequently. The truth of the matter is that what we consider to be a healthy diet in normal times is probably inadequate in a high stress, very active, crisis situation. There is a reason we like carbs, and fats, and sugars, and that reason is our body needs these things. The human palate developed in times when being physically active and dealing with life threatening events was the norm, and when a steady supply of food was not a guarantee. Hence the urge to get all we can when we can, which leads to rampant obesity in modern sedentary times but is adaptive to survival in harder times.
Over the phone from the company’s headquarters in Salt Lake City, Shields attributed the spike to the onslaught of natural disasters that left thousands of Americans without food in 2017, and rattled many more. “You got the hurricane that hit Florida, you got the hurricane that hit the Houston area, you got the hurricane that devastated Puerto Rico,” he said. “Geologists are coming out and saying that California is severely overdue for a big earthquake. You got these major events that are taking place that affect mainstream America. So how do you protect your family?”
Stay positive: the world is probably not ending, and there is a good chance that it will be an even better place for our children than it is for us. But the universe is a harsh mistress, and there is only so much faith we should be putting in good fortune, in benevolent governments, or in the wonders of modern technology. So, always have a backup plan.
Resources abound. With a modest amount of computer knowledge, you can Google around the internet to find all sorts of emergency food and food storage advice. Be an informed consumer. Learn about the foods that store well and also about pre-packaged meals that only require a bit of hot water to create a good-tasting and satisfying food experience.
Now, a word of caution: beware of debt. Many of us are taught that owing money is normal, even desirable; indeed, for middle-class folks, some forms of indebtedness may be difficult to avoid. But unnecessarily accrued debt cuts into your bottom line in two insidious ways. First of all, monthly installment payments limit your flexibility in an emergency - so if your income shrinks, your savings will be depleted at a merciless and non-negotiable rate. Secondly, high-interest loans, such as credit cards, amount to giving out a good chunk of your income without earning anything useful in return. They are akin to voluntarily accepting a pay cut.
And why shouldn’t they? National Geographic Channel’s Doomsday Preppers doesn’t exactly help viewers understand the plight of the average prepper, the one without 60 guns, scuba diving equipment, a bunker and an armored personnel carrier. “I knew going into it that they would try to sensationalize a lot of stuff,” says Allen, a Springfield, Missouri survivalist who refused to divulge his last name; he appeared on the show in 2012 showing off his aquaponics setup. “If Doomsday Preppers had shown typical preppers on a typical day, it would’ve been pretty boring.”
Mindset is everything. Mental preparation comes first. I would change number 12 to number 1 and say,”practice, practice, practice…”. A wilderness solo for a few days (after you “practice, practice, practice…” for a while) will cause a dramatic change in your self reliance level. It did mine and that’s why almost everything I acquire has multiple possible uses. For instance, my business card case is metal and has possibilities as a weapon and a signaling mirror. “Wildwood Wisdom” by Ellsworth Jaeger is a good place to start. He shows how to “think” survival like no one else.
Prepping is more about planning, knowledge, and skills than actually purchasing a lot of useless gadgets. I walked away from the consumer lifestyle many years ago and now live on an off-grid homestead. That said, there are always items that preparedness-minded people, like myself, keep their eyes open for. We are always looking for good deals on all things canning, such as jars, lids, pressure canners, and water bath canners. Or perhaps a higher-ticket item, such as a food dehydrator.
To maintain sanity while trying to enumerate risks, I found that it's best to focus on broad outcomes instead of trying to track down every single way for things to go south. Say, it should not matter if you are laid off because of a downsizing, because your new boss hates you, or because they finally catch you stealing paperclips. The outcome is the same: you are out of a job and urgently need a way to pay your bills.
Mountain House, Wise Food, My Patriot Supply, and Ready Store need to get better in this regard. In some cases, we had to call a company and dig deeper than reasonable in order to find out calorie content — or we had to look at individual nutritional labels to reverse engineer the math. In other cases they called something a “1-month bucket” but that was based on silly calorie numbers.
Preppers Survive gets quite a few emails each month. My favorite emails are from newbie Preppers because they have an intensity and an urgency in their comments and questions. This intense urgency is how I felt when I first started prepping. I laboriously looked for articles on prepping for beginners. It felt like it haunted my every waking thought for months. I have been prepping for eight years and have learned many lessons over the years. Perhaps a universal lesson I’ve learned is that there is no magic formula!
Then a woman wearing a fanny pack, Marcia Brumfield, reads aloud the day’s headlines from decidedly non-MSM sources. The United Nations is taking over the Chicago Police Department to perform population control, evidently. A train crash killed 70 in Seattle. (The figure at the time was actually seven.) It’s implied that Antifa is to blame. “They want a war,” Brumfield says. “They’re the elites, and they want population control.” Last on the docket, “they” are using direct energy weapons to start wildfires in California. It’s unclear who “they” are, but apparently, they’re after the fruits and nuts.
I buy dry beans and can them myself. I know it sounds like a lot of work but its super easy and MUCH cheaper than store bought canned beans. I tend to have some empty canning jars so to keep as many full as possible I fill the empties with beans and have even canned water. An empty jar is just taking up space and provides NOTHING. The dry beans are good for long term and the self-canned are great for quick meals. The best of both worlds!
But in 1961 John F. Kennedy encouraged “every citizen” to help build fallout shelters, saying, in a televised address, “I know you would not want to do less.” In 1976, tapping into fear of inflation and the Arab oil embargo, a far-right publisher named Kurt Saxon launched The Survivor, an influential newsletter that celebrated forgotten pioneer skills. (Saxon claimed to have coined the term “survivalist.”) The growing literature on decline and self-protection included “How to Prosper During the Coming Bad Years,” a 1979 best-seller, which advised collecting gold in the form of South African Krugerrands. The “doom boom,” as it became known, expanded under Ronald Reagan. The sociologist Richard G. Mitchell, Jr., a professor emeritus at Oregon State University, who spent twelve years studying survivalism, said, “During the Reagan era, we heard, for the first time in my life, and I’m seventy-four years old, from the highest authorities in the land that government has failed you, the collective institutional ways of solving problems and understanding society are no good. People said, ‘O.K., it’s flawed. What do I do now?’ ”
Craig Compeau is a third-generation Alaskan who is prepping for a government takeover. Craig has set up a remote bugout InterShelter in the Alaskan wilderness. We also meet 44-year-old adventurer David Lakota who depends on his intuition and connection to nature to survive a giant tsunami and the mountainous terrain of Hawaii. During the program David and his girlfriend Rachaelle bug out with minimal supplies from the Kalalau Valley on Kaua'i to the 4000' high plateaus above.
Don’t let prepping overwhelm you because there are many companies wanting you to buy their product. And I agree with pat Henry, things are not as bad as what many think. I have been listening to doomsday talkers since 2011 about the imminent collapse around the corner and there will always be people saying this. So don’t rush to spend thousands of dollars. Do a little at a time and stay within your means. This is a good article because it gives you general categories such as a means to purify water, then food, then medicine, then security and also… Read more »
Most preppers don’t actually have bunkers; hardened shelters are expensive and complicated to build. The original silo of Hall’s complex was built by the Army Corps of Engineers to withstand a nuclear strike. The interior can support a total of seventy-five people. It has enough food and fuel for five years off the grid; by raising tilapia in fish tanks, and hydroponic vegetables under grow lamps, with renewable power, it could function indefinitely, Hall said. In a crisis, his SWAT-team-style trucks (“the Pit-Bull VX, armored up to fifty-calibre”) will pick up any owner within four hundred miles. Residents with private planes can land in Salina, about thirty miles away. In his view, the Army Corps did the hardest work by choosing the location. “They looked at height above sea level, the seismology of an area, how close it is to large population centers,” he said.
“Next thing I see is, they hanged the colored boy, ’cause they caught him stealing. And they had established, I think, about 1,000 trees in the forest out in Mark Twain to hang people from if they catch them stealing or whatever. And I had a big dog—my dog died of bone cancer of all things two years ago. Buddy was half-Rottweiler, half-German shepherd. He was a dog, and he was with me in this. And I also have a police riot gun, a 12-gauge, that holds eight magnum shells. So I’m seeing all this stuff happening, and then I look around, and my dog’s gone. So I picked up my shotgun and went to look for my dog, and I found five men, and they were already skinning him to eat.”
Monitor what your family eats for a week and use that as a guideline for getting started. The advantage of doing this is you will learn what your family likes so that you can shop accordingly. You would be surprised at how many people can’t remember what they ate yesterday let alone a week ago. Try to write everything down so that you don’t have to rely upon your memory. |
987 So.2d 286 (2008)
STATE of Louisiana
v.
Robert JACOBS.
No. 2007-1370.
Court of Appeal of Louisiana, Third Circuit.
June 5, 2008.
*287 Michael Harson, District Attorney, Michele S. Billeaud, Assistant District Attorney, Lafayette, LA, for Plaintiff/Appellee, State of Louisiana.
Carey J. Ellis, III, Louisiana Appellate Project, Rayville, LA, for Defendant/Appellant, Robert Jacobs.
Robert Jacobs, Basile, LA, In Proper Person.
Court composed of JOHN D. SAUNDERS, GLENN B. GREMILLION, and ELIZABETH A. PICKETT, Judges.
GREMILLION, Judge.
In this case, Defendant, Robert Jacobs, was found guilty of one count of forcible rape, in violation of La.R.S. 14:42.1, and one count of aggravated burglary, in violation of La.R.S. 14:60. Thereafter, he was sentenced to thirty years at hard labor for the forcible rape conviction and ten years at hard labor for the aggravated burglary conviction with the sentences to run concurrently. This appeal followed.
*288 Appellate counsel filed an Anders brief in this matter. Upon completion of a thorough independent review of the record, as required by State v. Benjamin, 573 So.2d 528 (La.App. 4 Cir.1990), we identified a non-frivolous issue and denied defense counsel's motion to withdraw and ordered both the State and Defendant to brief the issue of double jeopardy.
Defendant filed a pro se brief alleging that the evidence was insufficient to sustain a conviction and that his sentence was excessive.
For the following reasons, we hold that the convictions for aggravated burglary and forcible rape constitute double jeopardy. Therefore, we reverse the conviction for aggravated burglary, enter a conviction for simple burglary, and remand the matter for resentencing on the simple burglary conviction. We find that Defendant's pro se assignments lack merit, and we affirm the conviction of forcible rape.
SUFFICIENCY OF EVIDENCE
When multiple issues are raised on appeal and sufficiency of the evidence is one of the alleged errors, the reviewing court should first determine whether the evidence is sufficient, as a ruling that the evidence is insufficient would necessitate an acquittal. State v. Hearold, 603 So.2d 731 (La.1992). In his first pro se assignment of error, Defendant alleges insufficiency of evidence. Even though we find that this assignment of error without merit under Hearold, we shall address it first in our discussion.
In State v. Touchet, 04-1027, pp. 1-2 (La.App. 3 Cir. 3/9/05), 897 So.2d 900, 902, this court stated:
With regard to sufficiency of the evidence, this court sets forth as follows in State v. Lambert, 97-64, pp. 4-5 (La. App. 3 Cir. 9/30/98), 720 So.2d 724, 726-27:
When the issue of sufficiency of evidence is raised on appeal, the critical inquiry of the reviewing court is whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime proven beyond a reasonable doubt. Jackson v. Virginia, 443 U.S. 307, 99 S.Ct. 2781, 61 L.Ed.2d 560 (1979); State ex rel. Graffagnino v. King, 436 So.2d 559 (La.1983); State v. Duncan, 420 So.2d 1105 (La.1982); State v. Moody, 393 So.2d 1212 (La. 1981). It is the role of the fact finder to weigh the respective credibility of the witnesses. Therefore, the appellate court should not second-guess the credibility determination of the trier of fact beyond the sufficiency evaluations under the Jackson standard of review. See King, 436 So.2d 559, citing State v. Richardson, 425 So.2d 1228 (La.1983).
In order for the State to obtain a conviction, it must prove the elements of the crime beyond a reasonable doubt. In order for this court to affirm a conviction, the record must reflect that the State has satisfied this burden of proving the elements of the crime beyond a reasonable doubt. State v. Kennerson, 96-1518 (La.App. 3 Cir. 5/7/97), 695 So.2d 1367.
Defendant in this case was convicted of one count of forcible rape in violation of La.R.S. 14:42.1(A), which states in part:
Forcible rape is rape committed when the anal, oral, or vaginal sexual intercourse is deemed to be without the lawful consent of the victim because it is committed under any one or more of the following circumstances:
(1) When the victim is prevented from resisting the act by force or threats of *289 physical violence under circumstances where the victim reasonably believes that such resistance would not prevent the rape.
At trial, the State offered the victim's testimony that Defendant broke into her motel room, took the money from her purse, and engaged in non-consensual sex with her. He fondled her breast before having intercourse with her and she reasonably believed that resisting his advances would not have prevented the rape.
The second offense Defendant was convicted of was aggravated burglary in violation of La.R.S. 14:60, which states, in pertinent part:
Aggravated burglary is the unauthorized entering of any inhabited dwelling, or of any structure, water craft, or movable where a person is present, with the intent to commit a felony or any theft therein, if the offender,
(1) Is armed with a dangerous weapon; or
(2) After entering arms himself with a dangerous weapon; or
(3) Commits a battery upon any person while in such place, or in entering or leaving such place.
Based on the evidence presented, we find that sufficient evidence was presented to support the charge of forcible rape and aggravated battery. However, we find, as follows, that the evidence cannot be used to support both charges as that constitutes a violation of double jeopardy.
DOUBLE JEOPARDY
In State v. Cloud, 06-877 (La. App. 3 Cir. 12/13/06), 946 So.2d 265, 269-70, writ denied, 07-0086 (La.9/21/07), 964 So.2d 331, we summarized the analysis required in determining double jeopardy:
In State v. Barton, 02-163, pp. 17-18, (La.App. 5 Cir. 9/30/03), 857 So.2d 1189, 1201-02, writ denied, 03-3012 (La.2/20/04), 866 So.2d 817, the court summarized the two tests used by Louisiana courts use [sic] in examining violations of double jeopardy as follows:
The "distinct fact" test, commonly referred to as the Blockburger test, is taken from Blockburger v. United States, 284 U.S. 299, 304, 52 S.Ct. 180, 182, 76 L.Ed. 306 (1932) as follows:
The applicable rule is that where the same act or transaction constitutes a violation of two distinct statutory provisions, the test to be applied to determine whether there are two offenses or only one, is whether each provision requires proof of an additional fact which the other does not.
Accord, State v. Knowles, 392 So.2d 651, 654 (La.1980).
The second test is the "same evidence" test. In State v. Steele, 387 So.2d 1175, 1177 (La.1980), the Louisiana Supreme Court explained that test as follows:
If the evidence required to support a finding of guilt of one crime would also have supported conviction of the other, the two are the same offense under a plea of double jeopardy, and a defendant can be placed in jeopardy for only one. The test depends on the evidence necessary for conviction, not all the evidence introduced at trial....
The "same evidence" test is broader than Blockburger, "the central idea being that one should not be punished (or put in jeopardy) twice for the same course of conduct." State v. Steele, 387 So.2d at 1177. Although the Louisiana Supreme Court has accepted both the Blockburger test and the same evidence test, it has principally relied on the "same evidence" test to evaluate double *290 jeopardy claims. State v. Miller, 571 So.2d 603, 606 (La.1990).
In his supplemental brief, Defendant alleges his convictions for aggravated burglary and forcible rape violate the principles of double jeopardy as the evidence necessary to prove the aggravated burglary offense is the same evidence necessary to prove the forcible rape offense.
Our review of the record reveals that Defendant in this case was not armed with a dangerous weapon when he entered the victim's hotel room, nor did he arm himself with a dangerous weapon while within. Accordingly, the only possible theory available to sustain an aggravated burglary conviction is that he committed a battery while in the room. "Battery is the intentional use of force or violence upon the person of another...." La.R.S. 14:33. Accordingly, we find that Defendant's rape of the victim constituted a battery as defined in La.R.S. 14:33.
In State v. Joseph, 05-186 (La.App. 3 Cir. 11/2/05), 916 So.2d 378, we vacated an armed robbery conviction on the basis that the defendant had also been convicted of aggravated burglary, where at trial, the same evidence would have been used to secure both convictions. The defendant in Joseph kicked down the front door and entered the home of the victim and took a gun from her. Joseph, 916 So.2d 378. It was determined at the guilty plea proceedings that the defendant took nothing else from her. Id. On appeal, the defendant argued that since at the time he broke into the victim's home and took the gun from her he was not armed, he could not be charged with armed robbery. The court in Joseph held:
The state specifically stated that the "taking" upon which the charge of armed robbery was based was the gun taken from Mrs. Dartez. Charging the defendant with both aggravated burglary and armed robbery, based upon the same set of facts, clearly violates the "same evidence" test as set forth in [State v.] Crosby [, 338 So.2d 584 (La. 1976),] and [State v.] Steele [, 387 So.2d 1175 (La.1980) ].
Id. at 384.
In a recent case, State v. Williams, 07-931, p. 3 (La.2/26/08), 978 So.2d 895, 896, the supreme court discussed the issue of the State's recourse when it violated a defendant's constitutional right against double jeopardy and stated:
As opposed to quashing the prosecution altogether and setting aside defendant's guilty plea and sentence, the court of appeal should have, assuming the correctness of its premise, reduced defendant's conviction to the misdemeanor offense of flight from an officer under R.S. 14:108.1(A) and remanded the case to the trial court for resentencing.
In Williams, the defendant pled guilty to aggravated flight from an officer, in violation of La.R.S. 14:108.1(C), as well as several other traffic related offenses. Id. On appeal, the defendant claimed that charging him with aggravated flight from an officer in conjunction with the underlying traffic offenses constituted a double jeopardy violation; the appellate court reversed the defendant's conviction for aggravated flight from an officer. Id. The supreme court noted that the appellate court had properly determined that the same evidence of the underlying traffic offenses was the bases for bringing the aggravated flight from an officer offense, and thus, a double jeopardy violation occurred. Id. However, as noted above, when reversing the ruling of the appellate court, the supreme court stated that it was unnecessary to vacate the prosecution altogether if there was evidence presented at trial to find the defendant guilty of a lesser *291 included offense that was not barred by double jeopardy. Id.
In our review of the record, we find that sufficient evidence was presented at trial to find Defendant guilty of simple burglary. La.R.S. 14:62(A) defines simple burglary as "the unauthorized entering of any dwelling, vehicle, watercraft, or other structure, movable or immovable, or any cemetery, with the intent to commit a felony or any theft therein as set forth in R.S. 14:60." The record indicates that Defendant broke into the victim's hotel room and stole between $180.00 and $200.00 from her purse. Those facts establish the basis for a simple burglary conviction. Accordingly, we agree with Defendant's allegation that his prosecution for both forcible rape and aggravated burglary constituted a double jeopardy violation and the conviction for the aggravated burglary is reversed. Joseph, 916 So.2d 378. However, in accordance with Williams, we shall enter a verdict of guilty of the lesser included offense, simple burglary. Williams, 978 So.2d 895. See also La.Code Crim.P. art. 814(A)(42).
EXCESSIVE SENTENCE
In his second pro se assignment of error, Defendant alleges that his sentences are excessive. Since we have reversed Defendant's conviction for aggravated burglary conviction based on double jeopardy, we will not address his excessive sentence claim as to that conviction. As the Defendant's only allegation is that his sentences are excessive, we will evaluate this claim as a bare claim of excessiveness.
We have set forth the following standard to be used in reviewing excessive sentence claims:
La. Const. art. I, § 20 guarantees that, "[n]o law shall subject any person to cruel or unusual punishment." To constitute an excessive sentence, the reviewing court must find the penalty so grossly disproportionate to the severity of the crime as to shock our sense of justice or that the sentence makes no measurable contribution to acceptable penal goals and is, therefore, nothing more than a needless imposition of pain and suffering. State v. Campbell, 404 So.2d 1205 (La.1981). The trial court has wide discretion in the imposition of sentence within the statutory limits and such sentence shall not be set aside as excessive absent a manifest abuse of discretion. State v. Etienne, 99-192 (La.App. 3 Cir. 10/13/99); 746 So.2d 124, writ denied, 00-0165 (La.6/30/00); 765 So.2d 1067. The relevant question is whether the trial court abused its broad sentencing discretion, not whether another sentence might have been more appropriate. State v. Cook, 95-2784 (La.5/31/96); 674 So.2d 957, cert. denied, 519 U.S. 1043, 117 S.Ct. 615, 136 L.Ed.2d 539 (1996).
State v. Barling, 00-1241, 00-1591, p. 12 (La.App. 3 Cir. 1/31/01), 779 So.2d 1035, 1042-43, writ denied, 01-0838 (La.2/1/02), 808 So.2d 331.
In order to decide whether a sentence shocks the sense of justice or makes no meaningful contribution to acceptable penal goals, we have also held:
[A]n appellate court may consider several factors including the nature of the offense, the circumstances of the offender, the legislative purpose behind the punishment and a comparison of the sentences imposed for similar crimes. State v. Smith, 99-0606 (La.7/6/00); 766 So.2d 501. While a comparison of sentences imposed for similar crimes may provide some insight, "it is well settled that sentences must be individualized to the particular offender and to the particular offense committed." State v. Batiste, 594 So.2d 1 (La.App. 1 Cir.1991). *292 Additionally, it is within the purview of the trial court to particularize the sentence because the trial judge "remains in the best position to assess the aggravating and mitigating circumstances presented by each case." State v. Cook, 95-2784 (La.5/31/96); 674 So.2d 957, 958.
State v. Smith, 02-719, p. 4 (La.App. 3 Cir. 2/12/03), 846 So.2d 786, 789, writ denied, 03-0562 (La.5/30/03), 845 So.2d 1061.
In the instant case, Defendant was convicted of forcible rape, in violation of La. R.S. 14:42.1. The maximum sentence for said offense is forty years at hard labor. La.R.S. 14:42.1. For this conviction, the trial court sentenced the Defendant to serve thirty years at hard labor. At sentencing, the trial court reviewed the Defendant's criminal history which included: a 1980 conviction in North Carolina for breaking and entering and larceny; a 1985 conviction for simple assault; a 1994 conviction in North Carolina for distribution of a Schedule II controlled dangerous substance; a 1994 conviction in North Carolina for possession with intent to distribute cocaine; a 1996 conviction for simple burglary; a 1991 conviction in North Carolina for DWI; a 2001 conviction for distribution of a Schedule I controlled dangerous substance; a 2001 conviction in North Carolina for DWI second; and a 2003 conviction for possession of drug paraphernalia. Also at sentencing, the trial court considered the aggravating circumstances of the offenses, and stated:
First is the brutality of the crime for which he was convicted and the evidence at trial showed the following:
The victim, [L.S.], a visitor to Lafayette who was who had rented a room at the Roadway Inn, was awakened April 15, 1996 at about 3:30 a.m. She was awakened by a loud crashing sound and the presence of a black male standing above her in the room. She stated that the offender demanded money and her car keys or he would shoot her. [L.S.] gave him a hundred and seventy to two hundred dollars ($170.00-$200.00) in cash from her purse. Mr. Jacobs then removed the bed sheet and proceeded to rape [L.S.][1]
Initially, we note that the sentence is not the maximum that Defendant could have received. Moreover, we find that the sentence imposed by the trial court is clearly supported by the record. See State v. Carter, 04-482 (La.App. 5 Cir. 10/26/04), 888 So.2d 928, where the trial court held that a thirty-seven-year enhanced habitual offender sentence for forcible rape was not excessive. Accordingly, Defendant's allegation that his sentence is excessive is without merit.
CONCLUSION
We find that the convictions for aggravated burglary and forcible rape constitute double jeopardy. Therefore, the conviction for aggravated burglary is reversed. However, we enter a conviction for simple burglary and remand the matter for resentencing on the simple burglary conviction. We find no merit in Defendant's other assignments of error and affirm the conviction for forcible rape and the sentence of thirty years at hard labor without benefit of probation, parole, or suspension of sentence.
AFFIRMED IN PART, REVERSED IN PART, CONVICTION ENTERED, AND REMANDED FOR SENTENCING.
SAUNDERS, J., agrees in part, dissents in part, and assigns written reasons.
*293 SAUNDERS, J., agrees in part, dissents in part, and assigns written reasons.
I agree with the majority opinion that Defendant's sentence for forcible rape was not excessive. However, I disagree with the majority that Defendant's conviction for aggravated burglary should be reversed.
Aggravated burglary is defined in La. R.S. 14:60, which states, in pertinent part:
Aggravated burglary is the unauthorized entering of any inhabited dwelling, or of any structure, water craft, or movable where a person is present, with the intent to commit a felony or any theft therein, if the offender,
(1) Is armed with a dangerous weapon; or
(2) After entering arms himself with a dangerous weapon; or
(3) Commits a battery upon any person while in such place, or in entering or leaving such place.
The majority finds that under the "same evidence" test in State v. Steele, 387 So.2d 1175 (La.1980), Defendant's convictions for aggravated burglary and forcible rape violate the principles of double jeopardy as the evidence necessary to prove the aggravated burglary offense is the same evidence necessary to prove the forcible rape offense. I do not agree.
Our rape statute, La.R.S. 14:41, states that "any sexual penetration, when the rape involves vaginal or anal intercourse, however slight, is sufficient to complete the crime." Louisiana Revised Statute 14:33 defines battery, in pertinent part, as "the intentional use of force or violence upon the person of another...."
Defendant was convicted of forcible rape in violation of La.R.S. 14:42.1(A), which states in part:
Forcible rape is rape committed when the anal, oral or vaginal sexual intercourse is deemed to be without the lawful consent of the victim because it is committed under any one or more of the following circumstances:
(1) When the victim is prevented from resisting the act by force or threats of physical violence under circumstances where the victim reasonably believes that such resistance would not prevent rape.
Our supreme court, in State v. Ordodi, 06-207, pp. 14-15 (La.11/29/06), 946 So.2d 654, 662, overturned this court's reversal of a conviction by stating, "[i]n reviewing the evidence of the defendant's actions ... we cannot say that the jury's determination is irrational under the facts and circumstances presented to them." I read Ordodi to stand for the principle that we should uphold a conviction if we can find that the totality of the circumstances give the jury a rational basis to find a certain element of a crime, regardless of whether the court or jury can elucidate which specific action(s) made the finding rational.
In the present case, the victim testified that Defendant fondled her breasts after he had entered the dwelling she was inhabiting without authorization. Thus, the jury rationally could have found that Defendant, once he entered the hotel room, committed a garden variety battery upon the victim prior to committing the battery by penetration necessary to constitute forcible rape. Such a finding would necessitate upholding Defendant's conviction for aggravated burglary.
Fondling the victim's breasts would serve as the battery necessary after entering the inhabited dwelling in order for Defendant to be guilty of aggravated burglary. However, it would not serve as the specific type of battery necessitated by forcible rape, i.e. "anal, oral or vaginal sexual intercourse" or even generic rape, *294 "any sexual penetration." Had Defendant entered the room, fondled the victim's breasts, then left, he could not be convicted of forcible rape, but he could have been convicted of aggravated battery.
Here, two mutually exclusive sets of evidence exist in order to convict Defendant of both aggravated burglary and forcible rape.
In regards to aggravated burglary, Defendant:
1) entered an inhabited dwelling without authorization (the hotel room);
2) where a person is present (the victim);
3) with the intent to commit a felony or theft therein; and
4) committed a battery upon any person while in such place (fondled the victim's breasts).
In regards to forcible rape, per the victim's testimony, Defendant:
1) had anal, oral or vaginal sexual intercourse with her;
2) without her lawful consent;
3) when she was prevented from resisting the act by force or threats of physical violence where she reasonably believed that resisting his advances would not have prevented the rape.
I think that it is clear that these are two separate courses of conduct proven by mutually exclusive sets of evidence. Neither require the "same evidence" to prove every element of each crime. Therefore, I feel that Defendant's conviction for aggravated burglary should be affirmed.
NOTES
[1] We use of the initials of the victim in compliance with La.R.S. 46:1844(W).
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November 11, 2009
I've been checking my Site Meter quite a few times in the last day. I've been pleased and then a little ashamed of myself as I see the phenomenal power of one particular post title to attract search engine traffic. This post was originally titled "Things the Site Meter dragged in." I've tweaked it a little to make my point. I'm not traffic-greedy — not too much. Just trying to make my point.
While I was hanging out on Site Meter, a couple other things got my attention. It's my general policy not to respond to bloggers who attack me — otherwise it would be a traffic-building strategy to attack me — but I do make exceptions as the whim strikes me. So, let's look at what Roy Edroso — of Alicublog and the Village Voice is saying about me.
But TMZ — I don't read it much, but, again, I'll guess — does not itself parade as Christian. Prejean does, and so she will be held to the high standards of Christianity, while TMZ can say and do whatever it wants. ("When we are cursed, we bless; when we are persecuted, we endure it; when we are slandered, we answer kindly. ")
TMZ is following Rule 4 of Saul Alinsky's "Rules for Radicals":
Scripture and Saul Alinsky? This explains so much: Althouse is The Anchoress!
Despite his inclusion of that St. Paul quote, Edroso cuts my quote of Alinsky's Rule 4, which happens to use Christianity as the example of the effectiveness of demanding that your enemies live up to their own rules. Alinsky wrote: "You can kill them with this, for they can no more obey their own rules than the Christian Church can live up to Christianity." It's hardly some odd quirk of mine to combine scripture and Alinsky. Edroso, in his usual fashion, looks for ways to make me look flaky — along with the other bloggers he's made it his business to mock. (The link to The Anchoress hints at Edroso's approach. Check out his latest Village Voice column for a more comprehensive example of how he works.)
Back to Edroso:
This argument that hypocrisy doesn't exist for the Elect...
What argument? Where did I argue that Christians aren't responsible for hypocrisy? I simply don't.
.... is by now an old rightwing favorite....
So just pull it out of you frumpy bag of liberal complaints about right-wingers. I thought you were trying to fisk my post, Roy. But, no, I'm either this distinct writer that you love to make fun of or I'm indistinguishable in the blurry mass of rightish bloggers that you've looked at before and have grown weary of squinting at.
... and the quality of Althouse's reasoning hasn't changed much from the old days.
Well, you haven't come close to nailing anything I've said in this post, so why bother to be specific about anything I've said in the past? You can't even read the post currently in front of your face, yet you think everyone already knows what it is I've said in "the old days." Maybe Roy is tired and on autopilot. But maybe, as he worked his way through what I'd written, confident in his ability to spew snark, he saw that my post actually cohered and that it was pretty damned sharp and funny, and he consciously decided to blur his observations so he could still get his post up. The poor wilted man. The option of actually liking what I'd written is inconceivable within the little framework he's built for himself. What would happen to that Village Voice gig?
But the Jesus stuff was a shock. I went down into her comments...
He couldn't figure out anything to say about what I wrote — "the Jesus stuff" — and, desperate, he dove into the comments looking for something repulsive. What he came up was from Florida, a specific, familiar commenter here:
... a quick scan suggests that the old let's-pretend liberals (what were their names, again? Rainbow? Sunshine?) seem to have fled or outed themselves, and the remnant are leaving stuff like this:
What's difficult as hell to do is to live up to the standards that would be set up for Christians by the butt-buggering sodomites. The rapists of 13-year-old children.
"Jesus stuff"... "stuff like this"... Roy is not editing and dealing with sloppy word repetitions, and, worse, he's not bothering to figure anything out. It's just stuff. He found the most unsightly quote and then — without reason — counted on his readers to believe that it exemplifies what is generally in the comments at my blog. How utterly flabby and lame.
Now, as for the comment he cherry-picked, Edroso has no idea what it means and makes no attempt to figure it out. He has not, like the regular comment readers here, been exposed to the way Florida writes and the things he writes about. He doesn't know about Florida's longstanding Roman Polanski theme — which began here and which involves a fair amount of antagonism toward me. It's likely that Edroso thinks he's come across some rabid homophobia, but, in context, I know that "butt-buggering sodomites... rapists of 13-year-old children" refers to Polanski and the Hollywood-type liberals who've defended him. Florida's comment is not part of a mass of "stuff like this" in the comments. It's something particular, incisive, and satirical, and, if you are going to focus on it, you'd better take some time to figure out what it means. But Edroso is happy to see something that looked like shit and to splatter it onto his post and then, childishly, to demand that onlookers see how ugly things are over at Althouse.
Amazingly, Althouse is still removing comments...
Huh? Where did that come from? What comments does he think I've removed? He's trying to pin that one comment on me by asserting that I moderate the comments, so that anything that is left, I've approved of. That is either a lazy mistake or a nasty lie. My approach to the comments is well known: I have a strong free speech policy, and I leave vile things in. To imply that whatever is left has my stamp of approval is cheap and unethical.
... perhaps because they don't come up to the standards of this gem, or because they're actually messages from her employers trying to reach her because her phone has gone dead and her windows are boarded up.
He ends with a comic image, intended as a play on my name, the "old house" that he's used in his post title. Unfortunately, he hasn't built the foundation for what could have been a well-written joke. The material he thought he had just wasn't there.
Den Beste isn't still blogging, is he?
Roy makes a second attempt at humor, and, while I'm familiar with Den Beste, I have no idea why this is supposed to be funny. Althouse is The Anchoress... Althouse is Den Beste? Everything is melting in the mind of Roy Edroso.
I get that many gays want to turn Carrie Prejean into some sort of Anita Bryant, which is completely unfair, unjustified, and dishonest. As Donald Trump noted, Prejean's views on gay marriage are no different than Barack Obama's. I disagree with Prejean on that issue, but she is entitled to her opinion. I also think Perez Hilton is an ugly little troll and scab of a person. So get over it.
In a way, not much different than what Andrew Sullivan did to Sarah Palin. Sarah Palin was not some anti gay person. She was Christian but not some rabid creationist, yet Sully and his mob of liars sure painted her that way.
But all that said, Carrie Prejean made the decision to sue the California Ms. America Pagent. She cannot complain when they find some compromising video of her (that violate the pagent rules) and use it against her. Sorry. I would have been defending her if TMZ came out of nowhere with this and went after her, but that is not exactly what happened.
Meh... yet another bored blogger taking a swipe at Althouse in the high school social-lioness vein. "Oh look, a target I can abuse with my scathing wit." I swear, sometimes I see too many bloggers take their hobby as an excuse to exercise their inner juvenile. Most of us overcame this sort of behavior before or while in high school, but then there are the Edroso's among us who never let it go.
Assuming it ever becomes legal in California (hey wait California has a civil option that is marriage in every way but name) Perez Hilton could only exercise gay marriage because his exploitive site generate enough money that he could buy a husband. He could not win one otherwise.
The only thing I can say is that the dark underbelly of political-correctness is the instant bellyaching at what people say.
Sure, freedom of speech means being responsible for what you say (something a lot of 1st Amendment advocates tend to forget), but we're all so tense about it now...so ready for the "gotcha" moment when someone we dislike says something we don't agree with...it's obvious that the US won't rot from within. In the end, we'll all die of hypertension.
"Well I think it's great that Americans are able to choose one way or the other. We live in a land where you can choose same-sex marriage or opposite marriage. And, you know what, in my country, in my family, I think that I believe that marriage should be between a man and a woman, no offense to anybody out there. But that’s how I was raised and I believe that it should be between a man and a woman."
This above is Ms. Prejean's horrible double plus ungood thoughtcrime for which the left demands she be ostracized from the company of decent people everywhere.
If you break it down, though, its hard to see what all the fuss is about. The first two lines seem to be very pro gay marriage. She's glad people have the right to choose, we can go either way. Past that, she shifts to a personal focus, and says, in HER LIFE, she thinks it should be between a man and a woman.
That's it. That's all it takes to get the gay mafia to try to destroy you these days. Seems kind of lame in hindsight really. Kind of like the TMZ fisking above, its much ado about nothing.
Yeah I know this is all about some tiny blogger swiping at Althouse, but I mean, come on. This whole Prejean story is not about anything but people's preconceived notions about gay marriage and the fact Prejean is hot. Gay advocates love showing Christians as hypocrites. But does Prejean having a position against gay marriage make her one? I do not think so. She is a young woman who made a foolish tape and did not consider that prior to filing a lawsuit. Plus stories about secret sex tapes are a sure generator of hits and comments.
Lester Kinsolving always referred to the Voice as The Lower Manhattan Belch and, having seen Voice writers on the tube every now and again, particularly with Ubermoron, I can understand Les' reasonong.
Ann, why would you even care about what somebody like that wrote? Somebody with something intelligent to say - Mickey Kaus, Victor Davis Hanson, Roger Simon - their opinions on my work would be welcome feedback.
I loved your "The poor wilted man" comment.Standing up strong and sturdy like steel when critcised falsely has become a great talent of La Althouse, the Alaskan Rogue and the California Christian. The liberal men seem to be wilting into metrosexual boys when facing a challenger these days. I also note that Florida's florid prose is now the weapon most useful when attacking Althouse as a crazy place. Hmmm?
Why is Florida's comment that sodomites will spend eternity burning in hell "unsightly" to Althouse? If you are a Christian, a genuine believing Christian as opposed to a cafeteria Christian, that's exactly where sodomites will spend eternity. So it is an honest, not an unsightly statement. Of course it is also gauche and declasse and an embarrassment to a withit bien pensant like Althouse. First things first.
I originally came here thinking you were a muling idiot Lefty Ann (I can no longer remember the original lede any longer) ...and found out I was wrong.
Rather, I found you're occasionally witty, generally civil, seldom petty, you have a decided panache, and you're always worth reading (even when I agree not one whit).
Your one minor fault is a tendency to pay entirely too much attention - and in a too-thoughtful fashion - to people of a political 'suasion (and often juvenile vanity) that admits to no alternative viewpoint. And you - oddly, for someone of such obvious acuity - expect such to write and reason honestly.
Which they simply aren't capable of. Case in point.
...I think your point about distributing her unfortunate tape being possible trafficking in child-porn, was a brilliant little insight.
St. Augustine prayed to be freed from the temptations of the flesh, but not just yet. As a corollary to St. Augustine, many Christians would prefer to have Carrie Prejean as their spiritual guide rather than Mother Theresa.
Florida the woman comments like a take no prisioners man with the best hostility that a conservative can muster against the liberal talking points...and then she suddenly blends in a violent insurrection comment that can easily be used to get one thrown out of the game for cause. Just as there are things best not said on Airline flights anymore,there are threats of violence that are best not said on an internet salon style Blog. He/she is a skilled writer that is well spoken and has very readable prose. That too is not the usual style seen in a authentic angry and not going to take it anymore conservative. We will see.
I think there are an awful lot of men who would love to watch their wives or girlfriends masturbate with abandon to orgasm on Saturday night and then watch them pray beatifically during church the next morning.
It's possible that the relationship between "Althouse" and "Den Beste" relates back to Dutch immigrants in the eighteenth century.
As the story was related to me back when we were reading Edna Ferber's So Big, the immigrants were not used to using last names so they invented whimsical ones to keep the authorities happy. That's why there are so many Deyoungs (and de Youngs and De Jongs), for instance, and Van Buskirks (which I think means "from the church in the woods"). "Den Beste" is very whimsical -- "the best." Althouse and its variants (like "Althoff") probably meant that your ancestor wanted the authorities to know that he came from an old and established family (or "house," as in the House of Windsor).
Strange that I can remember nuggets like this from high school but can't remember my doctor's phone number.
As a corollary to St. Augustine, many Christians would prefer to have Carrie Prejean as their spiritual guide rather than Mother Theresa.
Many, really?
Do some folks dislike Christians because they feel they believe in a fairy tale? If so, fine then just let marinate in our delusion.
Or is it that we're "hypocritical"? If so it seems you'd rather we just admit we struggle to resist temptation and not speak of a desire to live otherwise. Except that its not what we believe As Paul stated in Romans chapter 7
We know that the law is spiritual; but I am unspiritual, sold as a slave to sin. I do not understand what I do. For what I want to do I do not do, but what I hate I do...What a wretched man I am! Who will rescue me from this body of death?
So it is an honest, not an unsightly statement.Having been told (by a used car dealer!) that I was going to hell for not going to church (the least of my sins), I believe it can be both honest and rude and off-putting.
Den Beste retired on his own volition. He didn't lose his relevancy, he walked away from it.
Now he blogs about anime because that's what he wants to do. Of course, that means a pretty small audience. He didn't like dealing with people who nitpicked or did their best to misunderstand him. His style is to put something out for other people to read, and to ignore any reactions he finds annoying. Even now he deletes comments or closes posts because of topic drift. Any political post he makes has comments turned off.
Unfortunately, that's not how the internet works, and he just wouldn't play the game. So, he had his shot at blogging greatness and decided he wasn't up to it, or it wasn't worth it.
Naturally, I don't see Althouse as being like this at all. Quite the opposite.
Anyway, The Belmont Club is a lot like what Den Beste used to write, only with comments. You can even see Cedarford in a more congenial environment.
Everybody wants to go to heaven. Nobody wants to die.Everybody wants to know the reason without even asking why.Everybody wants to be the one to laugh. Nobody wants to cry.Everybody wants to hear the truth but people keep on telling lies.Everybody wants to know the reason without even asking why.Everybody wants to go to heaven. Nobody wants to die.
Al Fields/Tom Delaney/Timmie Rogers for Tommy Dorsey (the B side of his 1950 record, Goofus) Later performed by Ellen McIlwaine in 1972 (rereleased in 1998). Performed without attribution by Rhiannon on "Flight"
I think there are an awful lot of men who would love to watch their wives or girlfriends masturbate with abandon to orgasm on Saturday night and then watch them pray beatifically during church the next morning.
Careful about using Jesus' lack of mention as a source for his approval. He didn't mention all kinds of things we would even still agree are wrong. Molestation, for instance isn't mentioned.
His audience was primarily conservative Jews, so he made specific mention of the sins that these folks might not be worried about. We start with the assumption that he assumed the conservative Jewish moral framework as found in Moses, and then go from there. He specifically opened the door wider in some areas so we are given leeway on such things (such as the sabbath).
Indeed, he said even lusting is a sin, so it's hard to argue he had a more open sexual ethic than others of his time, when every indication suggests it was quite more narrow.
At the same time, who Jesus judged was pretty much unpredictable even in the Gospels. So we can argue for a certain ethic as reflecting Scripture, but we're on shaky ground whenever we say this or that person will be certainly judged one way or another. There's a lot of stuff in Scripture (such as in Matthew 25) which seems to be quite important in the final analysis.
I've long thought that heaven will be filled with people I didn't expect, and will be lacking a lot of people who I did expect.
Like Aslan told the children, we're not told how anyone else's story ends.
Though, if I were to venture a guess, I'd say that there's just about no way we'll be seeing the folks from Westboro baptist in the happy side of eternity. Hitler won't be there either--he messed with the wrong sort.
Most other people... we're just not given the final word on that. And if we think we do, God might well remind us we don't.
I think there are an awful lot of men who would love to watch their wives or girlfriends masturbate with abandon to orgasm on Saturday night and then watch them pray beatifically during church the next morning.
For those of you who enjoyed his work, surely you must see others here and there on the internet who appear to be his ghost. I know I do. Whether any are Den Beste or not is probably irrelevant, but personally, I love that I still "see" him here, there and everywhere! Sometimes I even imagine that he is having some fun.
Fitting that Bruce Springsteen, one of their decendants, is called the Boss.
As for Althouse, I do like Altbier (old beer), which is what they call the remaining German ales (prior to the introduction of the lager yeasts and techniques in the mid 19th century, Germans mostly drank ale like their British cousins).
The surname Prejean has from the the very start led me to think of Sister Helen Prejean, a Roman Catholic nun, and her book Dead Man Walking and how that and the film turned me in favor of the death penalty for the first time in my life and so why is she in a bikini?
If the goal is to show how Edroso is not trustworthy, this post falls far short of the mark. Most people would stop reading after the first sentence and their eyes would glaze over long before the end.
I try to show how people are lying and misleading and the like or that they can't think things through. And, I try to get to the point and start with one or two topic sentences telling people what I'm going to tell them.
In this case, I'd comb Edroso's past entries for examples of him lying/misleading and then I'd attempt to show his readers how he misled them.
For a recent example of a blog fight, see this. For something more important, here's me pointing out that Obama lied; that's part of a series.
On the one hand, I don't want people in the Instapundit orbit to learn how to do things in a better way, but OTOH it's getting lonely being one of the only persons who knows how to do things the right way.
"Everybody wants to go to heaven. Nobody wants to die.Everybody wants to know the reason without even asking why.Everybody wants to be the one to laugh. Nobody wants to cry.Everybody wants to hear the truth but people keep on telling lies.Everybody wants to know the reason without even asking why.Everybody wants to go to heaven. Nobody wants to die.
Al Fields/Tom Delaney/Timmie Rogers for Tommy Dorsey (the B side of his 1950 record, Goofus) Later performed by Ellen McIlwaine in 1972 (rereleased in 1998). Performed without attribution by Rhiannon on "Flight"'
I like Albert King's version.
Ellen McIlwaine....that's a name from the past I'd forgotten about. I played with with her back in the day in Woodstock. She was a big girl with a great voice. Good guitar player too. She tried to hit on me but I couldn't go there.
And if you get so upset when you perceive you've been misunderstood, why not be more expansive and direct in your posts? You spend so much time here explaining, why not have been more precise in the first place. If you don't wanna, that's fine. I get it. But you can't be surprised when your meaning and your opinions are not entirely clear.
Well, I would echo those who say that comparison to Den Beste is hardly an insult.
It is, however, inapt, from my limited readings of his posts. Everything I read of his was--well, you wouldn't call it elliptical. He was trying to communicate specific ideas in a clear fashion—often in a sphere which doesn't care for that sort of thing—which is why he isn't doing it any more. :)
i know that it's hard to resist returning fire when attacked, but look at how the comment threads can devolve into a couple of people sniping at each other.. it's boring. honestly, i didn't 'get' your prejean post either, but so what? i find enough of interest here to make regular visits, maybe leave a thought or two of my own, and then just move along...seems to work out pretty well for me.i suggest sticking to the theory that there is no such thing as bad publicity. as unfair as the fisking may have been, you got a mention that probably sent some curious folks over to check out your site so, in the end, it's a 'win' for you. feel better now?.. wait! don't answer that! |
When Chris Sale started to slide in the first round of the draft because of signability, it was a surprise that the thrifty White Sox were the team that selected him. Now comes a bigger surprise: the first- or second-rated college pitcher on most draft boards has agreed to terms for a bonus equal to MLB’s bonus recommendation for his No. 13 slot a year ago: $1.656 million.
Sale will take a physical on Monday and likely will sign his deal on Tuesday. He’s the highest-drafted player to agree to terms so far this summer. … While Sale will get less money than anticipated, the White Sox will give him every opportunity to crash their big league bullpen, perhaps as early as August. He’ll initially report to high Class A Winston-Salem, with an anticipated promotion to Triple-A Charlotte in mid-July. After spending this summer as a reliever, he’ll work in the Arizona Fall League as a starter and get the opportunity to make Chicago’s rotation in spring training next year.
As for the perceived discount the Sox might have received by agreeing to terms less than two weeks after the draft, Sale has a chance to more than make up any difference with a major league promotion that would start his service time clock.
In addition, that also would include a placement on the 40-man roster with a chance to make the major league team out of spring training in 2011.
Inside the Pick: Every draft has one player who takes a surprising fall, and this year it was Sale. For the player some thought was the best college pitcher in the draft to fall to 13th overall is a massive get for the White Sox.What He is: Sale is the rare pitcher who combines size (6-foot-6), velocity (up to 96 mph), and plus command from the left side. His changeup was among the best in the draft, and he consistently dominated week after week, including in his few starts against top-notch competition.What He is Not: Sale’s low three-quarters arm slot gives some scouts concern. It prevents him from being able to get around on his slider, and gives right-handed hitters a very long look at the ball.Path with the White Sox: Sale shouldn’t have too many problems at the lower levels based solely on his velocity and command. If he can find a dependable breaking ball, he has a chance to really move quickly.
Comments: This tall right-hander was creating a lot of buzz later in the spring when reports of him touching 98 mph spread like wildfire. His secondary stuff isn’t as good as the heater, though his curve ball has improved this year and his changeup has a chance to be a decent offering. There’s not a ton of life in the fastball, but he throws without much effort. People were pouring in to see him late, and that kind of arm strength tends to do very well in the Draft.
Comments: Heading into the spring, the thought was that Reed would be one of the more sought-after college relievers in the class, but the San Diego State product was stretched out over the winter in order to be the team’s Friday starter. He has performed even better than most could have expected, showing the ability to throw three pitches and adjusting easily to the role. A broken pinky on his pitching hand slowed him down for a few weeks, but presuming he picks up where he left off, Reed is likely a college arm moving up draft boards everywhere. Enhanced Scouting Report
June 15, 2010
As Sale himself tells it, “My freshman year I really struggled. I was having trouble getting outs. There was a span where I was pitching good, but during mid-summer my fastball was really flat. I kind of hit the wall.”
… “I was talking with some of the coaches there and they were saying you can’t keep doing the same thing you’re doing, you have to try something different,” Sale said. “So I dropped down and tried a different arm slot (a three-quarters delivery). I saw immediate results with it. It was night and day. My velocity went up, I got the most out of my change-up, and I got better with the slider.”
… “What the change in arm angle did was create movement and sink on his pitches,“ Tollett said. “He had the belief now that he could get it done. I started putting him in situations where he could be successful, where he didn’t have to worry about results. Then I put him in some big ball games and started to see what his future could look like.”
… “I’m stoked to start my career,” Sale said. “I know Ozzie Guillen is a crazy manager, but I feel like I’m really going to get along with this guy. He wouldn’t have that crazy reputation if he weren’t competitive like I am. I just want to be one of the main guys they depend on and eventually win the World Series, which is everything.”
Morehead State graduate and former baseball player J.D. Ashbrook has signed a contract with the Chicago White Sox. Ashbrook has been assigned to Bristol Sox, Chicago’s rookie level (Appalachian League) farm team in Bristol, Va. He will join MSU teammate Drew Lee, who was drafted by the White Sox in the 12th round of the Major League Baseball draft last week.
The Eagles’ leading hitter this past season, Ashbrook capped his career by hitting .432 with 82 hits, 69 runs (a mark that was in the top five nationally), 15 doubles, 18 home runs and 55 RBI. He led Morehead State and ranked in the top three in the Ohio Valley Conference in five offensive categories (batting average, slugging percentage, on-base percentage, runs scored and home runs). He earned First Team All-OVC honors and was a Ping! Baseball Third Team All-American.
June 14, 2010
Q: Which players drafted in the first or sandwich rounds will become their team’s No. 1 overall prospect as soon as they sign?
A: … In fact, after the top three choices, I only see two more draftees who would immediately become their organization’s best prospect. I believe in Florida Gulf Coast lefthander Chris Sale’s (No. 13, White Sox) durability and ability to remain a starter, so I’d take him over Tyler Flowers and Dan Hudson with the White Sox. I have no worries about Arkansas third baseman Zack Cox’s (No. 25, Cardinals) power or ability to remain at the hot corner, so I’d choose him over Shelby Miller. However, both of those are close calls and there are a number of clubs that did have concerns about Sale and Cox.
The Chris Sale pick was solid, but there is not a lot to like about the rest of the draft. I like Addison Reed and Rangel Ravelo looks like an interesting prospect, but I don’t see a great deal to get excited about.
June 13, 2010
It’s rare that the Sox draft a high school middle infielder as high as the 11th round, but they’re making a serious effort to sign Chaparral (Ariz.) shortstop James McDonald. McDonald said that he’s not sure whether to start his professional career or fulfill a scholarship offer from Arizona State. “I’m weighing a few things right now,” McDonald said. McDonald recently graduated from the same school that produced Paul Konerko.
Tampa trio signs: Three players drafted out of the University of Tampa signed with the White Sox: C Mike Blanke (14th round), 1B/DH Mike Schwartz (17th) and RHP Austin Evans (23rd), a former Chamberlain High standout.
The Sox went back to Tampa to grab the Sunshine Conference Player of the Year. Schwartz was also a semifinalist for the Tino Martinez award, presented annually to the nation’s top Division-II player. He hit .415 and set a school record while leading the nation with 75 walks. So it only goes to figure he had an impressive OBP [.596]. Schwartz finished with 11 homers and 55 RBIs.
Friday was a very special day for former East Burke baseball standout Ethan Icard. It was the day his dream of playing professional baseball came true. Icard, a 6-foot-2 right-handed pitcher signed a deal with the Chicago White Sox on Friday evening. He will begin his professional career when he reports to the Bristol, Va. White Sox of the Rookie League on Wednesday.
… Icard spent the last two seasons playing at Wilkes Community College. In 2010, he was 8-4 overall with a 4.14 ERA. In 87 innings, he struck out 93 batters. In 2009, Icard posted a 9-3 overall pitching record with a 3.40 ERA. He had 68 strikeouts in 79 innings pitched.
June 11, 2010
The White Sox were known to be targeting college pitchers, and they picked four of them to start their draft. BA’s top-rated lefthander, slender strike-thrower LHP Chris Sale (1), fell to them at No. 13 overall. He had a 10-1 strikeout-walk ratio and could move quickly with his plus fastball and changeup and improved slider. He could be an absolute steal with a double-digit pick. RHPs Jacob Petricka (2), Addison Reed (3) and Thomas Royse (3s) give them three solid righthanded options, with Reed a potential fast riser if he moves back to a relief role. The position-player crop offers less upside, with hard-hitting junior-college 2B Joe Terry (8) and toolsy SS Tyler Saladino (7) the most intriguing prospects.
1) Chris Sale, LHP, Florida Gulf Coast University: No one expected Sale to fall this far, 13th overall. He’s a steal in this slot. Although his delivery is unconventional, he repeats it well and I’m not convinced that his injury risk is any higher than any other pitcher.
2) Jacob Petricka, RHP, Indiana State University: Raw before this year, Petricka improved his mechanics this year and got his fastball up to 98 MPH at times. He still needs refinement, but has a lot of potential as a relief arm.
3) Addison Reed, RHP,San Diego State: Very polished, Reed throws 89-92 as a starter but hit the mid-90s when used as a closer in ’09. He has a good slider and changeup. If used in rotation, he looks like a number three or four starter, but if he moves to the pen he could move very fast as a closer through the system.
3S) Thomas Royse, RHP, University of Louisville: Another polished arm, with a 90 MPH fastball and a workable slider and changeup.
But Hollis does have what Simonds called a “plus-plus fastball” that runs in the 92-93 mph range. “In the minor leagues, the focus is a little more on development,” Simonds said. “In college, we have a limited number of games. “He’s got some good run on his fastball,” he said of Hollis. “If he picks up a couple miles on his fastball and picks up a second pitch, gets more consistency with his change-up or curve, who knows what will happen?” Hollis said he agrees that his “arm strength” is what attracted the scouts, “that and a little bit of athleticism.”
Hollis said he has talked with a White Sox scout and is waiting for the contract papers in the mail. “I’m definitely signing, for sure,” he said. “Right now I’m just sitting back and being patient.” |
"Paris, April 1 958." "Dear family," "Memory is a strange muscle." "It moves on its own when we least expect it." "Today I went to the theatre where we are to perform." "While climbing the stairs I asked myself:" ""Have I locked the door?" "."" "as if I was home." "I remembered the stairs, the strange way that grandmother looked at them, as if it was a forbidden place." "Poor grandma." "Daughter!" "Lean on me, mother." "One, two..." "Celia!" "Don't be afraid." "Come on." "I'm not sure you remember, she was so afraid of falling backwards." "Nobody understood why, but we all walked behind her to help." "I remember, although I might be making it up, one Christmas Eve she drank a bit too much, and it was the only time she spoke about it." "If I ever fall down I'll never get up again." "But we're all here to help you." " lt's all the same." " Ernesto!" " Come on!" " Merry Christmas!" "The real discovery came later." "For one reason or another we never spoke about it again." "However the whole family continued their efforts to help grandmother." "Mom searched the whole city for shoes with nonskid soles and things of the kind." "Nora became a human cane." "Jorge and I could only play in the garden." "Dad had all the floor tiles changed and forbade carpets." "The house became a little strange but our life went on the same." "And it wasn't worse than others." "white lies" "What are you doing there:" "I couldn't sleep." "Why didn't you come:" "I had work to do." "It was my farewell, Jorge." "Well..." "Next time I'll go." " Here." " The last one." " Have it." " What do you want:" "Smoke." " Do you have everything ready:" " Yes, Auntie prepared everything." "Did you speak to Mom:" "I didn't want to worry her." "You're shameless." "What's better:" "To tell her the truth and sadden her:" "No..." "I don't know." "She'll find out anyway." "Why:" "Are you going to tell her, Jorge:" "No..." "Nora:" "No." "Then how will she find out:" "Eventually Mom always finds out about everything." "Put your hand like this." "What are you doing:" "Stop talking nonsense." "Here, put it out." " Listen to me." " Don't do noise." "Who is she:" "Patricia:" "Nice picture." " When did she give it to you:" " Just now." " Did you see her last night:" " Yes." " So:" " So..." "So what:" "In the end, yes." " Did you tell her:" " Yes." "And she thinks it's a great idea." "That I can be successful in Paris." "Like other musicians." "That's what they say." " Excuse me." " How will I do in Paris:" "Great!" "Where did you go dressed like that:" "To mass." " Where did he go:" " To mass, yes." " What about breakfast:" " What:" " You won't prepare it:" " Why me:" "Because you make it delicious, you're the best." "Ok, ok, I'm going." "Jorge..." "Why don't you check if the car's arrived:" "Slightly out of tune." "They'll send you back soon." " l hope." " Don't start, Mom." "How many students did the teacher invite:" "One." "But it's for so long, you're still so young." "Three months." "I'll be back before you know it." " Will you write to me:" " No, not even a single letter." "It's cold, stay in bed." "Pablo..." " Take care." " Take care." "And don't go around partying too much." "The car is here." "Are you ready:" "Yes." "Can you help me with this:" "It doesn't close." "Pablo!" "Excuse me." "Pablo, before you finish I want you to pack this." " What is it:" " Something for the trip." "Uncle!" "It's what your father would have wanted to do." "Yes, sure." "Go to Paris to play in a cabaret." " Dad would have loved it!" " Ok, let's go." "I'll tell Nora." "Don't listen to your brother." "He's so inexperienced." "Pablo." "I made something for the trip." "They serve meals on the ship." "You never know what they use to prepare them." "Take it!" "What is it:" " Sandwiches." " For the journey." "Can you take this for me:" " Pablo..." " What:" " l don't know how this works." " Simple." " There." " Okey." "It's late, come on, you'll miss your ship." "Mom." "What did I tell you:" "So we can all be in the photograph." "Let's go to the car." "Let's go." "Can you believe this woman:" "Give me your hand." "Here:" "Come on, it's my turn." "Come on." " What:" " Come on." "A picture:" "Mom should be in the middle." " Ahí." "Ahí, ma." " !" "Pará!" " Smile." " No, wait." "Come, Pablo." "I'll take it." "Get ready..." "One..." "Two..." "Three." " What's the matter:" " The engine won't start." " Maybe it ran out of fuel." " No, it's flooded." " What's the matter, Ernesto:" " lt's flooded!" " Can't you do something:" " What do you want me to do:" "Jorge..." "Take." "Take care of it." "Try again." " He'll miss the boat." " He won't!" " There it goes..." " That's it." "Bye!" "Be a good boy!" "Mom..." " Something else:" " What:" " Something else:" " No, it's fine." "Take a deep breath." "Again." "Again." "Jorge..." "Hello." "Hello." "It's been a while." "How are you:" " l'm fine, studying." " That's good!" "How are your Aunt and Uncle:" " Fine." " Say hello to them for me." "And Pablo:" "How is he:" "Fine." "He was to send us a postcard from a stop at a port, but it seems he didn't have the time..." " Didn't he write to you:" " No." "Well, you know how things are." "To arrive in a new place..." "Yes, it must be a mess." "Ok, I'm going..." "Regards." "I'll prescribe her some vitamins." " She's worried, that's all." " Yes, that's all..." "But it's all she talks about all day." "When did your nephew leave:" "About..." "Next Thursday it will be a month and a half." "Boys don't realize those things." "Yes, but he should send a letter to his mother, at least." "Maybe you could write it yourselves." "A short note, to calm her down." "Dear family:" "I'm sorry I couldn't write before, but rehearsals take very long." "Paris is a beautiful city." "I hope everyone is fine." "A big hug, and a kiss for mom, Pablo." "Very nice, isn't it:" " Rubbish." "He doesn't say anything." " What do you want him to say:" "Where's the stamp:" " l threw it away." " Why did you do that:" "It was on the envelope. I was so excited when I opened it that I tore it apart." "How are we going to answer to him:" "I copied the address on a piece of paper." "So, let's write to him now." "Fetch a pen and paper." "Dear, unruly Pablo, I was very glad." " We were very glad." " We were very glad... to receive your postcard... but we are also a little worried." "You didn't tell us about yourself." "We are glad everything is fine, but we want you to come back soon." "Look after yourself." "A big kiss." "Mom." "It's my fault." "I should have written something else." "We did it in a hurry." "What I'm worried about is Pablo." "What should we do:" "Keep waiting:" "I was thinking..." "Do you remember that employee we had:" "She married a Frenchman..." " Adela..." "Azucena..." " Almudena." "Almudena." "They moved to Paris." "Dad was so good to them in the past." "We can write her, and ask her to help us find Pablo." "Could she look for him:" "At least she can go to that place where he was to play." "Meanwhile she can send another letter to Pablo." "Another letter:" "I'll send it in an envelope and she only has to send it back." "We can give her some money." "What should we tell Mom now?" "." "We can tell her he is doing very well, playing with his teacher, that they asked him to play in more concerts." "Avery good offer, one he can't refuse." "In Paris... for a while." "For a little while, that's why he accepted it." "The offer is to play with an opera singer who is on a tour." " A famous singer." " An aristocratic woman..." " Called:" " Margarita!" " A French name..." " Veronique:" "Veronique..." " Mimi:" " Yes, Mimi Pinzon..." "Give me a break!" "Ludovica:" "And where is he:" "He's staying in a very elegant hotel in the center of Paris." "From the windows he can see the Eiffel Tower..." "With flags from every country..." "The hotel has a café" "The hotel has a café as big as our house... with glass chandeliers and brass doors." "Madam!" "Nora!" "It's Autumn here and the streets are covered with fallen leaves." "There are cafes everywhere, crowded until late at night." "Everyone is so elegant." "Last night the teacher and I had dinner with a very famous opera singer who came to congratulate us." "Her name is Marie Bergere." "She wants us to accompany her in some concerts that she is giving in cities all over France." "Can you imagine such a trip:" "It's an incredible opportunity for my career." "I hope you are as happy as I am." "I love you a lot." "A big hug, and a kiss for Mom." "Pablo." "Hey, good." "Our boy is doing well." "I'm so proud!" " Yes..." " Of course!" " What's the matter, Mom:" " l don't know." "I have something in my stomach." "Happiness!" "Yes." "But..." "I'm thinking of Patricia." "How will she react to the news:" " She'll be glad." " Sure." "We haven't heard from her for a while." "Why hasn't she come over anymore:" "Perhaps she doesn't want to bother us, with Pablo gone... I'm sure she doesn't know anything." "We should tell her." "Let's invite her for a meal." "We have to look after Patricia until Pablo returns." "It's the least we can do for him." " Come in!" " Thank you." "I brought this." "Mom loves chocolates." "You should give them to her." " Are you staying here:" "I'll bring her down." " Yes." "Patricia." " Hello." " Thank you for coming." "How could I not come:" " Have you had news:" " No, and you:" "We're trying to find out about him through a friend of the family in Paris." "She went to the place where he was going to play and it was shut down." "That's so strange." "That's Pablo... I don't know." "I'm scared." "Scared of what:" "Don't be silly." "I brought this." "You shouldn't have." "You're already one of the family." "Norita, put them on a plate, come on." "Excuse me." "See you later." "You're sad." "What's wrong:" "Nothing." "I was studying a lot." "Look me in the eyes." "You're lying!" "You don't need to feel that way." "Pablo loves you." "The thing is that he had an important offer for his future" "For the future of both of you." "Yes, I know... but it's difficult to think he is so far away." "I miss him too." "Between us, Pablo was always my favorite." "You're so lucky." "He is as well." "I believe that when he returns, he'll want to marry quickly." "Seriously, it's a premonition I have." "You may be right, but we have to wait." "We can't get our hopes up." " One can't live without hopes." " One can't live without hopes." " You'll be a beautiful bride." " Thank you." " But I think we should wait for a while." " No, on the contrary." "Let's begin preparing everything ourselves." "Dear Pablo, comma." "How could you start such an adventure without asking us:" "Are you forgetting about your family:" "You must finish your work and return." "You have commitments here as well." "What does your teacher say about all this?" "I don't want you to listen to everything he says." "You have to think about us." "Be careful." "France can be a dangerous country." "Return as soon as possible." "We need you, Mom." "Dear family, I know Mom is right, I was selfish." "But it was the only way to make a quick decision, lf you knew how difficult it was for me." "But, well, it's done." "Fortunately everything is working out very well." "Marie is a great singer, very thin, bony." "She always wears feathers on the stage;" "sometimes green, other times, black." "They always match her shoes." "She likes to wear eccentric hats, like Aunt Celia." "I told her we have a hat store, one of the most well-known shops in Argentina." "Well, I exaggerated a bit." "Last week we had our first concert." "It was in the Palace of Versailles." "You can't imagine how big it is." "There are almost 200 bathrooms." "I was so nervous that I got lost." "The concert was a success." "There were a lot of important guests, including ministers and film stars." "It's a pity I couldn't understand them." "I have to start learning French." "At least a few lessons..." "Excuse me." "You can't imagine how happy I am." "But don 't think this is easy for me, I miss you all, especially Patricia." "I sent several letters to her, but she hasn't replied yet." "You didn't write to him:" "I didn't receive any letters, yet." "Why don't you write to him now:" "Nora, fetch a sheet of paper for Patricia." "Not now." "I have to think of what to write." " But you'll write soon." " Yes." "It's a time of sacrifice for us all, I know that." "How lucky that Jorge is taking care of business, otherwise we'd be on the street." "I see French girls walking along the Seine and think of Nora." "Her commitment to her classes with those dull students who can't even learn the tables... I also think of auntie and uncle, always so supportive." "Uncle used to tell me:" ""You have to go far in life, very far." "So we can no longer hear you. " He was right finally." "Auntie would go mad in Champs Elysees." "There are trees shaped like animals." "A bear, a giant rabbit... ln Autumn the perfume of the trees fills the city." "I wish you were here with me." "Look what has arrived from Paris." "I love you all." "Pablo." "No." "Auntie, did the postman come:" "Yes." "He brought a package from Paris." "Your mother has it." " ls Patricia here:" " Yes, she's in the back." " Hi." " Look Jorge!" "A gift from Pablo." " What is it:" " l don't know..." " A kind of lamp." " lt's got a pattern inside." " What is it Nora:" " l don't know." "Does it revolve:" " l'll catch it." " No!" "Be careful!" "What a shame, your husband!" "And you:" "Help him go upstairs." "Don't let the children see him." " Let's cook it!" " lt's mine, leave it!" "Dad gave it to me." " Mom, where's Mr. Rabbit:" " lsn't he in the garden:" "We can't find him anywhere." " He must have gone into the forest." " The forest:" "Sure." "Rabbits live in the forest." "Dad brought him so that he could spend a holiday with us." "Perhaps he got tired of being so far away and returned..." " But, why:" " Perhaps he missed home." "Yes:" "Excuse me." "Mr. Millstein, come in." "I'm sorry to bother you in your own house, but I haven't seen you in the store lately." "I'm working a lot at home." "Yes, your uncle just told me that." "What can I do for you:" " l wanted to tell you the store is having some problems. -l know." "Then you'll agree that we should make some changes." " What kind of changes:" " First of all, to cut down expenses." "Perhaps we can do without one of the employees," "Or raise the prices." "Yes, that's reasonable." "Which of the options:" "I wouldn't dispense with one of the employees." "Perhaps reduce wages... I don't know." "You can figure this out better than me." "Do you know the wise saying:" ""The eye of the owner fattens the calf:" "My father used to say it." "Your father was a smart man." "If I were you, I would follow his advice." "I'll keep that in mind." "Now if you excuse me, I have to go back to work." "But we haven't decided what to do yet." "The lemons are so little." "They aren't ripe yet." " lf you want I can ripen some for you." " No, leave them." "Norita, cross lemons out." "Nora..." "Cross peppers out." "Do you have apples there:" "Apples, three kilos." "Stand up straight." "Do you know where they sat her:" "On the wicker chair." "She looks beautiful, it frames her." "What an idea to sit her on a wicker chair!" "That will blur the background." "Bring a green chair from the dining room." "That will emphasize her neck." "The neck..." "Nora!" "Don't use that chair." "Your mother says to bring one from the dining room." " Tell me, what's her hair like:" " Nora is tidying it." "She's leaving a fringe on her forehead." "That fringe, oh my god." "Clear her forehead, that tuft always covering her eye." "It's horrible, poor thing." "Nora!" "Don't leave that tuft covering her eye." " Like this:" " Yes." "I can't tell her it's horrible..." "What is she holding in her hands:" "Nothing, she has them crossed." "Make her hold a jasmine." "Nora!" "Your mother says that she should hold a jasmine!" "But the dress is pale." "In that case, a rose." "Nora!" "Not a jasmine;" "a rose would be better then." " Make up your minds!" " We're doing what we can!" "Celia!" "Don't shout at Norita." "They brought a rose for her." "Red..." "Red like blood." "A smile, please." "The garden is covered with flowers and you're still in France." "I hope that..." "No, we hope... that with these photos, you will remember your family." "Fa...mi..." "ly." "We love you madly." "Beautiful eyes..." "Raise your leg." "That's it." "Let's see." "Nice shoulder." "That's right." "Very well!" "Another one." "Your eyes glowing for uncle Ernesto, come on!" "The Naked Maja!" "What's the matter:" "Oil." " Did you ask Uncle:" " He's busy." "Can you use cooking oil:" "I'll check." "Hundreds, tens... and units." "How many there are:" " Uncle:" " Jorge?" "Can you open this for me?" "What are you doing:" " The key got stuck." " Which key, Uncle:" "The inventory:" "I'll keep it for you." "Dear family, I have great news to share with you." "Marie offered us to make a record with her." "Norita, the scissors!" "I'm sending you one, I hope it arrives in one piece." "It's on sale in all the shops in Paris." "I hope it didn't break." "There were very good critics in the papers." "I hope you like it." "Even better, we have many concerts to promote it already scheduled." "Not only in France, we'll tour Germany." "I have to prepare the luggage." "I love you all." "Take it, Norita." "Pablo." "Grands Opéras Françaises, Marie Berger." " This is wonderful!" " So important, isn't it:" " What are you doing, Mom:" " Let's listen to it!" "Leave it to us, you can listen to it from here." "No, I want to listen to it properly." "I'll come with you, wait." "Hold it for me." "And those musicians he brought:" "Does he think this is a cabaret:" "They're his friends, grandma." "Did you see the garden:" "No, you never see anything." "Only the naked dancers are missing!" "Mother, a party, once in a while..." "Once in a while your husband comes to visit." "Show a little respect, grandma." "My brother supplies for all our needs." "Respect:" "This is a family house, dear, and in my family..." "Please, stop fighting!" "The guests are arriving." "The guests, the guests." " Welcome." " Thank you." " Mr. Millstein." " Thank you for the invitation." " Please, step into the garden." " Yes, thank you." " The children room." " lt's really pretty." "Do you smoke:" "Thank you." "Norita!" "Come here." "Go upstairs to see where your father is." "Tell him I need to talk to him." "Mom, mom!" "This is the last time I hear you say something like that." "Mrs. Millstein felt bad and dad was helping her." "is that clear:" "Go and wash your face." "Doctor:" "Do you know an Opera Singer, called Marie Bergere:" "What:" "Marie Bergere:" " Yes." " The French singer:" "Yes." "Yes, I know her." "Let's see." "Take a deep breath." "Leave everything here." "I'll take care of that." "Excuse me." "Your uncle raised the prices again:" "Talk to him, I wouldn't charge you a thing." "Lito!" " Can you give me some water:" " Yes, sorry." "Why do you always treat me bad:" "Stop that." "My aunt is around." "Where:" "Under the table:" "No, she's with the doctor." "She took Mom's tests to him." " How is your Mom:" " Not very good." "She's worried about Pablo." "And your brother:" "He's doing very well." "He's touring with his band." " Really:" "What a surprise!" " Surprise:" "You know, the kind of friends he travelled with..." " l don't mean anything, but..." " Then don't say anything." "What's wrong:" "What have I done to you:" "You make me feel nervous, Lito." "Why so nervous:" "I have things to do." "You do too." "When are you going to have some time for me:" "When my brother comes back, we'll talk." "And what if he never does:" "Go away, Lito." " Ernesto, we are not making anything." " l know." "Today I went to the workshop and I talked to Caceres." "We're going to reduce the production." " Did you go to the Consulate:" " Yes, I did." " And:" " Nothing." "They only know he entered France." "What are we going to do:" "The only option is for somebody to go there." "And keep looking for him." " Yes, or claim him." " Claim him:" "At the mortuary, Celia." "The mortuary." "Such a pessimist." "We must be reasonable, Celia." "It's a possibility." " lt's Pablo's face, look." " And this..." "Maybe this is his room..." "It looks nice." "Such a good idea to send us these drawings." "He's more and more like Dad." "You haven't been to the club lately." "I don't go out much, actually." "You should go out, have fun..." "meet someone..." "That's what Pablo always says." "Pablo knows how to have fun." " l have to take care of Mom." " Sure." "Everyone has commitments." "Yes, of course." " Do you miss Pablo:" " Yes." "Like everyone else." "I'm sure he's fine." "And he'll come back soon." "I don't know what to think." "Well, we have to think about the wedding now." "Wedding:" "Patricia." "Hello, Jorge." "How are you:" "How did you do on your exam:" "Good." " That's good." " Yes." " Shall we go:" " Yes." " Patricia:" " Yes:" "Are you staying for dinner tonight:" " No, I can't." " Another day, then." "Another day, yes." "Let's go." "Mom is growing impatient." "Excuse me." "Did you see Patricia today:" "She's weaker every day." " Yes, poor thing." " Why poor:" "She should think more about Pablo." "Well, she's helping us a lot, isn't she:" "I think she's losing hope." "But I'm sure Pablo is fine." "Don't you think, Jorge:" "Sure!" "Besides, we can't think of him all day." "Pablo is a grown up and knows how to look after himself." "We have other things to take care of." " The store, for example." " Mom's health." "Despite what the doctor says, I see her improving every day." "Her spirit lifts every time she receives a present from Paris." "Yes, but we have to think about our finances." "How much is this comedy costing us:" "Mom's health is not a joke." "Of course." "But do you have any idea of how business is going:" " Not so well." " Like hell." "Ernesto!" "That's the way it is." "The numbers aren't good." "How to pay our debts:" "Production on the farm isn't good, either." "The foreman cannot handle it on his own." " Millstein says..." " Millstein will lead us to bankruptcy." "Since he took over things have worsened." "We must do something." "Like what:" "I don't know." "We must think about it." "I have an idea." "Dear family, I'm writing from the train that takes us on another tour." "From my window I can see beautiful houses under the snow." "It's a wonderful landscape, but I can't stop thinking about you." "One learns to value things when they are far away." "I miss my bed, Auntie's meals, Uncle's jokes... I was trying to find a place in town where they make pasta... I imagine Norita is still giving lessons and Jorge is taking care of the store." "It's hard to think that life continues the same, while I'm here in Paris... I saw a picture, and without a second thought I bought it." "It sometimes goes unnoticed but for me, here in Paris, the memory of the family is greater everyday." "I can't forget dad screaming:" ""Come back, you half-wit" when I broke the dinning room glass." "I think the glass was never replaced." "But I miss Patricia the most." "I think more of her everyday, I even write her name on steamy windows." "Please, convince her that this is the best for us." "Soon we'll finish the concerts, although the distance between cities is bigger." "Next week we are going to Berlin." "Then, Frankfurt, Viena, Milan, Rome... I hope we can soon be together." "Travels are more enjoyable when you share them with someone." "You can 't imagine how much I miss you all." "Pablo." "You look just like me the day I married." " lt should be... that way." " Yes." "It bothers me here." "Take it off and I... lt's the emotion." "Patricia." " What's the matter:" " l feel ridiculous." " Why:" " Jorge..." "Come in." "What's all this:" "Pablo's life in France." "I have something for you." "Pablo's favorite book." "He would want you to have it." "Pablo didn't read books." "Never mind, I accept it." "From you, not from Pablo." "Thank you." "Didn't you see Patricia:" " She left." " What did she do with the dress:" "She took it." "She liked it so much, she wanted to show it to her family." "That's so nice." "I'll tell your mom." "Attention!" " Very good!" " One more time, dad." "No, tomorrow." "Now Uncle and I have to leave." "What's that:" "Voilá!" "You should be the Finance Minister." "Don't play with the food." "Good morning." "Excuse me for a minute." "Keep eating, children." "Norita..." "Norita, are you ready:" "I'm almost done." "They're bringing her down." "Very good!" "You're going to kill me." "Be careful, Uncle." "Easy..." "Watch the door." "Be careful." "Be careful." " There you go." " A bit closer..." "Here Mom, I'll fetch the food." " Are you cold:" " l'm fine." "Just a bit out of breath." "Mom, we have a surprise for you." " Pablo will call tonight." " What do you mean:" "From Europe:" " ls that possible:" " lt's very expensive and difficult, but it's possible." " Excuse me." " That looks so good!" " Let's see." " What time is he going to call:" "I don't know, it depends on an international operator." "Who wants some salad:" "Mom, do you want salad:" "No, no, later." " Shall we make a toast:" " Yes, of course!" " Merry Christmas!" " Cheers." "Merry Christmas!" "Merry Christmas!" " To Pablito!" " To Pablo!" "Hello:" "Operator:" "Yes, I'll wait." "Pablo!" "Pablo!" "It's been a while!" "How are you:" "We're fine here." "We're all working hard." "What:" "Yes, I'll put her on the phone." "Hello:" "Hello:" "Pablo:" "Pablo, son!" "How are you:" "I don't understand!" "I know." "love you too so much!" "Hello:" "Hello!" "Pablo:" " Take me upstairs, please." " l'll take you." " Call the doctor, Ernesto." " Hello:" "Pablo:" "Pablo:" "Pablo:" "It was not a long distance call." "It was from Avellaneda." "What's the difference:" "You don't have to worry about money." "Who's talking about money:" "Nora and I have talked about this." " We decided that we're going to sell some furniture and clothes." "What:" "We both have clothes that we don't wear." "And Millstein always liked the chandelier in the living room." "Well, now he can buy it." "Don't you think we'd be better move to a smaller house:" "To take Mom out of this house:" "With what it means to her:" "To us:" " lt's the family house." " l think that..." "The house is the house." "We are not leaving it." "Period." "Doctor, how is she:" "The situation is complicated." " Be honest, please." " Four months." "Five." "I'm sorry." " This has gone up again." " The new government." "It's temporary until things settle down again." "That's what all governments say." "Dreams keep hope alive." "It's an antique, isn't it:" " Do you like it:" " Yes, very much." "It belonged to my father." "He won it in a brothel, playing cards." "If he won the bet, he'd keep the owner's woman," " a Polish woman with green eyes." " And if he lost:" "He'd have to give up his daughter." "What happened:" "The game was even, everyone in the brothel was there." "In the last hand dad was winning, but the police appeared." "There was a terrible stir." "Some ran away." "The polish girl was deported." "Her husband didn't even stop to protect her." "Dad grabbed the lamp and broke it on a policeman's head." "That's how he escaped." "I'll buy it." " l don't know..." "It's very valuable." " Tell me how much." "Mom, Mr. Millstein wants to say hello." "Excuse me." "Good evening." " How are you, Madam:" " Here I am." " How's the store doing:" " Much better." "It will be a great store, some day." " Like Gatt Chavez." " Something like that." "Why not:" "Your husband always had a good nose for business." "Yes." "Osvaldo was an intelligent man." "He also had a very good taste..." "in general." "What about your wife:" "Fine." "A beautiful woman." "You are a very lucky man." " Yes, that's true." " Well, I'll show you to the door." "Wait." "Celia, look in the wardrobe, on the upper shelf." " lt's late, Mom." " Just a second, Jorge." "The purple box." "Thank you." "Do you like it:" "It's very elegant." "Osvaldo loved it." "I kept it for a special occasion." " lt's unique." " Take it." " What:" " lt's a gift." "It will look better on your wife." " She would thank you, but..." " Try it on." "Precious..." "Take it." "Thank you so much." "No, thank you for all you do for us." "Well, I'd better leave now." "Good night." "I'll show you to the door." " What are you doing:" " Can't I give a gift:" "Don't you remember his wife left him:" "Besides, everybody knew he was cuckolded." "She took the shirt off his back." "Don't you remember:" "Terrible..." "I didn't remember." "How are the lessons:" "I'm not giving lessons anymore." "Too much housework." "Why don't you go out a bit:" "To distract yourself." "No." " Why not:" " Because. I can't." "They need me here." " Thank you." " Thank you." " Goodbye." " Goodbye." "Yes:" "It's Patricia." "Can I come in?" " Are you all right:" " Yes, why:" "I thought that..." "Mom's getting worse." "We had to bring oxygen." "I just wanted to see you." "And see if you are well." " l'm fine, yes." " Ok." "Wait." "No." "No." "Pablo." "What are we going to do when he returns:" "He won't return." "Why not:" "Pablo can't be alive." "Why can't he:" "Because we never got any news from him, Jorge." "Not even a postcard." "We don't know what happened to him." "He vanished." "Because if he were alive and he were doing this to us, he would be a bastard." " Pablo did send a letter." " What:" "Six months ago." "Nobody knew." "It arrived when I was by myself." "I didn't show it to anybody." " What:" " Pablo sent a letter." "He said he's all right, that things didn't turn out as expected, but he was looking for other opportunities." "When he has enough money for the ticket, he will return." " You're lying to me." " No, it's true." "I have the letter, I can show it to you." "I don't want to see it." "It's in the right drawer." "Look!" "Look!" "Don't you think Patricia is acting strange:" " Why strange:" " l don't know, she looks confused." "Perhaps she's overwhelmed with the wedding arrangements." "Yes, we shouldn't put pressure on her." "It's so much work... for all." "You shouldn't have fired the maid." "She was an unnecessary expense." "Maybe..." "But you all look so tired." " You don't look very good, Celia." " l'm better than ever." "Are you sure:" "It's the asthma." "It comes and goes." "My brother was the same." "He came and went." "Until one day he didn't come anymore." "And with Ernesto, how are you:" "Well." " Sure:" " Please... let's not start again." "If I say well, it means well." " See:" "You're out of breath again." " lt's the asthma, I told you." "You need fresh air." "Yes." "Sometimes I envy Pablo." "He must be well with his asthma." "You left it downstairs." "Aunt!" "We have to do some tests." "When:" "Tomorrow." "She'll have to stay at the hospital." " At the hospital:" " Yes, this is not a joke." "Will the tests be expensive:" "Don't worry." "I'll arrange that with your nephew." "What if I leave a note instead:" "You can't leave without saying goodbye." " Celia, Take care." " You too." "Say hello to the foreman, and to his wife." "I'll do it." "Dear Pablo:" "Change of the season has brought us some surprises." "Aunt Celia is not feeling very well, it's nothing too serious, don't worry." "The doctor said that all she needs is to spend some time in the countryside." "Uncle went with her, of course, two weeks ago." "They called from the village yesterday." "The farm seems to be improving." "This year the sheep had double breeding." "Patricia went on a trip with some classmates, too." "That's why she hasn't visited us for a couple of weeks." "Excuse me." "As you can see, you are not the only one who has been moving around." "I finished the letter." "Kisses to you." " Shall I read it:" " No, I'm tired." "Won't you sign it:" "Come on." "No, you sign it." "Hello." "Uncle!" "How's Aunt:" "Uh..." "What are you going to do:" "I understand." "The store:" "Fine as usual." "is it raining there:" "All the roads are blocked..." "No, if you're fine, stay as long as you want." "I'll tell them, don't worry." "Goodbye." "Kisses to Auntie." "We know it is hard, Uncle, but there's no other choice." "If Mom sees you she will ask about Auntie." "Yes, of course." "Besides, the people on the farm need a guide." "It'll be good for you to have other things to think about." "Yes, you're right." "This house holds too many memories." "I must insist, are you sure you won't take my offer:" "I believe my brother was clear." "The piano is not for sale." "Such a pity." " Here you are." " Thank you." "As soon as I have the money, I'll bring it." "Yes." "With this weather I'd prefer not to leave the house." "Thank you." " l'm leaving." " Aren't you staying for dinner:" "No." "All right." "See you." "Nora, I'm not coming back." "What:" "I've been thinking." "I can't go on. I'm sorry." " But Mom..." " Nora, she knows." " What:" " She realizes." "You're shameless." "I understand. I apologize." "I know that..." "You're making it up to justify yourself." "Did you forget about Pablo:" "Or did you find another man:" "I'm leaving." "Dear Mom, I hope that Aunt Celia gets better from her asthma." "The country will surely do her good, it did me good." "Living in the city is not healthy." "Last week here, a tiger escaped from the zoo." "Can you imagine?" "On the radio they asked people to stay in their houses." "People closed the doors and windows, fearing the tiger might enter." "Meanwhile, the tiger walked freely through the city, starving, scratching billboards and roaring." "In the end they caught it in a butcher shop." "They added poison to the meat." "The poor tiger crawled to the Seine and threw himself in." "From my window, I saw his body pass, floating on the river, swollen like a feather cushion, orange and black." "I received a letter from Patricia, telling me about her trip to the lakes in the South." "At least, there are no tigers there." "She says that the landscape was beautiful, but that the best thing about traveling is to return home." "I know we will meet soon, and I will give you a big hug." "I promise." "Pablo." "He writes better and better, doesn't he:" "Aren't you going to reply:" "No." "You write to him." "Tell him the news." " l'll leave it here." " Thank you, son." "Nora, what do you do with the stamps:" "What:" "What do you and Jorge do with the stamps:" "Jorge removes them with steam." "I stick them on a sheet and we cover them with tracing paper." "In the green album." "Don't you remember:" "Incredible..." "So much effort you put into this." "It's nothing, Mom, what are you saying:" "You're so good to me." "Uncle Ernesto called today." "He says that the fields won't be ready until next year." "With some luck." "Too bad." "Yes." "Lito came to the shop." "How is he:" "He's getting married." "Really:" "To whom:" "To the fisherman's daughter." "She's pregnant." "He doesn't want to be involved." "Her father is forcing him." "What a disaster, that boy..." "Did you hear that noise:" "No." "Jorge!" "ARGENTlN EAN TANGO musicians SUCCEED in paris" "Jorge!" "What is she doing here:" "Mom!" "Grab her legs, Nora." "Grab her legs!" "Sometimes the house seems too big." "Without the maid, and Aunt and Uncle on the farm, it seems to have too many rooms." "There are some places I don't enter anymore." "It will remain like this until we get used to it... or until you return." "You can 't imagine how much we wish to see you." "Patricia wants to organize a welcome party for you." "She asked me not to tell you, but I can't keep secrets from you." "If we can't trust our family, who can we trust?" "Nice earrings." "Do you like them:" "They are from Paris." "It seems this winter is colder than usual." "It hasn't stop snowing since New Year's Eve." "No." "Pablo told me there's so much snow that people can't get out of their houses." "He's lucky to live on the third floor." "Anyway, he always finds a way out of everything." "To go to work he skates on the Seine." " You must be lying..." " No, it's true!" |
Opinion issued April 15, 2010.
In The
Court of
Appeals
For The
First District
of Texas
————————————
NO. 01-09-00822-CV
———————————
Texas Department of Public Safety, Appellant
V.
Kristina Ann
Potter, Appellee
On Appeal from the County Court at Law
Austin County, Texas
Trial Court Case No. 09CV4474
MEMORANDUM OPINION
After
Kristina Potter refused to perform field sobriety tests or provide a blood or
breath specimen following her involvement in a car accident, the Texas
Department of Public Safety (Department) suspended her driving-license privileges
for 180 days. See Tex. Transp. Code Ann.
§§ 724.035, 742.042 (Vernon Supp. 2009).
An administrative law judge (ALJ) upheld the suspension, and Potter
appealed the decision to county court.
The county court granted Potter’s appeal and reversed the
suspension. The Department now appeals
that ruling, contending that the county court failed to apply the proper
standard in reviewing the administrative decision. We reverse the county court’s judgment and reinstate the suspension.
Background
The accident
In the early morning hours of
November 29, 2008, Texas State Trooper Vacek was dispatched to a one-vehicle
rollover accident on State Highway 159 in Bellville. When he arrived, Vacek first spoke with Michael
Blezinger, who told him that he had reported the accident. Potter stood near a drainage ditch beside the
road and an overturned gray Jeep Liberty.
Blezinger pointed at Potter and told Vacek that she was the driver of
the Jeep, and that he thought she had been drinking.
Vacek walked over to Potter, noting
various items, apparently thrown from the car during the rollover, strewn all
over the ground. In particular, he noticed
an open can of beer that appeared to have condensation on it. When he approached, Potter identified herself
as the driver of the vehicle. Once Vacek
established that Potter did not need medical attention, he asked her to explain
what happened. Potter said that she lost
control while she was trying to send a text message.
During her interaction with Vacek,
Potter was crying uncontrollably and had several emotional outbursts. Vacek also noticed that Potter’s eyes were
bloodshot and glassy and that her breath smelled strongly of alcohol. Vacek asked Potter if she had been drinking. Potter admitted to having two beers, but said
that she did not remember how long it had been since she drank them.
When Vacek asked Potter if she was
willing to perform field sobriety tests, Potter replied that she was told to
wait for her attorney to arrive. Based
on his observations, Vacek concluded that Potter had lost the normal use of her
mental and physical faculties due to alcohol ingestion, placed Potter under
arrest, handcuffed her, and placed her in the patrol car of a local deputy at
the scene.
When Potter’s attorney arrived,
Potter consulted with him. Then, the
deputy took Potter to the Austin County jail while Vacek continued his
investigation of the accident scene. When
he was finished, Vacek met Potter at the jail.
He requested that she give a breath specimen to analyze the
concentration of alcohol in her system and began to read her the statutory
warning informing her that her license would be suspended for 180 days if she refused
to do so.
After Vacek finished the first
paragraph, Potter told him that she was going to refuse to give a specimen. Vacek finished reading the statutory warning
and gave Potter a copy of the form. Potter
next complained of wrist pain and was taken to a nearby hospital. Once there, she refused to submit to a blood
exam, but consented to an x-ray.
Proceedings below
At Potter’s request, a hearing on
the suspension took place before an ALJ.
The ALJ decided that the Department was authorized to suspend Potter’s
license for the prescribed period, based on findings that (1) Potter was
operating the Jeep at the time of the accident, (2) probable cause existed to
believe that Potter was operating a motor vehicle in a public place while
intoxicated, based on Vacek’s observations of her condition and her own admission
that she had consumed alcoholic beverages before operating the Jeep, and (3)
Potter refused to perform any field sobriety tests or provide any breath or
blood specimen.
Potter appealed the suspension to
the county court at law. After reviewing
the hearing transcript and evidence presented to the ALJ, as well as arguments
of counsel, the county court signed an order granting Potter’s appeal. The Department timely filed its appeal of
this order.
Discussion
Standard of review
“[C]ourts review administrative license suspension decisions
under the substantial evidence standard.” Mireles
v. Tex. Dep’t of Pub. Safety, 9 S.W.3d 128, 131 (Tex. 1999); see Tex.
Transp. Code Ann. § 724.047 (Vernon 1999) (“Chapter 524 governs an
appeal from an action of the department, following an administrative hearing
under this chapter, in suspending or denying the issuance of a license.”); id. § 524.043 (Vernon 2007)
(establishing rules for appeal but not defining the scope of review). In contested cases, if more than a scintilla
of evidence supports the administrative findings, we affirm those findings;
“[i]n fact, an administrative decision may be sustained even if the evidence
preponderates against it.” Mireles, 9 S.W.3d at 131. Courts may not substitute their judgment for
the judgment of the state agency on the weight of the evidence on
questions committed to agency discretion but . . . (2) shall reverse
or remand the case for further proceedings if substantial rights of the
appellant have been prejudiced because the administrative findings, inferences,
conclusions, or decisions are: . . . (E) not reasonably supported by
substantial evidence considering the reliable and probative evidence in the
record as a whole. . . .
Tex. Gov’t Code Ann. § 2001.174 (Vernon 2008). We review the county court’s substantial
evidence review of the administrative ruling de novo. See
Tex. Dep’t of Pub. Safety v. Alford, 209 S.W.3d 101, 103 (Tex. 2006)
(noting that ALJ’s findings are entitled to deference but that “whether there
is substantial evidence to support an administrative decision is a question of
law” and as such, neither county court nor ALJ’s determination of issue is
entitled to deference on appeal).
License suspension
Under the Transportation Code, if a peace officer arrests a person
and he has reasonable grounds to believe that the person is driving while
intoxicated, he may request specimens of the person’s breath or blood. Tex.
Transp. Code Ann. § 724.012(a)(1) (Vernon Supp. 2009). If the person refuses to submit to the taking
of a specimen, the Department must suspend the person’s license to operate a
motor vehicle on a public highway for 180 days.
Id. § 724.035(a)(1)
(Vernon Supp. 2009). If a person’s
license is suspended under this chapter, she may request a hearing on the
suspension. Id. § 724.041 (Vernon Supp. 2009). At the hearing, the issues, as applicable
here, are whether:
(1) reasonable
suspicion or probable cause existed to stop or arrest the person;
(2) probable cause existed to
believe that the person was:
(A) operating a motor vehicle in a public place while
intoxicated;
. . . .
(3) the
person was placed under arrest by the officer and was requested to submit to
the taking of a specimen; and
(4) the
person refused to submit to the taking of a specimen on request of the officer.
Id. § 724.042 (Vernon Supp. 2009). Applying the applicable standard of review,
then, the reviewing court must uphold the administrative decision if the record
contains substantial evidence to support an affirmative finding on each of
these issues.
Reasonable suspicion for stop or probable cause for arrest
Officer Vacek’s offense report recites that Blezinger
identified Potter as the driver and stated that he thought that she had been
drinking. When Officer Vacek approached
Potter, he observed that Potter had glassy eyes, was crying, and was otherwise behaving
very emotionally, which are consistent with intoxication. Contrary to Potter’s assertion, a witness
does not have to be an expert to testify that a person he observes is
intoxicated by alcohol; a police officer’s lay opinion testimony that a person
is intoxicated is probative. Henderson v. State, 29 S.W.3d 616, 622
(Tex. App.—Houston [1st Dist.] 2002, pet. ref’d). Blezinger and Vacek’s observations provide
more than a scintilla of evidence in support of the ALJ’s finding that Vacek
had reasonable suspicion for the stop.
Probable cause to believe that the licensee was driving a motor vehicle
in a public place while intoxicated
A license suspension is a civil matter, requiring only
probable cause to believe the driver was driving while intoxicated. See Tex.
Transp. Code Ann. § 724.048(a) (Vernon 1999); Mireles, 9 S.W.3d at 131; Tex.
Dep’t of Pub. Safety v. Butler, 110 S.W.3d 673, 675 (Tex. App.—Houston
[14th Dist.] 2003, no pet). Probable
cause to arrest exists when the facts and circumstances that are apparent to
the arresting officer support a reasonable belief that an offense has been or
is being committed. Amores v. State, 816 S.W.2d 407, 413 (Tex. Crim. App. 1991). Probable cause requires more than a suspicion
but far less evidence than that needed to support a conviction or to support a
finding by a preponderance of the evidence. See
Guzman v. State, 955 S.W.2d 85, 87 (Tex. Crim. App. 1997).
Potter’s statement to Vacek that she lost control of the
vehicle while texting constitutes an admission that she was driving the vehicle
when it crashed. As for the
administrative finding that Potter was intoxicated, evidence of her
uncontrollable crying, emotional outbursts, and glassy, red eyes—coupled with evidence that her breath
smelled strongly of alcohol and of a beer can with condensation on it found at
the scene—constitutes
substantial evidence in its support. See Tex. Dep’t of Pub. Safety v.
Perkins, No.
01-04-00093-CV, 2004 WL 2749141, at *6 (Tex. App.—Houston [1st Dist.] 2004, no
pet.) (finding probable cause based on officer’s report that Perkins’s eyes
were red and glassy, and his breath had very strong odor of alcohol); Tex. Dep’t of Pub. Safety v. Pruitt, 75
S.W.3d 634, 640–41 (Tex. App.—San Antonio 2002, no pet.) (finding probable
cause for arrest and to believe Pruitt was operating a motor vehicle on a
public roadway while intoxicated where Pruitt admitted to officer that he was
driving vehicle involved in accident, officer smelled mild odor of alcohol on
Pruitt’s breath, Pruitt’s speech was slurred, and Pruitt admitted to officer
that he had been drinking); see also Tex.
Dep’t of Pub. Safety v. Varme, 262 S.W.3d 34, 41 (Tex. App.—Houston [1st
Dist.] 2008, no pet.) (holding that officer had probable cause to arrest Varme;
officer observed Varme speeding and observed that Varme had strong odor of
alcohol and slurred speech; Varme admitted he had been drinking, his balance
was “poor,” and his eyes were “bloodshot”).
Potter contends that the fact that she was crying and emotional, and had
glassy, red eyes is no evidence that she was driving while intoxicated because
it equally supports a reasonable inference that she had a natural reaction to
the accident as it does the ALJ’s finding that there was probable cause that
she was driving while intoxicated.
Potter, however, does not account for the officer’s additional
observation that Potter’s breath smelled strongly of alcohol, which renders her
benign explanation less plausible. The
equal inference rule thus does not apply here.
See Lozano v. Lozano, 52
S.W.3d 141, 148 (Tex. 2001) (observing that equal inference rule precludes fact
finder from reasonably inferring ultimate fact from meager circumstantial
evidence which could give rise to any number of inferences, none more probable
than another).
In her appeal of the ALJ’s decision to the county court,
Potter also contended that the Department failed to prove a temporal link
between her driving and intoxication. To
the extent the county court relied on that contention as grounds for granting
Potter’s appeal, it erred. When Officer
Vacek appeared at the scene within minutes of the accident report, he noticed
condensation on the open can of beer near the vehicle, signs of intoxication, and
a strong smell of alcohol on Potter, and Potter herself admitted to Officer Vacek
that she had drunk beer earlier that night.
These facts and circumstances are sufficient to warrant the belief of a
person of reasonable caution that Potter had consumed alcohol close enough in
time to the accident to have been impaired by it at the time. We thus hold that substantial evidence
supports the ALJ’s finding that probable cause existed to arrest Potter and to
believe that Potter was operating a motor vehicle on a public roadway while
intoxicated.
The licensee refused to perform field sobriety tests or provide a blood
or breath specimen for testing
Potter does not dispute that she refused to perform a field
sobriety test or provide a blood or breath specimen, but she specifically
points to the absence of testing results as supporting her contention that
substantial evidence does not support the ALJ’s decision. But the fact that Potter refused the testing supports,
rather than undermines, an inference that Potter was intoxicated at the time of
her arrest. Refusal to submit to testing
is a factor that weighs in favor of finding probable cause of DWI. See
Partee v. Tex. Dep’t of Pub. Safety,
249 S.W.3d 495, 501–02 (Tex. App.—Amarillo 2007, no pet.); Tex. Dep’t of Pub. Safety v. Nielsen,
102 S.W.3d 313, 317 (Tex. App.—Beaumont 2003, no pet).
Conclusion
Substantial evidence supports the ALJ’s decision to suspend
Potter’s driver’s license for 180 days under sections 724.042 and 724.035 of
the Texas Transportation Code. We
therefore reverse the judgment of the county court and render judgment
reinstating the suspension of Potter’s driving-license privileges. See
Tex. Transp. Code Ann. § 2001.174(1).
Jane
Bland
Justice
Panel
consists of Justices Jennings, Hanks, and Bland.
|
676 F.Supp. 140 (1987)
KLEIER ADVERTISING, INC., Plaintiff,
v.
NAEGELE OUTDOOR ADVERTISING, INC., Defendant.
Civ. A. No. C 85-1067-L(A).
United States District Court, W.D. Kentucky, Louisville Division.
December 18, 1987.
*141 Jack A. Wheat, Robert, Miller & Thomas, Louiseville, Ky., for plaintiff.
M. Stephen Pitt, William Hollander, Wyatt, Tarrant & Combs, Louisiana, Ky., for defendant.
MEMORANDUM AND ORDER
ALLEN, Senior District Judge.
This copyright infringement action is scheduled for jury trial on January 11, 1988. The matter is now before the Court on defendant's motion for summary judgment, and on plaintiff's motion for sanctions.
Defendant Naegele contends that the damages, if any, recoverable by plaintiff Kleier must exclude actual and statutory damages. The basis for Naegele's argument is that it was an "innocent infringer" within the meaning of 17 U.S.C. Sec. 405(b). That statutory subsection provides, in part, as follows:
Any person who innocently infringes a copyright, in reliance upon an authorized copy ... from which the copyright notice has been omitted, incurs no liability for actual or statutory damages ... for any infringing acts committed before receiving actual notice that registration for the work has been made ... if such person proves that he or she was misled by the omission of notice.
Materials of record reflect Kleier's representation that it routinely placed copyright notification on its designs, but Kleier has not offered any testimony that the drawing provided to Naegele did bear copyright notice. Naegele contends that this circumstance means that Kleier has failed to create a dispute of fact regarding omission of notice. Kleier, on the other hand, points out that Naegele's witnesses have not testified that the drawing bore no copyright notice, but only that they do not recall seeing a notice.
While it represents a very close question, we are inclined to believe that the present state of the record does reflect a dispute of fact concerning omission of copyright notice. Nonetheless, for purposes of this motion, we will assume that the drawing provided by Kleier to Naegele did not bear a copyright notice. In all other respects, we take all facts and inferences in favor of Kleier, the non-movant.
Viewed from this standpoint, the following chronology appears. In March or April of 1983, Kleier provided Naegele with rough drawings of the design in question, and we assume those drawings did not bear a copyright notice. In August 1984, having learned of Naegele's unauthorized use of the design, Kleier notified Naegele that the design belonged to Kleier, and that its use constituted copyright infringement. Kleier obtained a copyright registration certificate bearing the date September 9, 1985. Naegele was not aware of the registration until November 19, 1985, when it was served with the present lawsuit. On approximately December 3, 1985, Naegele removed the last infringing work.
Naegele's argument is that it has presented evidence that it was misled by the omission of the copyright notice, and that it did not have "notice that registration for the work [had] been made" until November 19, 1985. No infringing work was erected after that date, and a short time later the last of the previously erected infringing work was removed. Accordingly, argues Naegele, it is an "innocent infringer" entitled to the protection of 17 U.S.C. Sec. 405(b). Distilled to its essence, Naegele's view of the law is that once a defendant has presented some evidence of having been initially misled by omission of copyright notice, that defendant is necessarily an innocent infringer until receipt of actual notice of formal registration.
*142 Kleier's view of the statutory provision is somewhat different. Kleier contends that Naegele could not claim the status of an "innocent" infringer after being notified of Kleier's copyright claim, despite the fact that such notification occurred a year prior to formal registration. In support of this argument, Kleier has cited the Court to cases that have construed 17 U.S.C. Sec. 405(b) in conjunction with Sec. 405(a). Sec. 405(a) sets forth the circumstances in which omission of copyright notice "does not invalidate the copyright in a work." There appears to be no dispute that the design in question here falls within those circumstances. Kleier appears to argue that if its copyright could statutorily survive omission of copyright notice, then notice of that copyright, regardless of registration, must destroy Naegele's status as an "innocent infringer."
In M. Kramer Mfg. Co., Inc. v. Andrews, 783 F.2d 421 (4th Cir.1986), the court recognized that "innocence" of the defendants was a question of fact. Nonetheless, the court reversed the trial court's determination that defendants were innocent infringers, holding that such a conclusion was clearly erroneous in the presence of evidence that defendants knew plaintiff was claiming a copyright in the game. The appellate court noted, inter alia, that defendants had received a letter from plaintiff stating plaintiff's copyright claim. The court observed, at page 447:
[W]e find it impossible to conclude that the defendants relied on the lack of notice to conclude that the work was in the public domain.... While it may be that the defendants believed that Kramer did not own a valid copyright ... the evidence is clear that they were not misled by the lack of proper copyright notice when they knew that various parties were claiming copyrights in the game.
In Canfield v. Ponchatoula Times, 759 F.2d 493 (5th Cir.1985), the court was primarily concerned with interpretation of the requirements of 17 U.S.C. Sec. 405(a). In the course of its analysis, the court noted the importance of reading sections (a) and (b) together in order to effectuate Congressional intent to encourage notice. The court observed, at pages 498-499, "A publisher who reprints an unnoticed work which falls within one of the 405(a) exceptions has the burden, under section 405(b), of proving good faith."
In Wales Indus. Inc. v. Hasbro Bradley, Inc., 612 F.Supp. 510 (S.D.N.Y.1985), the court suggested that the question of whether an infringer is "innocent" is coterminous with the question of whether he acted with a good faith belief that the work was in the public domain. The court concluded that the infringer's "innocence" was a question of fact to be resolved at trial, since the infringer had received notification of the copyright claim. It is significant that the copyright was not recorded until after the litigation had begun; thus, the notification of the claim necessarily predated recording.
Similarly, in Williams v. Arndt, 626 F.Supp. 571 (D.Mass.1985), registration of copyright was obtained only ten days prior to the filing of the litigation. This was not a factor in the court's consideration of the "innocence" issue. The court noted that the infringer had received a letter from the copyright claimant's attorney advising him "to stop selling the program because it was [plaintiff's] property," and held that the defendant had failed to satisfy his burden of proof that he "acted in good faith or reasonably relied upon the absence of a copyright notice." The court showed no concern with the date of registration, but relied on the rationale behind the subsection, which is that one acting "in good faith and with no reason to think otherwise" should be able to assume that a work bearing no copyright notice is in the public domain. 1976 U.S.Code Cong. & Admin. News 5659, 5764.
17 U.S.C. Sec. 408 clearly provides that registration is not required in order for a copyright to have validity. It seems clear that the overall thrust of the legislative scheme is to encourage copyright notice, not to punish copyright holders who fail to register their ownership. We cannot agree with Kleier that such a purpose would be furthered by withholding "innocent *143 infringer" status from anyone who fails to investigate or inquire before copying a work that appears to be in the public domain. On the other hand, we cannot agree with Naegele that such a purpose would be furthered by allowing "innocent infringer" status to be terminated only by formal registration.
As we read 17 U.S.C. Sec. 405(b), there are five elements to an "innocent infringer" defense. The party desiring this protection must show (1) innocent infringement (2) in reliance on (3) an authorized copy (4) which omitted the copyright notice, and (5) that the party was misled by the omission. We believe that Naegele's statutory analysis errs in rendering the first requirement a nullity, melding it seamlessly with elements (2) and (5).
On the present state of the record, we believe there is a genuine issue of fact as to whether Naegele's infringement was innocent, which we equate with having a good faith belief that the work was in the public domain. This dispute arises from such factors as the original source of the design, notification of Kleier's copyright claim, and the conflicting evidence regarding custom in the industry. The motion for partial summary judgment must be overruled.
Turning now to plaintiff's motion for sanctions, we note that Naegele contends vigorously that sanctions are inappropriate. The Court has already compared the information requested during the discovery process with both the information provided then and the information proposed for introduction at trial. In continuing the trial, we expressed our belief that Naegele had not properly complied with its duties as a litigant during discovery. We continue to believe that determination was correct.
The most extreme sanction would presumably have been that originally proposed, i.e., proceeding with trial and prohibiting the introduction of the new evidence. Instead, we agreed to continue the trial to allow defendant to use the evidence without unfair prejudice to plaintiff. As we explained at the time of the continuance, it is entirely appropriate that Naegele, having necessitated the continuance, should pay any additional expenses resulting from that continuance.
We will sustain the request for sanctions and will make an award after the conclusion of the trial. At that time we will expect Kleier to be in a position to present its itemization of additional fees and expenses attributable to the continuance of the trial.
Accordingly,
IT IS ORDERED that defendant's motion for partial summary judgment is overruled.
IT IS FURTHER ORDERED that plaintiff's motion for sanctions is sustained.
IT IS FURTHER ORDERED that within ten days of the conclusion of the trial, plaintiff shall tender to the Court its request for fees and expenses attributable to the continuance of the trial.
|
22 Session Management for Clustered Applications
Clustered applications require reliable and performant HTTP session management. Unfortunately, moving to a clustered environment introduces several challenges for session management. This article discusses those challenges and proposes solutions and recommended practices. The included session management features of Oracle Coherence*Web are examined here.
22.1 Basic Terminology
An HTTP session ("session") spans a sequence of user interactions within a Web application. "Session state" is a collection of user-specific information. This session state is maintained for a period, typically beginning with the user's first interaction and ending a short while after the user's last interaction, perhaps thirty minutes later. Session state consists of an arbitrary collection of "session attributes," each of which is a Java object and is identified by name. "Sticky load balancing" describes the act of distributing user requests across a set of servers in such a way that requests from a given user are consistently sent to the same server.
Coherence is a data management product that provides real-time, fully coherent data sharing for clustered applications. Coherence*Web is a session management module that is included as part of Coherence. An HTTP session model ("session model") describes how Coherence*Web physically represents session state. Coherence*Web includes three session models. The Monolithic model stores all session state as a single entity, serializing and deserializing all attributes as a single operation. The Traditional model stores all session state as a single entity but serializes and deserializes attributes individually. The Split model extends the Traditional model but separates the larger session attributes into independent physical entities. The applications of these models are described in later sections of this article.
"Select the Appropriate Session Model" in the Coherence FAQ provides more information on the Monolithic, Traditional, and Split Session models. It also describes how to configure Coherence to use a particular model.
22.2 Sharing Data in a Clustered Environment
Session attributes must be serializable if they are to be processed across multiple JVMs, which is a requirement for clustering. It is possible to make some fields of a session attribute non-clustered by declaring those fields as transient. While this eliminates the requirement for all fields of the session attributes to be serializable, it also means that these attributes will not be fully replicated to the backup server(s). Developers who follow this approach should be very careful to ensure that their applications are capable of operating in a consistent manner even if these attribute fields are lost. In most cases, this approach ends up being more difficult than simply converting all session attributes to serializable objects. However, it can be a useful pattern when very large amounts of user-specific data are cached in a session.
The J2EE Servlet specification (versions 2.2, 2.3, and 2.4) states that the servlet context should not be shared across the cluster. Non-clustered applications that rely on the servlet context as a singleton data structure will have porting issues when moving to a clustered environment. Coherence*Web does support the option of a clustered context, though generally it should be the goal of all development teams to ensure that their applications follow the J2EE specifications.
A more subtle issue that arises in clustered environments is the issue of object sharing. In a non-clustered application, if two session attributes reference a common object, changes to the shared object will be visible as part of both session attributes. However, this is not the case in most clustered applications. To avoid unnecessary use of compute resources, most session management implementations serialize and deserialize session attributes individually on demand. Coherence*Web (Traditional and Split session models) normally operates in this manner. If two session attributes that reference a common object are separately deserialized, the shared common object will be instantiated twice. For applications that depend on shared object behavior and cannot be readily corrected, Coherence*Web provides the option of a Monolithic session model, which serializes and deserializes the entire session object as a single operation. This provides compatibility for applications that were not originally designed with clustering in mind.
Many projects require sharing session data between different Web applications. The challenge that arises is that each Web application typically has its own class loader. Consequently, objects cannot readily be shared between separate Web applications. There are two general methods for working around this, each with its own set of trade-offs.
Place common classes in the Java CLASSPATH, allowing multiple applications to share instances of those classes at the expense of a slightly more complicated configuration.
Use Coherence*Web to share session data across class loader boundaries. Each Web application is treated as a separate cluster member, even if they run within the same JVM. This approach provides looser coupling between Web applications (assuming serialized classes share a common serial Version UID), but suffers from a performance impact because objects must be serialized-deserialized for transfer between cluster members.
22.3 Reliability and Availability
An application must guarantee that a user's session state is properly maintained to exhibit correct behavior for that user. Some availability considerations occur at the application design level and apply to both clustered and non-clustered applications. For example, the application should ensure that user actions are idempotent: the application should be capable of handling a user who accidentally submits an HTML form twice.
With sticky load balancing, issues related to concurrent session updates are normally avoided, as all updates to session state are made from a single server (which dramatically simplifies concurrency management). This has the benefit of ensuring no overlap of user requests occurs even in cases where a user submits a new request before the previous request has been fully processed. Use of HTML frames complicates this, but the same general pattern applies: Simply ensure that only one display element is modifying session state.
In cases where there may be concurrent requests, Coherence*Web manages concurrent changes to session state (even across multiple servers) by locking sessions for exclusive access by a single server. With Coherence*Web, developers can specify whether session access is restricted to one server at a time (the default), or even one thread at a time.
As a general rule, all session attributes should be treated as immutable objects if possible. This ensures that developers are consciously aware when they change attributes. With mutable objects, modifying attributes often requires two steps: modifying the state of the attribute object, and then manually updating the session with the modified attribute object by calling javax.servlet.http.HttpSession.setAttribute(). This means that your application should always call setAttribute() if the attribute value has been changed, otherwise, the modified attribute value will not replicate to the backup server. Coherence*Web tracks all mutable attributes retrieved from the session, and so will automatically update these attributes, even if setAttribute() has not been called. This can help applications that were not designed for clustering to work in a clustered environment.
Session state is normally maintained on two servers, one primary and one backup. A sticky load balancer will send each user request to the specified primary server, and any local changes to session state will be copied to the backup server. If the primary server fails, the next request will be rerouted to the backup server, and the user's session state will be unaffected. While this is a very efficient approach (among other things, it ensures that the cluster is not overwhelmed with replication activity after a server failure), there are a few drawbacks. Because session state is copied when the session is updated, failure (or cycling) of both the primary and backup servers between session updates will result in a loss of session state. To avoid this problem, wait thirty minutes between each server restart when cycling a cluster of server instances. The thirty-minute interval increases the odds of a return visit from a user, which can trigger session replication. Additionally, if the interval is at least as long as the session timeout, the session state will be discarded anyway if the user has not returned.
This cycling interval is not required with Coherence*Web, which will automatically redistribute session data when a server fails or is cycled. Coherence's "location transparency" ensures that node failure does not affect data visibility. However, node failure does impact redundancy, and therefore fresh backup copies must be created. With most Coherence*Web configurations, two machines (primary and backup) are responsible for managing each piece of session data, regardless of cluster size. With this configuration, Coherence can handle one failover transition at any time. When a server fails, no data will be lost if the next server failure occurs after the completion of the current failover process. The worst-case scenario is a small cluster with large amounts of session data on each server, which may require a minute or two to rebalance. Increasing the cluster size, or reducing the amount of data storage per server, will improve failover performance. In a large cluster of commodity servers, the failover process may require less than a second to complete. For particularly critical applications, increasing the number of backup machines will increase the number of simultaneous failures that Coherence can manage.
The need for serialization in clustered applications introduces a new opportunity for failure. Serialization failure of a single session attribute will ordinarily prevent the remaining session attributes from being copied to the backup server and can result in the loss of the entire session. Coherence*Web works around this by replicating only serializable objects, while maintaining non-serializable objects in the local server instance.
One last issue to be aware of is that under heavy load, a server can lose session attribute modifications due to network congestion. The log will contain information about lost attributes, which brings up the most critical aspect of high-availability planning: Be sure to test all of your application components under full load to ensure that failover and failback operate as expected. While many applications will see no difficulties even at 99-percent load, the real test of application availability occurs when the system is fully saturated.
22.4 Scalability and Performance
Moving to a clustered environment makes session size a critical consideration. Memory usage is a factor regardless of whether an application is clustered or not, but clustered applications also need to consider the increased CPU and network load that larger sessions introduce. While non-clustered applications using in-memory sessions do not need to serialize-deserialize session state, clustered applications must do this every time session state is updated. Serializing session state and then transmitting it over the network becomes a critical factor in application performance. For this reason and others, a server should generally limit session size to no more than a few kilobytes.
While the Traditional and Monolithic session models for Coherence*Web have the same limiting factor, the Split session model was explicitly designed to efficiently support large HTTP sessions. Using a single clustered cache entry to contain all of the small session attributes means that network traffic is minimized when accessing and updating the session or any of its smaller attributes. Independently deserializing each attribute means that CPU usage is minimized. By splitting out larger session attributes into separate clustered cache entries, Coherence*Web ensures that the application only pays the cost for those attributes when they are actually accessed or updated. Additionally, because Coherence*Web leverages the data management features of Coherence, all of the underlying features are available for managing session attributes, such as near caching, NIO buffer caching, and disk-based overflow.
Figure 22-3 illustrates performance as a function of session size. Each session consists of ten 10-character Strings and from zero to four 10,000-character Strings. Each HTTP request reads a single small attribute and a single large attribute (for cases where there are any in the session), and 50 percent of requests update those attributes. Tests were performed on a two-server cluster. Note the similar performance between the Traditional and Monolithic models; serializing-deserializing Strings consumes minimal CPU resources, so there is little performance gain from deserializing only the attributes that are actually used. The performance gain of the Split model increases to over 37:1 by the time session size reaches one megabyte (100 large Strings). In a clustered environment, it is particularly true that application requests that access only essential data have the opportunity to scale and perform better; this is part of the reason that sessions should be kept to a reasonable size.
Another optimization is the use of transient data members in session attribute classes. Because Java serialization routines ignore transient fields, they provide a very convenient means of controlling whether session attributes are clustered or isolated to a single cluster member. These are useful in situations where data can be "lazy loaded" from other data sources (and therefore recalculated in the event of a server failover process), and also in scenarios where absolute reliability is not critical. If an application can withstand the loss of a portion of its session state with zero (or acceptably minimal) impact on the user, then the performance benefit may be worth considering. In a similar vein, it is not uncommon for high-scale applications to treat session loss as a session timeout, requiring the user to log back in to the application (which has the implicit benefit of properly setting user expectations regarding the state of their application session).
Sticky load balancing plays a critical role because session state is not globally visible across the cluster. For high-scale clusters, user requests normally enter the application tier through a set of stateless load balancers, which redistribute (more or less randomly) these requests across a set of sticky load balancers, such as Microsoft IIS or Apache HTTP Server. These sticky load balancers are responsible for the more computationally intense act of parsing the HTTP headers to determine which server instance will be processing the request (based on the server ID specified by the session cookie). If requests are misrouted for any reason, session integrity will be lost. For example, some load balancers may not parse HTTP headers for requests with large amounts of POST data (for example, more than 64KB), so these requests will not be routed to the appropriate server instance. Other causes of routing failure include corrupted or malformed server IDs in the session cookie. Most of these issues can be handled with proper selection of a load balancer and designing tolerance into the application whenever possible (for example, ensuring that all large POST requests avoid accessing or modifying session state).
Sticky load balancing aids the performance of Coherence*Web but is not required. Because Coherence*Web is built on the Coherence data management platform, all session data is globally visible across the cluster. A typical Coherence*Web deployment places session data in a near cache topology, which uses a partitioned cache to manage huge amounts of data in a scalable and fault-tolerant manner, combined with local caches in each application server JVM to provide instant access to commonly used session state. While a sticky load balancer is not required when Coherence*Web is used, there are two key benefits to using one. Due to the use of near cache technology, read access to session attributes will be instant if user requests are consistently routed to the same server, as using the local cache avoids the cost of deserialization and network transfer of session attributes. Additionally, sticky load balancing allows Coherence to manage concurrency locally, transferring session locks only when a user request is rebalanced to another server.
22.5 Conclusion
Clustering can boost scalability and availability for applications. Clustering solutions such as Coherence*Web solve many problems for developers, but successful developers must be aware of the limitations of the underlying technology, and how to manage those limitations. Understanding what the platform provides, and what users require, gives developers the ability to eliminate the gap between the two. |
UFO ROUNDUP
Volume 5
Number 41
October 12, 2000
Editor: Joseph Trainor
UFO Roundup and the UFOINFO site are operated on a "Not For Profit" basis. You can help to keep UFO Roundup operating by making a donation.
CHEMTRAILS CAUSE WEIRD PHENOMENON IN MICHIGAN
A strange incident involving chemtrails and two
white helicopters occurred in Brighton, Michigan on
Sunday, October 8, 2000, around 8 a.m.
Commercial artist Michael reported, "My mother,
who lives on a lakefront property, looked out the large picture
window overlooking the lake. She noticed in the sky planes
making contrails into a huge checkerboard shape. She
had a disposable camera which she received free in the
mail and was able to take of the most incredible event she
had ever seen."
"It was a partly cloudy day, and the sky was very blue,
and within 15 minutes she said the sky had turned
pitch black. There in the photo you can see the reddish-
brown thick fog move across the lake in the same
window. She took (several) photos from the large
window and it was so black that the lake was not visible."
"Around 10 a.m., the smoke/fog cleared, and she saw two copters
painted white with no markings hovering over the lake and
unfortunately she does not have a photo of this. They left
soon, and (looking up) she noticed the huge Xs formed
from contrails."
(Editor's Note: United Nations helicopters are usually
painted white.)
After she phoned her son Michael, "I went over there
to visit and look at the photos and to help calm her down.
I'm an artist by trade, and I have a gift for seeing very
clear and have a keen eye for detail."
While examining his mother's photos, Michael
noticed that the camera had picked up a very strange
object in the sky above the lake.
"While looking at the photos, I noticed a small
white/blue light about 20 feet (6 meters) above tree level.
I looked close to see if it was some glitch or flash from the
camera, but it was not...I was totally in awe so I went to
take the photo and have it enlarged. What we got back
shocked me so much--that's why I'm writing now."
The blue/white UFO "was like one of those plasma
balls where you touch the glass globe and the lightning
inside responds. It's a very clear and sharp image of
blue lightning contoured into an egg shape. I can see the
streaks binding and forming the egg shape. I thought
maybe ball lightning, but what's strange about the image
is (that) I discovered that the egg shape is not formed by
the lightning but appears to be formed by the
surrounding atmosphere."
"This may sound strange but when you look close, the sky
is a darker shade outside the egg shape and within the egg
shape the sky is much lighter, and images such as the
trees also seem to bend as if putting a magnifying glass
on the photo."
"I examined it for three hours, trying to come up with
an answer. I have none!"
Brighton is on Interstate Highway I-96 about 30 miles
(48 kilometers) east of Detroit. (Email Form Report)
(Editor's Comment: Filaments of an electrical nature
have already been reported precipitating from the
chemtrails. The phenomenon at Brighton is clearly
electrical. Perhaps some physicist can explain what's
going on. Weather modification, perhaps?)
CHUPACABRA SPOTTED ON A ROOFTOP IN CHILE
"Janitor Jesus Barrientos is the latest victim of the
mythic Chupacabra. He was left shaking with fear and
his hair standing up after having seen the strange beast
up close, as he states, on the rooftop of the four-story
building where he works. The 42-year-old resident of
Iquique cannot be disabused of the notion that what he
saw was indeed the strange Chupacabra, although some
may not believe him."
"Still on the nervous side, he told La Cuarta (newspaper)
that 'around 10:30in the evening, he went up to the roof to
arrange some boxes. It was well-lit, between the
moonlight and the light coming from the Calle Tarapaca
(street). Then I turned halfway around and saw that there
was some kind of bird on top of the doorway.'"
"Barrientos thought at first it was a jote (a large bat
indigenous to northern Chile--J.T.) 'But when I tried to
shoo it away, because jotes leave their droppings on
the walls, I realized it was an animal with an
elongated face, bulging eyes, sharp teeth and makes
squealing sounds like a puppy,' he recalled."
"He then froze, unable to do anything. This allowed
him to get a better look at it."
"'It had long ears and was black in color, measuring
a meter (3 feet, 4 inches) long and had large wings like
those of a bat.'"
"He thought the creature was about to pounce on him,
but as he broke into a run, the creature spread its wings and
flew off over Iquique."
"'I don't know how, but three seconds later, I was in the
building's lobby. I told what had just happened to some
children who were outside playing ball and they ran away
in terror,' explained the frightened janitor."
"Although he acknowledged that it was the first time
he had seen the bloodthirsty Chupacabra up close, Jesus
Barrientos remarked that others in the northern city
claimed to have seen it standing in top of the dome
of the city's cathedral."
Iquique is a large city located about 150 kilometers
(90 miles) south of Chile's border with Peru. (See the
Chilean newspaper La Cuarta for October 8, 2000.
Muchas gracias a Scott Corrales, autor de los libros
Chupacabras and Other Mysteries y Forbidden
Mexico para eso articulo de diario.)
THREE UFOs CAVORT OVER WESTERN PENNSYLVANIA
On Saturday, October 7, 2000, at 9 p.m.,
Mr. and Mrs. Alan Yost ""drove up on the hill above
our place in the trailer court" in Portersville,
Pennsylvania "to see if any thunderstorms were headed
in our direction from the north. I was outside our van,
checking the electrostatic meter I had made when my wife
called me back inside to see what she had been
observing through her binoculars."
""Using my binoculars, I was able to clearly
see a small but brilliant point of light which was flicking
about in an extremely unusual manner, changing color as
it did so. It would be crimson red in one spot, then
blink out only to re-appear in the same instant in
another but would now be brilliant green, or a silver
blue/white. I observed this one for a few minutes, then I
checked for a reference point of land so I could make
sure that its (the UFO's) movement was not caused by
my binoculars. I was able to put the tree line just
inside the bottom of the lens and still see the object.
It was definitely doing the moving as the tree line
remained perfectly still."
"Then I was able to see that there was not only one
but three or more of these 'objects' all doing the same
'dance in the sky.' I also noticed that whenever they
blinked out and re-appeared they would form a perfect
triangle. The size of the triangle was constantly
changing as they darted about."
The UFOs "remained in the same quadrant of the
sky--a couple of miles due west" of the hilltop.
"Many airplanes were also coming into and out of
Pittsburgh International Airport. One of their main flight
paths goes straight over the hill where we were, and I was
able to track the airplanes quite well with my binoculars."
All during the time of observation, the UFOs formed
triangular formations in the same quadrant of sky.
"We were able to view the objects doing their 'dance'
for 25 minutes, and then they suddenly disappeared."
(Many thanks to Alan Yost for this report.)
MYSTERIOUS BLUE METEOR SIGHTED IN MAINE
On Saturday, October 7, 2000, at 10 p.m.,
Jean C. and her daughter were driving on Interstate
Highway I-95 between Howland and Lincoln, Maine
when the daughter spotted something unusual in the
dark night sky.
"About 10 p.m., my daughter and I saw a
meteorite burn up in the atmosphere," Jean reported, "
"This meteorite had a long tail. We believe that it exploded
because there was a flash of blue, then it disappeared.
There were other people on the road at the time so it
must have been seen by more people than just us.
We were heading towards the Lincoln area in Maine."
(Email Form Report)
UFOs SIGHTED IN SOUTHERN ITALY AND SARDINIA
On Tuesday, September 26, 2000, "a strange light
was photographed hovering over Avellino," a city in
Italy's Campania province about 120 kilometers
(72 miles) east of Napoli (Naples). "Witnesses
noticed 'a rod of light illuminating the mountainside.'
The UFO moved sharply in a horizontal motion, then
straight up in a vertical motion before 'flying away at
a tremendous velocity.'" (See the Italian newspaper
Il Mattino for September 27, 2000.)
Four days earlier, on Friday, September 22, 2000,
at about 10 p.m., "several motorists driving up a
mountain near Bosa," a town on the Mediterranean
island of Sardinia located 100 kilometers (60 miles)
southeast of Sassari, "spotted an elongated object
(hovering) above the pass."
"The object seemed to be rotating slowly (on its
longitudinal axis--J.T.) and it changed colors while
emitting a very bright and intense light. People stopped
their cars, got out and observed the object for nearly
one hour. A few motorists with cameras took photos
of the OVNI (Italian acronym for UFO--J.T.)"
(See the newspaper L'Unione Sarda for September 25,
2000. Grazie a Edoardo Russo, Antonio Cuccu e
Gildo Persone di Centro Italiano di Studi Ufologici
per questi rapporti.)
DISCOVERY LAUNCH BESET BY TECHNICAL PROBLEMS
""The heralded 100th launch of the space shuttle
program was scrubbed Tuesday," October 10, 2000,
"by a human goof. Someone had left an 8-ounce
metallic pin in a perilous place--on an oxygen line
between the shuttle and its huge external fuel tank."
"Spotted during a final inspection, with the seven
astronauts strapped into the shuttle Discovery, the
extraneous part forced NASA to cancel the launch.
Engineers feared that the pin could ricochet between
the shuttle and the fuel tank, possibly detonating an
explosion."
"NASA spokesman Joel Wells said the part, used to
secure handrails and platforms for shuttle maintenance
crews, was left behind 'in a hard-to-reach location.'"
"It was found by 'the inspection team,' a crew that
inspects the entire shuttle assembly--the orbiter, its
booster rockets and the external fuel tank--three hours
before launch. The crew had been looking for ice
formed by gases released by the spacecraft on
the launch pad."
This was the latest in a series of delays that
have postponed the launch of Discovery, which was
scheduled to fly last week.
Discovery and its crew of seven astronauts had
been scheduled to lift off Thursday evening," October 5,
2000, "from Cape Canaveral on a mission to add two
segments to the International Space Station."
"NASA scrubbed the launch of Discovery for
at least 24 hours, citing concerns about the shuttle's
large external fuel tank...The space agency says
it was not sure whether a problem existed with
Discovery's tank, but film from the launch of space
shuttle Atlantis in September revealed that an
explosive bolt used to separate the tank from the
orbiter was protruding."
Bad weather over the weekend, and "gusty
wind at Cape Canaveral forced NASA to delay Monday
(October 9, 2000) night's launch of space shuttle
Discovery...The flight was already four days late
because of mechanical problems which were
resolved over the weekend."
"The wind limit (for shuttle launches) is 48 miles
per hour; (Monday's) gusts reached more than 51 miles
per hour, NASA spokesman Bruce Buckingham said."
"During the 11-day mission, the astronauts will add two
new segments to the International Space Station. Until
that is completed, no one can move in." (See the
Chicago Tribune for October 11, 2000, "8-ounce pin
causes expensive new delay for shuttle launch," page 3;
and USA Today for October 6, 2000, "NASA postpones
100th shuttle launch," page 4A, and for October 10, 2000,
"Wind delays shuttle again," page 3A.)
CHINESE SPACE AGENCY LAUNCHES MOON PROGRAM
"China's budding space program plans to explore
the moon for commercially-useful resources and hopes
to some day take part in an international expedition,
members of the Chinese space agency said
Wednesday," October 4, 2000.
"Although details are few, the experts made one
thing clear: China sees manned space flight as the key
to securing its international status and economic revival."
"'If China since the 1960s had not had the atomic
bomb and the hydrogen bomb, nor launched its own
satellites, China would not be regarded as an influential,
powerful country,' Luan Enjie," director of China's State
Aerospace Bureau, "told the audience of foreign
dignitaries and Chinese schoolchildren at the start of
the UN-declared World Space Week."
"Started in the 1970s, the Chinese space program
successfully built a spacecraft for manned exploration
putting the Shenzou (Chinese for Sacred Vessel--J.T.)
into orbit last November (1999)."
"China hopes to send astronauts aloft, joining the
United States and Russia as the only nations with
domestic manned space programs."
Previous Chinese "media reports indicated a
second test flight would come before the year's end and
a manned mission may soon follow. Luan revealed little
about a timetable, saying only that several missions
will follow 'successful flight of an unmanned
experimental spacecraft.'"
"But he was specific about the program's long-term
goals. 'We will conduct exploration of the moon and
actively join international activities for Mars exploration.'"
"China's manned space program, given the secret
designation Project 921, has gathered momentum in
recent years, getting help from more experienced
Russia and bigger budgets from a government eager
not to fall further behind the West." (Many thanks to
Steve Wilson for this report.)
GEOLOGISTS SAY "BIG WAVE" COULD HIT THE USA
"This is not science fiction. It could happen
tomorrow or several decades from now--an insignificant
piece of time, geologically speaking--but it will happen.
The volcano Cumbre Vieja (Spanish for Old Woman's Peak-
J.T.), located on the Atlantic Ocean island of La Palma,
is thoroughly unstable and could collapse at any moment."
La Palma is the largest of the Canary Islands, located
west of Morocco.
"The island will split in two. Half a trillion tons of rock
will fall into the sea within seconds and form a colossal
wave measuring some 560 meters )1,868 feet) in
height traveling westwards at a speed of 720 kilometers
per hour (432 miles per hour). A gigantic tsunami will
devastate the islands of the Caribbean and the Eastern
Seaboard of the USA. Water from the wave will
penetrate more than 20 kilometers (12 miles)
inland."
"This would seem to be the plot of a disaster
movie, but they are in fact the computations of of a
team of Swiss scientists concerning measurements
taken and then incorporated into an advanced geological
profiling program. The results have been published in
the Journal of Vulcanology and Geothermal Research."
"'It could happen at any time, within 10 years or
10 decades. But please note this: if I lived in Miami
or New York, and I heard that Cumbre Vieja was
erupting, I wouldn't listen to the news a second
longer,' Dr. Simon Bay of London's University College
told the BBC."
"Scientific fears are based not only on the
geophysical computations which indicate that the
current island of La Palma, which has only 706 square
kilometers of surface area and is 2,406 meters
(7,940 feet) in height, is in a precarious geotechnical
balance,, they are also concerned about a new
eruption of the Cumbre Vieja volcano, which isn't
far-fetched considering that it has exploded a dozen
times in the last 100,000 years, according to Bay's
calculations, and the last eruption on La Palma
occurred in 1971."
"'This is a much more vivid danger than having
an asteroid fall. This could be a catastrophe not only
for the island's residents but for the people on the
other side of the ocean who have never heard of
La Palma,' Bay said." (See the Spanish newspaper
Sociedad for October 6, 2000, "Scientists say the
island of La Palma will collapse and devastate the
Caribbean." Muchas gracias a Scott Corrales
para eso articulo.)
(Editor's Comment: Remember all those strange
"Big Wave" dreams people were having, which have
been reported here in UFO Roundup? Maybe they're
picking up psychic emanations of this future disaster.
For more on "Big Wave" dreams, see this week's
feature story.)
READER FEEDBACK:
DUBYA'S NO SATANIST
Glen E. Zook of Texas writes, "The photograph of
Gov. George W. Bush on page 9 of 'The Globe' does
NOT show him making a pagan sign, etc. What he is
doing is making the 'Hooked Horns' sign of the University
of Texas. The team name of the University of Texas is
the Texas Longhorns (a breed of cattle--G.E.Z.) and the
mascot is a longhorn named 'Bevo.' This hand gesture is
made at football games, etc."
"I moved to Texas after I graduated from Georgia
Tech in Atlanta, Ga. However, I have lived in the state
for 33 years and have seen this gesture many, many
times."
ANN ARBOR UFO COULD HAVE BEEN A BLIMP
Greg Andrews of Michigan writes, "I'm going out on
a limb here, but I'll bet those people were looking at
one of the many sport blimps that show up to provide
aerial coverage of the University of Michigan football
games. Some of these blimps have impressive lights
on them for night advertising, which look really odd
if you see it at an angle or from a distance."
"I'm not saying that it wasn't something more exotic,
but it's a pretty good guess that it was a blimp."
from the UFO Files...
2060: SECOND NOAH!?
This week's article in the Journal of Vulcanology
and Geothermal Research has rekindled interest in
the recent spurt of "Big Wave" dreams experienced
by some of the psychics.
Since 1987, your editor has had six dreams about
a monstrous tidal wave hitting the eastern shores of the
USA. Some were truly frightening, but the most vivid,
most detailed and most memorable dream dealt with the
aftermath of the "Big Wave."
I had this dream in April of 1996. I dreamed I was sitting
at a desk in a darkened room. In front of me was a very
odd-looking desktop computer. I groped for the on-switch,
but I couldn't find it. Then I accidentally moved my hand across
the screen, and it came on. A curved keyboard automatically
came out of a panel of what I thought was the CPU.
Figuring to access AOL, I typed "Menu" and hit what I thought
was the Enter tab. The computer began beeping and making
weird geometric patterns onscreen. The keyboard went in and
out of its aperture like a cuckoo clock. I thought, I need some
technical assistance with this thing, and, waving my hand
in front of the screen, I shut it down and left the room.
I found myself in a darkened upstairs hallway. I groped for
a light switch, found it and flicked it. Nothing.
(Editor's Note: Apparently the computer had its own
built-in power pack.)
Making my way downstairs, I saw that the first floor
was a complete shambles. Overturned furniture, debris,
patches of silt and muck on the floor. An overwhelming
damp, dank scent like seawater.
I went outside. Instantly I recognized the neighborhood.
I was on the east side of Peck Street, in my childhood
hometown of Attleboro, Massachusetts, about midway
between North Main and Bank Streets. There was no
mistake. This was Peck Street, the same street I had
walked on my way to school for 12 years. Like Dickens,
I could walk it blindfolded.
But Peck Street had changed a bit. The Roman
Catholic and Episcopalian churches still stood sentinel
on each corner of Peck and North main. But they looked
like stone islands in a vast lake. The whole corner was
underwater. A similar "lake" occupied the wetlands
north of the street, running along Bank Street.
The Duffy-Poole Funeral Home, at the corner of
Peck and Danforth Streets, was gone, replaced by a
garden apartment complex with a first-floor cafe and
gift shop. Same story across the street, where the old
Victorian homes stood. Then I spotted the ranch house.
Different paint scheme but the same house, only now it
looked like one of the oldest homes on the street.
Now, I remember when that house was built. It was
back in 1957, when I was in the second grade. The
following spring, the owner planted maple saplings in
the yard. Today they're mature maples. But in my
dream, the remaining trees looked about a century old.
Meaning I was seeing Peck Street in about 2060 A.D.
I figured that out later, though. My initial reaction
was one of horrified shock. What happened to
Attleboro!?
The area looked as if it had been hit by a massive
tidal wave of hurricane. Flood damage was everywhere.
Shattered walls, overturned cars, downed trees, ponds
littered with debris. The earth was sodden underfoot as
I made my way across the lawn toward the sidewalk.
There was no sign of any other humans.
Where is everybody? I wondered.
Looking toward a downed maple tree, I saw what I at
first thought was a bundle of clothes in the water. Then I
realized it was a man. I plunged into the thigh-deep
water on the street and pulled him up onto the lawn.
I rolled him over. He was a man in his early twenties,
with a gold stud in each ear lobe and a forked beard
and a curious haircut--slight bangs with a curled ponytail.
Denim jacket and dark slacks. I put my hand on his
throat. No pulse. He was dead. Rigor had come and gone,
so I guess he was in the water for a day or two.
Just then, I heard a soft whirring noise. Looking up I
saw an unusual white craft flying from west to east at an
altitude of about 2,000 feet. I gaped in astonishment.
I don't believe it! A UFO!
The object stopped. Some kind of canopy slid open
and a man in black stood up. All at once, a light began
winking at me. I heard a sound like angry bees on my
left, and vertical fountains erupted in the water all
around me. He's shooting at me!
Grabbing a quick breath, I did a belly flop into
the water. Went under and stayed under, gripping sunken
rocks and debris to keep myself submerged. My lungs
began to burn, but I didn't dare surface. Then I
remembered the fallen maple tree just ahead. Doing a
tadpole crawl along the bottom, I reached the branches,
then pulled myself along into deeper water until I was close
to the trunk. My face poked out of the water, and I drank
in long breaths of air.
Peering through the leaves, I could see the unusual
aircraft fifty feet above. It was some kind of hybrid
airplane/hovercraft. The studdy white fuselage was
like an A-6 but with a huge, broad, bell-shaped
rotorfan underneath it. There was a conventional
empennage--upright tail and stabilizers, and thrust was
provided by two small turbofan engines on outrigger
pylons near the tail. On the tail I saw the black
wreathed globe symbol of the United Nations with a
logo underneath reading World Air Service.
It was a two-seater, side-by-side cockpit. The
bubble canopy was up. Both men wore black flight
suits with large sky-blue helmets with Polaroid sun
visors. One handled the controls; the other stood
upright, toting what looked like a bull[up-style
automatic weapon with a banana clip.
The World Air Service hovercraft drifted around
overhead for another five minutes. Its rotor raised
ripples on the pond, and I got a few mouthfuls of
brackish saltwater. Then the clear canopy descended, and
it resumed its eastward flight.
I gave it another five minutes and staggered out of the
street pond. They must have thought I was a looter, I
reflected, shivering as the wind began to pick up.
(Editor's Comment: Or perhaps the flying UN police
of 2060 don't bother to arrest and question suspects.
Perhaps they merely gun them down.)
Seeking shelter, I wandered through backyards.
Most of the doors I tried were locked. But then I got
lucky. The house I entered had severe flood damage
on the first floor, but the second-story bedrooms
were dry. I found a bedroom, doffed my soaked clothes,
wrung the water out of them with my bare hands, and
let them air-dry while I warmed myself beneath the
bed's blankets.
I must have dozed for awhile, because the next
thing I knew, a Pomeranian dog hopped onto the
bedspread and began barking. Sitting up, I ruffled
the fur on the back of his neck and asked, "Where
did you come from?"
Suddenly, I heard a woman's voice on the first floor.
"Honey, I think somebody's up there." Then a but
louder from the stairwell. "Hello? Who's there?"
And I woke up.
Reading about the Cumbre Vieja volcano in the
Canary Islands I wonder if I was given a glimpse of the
aftermath of that disaster. Attleboro is about 15 miles
north of Narragansett Bay, the nearest arm of the
Atlantic Ocean, so it's conceivable that the city might
fall within the flood zone.
Even if it does get a bit banged up, it's comforting
to know that Attleboro will still be there sixty years
from now. I wish I could say the same about the
Temple Mount. The way things are going, by the
year 2060, they're liable to be calling that place
Radioactive Crater Lake.
O JERUSALEM DEPT.: No jokes this week,
readers. The situation is too serious for that.
The death toll is already over one hundred, and
the wounded number in the thousands.
Today it's a platoon-level war, with mobs rioting
on the side. But it could escalate into heavy weapons
and big battalions any time now.
Here are a few things the Zionist sympathizers in
mass media had withheld from the USA public.
(1) On Sunday, October 8, thousands of Hasidic
Jews attacked an upscale restaurant in Tel Aviv,
setting it on fire and threatening to burn the Arab waiters alive.
(2) On Tuesday, October 10, Ehud Barak made
common cause with the Likud, inviting them to join a
coalition government. Yes, that's the same Likud whose
poster boy, Gen. Ariel Sharon, led his merry band of
goat molesters into the Haram as-Sharif September 28
and desecrated the Al-Aqsa mosque, thereby setting
off the current war of religion.
(3) Also on Tuesday, October 10, Jews firebombed
the Mahmoudin Mosque in Jaffa, presumably in retaliation
for the Muslims' destruction of Joseph's Tomb.
(4) Jews also firebombed the Hassan Ben Mosque.
While these incidents have not been mentioned on
American network TV, let me assure you, they are the
Number One topic of conversation at the bazaar in
Quetta, Pakistan.
Eleven weeks ago, Tackanash, Francisco Marto and
Jacinta Marto came to me in a dream and warned that
"a major war will soon break out in the Middle East."
Will these dream-predictions all come true? We'll
know for certain on November 8, 2000. Until then,
readers, keep hoping and praying and working for peace.
Join us in seven days for more UFO and paranormal
news from around the planet Earth, brought to you by
"the paper that goes home--UFO Roundup." See you
next week!
UFO ROUNDUP: Copyright 2000 by Masinaigan
Productions, all rights reserved. Readers may post
news items from UFO Roundup on their websites or in
newsgroups provided that they credit the newsletter
and its editor by name and list the date of issue in
which the item first appeared. |
This post was originally titled, “Asleep at the wheel: Junk science gets promoted by Bill Gates, NPR, Ted, University of California, Google, etc.,” but I decided the above quote had better literary value.
We’ve had a few posts now about discredited sleep scientist Matthew Walker; see here and here, and here, with the disappointing but unsurprising followup that his employer, the University of California, just doesn’t seem to care about his research misconduct. According to his website, Walker is employed by Google as well.
Heart attacks
Also disappointingly but unsurprisingly, further exploration of Walker’s work reveals further misrepresentations of research.
Markus Loecher shared this investigation of some attention-grabbing claims made in the celebrated Ted talk, “Sleep is your superpower.”
Here’s Walker:
I could tell you about sleep loss and your cardiovascular system, and that all it takes is one hour. Because there is a global experiment performed on 1.6 billion people across 70 countries twice a year, and it’s called daylight saving time. Now, in the spring, when we lose one hour of sleep, we see a subsequent 24-percent increase in heart attacks that following day. In the autumn, when we gain an hour of sleep, we see a 21-percent reduction in heart attacks. Isn’t that incredible? And you see exactly the same profile for car crashes, road traffic accidents, even suicide rates.
“Isn’t that incredible?”, indeed. This reminds me of the principle that, if something is being advertised as “incredible,” it probably is.
Loecher decided to look into the above claim:
I [Loecher] tend to be sensitive to gross exaggerations disguised as “scientific findings” and upon hearing of such a ridiculously large effect of a one-day-one-hour sleep disturbance, all of my alarm bells went up! Initially I was super excited about the suggested sample size of 1.6 billion people and wanted to find out how exactly such an incredible data set could possibly have been gathered. Upon my inquiry, Matthew was kind enough to point me to the paper, which was the basis for the rather outrageous claims from above. Luckily, it is an open access article in the openheart Journal from 2014. Imagine my grave disappointment to find out that the sample was limited to 3 years in the state of Michigan and had just 31 cases per day! On page 4 you find Table 1 which contains the quoted 24% increase and 21% decrease expressed as relative risk (multipliers 1.24 and 0.79, respectively):
Loecher notes the obvious multiple comparisons issues.
But what I want to focus on is the manipulation or incompetence (recall Clarke’s Law).
To start with, here’s the summary from the above-linked article:
Now, we could argue about whether the data really show that daylight savings time “impacts the timing” of acute myocardial infarction—arguably, the data here are consistent with no effect on timing at all! But let’s set that aside and focus on the other point of their summary: daylight savings time “does not influence the overall incidence of this disease.”
This completely contradicts Walker’s theme of sleep deprivation being dangerous. It did not influence the overall incidence of the disease!
Presumably Walker realized this: even if he didn’t read the whole article, he must have read the abstract, at least to pull out those 24% and 21% numbers. (Or maybe Walker’s research assistant did it, but no matter. If Walker gets credit for the book and the Ted talk, he also gets blame for the errors and misrepresentations that he puts out under his name.)
So . . . he read a paper claiming that, at most, daylight time is associated with some time-shifting of heart attacks, and he misrepresents that as being associated with an increase.
Also, he says is “a global experiment performed on 1.6 billion people,” but he’s reporting results on one U.S. state. He must have realized that too, no, that this was not a N = 1.6 billion study???
But wait, there’s more. We switch to daylight time 2am on Sunday. So you might expect the largest effects to occur on Sunday—that day with the sleep deprivation. Or maybe Monday, the first day back at work. All sorts of things are possible. The point is that that, by saying it as “that following day,” Walker is hiding the choice. If it’d been Sunday, it would’ve been “the very day of,” etc. And then when he talks about autumn, he doesn’t say “that following day,” just leaving the (false) impression that it’s the same pattern both seasons.
Tuesday, huh?
I also wonder about Walker’s other claim, that at the switch to daylight or standard time “you see exactly the same profile for car crashes, road traffic accidents, even suicide rates.”
Exactly the same, huh? I’ll believe it when I see the data, and not before.
Testicles
Loecher also looks into Walker’s claim that “Men who sleep five hours a night have significantly smaller testicles than those who sleep seven hours or more.” There seems to be no good evidence for that one either.
Ted and Edge and all the rest
I hate the whole Ted talk, Edge foundation, Great Man model of science. It can destroy people. As I wrote last year:
Don’t ever think you’re too good for your data. . . . Which reality do we care about? The scientific reality of measurement and data, or the social reality that a Harvard [or University of California] professor can get caught falsifying data and still be presented as an authority on science and philosophy. Ultimately, both realities matter. But let’s not confuse them. Let’s not confuse social power with scientific evidence. Remember Lysenko. . . . OK, why am I picking on these guys? Marc Hauser and the Edge foundation: are these not the deadest of dead horses? But remember what they say about beating a dead horse. The larger issue—a smug pseudo-humanistic contempt for scientific measurement, along with an attitude that money plus fame = truth—that’s still out there.
An always-relevant quote
From Dan Davies: Good ideas do not need lots of lies told about them in order to gain public acceptance.
A message to Bill Gates, NPR, Ted, University of California, Google, etc.
It’s not your fault that you got scammed. I mean, sure, it’s kind of your fault for not checking, but that’s easy to say after the fact. Anyone can get scammed. I’ve been scammed! My political scientist colleague Don Green got scammed! Harvard got scammed by that disgraced primatologist. Cornell got scammed . . . George Schultz got scammed . . . maybe you’ve heard about that one. People get scammed. Scammers scam people, that’s what they do.
You got scammed. That’s in the past, now.
The question is: Are you gonna continue to let yourself get scammed?
I’ll break that down into 2 questions:
1. Do you now, at last, realize you’ve been scammed? (If not, what would it take? An actual manipulated graph?? No, I guess not; we already have one of those!)
2. If your answer to the first question is Yes, then are you gonna decide that it’s worth your while to continue to get scammed, because the cost in effort and bad publicity is worse than the cost of continuing to promote this stuff?
If the answer to question 1 is No, that’s just sad, that people could see all this evidence and still not get the point.
If the answer to question 1 is Yes and the answer to question 2 is No, that’s even sadder.
A quick google search appears to reveal six separate appearances by Walker on NPR, with the most recent being this June, several months after Guzey’s takedown of Why We Sleep. But I’m guessing that, once NPR had Walker on once or twice, he became a known quantity for them, so they just put him in the Expert category.
Ted? They’ve had iffy talks before, I guess it comes with the territory. They’re probably focusing on scheduling and promoting new talks, not on problems with talks they’ve already posted.
Bill Gates? He endorsed Walker’s book and now he’s moved on. Gates probably doesn’t care about an endorsement that’s sitting in the past.
The University of California? They know about the problems with Walker’s work but they’ve carefully looked away. I think they’re basically Yes on question 1 and No on question 2, except that they’ve tried really hard to avoid answering question 1. At some level, they must know they’ve been scammed, but as long as they avoid looking at Walker’s work carefully (even to the extent of carefully reading a few blog posts), they can maintain a facade of uncertainty.
Google? I have no idea. I don’t know what Walker does for Google. Maybe he’s doing great work for them. Yes, he has a problem with exaggerating research claims in publications and public talks, but maybe he does excellent work when the lights of publicity are not shining. In that case, he’s not scamming Google at all.
Also, Walker could well be scamming himself. I’m not trying to paint him as some cackling villain here. I could well imagine he’s a true believer in the healing power of sleep, and that when he misrepresents the evidence, in his view that’s just because he doesn’t have all the data at hand. Sure, they didn’t really have data on 1.6 billion people, but if they did, it would undoubtedly confirm his views. He has a direct line to the truth, and he’d be remiss if he didn’t shout it from the treetops.
The trouble is, people who think they have a direct line to the truth, often’t don’t. Recall the above quote from Dan Davies. Tony Blair probably thought those WMDs were real too, at some point—or, if they weren’t, they could’ve been, right? And the war was a good idea anyway, right? Etc. To return to sleep studies: the data support the theory, and once you believe the theory, you don’t need the data anymore.
As always, I’d have no problem if this guy were to just straight-up give inspirational talks and write inspirational books. He could just say that he personally believes in the importance of sleep, and his broad reading and experience has lead him to this conclusion. It’s when he misrepresents data, that’s where I have the problem (even though the University of California doesn’t seem to mind). |
MORRISTOWN, N.J., March 13, 2019 (GLOBE NEWSWIRE) -- Melinta Therapeutics, Inc. (NASDAQ: MLNT), a commercial-stage company, developing and commercializing novel antibiotics to treat serious bacterial infections, today reported financial results and provided a business update for the fourth quarter and full-year ended December 31, 2018. In 2018, Melinta achieved several key milestones within its commercial, development and business development operations critical to positioning the company for long-term growth.
“We are pleased with the decisive actions we took in 2018 to realign the business and help position Melinta for future growth and stockholder value creation. In the past year, the Company has made significant strides to streamline operations and strengthen its balance sheet, while at the same time executing against our sales and clinical goals,” said John H. Johnson, chief executive officer of Melinta. “As a result, we delivered revenues of $96.4 million, driven by $46.6 million in net product sales. In addition, the positive results we reported in 2018 give us confidence in the commercial potential of our products and pipeline.”
“We have several upcoming milestones in 2019, including opportunities to potentially expand product labels and increase our marketing territory. We believe that the Company’s efforts over the past year coupled with our strategic initiatives underway position Melinta to continue leading the global fight against antimicrobial resistance and delivering anti-infective solutions to patients,” continued Johnson.
Fourth Quarter and Full-Year Results
-- In the fourth quarter, sales of commercial products increased 32% compared to the third quarter of 2018, driven by strong Vabomere® (meropenem and vaborbactam) and Orbactiv® (oritavancin) performance -- Delivered full-year 2018 revenues of $96.4 million, including $46.6 million in net product sales -- Melinta ended the year with $81.8 million of cash and cash equivalents
Portfolio Updates
-- Vabomere received European Commission approval in November 2018 for the following indications in adult patients: -- Complicated intra-abdominal infections (cIAI) -- Complicated urinary tract infections (cUTI) -- Hospital-acquired pneumonia including ventilator associated pneumonia (HAP/VAP) -- Bacteraemia that occurs in association with any of these infections -- Infections due to aerobic Gram-negative organisms where treatment options are limited -- Reported positive top-line results from the Phase III trial of Baxdela® (delafloxacin) for the treatment of adult patients with community-acquired bacterial pneumonia (CABP) in October 2018 -- Began preparation of supplemental new drug application (sNDA) to the U.S. Food and Drug Administration (FDA) for Baxdela in CABP, which is expected to be filed in the second quarter of 2019 -- Entered into a commercial agreement with Menarini Group to commercialize Vabomere, Orbactiv and Minocin®(minocycline) for injection in 68 countries outside of the U.S. in October 2018
Business Highlights
-- John H. Johnson named permanent chief executive officer -- Closed the initial $75 million disbursement under the previously announced $135 million convertible loan facility from Vatera Healthcare Partners, LLC on February 22, 2019 -- Implementation of operating cost reduction initiatives expected to deliver significant cost savings in 2019 -- Strengthened Board of Directors and senior leadership team through new appointments adding beneficial experience and expertise to Melinta -- Effected a one-for-five reverse stock split of the Company’s common stock on February 22, 2019
“We were pleased to announce the closing and receipt of the initial $75 million disbursement of the $135 million convertible loan facility from Vatera in February 2019,” said Peter Milligan, chief financial officer of Melinta. “We believe this funding, along with existing cash and cash from future revenue, will provide valuable liquidity to support the Company’s operations as we continue to take steps to become cash-flow positive. We will continue to exercise disciplined post-integration stewardship of cash resources and spending to achieve significant operating expense savings in 2019.”
2019 GuidanceThe Company provides guidance for the full-year 2019 as follows:
-- Net product sales of approximately $65 million -- Gross margin of approximately 55%, including intangible assets amortization -- Operating expenses of approximately $140 million
Upcoming Potential Catalysts
-- Expected sNDA submission to FDA for Baxdela for treatment of CABP -- European Commission approval decision for delafloxacin (to be marketed under the brand name Quofenix) for acute bacterial skin and skin structure infections (ABSSSI) -- Country approvals for Baxdela in South America and Central America -- Execute Latin America commercialization agreement for Vabomere, Orbactiv and Minocin for injection
Fourth Quarter and Full-Year 2018 Financial ResultsMelinta reported revenue of $35.5 million and $96.4 million, respectively, for the fourth quarter and full-year ended December 31, 2018. Revenue from product sales was $14.6 million for the quarter and $46.6 million for the full-year, representing the first year of product sales in the Company’s history.
Cost of goods sold (“COGS”) was $9.0 million and $41.1 million, respectively, for the fourth quarter and full-year ended December 31, 2018, of which $3.9 million and $16.4 million was comprised of non-cash amortization of intangible assets. In addition, for the fourth quarter and full-year ended December 31, 2018, we recorded $1.0 million and $8.0 million, respectively, in charges related to inventory that is approaching shelf life, primarily driven by product launches. There were no product sales and therefore no costs of goods sold in the prior year period.
Research and development (“R&D”) expenses were $10.4 million and $55.4 million, respectively, for the fourth quarter and full-year ended December 31, 2018, compared to $11.6 million and $49.5 million for the same periods in 2017. Selling, general and administrative (“SG&A”) expenses were $29.5 million and $133.3 million for the fourth quarter and full-year ended December 31, 2018, compared to $37.3 million and $63.3 million for the same periods in 2017. R&D and SG&A expenses increased primarily as a result of the additional costs associated with the acquisition of The Medicines Company infectious disease business (“IDB”) and the Cempra merger. In addition, SG&A included severance-related costs of $8.9 million and $12.3 million, respectively, for the fourth quarter and full-year ended December 31, 2018, as well as an offsetting gain of $8.8 million from the remeasurement of contingent consideration associated with the acquisition of the IDB from The Medicines Company in January 2018. Also, during the fourth quarter of 2018, we recognized goodwill impairment charges of $25.1 million related to the acquisition of the IDB in the first quarter of 2018.
Net loss was $44.1 million, or $3.94 per share, for the fourth quarter of 2018, compared to a net loss of $20.9 million, or $7.40 per share, for the fourth quarter of 2017. Net loss was $157.2 million, or $17.12 per share, for the year ended December 31, 2018, compared to a net loss of $78.2 million, or $109.28 per share, for 2017. Net loss per share year-over-year was impacted by changes in share count as a result of the Cempra merger and financing related to the acquisition of the IDB, as well as a one-for-five reverse stock split effective on February 22, 2019.
Conference Call and WebcastMelinta’s earnings conference call for the fourth quarter and full-year ended December 31, 2018 will be broadcast at 4:30 p.m. ET on March 13, 2019. The live webcast can be accessed under “Events and Presentations” in the Investor Relations section of Melinta’s website at www.melinta.com.
A live webcast of the call will be available online from the Investor Relations section of the company website at www.melinta.com and will be archived there for 30 days. A telephone replay of the call will be available by dialing 855-859-2056 for domestic callers or 404-537-3406 for international callers and entering the conference ID # 1698998.
About Melinta TherapeuticsMelinta Therapeutics, Inc. is the largest pure-play antibiotics company, dedicated to saving lives threatened by the global public health crisis of bacterial infections through the development and commercialization of novel antibiotics that provide new therapeutic solutions. Its four marketed products include Baxdela® (delafloxacin), Vabomere® (meropenem and vaborbactam), Orbactiv® (oritavancin), and Minocin® (minocycline) for Injection. This portfolio provides Melinta with the unique ability to provide providers and patients with a range of solutions that can meet the tremendous need for novel antibiotics treating serious infections. Visit www.melinta.com for more information.
As more fully described in our Annual Report on Form 10-K for the year ended December 31, 2017, the former private company Melinta was determined to be the accounting acquirer in our November 2017 reverse merger with Cempra and, accordingly, historical financial information for the fourth quarter and full year 2017 presented in this press release reflects the standalone former private company Melinta until November 3, 2017, and, therefore, period-over-period comparisons may not be meaningful.
Non-GAAP Financial MeasuresTo supplement our financial results presented on a U.S. generally accepted accounting principles, or GAAP, basis, we have included information about non-GAAP adjusted EBITDA, a non-GAAP financial measure, as a useful operating metric. We believe that the presentation of this non-GAAP financial measure, when viewed with our results under GAAP and the accompanying reconciliation, provides supplementary information to analysts, investors, lenders, and our management in assessing the Company’s performance and results from period to period. This non-GAAP measure closely aligns with the way management measures and evaluates the Company’s performance. This non-GAAP financial measure should be considered in addition to, and not a substitute for, or superior to, net income or other financial measures calculated in accordance with GAAP. Non-GAAP Adjusted EBITDA is not based on any standardized methodology prescribed by GAAP and represents GAAP net income (loss), which the Company believes is the most directly comparable GAAP measure, adjusted to exclude interest income, interest expense, depreciation and amortization, stock based compensation expense, changes in the fair value of our warrant liability, impairment charges, bargain purchase gains, gains or losses on extinguishment of debt, acquisition-related costs, gains on the reversal of loss contracts, and other adjustments, including the remeasurement of contingent consideration related to our acquisition of IDB and launch-related excess and obsolete inventory. Non-GAAP financial measures used by us may be calculated differently from, and therefore may not be comparable to, non-GAAP measures used by other companies.
Cautionary Note Regarding Forward-Looking StatementsCertain statements in this communication constitute “forward-looking statements” within the meaning of Section 27A of the Securities Act and Section 21E of the Securities Exchange Act and are usually identified by the use of words such as “anticipates,” “believes,” “estimates,” “expects,” “intends,” “may,” “plans,” “projects,” “seeks,” “should,” “will,” and variations of such words or similar expressions, including statements related to guidance. We intend these forward-looking statements to be covered by the safe harbor provisions for forward-looking statements contained in Section 27A of the Securities Act and Section 21E of the Securities Exchange Act and are making this statement for purposes of complying with those safe harbor provisions. These forward-looking statements reflect our current views about our plans, intentions, expectations, strategies and prospects, which are based on the information currently available to us and on assumptions we have made and include statements regarding: expectations with respect to our financial position, results and performance. Although we believe that our plans, intentions, expectations, strategies and prospects as reflected in or suggested by those forward-looking statements are reasonable, we can give no assurance that the plans, intentions, expectations, strategies or prospects will be attained or achieved. Furthermore, actual results may differ materially from those described in the forward-looking statements and will be affected by a variety of risks and factors that are beyond our control.
Risks and uncertainties for Melinta include, but are not limited to, the fact that we have incurred significant operating losses since inception and will incur continued losses for the foreseeable future; our limited operating history; our need for future capital and risks related to our ability to obtain additional capital to fund future operations; risks related to the satisfaction of the closing conditions for the remaining two disbursements under the loan agreement with Vatera, including any consequences of a failure to close on the two disbursements under the Vatera loan financing; risks related to compliance with the covenants under our facilities with Vatera and Deerfield; uncertainties of cash flows and inability to meet working capital needs as well as other milestone, royalty and payment obligations, including as a result of the outcome of the pending litigation with respect to, and any requirement to make, payments potentially due to The Medicines Company; risks that may arise from the consummation of the Vatera loan financing and the effectiveness of the amendment to the Deerfield facility agreement, including potential dilution to our stockholders and the fact that Vatera will beneficially own a substantial portion of our common stock; the fact that our independent registered public accounting firm’s report on the Company’s 2016, 2017, and 2018 financial statements contains an explanatory paragraph that states that our recurring losses from operations and our need to obtain additional capital raises substantial doubt about our ability to continue as a going concern; our substantial indebtedness; risks related to the commercial launches of our products and our inexperience as a company in marketing drug products; the degree of market acceptance of our products among physicians, patients, health care payors and the medical community; the pricing we are able to achieve for our products; failure to obtain and sustain an adequate level of reimbursement for our products by third-party payors; inaccuracies in our estimates of the market for and commercialization potential of our products; failure to maintain optimal inventory levels to meet commercial demand for any of our products; risks that our competitors are able to develop and market products that are preferred over our products; our dependence upon third parties for the manufacture and supply of our marketed products; failure to achieve the benefits of our recently completed transactions with Cempra and The Medicines Company; failure to establish and maintain development and commercialization collaborations; uncertainty in the outcome or timing of clinical trials and/or receipt of regulatory approvals for our product candidates; undesirable side effects of our products; failure of third parties to conduct clinical trials in accordance with their contractual obligations; our ability to identify, develop, acquire or in-license products; difficulties in managing the growth of our company; the effects of recent comprehensive tax reform; risks related to failure to comply with extensive laws and regulations; product liability risks related to our products; failure to retain key personnel; inability to obtain, maintain and enforce patents and other intellectual property rights or the unexpected costs associated with such enforcement or litigation; risks relating to third party infringement of intellectual property rights; our ability to maintain effective internal control over financial reporting; unfavorable outcomes in any of the class action and shareholder derivative lawsuits currently pending against the Company; and the fact that a substantial number of shares of common stock may be sold into the public markets by one or more of our large stockholders in the near future. Many of these factors that will determine actual results are beyond Melinta’s ability to control or predict.
Other risks and uncertainties are more fully described in our Annual Report on Form 10-K for the year ended December 31, 2018, our Revised Definitive Proxy Statement filed January 29, 2019, and in other filings that Melinta makes and will make with the SEC. Existing and prospective investors are cautioned not to place undue reliance on these forward-looking statements, which speak only as of the date hereof. The statements made in this press release speak only as of the date stated herein, and subsequent events and developments may cause our expectations and beliefs to change. While we may elect to update these forward-looking statements publicly at some point in the future, we specifically disclaim any obligation to do so, whether as a result of new information, future events or otherwise, except as required by law. These forward-looking statements should not be relied upon as representing our views as of any date after the date stated herein. |
'Collateral': The Best Movie Tom Cruise Will Probably Ever Make
By Petr Knava | Film | April 20, 2018 |
A taxi glides forward on deserted nighttime streets. We see it from above and behind as the camera tracks it. Slowly we pull in closer, tightening the frame as glimpses of neon slide past. Billboards and shop signs and parking lots. A lone silver car enters the scene, heading in the opposite direction. It makes a turn, away from our taxi, and is gone just as quickly as it appeared. The effect is palpable: Whoever is inside that cab is alone, isolated in the stillness of these anonymous streets, bathed in intermittent light but seen by no one.
The whole sequence only takes up six seconds but even in such a short sliver of time the fingerprints of its creator are immediately apparent. Michael Mann shoots Los Angeles like nobody else on Earth. There are not many people who can shoot anything the way Mann shoots L.A. The Chicago-born filmmaker has an affinity with the Southern Californian city that allows him to transform it onscreen in ways other directors can only dream of. He finds banal and unknown corners and makes them into landmarks. He traces roads and alleyways like nerve fibres running through a living organism. He levitates his camera above the sprawling and disconnected city in such a way so as to transform it, the chaotic and roiling metropolis becoming a serene constellation of lights in his hands, a dreamlike background both integral and distant. Mann’s other movie—his gem of gems, Heat—is a masterclass in how to use an urban setting to invoke feeling. Whether it’s the disorienting angular array of lights and fun house mirror-like reflections of Vincent Hanna’s skyscraper-slaloming helicopter ride, or the view from Eady’s house on the hillside from where the city appears as if a lake of fireflies glimpsed through a haze, the director casts Los Angeles almost a separate character in its own right, sometimes beautiful and enchanting, but often apathetic, if not outright hostile.
In 2004’s Collateral, L.A. fits this description perhaps even better than in Heat. The effect Mann goes for here is one of isolation, anonymity. Indeed that is the crux of Collateral’s thesis: That the city—all cities in a way, but more specifically this city—can be incredibly indifferent to the struggles of those who inhabit it; that the humans living there are fundamentally alone, despite their vast number. That connection is rare. In short: That nobody cares.
It all comes across as an oddly melancholy and affecting description for a movie the plot of which sounds like a high concept elevator pitch:
‘A silver haired assassin called Vincent, played by Tom Cruise, arrives in Los Angeles for one night. He has five targets on his list that he must take out before dawn, so he hires a cab for the night to ferry him between stops. The initially unwitting cabbie, played by Jamie Foxx, soon realises what’s going on, effectively finding himself both a hostage as well as an accomplice. Will he be able to save himself, and perhaps some of the potential victims, before the night is out?’
But while the pitch itself may sound hokey, the movie itself is anything but. A thriller on the face of it, Collateral is a piece of work that runs on genuine human feeling, more akin to a drama than anything else. This is in part due to Mann’s precise direction and evocative camerawork, but also thanks to the work he did on Stuart Beattie’s script. Originally set in New York and trading a lot more in cultural stereotype, Australian Beattie’s initial screenplay was a bit of a diamond in the rough before Mann got a hold of it. Said Mann of Beattie’s script:
I didn’t like the screenplay, I didn’t like the dialogue, I didn’t like [the] writing, but if you took the screenplay, and put it under an MRI, or an X-ray machine, and took a look at it, you realize this thing has beautiful, beautiful bones. It’s one of the most beautifully constructed stories I’d had ever run into. And it was gemlike, and it all took place in one night, and the roles each guy played in the other’s realization of himself, and it was just a beautiful piece of writing by [Stuart] Beattie. But I loved the story structure of it, so I rewrote it.
Michael Mann is a director often praised for his technical ability—and rightfully so, as he remains one of the finest craftsmen of his time—but it should never be forgotten that he, like David Fincher, has a deep understanding of what makes people tick. He knows how to write stories grounded in humanity, in our hopes and dreams and fears, and he is intuitively aware of how important it is to connect that way with the audience. The mechanics of the plot and the methods of telling it are important, but they are nothing without characters we care about. In Collateral, both aspects of this virtuous kind of filmmaking are supremely evident. On the one hand you have that gorgeous cinematography, a portion of it filmed on traditional celluloid, but much of it done with digital, using the Viper FilmStream High-Definition Camera. 2004 is not that long ago, but it was a quite dramatically different time in cinema to the one we see today. The vast majority of movies were still being shot on film, and while the industry was already slowly adapting to what would eventually become the new visual norm, it was Mann and his cinematographers, Dion Beebe and Paul Cameron, who were responsible for putting forward one of the landmark cases for digital. Their work on Collateral would garner an American Society of Cinematographers (ASC) nomination for outstanding achievement in cinematography—an unprecedented mark of industry acceptance for digital work at the time and a harbinger of things to come. Camera tech has moved on since then, but the digital shooting in Collateral still looks amazing to this day. Beebe hit the nail on the head when he said, years later:
We have seen an emergence of what I think is a digital aesthetic. It’s a beautiful aesthetic, and it plays to the strength of that medium, which is the very open bottom of the curve. It can look into shadows; it’s got an amazing range. Digital gives us the ability to work from a base of ambient light, essentially. Because of that, you tend to light in a very different way. And I do think ‘Collateral’ helped launch that because it played to the strengths of the format. We never set out to replicate a film look, but rather to discover a digital one…Film has a unique texture and tone, and digital has its own unique texture and tone. It would be a sad day if we lost the ability to choose between them.
Indeed we have now in 2018 arrived at a time when digital has almost totally eclipsed film in industry uptake, but to look at Collateral is to look at a piece of work that stands out as one of the prime examples of how good it can be when the two are used together, with the painterly celluloid compositions playing off the more urgent and gritty digital work that often washes out the Los Angeles skyline in the background, providing the sense of floating isolation that the movie needs.
Collateral’s wonderful cinematography is matched by a pair of pitch-perfect performances. Tom Cruise and Jamie Foxx deliver some of the finest turns of their careers here. But the movie’s production was not straightforward, and one of the twists in that story is that Adam Sandler was originally attached to play Max, the unfortunate cabbie who is forced into enabling Vincent’s bloody itinerary. Now, Adam Sandler gets a lot stick. Deservedly so, I might add, as the vast majority of his output is lazy, offensive, offensive in its laziness, and lazy in its offensiveness. But we’ve all seen Punch-Drunk Love. We know that—when harnessed by the right director—the man can act. There’s no way to tell how things might have been, but it’s likely that Michael Mann could have coaxed one of those once-in-decade performances out of Sandler. Nevertheless that remains pure speculation, because Sandler passed on the project due to other commitments.
We will never know if Sandler would have brought the goods for Collateral. All we do know, is that the man who ended up in the role instead completely owns it. Jamie Foxx knocks it out of the goddamn park as Max. Here is a man with whom we are with for almost the entirety of the movie’s running time, much of it in the cramped confines of his meticulously maintained cab. To sell his character, and his transformation, requires a great deal of control and understanding—and Foxx delivers with aplomb. We feel his journey intensely. Foxx’s Max is a deeply sympathetic and relatable character, trapped as he is in a holding pattern of life by his own fears. Max is stuck and unhappy, somewhat resigned to his fate, but at the same time he is quick, empathetic, and still has dreams, although we meet him at a time in his life when he seems to be slowly becoming content with letting them stay just that. Then along comes Vincent, and suddenly the stupor of Max’s years is shaken, violently, in far more terrifying and immediate ways than any paralysing anxiety he may have felt over his potential future before. Through this mortal threat, Max is vivified. Vincent, a cold-blooded killer with a penchant for nihilist repartee, brings out something in Max. As the night wears on, his fear transmutes into defiance. His personal safety stops mattering to him. At one point, he tosses Vincent’s mission-vital briefcase onto a freeway, and stands, scared but resolute, to meet the assassin’s fury. Later, near the climax of the movie, he calls out Vincent’s bullshit and vacant speechifying while speeding faster and faster down downtown L.A. The tipping point has been reached and Max can take no more. Suddenly the tables are turned and it is Vincent who’s scared. What has he unleashed in this mild-mannered cabbie? ‘Go fuck yourself!’ Max spits at Vincent, as he throws the car into a barrier at high speed, all sense of self-preservation now gone, putting his life into the hands of fate. It’s a tremendously heroic moment on Max’s part, and it only works because the character’s journey to this place has been so fully fleshed out. Jamie Foxx deserves all the credit for taking a fantastic script and making it sing.
Which brings us to Vincent. Tom Cruise’s greatest role, in what is probably the best film he will ever make. Hey, don’t worry, I see you, Magnolia. I’m not taking anything away from you, and I understand that direct comparisons between such wildly different movies are fundamentally silly, but there is just something about Vincent. Perhaps a better way to put it is not that Vincent is Tom Cruise’s greatest role, but that it is his most Tom Cruise role. Cruise is not exactly an actor with a dazzlingly wide range, or the most subtlety. His is a style of acting that relies heavily on physicality, charisma, and a certain dead-eyed intensity, and he brings all of that to Vincent—whose way of carrying and handling himself immediately sells the notion that this is more of a walking weapon rather than a man—but there’s something more here too. A hidden reservoir of internal conflict, starting to bubble slowly as the night goes on, and the nuanced way Cruise manages to portray these layers is quite unprecedented in his body of work. Vincent is meticulous in how he presents himself to world, priding himself on clinical detachment and cool professionalism. Yet something changes in him on his journey with Max, just as much as Max is transformed by Vincent. The two seem to have a genuine connection, and through a sort of two-way Stockholm syndrome, they bond, and though it all ends as it must, their impact on each other is undeniable. This co-evolution is one of the most compelling parts of Collateral, and Tom Cruise is a huge part of why it works. Where Cruise goes as an actor after he has aged past the point of being physically capable of leaping across roofs and grabbing onto planes will be an interesting thing to see. Whether he has it in him to transition into a different type of ‘serious’ performer is anyone’s guess. Collateral proves that he definitely had it in him once, and that seeing it coupled with his raw physicality was once a formidable sight indeed.
The movie is stacked with an excellent supporting cast too. Bruce McGill, Barry Shabaka Henley, Jada Pinkett Smith, Javier Bardem—they all flesh out Michael Mann’s L.A. beautifully, and they make Vincent and Max’s quasi-peripatetic quest a colourful and vibrant one. I am contractually obliged at this point to also highlight the star supporting player in all this: the Greatest Movie Detective of His Generation, Mark Ruffalo, who plays Detective Fanning, the one man who comes close to matching Vincent, and who almost rescues Max after one of the best shootouts in modern American cinema. There’s a real deliciousness to the way Collateral’s plot unfolds—a lean, relentless march of consequence and cause and effect, starting with the sheer chance that brings Vincent to Max’s cab—and Detective Fanning’s side of the story is a great illustration of that. It’s nothing new of course: Cop follows clues unwittingly left by criminal. But the urgency of the night, the fact that Vincent has everyone but Fanning fooled, and the intensity of Ruffalo’s performance makes it feel fresh. Despite the fact that I’ve spoken of Collateral largely as if it was a drama, the actual experience of watching it leaves you in no doubt of its thriller bonafides. The action is visceral, the suspense palpable.
I want to come back to that scene I mentioned at the start. Max’s taxi gliding through deserted streets. After that brief establishing shot, we cut into the cab, and a conversation between Vincent and Max. It’s a tense one, and the camera stays on Max in the front seat, with Vincent in the back, re-focusing on whoever is speaking. Max has just destroyed Vincent’s briefcase, and Vincent has told him the price to pay: Max is to go into a club to meet his contact, and to get a replacement for the briefcase’s content. It will be dangerous, possibly fatal, but Vincent leaves no doubt: Max has no choice here. On the drive to the club, Vincent is trying to establish a bit of normalcy, and he is waxing philosophical, but Max is taciturn. Something has shifted in him, and his relationship with Vincent is not what it was. The potential for agency has been glimpsed, and Max has been pushed almost as far as he will go. Vincent finishes his little speech, and you can tell he is discomfited by Max’s lack of engagement. Max, who previously had been hanging on his every word thanks to fear, now sits quiet, inscrutable. Uncharacteristically, Vincent trails off into silence with an uncertain, ‘…anyway…’ and we regard these two solitary people, adrift in a city that does not care, who had bonded, albeit perversely, through incredible circumstance. Now that bond has changed, and the loneliness of the metropolis reasserts itself. The taxi glides on, neon flits by, and suddenly things reach a perfect stillness. The car slows, and out of nowhere, two coyotes run across the road. One dashes across Max and Vincent’s way without pause. The second one slows as it passes and turns its head, its eyes glowing in the reflection of Max’s headlights. Both Max and Vincent stare, lost in the moment completely, as the coyote makes uncanny eye contact, appearing less of a physical form and more a manifestation of something mystical and unknown, something alive and vital in this city where a corpse can ride a train without anyone noticing. The coyote moves on and Chris Cornell’s mournful vocal comes onto the soundtrack. Max and Vincent carry on to the club, but they do so as if they had momentarily passed through another dimension. It’s an absolutely magical moment, and its poetic nature speaks to the kind of movie that Collateral is: A soulful, emotive, thrilling modern classic.
Petr is a staff contributor. You can follow him on Twitter. |
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9
Suppose 0 = m + 6*m - 294. Calculate the greatest common factor of m and 56.
14
Suppose -6*b + b = -105. Suppose -w + 2*w = b. What is the highest common factor of 3 and w?
3
Suppose 2*y = 5*y - 2*g - 21, 0 = -g - 3. Suppose -210 = 2*b - y*b. Calculate the greatest common factor of 10 and b.
10
Suppose -4*m + 110 + 33 = -5*f, 0 = -m + 4*f + 22. Calculate the greatest common divisor of 28 and m.
14
Suppose -d - 5*w = 10, 0 = -5*d - 0*d - w + 70. Let b = d - 12. Calculate the highest common divisor of 6 and b.
3
Let p be (576/45)/((-2)/20*-2). Calculate the greatest common factor of 32 and p.
32
Let w be 6/15 + 8/5. Let k be (1*-1)/(w/(-4)). Calculate the greatest common factor of 6 and k.
2
Suppose w - 2*t = 6, 5*w - 4*t - 50 = t. Let x be (1 - (-1)/2)*w. Suppose 0 = -16*n + 20*n - 56. What is the highest common factor of x and n?
7
Let q = 0 + 7. Calculate the greatest common factor of 56 and q.
7
Let b be 23/2 - 2/4. Suppose 7 = n - b. What is the highest common divisor of 12 and n?
6
Suppose 2*x - 5 = 1. Suppose 4*d = r + 10, -x*d = d + 4*r. What is the greatest common factor of 2 and d?
2
Let h(c) = c**2 - 14*c - 20. Let b be h(16). Calculate the highest common factor of b and 36.
12
Let h(p) = p**3 - 16*p**2 - 18*p + 20. Let w be h(17). Calculate the highest common factor of w and 33.
3
Suppose -3*k - k = 0. Suppose -3*i + 4*t = -11, k = 3*i + 2*t + 1. What is the highest common factor of 11 and i?
1
Let z(a) = a**2 - 7*a - 8. Let t be z(-4). Let f be -1 + (2 - 6/(-3)). Suppose -f*w = -5*w + 8. Calculate the greatest common divisor of t and w.
4
Suppose 4 = -4*r + 3*p, -p = -3*r + p - 2. Suppose -4*j - 27 = -2*g + 9, 36 = r*g + 4*j. What is the greatest common factor of g and 144?
18
Let l(z) = 2*z**3 + 2*z**2 + 1. Let k be l(3). Suppose 23 = -5*y + k. Let u be (-50)/(6/(-2) + 2). Calculate the highest common divisor of y and u.
10
Suppose 4*t - 11 - 49 = 0. Let p = -14 - -29. What is the greatest common divisor of p and t?
15
Let q be ((-5)/(-10))/((-3)/(-6)) + 10. Let t(i) = -i**3 - i**2 - i + 22. Let f be t(0). Calculate the greatest common divisor of f and q.
11
Let j(h) = -h**2 - 3*h - 1. Let y be j(-2). Let g(q) = 5 + 2*q**2 - q + 7*q + y. Let l be g(-5). What is the greatest common divisor of l and 13?
13
Suppose 0 = w - 4*s - 12, 5*s + 9 + 1 = 0. What is the greatest common divisor of 40 and w?
4
Let r be 19/2 + (-51)/34. Let d(k) = -k**3 + 8*k**2 + k + 5. Let x be d(r). What is the highest common divisor of x and 52?
13
Let f(y) = 35*y**2 + 1. Let k be f(-1). Let r = 24 + -15. What is the greatest common factor of k and r?
9
Let r = 39 + -3. Suppose -2*b = -5*b + 51. Let s = b + -5. What is the highest common divisor of r and s?
12
Suppose 0*i = -3*q + 4*i + 30, -16 = -2*q + 4*i. Let s = 16 - q. Let h(a) = a**2 + 3*a + 4. Let z be h(-6). What is the greatest common divisor of s and z?
2
Suppose 53*g = 49*g + 164. What is the greatest common divisor of 287 and g?
41
Let m be 882/5 - 4/10. Suppose 3*x - 5*v = 572, -5*v = x - 316 + 112. Let p be 5/(-30) + x/12. Calculate the greatest common divisor of p and m.
16
Suppose -5*u + 4*u = 3. Let j be -10*(u/(-3) + -2). What is the greatest common divisor of j and 1?
1
Suppose -3*r + q - 16 = 6*q, 4*r = q + 17. What is the highest common divisor of r and 6?
3
Let x(v) = -24*v - 15. Let w be x(-5). What is the greatest common divisor of 70 and w?
35
Suppose 96 = 4*t - 0*t. Calculate the greatest common factor of 36 and t.
12
Let d(y) = -y + 16. Let t be d(0). Suppose 5*i = -10 - 0. Let q = i + 18. What is the highest common divisor of q and t?
16
Suppose s + 19 = 33. What is the greatest common factor of s and 21?
7
Let d = -28 + 11. Let p = -9 - d. Calculate the highest common divisor of p and 8.
8
Let n be (0 - (-844)/10) + 24/(-60). Calculate the greatest common factor of 12 and n.
12
Suppose 4*m = -5*j + 5 - 48, -25 = 3*j + 2*m. Let h = j - -8. Calculate the greatest common factor of h and 10.
1
Let w = -20 - -22. Suppose -q + 2*q - 63 = 0. Suppose -b + q = w*b. Calculate the greatest common divisor of 3 and b.
3
Suppose 16*j - 2*j = 84. What is the greatest common divisor of 12 and j?
6
Let c = -126 - -142. Let o = -26 - -42. Calculate the greatest common divisor of c and o.
16
Let k = 50 - -181. Calculate the highest common divisor of 21 and k.
21
Let a = 46 - 27. Let q = a + -10. What is the highest common factor of q and 6?
3
Let a be (-1 - -1*3) + -2. Suppose a*i = -3*r - i + 1, -4*i = 5*r + 10. Let o be r + 2 + -1 + 1. What is the highest common divisor of o and 32?
4
Let z(g) = -g**3 + 9*g**2 - 8*g + 6. Let j be z(7). Calculate the greatest common divisor of 12 and j.
12
Let g(r) = -7*r - 2. Let v be g(-6). Calculate the highest common factor of 16 and v.
8
Let m = 384 + -258. What is the highest common factor of 18 and m?
18
Suppose 8 = -2*u + 6*u. Suppose -u*m + 32 = -12. Calculate the greatest common divisor of 55 and m.
11
Suppose -6*x - 60 = -7*x. Calculate the greatest common factor of x and 45.
15
Let n(r) = 3*r - 2. Let v be n(3). Suppose 33 = 2*i - v. Let z = -62 + 82. What is the highest common divisor of z and i?
20
Suppose 4*c + 14 - 54 = -2*o, 0 = 3*o + 3*c - 60. Let r be (6/9)/(2/(-66)). Let q = r - -32. Calculate the highest common factor of q and o.
10
Suppose 0 = 3*r - 2*r - 22. Calculate the highest common divisor of r and 11.
11
Let t = 159 + -95. Let f(q) = -4*q + 8. Let j be f(0). What is the highest common divisor of t and j?
8
Suppose -23 = 4*b + 2*v - 83, -v = 0. What is the highest common divisor of 45 and b?
15
Let j = -122 - -173. Suppose -2*b + 8 = -0*b. Suppose -j = -3*n - c, c = 5*n + b*c - 85. Calculate the highest common factor of 85 and n.
17
Let a(l) = -5*l - 223. Let s be a(-48). Let u(o) = 18*o**2 - o. Let z be u(1). Calculate the greatest common factor of s and z.
17
Let b be (-110)/4*(-12)/15. Let m = 109 + 45. Calculate the highest common factor of b and m.
22
Let x(r) = -r + 18. Let b be x(15). Suppose 2*u - 4*k = -0*k - 4, u - 18 = -b*k. What is the greatest common divisor of 24 and u?
6
Let u be 10*1/1*1. Suppose u = 4*f - 10. What is the greatest common divisor of 25 and f?
5
Let f = -21 - -41. Calculate the highest common factor of f and 20.
20
Let j = -4 - -64. Let w(q) = q**2 - 9*q - 6. Let u be w(10). Suppose -z = -f - 5*z - u, 2*f = -3*z + 12. What is the greatest common divisor of j and f?
12
Suppose -16 = 2*h - 4*h. Let w be 806/h - 2/(-8). Suppose -5*k = 4*z - w, -2*z - k = -0*z - 49. Calculate the greatest common factor of z and 36.
12
Let z be (-1)/1*(-30)/2. Suppose -1830 = -41*o + 630. What is the greatest common divisor of z and o?
15
Suppose -27 = 2*b - 135. Let h = -3 + 6. Suppose x - 72 = -h*x. What is the greatest common divisor of b and x?
18
Let a be (2 - (-6)/(-3))*1. Let y be -2 + (14 - (-1 - a)). Suppose z - 2*r = -r + 28, -z - 2*r = -22. What is the greatest common divisor of z and y?
13
Let y be 133/(-21) - 1/(-3). Let u be -2*y/(-15)*-15. What is the highest common factor of u and 60?
12
Suppose 36 = 3*b - 99. What is the highest common divisor of 18 and b?
9
Suppose -2*s = -s - 3. Suppose -s*q + 454 = -167. What is the greatest common divisor of q and 23?
23
Suppose 0 = 2*n + 18 - 74. What is the greatest common divisor of n and 42?
14
Suppose 3*i + 4*u - 39 = 0, -59 - 6 = -5*i + u. Let m = 6 + -1. Suppose -m*w + 3*c = -121, -41 = -w - 7*c + 2*c. What is the highest common factor of w and i?
13
Let u(b) = 24*b**2 + b + 2. Let z be u(-2). Let g(r) = -r + 18. Let d be g(6). What is the greatest common factor of d and z?
12
Suppose 0 = 16*a - 17*a + 8. Calculate the highest common divisor of a and 72.
8
Let j = -6 + 31. Suppose 175 = 4*w - j. What is the highest common divisor of w and 20?
10
Let a = 8 + -4. Suppose -43 = -a*x - 11. What is the highest common divisor of 8 and x?
8
Let u(i) = i**3 + 13*i**2 + 13*i + 30. Let z be u(-12). What is the greatest common divisor of 9 and z?
9
Suppose 56 + 72 = 2*m. What is the greatest common factor of 8 and m?
8
Let f be (4 - -16) + -1 + 1. Let d be 2*(35/2)/5. Let g(u) = u**3 - 7*u**2 + 8*u - 6. Let s be g(d). Calculate the highest common divisor of f and s.
10
Suppose -296 = -3*j - 3*z + 157, -j + 142 = 4*z. Calculate the greatest common divisor of 14 and j.
14 |
333 P.2d 607 (1958)
65 N.M. 119
William P. KEARNS, Jr., Chief of the Division of Liquor Control, Appellant,
v.
Juan P. ARAGON, d/b/a Juan's Beer Garden, Appellee.
No. 6450.
Supreme Court of New Mexico.
December 15, 1958.
Rehearing Denied January 16, 1959.
Charles B. Barker, Santa Fe, for appellant.
Chavez & Cowper, Belen, for appellee.
COMPTON, Justice.
This appeal is taken by the Chief of Liquor Control, hereinafter referred to as the Chief, from the order of the District Court of Santa Fe County setting aside his order revoking appellee's liquor license.
*608 Appellee, the holder of dispenser's license No. 199 authorizing him to operate a bar in Valencia County, New Mexico, was charged with making a sale of intoxicating liquor on Sunday in violation of Section 46-10-14, NMSA, 1953 Compilation.
At a hearing upon the complaint before the Chief, Eddleman, a state police officer, testified that appellee sold him a bottle of whiskey on Sunday, April 14, 1957. This testimony was partially corroborated by Daves, another state police officer. Appellee flatly denied making any such sale. In addition, appellee moved for dismissal on the ground that he had been entrapped into committing the offense. This motion was denied by the Chief.
The Chief found that appellee had made the illegal sale as charged, and pursuant to the authority vested in him by Section 46-6-2(g), NMSA, 1953 Compilation, revoked his license.
Appellee appealed the order of the Chief to the district court for Santa Fe County and the case was tried solely on the record made in the proceeding before the Chief. The district court reversed the decision of the Chief finding that the action of the state police in bringing about the alleged sale constituted entrapment.
The court also concluded that the action of the Chief was arbitrary, capricious and unreasonable.
Upon review, this court must determine whether the order or findings of the Chief were sustained by substantial, competent, relevant and credible evidence. Section 46-6-6, NMSA, 1953 Compilation. See Gonzales v. New Mexico State Board of Embalmers and Funeral Directors, 63 N.M. 13, 312 P.2d 541.
We believe the order of the Chief was so supported. A portion of Officer Eddleman's testimony was as follows:
"We drove up to the establishment of Juan's Beer Garden between the house and the bar. We got out of our car. At this time we noticed Juan and his wife and a little boy coming out of the bar. We approached them and went inside the bar and stopped right at the edge of the bar and asked if there would be any chance of buying any liquor. He then stated that it was Sunday and there would be no chance. We started out the door. He stated if one of you come later there might be a chance, so we got in our car and left. We fooled around town for a little while and then we went back at approximately 7 P.M. where at this time I left Officer Daves off about a half block from Juan's Beer Garden on the road. I approached the house. The house was dark and also the bar. I parked the car in the same place between the house and the bar and got out and knocked on the rear door of the house. Juan can to the door and I asked if there would be any chance of buying any liquor then. He stepped out of the door and on the steps and observed my car and he then stated, `You can buy some any time if you are by yourself.' So we went over to the bar. He unlocked the door and we went inside. He asked what kind I liked and how much and I said I would like to have a half-pint of Schenley's. He looked over the stock and told me he didn't have any Schenley's in stock and if H and H would be sufficient. I said it would. He gave me the bottle; I gave him a five dollar bill. He gave me back three dollars and a quarter. I then walked to the door, opened the door and stood right in front of the door holding the bottle in front of me where Officer Daves could see it, making conversation with Juan, Mr. Aragon. At this time he said he had to be very careful because there had been other raids from State Police and at this time I informed, I showed him my credentials and informed him I was a New Mexico State Police and that `You are under arrest' and he said `That's all right,' he said, `It's your word against mine.' I then said that Officer Daves was present and he then stated that he had *609 to go into the house. I told him to get in the car and he proceeded on in the house. I followed him in the first door and then turned around and came back out. At this time Officer Daves was there and I told him to go to the front door. I stood at the rear door. I moved my car from behind the house around to the north side of the house. I stood by the rear door. I heard, I don't know exactly what it was, it seemed like some drawers moving in the bedroom. I heard a screen open and about a minute later Officer Daves came around and told me the man had a gun sticking out the window. We then proceeded to get in my car and go over to the Town of Belen and phone Officer Stringfellow of the State Police. We then went to a Justice of the Peace and filed a complaint for illegal sale of liquor and resisting arrest, pending by Sergeant Vigil and Captain Bradford. We then called Sergeant Vigil at Albuquerque."
Appellee makes much of the fact that the court reporter and perhaps others, first understood Witness Eddleman to say that the whiskey he purchased was H & H, while the bottle placed in evidence was Ancient Age. The witness explained on cross-examination that he had said Ancient Age. We attach no particular significance to this point in view of the fact that when H and H and Ancient Age are spoken it is somewhat difficult for the ear to distinguish between the two terms.
Officer Daves testified in part as follows:
"* * * He (appellee) stated for us to go on but if one of us come back, that he would sell us some whiskey, some liquor. We left then and drove around town and observed other bars until around 7 P.M., and I guess. We then went back to Juan's Beer Garden and I got out around a half a block to a block from the bar and Officer Eddleman drove his car on up into the yard there and after I got out, I started walking toward the bar. It wasn't dark yet, but it was kind of hazy, and when I got I saw I did see Officer Eddleman and Mr. Aragon go into the bar and I kept on walking toward the bar and when they come out shortly, they stood there at the door for a few seconds, I don't know how long, and all of this time I was walking toward them and while they were standing there I saw a bottle in Officer Eddleman's hand that he was holding up in front of him. * * *"
The Chief who heard the testimony and had an opportunity to observe the demeanor of the witnesses, stated as follows in his order.
"that the testimony of the State's witness instant violation was very convincing. * * *"
After reviewing the testimony taken in the proceedings before the Chief we are of the opinion that the order was supported by substantial, competent, relevant and credible evidence. Even assuming that the action of the State police officers constituted entrapment, this fact alone does not render their testimony unsubstantial, incompetent, irrevelant or incredible. As we held in State v. Romero, 49 N.M. 129, 133, 158 P.2d 851, the mere circumstance, standing alone, that the State's witnesses were engaged in a species of entrapment does not render their testimony unworthy of belief. See In re Wellcome, 23 Mont. 450, 59 P. 445.
The Chief contends that since the appellee took the stand and denied under oath that he had made the alleged Sunday sale, he is precluded from raising the defense of entrapment. Appellee of course urges to the contrary. We have found well reasoned cases supporting both views, but as will be seen it is unnecessary to decide this point.
A proceeding before the Chief to revoke a liquor license is not a criminal proceeding; rather it is an administrative proceeding in the nature of a civil action. Bradley v. Texas Liquor Control Board, Tex.Civ.App., 108 S.W.2d 300; Commonwealth v. Lyons, 142 Pa.Super. 54, 15 A.2d *610 851; Kravis v. Hock, 137 N.J.L. 252, 59 A.2d 657. This is true even though the charge and ground for revocation is the violation of a penal statute. Keller v. Kentucky Alcoholic Beverage Control Board, 279 Ky. 272, 130 S.W.2d 821; Boyd v. Allen, 246 N.C. 150, 97 S.E.2d 864.
Section 46-6-4(m), NMSA, 1953 Compilation, makes this quite clear in providing that no admission of guilt, admission against interest or transcript of testimony taken in hearings before the Chief is admissible in a criminal prosecution against a licensee.
Nor is the object of an administrative proceeding to revoke a liquor license intended as a punishment of the licensee. The purpose is to insure so far as possible the decent and orderly conduct of a business affecting the public health, morals, safety and welfare. Flowers v. Benton County Beer Board, Tenn. 302 S.W.2d 335; Cornell v. Reilly, 127 Cal. App.2d 178, 273 P.2d 572. State control of the liquor business under the police power is so great as to range from complete prohibition to lesser degrees of regulation and constant surveillance. Boyd v. Allen, 246 N.C. 150, 97 S.E.2d 864. See Floeck v. Bureau of Revenue, 44 N.M. 194, 100 P.2d 225.
Hence, revocation proceedings are not governed by the rules of law applicable to criminal prosecutions. In such proceedings the offense need not be established beyond a reasonable doubt. Pennsylvania Liquor Control Board v. Summit Hill Rod and Gun Club, 184 Pa.Super. 584, 135 A.2d 781; Kravis v. Hock, 137 N.J.L. 252, 59 A.2d 657. The constitutional defenses of unreasonable search and seizure and self-incrimination are not available in similar proceedings. Camden County Beverage Co. v. Blair, D.C., 46 F.2d 648. In liquor license revocation proceedings proof of general reputation is not treated as substantive evidence to air in determining guilt or innocence. Commonwealth v. Lyons, supra. Likewise, and decisive for purposes of this case, entrapment is not a defense in an administrative proceeding to revoke a liquor license. In a civil proceeding for the forfeiture of contraband liquor, the Missouri court held that the defense of entrapment was not available since the "defendant is not being tried here for a criminal offense." State v. Ward, 361 Mo. 1236, 239 S.W.2d 313, 320.
Our decision goes no further than to hold that the defense of entrapment is not available in a proceeding to revoke a liquor license. Nonetheless, we wish to point out that many courts have gone considerably further in restricting the defense of entrapment. In some jurisdictions, notably Tennessee and New York, the defense of entrapment is not recognized in any criminal action. Goins v. State, 192 Tenn. 32, 237 S.W.2d 8; People On Complaint of Klein v. Schacher, Mag.Ct., 47 N.Y.S.2d 371.
In a number of jurisdictions the defense of entrapment has no application in criminal prosecutions for violating liquor laws. The rationale of these decisions is that to constitute entrapment the criminal intent must originate in the mind of the entrapper, and since no intent is necessary to violate liquor laws, an essential element of entrapment is absent. French v. State, 149 Miss. 684, 115 So. 705; State v. Driscoll, 119 Kan. 473, 239 P. 1105; State v. Merklinger, 180 Kan. 283, 303 P.2d 152; State v. Varnon, Mo., 174 S.W.2d 146; State v. Sheeler, 320 Mo. 173, 7 S.W.2d 340.
In the case of State v. Broaddus, 315 Mo. 1279, 289 S.W. 792, 795, the court stated this principle as follows:
"Whatever may be the general rule in regard to the effect upon the right to convict a defendant who has been entrapped into the commission of a crime (18 A.L.R. 146, 149), it is usually held to have no application to cases involving the sale of intoxicating liquors or other violations of the Prohibition Laws. In this class of cases criminal intent is not, as a rule, a necessary element and need not be shown."
In a similar vein is the following statement by the Virginia court in Bauer v. *611 Commonwealth, 135 Va. 463, 115 S.E. 514, 515:
"But whatever may be said against enticing one to commit crime, the decided weight of authority is that one who makes an unlawful sale of liquor, or unlawfully transports it, is not excused from criminality by the fact that he was induced to do the criminal act for the sole purpose of prosecuting him for it. Initiative on the part of the perpetrator of an offense of this nature is not essential to charge him with criminal responsibility."
In view of what has been said above, the judgment of the district court must be reversed and the cause remanded with a direction to set aside its judgment and enter another affirming the order of the Chief.
It is so ordered.
McGHEE and SHILLINGLAW, JJ., concur.
LUJAN, C.J., and SADLER, J., not participating.
|
---
abstract: 'We construct a path-integral representation of the generating functional for the dissipative dynamics of a classical magnetic moment as described by the stochastic generalization of the Landau-Lifshitz-Gilbert equation proposed by Brown [@Brown1963], with the possible addition of spin-torque terms. In the process of constructing this functional in the Cartesian coordinate system, we critically revisit this stochastic equation. We present it in a form that accommodates for any discretization scheme thanks to the inclusion of a drift term. The generalized equation ensures the conservation of the magnetization modulus and the approach to the Gibbs-Boltzmann equilibrium in the absence of non-potential and time-dependent forces. The drift term vanishes only if the mid-point Stratonovich prescription is used. We next reset the problem in the more natural spherical coordinate system. We show that the noise transforms non-trivially to spherical coordinates acquiring a non-vanishing mean value in this coordinate system, a fact that has been often overlooked in the literature. We next construct the generating functional formalism in this system of coordinates for any discretization prescription. The functional formalism in Cartesian or spherical coordinates should serve as a starting point to study different aspects of the out-of-equilibrium dynamics of magnets. Extensions to colored noise, micro-magnetism and disordered problems are straightforward.'
author:
- |
Camille Aron$^{1}$, Daniel G. Barci$^2$, Leticia F. Cugliandolo$^3$,\
Zochil González Arenas$^4$, and Gustavo S. Lozano$^{3,5}$\
$^1$[Department of Physics and Astronomy, Rutgers University, Piscataway, NJ 08854, USA]{}\
[& Department of Electrical Engineering, Princeton University, Princeton, NJ 08544, USA]{}\
$^2$[Departamento de F[í]{}sica Teórica, Universidade do Estado do Rio de Janeiro,]{}\
[Rua São Francisco Xavier 524, 20550-013, Rio de Janeiro, RJ, Brazil]{}\
$^3$[ Sorbonne Universités, UPMC Univ Paris 06, UMR 7589, LPTHE, F-75005, Paris, France]{}\
$^4$ [Centro Brasileiro de Pesquisas Físicas]{}\
[& National Institute of Science and Technology for Complex Systems,]{}\
[Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, RJ, Brazil,]{}\
[on leave from Instituto de Cibernética, Matemática y Física, Cuba]{}\
$^5$[Departamento de Física, FCEYN Universidad de Buenos Aires & IFIBA CONICET,]{}\
[Pabellón 1 Ciudad Universitaria, 1428 Buenos Aires, Argentina]{}
bibliography:
- 'magn-FDT.bib'
title: 'Magnetization dynamics: path-integral formalism for the stochastic Landau-Lifshitz-Gilbert equation'
---
Introduction
============
The control of magnetic materials [@Hillebrands2002; @Mattis1988; @Mattis1985], already at the heart of the information technologies developed in the second half of the twentieth century, is undergoing a second revolution with the development of spintronics [@Johnson1985; @Brataas12].
In ferromagnetic materials, the spin degrees of freedom carried by localized electrons tend to spontaneously long-range order below the Curie (second order) transition temperature. The so-called micromagnetic description consists in studying the local order parameter, $\mathbf{M}(\mathbf{x},t)$, the expectation value of the magnetization per unit volume averaged over, typically, a few lattice cells. In most relevant cases, this macroscopic composite object can be treated classically.
The spin-spin interaction is essentially due to the overlap of the electronic wave functions. Below the Curie temperature, this is the dominant interaction. The modulus of the local magnetization can be approximated by a temperature-dependent constant which takes the value of the spontaneous magnetization at the working temperature, [*i.e.*]{} $|\mathbf{M}(\mathbf{x},t)|=M_{{\rm s}}$. The direction of ${\mathbf M}$ is, instead, subject to the interactions and external forces, and it is non-uniform in space and varies in time.
When a ferromagnet is used to store information, bits are encoded in the orientation of the local magnetization. Usually, the magnetization is manipulated by applying Oersted fields generated by electric currents.
Very early, damping, *i.e.* the transfer of spin angular momentum from the magnetization of the macrospin $\mathbf{M}(\mathbf{x},t)$ to the environment, became a matter of fundamental but also applied interest. Indeed, this is an important limiting factor in the reduction of the remagnetization rate in magnetic recording devices. The complex environment of the macrospin offers many different mechanisms for damping (spin-orbit coupling, coupling to the lattice vibrations, spin-waves, *etc.*). In 1935, Landau and Lifshitz [@Landau-Lifshitz] (LL) proposed a phenomenological classical equation to account for all these processes through a unique damping coefficient. Though the LL equation yields reasonable results for small damping coefficient, it was initially taken to be unphysical as it predicts an acceleration of the magnetization precession at large damping. Some years later, Gilbert [@Gilbert55; @Gilbert04] cured this problem by proposing an equation in which damping enters in a different manner. Ultimately, the two equations are equivalent after a redefinition of the parameters. Today, the latter equation is known as the Landau-Lifshitz-Gilbert (LLG) equation. Its inherent non-linearity makes it a difficult problem to solve, but also the source of very rich phenomena. Explicit solutions can be obtained in some particular cases but the generic cases require numerical integration [@Bertotti-etal; @Cimrak2008]. The dynamics of magnetic moments ruled by the LLG equation have been the focus of considerable research over the last 60 years.
For sufficiently small ferromagnetic particles, thermal fluctuations can become relevant in determining the magnetization dynamics. In 1963, Brown [@Fuller63] proposed a simple extension of the LLG equation in which thermal agitation is introduced *à la* Langevin, *i.e.*, *via* the addition of a random magnetic field the correlation of which is proportional to the temperature. As already shown by Brown, the stochastic magnetization dynamics can also be analyzed within the Fokker-Planck framework, that is, *via* the partial differential equation satisfied by the time-dependent probability distribution. Since then, thermal effects in the magnetization dynamics have been studied in great detail [@Bertotti-etal]. Moreover, progress in computational capabilities have now made possible numerical solutions of realistic situations [@Cimrak2008; @Aditi2012].
A new means to manipulate the magnetization of ferromagnetic devices *via* the spin-transfer torque effect has opened a new perspective into magnetic storage technologies. It has also renewed the interest in the study of magnetization dynamics. Pioneered by the theoretical work by Slonczewski [@Slonczewski1996] and Berger [@Berger1996], it was realized almost two decades ago that one could also manipulate the magnetization by exchanging angular momentum with a spin-polarized current of electrons. This proposal rapidly found some experimental evidence [@Tsoi1998; @Myers1999] and, since then, the rapid advances in the field of spintronics have led to everyday life applications such as high-density magnetic recording devices (see, for instance, [@Brataas12] for a short review). Although quantum in origin, the spin-transfer torque effect can be handled phenomenologically by an appropriate generalization of the LLG equation. The LLG equation also appears in the context of molecular spintronics as a semi-classical limit of a full quantum problem [@Brataas02; @Parcollet05; @Brataas08; @Bode11].
In the quest for smaller and smaller devices with higher storage density capabilities, it has recently become crucial to take into account the effect of thermal fluctuations on the magnetization dynamics. Indeed, smaller magnetic domains are more prone to thermally activated magnetization reversal because the energy barrier is proportional to the volume of the domain. Furthermore, as one seeks to reduce the intensity of the currents used in magnetic devices (to reduce both power consumption and Joule heating), thermal fluctuations limit the signal-to-noise ratio.
Most of the existing literature dealing with thermal effects in the magnetization dynamics of nanoparticles and nano-devices analyze the problem either by direct numerical simulation of the stochastic LLG equation or *via* the study of the corresponding Fokker-Planck equation [@Coffey12]. Yet, within the study of general stochastic processes there exists also the possibility of approaching the problem *via* the path integral formulation of generating functionals [@Martin73; @Janssen76; @deDominicis76]. The use of generating functionals is an elegant and powerful method to derive generic properties of dynamical systems. Compared to the other approaches mentioned above, a path-integral is handy for computing moments, probability distribution functions, transition probabilities and responses. It is also particularly well suited when it comes to perturbation theory and renormalization group analysis, as one can easily set up a diagrammatic expansion. This approach has proven to be extremely useful to treat many physical systems. Two problems of current interest that have points in common with ours are the path-integral formulation of the motion of a Brownian particle confined to a finite volume [@Lubensky2007] and the path-integral formulation [@Andreanov05; @Velenich2008; @Kim2013] of a system of interacting Langevin processes [@Dean97].
In this manuscript, we build the framework for a path-integral description of the magnetization dynamics described by the stochastic LLG equation. The expert reader, eager to see the actions in their various forms, can jump to Eqs. (\[eq:S\_det\_cart00\]), (\[eq:S\_diss\_cart00\]) and (\[eq:S\_jac\_cart00\]) for the Landau action, and Eqs. (\[eq:SLLGjac-det\])-(\[eq:SLLGjac-jac\]) for the Gilbert action both in Cartesian coordinates; or to Eqs. (\[eq:action-det-sph-L2\])-(\[eq:esferica-jac\]) for the Landau action, and Eqs. (\[eq:action-det-sph-Gilbert-maintext\])-(\[eq:action-jac-sph-Gilbert-maintext\]) for the Gilbert action both in spherical coordinates.
The manuscript is organized as follows. In Sec. \[sec:landau-lifshitz-gilbert\] we introduce the stochastic LLG equation in its Landau-Lifshitz and Gilbert formulations, and we discuss the physical significance of each of its terms.
In Sec. \[sec:prescriptions\] we discuss the discretization of the stochastic integrals; the prescription used has to be carefully specified since it is a defining part of the dynamics in multiplicative random processes. We explain how the conservation of the magnetization magnitude imposes the Stratonovich discretization prescription if one persists in using the original LLG equation, or guides one into generalizations of it if the choice is to use other discretization schemes. This is particularly useful for numerical simulations for which the Itô prescription has been claimed to be simpler to implement.
In Sec. \[sec:functional\], we derive the generating functional of the local magnetization by using the Martin-Siggia-Rose-Janssen-deDominicis (MSRJD) path integral [@Martin73; @Janssen76; @deDominicis76], which was originally introduced in the context of conventional Langevin equations. Although, the MSRJD formalism is well understood for systems with additive noise or with inertia (see, for instance, [@AronLeticia2010]), the stochastic LLG equation is a Markovian first order stochastic differential equation with multiplicative white noise bringing in extra difficulties such as a non-trivial Jacobian [@arenas2010; @arenas2012a; @arenas2012; @Lubensky2007; @Honkonen] that contributes to the action.
In Sec. \[sec:spherical-coordinates\] we reset the general discretization scheme formulation of the stochastic LLG equation in the spherical coordinate system. *A priori*, this is the natural coordinate system for numerical simulations since the non-linear constraint on the modulus of the magnetization is built in, lowering the dimensionality of the problem from $3d$ to $2d$. However, the random noise transforms non-trivially to the new coordinate system and, in particular, it is correlated with the polar angles, a fact that has often been overlooked in the literature. We therefore correct the widespread but erroneous assumption stating that the two-dimensional random field in spherical coordinates is a simple Gaussian white noise with vanishing mean. We end this Section with the derivation of the generating functional in the spherical coordinate system.
Finally, in Sec. \[sec:recap\] we recap our results and we announce a number of applications of the formalism here introduced that we plan to investigate in the future.
Technical details are reported in the Appendices.
Magnetization dynamics {#sec:landau-lifshitz-gilbert}
======================
Let ${\mathbf M}({\mathbf x},t)$ be the three-dimensional vector describing the local magnetization in a ferromagnet and let us assume that its modulus is constant, and equal to the spontaneous magnetization of the ferromagnet at the working temperature $T$: $|{\mathbf M}({\bf x},t)| \equiv M_{{\rm s}}$. For simplicity, we also assume that the space dependence can be neglected, that is to say, we work in the macro-spin approximation, and we later introduce the time-dependent unit vector ${\mathbf m}(t)$ through ${\mathbf M}(t)=M_{{\rm s}}{\mathbf m}(t)$. We will not follow the historic route in the presentation but rather give a presentation that we find more natural.
Landau-Lifshitz-Gilbert (LLG) equation
--------------------------------------
Whenever thermal fluctuations are negligible, the dissipative dynamics of the magnetization can be described by the Landau-Lifshitz-Gilbert (LLG) equation [@Gilbert55; @Gilbert04] $${{\rm d}}_t \mathbf{M} = - \gamma_0 {\mathbf{M}} \wedge \left( {\mathbf{H}}_{{\rm{eff}}}
-\frac{\eta}{M_{{\rm s}}} {{\rm d}}_t \mathbf{M} \right)
\; ,
\label{eq:Gilbert}$$ where ${{\rm d}}_t$ denotes the time derivative ${{\rm d}}/{{\rm d}}t$. The modulus of the magnetization is automatically conserved thanks to the cross product denoted $\wedge$. $\gamma_0\equiv\gamma \mu_0$ is the product of $\gamma$, the gyromagnetic ratio relating the magnetization to the angular momentum, and $\mu_0$, the vacuum permeability constant. The gyromagnetic factor is given by $\gamma=\mu_B g/\hbar$ (in our convention $\gamma>0$ for the electronic spin) with $\mu_B$ Bohr’s magneton and $g$ Lande’s $g$-factor. The first term in the [rhs]{} describes the magnetization precession around the local effective magnetic field $\mathbf{H}_{{\rm{eff}}}$, while the second term is a phenomenological description of the dissipative mechanisms, introduced by Gilbert, which slow down this precession and push ${\mathbf M}$ towards the magnetic field ${\mathbf H}_{\rm eff}$ while keeping the modulus $M_{{\rm s}}$ fixed. In principle, dissipation could enter the problem with a memory kernel because the feedback of the environment on the magnetization involves, *a priori*, retardation effects. In that perspective, the choice of $\eta \mathbf{M} \wedge {{\rm d}}_t \mathbf{M} /M_{{\rm s}}$ for the dissipative torque can then be understood as the first term of a derivative expansion. The damping constant $\eta$ takes into account several dissipative mechanisms (spin-orbit coupling, magnon-phonon, magnon-impurity, etc.). Dimensions are such that $[H]= [\gamma_0]^{-1} [t]^{-1}$ and $[\gamma_0\eta]=1$. In most relevant cases, such as magnetic recording, one has $\gamma_0\eta\ll 1$.
The local effective magnetic field can be divided into conservative and non-conservative contributions, $$\mathbf{H}_{{\rm{eff}}}= \mathbf{H}_{{\rm{eff}}}^{\rm c} + \mathbf{H}_{{\rm{eff}}}^{\rm nc} \;.$$ The conservative contribution $\mathbf{H}_{{\rm{eff}}}^{\rm c}=-\mu^{-1}_0 \delta U/\delta {\mathbf{M}}$, with $U$ the energy per unit volume, can originate from an external (possibly time-dependent) magnetic field $\mathbf{H}_{{\rm{ext}}}$, and a crystal field $\mathbf{H}_{{\rm{ani}}}$ associated to the crystalline anisotropy, $$U=- \mu_0\mathbf{M} \cdot {\mathbf{H}}_{{\rm{ext}}} + V_{{\rm{ani}}}(\mathbf{M})
\; .$$ $V_{{\rm{ani}}}$ is here the anisotropy potential (per unit volume). Examples of anisotropy potentials are [@Bertotti-etal] $${V}_{{\rm{ani}}}(\mathbf{M}) = K \sum_{i\neq j} M^2_i M^2_j
\; , \qquad\qquad i,j = x,y,z
\; ,
\label{eq:cubic-anisotropy}$$ corresponding to a cubic crystalline structure (each of the three Cartesian axes is a minimum of this function), or $${V}_{{\rm{ani}}}(\mathbf{M}) = K (M_{{\rm s}}^2-M_{z}^2)
\; ,
\label{eq:uniaxial}$$ associated to the uniaxial symmetry (having a minimum along the so-called easy axis, here the $z$-axis). We will give a very timely example of non-conservative ${\mathbf H}^{\rm nc}_{\rm eff}$, the spin-torque term, in Sec. \[sec:spin-torque\]. From the very structure of the equation, one sees that only the instantaneous component of the effective field, ${\mathbf H}_{\rm eff}= {\mathbf H}^\perp_{\rm eff} + {\mathbf H}^\parallel_{\rm eff}$, that is perpendicular to the magnetization, *i.e.* ${\mathbf H}_{\rm eff}^\perp$ such that ${\mathbf H}_{\rm eff}^\perp \cdot {\mathbf M} =0$, has an effect on its dynamics. Indeed, the field appears as $${\mathbf M} \wedge {\mathbf H}_{\rm eff} = {\mathbf M} \wedge {\mathbf H}^\perp_{\rm eff}
\; .$$
The LLG equation can be written in the equivalent form [@Landau-Lifshitz] $${{\rm d}}_t {\mathbf{M}} =
- \frac{\gamma_0}{1+\gamma_0^2 \eta^2}
\mathbf{M} \wedge
\left(
{\mathbf{H}}_{{\rm{eff}}}
+ \frac{\eta \gamma_0}{M_{{\rm s}}} {\mathbf{M}} \wedge {\mathbf{H}}_{{\rm{eff}}}
\right)
\; ,
\label{eq:landau}$$ by simply factorizing the time-derivatives on the left-hand-side of Eq. (\[eq:Gilbert\]). In the rest of this manuscript, we shall refer to Eq. (\[eq:Gilbert\]) and Eq. (\[eq:landau\]) as the Gilbert and the Landau formulation of the same LLG equation, respectively.[^1] (We will come back to the passage from one to the other in Sec. \[sec:functional\].)
Depending on the space dimension and the interactions, the LLG can exhibit a variety of non-linear structures (solitons, spatio-temporal patterns, etc.), see [@Lakshmanan2013] for a review. In some particular cases explicit solutions are known but the generic problem requires numerical integration [@Bertotti-etal; @Cimrak2008].
Stochastic LLG equation
-----------------------
In 1963, Brown [@Fuller63] showed that thermal fluctuations can be taken into account by adding a random field, ${\mathbf H}$, [*à la*]{} Langevin in Eq. (\[eq:Gilbert\]) $${{\rm d}}_t {\mathbf{M}} = - \gamma_0 {\mathbf{M}} \wedge \left( \mathbf{H}_{{\rm{eff}}}+ \mathbf{H} - \frac{\eta}{M_{{\rm s}}}{{\rm d}}_t{\mathbf{M}} \right)
\label{eq:sLLG1}$$ or, equivalently, by adding this field in Eq. (\[eq:landau\]) $${{\rm d}}_t {\mathbf{M}} =
- \frac{\gamma_0}{1+\gamma_0^2\eta^2}
\mathbf{M} \wedge
\left[
(\mathbf{H}_{{\rm{eff}}} + \mathbf{H})
+ \frac{\eta\gamma_0}{M_{{\rm s}}} \mathbf{M} \wedge ( \mathbf{H}_{{\rm{eff}}} +\mathbf{H})
\right]
\; .
\label{eq:sLL1}$$ Assuming that the thermal environment is composed of a large number of degrees of freedom and that the time-scale on which they relax is the shortest one in the problem, it is natural to consider Gaussian white noise statistics for the stochastic field. In formal terms, $$\label{eq:HhatD}
\langle H_i(t) \rangle_{\mathbf H} = 0
\;, \qquad
\langle H_i(t) H_j(t') \rangle_{\mathbf H} = 2 D \delta_{ij} \delta(t-t')
\; ,$$ for all $i,j=x,y,z$. The parameter $D$ is such that the fluctuation-dissipation relation of the second kind (in Kubo’s terminology [@Kubo66]) is satisfied, that is to say, that the sLLG equation takes the magnetization to equilibrium, *i.e.* with a Gibbs-Bolztmann distribution function at the temperature $T$ of the environment. As we will show explicitly in Sec. \[sec:Fokker-Planck\], its relation to the parameters in the problem is $$D = \frac{\eta k_{\rm B}T}{M_{{\rm s}}V \mu_0}
\; .$$ $V$ is the volume of the sample and $k_{\rm B}$ the Boltzmann constant. Dimensions are such that $[D] = [t] [H^2]$.
In both Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]), the noise couples multiplicatively to the time-dependent magnetization. To completely define the Markovian dynamics of such a stochastic equation with multiplicative white noise, one needs to specify a prescription for the way in which the noise acts at a microscopic time level. As we will discuss in more detail in Sec. \[sec:prescriptions\], written as they are, Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]) have to be understood as Stratonovich equations, *i.e.* with a mid-point prescription [@Bertotti-etal; @Langevin-Coffey; @Martinez-etal], as this is the unique scheme consistent with the conservation of the modulus of the magnetization. Henceforth, we will refer to these equations as the [*stochastic Stratonovich*]{} Landau-Lifshitz-Gilbert equations. We will also show in Sec. \[sec:prescriptions\] how to generalize these equations to use other discretization schemes.
It can be useful to work with adimensional variables and parameters. If one defines $\gamma_0 M_{{\rm s}}t \mapsto t$, $\mathbf{M}/M_{{\rm s}}\mapsto \mathbf{m}$, $\mathbf{H}_{{\rm{eff}}}/M_{{\rm s}}\mapsto \mathbf{h}_{{\rm{eff}}}$, $\mathbf{H}/M_{{\rm s}}\mapsto \mathbf{h}$, and $\eta\gamma_0 \mapsto \eta$ the dynamical equation becomes $${\rm d}_t {\mathbf{m}} =-
{\mathbf{m}} \wedge \left(\mathbf{h}_{{\rm{eff}}} + {\mathbf{h}} - \eta \ {\rm d}_t{\mathbf{m}} \right)
\;,
\label{eq:sLLG1-adim}$$ or $${\rm d}_t {\mathbf{m}} =-
\frac{1}{1+\eta^2} \ \mathbf{m} \wedge
[(\mathbf{h}_{{\rm{eff}}}+ \mathbf{h}) + \eta \ {\mathbf{m}} \wedge(\mathbf{h}_{{\rm{eff}}}+ \mathbf{h} ) ]
\; .
\label{eq:sLL1-adim}$$ The Gaussian white noise ${\mathbf h}$ has zero average and correlations characterized by a new diffusion constant, $\gamma_0 D/M_{{\rm s}}\mapsto D$, $$\langle h_{i}(t) \rangle_{\mathbf h} = 0
\;, \qquad
\langle h_{i}(t) h_{j}(t') \rangle_{\mathbf h} = 2 D \ \delta_{ij} \delta(t-t')
\; .$$ All variables and parameters are now adimensional. Here again, the Gilbert and Landau stochastic Eqs. (\[eq:sLLG1-adim\]) and (\[eq:sLL1-adim\]) have to be understood as Stratonovich equations and are totally equivalent.
Spin-torque {#sec:spin-torque}
-----------
The LLG equation (\[eq:Gilbert\]) or its stochastic version (\[eq:sLLG1\]) can also be used to describe spin-transfer torque in magnetic multilayers [@Slonczewski1996; @Berger1996]. By means of this effect, a spin-polarized electric current flowing through the multilayer can affect the orientation of the magnetization in one of the layers (the free moving one). Although the origin of this effect is quantum mechanical, it can be phenomenologically studied by adding to the LLG equation an extra “torque" term which depends on the relative position of the layers, their polarization, the electrical current, and other properties of the material. This effect has been the topic of a tremendous amount of work during the last 15 years due to its many potential applications in the field of spintronics. In its simpler form, the Landau-Lifshitz-Gilbert-Slonczewski equation reads [@Stiles2006] $${{\rm d}}_t {\mathbf{M}} = - \gamma_0 {\mathbf{M}} \wedge \left(\mathbf{H}_{{\rm{eff}}} + {\mathbf H}
- \frac{\eta}{M_{{\rm s}}} {{\rm d}}_t \mathbf{M} \right)
- \frac{g \mu_B J {\cal P}}{2 M_{{\rm s}}^2 d e} \mathbf{M} \wedge (\mathbf{M} \wedge \mathbf{p})
\; ,
\label{eq:sLLG1-spintorque-dim}$$ where we singled out from ${\mathbf H}_{\rm eff}$ the spin-torque term. Here, $g\mu_B = \gamma\hbar$ with $\gamma$ the gyromagnetic ratio, $J$ is the current per unit area, ${\cal P}$ represents the (dimensionless) polarization function of the fixed layer, ${\mathbf p}$ is a unit vector in the direction of the fixed layer magnetization, $d$ the interlayer separation, and $e$ is the electric charge of the carriers. (Recall that in the macromagnetic approach ${\mathbf M}$ is the magnetization per unit volume.)
In dimensionless variables, this equation reads $${{\rm d}}_t {\mathbf{m}} = - {\mathbf{m}} \wedge \left( \mathbf{h}_{{\rm{eff}}} + {\mathbf h}
- \eta {{\rm d}}_t \mathbf{m} \right)
- \chi \mathbf{m} \wedge (\mathbf{m} \wedge \mathbf{p})
\label{eq:sLLG1-spintorque-adim}$$ with $$\chi=\frac{\hbar J}{2 M_{{\rm s}}^2 d e \mu_0} {\cal P}
\; ,$$ a dimensionless parameter.
The last terms in Eqs. (\[eq:sLLG1-spintorque-dim\]) and (\[eq:sLLG1-spintorque-adim\]) represent a torque that cannot be derived from a potential and provides a mechanism to exchange energy between the magnetic moment and the environment *via* the current that flows in the sample. Thus, a spin polarized current of electrons can be used to manipulate the dynamics of the magnetic moment, its spin flip rate and its precession frequency [@Brataas12].
Initial studies of spin-torque assisted dynamics focused on the zero temperature limit [@Stiles2006; @Berkov2008] while temperature effects were considered in [@Myers2002; @Koch2004; @Li2004; @Russek2005; @Apalkov2005; @Xiao2005]. Most of this literature addresses the problem [*via*]{} the numerical integration of the stochastic equation [@Cimrak2008] or the Fokker-Planck approach. A simple way to understand, at least qualitatively, thermal effects in spin-torque driven dynamics is by realizing that spin-torque effectively modifies the dissipation coupling. If the current is such that this dissipation is lowered, one can expect thermal effects to be more relevant than in the absence of spin torque. Even more so, spin torque may not only reduce the effective dissipation constant but also make it [*negative*]{} meaning that the system amplifies disturbances from equilibrium [@Koch2004].
Discretization prescriptions {#sec:prescriptions}
============================
In this Section, we discuss the time-discretization of the stochastic magnetization dynamics. Indeed, as in any stochastic differential equation, the discretization used to define the Wiener integral is a defining part of the model, and should be carefully taken into account to obtain sensible physical results [@Gardiner]. As we will show, in the way the stochastic equation is currently written \[either in the form in Eq. (\[eq:sLLG1\]) or in the one in Eq. (\[eq:sLL1\]), or in their adimensional versions\], it conserves the magnetization modulus [*only if*]{} the Stratonovich prescription is used. Although this is not a new result (see, e.g., [@Bertotti-etal]), one still finds quite confusing statements in the literature [@Martinez-etal; @Berkov2002]. In the following discussion, we first describe the discretization of generic stochastic equations and we later discuss the case of the stochastic LLG (sLLG) equation. We next show how Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]) have to be modified if one wishes to work with other stochastic calculi in order, notably, to ensure the conservation of the modulus of ${\mathbf M}$.
Rules of stochastic calculus {#subsec:rules}
----------------------------
Let us consider a set of time-dependent random variables $x_a(t)$ satisfying a set of first order differential equations, $${{\rm d}}_t x_a(t) = f_a({\bf x}(t)) + g_{aj}({\bf x}(t)) h_j(t)
\;,
\label{eq.Langevin}$$ where the $x_a$, with $a=1,\dots, N$ are the components of the stochastic variable ${\bf x}$ and $h_j$, with $j=1,\dots, M$ are the components of the Gaussian white-noise process ${\bf h}$ satisfying $$\left\langle h_i(t)\right\rangle_{\mathbf h} = 0 \; , \qquad\qquad \left\langle h_i(t) h_j(t')\right\rangle_{\mathbf h} = 2D \delta_{ij}\delta(t-t')
\;.
\label{whitenoise}$$ Here and in what follows, we use the Einstein summation convention over repeated indices. In Eq. (\[eq.Langevin\]), $f_a({\bf x})$ and $g_{aj}({\bf x})$ are the so-called drift term and diffusion matrix, respectively, and are arbitrary smooth functions of ${\bf x}(t)$ (but not of its time-derivatives). Notice that, in general, the diffusion matrix is rectangular as the number of random variables is not necessarily equal to the number of random processes.
Due to the fact that $h_j(t)$ has an infinite variance, Eq. (\[eq.Langevin\]) is ill-defined until the product $g_{aj}({\bf x}(t)) h_j(t)$ is given a proper microscopic meaning. This subtlety can be understood by looking at the integral $$\int g_{aj}({\bf x}(t)) h_j(t) \; {{\rm d}}t= \int g_{aj}({\bf x}(t))\; {{\rm d}}W_j(t) \ ,$$ where we have introduced the Wiener processes $W_j(t)$ as $h_j(t)={{\rm d}}W_j(t)/{{\rm d}}t$. The Riemann-Stieltjes integral is defined by using a set of times $t_0 < t_1 < \dots < t_N ={\cal T}$ in the interval $[t_0, {\cal T}]$ and constructing the sum $$\int_{t_0}^{\cal T} g_{aj}({\bf x}(t))\; {{\rm d}}W_j(t)=
\lim _{N\to\infty} \sum_{n=0}^{N-1} g_{aj}(\bar {\bf x}_n) \left[ W_j(t_{n+1})-W_j(t_n) \right]
\label{eq.Wiener}$$ where $\bar x_n$ is taken in the interval $[x_n,x_{n+1}]$ and the [rhs]{} of Eq. (\[eq.Wiener\]) converges in the mean-square sense[^2]. For a smooth measure $W_j(t)$ the limit converges to a unique value, regardless of the choice of the $\bar x_n$’s. However, a Wiener process $W_j(t)$ is not smooth; in fact, it is nowhere differentiable. Therefore, the value of the integral depends on the prescription used to choose the $\bar x_n$’s. There are several ways to define this integral that can be collected in the so-called “generalized Stratonovich prescription” [@Hanggi1978] or “$\alpha$-prescription” [@Janssen-RG], for which one uses $$\begin{aligned}
\bar {\bf x}_n &=& \alpha {\bf x}_{n+1} + (1-\alpha) {\bf x}_{n}
\; , \end{aligned}$$ with $0\le \alpha \le 1$, and $$g_{aj}(\bar {\bf x}_n)=g_{aj}(\alpha {\bf x}(t_{n+1}) + (1-\alpha){\bf x}(t_n))
\; .
\label{eq.prescription}$$ The case $\alpha=0$ corresponds to the pre-point Itô prescription and $\alpha=1/2$ coincides with the mid-point Stratonovich one. The post-point prescription, $\alpha=1$, is also used [@Hanggi1978; @Hanggi1982; @Klimontovich].
For Markov processes with multiplicative white-noise, each choice of $\alpha$ corresponds to a different stochastic evolution. For any physical problem, the prescription is dictated by the order of limits when sending the time scales associated to inertia and the relaxation of the thermal bath to zero [@Kupferman]. Once the prescription is fixed, the stochastic dynamics are unambiguously defined.
In the cases in which the time scale associated to inertia is much smaller than the relaxation time of the bath, Eq. (\[eq.Langevin\]) is given an unambiguous meaning by adding a little color to the Gaussian noise, *i.e* a finite variance [@Hanggi-shot], and by eventually taking the white-noise limit at the end of the calculations. This regularization procedure is equivalent to the Stratonovich prescription, $\alpha=1/2$ [@vanKampen; @Zinn-Justin]. In the present case of magnetization dynamics, there is [*a priori*]{} no term playing the role of inertia.
The rules of calculus applied to the stochastic variables also depend on the prescription. In particular, the chain rule used to differentiate an arbitrary function $Y({\bf x}(t))$ of a set of stochastic variables reads [@arenas2010; @arenas2012a; @arenas2012] $${{\rm d}}_t Y({\bf x}(t))=\frac{\partial Y}{\partial x_a}\; {{\rm d}}_t x_a +(1-2\alpha) D\; \frac{\partial^2 Y}{\partial x_a\partial x_b}\; g_{ak} g_{bk} \; .
\label{eq.chainrule}$$ Clearly, in the Stratonovich prescription ($\alpha=1/2$), Eq. (\[eq.chainrule\]) is the usual chain rule of conventional calculus. For $\alpha=0$, Eq. (\[eq.chainrule\]) is the so-called Itô formula. For the $\alpha=1$ prescription, the latter differentiation rule only differs from the Itô formula by the sign of the last term. In fact, these two prescriptions are related by a time reversal transformation $t\to -t$ and $\alpha\to (1-\alpha)$.
Discretization scheme for the sLLG equation {#sec:sLLGprescription}
-------------------------------------------
Let us start with the dimension-full Landau formulation of the sLLG equation, *i.e.*, with Eq. (\[eq:sLL1\]) that we recast in the generic form of Eq. (\[eq.Langevin\]) $${\rm d}_t M_i= g_{ij} \left(H_{{{\rm{eff}}}, j}+ H_j\right)
\; ,
\label{eq:sLLG-functional-int}$$ where we introduced the $3\times 3$ diffusion matrix $$g_{ij}=\frac{\gamma_0}{1+\eta^2\gamma_0^2} \ [\epsilon_{ijk} M_k + \frac{\eta\gamma_0}{M_{{\rm s}}} (M_{{\rm s}}^2 \delta_{ij} - M_i M_j)]
\;.
\label{Eq:gij}$$ The Latin indices take values $i, j=x,y,z$, $\epsilon_{ijk}$ is the completely antisymmetric Levi-Civita tensor and we are always assuming summation over repeated indices. $g_{ij}$ can be decomposed in symmetric and antisymmetric parts, $g_{ij} = g_{ij}^{{\rm s}}+g_{ij}^{{\rm a}}$, with $$\begin{aligned}
&& g_{ij}^{{\rm s}}= \frac{\gamma_0}{1+\eta^2\gamma_0^2} \frac{\eta\gamma_0}{M_{{\rm s}}} (M_{{\rm s}}^2 \delta_{ij} - M_i M_j)
\; ,
\\
&& g_{ij}^{{\rm a}}= \frac{\gamma_0}{1+\eta^2\gamma_0^2} \epsilon_{ijk} M_k
\; .\end{aligned}$$ It is simple to show that $g$ is transverse in the sense that $$g_{ij} M_j = M_i g_{ij} = 0 \; .$$ Equation (\[eq:sLLG-functional-int\]) then yields $$\mathbf{M} \cdot {\rm d}_t \mathbf{M} =0\;.
\label{eq:identity00}$$ Contrary to what it may seem, this result does not imply the conservation of the magnetization modulus, ${{\rm d}}(\mathbf{M}\cdot\mathbf{M}) /{{\rm d}}t = {{\rm d}}M_{{\rm s}}^2 /{{\rm d}}t =0$, for all discretization schemes. Indeed, using the appropriate generalized chain rule given in Eq. (\[eq.chainrule\]), replacing $$\label{eq.gg}
g_{ik}g_{jk}=
g_{ki}g_{kj} =
\frac{\gamma_0^2}{1+\eta^2\gamma_0^2}\left(M_{{\rm s}}^2 \delta_{ij}-M_i M_j \right)
= \frac{M_{{\rm s}}}{\eta} g_{ij}^{{\rm s}}\;,$$ and choosing $Y({\bf M})=\mathbf{M}\cdot \mathbf{M} = M_{{\rm s}}^2$, one finds $${{\rm d}}_t M_{{\rm s}}^2 = 4D (1-2\alpha) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}^2
\;,$$ where we used $M_i {\rm d}_t M_i =0$, Eq. (\[eq:identity00\]). Therefore, the physical constraint that the modulus of the magnetization be conserved by the dynamics can only be satisfied when giving a Stratonovich prescription ($\alpha =1/2$) to Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]).
$\alpha$-covariant expression of the sLLG {#sec:alpha-covariantLLG}
-----------------------------------------
If for any reason one prefers to work with a prescription with $\alpha\neq 1/2$ (for instance, to perform a numerical simulation with an algorithm based on the Itô calculus) while conserving the magnetization modulus, the equation has to be changed accordingly. An elegant way consists in replacing the time-derivative by the [*$\alpha$-covariant derivative*]{} $${\rm d}_t \mapsto {\rm D}^{(\alpha)}_t= {{\rm d}}_t + 2D (1-2\alpha) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2}
\;,
\label{eq.covariant}$$ so that the $\alpha$-covariant expression of the sLLG equation, in its dimension-full Landau formulation, reads $${\rm D}^{(\alpha)}_t M_i= g_{ij} \left( H_{{{\rm{eff}}},j} + H_j \right) \;.
\label{eq.LLG-covariant}$$ The same replacement in Eq. (\[eq:sLLG1\]) yields the $\alpha$-covariant expression of the Gilbert formulation of the sLLG equation. In both cases, this replacement is equivalent to adding a [*spurious drift term*]{} to the equation. Notice that the second term in Eq. (\[eq.covariant\]) is odd under time reversal as it should be for a time-derivative, since the time-reversal transformation includes the transformation $\alpha\to (1-\alpha)$ [@arenas2012].
Equation (\[eq.LLG-covariant\]) encodes a family of stochastic equations with different underlying prescriptions, *i.e.* different $\alpha$. The Stratonovich equation (\[eq:sLLG-functional-int\]) can naturally be recovered by setting $\alpha = 1/2$. We emphasize that the general-$\alpha$ Eq. (\[eq.LLG-covariant\]) is strictly equivalent to the Stratonovich equation (\[eq:sLLG-functional-int\]) and that the choice of $\alpha$ cannot have any consequence on the physical properties of the system. In particular, Eq. (\[eq.LLG-covariant\]) conserves the norm of the magnetization for any $\alpha$ since $M_i{\rm D}^{(\alpha)}_t
M_i=0$, which implies, using the generalized chain-rule in Eq. (\[eq.chainrule\]), ${{\rm d}}_t M_{{\rm s}}^2 =0$, and ensure the approach to Boltzmann equilibrium in conservative cases as we show the in the next Subsection.
The same kind of argument can be applied to the adimensional equations (\[eq:sLLG1-adim\]) and (\[eq:sLL1-adim\]).
Fokker-Planck approach {#sec:Fokker-Planck}
----------------------
An alternative method to study the time evolution of a stochastic process is the Fokker-Planck (FP) approach, in which the system is characterized by the probability of finding ${\bf M}$ (or ${\mathbf m}$) at time $t$. The probability distribution $P({\bf M}, t)$ satisfies a [*deterministic*]{} partial differential equation, the solution of which completely describes the dynamics of the system.
The FP equation associated to the sLLG equation in Gilbert’s formulation and for Stratonovich calculus was derived by Brown [@Fuller63], see also [@Bertotti-etal; @GarciaPalacios98]. We will show below that the $\alpha$-covariant stochastic equation (\[eq.LLG-covariant\]) leads to a FP equation that is [*independent*]{} of $\alpha$.
The FP method allows one to prove that the stochastic process described by Eq. (\[eq.LLG-covariant\]) leads, at long times and under conservative time-independent forces, to the equilibrium Gibbs-Boltzmann probability distribution for any value of $\alpha$, provided that the noise correlation $D$ is set by an Einstein relation.
### Derivation of the Fokker-Planck equation
In order to derive the Fokker-Planck equation, we begin with the identity $$P({\bf M},t+\Delta t) = \int {\hspace{-0em}\mathrm{d}{{\bf M}_0}\;} P({\bf M},t+\Delta t|{\bf M}_0,t)P({\bf M}_0,t)
\; ,
\label{Eq.Identity}$$ where $P({\bf M},t+\Delta t|{\bf M}_0,t)$ is the conditional probability of finding ${\bf M}$ at the time $t+\Delta t$, provided the system was in the state ${\bf M}_0$ at the previous time $t$ (note that ${\mathbf M}_0$ is not necessarily the initial magnetization here). The integral in Eq. (\[Eq.Identity\]) runs over all accessible values of ${\bf M}_0$. This equation holds for any value of $\Delta t$ but we will later focus on infinitesimal time increments.
To make contact with the stochastic process in the Langevin-like description, it is convenient to define the conditional probability in the following way: $$\label{eq.conditionalP}
P({\bf M},t+\Delta t|{\bf M}_0,t) = \langle \delta({\bf M} - {\bf M}(t+\Delta t)) \rangle_{\mathbf H}
\; ,$$ where the mean value is taken over the noise $\mathbf{H}$, and ${\bf M}(t+\Delta t)$ is determined by the stochastic equation (\[eq.LLG-covariant\]) with the initial condition ${\bf M}(t)={\bf M}_0$. Expanding Eq. (\[eq.conditionalP\]) in powers of $\Delta{\bf M}={\bf M}(t+\Delta t)-{\bf M}(t)={\bf M}(t+\Delta t)-{\bf M}_0$ we immediately obtain $$\begin{aligned}
&& P({\bf M},t+\Delta t|{\bf M}_0,t)
= \delta({\bf M}-{\bf M}_0) - \partial_i\delta({\bf M}-{\bf M}_0) \ \langle \Delta M_i\rangle_{\mathbf H} \nonumber \\
&&
\qquad\qquad\qquad\qquad\qquad+ \frac{1}{2}
\partial_{i}\partial_{j}\delta({\bf M}-{\bf M}_0) \ \langle \Delta M_i\Delta M_j\rangle_{\mathbf H} + \ldots
\qquad
\label{eq.delta_Cond}\end{aligned}$$ where $\partial_i \equiv \partial/\partial{M}_i$ and the ellipsis indicate terms involving higher order correlations.
The idea is to compute the correlations $\langle \Delta M_i\rangle_{\mathbf H}$ and $\langle \Delta M_i\Delta M_j\rangle_{\mathbf H}$ to leading order in $\Delta t$ and then take the limit $\Delta t\to 0$. To do this, we integrate the sLLG equation (\[eq.LLG-covariant\]) in the interval $(t, t+\Delta t)$ obtaining $$\Delta M_i = f_i ({\bf M}_0)\Delta t + g_{ij}[{\bf M}_0+ \alpha \Delta {\bf M}(t + \Delta t)]
\int_{t}^{t+\Delta t} {\hspace{-0em}\mathrm{d}{t'}\;} H_j(t')\;,
\label{eq.deltam}$$ where we have used the $\alpha$-discretization procedure to define the last Wiener integral as explained in Sec. \[subsec:rules\], $W_j(t+\Delta t) - W_j(t) = \int_t^{t+\Delta t} dt' H_j(t')$, and $$\begin{aligned}
\label{eq.f}
f_i ( {\bf M}_0)&=&g_{ij}({\mathbf M}_0) H_{{{\rm{eff}}},j}
- 2D \frac{\gamma_0^2}{1+\eta^2\gamma_0^2}\; (1-2\alpha) {M_0}_i\;, \\
\label{eq.gij}
g_{ij}( {\bf M}_0)&=&\frac{\gamma_0}{1+\eta^2\gamma_0^2} \ \left[\epsilon_{ijk} {M_0}_k + \frac{\eta\gamma_0}{M_{{\rm s}}}
(M_{{\rm s}}^2 \delta_{ij} - {M_0}_i {M_0}_j)\right]\;,\end{aligned}$$ see Eq. (\[Eq:gij\]). Solving Eq. (\[eq.deltam\]) to order $\Delta t$ (by expanding $g_{ij}$ in powers of $\Delta{\bf M}$ and solving iteratively), and computing the mean values using $\langle H_i(t)H_j(t') \rangle_{\mathbf H}=2D\delta_{ij}\delta(t-t')$, we finally obtain $$\begin{aligned}
\langle \Delta M_i\rangle_{\mathbf H} &=& f_i({\bf M}_0)\Delta t + 2D \alpha g_{k\ell}({\bf M}_0)\partial_k g_{i\ell}({\bf M}_0) \Delta t\,, \label{prom_deltax} \\
\langle \Delta M_i\Delta M_j\rangle_{\mathbf H} &=& 2 D g_{ik}({\bf M}_0)g_{jk}({\bf M}_0)\Delta t \,.
\label{prom_deltaxdeltay}\end{aligned}$$ Interestingly enough, the mean value as well as the two point correlation are of order $\Delta t$. Higher momenta of the distribution such as $\langle \Delta M_i\Delta M_j\Delta M_k\rangle_{\mathbf H}$ are of higher order in $\Delta t$ and do not contribute to the expansion in Eq. (\[eq.Pm\]) for sufficiently small $\Delta t$. It is important to note that these results depend on ${\mathbf M}_0$.
Replacing now Eq. (\[eq.delta\_Cond\]) into Eq. (\[Eq.Identity\]) and integrating over ${\bf M}_0$ we have $$\begin{aligned}
&&
P({\bf M},t+\Delta t)-P({\bf M},t)
= - \partial_i \ [ \langle \Delta M_i\rangle_{\mathbf H} P({\bf M},t) ] \nonumber \\
& &
\qquad\qquad\qquad\qquad\qquad\qquad
+ \frac{1}{2}
\partial_{i}\partial_{j} \ [\langle \Delta M_i\Delta M_j\rangle_{\mathbf H} P({\bf M},t) ]
+ \ldots
\qquad\qquad
\label{eq.Pm}\end{aligned}$$ Using the averages found in Eqs. (\[prom\_deltax\]) and (\[prom\_deltaxdeltay\]) and performing the continuum limit $\Delta t \to 0$ we finally find the desired partial differential equation for $P({\bf M},t)$, $$\begin{aligned}
\label{eq.FP0}
&&
\partial_t P({\bf M},t)
=
-\partial_i \left[ \left( f_i({\bf M})+ 2D \alpha g_{k\ell}({\bf M})\partial_k g_{i\ell}({\bf M}) \right)
P({\bf M},t) \right] \nonumber \\
& &
\qquad\qquad\qquad
+ \partial_i\partial_j \left[
D g_{ik}({\bf M})g_{jk}({\bf M})
\ P({\bf M},t) \right]
\;.
\label{eq:FP}\end{aligned}$$
It is instructive to rewrite Eq. (\[eq:FP\]) in the form of a continuity equation, $$\partial_tP({\bf M},t) +\boldsymbol{\nabla}\cdot \mathbf{J}({\bf M},t) = 0\;,$$ where the components of the current probability $\mathbf{J}({\bf M},t)$ are given by $$\begin{aligned}
J_i&=& \left[ f_i + D (2\alpha-1) g_{k\ell}\partial_k g_{i\ell} - D g_{ik}\partial_j g_{jk} -
D g_{ik}g_{jk}\partial_j \right] P \;.\end{aligned}$$ The two following properties of the diffusion matrix $g$ $$\begin{aligned}
g_{k\ell}\partial_k g_{i\ell} &=& -\frac{2 \gamma_0^2}{1+\eta^2 \gamma_0^2} {M_0}_i \;,\\
g_{ik}\partial_j g_{jk}&=&0 \; ,\end{aligned}$$ and the explicit form of $f_i$ given in Eq. (\[eq.f\]) allow us to arrive at the simpler expression, $$\begin{aligned}
J_i= \left( g_{ij} H_{{\rm eff},j} -
D g_{ik}g_{jk}\partial_j \right) P\;.\end{aligned}$$ Thus, the Fokker-Planck equation, related with the stochastic process governed by the $\alpha$-covariant sLLG equation (\[eq.LLG-covariant\]), is given by $$\label{eq:FP333}
\partial_tP({\bf M},t) =\partial_i
\left\{
\left[ g_{ij} H_{{\rm eff},j} -
D g_{ik}g_{jk}\partial_j \right] P({\bf M},t)
\right\}
\;.$$ Note that, as anticipated, this differential equation is $\alpha$-independent. Thus, the $\alpha$-covariant sLLG equation (\[eq.LLG-covariant\]) leads to a unique time evolution for the magnetization probability for any value of the parameter $\alpha$. Also, from $g_{ij} M_j=0$, it is immediate to check that the current probability is transverse, $ {\bf J} \cdot {\bf M}=0$, meaning that there is no dynamics in the direction of the magnetization and, consequently, the time evolution preserves the magnetization modulus.
### Approach to equilibrium
With the Fokker-Planck equation defined in Eq. (\[eq:FP333\]), we can study the asymptotic probability distribution. Any stationary state at long times, $$P^{\rm st}({\bf M})=\lim_{t\to\infty} P({\bf M},t)\;,$$ has an associated stationary current that satisfies $\partial_i J^{\rm st}_i=0$. However, solutions to this equation do not necessarily represent equilibrium distributions as they could be non-equilibrium steady states with non-vanishing probability current. Indeed, the equilibrium distribution is defined as a stationary solution of the Fokker-Planck equation with zero current, ${\mathbf J}_{\rm eq}={\mathbf 0}$, and it is expected to be reached asymptotically in the absence of explicit time dependent or non-potential forces.
Considering the [*Ansatz*]{} $P_{\rm eq}({\bf M})=
N \exp(-{\cal V}[{\bf M}])$ for the equilibrium probability, where $N$ is a normalization constant, the condition $J^{\rm eq}_i=0$ implies $$g_{ij} H_{{\rm eff},j} +
D g_{ik}g_{jk}\partial_j {\cal V} =0\;.$$ In order to solve it for ${\cal V}({\bf M})$, we assume that the effective magnetic field can be obtained from a potential energy density $H_{{\rm eff},i}=H^c_{{\rm eff},i} = -\mu_0^{-1} \partial_i U[{\bf M}]$. Then, $$-\mu_0^{-1} g_{ij} \partial_j U +
D g_{ik}g_{jk}\partial_j {\cal V} =0\;.$$ We can further simplify this equation by noting that the antisymmetric part contributes with a topological divergence-less term since $\partial_ i \left(g^{{\rm a}}_{ij} \partial_j U\right)= 0$ for symmetry reasons. Also, from Eq. (\[eq.gg\]), $g^{{\rm s}}_{ij}=(\eta/M_{{\rm s}}) g_{ik}g_{jk}$. Then the null stationary current condition takes the very simple form, $$g^{{\rm s}}_{ij} \partial_j \left( \frac{U}{\mu_0} -
\frac{DM_{{\rm s}}}{\eta} {\cal V}\right) =0\;,$$ with obvious solution ${\cal V}=\eta/(DM_{{\rm s}}\mu_0) \ U$. The equilibrium solution of the Fokker-Planck equation is of the Gibbs-Boltzmann type $P_{\rm GB}=N\exp(-\beta U V)$ provided we choose $$D=\eta k_{\rm B}T/(M_{{\rm s}}V \mu_0)
\label{eq:D}$$ which is the Einstein relation or, more generally, a consequence of the fluctuation-dissipation theorem of the second kind in Kubo’s terminology [@Kubo66].
Generating functional {#sec:functional}
=====================
It is a well established fact that stochastic process can be analyzed with the help of path integrals. Janssen [@Janssen76] introduced such a description for stochastic processes, a very convenient formalism to manipulate correlation and response functions, that is close in spirit to the operator approach of Martin-Siggia-Rose [@Martin73]. The formalism was later applied to quenched disorder by De Dominicis [@deDominicis76; @deDominicis78] and is often referred as the MSRJD formalism. Over the years, there have been numerous attempts to generalize the work of Janssen to the case of multiplicative noise, [*i.e.*]{}, the case in which the diffusion matrix depends on the stochastic variable. The literature on this problem is rather extensive and in many cases also confusing. No attempt will be made here to review this literature (the interested reader can look at [@Tirapegui82] for a thorough description of path integral methods in the stochastic context). Instead, we will focus on the specific problem at hand, the stochastic dynamics of the magnetization in the Cartesian and spherical coordinate systems.
Let us consider that the system is prepared at an initial time, $t_0$, and subsequently let evolve until the final time of the experiment, $\mathcal{T}$. It is common to consider the limit $\mathcal{T}\to \infty$, but we prefer to keep the final time arbitrary. In the rest of this manuscript, we will encounter many time-integrals of the form $\int_{t_0}^{\cal T} {\hspace{-0ex}\mathrm{d}{t}\;} \ldots $ and, for the sake of simplicity, we will most frequently simply denote them $\int{\hspace{-0em}\mathrm{d}{t}\;} \ldots$
The generating functional of observables averaged over thermal histories is defined as $$\begin{aligned}
\mathcal{Z}[\boldsymbol{\lambda}] = \langle \ \langle \
\exp \int_{t_0}^{\cal T} {\hspace{-0ex}\mathrm{d}{t}\;} \boldsymbol{\lambda}(t) \cdot \mathbf{M}_{\mathbf H}(t) \ \rangle_{{\rm i}}\ \rangle_\mathbf{H} \;,
\label{eq:uno}\end{aligned}$$ where $ \langle \cdots \rangle_{{\rm i}}= \int {{\rm d}}\mathbf{M}_0 \cdots P_{{\rm i}}[\mathbf{M}_0, {\mathbf H}_{\rm eff}(t_0)] $ is the average over the initial conditions, ${\mathbf M}_0 \equiv {\mathbf M}(t_0)$ with $|\mathbf{M}_0| = M_{{\rm s}}$, distributed with the probability distribution function $P_{{\rm i}}[\mathbf{M}_0, {\mathbf H}_{\rm eff}(t_0)]$ which is normalized to unity. The average over the realizations of the thermal noise, which are distributed according to the probability distribution functional $P_{\rm n}[\mathbf{H}]$, is denoted $$\begin{aligned}
\langle \cdots \rangle_\mathbf{H} \equiv \int{\mathcal{D}}{[\mathbf{H}]} \cdots P_{\rm n}[\mathbf{H}]
\; .\end{aligned}$$ $P_{\rm n}[\mathbf{H}]$ is also normalized to unity. In the rest of the manuscript, we use the notation $$\begin{aligned}
\langle \cdots \rangle \equiv \langle\langle \cdots \rangle_{{\rm i}}\rangle_\mathbf{H} \;.\end{aligned}$$ $\boldsymbol{\lambda}$ is a vector source that couples linearly to the fluctuating magnetization configuration $\mathbf{M}_{\mathbf H}(t)$ which is the unique solution to the sLLG equation for a given initial condition $\mathbf{M}_0$ and a given history of the noise $[\mathbf{H}]$. By construction ${\cal Z}[\boldsymbol{\lambda} = \mathbf{0}]=1$.
In the rest of this Section, we construct the MSRJD representation of the generating functional $\mathcal{Z}[\boldsymbol{\lambda}]$ according to the following steps. The first one is to exchange the dependence on the unique solution $[\mathbf{M}_{\mathbf{H}}]$ with a sum over all trajectories by imposing the equation of motion written in the form $\mbox{\textbf{Eq}}[\mathbf{M},\mathbf{H}]=\mathbf{0}$ *via* a delta functional: $$\begin{aligned}
&&
{\cal Z}[\boldsymbol{\lambda}] = \int {\cal D}[\mathbf{H}] \ P_{\rm n}[\mathbf{H}] \
\int {\cal D}[\mathbf{M}]\
P_{\rm i}[\mathbf{M}_0, {\mathbf H}_{\rm eff}(t_0)]
\nonumber\\
&&
\qquad\;\;
\times \
\delta\Big{[} \mbox{\textbf{Eq}}[\mathbf{M},\mathbf{H}] \Big{]}
\ |{\cal J}[\mathbf{M},\mathbf{H}]| \
\exp \int_{ t_0}^{\cal T} \! {\hspace{-0em}\mathrm{d}{t}\;} {\boldsymbol{\lambda}}(t) \cdot \mathbf{M}(t)
\;. \label{eq:generatingZ}\end{aligned}$$ The measure ${\cal D}[\mathbf{M}] $, defined precisely in App. \[app:discrete\], has to be understood as the sum, at each time step, over vectors $\mathbf{M}(t)$ in the entire $\mathbb{R}^3$ space. In particular, it includes the integration over the initial conditions at time $t_0$. As discussed in Sec. \[sec:sLLGprescription\], the constraint $|\mathbf{M}(t)| = cst$ is encoded in the equation of motion (see later Sec. \[sec:conservation\_modulus\]). Notice that, at the level of the path integral, this allows one to consider $M_x$, $M_y$ and $M_z$ as unconstrained variables, *i.e.* $|\mathbf{M}(t)| \neq \mbox{cst}$. The Jacobian ${\cal J}[\mathbf{M},\mathbf{H}]$ ensures that the [rhs]{} of Eq. (\[eq:generatingZ\]) does not depend on the particular formulation of $\mbox{\textbf{Eq}}[\mathbf{M},\mathbf{H}]$: $$\begin{aligned}
\mathcal{J}[\mathbf{M},\mathbf{H}] \equiv
\det_{ij;uv}
\begin{array}{c}
\displaystyle
\frac{\delta {\rm{Eq}}_{\it i}[\mathbf{M},\mathbf{H}](u)}{\delta M_{j}(v)}
\end{array}\end{aligned}$$ with the coordinate indices $i,j=x,y,z$ and the times $u,v$. (If one thinks in terms of discrete time, the equation is imposed by a product of $\delta$-functions starting at time indexed $n=1$ and ending at time indexed $n=N$. We next exponentiate the functional Dirac delta with the help of a Lagrange multiplier $[{{\rm i}}\hat{\mathbf{M}}]$. Afterwards, we average over the initial conditions $\mathbf{M}_0$ and the noise realizations $[\mathbf{H}]$. Finally, we obtain a path integral representation of $\mathcal{Z}[\boldsymbol{\lambda}]$ in which the trajectories are weighted by the exponential of an action functional $S[\mathbf{M},{{\rm i}}\hat{\mathbf{M}}]$: $${\cal Z}[{\boldsymbol{\lambda}}] =
\int {\cal D}[{\mathbf M}] {\cal D}[{{\rm i}}\hat {\mathbf M}] \
\exp\left[
S[{\mathbf M}, {{\rm i}}\hat {\mathbf M}] + \int {{\rm d}}t \ {\boldsymbol{\lambda}}(t) \cdot {\mathbf M}(t)
\right]
\; .$$
Landau formulation {#sec:MSRDJ}
------------------
In Sec. \[sec:landau-lifshitz-gilbert\], we presented two formulations of the same sLLG equation (Gilbert and Landau) with generic discretization prescriptions. These different starting points lead to distinct formulations of the generating functional that describe the same physics. In the presentation below, we choose to start with the dimension-full Landau formulation of the $\alpha$-covariant sLLG equation, *i.e.* with Eq. (\[eq.LLG-covariant\]) $$\begin{aligned}
{\rm{Eq}}_{Li}[\mathbf{M},\mathbf{H}] &\equiv& {\rm D}_t^{(\alpha)} M_i - g_{ij}( H_{{{\rm{eff}}},j}+H_j ) = 0
\; ,
\label{eq:def-Eq}\end{aligned}$$ and we construct a formalism that is valid in any $\alpha$-prescription. The subscript $L$ stands for Landau formulation here and in the rest of this Section. We collected in the magnetic field ${\mathbf H}_{\rm eff}$ all contributions from conservative as well as non-conservative origin, including the possible spin-torque terms. We discuss the generating functional obtained when starting from the Gilbert formulation, and its equivalence to the Landau formulation, in Sec. \[sec:Landau2Gilbert\] and App. \[app:path-integral:Gilbert\]. In Sec. \[sec:observables\] we recall how these generating functionals enable one to compute all cumulants and linear responses of the magnetization.
The operator in the determinant can be worked out explicitly and put into the form $$\frac{\delta {\mbox{Eq}}_{Li}(u)}{\delta M_j(v)}
=
\delta_{ij} {\rm d}_u \delta(u-v) + A_{ij}(v) \delta(u-v)\;,$$ with $$\begin{aligned}
A_{ij}
=
2
D(1-2\alpha) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2}
\delta_{ij}
-
\frac{\partial g_{ik}}{\partial M_j} ( H_{{{\rm{eff}}},k}+H_k )
-
g_{ik} \frac{\partial H_{{{\rm{eff}}},k}}{ \partial M_j}\end{aligned}$$ where we assumed that ${\mathbf H}_{\rm eff}$ is ultra-local in time in the sense that it involves only the magnetization evaluated at time $u$ but no time-derivatives, [*i.e.*]{} the effective magnetic field can be of the form ${\mathbf H}_{\rm eff}({\mathbf M}(u), u)$. From now on we will use the notation $\partial_i = \partial /\partial M_i$ as in Sec. \[sec:Fokker-Planck\]. Using that the inverse of $\delta_{ik} {\rm d}_u \delta(u-w)$ is proportional to the Heaviside function $ \delta_{ik}\Theta(w-v)$, the Jacobian becomes $$\begin{aligned}
\mathcal{J}_L[\mathbf{M}, \mathbf{H}]
& =
\; \det_{ik;uw} \left[ \delta_{ik}(u) {\rm d}_u\delta(u-w)\right]
\nonumber\\
&
\qquad\qquad \times
\det_{kj;wv} \left[
\delta(w-v) \delta_{kj}
+ \Theta(w-v) A_{kj}(v) \right]
\; .
\label{sec:discussRVsA}
\end{aligned}$$ We treat the second determinant in the way described in App. \[sec:determinants\]. Notice that $C_{kj}(w,v) = \Theta(w-v) A_{kj}(v)$ is causal. Usually, the expansion stops at the first order due to the causality of the operator $C$. However, when there is a white-noise dependence in this operator, as it is the case here, one has to be careful and consider the possible contribution of the second order term, $C^2$ [@Arnold2000; @Lubensky2007]. This is explained in App. \[sec:determinants\]. In the Cartesian framework, the contribution of the second order term is an irrelevant constant and only the first term has a non-trivial dependence on the magnetization field. We obtain $$\begin{aligned}
\label{eq:jacjacjac}
\mathcal{J}_L[{\mathbf M}, {\mathbf H}]
\propto \; &
\exp\ [ \alpha \int{} {\hspace{-0em}\mathrm{d}{t}\;} A_{ii}(t) ]
\;,
\end{aligned}$$ where the factor $\alpha$ comes $\Theta(0)=\alpha$ in the $\alpha$-prescription. Indeed, when working with continuous-time notations, it can be shown [@Gardiner] that the $\alpha$ discretization prescription introduced in Sec. \[sec:prescriptions\] translates into the prescriptions $\int_{t_1}^{t_2}{\hspace{-0ex}\mathrm{d}{t}\;} G(t) \delta(t-t_1) = (1-\alpha) G(t_1)$ and $\int_{t_1}^{t_2}{\hspace{-0ex}\mathrm{d}{t}\;} G(t) \delta(t-t_2) = \alpha G(t_2)$ for any $G(t)$ that is a causal functional of the random field. In particular, for $G(t)=1$, this can be conveniently collected into $\Theta(0) \equiv \alpha$. The integrand in Eq. (\[eq:jacjacjac\]) is $$A_{ii}(t) =
2
D(1-2\alpha) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2}
\delta_{ii}
+
\frac{2\eta\gamma_0^2}{1+\eta^2\gamma_0^2}
\frac{M_i}{M_{{\rm s}}} (H_{{{\rm{eff}}},i}+H_i )
-
g_{ik} \partial_i H_{{{\rm{eff}}},k}
\;.$$ Finally, dropping all terms that are constant in the overall normalization, we obtain $$\begin{aligned}
\mathcal{J}_L[{\mathbf M}, {\mathbf H}]
& \!\! \!\!
\propto \!\! \!\! &
\exp \left\{ \frac{\alpha\gamma_0^2}{1+\eta^2\gamma_0^2}
\frac{1}{M_{{\rm s}}}
\int{} {\hspace{-0em}\mathrm{d}{t}\;} \Big{[}
2 \eta \ \mathbf{M} \cdot {\mathbf{H}}_{{{\rm{eff}}}}
\right.
\nonumber\\
&&
\qquad\qquad
+ \eta
(M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H_{{{\rm{eff}}},i}
\nonumber\\
&&
\qquad\quad\;\;\;
\left.
+ M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H_{{\rm eff}, i}^{\rm nc} + 2 \eta \ \mathbf{M} \cdot {\mathbf{H}}
\Big{]}\! \right\}
\; .
\label{eq:Jcart-L}
\end{aligned}$$
Coming back to the generating functional ${\cal Z}[\boldsymbol{\lambda}]$, we now exponentiate the delta functional that imposes the sLLG equation as $$\begin{aligned}
\delta \Big{[} \mbox{\textbf{Eq}}_L[\mathbf{M},\mathbf{H}] \Big{]} \propto
\int {\cal D}[\hat{\mathbf{M}}] \
\exp \int{} {\hspace{-0em}\mathrm{d}{t}\;} \ {{\rm i}}\hat{\mathbf{M}} \cdot\mbox{\textbf{Eq}}_L[\mathbf{M},\mathbf{H}]
\; ,\end{aligned}$$ in which $\hat{\mathbf{M}}$ is integrated over the entire $\mathbb{R}^3$ space at each time slice and has dimension $[{{\rm i}}\hat {\mathbf M}] = [{\mathbf M}]^{-1}$. The integration over the Gaussian white noise $\mathbf{H}$ yields $$\begin{aligned}
&&
\int {\cal D}{[\mathbf{H}}]
\
\displaystyle
\exp \left\{
\int{} {\hspace{-0em}\mathrm{d}{t}\;}
\left(
{\frac{ 2\alpha \eta\gamma_0^2}{1+\eta^2\gamma_0^2} M_j H_j
-{{\rm i}}\hat{M}_i g_{ij} H_j
- \frac{1}{2} \frac{H_j H_j}{2D}}
\right) \right\}
\nonumber\\
&&
\qquad\qquad
\propto \exp \left\{ D \int{} {\hspace{-0em}\mathrm{d}{t}\;} \ g_{ji} g_{ki} {{\rm i}}\hat{M}_j {{\rm i}}\hat{M}_k \right\}
\; ,\end{aligned}$$ where the cross term vanishes thanks to the property $g_{ij} M_j =0$. We will also drop a factor that depends only on $M_{{\rm s}}^2$ in the overall normalization. Accordingly, the effect of the random field contribution coming from the Jacobian disappears. Altogether, we recast the generating functional in the form $${\cal Z}[\boldsymbol{\lambda}] =
\int {\cal D}[\mathbf{M}] {\cal D}[\hat{\mathbf{M}}]
\ \exp \left\{ S_L+\int{} \! {\hspace{-0em}\mathrm{d}{t}\;} \boldsymbol{\lambda} \cdot \mathbf{M} \right\}
\; .$$ The action $S_L$ is a functional of the histories of the magnetization $[\mathbf{M}]$ and the auxiliary field $[{{\rm i}}\hat{\mathbf{M}}]$. It reads $$\begin{aligned}
S_L =&\; \; \ln P_{{\rm i}}[\mathbf{M}_0, \mathbf{H}_{\rm eff}(t_0)]
\nonumber \\
& + \int{} {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat M_i \left( {\rm D}^{(\alpha)}_t M_i - g_{ij} H_{{{\rm{eff}}}, j} \right)
+ D \int{} {\hspace{-0em}\mathrm{d}{t}\;} g_{ji} g_{ki} {{\rm i}}\hat{M}_j {{\rm i}}\hat{M}_k
\nonumber \\
& + \frac{\alpha\gamma_0}{1+\eta^2 \gamma_0^2 } \frac{1}{M_{{\rm s}}} \int{} {\hspace{-0em}\mathrm{d}{t}\;} \Big{[}
2 \eta\gamma_0 \ \mathbf{M} \cdot {\mathbf{H}}_{{{\rm{eff}}}}
+ \eta\gamma_0 (M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H_{{\rm eff}, i}
\nonumber\\
& \qquad\qquad\qquad\qquad\qquad
+ M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H_{{\rm eff}, i}^{\rm nc}
\Big{]}\!
\; .
\label{eq:generating-functional0}\end{aligned}$$ Notice that we identified $\mathbf{M}_0$ with $\mathbf{M}(t_0)$ and we included the integral over the initial conditions, $\int{{\rm d}}\mathbf{M}_0$, into the functional integral $\int{\mathcal{D}}[\mathbf{M}]$ and their probability distribution, $P_{{\rm i}}(\mathbf{M}_0),$ into the action functional.
One identifies the contribution of the deterministic dynamics, $\widetilde S_{L,{\rm det}}$, the dissipative and thermal effects, $\widetilde S_{L,{\rm diss}}$, and the Jacobian $$S_L = \widetilde S_{L,{\rm det}} + \widetilde S_{L,{\rm diss}} + S_{L,{\rm jac}}\;.
\label{eq:SLandau}$$ Using the decomposition of $g_{ij}$ in symmetric and antisymmetric parts, $g_{ij} = g_{ij}^{{\rm s}}+g_{ij}^{{\rm a}}$, already used in Sec. \[sec:Fokker-Planck\], and renaming indices conveniently one has $$\begin{aligned}
\widetilde S_{L,{\rm det}} =
& \;\; \ln P_{{\rm i}}[\mathbf{M}(t_0), \mathbf{H}_{\rm eff}(t_0)]
+ \int {\hspace{-0ex}\mathrm{d}{t}\;}
{{\rm i}}\hat{M_i} \cdot \left( {\rm D}_t^{(\alpha)} M_i -g^{{\rm a}}_{ij} {H_{\rm eff}}_j \right)
\; ,
\label{eq:S_det_cart00}
\\
\widetilde S_{L,{\rm diss}} =& \;\;
\int {\hspace{-0ex}\mathrm{d}{t}\;}
\ g_{ij}^{{\rm s}}\ {{\rm i}}\hat{M_i} \left(
\frac{DM_{{\rm s}}}{\eta} \
{{\rm i}}\hat{M_j}
-
{H_{\rm eff}}_j
\right)
\;,
\label{eq:S_diss_cart00}
\\
S_{L,{\rm jac}}=& \;\;
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\frac{1}{M_{{\rm s}}}
\int {\hspace{-0ex}\mathrm{d}{t}\;} \Big{[}
2 \eta\gamma_0 \ \mathbf{M} \cdot {\mathbf{H}}_{{{\rm{eff}}}}
+ \eta\gamma_0
(M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H_{{\rm eff}, i}
\nonumber\\
&
\qquad\qquad\qquad\qquad\;\;\;
+ M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H_{{\rm eff}, i}^{\rm nc}
\Big{]}\!
\; .
\label{eq:S_jac_cart000}\end{aligned}$$ Remembering that $D$ is proportional to $\eta$ \[see Eq. (\[eq:D\])\], one sees that $\widetilde S_{L,{\rm diss}}$ vanishes at $\eta=0$ while the remaining deterministic and Jacobian parts, $\widetilde S_{L,{\rm det}}+S_{L,{\rm jac}}$, yield what one would have obtained starting from the equation without dissipation. This writing of the Landau action, shows that $g^{{\rm s}}$ contains the information on the dissipative aspects of the dynamics.
Note that $g^{{\rm s}}$ does not have an inverse. This is related to the “gauge invariance" of the action, that retains the same form under the parallel translation ${{\rm i}}\hat {\mathbf M} \to {{\rm i}}\hat {\mathbf M} + a {\mathbf M}$, with $a$ generic.
### Rewriting of the Jacobian {#sec:rewriting-Jacobian}
As mentioned in the introduction, one should distinguish the parallel and perpendicular components of the effective field ${\mathbf H}_{\rm eff}={\mathbf H}^\perp_{\rm eff} + {\mathbf H}^\parallel_{\rm eff}$. We will write them as $$H_{{\rm eff},i} = H_{{\rm eff}, i}^\parallel + H_{{\rm eff}, i}^\perp
=
f M_i + \epsilon_{ilk} M_l T_k
\; ,$$ where $f$ and ${\mathbf T}$ can be functions of ${\mathbf M}$. This separation is different from the separation in conservative and non-conservative contributions. Notice that ${\mathbf T}$ is not defined uniquely as any translation parallel to ${\mathbf M}$ leaves this relation unchanged. Using this separation, one proves that the Jacobian contribution to the action, $S_{L,{\rm jac}}$, is independent of the parallel component of the effective field, more precisely, it is independent of $f$. This arises due to the cancellation of the first term with one stemming from the second one.
The Jacobian contribution to the action then reads $$\begin{aligned}
&& S_{L,{\rm jac}} = \;\;
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\frac{1}{M_{{\rm s}}}
\int {\hspace{-0ex}\mathrm{d}{t}\;} \Big{[}
\eta\gamma_0
(M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H^\perp_{{{\rm{eff}}}_i}
\nonumber\\
&&
\qquad\qquad\qquad\qquad
+ M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H^\perp_{{{\rm{eff}}}_i}
\Big{]}
\; .
\label{eq:S_jac_cart00}\end{aligned}$$ As expected, we conclude that the full action does not depend on ${\mathbf H}_{\rm eff}^\parallel$.
### Conservation of the modulus {#sec:conservation_modulus}
The decomposition of the auxiliary field $ {{\rm i}}\hat{\mathbf{M}} = {{\rm i}}\hat {\mathbf M}_\parallel + {{\rm i}}\hat {\mathbf M}_\perp$ into a sum of parallel and perpendicular components to the magnetization ${\mathbf M}$ (*i.e.* ${{\rm i}}\hat{\mathbf{M}}_\perp \cdot {\mathbf M} = 0$ and ${{\rm i}}\hat{\mathbf{M}}_\parallel \wedge {\mathbf M} = {\mathbf 0}$) will allow us to show that the modulus $M_{{\rm s}}$ is conserved by the dynamics and to derive the Gilbert formulation of the action functional (see Sec. \[sec:Landau2Gilbert\] for the latter).
As $M_i g_{ij} = 0$, then $${{\rm i}}\hat M_i g_{ij} =
\frac{\gamma_0}{1+\eta^2\gamma_0^2} [ \epsilon_{jkl} M_k {{\rm i}}\hat M_l + \eta\gamma_0 M_{{\rm s}}{{\rm i}}\hat M_j ]
\; .$$ Therefore, we find $ g_{ji} g_{ki} {{\rm i}}\hat{M}_j {{\rm i}}\hat{M}_k =
M_{{\rm s}}^2 \gamma_0^2/ (1+\eta^2\gamma_0^2) \
{{\rm i}}\hat{\mathbf{M}}_\perp \cdot {{\rm i}}\hat{\mathbf{M}}_\perp$. This property allows us to rewrite the action in (\[eq:generating-functional0\]) in an equivalent form: $$S_L= {S}_{L,{\rm det}} + {S}_{L,{\rm diss}} + S_{L,{\rm jac}}\;,$$ with $$\begin{aligned}
{S}_{L,{\rm det}} =
& \ln P_{{\rm i}}[\mathbf{M}(t_0), \mathbf{H}_{\rm eff}(t_0)]
+ \int {\hspace{-0ex}\mathrm{d}{t}\;}
{{\rm i}}\hat{\mathbf{M}}_\parallel \cdot {\rm D}_t^{(\alpha)} \mathbf{M}
\nonumber \\
&+ \frac{1}{1+\eta^2\gamma_0^2}
\int {\hspace{-0ex}\mathrm{d}{t}\;}
{{\rm i}}\hat{\mathbf{M}}_\perp \cdot
\Big{[} {{\rm d}}_t \mathbf{M} -
\eta \gamma_0^2 M_{{\rm s}}\ \mathbf{H}_{{\rm{eff}}}
\nonumber\\
&
\qquad\qquad\qquad\;
-
\left( \eta\gamma_0 M_{{\rm s}}^{-1} \ {{\rm d}}_t \mathbf{M} \wedge \mathbf{M}
+ \gamma_0 \ {\mathbf M} \wedge \mathbf{H}_{{\rm{eff}}} \right) \Big{]}
\;,
\label{eq:S_det_cart0} \\
{S}_{L,{\rm diss}} =&
\frac{1}{1+\eta^2\gamma_0^2 }
\int {\hspace{-0ex}\mathrm{d}{t}\;}
{{\rm i}}\hat{\mathbf{M}}_\perp \cdot
\Big{[}
D \gamma_0^2 \, M_{{\rm s}}^2 \
{{\rm i}}\hat{\mathbf{M}}_\perp
\nonumber\\
&
\qquad\qquad\qquad +
\left( \eta\gamma_0 M_{{\rm s}}^{-1} \ {{\rm d}}_t \mathbf{M} \wedge \mathbf{M} + \eta^2\gamma_0^2 {{\rm d}}_t \mathbf{M}\right)
\Big{]}
\; .
\label{eq:S_jac_diss0}\end{aligned}$$ The Jacobian contribution, $S_{L,{\rm jac}}$, is again given by Eq. (\[eq:S\_jac\_cart00\]) as it does not involve ${{\rm i}}\hat{\mathbf M}$. We added and subtracted a term in what we called deterministic and dissipative contributions for later convenience. The dissipative part, ${S}_{L,{\rm diss}}$, only regroups terms that involve the interactions with the environment such as thermal effects and the dissipative torque. It does not depend on the deterministic forces acting on the problem, grouped in ${\mathbf H}_{\rm eff}$, that appear only in ${S}_{L,{\rm det}}$. At $\eta=0$, ${S}_{L,{\rm diss}}$ vanishes while the remaining deterministic part, ${S}_{L,{\rm det}}$, again yields what one would have obtained starting from the equation without dissipation. This cutting up will take a clear meaning in the Gilbert formulation of the generating functional (see Sec. \[sec:Landau2Gilbert\]).
The sector of the formalism that involves ${{\rm i}}\hat{{\mathbf M}}_\parallel$, the component of ${{\rm i}}\hat{\mathbf{M}}$ which is parallel to $\mathbf{M}$, encodes the conservation of the modulus of the magnetization. Indeed, the only term involving ${{\rm i}}{\hat{ \mathbf{M}}}_\parallel$ in the action functional given in Eqs. (\[eq:S\_det\_cart0\]) and (\[eq:S\_jac\_diss0\]) is $$\begin{aligned}
\int{} {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{{\mathbf M}}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M}
= \int{} {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{M}_\parallel \ \frac{\mathbf{M}}{M_{{\rm s}}} \cdot {\rm D}_t^{(\alpha)} {\mathbf M}
\;.\end{aligned}$$ If one were to integrate over $\hat M_\parallel$, this would yield a delta functional $$\begin{aligned}
\delta\left[ \mathbf{M} \cdot {\rm D}_t^{(\alpha)} {\mathbf M} \right]\;,\end{aligned}$$ that imposes the constraint ${\mathbf M} \cdot {\rm D}_t^{(\alpha)} {\mathbf M} = 0$ at all times, simply expressing the conservation of the modulus, ${{\rm d}}_t M_{{\rm s}}^2 = 0$, as we explained in Sec. \[sec:alpha-covariantLLG\].
Gilbert formulation {#sec:Landau2Gilbert}
-------------------
As we stressed in Sec. \[sec:landau-lifshitz-gilbert\], the Gilbert and Landau formulations of the sLLG equation, Eqs. (\[eq:sLLG1\]) and (\[eq:sLL1\]), or their adimensional form in Eqs. (\[eq:sLLG1-adim\]) and (\[eq:sLL1-adim\]), are strictly equivalent. In Sec. \[sec:MSRDJ\], we constructed a prescription-covariant functional formalism starting from the $\alpha$-covariant expression of the Landau formulation of the sLLG equation, namely Eq. (\[eq.LLG-covariant\]). Starting from the $\alpha$-covariant expression of Eq. (\[eq:sLLG1-adim\]) and following a similar route (see App. \[app:path-integral:Gilbert\]), one can construct another action functional corresponding to the Gilbert formulation of the problem. The ensuing Gilbert action functional reads (the subscript $G$ stands for Gilbert formulation): $$\begin{aligned}
S_G = S_{G,{\rm det}} + S_{G,{\rm diss}} + S_{G,{\rm jac}}
\label{eq:total-action-Gilbert}\end{aligned}$$ with $$\begin{aligned}
S_{G,{\rm det}} \! &\! = \! & \!
\ln P_{{\rm i}}[\mathbf{M}(t_0), \mathbf{H}_{\rm eff}(t_0)]
+ \int{\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M}
\nonumber \\
& & +
\int{\hspace{-0ex}\mathrm{d}{t}\;}
{{\rm i}}\hat{\mathbf{M}}_\perp \cdot
\left( \frac{1}{ M_{{\rm s}}^2} {\rm D}^{(\alpha)}_t \mathbf{M} \wedge \mathbf{M}
+ \gamma_0 \mathbf{H}_{{\rm{eff}}} \right)
\; ,
\;\;\;\;\; \label{eq:SLLGjac-det}
\\
S_{G,{\rm diss}} \! &\! = \! & \!
\int {\hspace{-0ex}\mathrm{d}{t}\;}
\gamma_0{{\rm i}}\hat{\mathbf{M}}_\perp \cdot \left( D \gamma_0 {{\rm i}}\hat{\mathbf{M}}_\perp
- \frac{\eta}{M_{{\rm s}}} \ {\rm D}^{(\alpha)}_t \mathbf{M} \right)
\; .
\label{eq:SLLGjac-diss}
\\
S_{G,{\rm jac}}
\! &\! = \! & \!
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\frac{1}{M_{{\rm s}}}
\int {\hspace{-0ex}\mathrm{d}{t}\;} \Big{[}
\eta\gamma_0
(M_i M_j -\delta_{ij} M_{{\rm s}}^2)\partial_j H^\perp_{{{\rm{eff}}}_i}
\nonumber\\
&&
\qquad\qquad\qquad\qquad
+ M_{{\rm s}}\epsilon_{ijk} M_k \partial_j H^\perp_{{{\rm{eff}}}_i}
\Big{]}
\; .
\label{eq:SLLGjac-jac}\end{aligned}$$ The Jacobian contribution, $S_{G,{\rm jac}}$, is identical to Eq. (\[eq:S\_jac\_cart00\]), $S_{G,{\rm jac}}=S_{L, {\rm jac}}$. The equivalence between the Landau and the Gilbert formulations simply corresponds to a transformation of the auxiliary field ${{\rm i}}\hat{\mathbf{M}}$. One passes from the Landau action functional given in Eqs. (\[eq:S\_det\_cart0\]) and (\[eq:S\_jac\_diss0\]) to the Gilbert formulation in Eqs. (\[eq:SLLGjac-det\]) and (\[eq:SLLGjac-diss\]) *via* the following change $$\begin{aligned}
\label{eq:Trans_L2G}
{{\rm i}}\hat{\mathbf{M}}_\perp \mapsto
-\frac{1}{M_{{\rm s}}} \left( \frac{1}{M_{{\rm s}}} {{\rm i}}\hat{\mathbf{M}}_\perp \wedge\mathbf{M} +
\eta\gamma_0 \ {{\rm i}}\hat{\mathbf{M}}_\perp \right)\;,\end{aligned}$$ which is a linear transformation with a constant Jacobian that can be dropped into the overall normalization. Conversely, one passes from the Gilbert action functional to the Landau formulation *via* the inverse transformation $$\begin{aligned}
\label{eq:Trans_G2L}
{{\rm i}}\hat{\mathbf{M}}_\perp \mapsto
\frac{1}{1+\eta^2\gamma_0^2} \left[ {{\rm i}}\hat{\mathbf{M}}_\perp \wedge\mathbf{M} -
\eta\gamma_0 M_{{\rm s}}\ {{\rm i}}\hat{\mathbf{M}}_\perp \right]\;.\end{aligned}$$
Observables {#sec:observables}
-----------
The generating functional can be used to evaluate the average of functions of the magnetization, in particular its $n$-times correlation functions, cumulants, and linear responses, by taking variations with respect to sources conveniently introduced in the action through linear couplings to the magnetization and the auxiliary field. We list a number of these observables below.
The averaged magnetization is given by $$\begin{aligned}
\langle M_i(t)\rangle =
\frac{1}{\mathcal{Z}[\boldsymbol{\lambda}=0]} \frac{\delta \mathcal{Z}[\boldsymbol{\lambda}]}{\delta \lambda_i(t)}\Big{\rvert}_{\boldsymbol{\lambda}=0}
\; . \end{aligned}$$
The two-time correlations can be obtained from the variation of the ${\mathcal Z}$ with respect to two sources: $$\begin{aligned}
\langle M_i(t)\, M_j(t')\rangle = \frac{1}{\mathcal{Z}[\boldsymbol{\lambda}=0]} \frac{\delta \mathcal{Z}[\boldsymbol{\lambda}]}{\delta \lambda_i(t) \, \delta \lambda_j(t')}\Big{\rvert}_{\boldsymbol{\lambda}=0}
\; . \end{aligned}$$ Similarly, one derives the $n$-times correlation functions by taking variations with respect to $n$ factors $\lambda_i$ evaluated at different times.
The cumulant generating functional is defined as $W[\boldsymbol{\lambda}] \equiv \ln \mathcal{Z}[\boldsymbol{\lambda}]$. For instance, one generates the second order cumulant as $$\left. \frac{\delta^2 W[\boldsymbol{\lambda}]}{\delta \lambda_i(t) \delta \lambda_j(t')} \right|_{{\mathbf \lambda} = {\mathbf 0}}
=
\langle M_i(t) M_j(t') \rangle - \langle M_i(t)\rangle \langle M_j(t') \rangle \; .$$
The linear response is the result of the effect of a linear perturbation of the local effective magnetic field, $\mathbf{H}_{\rm eff} \mapsto \mathbf{H}_{\rm eff} + \widetilde{\mathbf{H}}$, performed at a time $t'$ on the observable of choice. The equation of motion and the dynamic action do not depend on $H_{\rm eff}^\parallel$. Therefore, the only variation that may have an effect on the averaged observables is the one on $H_{\rm eff}^\perp$. The linear response of the magnetization component $M_i$ measured at a later time $t$, in the Landau formulation, is $$\begin{aligned}
R_{ij}(t,t') =
&
\left.
\frac{\delta \langle M_i(t)\rangle_{S_L} }{\delta {\widetilde{H}_j(t')}}
\right|_{\widetilde{\mathbf H}={\mathbf 0}}
\!\!\!
=
\left.
\frac{\delta \langle M_i(t)\rangle_{S_L} }{\delta {\widetilde{H}^\perp_j(t')}}
\right|_{\widetilde{\mathbf H}^\perp={\mathbf 0}}
\nonumber\\
= &
\;\;
\langle M_i(t) {{\rm i}}\hat M_k(t') g_{kj}[{\mathbf M}(t')] \rangle_{S_L}\;.
\nonumber\end{aligned}$$ The average has to be taken with the weight $\exp S_L$ with the Landau formulation of the action functional, $S_L$, given in Eqs. (\[eq:S\_jac\_cart00\]), (\[eq:S\_det\_cart0\]) and (\[eq:S\_jac\_diss0\]). The presence of the auxiliary field ${{\rm i}}\hat{\mathbf{M}}$ in the expression of the response is the reason why it is often referred to as the “response field”. This “classical Kubo formula” can be generalized to the response of any observables $A$: $$\begin{aligned}
R_{A\,j}(t,t')
\equiv &
\left. \frac{\delta \langle A(t) \rangle_{S_L}}{\delta \widetilde{H}_j(t')} \right|_{\widetilde{\mathbf{H}}=0}
=
\left. \frac{\delta \langle A(t) \rangle_{S_L}}{\delta \widetilde{H}^\perp_j(t')} \right|_{\widetilde{\mathbf{H}}=0}
\;\;
\nonumber\\
= & \;\;
\langle A(t) \, {{\rm i}}\hat M_k(t') g_{kj}[{\mathbf M}(t')] \rangle_{S_L}
\;.\end{aligned}$$ The trivial case in which $A$ is set to be a constant, gives $R_{A\,j}(t,t') = 0$ for all $t$ and $t'$, yielding the identity $$\begin{aligned}
\label{eq:KuboID0}
\langle {{\rm i}}\hat{M}_k(t) g_{kj}[{\mathbf M}(t')] \rangle_{S_L} =
0
\; . \end{aligned}$$
Within the Gilbert formulation of the $\alpha$-covariant generating functional, one can also compute the linear response function. Another classical Kubo formula expressing the linear response as a two-time correlator is found $$\begin{aligned}
R_{ij}(t,t')
&
=
\left. \frac{\delta \langle M_i(t) \rangle_{S_G}}{\delta \widetilde{H}_j(t')}
\right|_{\widetilde{\mathbf{H}}=0}
=
\left. \frac{\delta \langle M_i(t) \rangle_{S_G}}{\delta \widetilde{H}^\perp_j(t')}
\right|_{\widetilde{\mathbf{H}}^\perp=0}
\nonumber\\
&
= \;\; \langle M_i(t) \,\gamma_0 {{\rm i}}\hat{M}_{\perp\,j}(t') \rangle_{S_G}
\; , \end{aligned}$$ where the averages are weighted by $\exp S_G$ given in Eqs. (\[eq:total-action-Gilbert\]) with the contributions (\[eq:SLLGjac-det\]), (\[eq:SLLGjac-diss\]) and (\[eq:S\_jac\_cart00\]). Applied now to any observable $A$ this relation reads $$\begin{aligned}
R_{A\,j}(t,t')
= &
\;\; \langle A(t) \, \gamma_0 {{\rm i}}\hat{M}_{\perp\,j}(t') \rangle_{S_G}
\; . \end{aligned}$$ The trivial case in which $A$ is set to be a constant, gives $R_{A\,j}(t,t') = 0$ for all $t$ and $t'$, yielding the identity $$\begin{aligned}
\label{eq:KuboID0G}
\langle {{\rm i}}\hat{\mathbf{M}}_\perp(t) \rangle_{S_G} =
0
\; . \end{aligned}$$
Equilibrium dynamics {#sec:equilibrium_cond}
--------------------
The magnetization undergoes equilibrium dynamics if it is prepared in and let evolve under equilibrium conditions. More specifically, initial conditions at temperature $T$ have to be drawn from a Gibbs-Boltzmann distribution in a potential $U$ (per unit volume), the system has to evolve with the same (time-independent) potential $U$ with no additional non-potential fields, ${\mathbf H}_{\rm eff}^{\mathrm{nc}}={\mathbf 0}$, and it has to be in contact with a thermal bath in equilibrium at the same temperature.
Thermal initial conditions in the potential $U$ correspond to the Gibbs-Boltzmann probability distribution $$P_{{\rm i}}[\mathbf{M}_0, {\mathbf H}_{{\rm{eff}}}(t_0)] = {{\rm e}}^{\displaystyle -\beta V U[\mathbf{M}_0, \mathbf{H}_{{\rm{ext}}}(t_0)]-\ln Z[\mathbf{H}_{{\rm{ext}}}(t_0)]}$$ with $Z[\mathbf{H}_{{\rm{ext}}}(t_0)] \equiv \int{\hspace{-0em}\mathrm{d}{\mathbf{M}_0}\;} {{\rm e}}^{\displaystyle -\beta V U[\mathbf{M}_0, \mathbf{H}_{{\rm{ext}}}(t_0)]}$. The deterministic contribution to the Landau action functional in Eqs. (\[eq:S\_det\_cart00\])-(\[eq:S\_jac\_cart00\]) reads $$\begin{aligned}
S_{L,{\rm det}} =
& \;
\ln P_{{\rm i}}[\mathbf{M}_0, \mathbf{H}_{\rm eff}(t_0)]
+ \int {\hspace{-0ex}\mathrm{d}{t}\;}
{{\rm i}}\hat{M_i} \left( {\rm D}_t^{(\alpha)} M_i -g^{{\rm a}}_{ij} H^c_{{\rm eff},j} \right)
\; ,
\end{aligned}$$ with ${\mathbf H}^c_{\rm eff} = -\mu_0^{-1} \partial U/\partial {\mathbf M}$. The Jacobian can be expressed in terms of $U$ by using $H^c_{{\rm eff},i} = -\mu_0^{-1} \partial_i U$ in Eq. (\[eq:S\_jac\_cart000\]) or $H^c_{{\rm eff},i} = -\mu_0^{-1} P_{ij} \partial_j U$ in Eq. (\[eq:S\_jac\_cart00\]) with $P_{ij}$ the projector onto the direction perpendicular to the magnetization, $P_{ij} = \delta_{ij} - M_i M_j /M_{{\rm s}}^2$. The dissipative part, $S_{L,{\rm diss}}$, remains unchanged.
Spherical coordinate formalism {#sec:spherical-coordinates}
==============================
As the modulus of the magnetization $\mathbf{M}$ is constant, the vector rotates on a sphere of radius $M_{{\rm s}}$, and it is natural to work in a spherical coordinates system. In this Section, we present an equivalent functional formalism for the dynamics of the magnetization, that uses a system of spherical coordinates. In Sec. \[sec:sph\_LLG\_cov\] we present the sLLG equation in spherical coordinates and in any discretization prescription. We stress in Sec. \[sec:sph\_random\_field\] that the statistics of the random field are not as trivial as they are in a Cartesian description. Although the non-trivial character of the noise has been correctly treated in some references (see, for instance, [@Fuller63] and Sec. 4.4.5 in [@Gardiner]), this subtlety has led to mistaken statements [@Langevin-Coffey] and omission or lack of clarity in the literature [@Bertotti-etal; @Martinez-etal]. We hope to clarify this matter once and for all here. It is also important to note that the transformation from Cartesian to spherical coordinates is non-linear and one cannot naively apply it to the generating functional. We construct the corresponding path integral formalism starting from the dynamic equations in the spherical coordinate system in Sec. \[sec:contruct\_spherical\]. The resulting action functional is given by the sum of the terms in Eqs. (\[eq:action-det-sph-L2\]), (\[eq:action-diss-sph-L\]) and (\[eq:esferica-jac\]).
We introduce the usual coordinates $M_{{\rm s}}$, $\theta$ and $\phi$ where $M_{{\rm s}}$ is the radial component, $\theta$ the polar angle, and $\phi$ the azimuthal angle (see App. \[app:conventions\] for more details on the conventions used). The vector $\mathbf{M}$ defines the usual local basis ($\mathbf{e}_{M_{{\rm s}}}, \mathbf{e}_\theta, \mathbf{e}_\phi$) with $$\begin{aligned}
\mathbf{M}(M_{{\rm s}},\theta,\phi) &\equiv&
M_{{\rm s}}\, \mathbf{e}_{M_{{\rm s}}}(\theta,\phi)
\nonumber\\
&=&
M_{{\rm s}}\left(
\sin\theta \cos\phi \ {\mathbf e}_x + \sin \theta \cos \phi \ {\mathbf e}_y + \cos \theta \ {\mathbf e}_z
\right)
\; . \end{aligned}$$ Here and after, Greek indices such as $\mu$ or $\nu$ label the spherical coordinates $M_{{\rm s}}, \ \theta, \ \phi$, and Latin indices continue to label the Cartesian coordinates $x, \ y, \ z$. We collect the spherical coordinates in a vector $\Omega_\mu$. The rotation matrix is called $R$ and we give its explicit form in App. \[app:conventions\].
$\alpha$-covariant sLLG equation {#sec:sph_LLG_cov}
--------------------------------
Similarly to what was done in the Cartesian coordinate system, the Stratonovich sLLG equation in spherical coordinates should be modified to work in a generic $\alpha$-prescription, while maintaining the physics unchanged. We wish to find the equation satisfied by the spherical coordinates $M_{{\rm s}}, \theta, \phi$ knowing that the Cartesian components of the magnetization vector ${\mathbf M}$ satisfy the sLLG given in Eq. (\[eq.LLG-covariant\]) in the Landau formulation, $$\begin{aligned}
\mathbf{Eq}_L[\mathbf{M},\mathbf{h}] \equiv {\rm D}^{(\alpha)}_t \mathbf{M} - g \left( \mathbf{H}_{{\rm{eff}}} + \mathbf{H} \right) = {\mathbf 0}
\label{eq:LLG-recall}
\, ,\end{aligned}$$ and that the Cartesian chain rule in Eq. (\[eq.chainrule\]) applied to our problem reads $$\begin{aligned}
\label{eq:cr11}
{{\rm d}}_t & = {{{\rm d}}_t} M_i \ \partial_i +
\frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \left(M_{{\rm s}}^2 \delta_{ij} - M_i M_j \right) \, \partial_i \partial_j \; .\end{aligned}$$
We start by re-writing the chain rule in spherical coordinates. We first work out the first term in Eq. (\[eq:cr11\]) as $$\begin{aligned}
{{{\rm d}}_t} M_i \ \partial_i & =
-\frac{ 2D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}\partial_{M_{{\rm s}}}
\nonumber\\
&
\;\;\;\;\;
+ \frac{1}{M_{{\rm s}}}
\left[
g_{\theta \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) \ \partial_\theta
+ \frac{1}{\sin\theta} g_{\phi \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) \ \partial_\phi
\right]
\nonumber\end{aligned}$$ (see App. \[app:metric\]). The relevant elements of $g_{\mu\nu}$ are $$\begin{aligned}
g_{\theta\theta} = g_{\phi\phi} = \eta\gamma_0 g_{\theta\phi} = - \eta\gamma_0 g_{\phi\theta} = \frac{\eta\gamma_0^2 M_{{\rm s}}}{1+\eta^2\gamma_0^2}
\label{eq:g-elements-spherical}\end{aligned}$$ while $g_{M_{{\rm s}}\mu}=g_{\mu M_{{\rm s}}}=0$. In order to treat the second term of Eq. (\[eq:cr11\]) we notice that $$\begin{aligned}
(M_{{\rm s}}^2 \delta_{ij} - M_i M_j ) \partial_i \partial_j
&= M_{{\rm s}}^2 \nabla^2 - M_i M_j \, \partial_i \partial_j \;, \nonumber\end{aligned}$$ where $\nabla^2$ is the Laplacian operator that in spherical coordinates reads $$\begin{aligned}
\nabla^2 = \frac{1}{M^2_{{\rm s}}} \left( M_{{\rm s}}^2 \partial^2_{M_{{\rm s}}} + 2 M_{{\rm s}}\partial_{M_{{\rm s}}} + \cot\theta\partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right) \;.\end{aligned}$$ We also have $ M_i M_j \, \partial_i \partial_j
= M^2_{{\rm s}}\ \partial_{M_{{\rm s}}}^2
$. Therefore, the second term in Eq. (\[eq:cr11\]) becomes $$\begin{aligned}
\frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}^2 \left( \nabla^2 - \partial_{M_{{\rm s}}}^2 \right)\;.\end{aligned}$$ Altogether we have $$\begin{aligned}
\label{eq:cr22-maintext}
{{\rm d}}_t & =
\frac{1}{M_{{\rm s}}}
\left[
g_{\theta \nu_\perp} H_{\nu_\perp} \partial_\theta
+ \frac{1}{\sin\theta} g_{\phi \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) \ \partial_\phi
\right]
\nonumber\\
&
\;\;\;\;\;
+ \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}
\left( \cot\theta\partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right)\;.\end{aligned}$$ We now apply the differential operator (\[eq:cr22-maintext\]) to $M_{{\rm s}}$, $\theta$ and $\phi$, respectively, to obtain the equations of motion in spherical coordinates $$\begin{aligned}
{{\rm d}}_t M_{{\rm s}}&= 0\;, \\
{{\rm d}}_t \theta &= \frac{1}{M_{{\rm s}}} g_{\theta \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta \;,
\\
{{\rm d}}_t \phi &= \frac{1}{M_{{\rm s}}\sin\theta} g_{\phi \nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) \; ,\end{aligned}$$ and we use these identities in Eq. (\[eq:cr22-maintext\]) to re-write the time-differential operator in a form that is explicitly independent of the external and random fields $$\begin{aligned}
{{\rm d}}_t &= \ {{\rm d}}_t \Omega_{\mu_\perp} \ \partial_{\Omega_{\mu_\perp}}
+ \ \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}\left( \partial^2_\theta + \frac{1}{\sin^2\theta} \ \partial^2_\phi \right) \;.\end{aligned}$$ This is the chain-rule in spherical coordinates.
Introducing the covariant derivatives $$\begin{aligned}
{\rm D}_t^{(\alpha)} M_{{\rm s}}&\equiv {{\rm d}}_t M_{{\rm s}}\; ,
\label{eq:covDMs}\\
{\rm D}^{(\alpha)}_t(\theta) &\equiv {{\rm d}}_t \theta-\frac{D(1-2\alpha)\gamma_0^2}{(1+\eta^2\gamma_0^2)} \cot\theta \; , \label{eq:covDtheta} \\
{\rm D}^{(\alpha)}_t(\phi) &\equiv {{\rm d}}_t \phi \; ,
\label{eq:covDphi}\end{aligned}$$ we now recast Eqs. (\[eq:covDMs\])-(\[eq:covDphi\]) as $$\begin{aligned}
\mbox{Eq}^{\rm sph}_{L,M_{{\rm s}}}[M_{{\rm s}},\theta,\phi] &\equiv {\rm D}_t^{(\alpha)} M_{{\rm s}}= 0 \; ,
\label{eq:ralpha} \\
\mbox{Eq}^{\rm sph}_{L,\theta}[M_{{\rm s}},\theta,\phi] &\equiv M_{{\rm s}}\ {\rm D}^{(\alpha)}_t(\theta) - g_{\theta\nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) = 0 \; ,
\label{eq:thetaalpha} \\
\mbox{Eq}^{\rm sph}_{L,\phi}[M_{{\rm s}},\theta,\phi] &\equiv M_{{\rm s}}\sin\theta\, {\rm D}^{(\alpha)}_t(\phi) - g_{\phi\nu_\perp} ({H_{\rm eff}}_{\nu_\perp}+H_{\nu_\perp}) =0\;.
\label{eq:phialpha} \end{aligned}$$ Equation (\[eq:ralpha\]) encodes the conservation of the modulus. Using the explicit form of $g_{\mu\nu}$ given in Eq. (\[eq:g-elements-spherical\]), Eqs. (\[eq:thetaalpha\]) and (\[eq:phialpha\]) become $$\begin{aligned}
&& {\rm D}_t^{(\alpha)}(\theta) -
\frac{\gamma_0}{1+\eta^2\gamma_0^2}
\left[ H_{{\rm eff},\phi} + H_\phi + \eta\gamma_0 ( H_{{\rm eff},\theta} + H_\theta) \right]
= 0
\;,
\label{eq:spherical-Landau1}
\\
&&
\sin\theta \ {\rm D}_t^{(\alpha)}(\phi) - \frac{\gamma_0}{1+\eta^2\gamma_0^2}
\left[
\eta\gamma_0 ( H_{{\rm eff},\phi} + H_\phi )
- ( H_{{\rm eff},\theta} + H_\theta)
\right]
= 0
\; .
\qquad
\label{eq:spherical-Landau2}\end{aligned}$$
Had we started from the Gilbert formulation of the sLLG equation in Cartesian coordinates, we would have naturally obtained $$\begin{aligned}
{\rm D}^{(\alpha)}_t(\theta) + \eta\gamma_0 \ \sin \theta \ {\rm D}^{(\alpha)}_t(\phi) - \gamma_0 \left( H_{{\rm{eff}}, \phi} + H_\phi \right) = 0 \; ,
\label{eq:thetaalpha-Gilbert} \\
- \sin\theta\, {\rm D}^{(\alpha)}_t(\phi) + \eta\gamma_0 \
{\rm D}^{(\alpha)}_t(\theta) -\gamma_0 \left( H_{{\rm{eff}}, \theta} + H_\theta \right) =0 \;.
\label{eq:phialpha-Gilbert} \end{aligned}$$ In this form, the random field $H_\theta, H_\phi$ may be erroneously interpreted as being additive, and that all discretization prescriptions are equivalent in spherical coordinates. This is not the case as the time-derivative of $\phi$ in Eqs. (\[eq:phialpha\]) and (\[eq:phialpha-Gilbert\]) are multiplied by a function of $\theta$. Moreover, we will see in Sec. \[sec:sph\_random\_field\] that, in the local coordinate system, the random field has a non-trivial distribution that depends on the discretization.
Summarizing, we have shown how to write the sLLG equation in spherical coordinates in a generic $\alpha$-prescription. For each prescription the stochastic equations are [*different*]{} and one can simply encode the dependence on $\alpha$ by introducing $\alpha$-covariant time-derivatives. When treated with the correct rules of stochastic calculus, all equations yield the same physical results.
An interesting observation is that in the case of a planar ferromagnet, *i.e.* when the magnetization is bound to live on the plane (moving on a circle), the equations no longer have any explicit dependence on $\alpha$. In this case, one can project the equations on the $x,y$ plane by setting $\theta=\pi/2$ and the $\alpha$-covariant time-derivatives reduce to the usual time-derivatives. This means that the sLLG equation is the same for all discretization schemes. We will see in Sec. \[sec:sph\_random\_field\] that in the case $\theta=\pi/2$, the noise in polar coordinate is a usual Gaussian white noise with vanishing mean. In other words, the stochastic evolution in two dimensions is driven by an effective [*additive*]{} noise, despite its original multiplicative character. However, this property only holds in two dimensions and it is not true in general.
Random field statistics {#sec:sph_random_field}
-----------------------
The probability distribution function of the random noise in the Cartesian coordinate system is Gaussian with zero average. This statistics does not directly translate into another coordinate system. The distribution in the transformed system has to be carefully studied if one wishes to use the rotated components of the random field. As we found some misconceptions in the literature regarding this point, in this Subsection we derive this distribution in spherical coordinates. The reader who is just interested in the generating functional construction can jump over this Subsection and go directly to Sec. \[sec:contruct\_spherical\].
The equations of motion do not involve the radial component of the random field, $H_{M_{{\rm s}}}$. We are then naturally interested in deriving the probability distributions of the orthoradial components, $P^{\rm sph}_{\rm n}[H_\theta,H_\phi]$. Let us start with the statistics of the random field in the Cartesian basis. The probability distribution of histories for such an isotropic Gaussian white noise is given by $$P_\mathrm{n}[H_x,H_y,H_z] \propto \exp\left\{-\frac{1}{4D}
\int{} {\hspace{-0em}\mathrm{d}{t}\;} \left[ H_x(t)^2+ H_y(t)^2 + H_z(t)^2 \right] \right\}\;.$$ The rotation to the spherical coordinate system, $$\begin{aligned}
P^{\rm sph}_{\rm n}[H_{M_{{\rm s}}}, H_\theta, H_\phi] = |\mathcal{J}^{\rm rot}| \ P_\mathrm{n}[R^{-1}_{x\mu} H_\mu,R^{-1}_{y\mu} H_\mu,R^{-1}_{z\mu} H_\mu]\;,\end{aligned}$$ with $$R^{-1}_{i\mu}(\mathbf{M}) = R^{-1}_{i \mu}(\theta,\phi) =
\!\!
\begin{array}{cc}
\left[
\begin{array}{ccc}
\sin\theta\cos\phi & \cos\theta\cos\phi & -\sin\phi \\
\sin\theta\sin\phi & \cos\theta\sin\phi & \cos\phi \\
\cos\theta & -\sin\theta & 0
\end{array}
\right]
\; ,
\end{array}
\label{eq:inverse-rotation-matrix0}$$ involves the Jacobian $$\begin{aligned}
\mathcal{J}^{\rm rot}
\equiv
\mathrm{det}_{i\nu,tt'}
\frac{\delta R^{-1}_{i\mu}(t) H_\mu(t)}{\delta H_\nu(t')}
\; .
\label{eq:Jacobian-rot}\end{aligned}$$ After a series of transformations detailed in App. \[app:rotation-noise\] we set the calculation of the determinant in a form that allows us to use the identity (\[eq:identity\]) with a causal $C_{\mu\nu}(w,v)$. In the present case, the noise dependence in the operator $C$ requires to keep the second-order contribution in the expansion, but all higher order terms vanish [@Arnold2000; @Lubensky2007]. We therefore use Eq. (\[eq:identity-random-field\]). After a lengthy computation detailed in App. \[app:rotation-noise\] the Jacobian ${\cal J}^{\rm rot}$ is found to be $$\begin{aligned}
\ln\mathcal{J}^{\rm rot}
&=
\int{\hspace{-0ex}\mathrm{d}{t}\;} R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\nu_\perp}} \frac{\delta \Omega_{\nu_\perp}(t)}{\delta H_{\mu}(t)} H_\rho(t)
\nonumber\\
& -\frac12 \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;}
R_{\mu_\perp j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\nu_\perp}(t')}
R_{\nu_\perp k}(t') \frac{\partial R^{-1}_{k\sigma}(t')}{\partial \Omega_{\kappa_\perp}} \frac{\delta \Omega_{\kappa_\perp}(t')}{\delta H_{\mu_\perp}(t)}
\nonumber\\
& \qquad\qquad\qquad
\times
H_\rho(t) H_\sigma(t')
\; .
\nonumber\end{aligned}$$ The “responses" $ {\delta \Omega_{\tau_\perp}(t)}/{\delta H_{\nu_\perp}(t')}$ are causal, making the integrand in the last term vanish for all $t'\neq t$. However, as it involves two random field factors (which are delta correlated) it may still yield a non-trivial contribution at $t=t'$. We will see that in cases in which the “equal-time responses” $ {\delta \Omega_{\tau_\perp}(t)}/{\delta H_{\nu_\perp}(t)}$ vanish (as in, [*e.g.*]{}, non-Markovian processes) the Jacobian turns out to be trivial and equals one, $ \mathcal{J}^{\rm rot} = 1$. This is the case for the Itô convention. However, the sLLGs in spherical coordinates and generic discretization prescription yield finite and non-vanishing equal-time responses and, hence, a non-trivial ${\mathcal J}^{\rm rot}$.
Using a more compact notation, the probability distribution function reads $$\begin{aligned}
&&
\ln P^{\rm sph}_{\rm n}[H_\mu] = -\frac{1}{4D} \int {\rm d} t \ H^2_\mu(t) + \int{\hspace{-0em}\mathrm{d}{t}\;} L_\rho(t) H_\rho(t)
\nonumber\\
&&
\;\;\;\qquad - \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;}
Q_{\rho\sigma}(t,t')
H_\rho(t) H_\sigma(t')
\; ,\end{aligned}$$ with $$\begin{aligned}
L_\rho(t) &\equiv& R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\mu}(t)} \; , \\
Q_{\rho\sigma}(t,t') &\equiv& R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\nu}(t')} R_{\nu k}(t') \frac{\partial R^{-1}_{k\sigma}(t')}{\partial \Omega_{\kappa_\perp}} \frac{\delta \Omega_{\kappa_\perp}(t')}{\delta H_{\mu}(t)}
\; . \end{aligned}$$
The responses can be computed by first formally recasting the solutions of the equations of motion (\[eq:thetaalpha-Gilbert\]) and (\[eq:phialpha-Gilbert\]) into $$\begin{aligned}
\theta(t) &= \theta_0 + \int_{t_0}^t{\hspace{-0ex}\mathrm{d}{t'}\;} \!\! \ldots + \frac{\gamma_0}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0ex}\mathrm{d}{t'}\;} \left[ H_\phi(t') + \eta\gamma_0 H_\theta(t') \right]\,, \label{eq:integre_theta} \\
\phi(t) &= \phi_0 + \int_{t_0}^t{\hspace{-0ex}\mathrm{d}{t'}\;} \!\! \ldots + \frac{\gamma_0}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0ex}\mathrm{d}{t'}\;} \frac{1}{\sin\theta(t')} \left[ \eta\gamma_0 H_\phi(t') - H_\theta(t') \right]\,, \label{eq:integre_phi}\end{aligned}$$ where we only expressed explicitly the kernels involving the random fields. The argument exposed in App. \[app:rotation-noise\] allows one to recast the last term in a form in which the product of random fields $H_\rho(t) H_\sigma(t')$ is replaced by its average, $2D \delta_{\rho\sigma} \delta(t-t')$, contracting the indices of the factors $Q$ and cutting one of the time integrals. In short, one only needs the equal-time responses of the polar coordinates with respect to variations of the random fields. These read, using $\int_{t_0}^t{\hspace{-0em}\mathrm{d}{t'}\;} \delta(t'-t) = \Theta(0) = \alpha$, $$\begin{aligned}
\frac{\delta \theta(t)}{\delta H_\theta(t)} &= \frac{\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0em}\mathrm{d}{t'}\;} \delta(t'-t) = \frac{\alpha\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \,,
\label{eq:equal-time1} \\
\frac{\delta \theta(t)}{\delta H_\phi(t)} & \
=
\frac{\gamma_0}{1+\eta^2\gamma_0^2}
\int_{t_0}^t {\rm d} t' \ \delta(t-t') = \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\; ,
\\
\frac{\delta \phi(t)}{\delta H_\theta(t)} &= -\frac{\gamma_0}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0em}\mathrm{d}{t'}\;} \frac{1}{\sin\theta(t')} \delta(t-t') = - \frac{1}{\sin\theta(t)} \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \,, \\
\frac{\delta \phi(t)}{\delta H_\phi(t)} &= \frac{\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \int_{t_0}^t{\hspace{-0em}\mathrm{d}{t'}\;} \frac{1}{\sin\theta(t')} \delta(t-t') =
\frac{1}{\sin\theta(t)} \frac{\alpha\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \,.
\label{eq:equal-time4}\end{aligned}$$ The first terms in Eqs. (\[eq:integre\_theta\]) and (\[eq:integre\_phi\]) give vanishing contributions since their integrands are finite at all times.
Using these results one calculates $L_\rho$ and $Q_{\rho\rho}$: $$\begin{aligned}
L_\rho(t) &=& \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\left[ 2\eta\gamma_0 \delta_{\rho M_{{\rm s}}} + \eta\gamma_0 \cot\theta \delta_{\rho\theta} + \cot\theta \delta_{\rho\phi} \right]
\; , \\
Q_{\rho\rho}(t,t) &=& \frac{\alpha^2\gamma_0^2}{1+\eta^2\gamma_0^2} \left(1+\frac{1}{\sin^2\theta} \right)
\; , \end{aligned}$$ and, after another lengthy calculation detailed in App. \[app:rotation-noise\], we obtain the following expression for $P_{\rm n}^{\rm sph}$ in terms of the random field components and the magnetization polar angles: $$\begin{aligned}
P_{\rm n}^{\rm sph}[H_\theta,H_\phi]
\propto &
\exp \int{\hspace{-0em}\mathrm{d}{t}\;}
\!\!
\left\{ -\frac{1}{4D} H^2_{\mu_\perp} \! (t)
+ \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \cot\theta(t) \ [\eta\gamma_0 H_\theta(t) + H_\phi(t) ]
\right.
\nonumber\\
&
\left.
\qquad\qquad\qquad
- \frac{\alpha^2\gamma_0^2 D}{1+\eta^2 \gamma_0^2} \cot^2\theta(t)
\right\}
\; .\end{aligned}$$ Itô calculus provides a special case in which a conventional Gaussian distribution is recovered. We stress that there is another special case in which this distribution boils down to a standard Gaussian distribution (with zero mean and delta correlations) for all discretization prescriptions: the case in which the magnetization is constrained to rotate on the plane $\theta=\pi/2$.
Fokker-Planck approach {#fokker-planck-approach}
----------------------
Following steps similar to the ones in Sec. \[sec:Fokker-Planck\] and in [@Fuller63], now for the $\alpha$-scheme spherical equations of motion, one finds the $\alpha$-generic Fokker-Planck equation $$\begin{aligned}
\partial_t P(\theta, \phi; t) \! \! & \! = \! & \! \!
- \partial_\theta
\left\{ [f_\theta + D(2\alpha-1) \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta
\right.
\nonumber\\
&&
\left.
\qquad\qquad
+ D \frac{\gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta ] P(\theta, \phi;t)
\right\}
\nonumber\\
&&
-\partial_\phi[f_\phi P(\theta, \phi; t)]
\nonumber\\
&&
-\frac{D\gamma_0^2}{1+\eta^2\gamma_0^2}
\left\{
\partial_\theta^2 P(\theta,\phi;t)
+\partial_\phi^2 [ \frac{1}{\sin^2\theta} P(\theta,\phi;t) ]
\right\}\end{aligned}$$ with $$\begin{aligned}
f_\theta &=& \frac{D(1-2\alpha)\gamma_0^2}{1+\eta^2\gamma_0^2} \ \cot \theta + \frac{\gamma_0}{1+\eta^2\gamma_0^2}
(H_{{\rm eff}, \phi} + \eta\gamma_0 H_{{\rm eff},\theta} )
\; ,
\nonumber\\
f_\phi &=&
\frac{\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{\sin\theta} (\eta\gamma_0 H_{{\rm eff}, \phi} - H_{{\rm eff},\theta} )
\; . \end{aligned}$$ As in the Cartesian case one finds that the drift term in $f_\theta$ cancels the following term and all explicit $\alpha$ dependence disappears form the Fokker-Planck equation. One can check that in the conservative case $$H_{{\rm eff},\theta} = - (M_{{\rm s}}\mu_0^{-1}) \ \partial_\theta U
\qquad\qquad
H_{{\rm eff},\phi} = - (M_{{\rm s}}\mu_0^{-1}) \ \frac{1}{\sin\theta} \partial_\phi U$$ the stationary probability density $$P_{\rm eq}(M_{{\rm s}}, \theta,\phi) = N \sin\theta \ e^{-\beta V U(\theta,\phi)}
\label{eq:equil-Pi-sph}$$ with $N$ a normalisation constant is a solution to the Fokker-Planck equation. as long as $D$ is given by Eq. (\[eq:D\]).
Landau generating functional {#sec:contruct_spherical}
----------------------------
The purpose of this Subsection is to derive the generating functional in the spherical coordinate system. The steps performed in this Section are very similar to the ones performed in Sec. \[sec:functional\] when working with Cartesian coordinates.
Given an initial condition ${M_{{\rm s}}}_0$, $\theta_0$ and $\phi_0$ that we collect in the vector notation ${\mathbf \Omega}_0 = \mathbf{\Omega}(t_0)$, and a particular realization of the Gaussian and zero-mean random variables $[{\mathbf H}]$ in the Cartesian coordinate system, there is a unique trajectory of the variables $[M_{{\rm s}}]$, $[\theta]$ and $[\phi]$, collected in $[{\mathbf \Omega}]$, that obeys the equations of motion. The generating functional is defined as $$\begin{aligned}
\mathcal{Z}[\boldsymbol{\lambda}] = \langle \
\exp \int {\hspace{-0ex}\mathrm{d}{t}\;} \boldsymbol{\lambda}(t) \cdot \mathbf{\Omega}_{\mathbf H}(t) \ \rangle
\; ,\end{aligned}$$ where $ \langle \cdots \rangle $ denotes the average over initial conditions and random field realizations. $\boldsymbol{\lambda}$ is a source that couples linearly to the fluctuating magnetization configuration $\mathbf{\Omega}_{\mathbf H}(t)$.
Similarly to the Cartesian case, we construct the MSRJD representation of the generating functional $\mathcal{Z}[\boldsymbol{\lambda}]$ by imposing the equation of motion with a functional delta-function $$\begin{aligned}
&&
{\cal Z}[\boldsymbol{\lambda}] = \int {\cal D}[\mathbf{H}] \ P_{\rm n}[\mathbf{H}] \
\int {\cal D}[\mathbf{\Omega}] \
P_{\rm i}[\mathbf{\Omega}(t_0), {\mathbf {H}}_{\rm eff}(t_0)]
\nonumber\\
&&
\qquad\quad
\ \times {\prod_{n=1}^N [M_{{\rm s}}^2\sin\theta_{n}]^{-1}}
\delta\Big{[} \mbox{\textbf{Eq}}^{\rm sph}[\mathbf{\Omega},\mathbf{H}] \Big{]}
\nonumber\\
&&
\qquad\qquad
\; \; \times \
\ |{\cal J}^{\rm sph}[\mathbf{\Omega},\mathbf{H}]|
\ \exp \int {\hspace{-0em}\mathrm{d}{t}\;} {\boldsymbol{\lambda}}(t) \cdot \mathbf{\Omega}(t)
\;.
\label{eq:generatingZ24}\end{aligned}$$ $P_{\rm n}[\mathbf{H}]$ is the probability distribution of the random field in Cartesian coordinates, that we still take to be Gaussian with zero mean, delta correlated and variance $2D$. For the moment we leave the initial probability density $P_{\rm i}$ general. A particular case is the one in which it is given by the equilibrium weight (\[eq:equil-Pi-sph\]). The measure over the spherical coordinates, ${\cal D}[\mathbf{\Omega}]$, is defined in App. \[app:conventions\] and includes a summation over the initial conditions at time $t_0$. The geometric factor $\prod_{n=1}^N |M_{{\rm s}}^2 \sin \theta_n |^{-1}$ accompanies the $\delta$ function in the spherical coordinate system, see also App. \[app:deltafunction\]. The Jacobian ${\cal J}^{\rm sph}[\mathbf{\Omega},\mathbf{H}]$ is $$\begin{aligned}
\label{eq:defjac}
\mathcal{J}^{\rm sph}[\mathbf{\Omega},\mathbf{H}] \equiv
\det_{\mu\nu;uv}
\begin{array}{c}
\displaystyle
\frac{\delta {\rm{Eq}}^{\rm sph}_{\mu}[\mathbf{\Omega},\mathbf{H}](u)}{\delta \Omega_{\nu}(v)}
\end{array}\end{aligned}$$ with the coordinate indices $\mu,\nu=M_{{\rm s}},\theta,\phi$ and the times $u,v$.
At this point we have the freedom to write the equation of motion in the Landau or Gilbert formulation. The advantage of the former lies in the fact that the time derivatives are well separated from the other terms, thus simplifying the analysis. We choose to use a modified Landau formulation that we compactly write as follows: $$\begin{aligned}
&
{\rm Eq}^{\rm sph}_{L,M_{{\rm s}}} = {{\rm d}}_t M_{{\rm s}}= 0
\; ,
\nonumber\\
&
{\rm Eq}^{\rm sph}_{L,\theta} = {\rm D}_t^{(\alpha)}(\theta) -
\frac{\gamma_0}{1+\eta^2\gamma_0^2} \left[ H_{{\rm eff},\phi} + H_\phi + \eta\gamma_0 (H_{{\rm eff}, \theta} +H_\theta)\right] = 0
\; ,
\nonumber\\
&
{\rm Eq}^{\rm sph}_{L,\phi} = {\rm D}_t^{(\alpha)}(\phi)
- \frac{\gamma_0}{1+\eta^2\gamma_0^2} \frac{1}{\sin\theta} \left[\eta\gamma_0 (H_{{\rm eff}, \phi}+H_\phi ) - (H_{{\rm eff},\theta} +H_\theta ) \right] = 0
\; .
\nonumber\end{aligned}$$ This form is convenient since, as the derivatives are separated from the rest, it is relatively simple to compute the Jacobian (as opposed to what has to be done in the Gilbert formulation that we develop in App. \[sec:construct\_spherical\_Gilbert\]).
The operator in the determinant can be worked out explicitly as explained in App. \[app:MSRDJ-Jacobian-Gus\] $$\begin{aligned}
&&
{\cal J}_L^{\rm sph}
=
\exp
\left\{
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;}
\left[
\frac{D(1-\alpha)\gamma_0}{\sin^2\theta}
\right.
\right.
\nonumber\\
&&
\left.
\left.
\qquad\qquad
- \partial_\theta
\left[
H_{{\rm eff},\phi} + H_{\phi} + \eta\gamma_0 (H_{{\rm eff},\theta} + H_\theta)
\right]
\right.
\right.
\nonumber\\
&&
\left.
\left.
\qquad\qquad
+ \frac{1}{\sin\theta} \partial_\phi
\left[
H_{{\rm eff},\theta} + H_\theta
-
\eta\gamma_0 (H_{{\rm eff},\phi} + H_\phi)
\right]
\right]
\right\}
\; .
\label{eq:Jacobian-Landau-spherical}\end{aligned}$$ As found in the Cartesian calculation, it does not depend on the parallel component of the field, that in spherical coordinates means that ${\cal J}_L^{\rm sph}$ is independent of $H_{{\rm eff},M_{{\rm s}}}+H_{M_{{\rm s}}}$.
We next introduce an adimensional Lagrange multiplier $[{{\rm i}}\hat{\mathbf{\Omega}}]$ to exponentiate the functional delta: $$\int {\mathcal{D}}{[{{\rm i}}\hat{\mathbf \Omega}]} \exp \left\{ - \int \! {\hspace{-0em}\mathrm{d}{t}\;}
\left(
{{\rm i}}\hat\Omega_{M_{{\rm s}}} \mbox{{Eq}}^{\rm sph}_{M_{{\rm s}}}[{\mathbf \Omega}]
+
{{\rm i}}\hat\Omega_\theta \mbox{{Eq}}^{\rm sph}_\theta[{\mathbf \Omega}, {\mathbf H}]
+
{{\rm i}}\hat\Omega_\phi \mbox{{Eq}}^{\rm sph}_\phi[{\mathbf \Omega}, {\mathbf H}]
\right)
\right\}
\; .$$ We identify all the terms in the integrand of the exponent that involve the random field ${\mathbf H}$: $$\begin{aligned}
&&
-\frac{1}{4D} H_i^2
+ \frac{\gamma_0}{1+\eta^2\gamma_0^2}
\left(
{{\rm i}}\hat\Omega_\phi \frac{1}{\sin\theta} \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right)
+
{{\rm i}}\hat\Omega_\theta \left( R_{\phi i} + \eta\gamma_0 R_{\theta i} \right)
\right) H_i
\nonumber\\
&&
\qquad
+ \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\left( -\partial_\theta R_{\phi i}
- \eta\gamma_0 \partial_\theta R_{\theta i}
-\frac{\eta\gamma_0}{\sin\theta} \partial_\phi R_{\phi i}
+ \frac{1}{\sin\theta} \partial_\phi R_{\theta i}
\right) H_i\;.
\qquad\end{aligned}$$ The quadratic term in $H_i$ comes from its probability distribution. The first set of linear terms comes from imposing the equations of motion with the Dirac delta function. The third group of terms comes from the Jacobian. Contrary to the Cartesian case, the latter will yield non-trivial contributions to the action. After integration and a number of simplifications that use the explicit expression of the rotation matrix $R$ one finds that these terms give rise to $$\begin{aligned}
\frac{D \gamma_0^2}{1+\eta^2\gamma_0^2} \left[
\frac{({{\rm i}}\hat\Omega_\phi)^2}{\sin^2\theta} + ({{\rm i}}\hat\Omega_\theta)^2
+ 2\alpha {{\rm i}}\hat\Omega_\theta \cot\theta
+ \frac{\alpha^2}{\sin^2\theta}
\right]\end{aligned}$$ (apart from an irrelevant additive constant). The last term is of the same form as the first term in ${\cal J}_L^{\rm sph}$ and we will combine them together when writing $\widetilde S^{\rm sph}_{{\rm jac}}$ below.
We now perform the change of fields $$\begin{aligned}
{{\rm i}}\hat\Omega_\phi \mapsto \sin\theta \, {{\rm i}}\hat\Omega_\phi \;,\end{aligned}$$ which comes with a Jacobian $$\begin{aligned}
\prod_{n=0}^{N-1}
|
\sin\bar\theta_n
|\;, \label{eq:detedete4}\end{aligned}$$ where we were careful to evaluate the factors on the intermediate points $\bar \theta_n \equiv \alpha \theta_{n+1} + (1-\alpha) \theta_n$. Notice indeed that the discretization matters here since there is no trivial continuous limit of this expression. See also the discussion in Sect. \[subsec:rules\]. The product above can be re-writen as $$\begin{aligned}
\prod_{n=0}^{N-1}
|
\sin\bar\theta_n
|
=
{{\rm e}}^{(1-\alpha) \ln \left| \frac{\sin\theta_0}{\sin\theta_N} \right| }
\prod_{n=1}^{N}
|
\sin\theta_n
|
\;, \label{eq:detedetee4}\end{aligned}$$ where we used the development $$\begin{aligned}
\sin\bar\theta_n
=
\alpha \sin \theta_{n+1} + (1-\alpha) \sin \theta_n\;,\end{aligned}$$ and the fact that we do not need to consider higher order terms because they vanish from Eq. (\[eq:detedete4\]) once the limit $\delta t \to 0$ is considered. The product $\prod_{n=1}^{N}
| \sin\theta_n |$ in Eq. (\[eq:detedetee4\]) cancels exactely the geometric one accompanying the delta functions in Eq. (\[eq:generatingZ24\]).
We now put all these results together to write the generating functional $$\mathcal{Z}[\boldsymbol{\lambda}] =
\int {\mathcal{D}}[\boldsymbol{\Omega}] {\cal D}[\hat{\boldsymbol{\Omega}}] \
\exp\left( S_L^{\rm sph}[\boldsymbol{\Omega},\hat{\boldsymbol{\Omega}}] + \int{\hspace{-0em}\mathrm{d}{t}\;}\boldsymbol{\lambda} \cdot \boldsymbol{\Omega} \right)\;,$$ with the measure ${\cal D}[\boldsymbol{\Omega}] \equiv \lim\limits_{N\to\infty} \prod_{n=0}^N {{\rm d}}{M_{{\rm s}}}_n {{\rm d}}\theta_n {{\rm d}}\phi_n \, {M_{{\rm s}}}_n^2 |\sin\theta_n|$ (that includes the initial time $t_0$), the full action $$S_L^{\rm sph}= S^{\rm sph}_{L,{\rm det}} + \widetilde S^{\rm sph}_{L,{\rm diss}} + \widetilde S^{\rm sph}_{L,{\rm jac}}$$ and $$\begin{aligned}
S^{\rm sph}_{L,{\rm det}} \! & \! = \! & \!
\ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)] -
\int {\rm d}t \
\left\{
{{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}\right.
\nonumber\\
&&
\;
+ {{\rm i}}\hat\Omega_\theta
\left[ {\rm D}_t^{(\alpha)}(\theta) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} H_{{\rm eff}, \phi} \right]
\nonumber\\
&&
\left.
\;
+ {{{\rm i}}\hat\Omega_\phi} \left[ \sin\theta {\rm D}_t^{(\alpha)}(\phi) + \frac{\gamma_0}{1+\eta^2\gamma_0^2} H_{{\rm eff}, \theta} \right]
\right\} ,
\qquad
\label{eq:action-det-sph-L}
\\
\widetilde S^{\rm sph}_{L,{\rm diss}} \! & \! = \! & \!
\frac{D \gamma_0^2}{1+\eta^2\gamma_0^2}
\int {\rm d}t
\left[
{({{\rm i}}\hat\Omega_\phi)^2} + ({{\rm i}}\hat\Omega_\theta)^2
+
2\alpha {{\rm i}}\hat\Omega_\theta \cot\theta
\right]
\nonumber\\
&&
\;\;
+ \frac{\eta\gamma^2_0}{1+\eta^2\gamma_0^2}
\int {{\rm d}}t \left({{\rm i}}\hat \Omega_\theta H_{{\rm eff}, \theta} + \frac{{{\rm i}}\hat \Omega_\phi}{\sin\theta} H_{{\rm eff}, \phi}
\right)
,
\label{eq:action-diss-sph}\end{aligned}$$ $$\begin{aligned}
\widetilde S^{\rm sph}_{L,{\rm jac}} \! & \! = \! &\!
(1-\alpha) \ln \left| \frac{\sin\theta_0}{\sin\theta_N} \right| \nonumber \\
&&
+ \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;}
\left[
\frac{D\gamma_0}{\sin^2\theta}
- \partial_\theta
\left(
H_{{\rm eff},\phi} + \eta\gamma_0 H_{{\rm eff},\theta}
\right)
\right.
\nonumber\\
&&
\left.
\qquad\qquad\qquad\qquad
+ \frac{1}{\sin\theta} \partial_\phi
\left(
H_{{\rm eff},\theta}
-
\eta\gamma_0 H_{{\rm eff},\phi}
\right)
\right]
.
\end{aligned}$$
The expressions above can be modified to obtain a slightly more compact, and eventually more convenient, form. $\widetilde S_{L,{\rm diss}}^{\rm sph}$ includes a linear term in ${{\rm i}}\hat\Omega_\theta$ that can be replaced with the help of the identity $$\begin{aligned}
&&
\int d\phi \ \exp\left[ ({{\rm i}}\sigma \phi)^2 - {{\rm i}}\phi b - {{\rm i}}\phi a \right]
\nonumber\\
&&
\qquad\qquad
=
\int d\phi \ \exp\left[ ({{\rm i}}\sigma \phi)^2 - {{\rm i}}\phi b - \frac{a^2}{4\sigma^2} - \frac{ab}{2\sigma^2} \right]
\; .
\label{eq:identity-Gus}\end{aligned}$$ We apply it to the functional integration over ${{\rm i}}\hat \Omega_\theta$ by choosing $$\begin{aligned}
&&
\sigma^2 =
\frac{D\gamma_0^2}{1+\eta^2\gamma_0^2}
\; ,
\nonumber\\
&&
a=-\frac{2D\gamma_0^2\alpha}{1+\eta^2\gamma_0^2} \ \cot\theta
\; ,
\nonumber\\
&&
b =
{\rm D}_t^{(\alpha)}(\theta) -
\frac{\gamma_0}{1+\eta^2\gamma_0^2}
(H_{{\rm eff},\phi}+\eta\gamma_0 H_{{\rm eff}, \theta})
\; .
\nonumber\end{aligned}$$ The integration generates the terms $$\begin{aligned}
-\frac{a^2}{4\sigma^2} - \frac{ab}{2\sigma^2}
= &
-\frac{\alpha^2 D \gamma_0^2}{1+\eta^2\gamma_0^2} \ \cot^2\theta
\nonumber\\
&
+ \alpha\cot\theta \
[{\rm D}_t^{(\alpha)}(\theta) - \frac{\gamma_0}{1+\eta^2\gamma_0^2} (H_{{\rm eff},\phi}+\eta\gamma_0 H_{{\rm eff}, \theta})]
\; . \end{aligned}$$ We rewrite the full action as $S= S^{\rm sph}_{L,{\rm det}} + S^{\rm sph}_{L,{\rm diss}} + S^{\rm sph}_{\rm jac}$, with $S^{\rm sph}_{L,{\rm det}}$ given in Eq. (\[eq:action-det-sph-L\]) that we repeat here to ease the reading of the final result, $$\begin{aligned}
S^{\rm sph}_{L,{\rm det}} \! & \! = \! & \!
\ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)] -
\int {\rm d}t \
\left\{
{{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}\right.
\nonumber\\
&&
\;
+ {{\rm i}}\hat\Omega_\theta
\left[ {\rm D}_t^{(\alpha)}(\theta)
- \frac{\gamma_0}{1+\eta^2\gamma_0^2} H_{{\rm eff}, \phi} \right]
\nonumber\\
&&
\left.
\;
+ {{{\rm i}}\hat\Omega_\phi} \left[ \sin\theta {\rm D}_t^{(\alpha)}(\phi) + \frac{\gamma_0}{1+\eta^2\gamma_0^2}
H_{{\rm eff}, \theta}) \right]
\right\} ,
\qquad
\label{eq:action-det-sph-L2}
\\
S^{\rm sph}_{L,{\rm diss}} \! & \! = \! & \!
\frac{\gamma_0}{1+\eta^2\gamma_0^2}
\int {\rm d}t
\left[
D\gamma_0 \left( {{\rm i}}\hat\Omega_\phi \right)^2 + D\gamma_0 ({{\rm i}}\hat\Omega_\theta)^2
\right.
\nonumber\\
&&
\left.
\;\;\;\;\qquad\qquad + \eta\gamma_0
\left({{\rm i}}\hat \Omega_\theta H_{{\rm eff}, \theta} + {{{\rm i}}\hat \Omega_\phi} H_{{\rm eff}, \phi}
\right)
\right]
,
\label{eq:action-diss-sph-L}
\\
S^{\rm sph}_{L,{\rm jac}} \! & \! = \! &\! (1-\alpha) \ln \left| \frac{\sin\theta_0}{\sin\theta_N} \right| + \alpha \int {{\rm d}}t \ \cot\theta \ {\rm D}_t^{(\alpha)}(\theta)
\nonumber\\
&&
\;\; +
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;}
\!
\left[
\frac{(1-\alpha)D\gamma_0}{\sin^2\theta} - \cot \theta (H_{{\rm eff},\phi} + \eta\gamma_0 H_{{\rm eff},\theta})
\right.
\nonumber\\
&&
\qquad\qquad\qquad\qquad
- \partial_\theta
\left(
H_{{\rm eff},\phi} + \eta\gamma_0 H_{{\rm eff},\theta}
\right)
\nonumber\\
&&
\left.
\qquad\qquad\qquad\qquad
+ \frac{1}{\sin\theta} \partial_\phi
\left(
H_{{\rm eff},\theta}
-
\eta\gamma_0 H_{{\rm eff},\phi}
\right)
\right]
.
\label{eq:esferica-jac}
\end{aligned}$$ This completes the construction of the generating functional for the Landau formulation of the dynamics in the spherical coordinate system.
The construction of the Gilbert action reported in App. \[sec:construct\_spherical\_Gilbert\] leads to $$\begin{aligned}
S^{\rm sph}_{G,{\rm det}} \!\! & \!\! = \! \! & \!
\ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)]
-
\int {\rm d}t
\left\{ {{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}+ {{\rm i}}\hat\Omega_\theta
[ {\rm D}_t^{(\alpha)}(\theta) - \gamma_0 H_{{\rm eff}, \phi}
]
\right.
\nonumber\\
&&
\left.
\!\!
- {{\rm i}}\hat\Omega_\phi
[ \sin\theta {\rm D}_t^{(\alpha)}(\phi) + \gamma_0 H_{{\rm eff}, \theta}
]
\right\}
,
\label{eq:action-det-sph-Gilbert-maintext}\\
S^{\rm sph}_{G,{\rm diss}} \!\! & \!\! = \!\! & \!\!
\int {\rm d}t
\left[
D \gamma_0^2 ({{\rm i}}\hat\Omega_\phi)^2 + D \gamma_0^2 ({{\rm i}}\hat\Omega_\theta)^2
- {{\rm i}}\hat\Omega_\theta \eta\gamma_0 \sin\theta {\rm D}_t^{(\alpha)}(\phi)
\right.
\nonumber\\
&&
\left.
\qquad\quad
- {{\rm i}}\hat\Omega_\phi \eta\gamma_0 {\rm D}_t^{(\alpha)}(\theta)
\right]
\;,
\label{eq:action-diss-sph-Gilbert-maintext}
\\
S^{\rm sph}_{G,{\rm jac}} \!\! & \!\! = \!\! & \!
S^{\rm sph}_{L,{\rm jac}}
\label{eq:action-jac-sph-Gilbert-maintext}
\end{aligned}$$ and $S_G^{\rm sph} = S_{G, {\rm det}}^{\rm sph} + S_{G, {\rm diss}}^{\rm sph} + S_{G, {\rm jac}}^{\rm sph}$. One can easily check that one can go from the Landau to the Gilbert formalism and [*vice versa*]{} within the path-integral [*via*]{} a change of variables of the auxiliary fields, similarly to what we discussed in the Cartesian coordinate system around Eqs. (\[eq:Trans\_L2G\]) and (\[eq:Trans\_G2L\]): $$\begin{aligned}
{{\rm i}}\hat \Omega^L_\theta &=& {{\rm i}}\hat \Omega^G_\theta + \eta\gamma_0 \ {{\rm i}}\hat\Omega^G_\phi
\; ,
\\
{{\rm i}}\hat\Omega^L_\phi &=& \eta\gamma_0 \ {{\rm i}}\hat\Omega^G_\theta - {{\rm i}}\hat\Omega^G_\phi
\; ,\end{aligned}$$ with inverse $$\begin{aligned}
{{\rm i}}\hat \Omega_\theta^G &=& \frac{1}{1+\eta^2\gamma_0^2} \left[ {{\rm i}}\hat \Omega_\theta^L + \eta\gamma_0 \ {{{\rm i}}\hat \Omega_\phi^L} \right]
\; ,
\nonumber\\
{{\rm i}}\hat \Omega_\phi^G &=& \frac{1}{1+\eta^2\gamma_0^2} \left[\eta\gamma_0 \ {{\rm i}}\hat \Omega_\theta^L - {{{\rm i}}\hat \Omega_\phi^L} \right]
\; . \end{aligned}$$
Conclusions {#sec:recap}
===========
In this manuscript we revisited the stochastic approach to the dynamics of a magnetic moment under the effect of thermal noise, dissipation, magnetic field of potential origin and, also, non-potential forces such as spin-torque terms. We used the stochastic Landau-Lifshitz-Gilbert (sLLG) equation as a phenomenological description of the dynamics and we constructed a functional generating functional for physical observables.
We found rather confusing statements on the influence (or not) of the discretization scheme used to define the stochastic dynamics in discrete time in the literature [@Berkov2002]. Our first goal was to insist upon the fact that unless the Stratonovitch prescription is used to define the sLLG, a drift term has to be added to the equation of motion. The drift term ensures both the conservation of the magnetization modulus and the approach to Boltzmann equilibrium under conservative magnetic fields.
We also formulated the problem in the spherical coordinate system. Although this is the most natural framework to work in, due to the explicit conservation of the modulus of the magnetization, it has been the source of many confusing statements in the literature. For instance, it is stated in [@Martinez-etal] that the random field in the spherical coordinate system is additive. In Sec. 7.3.1 in [@Langevin-Coffey] it is written that the spherical components of the random field is a Gaussian with zero mean. In this paper we showed that the polar coordinate field acquires a non-vanishing average. We clarified these issues not only in the standard Itô and Stratonovich schemes but also in the general $\alpha$ prescription. This is an important result for the correct numerical study of the magnetization dynamics.
We then derived the drift term to be added to the equation for the polar angle. We showed that the evolution dictated by this $\alpha$ prescription stochastic equations leads to the equilibrium Gibbs-Boltzmann distribution independently of $\alpha$.
Next, we focused on the construction of the generating functional. We stressed that physical results should be independent of the framework used to write the path-integral, this being the Landau [*vs.*]{} Gilbert formulation of the dynamics, the $\alpha$-prescription, or whether we use Cartesian or spherical coordinates.
The equivalence between the Landau and Gilbert formulations at the level of the equations of motion was carefully discussed in several textbooks on this subject [@Bertotti-etal]. We showed explicitly how this equivalence is realized in the path-integral formalism.
We proved the independence of the $\alpha$-prescription in Sec. \[sec:Fokker-Planck\] within the framework of the Fokker-Planck equation. The $\alpha$-invariance of physical results can also be shown within the generating functional formalism but, as the action depends explicitly on $\alpha$, this feature is less trivial to show in this set-up. One way to prove invariance is to use an underlying BRST symmetry [@arenas2010]. Another possibility is to construct a perturbative expansion and to show invariance in this way [@Honkonen]. In both cases, an interplay between the contributions of all parts in the action, including the Jacobian, are necessary to establish invariance.
At the level of the stochastic equations of motion, one can go from Cartesian to spherical expressions by using the transformation rules for the change of basis and the generalized chain-rule for the time-derivative. In the Fokker-Planck formalism, a change of variables also allows one to relate Cartesian and spherical approaches. However, at the level of the path-integral, the equivalence is more subtle. As it is well-known from the results in [@Edwards64; @Jevicki76; @Tirapegui82; @Alfaro92], a non-linear change of variables in the path-integral generates non-trivial extra terms in the action (beyond the formal change of variables and the corresponding Jacobian). These are found also in this particular case. We have not discussed this issue in further detail in this manuscript since the more adequate scheme to do it is the BRST formalism [@Alfaro92] that we will develop elsewhere.
Our work can be extended in different directions. For simplicity, we presented the path-integral for a single magnetic moment. The sLLG equation can be easily generalized to the case of a space-dependent magnetization by introducing a Ginzburg-Landau free-energy functional [@Bertotti-etal; @Langevin-Coffey; @Martinez-etal]. The generalization of the generating functional construction to this case is straightforward. It will be useful to treat micromagnetism [@Ralph2008] and, in particular, the dynamics of magnetic domains.
A field in which the path-integral formulation of the stochastic dynamics has been specially successful is the one of systems with quenched randomness. As known since the work in [@deDominicis76], the average over quenched disorder is simple to perform within this functional framework and allows the analytic treatment of many interesting phenomena [@LesHouches].
Path integral measure {#app:discrete}
=====================
The time interval $t\in [t_0,\mathcal{T}]$ is divided in $N$ discrete time intervals, $t_n \equiv t_0 + n \Delta t$ with $n=0, \ldots, N$ and increment $\Delta t \equiv (\mathcal{T}-t_0)/N$. The continuous time limit is performed by sending $N$ to infinity while keeping ${\cal T}-t_0$ finite.
We define the path integral over functions defined on the time interval $[t_0,\mathcal{T}]$ as $$\begin{aligned}
\int{\mathcal{D}}{[{\mathbf x}]} \equiv \lim\limits_{N\to\infty} \prod_{n=0}^N \int {\hspace{-0ex}\mathrm{d}{{\mathbf x}_n}\;}
\; . \end{aligned}$$
When integrating over the magnetization, a 3-dimensional field in Cartesian coordinates, $$\begin{aligned}
\int{\mathcal{D}}{[\mathbf{M}]} \equiv \lim\limits_{N\to\infty} \prod_{n=0}^N \int {\hspace{-0ex}\mathrm{d}{\mathbf{M}_n}\;} \;,\end{aligned}$$ the integration on each time-slice is performed over the $\mathbb{R}^3$ space, and the spherical constraint is imposed by the equation of motion. More specifically, it is imposed through the ${{\rm i}}\hat{M}_\parallel$ sector of the path-integral expression of the generating functional, see Sec. \[sec:conservation\_modulus\].
Gilbert Cartesian generating functional {#app:path-integral:Gilbert}
=======================================
We start from the evolution equation in the $\alpha$-covariant Gilbert formulation in Cartesian coordinates, $$\mbox{\bf Eq}_G[ {\mathbf M}, {\mathbf H} ]
\equiv {\rm D}_t^{(\alpha)} {\mathbf M} + \gamma_0 \left( {\mathbf H}_{\rm eff} + {\mathbf H} - \frac{\eta}{M_{{\rm s}}} {\rm D}_t^{(\alpha)} {\mathbf M} \right) =
{\mathbf 0}
\; ,
\label{eq:Gilbert-alpha-gen}$$ and we impose this equation in a path integral over ${\mathbf M}$ as described in Sec. \[sec:functional\]. The Jacobian that ensures that the integration over $\mathbf{M}$ equals one is given by $$\begin{aligned}
\mathcal{J}_G[\mathbf{M},\mathbf{H}] \equiv
\det_{ij;uv}
\begin{array}{c}
\displaystyle
\frac{\delta {\rm Eq}_{Gi}(u)}{\delta M_{j}(v)}
\end{array}\end{aligned}$$ with Eq$_G$ given in Eq. (\[eq:Gilbert-alpha-gen\]). The operator in the determinant can be worked out explicitly and put into the form $$\frac{\delta \mbox{Eq}_{Gi}(u)}{\delta M_j(v)}
=
X_{ij}(u) {\rm d}_u \delta(u-v) + A_{ij}(v) \delta(u-v)$$ with $$\begin{aligned}
X_{ij}(u) &\equiv \delta_{ij} + \frac{\eta\gamma_0}{M_{{\rm s}}} \epsilon_{ijk} M_k(u)
\; ,
\\
A_{ij} &\equiv
\gamma_0 \epsilon_{ijk} ( {H_{\rm eff}}_k + H_k)
+ \gamma_0 \epsilon_{ilk} M_l \partial_j {H_{\rm eff}}_k
- \frac{\eta\gamma_0}{M_{{\rm s}}} \epsilon_{ijk} {\rm d}_t M_k
\nonumber\\
& \;\;\;\; + 2D (1-2\alpha) \frac{\gamma_0^2}{1+\eta^2 \gamma_0^2} \delta_{ij}
\;.\end{aligned}$$ Factorizing the operator $X_{ik}(u) {\rm d}_u \delta(u-w)$, with inverse $X^{-1}_{kj}(v) \Theta(w-v)$, $$\begin{aligned}
X^{-1}_{ij}(u) = \frac{1}{1+\eta^2 \gamma_0^2} \left[\delta_{ij} - \frac{\eta\gamma_0}{M_{{\rm s}}} \epsilon_{ijk} M_k(u)
+ \frac{\eta^2\gamma_0^2}{M_{{\rm s}}^2} M_i(u) M_j(u) \right]
\; , \end{aligned}$$ we write $$\begin{aligned}
\frac{\delta \mbox{Eq}_{Gi}(u)}{\delta M_j(v)}
= & \int {\hspace{-0em}\mathrm{d}{w}\;} \ X_{ik}(u) {\rm d}_u \delta(u-w)
\nonumber\\
&
\qquad \times \left[ \delta_{kj} \delta(w-v) + \Theta(w-v) X^{-1}_{kl}(v) A_{lj} (v) \right]
\; . \end{aligned}$$ The Jacobian becomes $$\begin{aligned}
& \mathcal{J}_G[\mathbf{M}, \mathbf{H}]
=
\; \det_{ik;uw} \left[ X_{ik}(u) {\rm d}_u\delta(u-w)\right]
\nonumber\\
&
\qquad \times
\det_{kj;wv} \left[
\delta(w-v) \delta_{kj}
+ \Theta(w-v) X^{-1}_{kr}(v) A_{rj}(v) \right]
\; .
\end{aligned}$$ \[sec:discussRVsA2\] Notice that the first factor is actually independent of $\mathbf{M}$. Indeed, using $\det_{ik;uw} [X_{ik}(u) {\rm d}_u \delta(u-w) ]=
\det_{ij;uv} [X_{ij}(u) \delta(u-v)] \det_{jk;vw} [\delta_{jk} {\rm d}_v\delta(v-w)]$, one easily finds $\det_{ij;uv} [X_{ij}(u) {\rm d}_u \delta(u-v) ]
\propto
\prod_u \det_{ij} [\delta_{ij} + \frac{\eta\gamma_0}{M_{{\rm s}}} \epsilon_{ijk} M_k(u)]
= \prod_u [1 + \eta^2\gamma_0^2]$, a trivial constant. We treat the second determinant, that depends upon $A_{ij}$ and hence $\mathbf{H}$, with the identity (\[eq:identity\]) to obtain $$\begin{aligned}
\mathcal{J}_G[{\mathbf M}, {\mathbf H}]
\propto \; &
\exp \left( \alpha \int {\hspace{-0ex}\mathrm{d}{t}\;} X^{-1}_{jr} A_{rj} \right)
\;. \end{aligned}$$ In this case only the first term in the expansion yields a non-trivial contribution. Performing the contractions with $X^{-1}_{jr}$, we find $$\begin{aligned}
\mathcal{J}_G[{\mathbf M}, {\mathbf H}]
& \!\! \!\!
\propto \!\! \!\! &
\exp \left\{ \frac{\alpha\gamma_0}{1+\eta^2 \gamma_0^2}
\int {\hspace{-0ex}\mathrm{d}{t}\;} \Big{[}
\frac{2\eta\gamma_0}{M_{{\rm s}}} \ \mathbf{M} \cdot ({\mathbf{H}_{\rm eff}} +\mathbf{H})
\right.
\nonumber\\
&&
\;\;
\left.
+ \frac{\eta\gamma_0}{M_{{\rm s}}} (M_k M_j -\delta_{kj} M_{{\rm s}}^2)\partial_j {H_{\rm eff}}_k
+ \epsilon_{jlk} M_l \partial_j {H_{\rm eff}}_k
\Big{]}\! \right\}
\nonumber
\end{aligned}$$ where we omitted a constant factor. This result coincides with the Jacobian in the Landau formulation, see Eq. (\[eq:Jcart-L\]), and $${\cal J}_G[{\mathbf M}, {\mathbf H}]
=
{\cal J}_L[{\mathbf M}, {\mathbf H}]
\; .$$
Coming back to the generating functional ${\cal Z}[\boldsymbol{\lambda}]$, we now exponentiate the delta functional with an auxiliary field ${{\rm i}}\hat {\mathbf M}$ that imposes Eq. (\[eq:Gilbert-alpha-gen\]) as $$\begin{aligned}
\delta \Big{[} \mbox{\textbf{Eq}}_G[\mathbf{M}, \mathbf{H}] \Big{]}
\propto
\int {\cal D}[\hat{\mathbf{M}}] \
\exp \int {\hspace{-0ex}\mathrm{d}{t}\;} \ {{\rm i}}\hat{\mathbf{M}} \cdot \mbox{\textbf{Eq}}_G[\mathbf{M},\mathbf{H}]
\; .
\nonumber\end{aligned}$$ From the very structure of the equation it is clear that after decomposing the auxiliary field in two components ${{\rm i}}\hat{\mathbf M}_\perp$ and ${{\rm i}}\hat {\mathbf M}_\parallel$ perpendicular and parallel to ${\mathbf M}$, respectively, one has $$\begin{aligned}
\delta \Big{[} \mbox{\textbf{Eq}}_G[\mathbf{M}, \mathbf{H}] \Big{]}
\propto &
\int {\cal D}[\hat{\mathbf{M}}_\perp] {\cal D}[\hat{\mathbf{M}}_\parallel] \
\exp \int {\hspace{-0ex}\mathrm{d}{t}\;} \ {{\rm i}}\hat{\mathbf{M}}_\perp \cdot \mbox{\textbf{Eq}}_G[\mathbf{M},\mathbf{H}]
\nonumber\\
&
\qquad\qquad
\times
\exp \int {\hspace{-0ex}\mathrm{d}{t}\;} \ {{\rm i}}\hat{\mathbf{M}}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M}
\; .
\nonumber\end{aligned}$$
The integration over the Gaussian white noise $\mathbf{H}$ involves the following terms in the exponential: $$\frac{2\alpha\eta\gamma_0^2}{(1+\eta^2\gamma_0^2) M_{{\rm s}}} \mathbf{M} \cdot \mathbf{H}
+ \gamma_0 {{\rm i}}\hat{\mathbf{M}}_\perp \cdot (\mathbf{M} \wedge \mathbf{H})
- \frac{\mathbf{H}^2}{2D}
\; .$$ The Gaussian integral then yields $D [ 4\alpha^2\eta^2\gamma_0^4/(1+\eta^2 \gamma_0^2)^2 + \gamma_0^2 (\epsilon_{ijk} {{\rm i}}{\hat M}_{\perp_i} M_j)^2] $. The first term is just a constant while the second one is non-trivial. We then recast the generating functional into the form $${\cal Z}[\boldsymbol{\lambda}] =
\int {\cal D}[\mathbf{M}] {\cal D}[\hat{\mathbf{M}}_\perp] {\cal D}[\hat{\mathbf{M}}_\parallel]
\ \exp \left(S_G+\int {\hspace{-0ex}\mathrm{d}{t}\;} \ \boldsymbol{\lambda} \cdot \mathbf{M} \right)
\; ,$$ where we neglected all trivial constant factors, with an action $S_G$ that reads $$S_G= \widetilde S_{G,{\rm det}} + \widetilde S_{G, {\rm diss}} + S_{{\rm jac}}\;,$$ and $$\begin{aligned}
&&
\widetilde S_{G,{\rm det}} =
\ln P_{{\rm i}}[\mathbf{M}_0, \mathbf{H}_{\rm eff}(t_0)]
+
\int {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf M}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M}
\nonumber\\
&&\qquad\qquad
+
\int {\hspace{-0em}\mathrm{d}{t}\;}
{{\rm i}}\hat{\mathbf{M}}_\perp \cdot \left({\rm D}^{(\alpha)}_t{\mathbf{M}} + \gamma_0 \mathbf{M} \wedge \mathbf{H}_{\rm eff}
\right)
\; ,
\;\;\;\;\;\;\;\;\; \\
&& \widetilde S_{G,{\rm diss}} =
\int {\hspace{-0em}\mathrm{d}{t}\;}
\left({{\rm i}}\hat{\mathbf{M}}_\perp \wedge {\mathbf{M}}\right) \cdot
\left( D \gamma_0^2 \ {{\rm i}}\hat{\mathbf{M}}_\perp \wedge {\mathbf{M}} - \frac{\eta\gamma_0}{M_{{\rm s}}} {\rm D}^{(\alpha)}_t{\mathbf{M}} \right)
\; ,
\label{eq:S_diss_cart}
\qquad
\\
&& S_{\rm jac}
=
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\int {\hspace{-0em}\mathrm{d}{t}\;} \Big{\{}
\frac{2 \eta\gamma_0}{M_{{\rm s}}} \ \mathbf{M} \cdot \mathbf{H}_{\rm eff}
\nonumber\\
&&
\qquad\qquad\qquad + \Big{[}\frac{\eta\gamma_0}{M_{{\rm s}}} (M_i M_j - \delta_{ij} M_{{\rm s}}^2) +\epsilon_{ijk} M_k) \Big{]}
\partial_j {H_{\rm eff}}_i
\Big{\}}
\; .
\;\;\;\;\;\;
\label{eq:Sjac-cart}\end{aligned}$$
For reasons that should become clear when reading Sec. \[sec:Landau2Gilbert\], we perform the change of (dummy) auxiliary fields from ${{\rm i}}\hat{\mathbf{M}}_\perp$ to ${{\rm i}}\hat{\mathbf{M}}_\perp '\equiv {{\rm i}}\hat{\mathbf{M}}_\perp \wedge\mathbf{M} \ M_{{\rm s}}^{-1}$. The Jacobian of this change of variables is a constant and the action functional now reads $S_G= S_{G,{\rm det}} + S_{G, {\rm diss}} + S_{{\rm jac}}$ with $$\begin{aligned}
S_{G, {\rm det}} &=
\ln P_{{\rm i}}[\mathbf{M}_0, \mathbf{H}_{\rm eff}(t_0)]
+
\int {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf M}_\parallel \cdot {\rm D}_t^{(\alpha)} {\mathbf M}
\nonumber\\
& \qquad
+
\int\! {\hspace{-0em}\mathrm{d}{t}\;}
{{\rm i}}\hat{\mathbf{M}}_\perp \cdot \!
\left( \frac{1}{M_{{\rm s}}} {\rm D}^{(\alpha)}_t{\mathbf{M}} \wedge {\mathbf M}
+ \gamma_0 M_{{\rm s}}\ \mathbf{H}_{\rm eff} \right)
\label{eq:S_det_cart-redef}
\ , \\
S_{G, {\rm diss}} &= \int {\hspace{-0em}\mathrm{d}{t}\;} {{\rm i}}\hat{\mathbf{M}} _\perp \cdot
\left( D \gamma_0^2 M_{{\rm s}}^2 \ {{\rm i}}\hat{\mathbf{M}}_\perp
- \eta\gamma_0 {\rm D}^{(\alpha)}_t{\mathbf{M}} \right)
\; ,
\label{eq:S_diss_cart-redef}\end{aligned}$$ where we used the identity ${{\rm i}}\hat{\mathbf{M}}_\perp \cdot {\rm D}_t^{(\alpha)}{\mathbf{M}} = - ({{\rm i}}\hat{\mathbf{M}}_\perp \wedge \mathbf{M}) \cdot (\mathbf{M} \wedge {\rm D}_t^{(\alpha)} {\mathbf{M}}) M_{{\rm s}}^{-2}$ and we dropped the prime: ${{\rm i}}\hat{\mathbf{M}}_\perp' \mapsto {{\rm i}}\hat{\mathbf{M}}_\perp$. $S_{\rm jac}$ is unchanged. In Sec. \[sec:Landau2Gilbert\] we presented the action functional given by the sum of the terms in Eqs. (\[eq:Sjac-cart\]), (\[eq:S\_det\_cart-redef\]) and (\[eq:S\_diss\_cart-redef\]) and we showed that it can be taken to the Landau form by a suitable change of the auxiliary field. We prove in this way that the functional representations of the Landau and Gilbert formulation of the stochastic dynamics are totally equivalent.
Spherical coordinate conventions {#app:conventions}
================================
We are using the spherical coordinate system in which $\theta$ the polar angle, $\theta\in[0,\pi]$, and $\phi$ the azimuthal angle, $\phi \in [0,2\pi]$. The local orthogonal unit vectors are ${\mathbf e}_\mu = (\mathbf{e}_{M_{{\rm s}}}, \mathbf{e}_\theta, \mathbf{e}_\phi)$. The link to the Cartesian basis is given by $$\begin{aligned}
M_x=M_{{\rm s}}\, \sin\theta \, \cos\phi \; , \qquad\quad
M_y=M_{{\rm s}}\, \sin\theta \, \sin\phi \; , \qquad\quad
M_z=M_{{\rm s}}\, \cos\theta \; .\end{aligned}$$ We use Latin indices to label Cartesian coordinates ($i=x,y,z$) while Greek indices refer to the local basis ($\mu = M_{{\rm s}},\theta,\phi$).
The rotation matrix linking Cartesian to local coordinates, ${\mathbf e}_\mu = R_{\mu i } {\mathbf e}_i$, is $$R_{\mu i}(\mathbf{M}) = R_{\mu i}(\theta,\phi) =
\begin{array}{cc}
\left[
\begin{array}{ccc}
\sin\theta\cos\phi & \sin\theta\sin\phi & \cos\theta \\
\cos\theta\cos\phi & \cos\theta\sin\phi & -\sin\theta \\
-\sin\phi & \cos\phi & 0
\end{array}
\right]
\end{array}
\label{eq:rotation-matrix}$$ with $R_{\alpha i} R_{\beta i } = \delta_{\alpha\beta}$. Notice that $\mathrm{det} R = 1$ and $R^{-1} = \ ^t\!R$: $$R^{-1}_{i\mu}(\mathbf{M}) = R^{-1}_{i \mu}(\theta,\phi) =
\begin{array}{cc}
\left[
\begin{array}{ccc}
\sin\theta\cos\phi & \cos\theta\cos\phi & -\sin\phi \\
\sin\theta\sin\phi & \cos\theta\sin\phi & \cos\phi \\
\cos\theta & -\sin\theta & 0
\end{array}
\right]
\; .
\end{array}
\label{eq:inverse-rotation-matrix}$$ and $R^{-1}_{i\alpha} R^{-1}_{i\beta} = \delta_{\alpha\beta}$.
The following properties are useful $$\begin{aligned}
&&
R_{\mu j} \frac{\partial R^{-1}_{j\rho} }{\partial \theta}
=
- \delta_{\mu M_{{\rm s}}} \delta_{\rho \theta} + \delta_{\mu\theta} \delta_{\rho M_{{\rm s}}}
\; ,
\nonumber\\
&&
R_{\mu j} \frac{\partial R^{-1}_{j\rho} }{\partial \phi} =
- \sin \theta \delta_{\mu M_{{\rm s}}} \delta_{\rho \phi} -\cos \theta \delta_{\mu\theta} \delta_{\rho \phi}
+ \sin\theta \delta_{\mu \phi} \delta_{\rho M_{{\rm s}}} + \cos \theta \delta_{\mu\phi} \delta_{\rho \theta}
\; .
\qquad\;\;\;\;\;
\nonumber\end{aligned}$$
\[app:deltafunction\]
The delta function is not a scalar in the sense that it transforms non-trivially under coordinate transformations. This can be simply seen by considering the property $$1 = \int{\hspace{-0em}\mathrm{d}{\mathbf{x}}\;} \delta^3(\mathbf{x}-\overline{\mathbf{x}})\;,$$ which after a coordinate change to the spherical basis reads $$1 = \int{\hspace{-0em}\mathrm{d}{\mathbf{\Omega}}\;} \delta^3(\mathbf{x}(M_{{\rm s}},\theta,\phi)-\mathbf{x}(\overline M_{{\rm s}},\overline \theta,\overline\phi))\;,$$ The measure is ${\hspace{-0em}\mathrm{d}{\mathbf{\Omega}}\;} = M_{{\rm s}}^2 \sin\theta \ {{\rm d}}M_{{\rm s}}\, {{\rm d}}\theta\, {{\rm d}}\phi$. The integrals run over $M_{{\rm s}}\geq 0$, $\theta\in[0,\pi]$ and $\phi\in [0, 2\pi]$. $\mathbf{x}(M_{{\rm s}},\theta,\phi)$ and $\mathbf{x}(\overline M_{{\rm s}},\overline\theta,\overline\phi)$ are the expressions for $\mathbf{x}$ and $\overline{\mathbf{x}}$ in terms of the spherical coordinates. Using the identity $$\delta(\mathbf{x}(M_{{\rm s}},\theta,\phi)-\mathbf{x}(\overline M_{{\rm s}},\overline\theta,\overline\phi)) = \left|\det_{i\mu} \frac{\partial \Omega_\mu}{\partial x_i}\right| \delta(M_{{\rm s}}-\overline M_{{\rm s}})
\delta(\theta-\overline\theta) \delta(\phi-\overline\phi)\;,$$ we get $$\begin{aligned}
1 &=& \int {\hspace{-0em}\mathrm{d}{\mathbf{\Omega}}\;} \frac{1}{M_{{\rm s}}^2 \sin \theta} \delta(M_{{\rm s}}-\overline M_{{\rm s}}) \delta(\theta-\overline\theta) \delta(\phi-\overline\phi)
\nonumber\\
&=& \int\ {{\rm d}}M_{{\rm s}}{{\rm d}}\theta {{\rm d}}\phi \ \delta(M_{{\rm s}}- \overline M_{{\rm s}}) \delta(\theta - \overline\theta) \delta(\phi-\overline\phi)
\; .
\label{eq:delta-spherical-Jacobian}\end{aligned}$$
\[app:metric\]
If $x_i$ are the Cartesian coordinates of the vector $\mathbf{x}$ and $x_\mu$ the coordinates of the same vector in another coordinate system, the Jacobian matrix of the coordinate change is $$\begin{aligned}
J_{i\mu} \equiv \frac{\partial x_i}{\partial x_\mu}
\; ,
\label{eq:Jacobian-matrix}\end{aligned}$$ and the Jacobian of the transformation is $
\mathcal{J} \equiv \det_{i\mu} J_{i\mu}
$.
We relate the derivatives with respect to Cartesian coordinates to those with respect to spherical coordinates as $$\partial_i = \frac{\partial x_\mu}{\partial x_i} \ \partial_\mu = J^{-1}_{\mu i} \ \partial_\mu
\; .$$
For the vector ${\mathbf M}$ transformed to spherical coordinates, the Jacobian matrix (\[eq:Jacobian-matrix\]) reads $$\begin{aligned}
J_{i\nu} = \left[
\begin{array}{ccc}
\cos\phi\sin\theta & M_{{\rm s}}\cos\phi\cos\theta & -M_{{\rm s}}\sin\phi\sin\theta \\
\sin\phi\sin\theta & M_{{\rm s}}\sin\phi\cos\theta & M_{{\rm s}}\cos\phi\sin\theta \\
\cos\theta & -M_{{\rm s}}\sin\theta & 0
\end{array}
\right]\end{aligned}$$ for $i=x,y,z$ and $\mu=M_{{\rm s}},\theta,\phi$.
With spherical coordinates, the integration measure is understood as $$\begin{aligned}
\int{\mathcal{D}}{[\mathbf{\Omega}]} \equiv \lim\limits_{N\to\infty} \prod_{n=0}^N \int {\hspace{-0ex}\mathrm{d}{M_{{{\rm s}}\,n}}\;} {\hspace{-0ex}\mathrm{d}{\theta_n}\;} {\hspace{-0ex}\mathrm{d}{\phi_n}\;} M_{{{\rm s}}\, n}^2 \, |\sin\theta_n| \;.\end{aligned}$$
Chain rule in spherical coordinates {#sec:chain-rule-sph}
===================================
The matrices introduced in App. \[app:metric\] and the properties listed above allow one to derive the chain rule in spherical coordinates from the one in Cartesian coordinates, $$\begin{aligned}
\label{eq:cr1}
{{\rm d}}_t
& =
{{{\rm d}}_t} M_i \ \partial_i +
\frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \left(M_{{\rm s}}^2 \delta_{ij} - M_i M_j \right) \, \partial_i \partial_j \;.\end{aligned}$$ The first term can be re-written as $$\begin{aligned}
{{{\rm d}}_t} M_i \ \partial_i & = {{{\rm d}}_t} M_i \ J^{-1}_{\sigma i} \frac{\partial}{\partial \Omega_\sigma}
= \left[ -\frac{ 2D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_i + g_{ij} \overline H_j \right] \ J^{-1}_{\sigma i} \frac{\partial}{\partial \Omega_\sigma} \nonumber \\
& = -\frac{ 2D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}\partial_{M_{{\rm s}}} + R_{i\mu} g_{\mu\nu} \overline H_\nu \ J^{-1}_{\sigma i} \frac{\partial}{\partial \Omega_\sigma} \nonumber \\
& = -\frac{ 2D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}\partial_{M_{{\rm s}}}
+ \frac{1}{M_{{\rm s}}}
\left(
g_{\theta \nu_\perp} \overline H_{\nu_\perp} \partial_\theta
+ \frac{1}{\sin\theta} g_{\phi \nu_\perp} \overline H_{\nu_\perp} \partial_\phi
\right) \;,
\nonumber\end{aligned}$$ where in the second line we introduced the equation of motion in Cartesian coordinates, in the third line we used $M_i \partial_i = M_{{\rm s}}\partial_{M_{{\rm s}}}$ and $g_{ij} \overline H_j = R_{i\mu} g_{\mu\nu} \overline H_\nu$, and in the last line we used the fact that $g_{M_{{\rm s}}\mu} = g_{\mu M_{{\rm s}}} = 0$. To shorten the notation we called $\overline {\mathbf H} = {\mathbf H}_{\rm eff} + {\mathbf H}$.
In order to treat the second term of Eq. (\[eq:cr1\]), we notice that $$\begin{aligned}
(M_{{\rm s}}^2 \delta_{ij} - M_i M_j ) \partial_i \partial_j
&= M_{{\rm s}}^2 \nabla^2 - M_i M_j \, \partial_i \partial_j \;, \nonumber\end{aligned}$$ with $\nabla^2$ the Laplacian operator in spherical coordinates $$\begin{aligned}
\nabla^2 = \frac{1}{M^2_{{\rm s}}} \left( M_{{\rm s}}^2 \partial^2_{M_{{\rm s}}} + 2 M_{{\rm s}}\partial_{M_{{\rm s}}} + \cot\theta\partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right) \;.\end{aligned}$$ We also have $$\begin{aligned}
M_i M_j \, \partial_i \partial_j
&= M_{{\rm s}}\ M_i \frac{\partial}{\partial M_{{\rm s}}} \partial_{i}
= M_{{\rm s}}\ M_i \frac{\partial}{\partial M_{{\rm s}}} \left[ J^{-1}_{\sigma i} \frac{\partial}{\partial\Omega_\sigma} \right] \nonumber \\
& = M_{{\rm s}}\ M_i J^{-1}_{\sigma i} \ \frac{\partial^2}{\partial M_{{\rm s}}\partial\Omega_\sigma}
+ M_{{\rm s}}\ M_i \ \partial_{M_{{\rm s}}} J^{-1}_{\sigma i} \ \frac{\partial}{\partial\Omega_\sigma}
\nonumber \\
& = M^2_{{\rm s}}\ \frac{\partial^2}{\partial M_{{\rm s}}^2} = M_{{\rm s}}^2 \ \partial^2_{M_{{\rm s}}}\;,\end{aligned}$$ where in the first line we used $M_i \partial_i = M_{{\rm s}}\partial_{M_{{\rm s}}} $ and we later used $M_i J^{-1}_{\sigma i} = M_{{\rm s}}\delta_{\sigma M_{{\rm s}}}$ and $M_i \partial_{M_{{\rm s}}} J^{-1}_{\sigma i} = 0$ to obtain the last line. Therefore, the second term in Eq. (\[eq:cr1\]) reads $$\begin{aligned}
\frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} M_{{\rm s}}^2 \left( \nabla^2 - \partial_{M_{{\rm s}}}^2 \right)\;.\end{aligned}$$ Altogether the chain rule in spherical coordinates is given by $$\begin{aligned}
\label{eq:cr2}
{{\rm d}}_t & =
\frac{1}{M_{{\rm s}}}
\left(
g_{\theta \nu_\perp} \overline H_{\nu_\perp} \partial_\theta
+ \frac{1}{\sin\theta} g_{\phi \nu_\perp} \overline H_{\nu_\perp} \partial_\phi
\right)
\nonumber\\
&
\;\;\;\;\;
+ \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}
\left( \cot\theta \ \partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right)\;.\end{aligned}$$ Applying this differential operator to $M_{{\rm s}}$, $\theta$ and $\phi$ respectively, we obtain $$\begin{aligned}
{{\rm d}}_t M_{{\rm s}}&= 0\;, \\
{{\rm d}}_t \theta &= \frac{1}{M_{{\rm s}}} g_{\theta \nu_\perp} \overline H_{\nu_\perp} + \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta \;,
\label{eq:equation1} \\
{{\rm d}}_t \phi &= \frac{1}{M_{{\rm s}}\sin\theta} g_{\phi \nu_\perp} \overline H_{\nu_\perp} \; .
\label{eq:equation2}\end{aligned}$$ We now define the covariant derivatives $$\begin{aligned}
{\rm D}^{(\alpha)}_t(\theta) &\equiv {{\rm d}}_t \theta-\frac{D(1-2\alpha)\gamma_0^2}{(1+\eta^2\gamma_0^2)} \cot\theta \; , \label{eq:covDtheta2} \\
{\rm D}^{(\alpha)}_t(\phi) &\equiv {{\rm d}}_t \phi \;.\end{aligned}$$ and we reintroduce the equations of motion (\[eq:equation1\]) and (\[eq:equation2\]) in Eq. (\[eq:cr2\]) to re-write the differential operator as $$\begin{aligned}
{{\rm d}}_t &=
{\rm D}^{(\alpha)}_t(\theta) \partial_\theta
+ {\rm D}^{(\alpha)}_t(\phi) \partial_\phi
+ \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}\left( \cot\theta\partial_\theta + \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right) \nonumber \\
&=
{{\rm d}}_t \theta \ \partial_\theta
+ {{\rm d}}_t \phi \ \partial_\phi
+ \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}\left( \partial^2_\theta + \frac{1}{\sin^2\theta}\partial^2_\phi \right)
\;.\end{aligned}$$ We finally obtain an expression for the chain rule in spherical coordinates that is independent of the external and random fields $$\begin{aligned}
{{\rm d}}_t &= \ {{\rm d}}_t \Omega_{\mu_\perp} \ \partial_{\Omega_{\mu_\perp}}
+ \ \frac{ D(1-2\alpha) \gamma_0^2}{1+\eta^2\gamma_0^2}\left( \partial^2_\theta + \frac{1}{\sin^2\theta} \ \partial^2_\phi \right) \;.\end{aligned}$$
Determinants {#sec:determinants}
============
We will be confronted to the task of calculating the determinant of an operator of the form $$\delta_{ab} \delta(u-v) + C_{ab}(u,v)
\label{eq:operator-form}$$ where $u$ and $v$ are times and $a$ and $b$ are coordinate labels in a generic coordinate system. Using the identity $$\det(1+C) = \exp \mbox{Tr}\ln (1+C)
\label{eq:identity}$$ and expanding $\ln(1+C)$ one has $$\det(1+C)
=
\exp \ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n}
\int \ {\hspace{-0ex}\mathrm{d}{u}\;} \
\left\{ \underbrace{C \circ C \circ ... \circ C}_{n \ \mathrm{times}} \right\}_{\mu\mu}\!(u,u)$$ The symbol $\circ$ indicates a matrix product and a time convolution. Typically, $C$ will be proportional to the Heaviside Theta function, $C_{ab}(u,v)=\Theta(u-v) A_{ab}(u,v)$, hence causal. In regular cases, $A$ does not diverge within the time interval and causality ensures that the terms with $n>1$ vanish. This simplification does not necessarily apply to the cases we deal with since the matrix $A$ depends on the white noise ${\mathbf H}$ and, roughly speaking, two such factors together are proportional to a temporal Dirac-delta function [@Arnold2000; @Lubensky2007]. Accordingly, we need to analyze each order in the expansion separately to decide which ones yield non-vanishing contributions.
Let us take $A_{ab}(u) = A^1_{ab}(u) + A^2_{abc}(u) H_c(u)$ where $A^1$ and $A^2$ do not depend on the random field. For concreteness, let us assume that the field $H_a$ has zero mean and correlations $\langle H_a(u) H_b(v) \rangle = 2D \delta_{ab} \delta(u-v)$. These are the $A$’s we will work with in this manuscript. The first order term, $n=1$, in the series is $$1\mbox{st} =
\Theta(0) \int {{\rm d}}u \ [A^1_{aa}(u) + A^2_{aac}(u) H_c(u) ]
\;.$$ The second order term, $n=2$, in the series is $$\begin{aligned}
&
2\mbox{nd} = \int {{\rm d}}u \int {{\rm d}}v \ \Theta(u-v) \Theta(v-u)
[A^1_{ab}(v) + A^2_{abc}(v) H_c(v) ]
\nonumber\\
&
\qquad\qquad
\times
[A^1_{ba}(u) + A^2_{bad}(u) H_d(u) ]
\; . \end{aligned}$$ Because of the two Theta factors, the only non-vanishing contribution may come from $u=v$ if the integrand diverged at this point. Let us now assume that one can replace a single random field factor by its average and two random field factors by their correlations: $H_a(u) \to
\langle H_a(u) \rangle = 0$ and $H_a(u) H_b(v) \to \langle H_a(u) H_b(v) \rangle = 2D \delta_{ab}
\delta(u-v)$. An argument to justify this procedure is given below. Thus, $$\begin{aligned}
2\mbox{nd}
& =
\int {{\rm d}}u \int {{\rm d}}v \ \Theta(u-v) \Theta(v-u) \ 2D\delta_{cd}
\delta(u-v) \ A^2_{abc}(v) A^2_{bad}(u)
\nonumber\\
& = \Theta^2(0) \
2D \int {{\rm d}}u
\ A^2_{abc}(u) A^2_{bac}(u)\end{aligned}$$ This term is non-vanishing. What about higher order terms? Fortunately, they all vanish. For instance, the third order term is $$\begin{aligned}
3\mbox{rd}
= &
\int {{\rm d}}u \int {{\rm d}}v\int {{\rm d}}w \
\Theta(u-v) \Theta (v-w) \Theta(w-u)
\nonumber\\
&
\qquad \times
[A^1_{ab}(v) + A^2_{abc}(v) H_c(v) ]
\
[A^1_{bd}(w) + A^2_{bde}(w) H_e(w) ]
\nonumber\\
&
\qquad \times
[A^1_{da}(u) + A^2_{daf}(u) H_f(u) ]
\nonumber\\
=&
\int {{\rm d}}u \int {{\rm d}}v\int {{\rm d}}w \
\Theta(u-v) \Theta (v-w) \Theta(w-u)
\nonumber\\
&
\qquad \times
A^1_{ab}(v) 2D \delta_{ef} \delta(w-u)
A^2_{bde}(w)
A^2_{daf}(u) +\dots
\nonumber\\
= &
\int {{\rm d}}u \int {{\rm d}}v \
\Theta(u-v) \Theta (v-u) \Theta(0)
\nonumber\\
&
\qquad \times
A^1_{ab}(v) 2D
A^2_{bde}(w)
A^2_{dae}(u) +\dots
\nonumber\\
=
& \;\; 0
\; . \end{aligned}$$ Similarly, one can prove that there are no further contributions to the series. In conclusion, $$\det(1+C) = \exp \mbox{Tr} \ln (1+C) = \exp [ \ \mbox{Tr}\ C - \frac{1}{2} \mbox{Tr}\ C^2 \ ]
\label{eq:identity-random-field}$$
We now justify heuristically the replacement of the random field and product of two random fields, in the exponentials, by their averages. Given a generic functional of the random field, $F[{\mathbf H}]$, multiplied by an exponential of the kind $${{\rm e}}^{ -\frac{1}{2} \int \int {{\rm d}}t {{\rm d}}t' \ Q_{ab}(t,t') H_a(t) H_b(t') }$$ with $Q_{ab}(t,t')$ a generic symmetric matrix in the $ab$ indices and the times $t$ and $t'$, let us consider its average over random field histories distributed according to a normal Gaussian pdf $$P_{\rm n}[{\mathbf H}] \propto {{\rm e}}^{-\frac{1}{4D} \int \int {{\rm d}}t \ H^2_a(t) }$$ that we indicate with $\langle \dots \rangle_0$. We now evaluate the average as $$\begin{aligned}
\mbox{Ave} = \langle F[\mathbf{H}] \ {{\rm e}}^{- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{ab}(t,t') \ H_a(t) H_b(t') }
\rangle_0
\nonumber\end{aligned}$$ With a Taylor expansion of the exponential, $$\begin{aligned}
\mbox{Ave} = &
\sum_{n=0} \frac{1}{n !\!} \left( - \frac12 \right)^n
\iint{\hspace{-0em}\mathrm{d}{t_1}\,\mathrm{d}{t'_1}\;} \ldots \iint{\hspace{-0em}\mathrm{d}{t_n}\,\mathrm{d}{t'_n}\;} Q_{a_1b_1}(t_1,t_1') \ldots Q_{a_nb_n}(t_n,t_n') \\
& \qquad \times \langle F[\mathbf{H} ] \ H_{a_1}(t_1) H_{b_1}(t_1') \ldots H_{a_n}(t_n)H_{b_n}(t_n')
\rangle_0\end{aligned}$$ we set the calculation in a way that we can use Wick theorem. Since $Q_{ab}(t,t') = 0 $ for all $t\neq t'$, most of the contractions of the fields on the right side of the average vanish, except for the ones that set $t_i=t_i'$ for all $i=1,\dots, n$. Therefore, the only non-vanishing contributions should be of the form $$\begin{aligned}
&
\langle F[{\mathbf H}] \rangle_0 \
\langle H_{a_1}(t_1) H_{b_1}(t'_1) \rangle_0
\; \ldots \; \langle H_{a_n}(t_n) H_{a_n}(t_n')] \rangle_0
\\
& \qquad\qquad = \langle F[{\mathbf H}] \rangle_0
\ (2D)^n \ \delta_{a_1 b_1} \ldots \delta_{a_n b_n}
\ \delta(t_1-t_1') \ldots \delta(t_n-t_n') \;.\end{aligned}$$ This can be re-exponentiated to recast the average as $$\begin{aligned}
& \langle F[\mathbf{H} ] \ {{\rm e}}^{- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{ab}(t,t') H_a(t) H_b(t')} \rangle_0
= {{\rm e}}^{-D \int{\hspace{-0em}\mathrm{d}{t}\;} Q_{aa}(t,t)} \ \langle F[\mathbf{H}] \rangle_0 \;.
\end{aligned}$$ In short, the result of the calculation is equivalent to the replacement $$H_a(t) H_b(t') \to \langle H_a(t) H_b(t')\rangle_0$$ in the exponential. This argument can be easily generalized to the case in which the random field has a non-zero average.
The line of reasoning followed in this Section is close in spirit to the one consider in [@Arnold2000]. A different but equivalent approach has been discussed in [@Lubensky2007] (see also [@Tirapegui-comment]). We remark, nevertheless, that we have not used the invertibility of the diffusion matrix $g$ as our $g$ is actually not invertible.
Random field in spherical coordinates {#app:rotation-noise}
=====================================
The probability distribution of the random field components, in the Cartesian coordinate system, is given by $$P_\mathrm{n}[H_x,H_y,H_z] \propto \exp\left\{-\frac{1}{4D}
\int{} {\hspace{-0em}\mathrm{d}{t}\;} \left[ H_x(t)^2+ H_y(t)^2 + H_z(t)^2 \right] \right\}\;.$$ The rotation to the spherical coordinate system, $$\begin{aligned}
P^{\rm sph}_{\rm n}[H_{M_{{\rm s}}}, H_\theta, H_\phi] = |\mathcal{J}^{\rm rot}| \ P_\mathrm{n}[R^{-1}_{x\mu} H_\mu,R^{-1}_{y\mu} H_\mu,R^{-1}_{z\mu} H_\mu]\;,\end{aligned}$$ involves the Jacobian $$\begin{aligned}
\label{eq:Jacobian-rot-app}
\mathcal{J}^{\rm rot}
&\!\! \equiv \!\! &
\mathrm{det}_{i\nu,tt'} \frac{\delta R^{-1}_{i\mu}(t) H_\mu(t)}{\delta H_\nu(t')}
\; . \end{aligned}$$
The Jacobian ${\cal J}^{\rm rot}$
---------------------------------
A series of simple operations allow us to factorize the Jacobian of the change of basis from Cartesian to spherical, ${\cal J}^{\rm rot}$ defined in Eq. (\[eq:Jacobian-rot-app\]), in two factors: $$\begin{aligned}
\mathcal{J}^{\rm rot}
& \!\!\! = \!\! & \mathrm{det}_{i\nu,tt'} \left[ R^{-1}_{i\nu}(t) \delta(t-t') + \frac{\delta R^{-1}_{i\mu}(t)}{\delta H_\nu(t')} H_\mu(t) \right]
\nonumber\\
&\!\!\! = \!\! & \mathrm{det}_{i\mu,tt''} \left[ R^{-1}_{i\mu}(t)\delta(t-t'') \right]
\nonumber\\
&& \qquad\qquad
\times \ \mathrm{det}_{\mu\nu,t''t'}
\left[ \delta_{\mu\nu}\delta(t''-t') + R_{\mu j}(t'') \frac{\delta R^{-1}_{j\rho}(t'')}{\delta H_\nu(t')} H_\rho(t'') \right]\;,
\nonumber\end{aligned}$$ that we can now compute since the first term is identical to one and the second one takes the form in Eq. (\[eq:operator-form\]) with $$C_{\mu\nu}(t,t') \equiv R_{\mu j}(t) \frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\nu(t')} H_\rho(t)
\; .$$ The factor $\frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\nu(t')}$ is proportional to $\Theta(t-t')$. Due to the random field dependence in $C$ we need to use the result in (\[eq:identity-random-field\]) to express the determinant [@Arnold2000; @Lubensky2007]. The first term in the sum, $n=1$, is $$\begin{aligned}
\ln \mathcal{J}^{\rm rot}_1 = \exp \int{\hspace{-0ex}\mathrm{d}{t}\;} R_{\mu j}(t) \frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\mu(t)} H_\rho(t)
= \int{\hspace{-0ex}\mathrm{d}{t}\;} L_\rho(t) H_\rho(t)
\; .\end{aligned}$$ The rotation matrix $R^{-1}_{j\rho}$ is a function of $\theta$ and $\phi$ (not of $M_{{\rm s}}$) and neither $\theta$ nor $\phi$ depend on the radial component of the noise $H_{M_{{\rm s}}}$. Therefore $$\begin{aligned}
\frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\nu(t')} \Rightarrow
\frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_\nu} \frac{\delta\Omega_\nu(t)}{\delta H_\mu(t)}
=
\frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\nu_\perp}(t')} \end{aligned}$$ and $$\begin{aligned}
L_\rho(t) =
R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta\Omega_{\tau_\perp}(t)}{\delta H_\mu(t)}
\; . \end{aligned}$$ The second term in the series, $n=2$, reads $$\begin{aligned}
\ln {\cal J}_2^{\rm rot} = & -\frac12 \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;}
R_{\mu j}(t) \frac{\delta R^{-1}_{j\rho}(t)}{\delta H_\nu(t')} H_\rho(t)
R_{\nu k}(t') \frac{\delta R^{-1}_{k\sigma}(t')}{\delta H_\mu(t)} H_\sigma(t')
\nonumber\\
= &
-\frac12 \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;}
Q_{\rho\sigma}(t,t') H_\rho(t) H_\sigma(t')\end{aligned}$$ with $$Q_{\rho\sigma}(t,t') \equiv R_{\mu j}(t) \frac{\partial R^{-1}_{j\rho}(t)}{\partial \Omega_{\tau_\perp}} \frac{\delta \Omega_{\tau_\perp}(t)}{\delta H_{\nu}(t')} R_{\nu k}(t') \frac{\partial R^{-1}_{k\sigma}(t')}{\partial \Omega_{\kappa_\perp}} \frac{\delta \Omega_{\kappa_\perp}(t')}{\delta H_{\mu}(t)}
\; .$$
Random field distribution {#app:randomfield}
-------------------------
Let us now collect all terms together in a compact notation such that the probability distribution of the random field reads $$\begin{aligned}
\ln P^{\rm sph}_{\rm n}[H_\mu] =& -\frac{1}{4D} \int {\rm d} t \ H^2_\mu(t) + \int{\hspace{-0em}\mathrm{d}{t}\;} L_\mu(t) H_\mu(t)
\nonumber\\
&- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') H_\rho(t) H_\sigma(t') \label{eq:pnoise1}
\; ,\end{aligned}$$ that vanishes for $t' \neq t$ because of the response functions involved in its expression. Therefore, the integrand of the last integral above vanishes for $t\neq t'$ but the integral may still yield a non- trivial contribution at $t=t'$ due to the presence of the two random field factors (which are delta correlated).
The quadratic weight can be given a usual form by completing the square between the first two terms under the integral $$\begin{aligned}
&& - \frac{1}{4D} H_\mu^2(t) + L_\mu(t) H_\mu(t) =
- \frac{1}{4D} \left[ H_\mu(t) - 2D L_\mu(t) \right]^2
+ D \ L^2_\mu(t),\end{aligned}$$ and the measure can be recast as $$\begin{aligned}
&&
\ln P^{\rm sph}_{\rm n}[H_\mu] = \ln P^{{\rm sph},0}_{\rm n }[H_\mu] + D \int{\hspace{-0em}\mathrm{d}{t}\;} L_\mu^2(t)
\nonumber\\
&&
\qquad\qquad\qquad
- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \, H_\rho(t) H_\sigma(t')\end{aligned}$$ where we singled out the conventional Gaussian part of the measure $$\begin{aligned}
\ln P^{{\rm sph},0}_{\rm n}[H_\mu] \equiv -\frac{1}{4D} \int {\rm d} t \ [H_\mu(t) - 2D L_\mu(t)]^2 \;.
\end{aligned}$$
We now rewrite the last term in a way that the noises appear as $H_\rho(t) - 2D L_\rho(t)$. This rewriting introduces two new terms, one that is linear in $H_\rho(t) - 2D L_\rho(t)$, another one in which this factor does not appear: $$\begin{aligned}
&&
- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ H_\rho(t) H_\sigma(t')
\nonumber\\
&& \qquad
=
- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ [H_\rho(t) - 2D L_\rho(t)] [H_\sigma(t') -2D L_\sigma(t')]
\nonumber\\
&& \qquad\;\;\;\;
+
\iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ 2D L_\rho(t) [H_\sigma(t') -2D L_\sigma(t')]
\nonumber\\
&&
\qquad\;\;\;\;
- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ 2D A_\rho(t)2D L_\sigma(t')\end{aligned}$$ The last term vanishes identically since $Q_{\rho\sigma}(t,t')$ is equal to zero for $t\neq t'$ and the accompanying factors do not diverge. A similar argument can be applied to the second term as two factors $H_\rho(t)-2D L_\rho(t)$ are needed to get a divergence in the integrand. The noise pdf then reads $$\begin{aligned}
&&
\ln P^{\rm sph}_{\rm n}[H_\mu] = \ln P^{{\rm sph},0}_{\rm n }[H_\mu] + D \int{\hspace{-0em}\mathrm{d}{t}\;} L_\mu^2(t)
\nonumber\\
&&
\qquad\qquad
- \frac{1}{2} \iint{\hspace{-0em}\mathrm{d}{t}\,\mathrm{d}{t'}\;} Q_{\rho\sigma}(t,t') \ [H_\rho(t) -2DL_\rho(t)] [H_\sigma(t') - 2D L_\sigma(t')]
\; . \end{aligned}$$
We conclude that the probability density of the random field is $$\begin{aligned}
&&
\ln P^{\rm sph}_{\rm n}[H_\mu] = -\frac{1}{4D} \int {\rm d} t \ [H_\mu(t) - 2D L_\mu(t)]^2 + D \int{\hspace{-0em}\mathrm{d}{t}\;} L_\mu^2(t)
\nonumber\\
&&
\qquad\qquad\qquad
- D \int {\rm d} t \ Q_{\rho\rho}(t,t)
\; . \end{aligned}$$
After a lengthy computation that uses the properties mentioned in App. \[app:conventions\] and the equal-time responses calculated in the main part of the text, Eqs. (\[eq:equal-time1\])-(\[eq:equal-time4\]), one derives $$L_\mu^2(t) =
\frac{\alpha^2 \gamma_0^2 }{1+\eta^2\gamma_0^2} \left[ \frac{4\eta^2\gamma_0^2}{1+\eta^2\gamma_0^2} + \cot^2\theta(t) \right]\;,
\label{eq:Acuadrado}$$ and $$\begin{aligned}
& Q_{\rho\rho}(t,t)
\nonumber\\
& \qquad
=
\left [\left( \frac{\delta \theta}{\delta H_\theta} \right)^2 + 2 \sin\theta \frac{\delta \theta}{\delta H_\phi} \frac{\delta \phi}{\delta H_\theta} + \left( \frac{\delta \phi}{\delta H_\phi} \right)^2 + \cos^2\theta \left( \frac{\delta \phi}{\delta H_\theta} \right)^2 \right]
\nonumber\\
& \qquad
=
\frac{\alpha^2\gamma_0^2 }{1+\eta^2\gamma_0^2}
\cot^2\theta +\dots\end{aligned}$$ with the dots being just constant terms. Therefore, apart from irrelevant additive constants we establish that $$\begin{aligned}
L_\mu^2(t) =Q_{\rho\rho}(t,t) = \frac{\alpha^2 \gamma_0^2}{1+\eta^2\gamma_0^2} \cot^2\theta(t) \;.
\label{eq:Acuadrado} \end{aligned}$$ In the end, the measure is $$P_{\rm n}^{\rm sph}[H_\mu] \propto \exp \left\{ -\frac{1}{4D} \int{\hspace{-0em}\mathrm{d}{t}\;} [H_\mu(t) - 2D L_\mu(t)]^2 \right\}
\; .$$ One concludes that the random fields remain delta correlated but they acquire a mean-value in the spherical basis.
It is also quite clear that the radial and angular sectors decouple: $$\begin{aligned}
P_{\rm n}^{\rm sph}[H_\mu] \propto
P_{\rm n}^{\rm sph}[H_{M_{{\rm s}}}] \ P_{\rm n}^{\rm sph}[H_{\mu_\perp}]
\; . \end{aligned}$$ As the equations of motion do not depend on the longitudinal noise the first term is irrelevant in the context of the LLG equation. The explicit form of the perpendicular sector of the random field distribution is $$\begin{aligned}
P_{\rm n}^{\rm sph}[H_{\mu_\perp}]
\propto & \
\exp \int{\hspace{-0em}\mathrm{d}{t}\;}
\left\{ -\frac{1}{4D} H^2_{\mu_\perp}(t)
+ \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \cot\theta(t) \ [\eta\gamma_0 H_\theta(t) + H_\phi(t) ]
\right.
\nonumber\\
&
\left.
\qquad\qquad\qquad
- \frac{\alpha^2\gamma_0^2 D}{1+\eta^2 \gamma_0^2} \cot^2\theta(t)
\right\}
\; .
\label{eq:Pn-random-noise-sph}\end{aligned}$$
The Jacobian ${\cal J}_L^{\rm sph}$ {#app:MSRDJ-Jacobian-Gus}
===================================
We compute here the Jacobian needed for the construction of the generating functional in the spherical Landau formalism used in Sec. \[sec:contruct\_spherical\]. $$\begin{aligned}
\label{eq:defjac2}
\mathcal{J}_L^{\rm sph}[\mathbf{\Omega},\mathbf{H}] \equiv
\det_{\mu\nu;uv}
\begin{array}{c}
\displaystyle
\frac{\delta {\rm{Eq}}_{L \mu}[\mathbf{\Omega},\mathbf{H}](u)}{\delta \Omega_{\nu}(v)}
\end{array}
\; , \end{aligned}$$ with the coordinate indices $\mu,\nu=M_{{\rm s}},\theta,\phi$ and the times $u,v$. From its definition one has $$\begin{aligned}
\mathcal{J}_L^{\rm sph}[\mathbf{\Omega},\mathbf{H}] &
=
\det_{uv} \left[ {\rm d}_u \delta_{u-v} \right] \
\det_{\mu_\perp\nu_\perp;uv}
\frac{\delta \mbox{Eq}_{L \mu_\perp}(M_{{\rm s}},\theta,\phi;u)}{\delta {\nu_\perp}(v)}
\nonumber\\
& =
\displaystyle
\det_{uv} \left[ {\rm d}_u \delta_{u-v} \right] \
\det_{\nu_\perp\nu_\perp;uw} [\delta_{\mu_\perp \nu_\perp} {{\rm d}}_u \delta_{u-w} ]
\nonumber\\
& \qquad \times \det_{\nu_\perp\nu_\perp;wv} [\delta_{\mu_\perp \nu_\perp} \delta_{w-v} + \Theta(w-v) A_{\mu_\perp\nu_\perp}(v) ]\end{aligned}$$ with $$\begin{aligned}
&&
A_{\theta\theta}(v)
=
\frac{\gamma_0}{1+\eta^2\gamma_0^2} \left[ \frac{D(1-2\alpha)\gamma_0}{\sin^2\theta}
- \partial_\theta \left(R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) (H_{{\rm eff},i} + H_i)\right]
\; ,
\nonumber\\
&&
A_{\theta\phi}(v)
=
- \frac{\gamma_0}{1+\eta^2\gamma_0^2}
\partial_\phi \left( R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) (H_{{\rm eff},i} + H_i)
\; ,
\nonumber\\
&&
A_{\phi\theta}(v)
=
- \frac{\gamma_0}{1+\eta^2\gamma_0^2}
\frac{1}{\sin\theta} \left[ \partial_\theta \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right)
\right.
\nonumber\\
&& \qquad\qquad\qquad\qquad\qquad\qquad
\left.
- \cot\theta \left( \eta\gamma_0 R_{\phi i} - R_{\theta i}\right)
\right] (H_{{\rm eff},i} + H_i)
\; ,
\nonumber\\
&&
A_{\phi\phi}(v)
=
- \frac{\gamma_0}{1+\eta^2\gamma_0^2}
\frac{1}{\sin\theta} \partial_\phi \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) (H_{{\rm eff},i} + H_i)
\; .
\nonumber\end{aligned}$$ The first two factors contribute irrelevant constants. The last one can be treated with the identity (\[eq:identity\]) where the time-dependent $2\times 2$ matrix with entries is $C_{\mu_\perp\nu_\perp}(w,v)=\Theta(w-v) A_{\mu_\perp\nu_\perp}(v)$. The causal character of $C$ cuts the expansion at its second order. The first contribution is $\mbox{Tr}\ C = A_{\theta\theta}+A_{\phi\phi}$, $$\begin{aligned}
\mbox{Tr} \ C &=&
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \left[ \frac{D(1-2\alpha)\gamma_0}{\sin^2\theta}
- \partial_\theta \left(R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) (H_{{\rm eff},i} + H_i)
\right.
\nonumber\\
&&
\left.
\qquad\qquad\qquad\;\;\; -
\frac{1}{\sin\theta} \partial_\phi \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) (H_{{\rm eff},i} + H_i)
\right]
\; .\end{aligned}$$ The second order term is given by $\mbox{Tr}\ C^2 /2= (A^2_{\theta\theta}+2A_{\theta\phi} A_{\phi\theta} + A^2_{\phi\phi})/2$. Keeping only the terms that are proportional to two random fields, and using $H_i(t) H_j(t') \to
\langle H_i(t) H_j (t') \rangle = 2 D \delta_{ij} \delta(t-t')$, see App. \[sec:determinants\], $$\begin{aligned}
&&
\mbox{Tr} \ C^2 =
\frac{2D\alpha^2\gamma_0^2}{(1+\eta^2\gamma_0^2)^2}
\int {{\rm d}}t
\ \Big{\{}
[ \partial_\theta \left(R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) ]^2
\qquad
\nonumber\\
&&
\qquad\qquad\qquad
+ \frac{1}{\sin^2\theta} [\partial_\phi \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right)]^2
+ 2 \ \partial_\phi \left( R_{\phi i} + \eta\gamma_0 R_{\theta i} \right)
\nonumber\\
&&
\qquad\qquad\qquad\qquad
\times
\left.
\frac{1}{\sin\theta} \left[ \partial_\theta \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right)
- \cot\theta \left( \eta\gamma_0 R_{\phi i} - R_{\theta i}\right)
\right]
\right\}
\qquad
\nonumber\\
&&
\qquad
= \mbox{cst} -
\frac{2D\alpha^2\gamma_0^2}{1+\eta^2\gamma_0^2}
\int {{\rm d}}t \
\frac{1}{\sin^2\theta}
\; . \end{aligned}$$ The two terms together yield $$\begin{aligned}
{\mathcal J}_L^{\rm sph}
&=&
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \ \left[ \frac{D(1-2\alpha)\gamma_0}{\sin^2\theta}
- \partial_\theta \left(R_{\phi i} + \eta\gamma_0 R_{\theta i} \right) (H_{{\rm eff},i} + H_i)
\right.
\nonumber\\
&&
\left.
\qquad\qquad\qquad\;\;\; -
\frac{1}{\sin\theta} \partial_\phi \left( \eta\gamma_0 R_{\phi i} - R_{\theta i} \right) (H_{{\rm eff},i} + H_i)
\right]
\nonumber\\
&&
+
\frac{D\alpha^2\gamma_0^2}{1+\eta^2\gamma_0^2}
\int {{\rm d}}t \
\frac{1}{\sin^2\theta}
\;. \end{aligned}$$ The first and last terms combine to yield a contribution proportional to $\alpha(1-\alpha)/\sin^2\theta$ and $$\begin{aligned}
&&
{\mathcal J}_L^{\rm sph}
=
\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int {{\rm d}}t \left\{ \frac{D(1-\alpha)\gamma_0}{\sin^2\theta}
- \partial_\theta [ (H_{{\rm eff},\phi} + H_{\phi}) + \eta\gamma_0 (H_{{\rm eff},\theta} + H_{\theta}) ]
\right.
\nonumber\\
&&
\left.
\qquad\qquad\qquad\qquad\qquad
-
\frac{1}{\sin\theta}
\partial_\phi [ \eta\gamma_0 (H_{{\rm eff},\phi} + H_\phi) - (H_{{\rm eff},\theta} + H_\theta) ]
\right\}
\; . \end{aligned}$$
Gilbert spherical generating functional {#sec:construct_spherical_Gilbert}
=======================================
We here construct the generating functional $\mathcal{Z}[\boldsymbol{\lambda}]$ by imposing the equations of motion in the Gilbert formulation $$\begin{aligned}
\mbox{Eq}^{\rm sph}_{G,M_{{\rm s}}} &\equiv {\rm d}_t M_{{\rm s}}= 0
\; ,
\label{eq:Ms-Gilbert-app}
\\
\mbox{Eq}^{\rm sph}_{G,\theta} &\equiv {\rm D}^{(\alpha)}_t(\theta) + \eta\gamma_0 \ \sin \theta \ {\rm D}^{(\alpha)}_t(\phi) - \gamma_0 \left( H_{{\rm{eff}}, \phi} + H_\phi \right) = 0 \; ,
\label{eq:thetaalpha-Gilbert-app} \\
\mbox{Eq}^{\rm sph}_{G,\phi} &\equiv - \sin\theta\, {\rm D}^{(\alpha)}_t(\phi) + \eta\gamma_0 \
{\rm D}^{(\alpha)}_t(\theta) -\gamma_0 \left( H_{{\rm{eff}}, \theta} + H_\theta \right) =0 \; .
\label{eq:phialpha-Gilbert-app} \end{aligned}$$ The Jacobian $$\begin{aligned}
\label{eq:defjac4}
\mathcal{J}_G^{\rm sph}[\mathbf{\Omega},\mathbf{H}] \equiv
\det_{\mu\nu;uv}
\begin{array}{c}
\displaystyle
\frac{\delta {\rm{Eq}}^{\rm sph}_{G\mu}[\mathbf{\Omega},\mathbf{H}](u)}{\delta \Omega_{\nu}(v)}
\end{array}
\; , \end{aligned}$$ with the coordinate indices $\mu,\nu=M_{{\rm s}},\theta,\phi$ and the times $u,v$, reads $$\begin{aligned}
\mathcal{J}_G^{\rm sph} [\mathbf{\Omega},\mathbf{H}]
&
=
\det_{uv} \left[ {\rm d}_u \delta_{u-v} \right]
\nonumber\\
& \displaystyle
\;\;\; \;\;\; \times
\det_{\mu_\perp\nu_\perp;uv} \left[ X_{\mu_\perp\nu_\perp}(u) {\rm d}_u \delta_{u-v} + A_{\mu_\perp\nu_\perp}(u) \delta_{u-v} \right]
\; .
\nonumber\end{aligned}$$ The first factor is due to the $M_{{\rm s}}$ diagonal element and it can only yield a constant contribution. We next focus on the second factor. $$\begin{aligned}
{\cal J}_G^{\rm sph}
\displaystyle
& \propto
\det_{\mu_\perp\rho_\perp;uw} \left[ X_{\mu_\perp\rho_\perp}(u) {\rm d}_u \delta_{u-w} \right]
\nonumber\\
& \qquad \times
\det_{\mu_\perp\rho_\perp;wv} \left[ \delta_{\rho_\perp \nu_\perp} \delta(w-v) + \theta(w-v) {X^{\,-1}_{\rho_\perp\sigma_\perp}}(v) A_{\sigma_\perp\nu_\perp}(v)
\right]
\nonumber\\
&
\displaystyle
=
\det_{\mu_\perp \nu_\perp; uv} [X_{\mu_\perp \nu_\perp}(u)\delta (u-v)]
\det_{\nu_\perp \rho_\perp; vw}[ \delta_{\nu_\perp \rho_\perp} {\rm d}_v\delta(v-w)]
\nonumber\\
& \qquad \times
\det_{\mu_\perp\rho_\perp;wv}
\left[ \delta_{\rho_\perp \nu_\perp} \delta(w-v) + \theta(w-v) {X^{\,-1}_{\rho_\perp\sigma_\perp}}(v)
A_{\sigma_\perp\nu_\perp}(v)
\right]
\nonumber\\
&
\displaystyle
\propto
\det_{\mu_\perp \nu_\perp; u,v} [X_{\mu_\perp \nu_\perp}(u)\delta (u-v)]
\nonumber\\
& \qquad \times
\det_{\mu_\perp\rho_\perp;wv}
\left[ \delta_{\rho_\perp \nu_\perp} \delta(w-v) + \theta(w-v) {X^{\,-1}_{\rho_\perp\sigma_\perp}}(v) A_{\sigma_\perp\nu_\perp}(v)
\right]
\;,
\label{eq:factorized-jac}\end{aligned}$$ with $$\begin{aligned}
X_{\mu_\perp\nu_\perp}(u) & \equiv \left[
\begin{array}{cc}
1 & \eta\gamma_0 \sin\theta_u
\\
\eta\gamma_0 & -\sin\theta_u
\end{array}
\right]\;, \\
{ X^{\,-1}_{\mu_\perp\nu_\perp}}(v)
& \equiv
\displaystyle
\frac{1}{1+\eta^2\gamma_0^2}
\left[
\begin{array}{cc}
1 & \eta\gamma_0\\
\displaystyle
\frac{\eta\gamma_0}{\sin\theta_v}
&
\displaystyle
-\frac{1}{\sin\theta_v}
\end{array}
\right]\;,\end{aligned}$$ and $$\begin{aligned}
&&
A_{\theta\theta}=
\frac{D(1-2\alpha)\gamma_0^2}{1+\eta^2\gamma_0^2} \frac{1}{\sin^2\theta}
- \gamma_0
\partial_\theta (H_{{\rm eff},\phi} +H_\phi)
\\
&& \qquad\qquad
+\frac{\eta\gamma_0^2}{1+\eta^2\gamma_0^2} \cot\theta \left[ \eta\gamma_0 (H_{{\rm eff},\phi} +H_\phi) - (H_{{\rm eff},\theta} +H_\theta) \right]
\; ,
\\
&&
A_{\theta\phi} = - \gamma_0 \partial_\phi (H_{{\rm eff},\phi} +H_\phi)
\; ,
\\
&&
A_{\phi\theta} =
+ \eta\gamma_0 \ \frac{D(1-2\alpha)\gamma_0^2}{1+\eta^2\gamma_0^2} \frac{1}{\sin^2\theta}
- \gamma_0
\partial_\theta (H_{{\rm eff},\theta} +H_\theta) \\
&& \qquad\qquad - \frac{\gamma_0}{1+\eta^2\gamma_0^2} \cot\theta \left[ \eta\gamma_0 (H_{{\rm eff},\phi} +H_\phi) - (H_{{\rm eff},\theta} +H_\theta) \right]
\; ,
\\
&&
A_{\phi\phi} =
- \gamma_0 \partial_\phi (H_{{\rm eff},\theta} +H_\theta)
\; . \end{aligned}$$ where we used the equations of motion (\[eq:thetaalpha-Gilbert-app\]) and (\[eq:phialpha-Gilbert-app\]) to replace the occurrences of ${\rm D}_t^{(\alpha)}(\phi)$ by its corresponding expression in terms of the random field. Indeed, making explicit the random field dependence of the Jacobian is crucial as we shall see below.
The absolute value of the first factor in Eq. (\[eq:factorized-jac\]) is $$\begin{aligned}
&
\Big{|}
\det_{\mu_\perp \rho_\perp; uv} X_{\mu_\perp \rho_\perp}(u) \delta(u-v)
\Big{|}
=
\prod_{n=0}^{N-1}
|
\sin\bar\theta_n
|\;, \label{eq:detedete}\end{aligned}$$ where we were careful to evaluate the determinant factors on the intermediate points $\bar \theta_n \equiv \alpha \theta_{n+1} + (1-\alpha) \theta_n$. Notice indeed that the discretization matters here since there is no trivial continuous limit of this expression. See also the discussion in Sect. \[subsec:rules\]. The product above can be re-writen as $$\begin{aligned}
\prod_{n=0}^{N-1}
|
\sin\bar\theta_n
|
=
{{\rm e}}^{(1-\alpha) \ln \left| \frac{\sin\theta_0}{\sin\theta_N} \right| }
\prod_{n=1}^{N}
|
\sin\theta_n
|
\;, \label{eq:detedetee45}\end{aligned}$$ where we used the development $$\begin{aligned}
\sin\bar\theta_n
=
\alpha \sin \theta_{n+1} + (1-\alpha) \sin \theta_n\;,\end{aligned}$$ and the fact that we do not need to consider higher order terms because they vanish from Eq. (\[eq:detedete\]) once the limit $\delta t \to 0$ is considered. The product $\prod_{n=1}^{N}
| \sin\theta_n |$ in Eq. (\[eq:detedetee45\]) cancels exactely the geometric one accompanying the delta functions in Eq. (\[eq:generatingZ24\]). In the following, we use this to drop it from the expressions.
We treat the third factor in Eq. (\[eq:factorized-jac\]) with the identity (\[eq:identity\]) and we use the causality of $C_{\rho_\perp\nu_\perp}(w,v)=\Theta(w-v) X^{-1}_{\rho_\perp\sigma_\perp}(v) A_{\sigma_\perp\nu_\perp}(v)$ to keep only the first two terms of the expansion. Performing the contractions with $X^{-1}_{\rho_\perp\sigma_\perp}$ and dropping a constant term in the overall normalization, we obtain $$\begin{aligned}
&&
\mbox{Tr} \ C =
\alpha \int{\hspace{-0ex}\mathrm{d}{t}\;} X^{-1}_{\nu_\perp\sigma_\perp}(t) A_{\sigma_\perp\nu_\perp}(t)
\nonumber\\
&& \qquad\;\;
= \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\int{\hspace{-0ex}\mathrm{d}{t}\;}
\left[
\frac{D(1-2\alpha)\gamma_0}{\sin^2\theta}
- \partial_\theta (H_{{\rm eff},\phi} + H_{\phi})
\right.
\nonumber\\
&&
\qquad\qquad\qquad\qquad\qquad
\left.
- \frac{\eta\gamma_0}{\sin\theta} \partial_\phi ( H_{{\rm eff},\phi} + H_\phi)
-\eta\gamma_0 \partial_\theta ( H_{{\rm eff},\theta} + H_\theta)
\right.
\nonumber\\
&&
\qquad\qquad\qquad\qquad\qquad
\left.
+ \frac{1}{\sin\theta} \partial_\phi ( H_{{\rm eff},\theta} + H_\theta)
\right]
\; . \end{aligned}$$ Note that the random field ${\mathbf H}$ is still present in this expression, as it was in the Cartesian framework calculation as well.
The second order term in the expansion is a half of $$\mbox{Tr } C^2 = \iint{\hspace{-0ex}\mathrm{d}{t}\;}{\hspace{-0ex}\mathrm{d}{t'}\;}
\Theta(t-t') \Theta(t'-t)
X^{-1}_{\sigma_\perp \mu_\perp}(t) A_{\mu_\perp \nu_\perp}(t) X^{-1}_{\nu_\perp \rho_\perp}(t') A_{\rho_\perp \sigma_\perp}(t')$$ that making the sums over the $\perp$ components and using the explicit form of $X^{-1}$ reads $$\begin{aligned}
\mbox{Tr } C^2 &=
\frac{1}{(1+\eta^2\gamma_0^2)^2} \iint{\hspace{-0ex}\mathrm{d}{t}\;}{\hspace{-0ex}\mathrm{d}{t'}\;}
\Theta(t-t') \Theta(t'-t) \nonumber \\
& \quad \times \Big{\{}
\frac{1}{\sin\theta(t)} \left[ A_{\phi\phi}- \eta\gamma_0 A_{\theta\phi} \right](t) \frac{1}{\sin\theta(t')} \left[A_{\phi\phi}- \eta\gamma_0 A_{\theta\phi} \right](t')
\nonumber\\
& \quad\quad +
2\frac{1}{\sin\theta(t)} \left[ \eta\gamma_0 A_{\phi\phi} + A_{\theta\phi} \right](t) \left[ \eta\gamma_0 A_{\theta\theta} -A_{\phi\theta}\right](t') \nonumber\\
& \quad\quad
+ \left[A_{\theta\theta} + \eta\gamma_0 A_{\phi\theta}\right](t) \left[A_{\theta\theta} + \eta\gamma_0 A_{\phi\theta} \right](t')
\Big{\}}
\nonumber
\;. \end{aligned}$$ We now replace $A_{\mu_\perp\nu_\perp}$ by their explicit form. Since the two $\Theta$ functions make the integrand vanish for $t\neq t'$, the non-vanishing contributions can only come from divergent equal-time terms. Owing to the delta-correlated nature of the random field, we only keep the terms that are quadratic in the random field, see App. \[sec:determinants\]. We find $$\begin{aligned}
&
\mbox{Tr} \ C^2
=
\frac{1}{(1+\eta^2\gamma_0^2)^2} \iint{\hspace{-0ex}\mathrm{d}{t}\;}{\hspace{-0ex}\mathrm{d}{t'}\;}
\Theta(t-t') \Theta(t'-t) \
H_i(t) H_j(t')
\nonumber \\
& \quad \times \left\{
\frac{\gamma_0}{\sin\theta(t)} \left[ \left( \partial_\phi R_{\theta i} + \eta\gamma_0 \partial_\theta R_{\phi i} \right) + \frac{\eta\gamma_0}{1+\eta^2\gamma_0^2}\cot\theta\left( \eta\gamma_0 R_{\phi i}- R_{\theta i}\right)\right](t) \right. \nonumber \\
& \quad \quad \times
\frac{\gamma_0}{\sin\theta(t')} \left[\left( \partial_\phi R_{\theta j} + \eta\gamma_0 \partial_\theta R_{\phi j} \right) + \frac{\eta\gamma_0}{1+\eta^2\gamma_0^2}\cot\theta\left( \eta\gamma_0 R_{\phi j}- R_{\theta j}\right) \right](t') \nonumber\\
& \quad\quad -
2\frac{\gamma^2_0}{\sin\theta(t)} \left[ \eta\gamma_0\partial_\phi R_{\theta i} + \partial_\phi R_{\phi i} \right](t) \nonumber \\
& \qquad \qquad \times
\left[ \cot\theta \left(\eta\gamma_0 R_{\phi j} - R_{\theta j} \right) + \left( \partial_\theta R_{\theta j} - \eta\gamma_0 \partial_\theta R_{\phi j} \right) \right](t') \nonumber\\
& \quad\quad
+ \eta^2\gamma_0^4 \left[ \partial_\theta R_{\theta i} + \partial_\theta R_{\phi i} \right](t) \left[\partial_\theta R_{\theta j} + \partial_\theta R_{\phi j} \right](t')
\Big{\}}
\; .
\nonumber\end{aligned}$$ Following the same steps as in App. \[app:randomfield\], we now replace the product of random fields $H_i(t) H_j(t')$ by its average over the Gaussian measure, $2D \delta_{ij} \delta(t-t')$, see again App. \[sec:determinants\]. After a tedious but straightforward computation, dropping constant terms, we obtain $$\begin{aligned}
-\frac{1}{2} \mbox{Tr } C^2 = \frac{D\gamma_0^2\alpha^2}{1+\eta^2\gamma_0^2} \int{\hspace{-0em}\mathrm{d}{t}\;}
\frac{1}{\sin^2\theta}
\; . \end{aligned}$$ Finally, putting all terms together, the Jacobian is $$\begin{aligned}
&& {\cal J}_G^{\rm sph}
=
\exp\left\{ (1-\alpha) \ln \left| \frac{\sin\theta(t_0)}{\sin\theta(t_N)} \right| \right\}
\nonumber\\
&&
\qquad
\times
\exp \left\{\frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \int{\hspace{-0ex}\mathrm{d}{t}\;}
\left[
\frac{D(1-2\alpha)\gamma_0}{\sin^2\theta}
- \partial_\theta (H_{{\rm eff},\phi} + H_{\phi})
\right.\right.
\nonumber\\
&&
\qquad\qquad\qquad\qquad
- \frac{\eta\gamma_0}{\sin\theta} \partial_\phi ( H_{{\rm eff},\phi} + H_\phi)
-\eta\gamma_0 \partial_\theta ( H_{{\rm eff},\theta} + H_\theta)
\nonumber\\
&&
\qquad\qquad\qquad\qquad
\left.\left.
+ \frac{1}{\sin\theta} \partial_\phi ( H_{{\rm eff},\theta} + H_\theta)
+ \frac{\alpha\gamma_0 D}{\sin^2\theta}
\right] \right\}
\; . \end{aligned}$$ As found in the Cartesian calculation and in the spherical construction for the Landau formulation of the dynamics, the Jacobian ${\cal J}_G^{\rm sph}$ does not depend on the parallel component of the effective field, $H_{{\rm eff},M_{{\rm s}}}+H_{M_{{\rm s}}}$. Moreover, we find that the Landau and Gilbert Jacobian in spherical coordinates coincide. see Eq. (\[eq:Jacobian-Landau-spherical\]) and App. \[app:MSRDJ-Jacobian-Gus\] for the Landau calculation.
We next introduce a Lagrange multiplier $[{{\rm i}}\hat{\mathbf{\Omega}}]$ to exponentiate the functional delta: $$\int {\mathcal{D}}{[{{\rm i}}\hat{\mathbf \Omega}]} \exp \left\{ - \int \! {\hspace{-0em}\mathrm{d}{t}\;}
\left(
{{\rm i}}\hat\Omega_{M_{{\rm s}}} \mbox{{Eq}}^{\rm sph}_{G,M_{{\rm s}}}[{\mathbf \Omega}]
+
{{\rm i}}\hat\Omega_\phi \mbox{{Eq}}^{\rm sph}_{G,\phi}[{\mathbf \Omega}, {\mathbf H}]
+
{{\rm i}}\hat\Omega_\theta \mbox{{Eq}}^{\rm sph}_{G,\theta}[{\mathbf \Omega}, {\mathbf H}]
\right)
\right\}
\; .$$ We identify all the terms in the integrand of the exponent in the exponential that involve the random field ${\mathbf H}$: $$\begin{aligned}
&&
-\frac{1}{4D} H_i^2
+ \gamma_0
\left(
{{\rm i}}\hat\Omega_\theta R_{\phi i}
+
{{\rm i}}\hat\Omega_\phi R_{\theta i}
\right) H_i
\nonumber\\
&&
\qquad
+ \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\left( -\partial_\theta R_{\phi i}
-\frac{\eta\gamma_0}{\sin\theta} \partial_\phi R_{\phi i}
- \eta\gamma_0 \partial_\theta R_{\theta i}
+ \frac{1}{\sin\theta} \partial_\phi R_{\theta i}
\right) H_i\;.
\qquad\end{aligned}$$ After integration and a number of simplifications that use the explicit expression of the rotation matrix $R$ we find that these terms give rise to $$\begin{aligned}
D \gamma_0^2 \left[
({{\rm i}}\hat\Omega_\phi)^2 + ({{\rm i}}\hat\Omega_\theta)^2
+ \frac{2\alpha}{1+\eta^2\gamma_0^2} \left( {{\rm i}}\hat\Omega_\theta + \eta\gamma_0 {{\rm i}}\hat\Omega_\phi \right) \cot\theta
+ \frac{\alpha^2}{1+\eta^2\gamma_0^2} \frac{1}{\sin^2\theta}
\right]\end{aligned}$$ (apart from an irrelevant additive constant). Note that minus this form equals the terms in the exponential of the transverse random field measure in spherical coordinates, Eq. (\[eq:Pn-random-noise-sph\]), after the identification ${{\rm i}}\hat\Omega_\theta \to - H_\phi/(2\gamma_0 D)$ and ${{\rm i}}\hat\Omega_\phi \to - H_\theta/(2\gamma_0 D)$ (plus a constant). We put all these results together to write the generating functional $$\mathcal{Z}[\boldsymbol{\lambda}] = \int
{\cal D}[\boldsymbol{\Omega}] {\cal D}[\hat{\boldsymbol{\Omega}}] \exp\left( S_G^{\rm sph}[\boldsymbol{\Omega},\hat{\boldsymbol{\Omega}}]
+ \int{\hspace{-0em}\mathrm{d}{t}\;}\boldsymbol{\lambda}(t) \cdot \boldsymbol{\Omega}(t) \right)\;,$$ the full action $$S_G^{\rm sph}= \widetilde S^{\rm sph}_{G,{\rm det}} + \widetilde S^{\rm sph}_{G,{\rm diss}} + \widetilde S^{\rm sph}_{G,{\rm jac}} \;,$$ and the terms $$\begin{aligned}
\widetilde S^{\rm sph}_{G,{\rm det}} \! & \! = \! & \!
\ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)]
-
\int {\rm d}t
\left[ {{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}\right.
\nonumber\\
&&
\left.
\;\;
+ {{\rm i}}\hat\Omega_\theta
( {\rm D}_t^{(\alpha)}(\theta) - \gamma_0 H_{{\rm eff}, \phi} )
- {{\rm i}}\hat\Omega_\phi (\sin\theta {\rm D}_t^{(\alpha)}(\phi) + \gamma_0 H_{{\rm eff}, \theta})
\right]
\;,
\label{eq:action-det-sph-Gilbert-tilde}\\
&&
\nonumber\\
\widetilde S^{\rm sph}_{G,{\rm diss}} \! & \! = \! & \!
\int {\rm d}t
\left[
D \gamma_0^2 ({{\rm i}}\hat\Omega_\phi)^2 + D \gamma_0^2 ({{\rm i}}\hat\Omega_\theta)^2
-
{{\rm i}}\hat\Omega_\theta
\eta\gamma_0 \sin\theta {\rm D}_t^{(\alpha)}(\phi)
- {{\rm i}}\hat\Omega_\phi \eta\gamma_0 {\rm D}_t^{(\alpha)}(\theta)
\right.
\nonumber\\
&&
\;\;
\left.
+ \frac{2\alpha\gamma_0^2 D}{1+\eta^2\gamma_0^2} ( {{\rm i}}\hat\Omega_\theta + \eta\gamma_0 {{\rm i}}\hat\Omega_\phi) \cot\theta
\right]\;,
\label{eq:action-diss-sph-Gilbert-tilde}
\\
\widetilde S^{\rm sph}_{G,{\rm jac}} \! & \! = \! &\!
(1-\alpha) \ln \left| \frac{\sin\theta(t_0)}{\sin\theta(t_N)} \right|
+
\frac{\alpha\gamma_0^2 D}{1+\eta^2\gamma_0^2} \int{\hspace{-0em}\mathrm{d}{t}\;} \frac{1}{\sin^2\theta}
\nonumber\\
&&
+ \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2}
\int {\rm d}t
\left[
- \partial_\theta H_{{\rm eff},\phi}
- \frac{\eta\gamma_0}{\sin\theta} \partial_\phi H_{{\rm eff},\phi}
\right.
\nonumber\\
&&
\left.
\qquad\qquad\qquad\qquad\qquad
-\eta\gamma_0 \partial_\theta H_{{\rm eff},\theta}
+ \frac{1}{\sin\theta} \partial_\phi H_{{\rm eff},\theta}
\right]\;.
\end{aligned}$$ (We canceled the last term in the result from the integration over $H_i$ with one term from ${\cal J}^{\rm sph}_{G,{\rm jac}}$.)
We now use the identity (\[eq:identity-Gus\]) to bring the action $S^{\rm sph}_{G}$ into a form that is closer to the one in the Landau formulation. We apply this identity to the integration over ${{\rm i}}\hat \Omega_\phi$ and ${{\rm i}}\hat \Omega_\theta$ separately with $$\begin{aligned}
&
\sigma^2= D\gamma_0^2
\nonumber\\
&
a = - \frac{2\alpha \gamma_0^2 D}{1+\eta^2\gamma_0^2} \eta\gamma_0 \cot\theta
\nonumber\\
&
b
= -\sin\theta {\rm D}^{(\alpha)}_t(\phi) - \gamma_0 H_{{\rm eff},\theta} + \eta\gamma_0 {\rm D}^{(\alpha)}_t(\theta)
\nonumber\end{aligned}$$ for ${{\rm i}}\hat \Omega_\phi$, and $$\begin{aligned}
&
\sigma^2 = D \gamma_0^2
\nonumber\\
&
a = - \frac{2\alpha \gamma_0^2 D}{1+\eta^2\gamma_0^2} \cot\theta
\nonumber\\
&
b =
{\rm D}^{(\alpha)}_t(\theta) - \gamma_0 H_{{\rm eff},\phi} + \eta\gamma_0 \sin\theta {\rm D}^{(\alpha)}_t(\phi)
\nonumber\end{aligned}$$ for ${{\rm i}}\hat \Omega_\theta$. The new terms generated by the identity are $$\begin{aligned}
- \frac{a^2}{4\sigma^2} - \frac{ab}{2\sigma^2}
& \!\! = \!\! &
-
\frac{\alpha^2\gamma_0^2 D}{(1+\eta^2\gamma_0^2)^2} \eta^2\gamma^2_0 \cot^2\theta
\nonumber\\
& &
+
\frac{\alpha}{1+\eta^2\gamma_0^2} \eta\gamma_0 \cot\theta \
[-\sin\theta {\rm D}^{(\alpha)}_t(\phi) - \gamma_0 H_{{\rm eff},\theta} + \eta\gamma_0 {\rm D}^{(\alpha)}_t(\theta)]\end{aligned}$$ in the first case, and $$\begin{aligned}
- \frac{a^2}{4\sigma^2} - \frac{ab}{2\sigma^2}
& \!\! = \!\! &
-
\frac{\alpha^2\gamma_0^2 D}{(1+\eta^2\gamma_0^2)^2} \cot^2\theta
\nonumber\\
& &
+
\frac{\alpha}{1+\eta^2\gamma_0^2} \cot\theta \
[ {\rm D}^{(\alpha)}_t(\theta) - \gamma_0 H_{{\rm eff},\phi} + \eta\gamma_0 \sin\theta {\rm D}^{(\alpha)}_t(\phi)]\end{aligned}$$ in the second case. Adding them up one finds the total contribution $$\begin{aligned}
-
\frac{\alpha^2\gamma_0^2 D}{1+\eta^2\gamma_0^2} \cot^2\theta
+ \alpha \cot\theta {\rm D}^{(\alpha)}_t(\theta)
- \frac{\alpha\gamma_0}{1+\eta^2\gamma_0^2} \cot\theta \
[\eta\gamma_0 H_{{\rm eff},\theta}+H_{{\rm eff},\phi}
]
\; . \end{aligned}$$ We will add the first and last term to $\widetilde S_{G,{\rm jac}}$ to get $S_{L,{\rm jac}}^{\rm sph}$, see Eq. (\[eq:esferica-jac\]). In order to put together all terms in $1/\sin^2\theta$ we dropped an irrelevant constant. We are left with the rest of the contributions that we rearrange as $$\begin{aligned}
S^{\rm sph}_{G,{\rm det}} \!\! & \!\! = \! \! & \!
\ln P_{\rm i}[{\mathbf \Omega}_0, {\mathbf H}_{\rm eff}(t_0)]
-
\int {\rm d}t
\left[ {{\rm i}}\hat\Omega_{M_{{\rm s}}} {\rm d}_t M_{{\rm s}}+ {{\rm i}}\hat\Omega_\theta
( {\rm D}_t^{(\alpha)}(\theta) - \gamma_0 H_{{\rm eff}, \phi}
)
\right.
\nonumber\\
&&
\left.
\!\!
- {{\rm i}}\hat\Omega_\phi
( \sin\theta {\rm D}_t^{(\alpha)}(\phi) + \gamma_0 H_{{\rm eff}, \theta}
)
\right]
,
\label{eq:action-det-sph-Gilbert}\\
S^{\rm sph}_{G,{\rm diss}} \!\! & \!\! = \!\! & \!\!
\int {\rm d}t
\left[
D \gamma_0^2 ({{\rm i}}\hat\Omega_\phi)^2 + D \gamma_0^2 ({{\rm i}}\hat\Omega_\theta)^2
- {{\rm i}}\hat\Omega_\theta \eta\gamma_0 \sin\theta {\rm D}_t^{(\alpha)}(\phi)
\right.
\nonumber\\
&&
\left.
\qquad\quad
- {{\rm i}}\hat\Omega_\phi \eta\gamma_0 {\rm D}_t^{(\alpha)}(\theta)
\right]
\;,
\label{eq:action-diss-sph-Gilbert}
\\
S^{\rm sph}_{G,{\rm jac}} \!\! & \!\! = \!\! & \!
S^{\rm sph}_{L,{\rm jac}}
\label{eq:action-jac-sph-Gilbert}
\end{aligned}$$ and $S_G^{\rm sph} = S_{G, {\rm det}}^{\rm sph} + S_{G, {\rm diss}}^{\rm sph} + S_{G, {\rm jac}}^{\rm sph}$.
[**Acknowledgements.**]{} We thank H. Hüffel and F. Romà for very useful discussions. We acknowledge financial support from ANR-BLAN-0346 (FAMOUS), PICT-2008-0516 (Argentina), NSF grants No. DMR-0906943 and DMR-1151810 (USA) and the Fundação de Amparo à Pesquisa do Estado do Rio de Janeiro (FAPERJ) and Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq). DGB thanks the ICMP at the University of Illinois at Urbana-Champaign, where part of this work was developed. GSL thanks CNRS for an associate researcher position at LPTHE, Jussieu. LFC and GSL thank the ICTP Trieste for hospitality during the first steps of this investigation. ZGA is a CNPq fellow (Brasil).
[^1]: We found some contradictions in the literature concerning the relation between the parameters in the two formulations. To be more precise, we find that the parameters transform as in [@Bertotti-etal; @Cimrak2008] but differently from what is shown in [@Berkov2007].
[^2]: A sequence of random variables $X_n$ converges in the mean-square sense to another random variable $X$ if $\lim_{n\to\infty} \langle (X_n -
X)^2 \rangle = 0$ [@Gardiner].
|
Archive | November 2013
This blog post is the second part of a 2-part series on the key highlights from ‘A Night of Hope’, an inspirational live event of worship and celebration, by bestselling author and transformational pastor, Joel Osteen.
Some of the highlights of Joel and Victoria’s messages of hope, transformation and purpose (PART II):
1. Our first mission field is to our families. Everything flows from the family. Value your relationships. Agree to disagree respectfully. Everyone has different backgrounds, education, upbringing, belief system etc., so learn to accept and respect one another. Pick your fights. Know what’s worth fighting about and what to let go. Sometimes you have to keep your mouth shut and sow that act of compromise as a seed.
2. In life you’ve got to stand up and fight for what you want. Live a life of FAITH in action and focus on touching one life at a time. Everyday is an opportunity to do something different and better!
3. In pursuing your purpose in life, it is not how you start, it is how you finish. Take a step and tell yourself empowering stories. If the inner conversation is not taking you towards your goals, have a different conversation with yourself and make it louder!
4. Are you going to go forward or will you stay stuck staring behind through your rear view mirror? Let go and forgive all of yesterday’s pain. God made you to be free of excess baggage. His promise is to always make your burden lighter.
5. In life there are two types of bags that you get to carry around. It is either one or the other. The first is the special positive bag filled with joy, thanksgiving and service etc.
While the other is the negative bag. Are you dragging around all the negative baggage from your past with you in the present? Which bag do you carry: Disappointment bag, Hurt bag, Regret bag, Anger bag, Bitter bag? Isn’t time to let go and let GOD?
6. Manage your happiness by managing your expectation, your sense of happiness is a choice. You have control over the type of relationships you wish to co-create.
Only what you allow happens. Love yourself enough to honour God in you by giving and asking for the best. treat yourself with respect.
7. Speak words of faith and affirmation to any difficult situation and then take action in line with your words.
“The tragedy of life is not death but what we let die inside of us while we live.” ~Norman Cousins~
Disclaimer: The highlights above are based on personal notes and understanding of Joel and Victoria Osteen’s messages. No intentional omission or error is intended. I hope something on this list resonates and plants an active seed in your life.
Have an abundantly blessed day and an awesome life ahead!
-Juliet ‘Kego Ume-Onyido, MBA
Poet | Master-Certified Leadership Coach-Trainer -Consultant|
~Take empowered ACTION towards a Healthier, Sexier, Wealthier YOU!~
————————————————————
Blogger Bio:
The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]!
She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook.
Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?”
On the sidelines of the Port Harcourt Book festival, I caught up with festival headliner, Chika Unigwe, and engaged her in this interview where she talked about her life after winning the coveted NLNG prize. She spoke also on other sundry issues.How has life been since the NLNG prize? How has life been? It’s been a lot easier to convince other people that writing is a serious business and that’s what winning a big prize always does. Suddenly people who help baby sit your kids so you can go and gallivant round the world and do things start taking you seriously. It’s been such a great honour to be recognised in my country. Of everything I would want to win, the NLNG was top of the list simply because it is something from Nigeria. It’s been nice coming back to Nigeria as a writer some people have heard of…
(Note, these are not the same as new year resolutions. Please refer to this previous post for more on the ‘I AM statements: http://wp.me/p1o3v6-1a).
One of the many 50 statements that I wrote down was: “In 2014, I AM attending a live event of inspirational worship and celebration by bestselling author and pastor Joel Osteen.”
Then, I simply stood in the flow gratitude and acceptance of allowing this statement to manifest and it did happen!
Well, fast forward to a few months ago, when randomly, a friend of mine called me up excitedly to tell me the great new: Joel and Victoria Osteen were coming to Toronto for an evening of worship, music and motivation. The sad news was it was happening that night, intact 3 hours from the time she called me!
The event was tagged: ‘A Night of Hope.’ First I made the conscious decision and voiced it out and wrote it down: ‘I AM attending this event tonight.’
And I held on to the hope that even though we were informed about this so late, there was still hope that our creator of midnight hours and crossover miracles would come to our rescue:-)After a frantic search online for any available, last minute ticket(s), a few phone calls to sort out babysitting, we were soon both Air Canada Centre, ACC-bound!
It was a life-affirming day for me because even though the messages may not be new, Joel and victoria shared them with such authenticity and power that it resonated and stayed with me till today. The energy that filled ACC dome was deeply moving and so incredible!
Apparently, I was not the only one who took copious notes. My friend had also sent me an email which contained her biggest take-aways from that evening. So we both collated our list of highlights and though we’d share, so here it goes! P.S: It would be done in a two-part series, so look out for part two tomorrow.
Some of the highlights of Joel and Victoria’s messages of hope, transformation and purpose (PART I):
1. Let everyday be a new beginning for you. Forgive yourself and let go of the feelings of guilt and condemnation. Don’t sit on the sidelines of life, get back in the game and play at 100%!
2. God never allows you to experience difficulties without a divine purpose. Use your faith not to pray away difficulties but rather, surrender and allow the storm to lead you exactly where you should go.
3. Quit fighting back, relinquish control, surrender, so that God’s will may be done. Trust him and know that your storms are not a surprise to him. Burn up the limiting beliefs and shake off the self-pity!
4. You would not have been given a destiny without being equipped and empowered by God to fulfill it.
Each day is a step forward towards your purpose and destiny. Start the day how you want the day to be. Set very clear intentions and be in tune with your attention.
Be grateful everyday for the gifts of life and love. Shake off the bad ‘stuff’ by changing your internal recording and inner movie. Learn to change your dial/channels!
5. Affirm daily who you are1 Your ‘I AM’ statements are very powerful; ‘I am creative, I am fun, I am strong, I am healthy, I am wealthy, I am magnificent, I am a masterpiece.’ Indeed, you are God’s masterpiece, equipped, approved, blessed, forgiven, NOT average, not mediocre!
6. Stop the self-abuse and self-flagellation! You have enough people against you, you don’t have to be against yourself.
There are lots of negative thoughts AND comments, from people that you have to ignore. Know how to take the learnings and corrections in criticism without attaching yourself to the negativity of its sting.
You only have so much emotional energy each day. There are even some family members and ‘friends’ that you may have to sometimes distance yourself from.
7. Unforgiveness is like a poison inside you, Release yourself and release people. Write letters to everyone who’s ever hurt ou and who you’ve ever hurt. Do anything you can to help yourself. Know who you are and whose you are; victors and not victims!
8. Are you still tied to the victim mentality? Are you still choosing to be married to your pain?
You CANNOT drag your baggage of pain over and over again, let it go! dream another dream.
Quit thinking about it. Change the channel. Quit reliving negative memories. When you play negative movies in your mind, you will only feel negative emotions.
Be disciplined in your thoughts. Think only pure thoughts, start changing the channels of your thoughts.
9. How you tell your stories of your wound matters. When you tell it, do you tell it from an empowered place, knowing the wound is already healed or when you talk about it, are you still stuck in the drama of reliving the pain?
10. Beauty for ashes! You have to decide and let go of the ashes before you can see and receive the beauty.
It is an act of faith-let go of the pain and the blame. Do not live life looking in your rear view mirrors.
11. Seasons come and seasons go. A season of mourning does not equate to a LIFETIME of mourning!
Shake off the pain of the past. Strain towards what lies ahead. The past is dead and gone, we can choose to be like the mountain climber, who cut of his infected arm so that he may live. Stop rehearsing and rehashing your old pains.
12. I BELIEVE AND DECLARE THAT THE REST OF YOUR LIFE WILL BE THE BEST OF YOUR LIFE!
Disclaimer: The highlights above are based on personal notes and understanding of Joel and Victoria Osteen’s messages. No intentional omission or error is intended. I hope something on this list resonates and plants an active seed in your life.
Have an abundantly blessed day and an awesome life ahead! ❤
-Juliet ‘Kego Ume-Onyido, MBA
Poet | Master-Certified Leadership Coach-Trainer -Consultant|
~Take empowered ACTION towards a Healthier, Sexier, Wealthier YOU!~
————————————————————
Blogger Bio:
The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]!
She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook.
Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?”
On this site I talk about blocks to personal/spiritual growth and uncovering them so we are able to have an insight for living. Well, I’ve discovered a big core block for myself. Here’s how the discovery of it went:
In the coaching group I’m leading, at the end of the call when it was her turn to share what she got out of the call, one of the members said that she see’s the little girl in each of us (5 women including me).
Then I said, “You want to know what kind of little girl I was? I loved skirts that twirl. I put on shows in the neighborhood organizing the kids a little younger then I. We made and sold tickets. My mother hung an old bedspread on the clothesline and we put on some kind of show. I don’t remember the show but I do remember that…
The pain and shock caused by a loss may lead to extreme, and sometimes unhealthy, new patterns of behaviour.
If these patterns last beyond a temporary period of time, then perhaps, it is important to seek empathetic help and support from professionals and/or loved ones.
(Various researches have shown that the presence, support and love from loved ones and even strangers, make a huge difference to the healing curve).
Of the many emotions one experiences after a loss, perhaps the three really important ones to watch out for are Denial, Guilt and Shame.
This is because other emotions-anger, sadness, fear hurt, regret and pain, which are warranted emotions, when expressed in a healthy way, may lead the person to a sense of release, acceptance and closure over time.
On the other hand, feelings of denial, shame and guilt prolong the healing period and may make one sink in deeper into a prolonged, unhealthy spiral of mourning and grieving.
To grief fully, without reservation, is itself, an important piece of the healing process. The loss of someone or something very dear to us, creates a shift in our perspective of the world and life in general.
This is as it should be because we are not the same person we were before the loss and we can never go back to being that old person. Irrevocably, we are changed, for better or worse, by that singular experience. And it still comes down to the choices we make, either consciously or unconsciously.
An interesting and empowering thing about the pain of loss is that if we pay close attention, the purpose of the death should compel us re-prioritize our lives.
And it should also push us or inspire us to pursue only those things that give us the most joy, as well as adding the most value.
The loss then simply acts as a boulder, and it’s role is to make us pause and reflect, as we are reminded that with every breath we take, death looms nearer, waiting in the shadows.
Each day we wake up is a day closer to the end of the journey. What is the quality of the memories we wish to celebrate at the end?
What is the life story we want told? Begin to live the future you dream of for yourself NOW, because the choices you make now, create the tomorrow you desire or despise! You get to tell your story, BE and LIVE the story you want told.
Death offers us a chance to pause, take a deep breath, and recall shared memories of our loved ones.
It allows us an opportunity to really stop everything, as we share our grief and connect with the deceased by building a legacy that upholds and reflects their values and purpose.
Therefore, we must seek grace so that we do not waste the inherent power and beauty that our loss affords us. Everything has a purpose, nothing is an accident.
Thus, the purpose of death becomes that of a jarring or gentle reminder, an alarm clock that wakes us up and draws the attention of the living towards their own path, their own purpose.
Periods of grief are also a time to also take another hard look at our lives and course-correct our track, if necessary. It is a time to strengthen existing bonds or heal broken ones. Death is a destroyer of arrogance.
It is in periods of intense sorrow that we ask the most important WHYs. The answers are already within us, we simply need the right questions to unlock what we already know. Death allows us to question what is truly important to us about living.
There can be no greater opportunity for growth, learning and transformation than through death. It lends itself to such a literal and metaphoric finality that we are forced to pay immediate attention to the pain it elicits.
And when we are courageous enough to face, feel and conquer ours fears/pains, we are in a better place. The more specific we get with our pain, the easier and faster it dis-integrates. “Sorrows are our best educators. A person can see further through a tear than a telescope.” ~Lord Byron~
To everyone and anyone experiencing intense sorrow over the loss of someone or something precious, I join others across our global WWN community in reaching out to you.
We share our common connectedness and exchange our energy of understanding, of empathy, of unconditional love and of healing.
Know that God walks with you, always, especially in the valleys, his light is there to comfort and guide your ways.
We hold sacred space for the living survivors and also for the living who’ve moved on. Time in itself doesn’t heal, I’d like to think that we choose to heal, in time.
We choose to heal and live and thus honour the spirit of the dead. If not, what difference would it then make if we either lived or die. Remember that death is itself a metaphor for life and vice versa. One journey starts when the other end, so loved ones never really die, they are merely transformed.
Everything and everyone is energy and because we have shared the sacred space of living with them, they leave a part of themselves with us, the most important parts of them; their love, spirit, essence and core.
As we grief and mourn for different reasons, let us reflect deeply on the truth that one of the greatest gifts of deep loss is the profound understanding that we must all learn to begin to surrender to life, be more accepting and allowing of letting go, while focusing on embracing both our nothingness and our majesty, both our humanity and our divinity.
Blogger’s Note: This post was inspired by a dear friend who recently lost a beloved spouse. In the death of a loved one, we are all reminded of the precious gift of life. And even as we mourn, we hold firm in faith. We are strong believers; we believe in resurrection, we believe that the deceased are with us, even though we no longer physically see them. Also, we know and believe that this too shall pass and although the pain may sometimes be overwhelming, we have faith in the abiding grace of God to lead us through the storms.
This is thanksgiving weekend in the USA, and so, we lift up our heartfelt prayers of love and thanksgiving. May the power of our collective wishes give healing and peace to those among us who mourn.
For indeed, ALL things work together for those who believe. The task is to let go and believe! May the souls of the faithfully departed, Rest In Perfect Peace of our Lord. Through the pain and the storm of your loss, may you be willing, ready and open to love. In love were you created, with love were you moulded, through love were you redeemed. At your core, you are love!
Are you or anyone you know experiencing intense sorrow over the passing of a loved one? Two (2) books that I highly recommend for anyone who’s grieving are:
1. A TIME TO GRIEVE: Meditations for healing after the death of a loved one, by Carol Staudacher;
2. HEALING AFTER LOSS: Daily Meditations for working through grief,by Martha Whitmore Hickman
-Juliet ‘Kego Ume-Onyido, MBA
Poet | Master-Certified Leadership Coach-Trainer -Consultant|
~Take empowered ACTION towards a Healthier, Sexier, Wealthier YOU!~
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Blogger Bio:
The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]!
She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook.
Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?”
Today’s reflection is focused on the power of ASKING QUESTIONS. Sometimes, it is not the answers that we find that give us the biggest shifts and transformation. Often, it is the questions that we ask ourselves or are asked by others that open up our hearts and minds to possibilities we never imagined. The act of seeking the answers becomes a metaphor for the journey of life.
Begin to pay attention to the questions that keep you awake at night, the questions that never seem too far from your mind, the questions that you run away from confronting. Those are probably the questions that have the biggest relationship with your life purpose and destiny.
WWN Reflection DAY 27: Take ACTION and Transform Your Life!
Here are some questions to reflect upon as you enjoy the rest of the week:
1. This mid-week, reflect and ask yourself: Am I on the ‘WOE me’ or ‘WOW me’ axis of life’s equation?
WOE ME= Making excuses and having reasons to blame others for the drama and crap in your life! You are an expert at pointing fingers outwards, talking about other people’s limitations and never yours. You play the victim card. Failure and stagnation are guaranteed states in this zone.
WOW ME=You take ownership and responsibility for both your awesomeness and your crap! You understand that you are a co-heir and co-creator with God. You focus on the learning in any situation, you seek to provide solutions and to add value. You are at cause for your life. You are in control of your results. You look inwards for answers. Success and purposeful living is guaranteed here.
Note: You get to choose only one side at any given time….you cannot be in both! And if you’re in neither, you may be sitting on the ‘stuck’ fence, where life seems to be ‘happening’ to you. It is important to also note that as human beings, we will definitely find ourselves hanging out in the ‘woe me’ quadrant once in a while. The key is not to stay there for too long and also to celebrate the awareness of your lessons and learnings while you’re there or after you get out! So, be gentle with yourself and others, we’re all doing the very best we can with the resources we have.
2. Did you know that there’s a behavioural link between Self-Esteem, Over-Eating, Over-Spending, Over-Complaining and generally feeling ‘out of balance’ in life? They often have a common root and if you destroy the root cause, every thing else crumbles and life RE-ALIGNS back into shape! Are you aware of what your root cause is? Sometimes the manifesting ‘problem’ is simple a symptom of something deeper.
3. “Do you want a successful career or a close relationship with your family? Both! Do you want a focus on business or have fun and play? Both! Do you want money or meaning in your life? Both! Do you want to earn a fortune or do the work you love? Both! Unsuccessful people always choose one, successful people choose both. Do you realize that you always have options and indeed, by God’s grace and through hard work/working smart, you can have it all.” ~T. Harv Eker~
4. “Are you stressed? Do you take time to relax? Do you take things so seriously? Laugh as much as you can! Play! When we’re adults, sometimes we forget to play and or we think we shouldn’t be wasting time on play when the opposite is true – PLAY! PLAY! PLAY! That’s where our true joy stems from, the most innocent part of who we are, our inner child that’s so excited about life and all its blessings! Are you letting your inner child out?” ~Patricia Grace Tomasi, Life Coach~
5. Do you suffer because you think you do not have enough OR because you’ve accepted a fallacy that you can never have enough, and so you suffer? (Re-read this and ponder on it for a few minutes) 🙂 Do you realize that you have an innate ability to co-create everything you desire, want or need? Do you understand that you are enough and you always have enough? Do you play the compare and contrast game? Do you compare yourself against others or compare the present to the past or an imaginary future? Do you comprehend that this is the root cause of most unhappiness? Are you always looking at the other side and thinking the grass greener? Are you celebrating the beauty of NOW and looking inwards to find solutions unique to you or are you blindly following the dictates of the external world around you?
6. What if your problem is not YOUR problem? What if your problem is simply just a problem? What if you stopped taking your challenges and problems so personally? What if you could ‘remove’ yourself from your problem and look at them through someone else’s eyes? What if you took a new perspective, an ‘eagle-eyed’ overview of the problem and became open to new ways of ‘seeing’ them? What if the whole essence of the problems is to make you grow and transform into someone who resources creatively to resolve and solve said problems? What if all your problems have solutions and you role is to simply explore new ideas, perspectives and be open to others around you, in order to find the answers you seek?
7. What’s your purpose? Are you living in alignment with your purpose? What are your most important values in different spheres of life? What kind of life would you rather be living if you had an abundance of money, time, energy? LIVE IT NOW! Do you have the faith to believe in the formless and not in the formed physical reality? Are you speaking, feeling and living your truth? Do you realize that in order to manifest your dreams into reality, you MUST become the person who is capable of achieving those goals and dreams? WHAT you have and do flow directly from WHO you are BEING. The equation for the law of manifest ion is this: BE-DO-HAVE!
Warmest Regards, Blessings & Cyber-hugs,
-Juliet ‘Kego Ume-Onyido, MBA
Poet | Master-Certified Leadership Coach-Trainer -Consultant|
~Take empowered ACTION towards a Healthier, Sexier, Wealthier YOU!~
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Blogger Bio:
The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]!
She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook.
Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?”
“The secret of change is to focus all your energy, not on fighting the old, but on building the new.” ~Socrates~
WWN Reflection DAY 26: Take ACTION and Transform Your Life!
Today’s focus is on revisiting some old sayings, quotes and proverbs and adapting them to become more aligned with this new value-based, empathy-driven economy. I think that perhaps sometimes we are so set in a particular model of the world that it holds us back from enjoying the fullness of life all around us.
I love the idea of periodically ‘checking in’ on our existing value construct and even loosening our Model of the World (MOTW), in order to allow new perspectives and pathways of creative solutions.
Sometimes, we hold beliefs and run unconscious programs that are in conflict with what we wish to manifest in life.
Just because something has always been a particular way does not mean it cannot be looked at differently and given a ‘newer’, more empowering interpretation. So here are my newest ways of looking at the world.
1. Old Economy: “Fake it until you make it.” Which loosely translates to living a life that has little or nothing to do with authenticity, tell ‘made up’ stories (not your true stories), simply to brag, impress and make yourself look ‘bigger.’ The irony is of course that in living and doing business this way, you diminish your true value. This is also one of the main reasons people rack up obscene high-debt levels!
New Economy: “Focus all your energy on making it, so that you never have to fake it!” This suggests that you channel every resource you have towards your goals. Become one with your goals, and take quantum leaps and create value by solving problems, while sharing your truth and telling your unique story and journey! People can sense, small and feel B.S from a mile, so be yourself, period. It’s also way healthier for your life overall. As the saying goes: “When you tell the truth you do not have to remember anything.”
So rather than blindly following the ‘Joneses’, begin to set yourself apart as an original and simply take action towards your purpose. Life is much more fun and less stressful in the ‘REAL’ zone. The ‘FAKE zone, may initially be thrilling, however it ultimately drains, depresses and depletes because the brain simply does not have that strong a firewall to fuel the various incongruent parts! It is healthier to ‘sew your cloth according to your material’ and not according to your size.
2. Old Economy: “Forgive but don’t forget.” In order words, cling on to the myth of your non-existent pain in the present and create a future based on it. Fight the healing power of time and continue to perpetuate your ‘woe me’ story.
New Economy: “Forgive AND Forget.” The whole essence of forgiveness is the willingness, courage and acknowledgement of what has happened, the vulnerability to embrace and feel the pain it caused and yet decide to let it go. Forgiveness is total surrendering and acceptance. You forgive and forget both the pain and its perpetrator, rather, focus on what the experience taught you.
It is a DECISION to release and free up your heart to love and experience joy fully.
True forgiveness does not hold on to the event, rather it filters only the learnings from the event. It also gifts you with the ability to set firmer and clearer boundaries to others.
So with the passage of time, re-telling the story of your past pain simply becomes content-free (less focused on the drama), and more focused on preserving and sharing the learnings. This is true empowerment.
3. Old Economy: “It is better to teach a man how to fish than to give him fish.” Sometimes, it is important to know the other person’s model of the world and perhaps even enter it in order to gently, yet firmly guide them to navigate their way to a new understanding and hopefully, embrace healthier options and choices.
New Economy: “It is good to give a man fish, it is better to teach him how to fish and it is best to give him some fish while you teach him, lest he quenches before the lessons are finished.” In an empathy-driven economy, we acknowledge that one size never fits all and there’s a need to meet people at their level in order to lift them up to where they really belong or aspire to reach.
4. Old Economy: The law of attraction was based on feeling only ‘positive’ feelings, using your powers of imagination and focus. It was largely based on the notion that ‘You attract whatever you want.’
New Economy: This postulates a revised law of attraction based on feeling ALL your feelings, gaining mastery of your internal representation (state mastery) and the idea that what ever you are, have or do, essentially flows from who you are BEING. Thus, ‘you attract who you are.’
It also focuses a lot on taking congruent and consistent ACTION. The law of Attraction is simply the law of manifestation (of your actions). Thus, the questions you should answer are: ‘Who are you really BEING when you’re DOING what you’re doing? ‘Are you congruent and are your values aligned, in your thoughts, words and action steps, in both your inner and outer lives?’ In the words of Aristotle: We are what we repeatedly do!
4. Old Economy: “When life hands you lemons, you make lemonade.”
New Economy: Here, there’s a need to reflectively think about what you do in the wake of any situation. Is your default reaction to see it through the ‘victim lens’ or do you see life through the ‘opportunity lens?’ In the new economy, everything you encounter and everyone you interact with offer you new learning and an opportunity for collaboration, synergy and growth. You must have a deep awareness of who you are and also have the courage to embrace all of you, both your weaknesses and your strengths!
Thus, When life hands you Lemons:
a) YOU complain and gripe that they are not ripe enough, big enough, sweet enough. OR
b) YOU ignore them and waste your time searching for apples, till someday, you get famished and realize the lemons are now rotten and have gone bad. OR
c. YOU get angry and become permanently mad at the world. To express your self-justified anger and self-inflicted pain, you throw the lemons at others.
Or cut them up and squirt the juice into people’s eyes so that they too can experience your pain and desolation. And then you all hang out and swap stories of your pain, while drinking your bitter tequila/gin/lemon filled cup. OR
d) YOU are grateful for your lemons and embrace the challenge and opportunity they hold. And even though you may prefer apples or oranges, you decide to take action, turn them into lemonade and sell it all for profit.
Also, you plant the seeds and grow a lemon orchard. You begin to attract like-minded people who embraced their lemons. And you share ideas and joint-venture with them. Then, with the profits from your deals, you buy apples (your preferred fruit) 🙂 and bigger, riper, sweeter lemons which you sell (and give some away) to those in group (a), (b) and (c)!
In fact, you become so busy creating different opportunities, and consequently, enriching your inner and outer world. Your lemons suddenly become the keys that unlock your life’s purpose! It all starts with a simple step.
Whatever skills, talents, energy, money, time, passions, pains, relationships/networks…be grateful for them and use them passionately, powerfully and purposefully.
Everything you have in your life right NOW, whether good or ‘bad’, are your life lemons. the choice of what to do with them is yours.
You have the unique talents and skills to co-create your reality and design your destiny. Are you ready to take a chance and bet on YOU? Are you ready to get out of your own damn way? 🙂
The questions then become: Will you continue to sit on the toxic fence and continue telling ‘woe me’ stories of blaming, complaining, condemning and justifying why life handed you ‘bad’ lemons OR will today be the day you decide to take ACTION in the direction of your dreams and goals?
Are you ready to hear, see and live your truth by telling ‘wow me’ stories of yourself, taking control of your destiny and owning up to the responsibility and consequences for your actions and results?
Your goals are your sacred contracts you hold with yourself. If you are not willing to honour your commitment to yourself, it is near impossible to honour your commitment to others. Conversely, the universe returns to you exactly what you put out.
Say your goals exactly how you want them and take congruent actions to fulfil them. BE who you want to become. You can attract only what and who you are. Dream wonderful dreams and co-create your destiny with God!
The preceding is a guest post from Juliet Ume, MBA –Co-Founder and Executive Director at Whole Woman Network. Juliet is the author of the upcoming books: “UN-Locking Your HeArt of Leadership” and “Today, I Will Not Bow”. A self-described Life-Connoisseur, who loves life and the whole human experience, Juliet was nicknamed a ‘reminderist’, [one who reminds us of that which we already know; that we are not fractured or broken and NOW is the perfect time to replace that fallacy with a new, beautiful truth: we are worthy, empowered, complete, whole creatures and our life journey is to return to wholeness]!
She is a passionate advocate of WomEntrepreneurship, Leadership, Investment & Financial Literacy for women and youth (especially girls). Her mission is simply to engage, educate and empower women, regardless of their levels of income or background, to return to ‘wholeness’ and live Healthier, Sexier, Wealthier Lives using Faith-based, Scientific and Universal (Common-Sense) principles! Follow her on Twitter: @wholewomaninc, @julietumeinc. Enjoy some of her portfolio of poems on her Floetry Blog and follow her daily reflective posts on Facebook.
Her message is simply: “To use the power of written-spoken-sung WORDS to connect, heal, empower, change and transform our inner and outer worlds. Words have power in the meaning and interpretation we choose to give them and all of life is synchronistic poetry in motion! Are you telling empowering stories about yourself and others?” |
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wrolittiftti published by kr1dek se bingham mmrilyvllx t\y,sw t v\n 4 1830 yo l......._n 4 the wmters cahoi.imay is published every tues day at'thkee dollars per annum payable at tlie montlis.h iii seven weeks fewer peas by five fais/tela than thc other three yet they weighed more when kil led by 0 stone and four pounds upon an aver age or six stones twelve pounds upon the whole the poet the powers of mind necessary to produce those different results are not the same reesqn governs the one and imagina tion the other the former is confined to argument and truth the latter to imagery and sentiment the orator analyzes aud reasons compares and deduces j tiie poet combines and imitates ; of happiness ; — that to secure these rights gov ernments are instituted among men deriving their just powers from the consent of the gov erned ; — that whenever any form of government becomes destructive of these ends it is the right of thc people to alter or abolish it anil to institute a new government laying its foundation on suclj principles and organizing its pow era in such form as to them shall seem most likely to effect their safety and happiness prudence indeed will dictate that governments long established should not be changed for light and transient causes anel accordingly all experience hath shown that man kind are more disposed to suffer while evils are sufferable than to right themselves by abolishing the forms to which they are accustomed ilu when a long train of abuses and usurpations pur suing invariably thc same object evinces u design to reduce them under absolute despotism it i their right it is their duly to throw off such gov ernment and to provide new guards for their fu ture security such has bcen the patient suffer ance of these colonies ; anel such is now thc nr cc-siiy which constrains them to alter their forme .-■. systems of government — the history e,f tb present kin of grcat-brtain i a history of rr pealed injuries and usurpations all having in ep . lect object thc establishment of an absolute tyi anny over these states to prove this let fact be submitted to a candid world : — hix^no paper will be discontinued until 1i arrearages are paid unless at tlie discretion of thc editors whoever will become responsible for the payment of nine papers shall receive a tenth gratis l'mityuhtvvvtt adv terms will be inserted ou the customary from " letteus from washington no advertisement inserted until it has been paid for or its payment assumed by sonic person in this town or its vicinity " his eye in a line phrenzy rolling dotli glance from heaven to earth from earth i-i heaven and embodies forth the forms of things un known the orator must exist in the living world ; the poet may live in a world of his own creation memory and judgment are lhe powers employed by the former imagina tion and invention those exercised by tiie lat ter in moving the heart and exciting the passions they differ only in the means em ployed to produce this effect anel in this alone they approximate ihe examples are numerous to establish the correctness of these positions cicero was a great orator but a bad pott ; pope was a great poet but a bad orator in short oratory ancl poetry have never been united in one individual but to return with all the excellencies i have mentioned mr calhoun has some great faults l icn,af>piirticnt says the duke de la rochefocault '"■t/tt'au.v grands homines pavoir iegrands defauts ,> he wants i think consistency and perseverance of mind and seeus incapable ot long continued antl j patient investigation what he does not see hat tiie tu st examination he seldom takes pains i j to search tor ; but still the lightning glance oi lus mind and the rapidity with which hc analyzes never fails to furnish him with all i that may be necessary for his immediate pur poses in his legislative career which 1 though shirt was uncommonly luminous his iuve u novelty and his apparent solici itude to astonish were so great that he has occasionally been known to go beyond even : the dream ol political visionaries antl to pro pose schemes which were in their nature im i practicable or injurious and which he seemed jto o/1-.r merely lor the purpose of displaying the affluence of his mind and lhe fertility ot ihis ingenuity youth aud tbe necessary want ol experience may be pled as an apol ogy lor his eccentricities of conduit and his apparent aberrations lhe wisdom of age and a more conect and extensive accptaint ance with men anel things will doubtless allay the ardor ot his mind ami lessen the fervor ot his temperament like our eccentric countryman darwin he is capable of broach ing new theories but wants the persevering investigation tension of thtught ancl patience ol judgmeni,nccess-'ry tu bring them to matu rity or to render them beneficial men like these are often both very serviceable and in jurious to society in such a body as the | congress of the united states where tlie concentrated wisdom of the nation is assem bled such a man's sphere of usefulness can not be correctly ascertaineel or defined — amidst the variety ol schemes hh ingenuity suggests and his restless emulation urges him to propose many will no doubt be found to be practicable ; and though be cannot himself pause to mature them the mass of mind bv which he it stti rounded and on which he blazes vvill reduce them to shape and give to his ingenious novelties " a local habitation and a name in short mr calhoun is one of those beings whom you can only trace lilte the comet by the light which he casts upon his path or the blaze which he leaves in bis train but the situation to which he has re cently been elevated has 1 fear abridged his sphere ot uselulness ; ancl as secretary of war mr calhoun who occupied every tongue during the sessions of the national legisla ture may dwindle into obscurity but will never be forgotten mr calhoun is a young man oi about thirty-five years of age his torm is above the middle size but meagre bony and slender : his face wants beauty but his eye possesses all the brilliancy and lire nf genius lie is a native of the south and has i understand been educated for tlie bar it is not my in tention to enter into any abstract speculations on the influence of climate upon the human intellect on this subject much ingenuity and learning have bcen wasted and the vis ionary theories of buffon kaynal c have bcen laid aside as the lumber of tlie schools or the idle sporting of fancy ; but it has al ways appeared to me that sonic climates are mere propitious to genius and the rapid dc vclopement of the intellectual powers than others the soft and voluptuous climate of ionia for example is better adapted to nour ish and expand the genius of man than the inclement blasts and " thick litotian air 1 ' of northern latitudes be this however as it may whether mr calhoun be indebted to climate to nature or to circumstances lor the powers he possesses he is urcpues tionably an extraordinary young man he started up on the theatre ef legislation a political roscius and astonished the vete rans around him by the power of his mind and the rcsistlessness of his eloquence he has the ingenuity without the sophistry of godwin to whose mind i think his bea.*s no trilling analogy on all subjects whether abstract or ordinary whether political or moral hc thinks with a rapidity that no diffi culties can resist aud with a novelty that never fails to delight lie has the brilliancy | without the ornament of burke the fire with out the literature of pitt with an inven tion which never abandons him and whose fertility astonishes he seems to loath thc pa rade of rhetoric and the glitter and decora tions of ait his style of eloquence is pe culiar and extraordinary ; without any appa rent pageantry of imagination or any of the flower-woven beauties of language he seizes on the mind which like the unfortunate bird under the influence of fascination becomes passive and obedient to the power it neither can nor wishes to resist in the " tempest and whirlwind of his eloquence his argu mentation is so rapid his thoughts are so novel and his conclusions so unexpected vet apparently correct that you can neither anti cipate nor think ; the attention is rit eteel and the mind occupied alone with the subject which lie is handling and it is not until the fascination of his manner has subsided that you feel inclined to reason or become capa ble of detecting his errors pi ven then his witchery lingers cn the imagination and casts a veil over the judgment which it cannot im mediately remove and which in opposition to the strongest efforts tends to obscure its perceptions ancl weaken its energies i have heard gentlemen who were associated with him declare that when he spoke tbey were for some time after he had closed unable to remove the spell by which they were bound ; and that even by condensing almost to obscu rity they could not answer the whole of his iiunierous arguments and ingenious deduc tions without occupying too much ofthe time of the house and yet he has never been known to attempt but one rhetorical flourish and in that be unfortunately failed his ora torical style has none of the embellishments of art or the witcheries of fancy but is al most to dryness plain unadorned and con cise he has nothing in him poetical — his creations are not those of imagination in wdiich i think he is somewhat deficient you never see him employed in weaving garlands or strewing flowers on your path ; be never strives to lap ia elysium to delight in the rainbow colors and eractic blaze of fancy his light ir the light of reason clear unre fracted ancl luminous between oratory and poetry there is i con ceive an essential difference conviction is the object of the orator and pleasure that of x/"ah letters to tbe editors must bc post-paid or thev will notbc attended to attluu\3 litistuwi like the first mortals blest is he from debts and usury and business free jlith his oii'n team who ploughs tlie coil which grateful once confessed his fa thc •'.- toil the farmer's text book great profits in agriculture can result only from great improvements of the soil great improve ments of thc soil can result only from unremit ting industry the chief study of every farmer should be what it useful and what ia uaelesa ex pense in relation to his art the discrimination he has refused his assent to laws the mo-it wholesome anel necessary for the public good hi has forbidden his governors to pass laws of immediate and pressing importance unless suspended in their operation till his assent should bc obtained ; and when so suspended he has ut terly neglected to attend to them he has refused to piss other laws for the ac commodation of large districts of people unless those people would relinquish the right of repre sent tion in the legislature — a right inestimable to them and formidable to tyrants only he has called together legislative bodies at places unusual uncomfortable and distant from . the depository of their public records for the soles purpose cf fatiguing them br compliance with j his measures between these is the master key of the farmer's prosperity the first should bc incurred with a freedom little short ot profusion thc last should be shunned as the sailor shuns the rocks where are seen the wreck of the hopes of preceding mariners in this art and almost in this art alone " it is the liberal hand which makcth rich " liberality in providing utensils is thc saving both of time and of labour the more perfect bis instruments thc more profitable are they he has dissolved representative houses repeat cdly for opposing with manly firmness his in vasions em the rights of the people he has refused for a long time after ur.h di solutions to cause others to be elected ; whereby the legislative powers incapable of annihilation have returned to the people at large for their ex ercise ; the state remaining in thc nic;,:i time ex posed to all the danger of invasion from without and convulsions wilhin so also is it with ij^workirfg c^.tlc and ills stock the most perfect in their kin is are ever the most profitable liberality in good barns and warm s_icl_crs is the source of health strength and comfort to ani mals ; causes them to thrive on less food and se cures from damage all sorts of crops liberality also in the provision of food fpr do mestic animals is the source of flesh muscle and manure he bas endeavored to prevent thc population of these states ; for that purpose obstructing tho laws for naturalization of foreigners ; refusing to pass others to encourage their migrations hither and raising tlie condition of new appropriation of lands liberality to the earth in seed culture and compost is lhc source of its bounty he has obstructed the administration of jin nee by refusing his assent to laws for establish ing judiciary powers ili # bas made judges dependent on his will alone for the tenure of their offices and the amount antl payment of their salaries lis has erected a multitude of new offices and sent hither swarms of officers to hart-ass our people and eat out their substance he has kept among us in times of peace siritv cling armies without the consent of our legisla tures thus it is in agriculture as in every part of creation a wise antl paternal providence has in separably connected our duty and our happiness in cultivating the earth thc condition of man's success is his industry upon it in raising domestic animals tlie condition of his success i.s kindness ancl benevolence to them in making thc productiveness of the earth de pend upon the diligence antl wisdom of the culti vator the universal l-'athcr has inseparably con ncclcd the fertility of his creation with the stron gest intellectual inducements and tlie highest moral motives he has affected to render the military indepen elcrit of and superior to thc civil power he has combined with others to subject us to a jurisdiction foreign to our constitution and un acknowledged by our laws ; — giving his assent lo their acts of pretended legislation — for quartering large bc.lics of troops anion us : — in putting the brutal world under his dominion be bus placed the happiness of which their nature is susceptible under the strong guarantee oi m:m's interest for protecting them hy a mot dial front punishment for any murders which they shoultl commit on the inhabitants of these state : — instead therefore of repining at his lot let the cultivator of the ground consider his as among thc highest and happiest of all human destinies mnce in relation to the earth he is the instru ment of heaven's bounty : and in relation to the inferior orders of creation the almoner of prov idence for rutting off our trade with all parts of thc world : — for imposing taxes on us without our con sent : — i'or depriving us in many cases of the benefits of trial by jury : — for transporting us beyond seas to bc tried for pretended offences s • for abolishing the free system of english laws in a neighboring province establishing therein an arbitrary govern ment and tenft_rging its boun daries so as lo render it at once an example and lit instrument for introducing thc t.amc absolutes rule into these colonies — management t_f vila the importance of the following experiment with respect to the treatment of hogs copied from a london newspaper has induced a member of the society foi'-promothig agriculture to rcepiest thut it may bc published in their next collection for the attention of the american farmer deelliauon *»!_ independence a i vim mhi's lliri.aluvion 11 v tlllf 11 ll'll j'sknt.vrl vks iii - tin i'mtiai states 01 awulic it cuxobesi as8emb-.sd ji i.v -., 1776 for taking away our charters abolishing out most valuable laws and altering fundamentally the forms of our governments : — ■for suspending our legislatures and declaring themselves invested vith power to legislate for ut in all cases whatsoever wren in the course of human events it be comes necessary for oiic people to dissolve the political bands which have connected them with another and to assume among the poweis of the earth the separate and equal station to whieb ihe laws of nalur and of nature's god entitle them ; a decent respect to the opinions of man kind requires that ihey should declare the causes which impel them to the separation v hold these truths to be stli evident tha ii mr are created equal ; th.it tbey arc endowed by their creator with certain unalienable i ights ■! jut among u'r.i a*e l f «*> liberty m & the puwitt " thc following experiment w:.s lately made bv a gentleman of norfolk six pigs ofthe nor folk breed ancl of nearly equal weight were put to keeping at thc same time und treated the same us to food and litter for about seven weeks — three 06 them were left to shift lor themselves as to cleanliness ; thc other three were kept as clean as possible by a nun employed for the purpose h/ith a currycomb snd brush the l s risuincil lie abdicated government here by declaring us out of his protection and waging war against us lie has plundered our seas ravaged our • asis burnt our town and destroyed the lives of o'm people he is tt this time transporting large armies of foreign mercenaries to complete the worlds of firth desola'f on r.ntftyi nn <• already ycgt.n,y..ut * jr calhoun and mr godwin are alik oonsp-cuoua for viliat i call ingenuity u cftnt-rxuititigiastifel frwt imagination . brill's nu i key applied tn g^ifu ..
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wrolittiftti published by kr1dek se bingham mmrilyvllx t\y,sw t v\n 4 1830 yo l......._n 4 the wmters cahoi.imay is published every tues day at'thkee dollars per annum payable at tlie montlis.h iii seven weeks fewer peas by five fais/tela than thc other three yet they weighed more when kil led by 0 stone and four pounds upon an aver age or six stones twelve pounds upon the whole the poet the powers of mind necessary to produce those different results are not the same reesqn governs the one and imagina tion the other the former is confined to argument and truth the latter to imagery and sentiment the orator analyzes aud reasons compares and deduces j tiie poet combines and imitates ; of happiness ; — that to secure these rights gov ernments are instituted among men deriving their just powers from the consent of the gov erned ; — that whenever any form of government becomes destructive of these ends it is the right of thc people to alter or abolish it anil to institute a new government laying its foundation on suclj principles and organizing its pow era in such form as to them shall seem most likely to effect their safety and happiness prudence indeed will dictate that governments long established should not be changed for light and transient causes anel accordingly all experience hath shown that man kind are more disposed to suffer while evils are sufferable than to right themselves by abolishing the forms to which they are accustomed ilu when a long train of abuses and usurpations pur suing invariably thc same object evinces u design to reduce them under absolute despotism it i their right it is their duly to throw off such gov ernment and to provide new guards for their fu ture security such has bcen the patient suffer ance of these colonies ; anel such is now thc nr cc-siiy which constrains them to alter their forme .-■. systems of government — the history e,f tb present kin of grcat-brtain i a history of rr pealed injuries and usurpations all having in ep . lect object thc establishment of an absolute tyi anny over these states to prove this let fact be submitted to a candid world : — hix^no paper will be discontinued until 1i arrearages are paid unless at tlie discretion of thc editors whoever will become responsible for the payment of nine papers shall receive a tenth gratis l'mityuhtvvvtt adv terms will be inserted ou the customary from " letteus from washington no advertisement inserted until it has been paid for or its payment assumed by sonic person in this town or its vicinity " his eye in a line phrenzy rolling dotli glance from heaven to earth from earth i-i heaven and embodies forth the forms of things un known the orator must exist in the living world ; the poet may live in a world of his own creation memory and judgment are lhe powers employed by the former imagina tion and invention those exercised by tiie lat ter in moving the heart and exciting the passions they differ only in the means em ployed to produce this effect anel in this alone they approximate ihe examples are numerous to establish the correctness of these positions cicero was a great orator but a bad pott ; pope was a great poet but a bad orator in short oratory ancl poetry have never been united in one individual but to return with all the excellencies i have mentioned mr calhoun has some great faults l icn,af>piirticnt says the duke de la rochefocault '"■t/tt'au.v grands homines pavoir iegrands defauts ,> he wants i think consistency and perseverance of mind and seeus incapable ot long continued antl j patient investigation what he does not see hat tiie tu st examination he seldom takes pains i j to search tor ; but still the lightning glance oi lus mind and the rapidity with which hc analyzes never fails to furnish him with all i that may be necessary for his immediate pur poses in his legislative career which 1 though shirt was uncommonly luminous his iuve u novelty and his apparent solici itude to astonish were so great that he has occasionally been known to go beyond even : the dream ol political visionaries antl to pro pose schemes which were in their nature im i practicable or injurious and which he seemed jto o/1-.r merely lor the purpose of displaying the affluence of his mind and lhe fertility ot ihis ingenuity youth aud tbe necessary want ol experience may be pled as an apol ogy lor his eccentricities of conduit and his apparent aberrations lhe wisdom of age and a more conect and extensive accptaint ance with men anel things will doubtless allay the ardor ot his mind ami lessen the fervor ot his temperament like our eccentric countryman darwin he is capable of broach ing new theories but wants the persevering investigation tension of thtught ancl patience ol judgmeni,nccess-'ry tu bring them to matu rity or to render them beneficial men like these are often both very serviceable and in jurious to society in such a body as the | congress of the united states where tlie concentrated wisdom of the nation is assem bled such a man's sphere of usefulness can not be correctly ascertaineel or defined — amidst the variety ol schemes hh ingenuity suggests and his restless emulation urges him to propose many will no doubt be found to be practicable ; and though be cannot himself pause to mature them the mass of mind bv which he it stti rounded and on which he blazes vvill reduce them to shape and give to his ingenious novelties " a local habitation and a name in short mr calhoun is one of those beings whom you can only trace lilte the comet by the light which he casts upon his path or the blaze which he leaves in bis train but the situation to which he has re cently been elevated has 1 fear abridged his sphere ot uselulness ; ancl as secretary of war mr calhoun who occupied every tongue during the sessions of the national legisla ture may dwindle into obscurity but will never be forgotten mr calhoun is a young man oi about thirty-five years of age his torm is above the middle size but meagre bony and slender : his face wants beauty but his eye possesses all the brilliancy and lire nf genius lie is a native of the south and has i understand been educated for tlie bar it is not my in tention to enter into any abstract speculations on the influence of climate upon the human intellect on this subject much ingenuity and learning have bcen wasted and the vis ionary theories of buffon kaynal c have bcen laid aside as the lumber of tlie schools or the idle sporting of fancy ; but it has al ways appeared to me that sonic climates are mere propitious to genius and the rapid dc vclopement of the intellectual powers than others the soft and voluptuous climate of ionia for example is better adapted to nour ish and expand the genius of man than the inclement blasts and " thick litotian air 1 ' of northern latitudes be this however as it may whether mr calhoun be indebted to climate to nature or to circumstances lor the powers he possesses he is urcpues tionably an extraordinary young man he started up on the theatre ef legislation a political roscius and astonished the vete rans around him by the power of his mind and the rcsistlessness of his eloquence he has the ingenuity without the sophistry of godwin to whose mind i think his bea.*s no trilling analogy on all subjects whether abstract or ordinary whether political or moral hc thinks with a rapidity that no diffi culties can resist aud with a novelty that never fails to delight lie has the brilliancy | without the ornament of burke the fire with out the literature of pitt with an inven tion which never abandons him and whose fertility astonishes he seems to loath thc pa rade of rhetoric and the glitter and decora tions of ait his style of eloquence is pe culiar and extraordinary ; without any appa rent pageantry of imagination or any of the flower-woven beauties of language he seizes on the mind which like the unfortunate bird under the influence of fascination becomes passive and obedient to the power it neither can nor wishes to resist in the " tempest and whirlwind of his eloquence his argu mentation is so rapid his thoughts are so novel and his conclusions so unexpected vet apparently correct that you can neither anti cipate nor think ; the attention is rit eteel and the mind occupied alone with the subject which lie is handling and it is not until the fascination of his manner has subsided that you feel inclined to reason or become capa ble of detecting his errors pi ven then his witchery lingers cn the imagination and casts a veil over the judgment which it cannot im mediately remove and which in opposition to the strongest efforts tends to obscure its perceptions ancl weaken its energies i have heard gentlemen who were associated with him declare that when he spoke tbey were for some time after he had closed unable to remove the spell by which they were bound ; and that even by condensing almost to obscu rity they could not answer the whole of his iiunierous arguments and ingenious deduc tions without occupying too much ofthe time of the house and yet he has never been known to attempt but one rhetorical flourish and in that be unfortunately failed his ora torical style has none of the embellishments of art or the witcheries of fancy but is al most to dryness plain unadorned and con cise he has nothing in him poetical — his creations are not those of imagination in wdiich i think he is somewhat deficient you never see him employed in weaving garlands or strewing flowers on your path ; be never strives to lap ia elysium to delight in the rainbow colors and eractic blaze of fancy his light ir the light of reason clear unre fracted ancl luminous between oratory and poetry there is i con ceive an essential difference conviction is the object of the orator and pleasure that of x/"ah letters to tbe editors must bc post-paid or thev will notbc attended to attluu\3 litistuwi like the first mortals blest is he from debts and usury and business free jlith his oii'n team who ploughs tlie coil which grateful once confessed his fa thc •'.- toil the farmer's text book great profits in agriculture can result only from great improvements of the soil great improve ments of thc soil can result only from unremit ting industry the chief study of every farmer should be what it useful and what ia uaelesa ex pense in relation to his art the discrimination he has refused his assent to laws the mo-it wholesome anel necessary for the public good hi has forbidden his governors to pass laws of immediate and pressing importance unless suspended in their operation till his assent should bc obtained ; and when so suspended he has ut terly neglected to attend to them he has refused to piss other laws for the ac commodation of large districts of people unless those people would relinquish the right of repre sent tion in the legislature — a right inestimable to them and formidable to tyrants only he has called together legislative bodies at places unusual uncomfortable and distant from . the depository of their public records for the soles purpose cf fatiguing them br compliance with j his measures between these is the master key of the farmer's prosperity the first should bc incurred with a freedom little short ot profusion thc last should be shunned as the sailor shuns the rocks where are seen the wreck of the hopes of preceding mariners in this art and almost in this art alone " it is the liberal hand which makcth rich " liberality in providing utensils is thc saving both of time and of labour the more perfect bis instruments thc more profitable are they he has dissolved representative houses repeat cdly for opposing with manly firmness his in vasions em the rights of the people he has refused for a long time after ur.h di solutions to cause others to be elected ; whereby the legislative powers incapable of annihilation have returned to the people at large for their ex ercise ; the state remaining in thc nic;,:i time ex posed to all the danger of invasion from without and convulsions wilhin so also is it with ij^workirfg c^.tlc and ills stock the most perfect in their kin is are ever the most profitable liberality in good barns and warm s_icl_crs is the source of health strength and comfort to ani mals ; causes them to thrive on less food and se cures from damage all sorts of crops liberality also in the provision of food fpr do mestic animals is the source of flesh muscle and manure he bas endeavored to prevent thc population of these states ; for that purpose obstructing tho laws for naturalization of foreigners ; refusing to pass others to encourage their migrations hither and raising tlie condition of new appropriation of lands liberality to the earth in seed culture and compost is lhc source of its bounty he has obstructed the administration of jin nee by refusing his assent to laws for establish ing judiciary powers ili # bas made judges dependent on his will alone for the tenure of their offices and the amount antl payment of their salaries lis has erected a multitude of new offices and sent hither swarms of officers to hart-ass our people and eat out their substance he has kept among us in times of peace siritv cling armies without the consent of our legisla tures thus it is in agriculture as in every part of creation a wise antl paternal providence has in separably connected our duty and our happiness in cultivating the earth thc condition of man's success is his industry upon it in raising domestic animals tlie condition of his success i.s kindness ancl benevolence to them in making thc productiveness of the earth de pend upon the diligence antl wisdom of the culti vator the universal l-'athcr has inseparably con ncclcd the fertility of his creation with the stron gest intellectual inducements and tlie highest moral motives he has affected to render the military indepen elcrit of and superior to thc civil power he has combined with others to subject us to a jurisdiction foreign to our constitution and un acknowledged by our laws ; — giving his assent lo their acts of pretended legislation — for quartering large bc.lics of troops anion us : — in putting the brutal world under his dominion be bus placed the happiness of which their nature is susceptible under the strong guarantee oi m:m's interest for protecting them hy a mot dial front punishment for any murders which they shoultl commit on the inhabitants of these state : — instead therefore of repining at his lot let the cultivator of the ground consider his as among thc highest and happiest of all human destinies mnce in relation to the earth he is the instru ment of heaven's bounty : and in relation to the inferior orders of creation the almoner of prov idence for rutting off our trade with all parts of thc world : — for imposing taxes on us without our con sent : — i'or depriving us in many cases of the benefits of trial by jury : — for transporting us beyond seas to bc tried for pretended offences s • for abolishing the free system of english laws in a neighboring province establishing therein an arbitrary govern ment and tenft_rging its boun daries so as lo render it at once an example and lit instrument for introducing thc t.amc absolutes rule into these colonies — management t_f vila the importance of the following experiment with respect to the treatment of hogs copied from a london newspaper has induced a member of the society foi'-promothig agriculture to rcepiest thut it may bc published in their next collection for the attention of the american farmer deelliauon *»!_ independence a i vim mhi's lliri.aluvion 11 v tlllf 11 ll'll j'sknt.vrl vks iii - tin i'mtiai states 01 awulic it cuxobesi as8emb-.sd ji i.v -., 1776 for taking away our charters abolishing out most valuable laws and altering fundamentally the forms of our governments : — ■for suspending our legislatures and declaring themselves invested vith power to legislate for ut in all cases whatsoever wren in the course of human events it be comes necessary for oiic people to dissolve the political bands which have connected them with another and to assume among the poweis of the earth the separate and equal station to whieb ihe laws of nalur and of nature's god entitle them ; a decent respect to the opinions of man kind requires that ihey should declare the causes which impel them to the separation v hold these truths to be stli evident tha ii mr are created equal ; th.it tbey arc endowed by their creator with certain unalienable i ights ■! jut among u'r.i a*e l f «*> liberty m & the puwitt " thc following experiment w:.s lately made bv a gentleman of norfolk six pigs ofthe nor folk breed ancl of nearly equal weight were put to keeping at thc same time und treated the same us to food and litter for about seven weeks — three 06 them were left to shift lor themselves as to cleanliness ; thc other three were kept as clean as possible by a nun employed for the purpose h/ith a currycomb snd brush the l s risuincil lie abdicated government here by declaring us out of his protection and waging war against us lie has plundered our seas ravaged our • asis burnt our town and destroyed the lives of o'm people he is tt this time transporting large armies of foreign mercenaries to complete the worlds of firth desola'f on r.ntftyi nn |
Initially I had Transportation Secretary Ray LaHood cast as the bad guy. He met with Detroit Mayor Dave Bing (D) and Gov. Rick Snyder (R) last week, so I presume this announcement has been festering since then. Even Detroit City Council had no clue, interviewing project managers just this week. It becomes apparent, however, Mayor Bing made the decision; perhaps under duress from Gov. Snyder who is not a rail proponent. In place of the Woodward light rail line is a proposal for several bus rapid transit lines. According to Bing, this is the right decision for Detroit and the region. Except no one asked the transit folks at SEMCOG, or Detroit City Council, or Detroit’s congressional delegation, any of which seem none too happy with this turn of events.
Mayor Bing contends the same money will buy bus rapid transit from downtown Detroit out Woodward and Gratiot into Oakland and Macomb Townships, a line between those suburban endpoints, and another connecting downtown Detroit with Metro Airport. There’s no question such a plan would serve more than Woodward light rail alone. As M-1 Rail points out, however, there’s been no work on funding, no environmental impact studies, or any other preparatory work. Bus rapid transit is, thus, at least a couple of years down the road—pun intended—before the first shovel-ful of dirt is turned. Never mind Detroit already has two dysfunctional bus systems. The “plan” is to overlay bus rapid transit so it complements the current Detroit Department of Transportation (D-DOT) and Suburban Mobility Authority for Rapid Transt (SMART) bus systems. Just what we need, a third metro Detroit bus system.
Besides my predictable chagrin at yet another nail in the coffin of Detroit rail transit, the region is left as the only major metropolitan area without an integrated transit system and, particularly, no light or commuter rail or subway systems. Taking a more pragmatic view, however, loss of the Woodward light rail line equates to a loss of an estimated $3 billion in development along the light rail route. Bus systems do not bring the same degree of transit-oriented development as rail. Did I point out the entrepreneurs behind M-1 Rail still want to proceed with at least phase I construction?
Asked if he’d support increasing Michigan’s gas tax, given that the state has the nation’s worst-maintained roads, Snyder said no, “because we need to get efficient first” with the state’s existing transportation funds. …
“So let’s get efficient about where we’re deploying these dollars. There’s a much better way to do things, and that’s what we should focus on first.”
First, the Governor wants a revenue-neutral change in the fuel tax. Snyder’s plan eliminates the 19-cent “current gas tax on consumers”, shifting it to a percentage at the wholesale level. Wow! I won’t have to pay state gas tax anymore! Except, does anyone believe wholesalers won’t pass the cost of that tax onto retailers? Is the average retailer likely to discount his pump price by the amount of the wholesale tax passed to him? As the Brits would say, not bloody likely. While this proposal is initially revenue-neutral for the gas tax, a percentage tax on wholesale fuels will go up as prices rise. The proposal includes another hidden tax increase. Michigan levies sales tax, presently 6% on goods sold, including gasoline. Retailers don’t include the current 19-cent gas tax when calculating the sales tax. Since the wholesale tax will be part of the price retailers pay, it will now become subject to the 6% sales tax. On day one of a wholesale tax, Michigan will collect more than a penny per gallon in additional taxes from consumers. So much for “revenue-neutral”; never mind Michigan’s fuel taxes are already among the highest in the country.
It’s a big hit to people’s wallets in a state still struggling to rebound from a decade-long recession. A family with three cars registered to one person would have to fork over $360 extra all at once.
From my perspective, the increased vehicle registration fees are neither logical nor beneficial. Snyder says they will raise about $1.4 billion for roads. They will also price many out of their cars in a state with few functioning transportation options. Don’t be surprised if there is an increase in license plate thefts or cutting their corners off to get someone else’s current year tab. Here’s a novel concept: how about charging heavier weight vehicles for the road damage they cause? A 5,000-pound car exerts a mere 2,500 pounds per axle while Michigan allows up to 17,000 pounds—nearly seven times that of the car—per axle. Financing road repairs also needs to ensure non-resident users pay their share, not just Michiganians. Earlier this year, a bipartisan legislative report said Michigan needs $1.4 billion more for roads each year. Coincidence? I think maybe not.
Mon, 17 Oct 2011
Detroit and its suburbs enjoy bus service from not one, but two dysfunctional systems. Detroit Department of Transportation (DDOT) buses primarily serve the city while Suburban Mobility Authority for Regional Transportation (SMART) buses serve the suburbs, including forays into downtown Detroit. It’s not at all uncommon to see buses from one, the other, or both, chasing each other—even leap-frogging as one stops while another goes to the next stop. As many as half of DDOT’s buses are in the shop waiting to be fixed. Even former mayor Kwame Kilpatrick knew way back in 2004 that DDOT was a broken system. As for SMART, individual suburbs can opt out, so the system has traverse these unserved areas to connect those that are served. Declining property values left SMART underfunded by its millage, so the system plans to lay off 123 and cut or eliminate service on 36 routes.
Nine years ago, Southeast Michigan was on the cusp of a solution called the Detroit Area Regional Transportation Authority (DARTA). After years of negotiating and political maneuvering, the Michigan House and Senate had passed the necessary legislation. Then, in a moment of extreme self-importance and political spitefulness, the Jaba-the-Hut-esque John Engler (R) vetoed the bill mere nanoseconds before his rotundness rolled out of office as his term as governor expired. Thanks, John. The region has been paying the price ever since.
The elephant in the room is still getting city and suburbs to put their differences aside and craft a true, workable transit solution for Southeast Michigan. Imagine how much farther along we would be if Engler hadn’t been such a jackass.
Mon, 10 Oct 2011
Michiganians want good roads and there is no doubt a good transportation infrastructure is important to Michigan’s economy. Of course, this takes money and there’s no secret Michigan is struggling with budget deficits. Last month, a bipartisan legislative committee recommending doubling Michigan’s road funding. The Michigan Department of Transportation (MDOT) even made a propaganda film, using my tax dollars, to justify it. And now, Gov. Rick “No New Gas Tax” Snyder flip-flopped, à la Romney, and climbed on board the tax increase steam roller.
I want good roads, just like everybody else. But I’m not convinced MDOT is spending our money as wisely as they say. I get the whole Federal-State match thing, but to squander 20% on stupid stuff to get the 80% is not solving the problem. I offer Exhibit A: mile marker signs with the direction, highway designation, and, in urban areas, placed every 1-2 tenths of a mile. If someone needs to be reminded what highway they’re on and which direction they’re going every 2/10ths of a mile, they shouldn’t be driving. Even if these markers cost the same as the originals, which they don’t, the cost has skyrocketed 5 times; for no significant value. The irony is the example pictured was part of a Detroit News article warning how bad Michigan’s roads are going to get. And don’t even get me started on the project a few years ago when the replaced all of the big green signs for better night visibility. Why not replace them as they wore out or got damaged?
As Exhibit B, I offer Michigan’s so-called Intelligent Transportation System (ITS), intended to facilitate traffic around greater Grand Rapids and southeast Michigan (metro Detroit). The most visible aspect of ITS are the nearly 100 variable message signs (VMS) like the one pictured, including those at Grayling and Clare for which there is no traffic congestion justification. The VMS routinely depict messages about as useful as the one pictured near Grand Rapids. With fall approaching, you can expect them to say “Don’t veer for dear.” I spend a lot of time on the road and I think I can count one one hand the number of times a VMS has assisted my travels in any meaningful way.
But ITS is more than just useless electronic signs. It includes nearly 270 closed circuit TVs, not counting the out-state ones like those in the upper peninsula, obviously with no congestion management purpose. And it includes two manned operations centers. MDOT’s website shows 3 people in the metro Detroit center, presumably a typical shift of staff that “oversees a traffic monitoring system”“. Neither these MDOT employees nor the VMS they are masters of contribute substantially to reducing congestion. At what expense are we gaining such miniscule benefit?
For Exhibit C, I offer the I-94/I-696 interchange. MDOT completely reconstructed this interchange in 2010 to the same exact specifications as existed previously. Here’s the problem with that: two lanes exit from I-94 east and west each to become four lanes of I-696 west, except the right lane becomes exit only in a quarter mile at Gratiot, a major arterial. Why didn’t MDOT add another lane to accomodate this and allow four lanes to continue past Gratiot? Gratiot’s westbound on-ramp restores the fourth lane. The same intersection was previously rebuilt, again to the same standards, in the late 1990s. So, despite changes in traffic volumes and flows, MDOT has rebuilt the I-94/I-696 interchange twice to 40-year-old (1968) design criteria.
While I could keep going on, let me finish with Exhibit D, the 30 MDOT transportation service centers across the state. This includes five in metro Detroit alone. At least MDOT plans to consolidate some service centers. I hope they reduce their seemingly large fleet of red minivans, with several to a dozen or more at each service center.
Before MDOT expects additional state revenues for road projects, they need to show they’re fiscally responsible and working smart with what they get. The additional lanes at the reworked Okemos/I-96 interchange is proof they can when they want to. Oh, and don’t use my tax dollars to lobby me about your funding.
The straw poll results pile on Gov. Rick Perry’s poor performance at Thursday’s debate, adding to the Perry is out meme. Whether Perry can salvage his bid remains to be seen. In any case, it should not give pause to seriously consider Romney.
Beyond Romney’s opposition to national health care reform and auto company bailouts, Mitt says he’s part of the middle class, in the 80-90% with us. I guess he feels our pain, too. Never mind, despite his father having been CEO of American Motors before his election as Governor of Michigan, Mitt wanted US automakers to go belly up. Never mind, as Massachussetts Govenor, he signed into law the very legislation on which Obamacare is modeled.
Romney said he, too, would propose financial fixes for Social Security, most likely a slight increase in the retirement age for younger workers and a decrease in the plan’s growth rate for higher-income retirees.
“It can’t keep going forever the way it is,” Romney said.
Seems to me, a used car salesman is more trustworthy and believable than Mitt Romney.
Tue, 20 Sep 2011
Michigan Department of Transportation (MDOT) and billionaire Manuel (Matty) Moroun’s Detroit International Bridge Co. (DBIC) had a legal agreement on the Gateway Project to connect I-75 and I-96 directly to the privately-owned Ambassador Bridge. Construction, which cost Michigan taxpayers $230 million and shut down I-75 to facilitate construction for over a year. Still, DBIC failed to live up to its commitments and 18 months after a court order to comply, DBIC is no closer to meeting its obligations.
What’s really interesting about this is both former Gov. Jennifer Granholm (D) and current Gov. Rick Snyder (R) support the Detroit River International Crossing (DRIC) public span, at odds with Moroun’s second private span.
Wed, 24 Aug 2011
In the last election, Michigan voters turned out US Rep. Carolyn Cheeks Kilpatrick (D), gave newcomer Rick Snyder (R) the governor’s office instead of several seasoned politicos, and changed the state legislative landscape. Despite reelecting all but one US Congressional incumbent in the general election (throw out the incumbents, but mine’s ok), it seemed like Michigan voters might actually be starting to think for themselves. Could it be they’re no longer interested in superfluous hype? Will they really hold elected officials accountable to do their jobs?
I wanted to be where I could hear the waves. As a boy, we spent summers on Lake Huron and I could hear the crashing waves at night. It was one of my favorite things in the world; being near the water and the waves was something I very badly wanted to experience again.
Uh, Mitt, then why not come back to Michigan? He’s the son of a Michigan governor (George W. Romney), but went into politics in Massachussetts. He doesn’t own any property in Michigan, chosing three other states instead. And, even though his father was the head of American Motors before getting into politics, Mitt opposed automaker bailouts, writing an op-ed titled “Let Detroit Go Bankrupt” in the New York Times.
Wed, 03 Aug 2011
Our penny-wise, dollar-foolish, dysfunctional so-called representatives (Congressmen and Senators) in Washington barely managed to cobble together a debt ceiling deal before the economy tumbled into the abyss. Then they went home for a month-long vacation, leaving the Federal Aviation Administration (FAA) without appropriations to operate. As a result, about 4,000 FAA employees are on furlough, meaning they don’t work and they don’t get paid. How many of them, do you suppose, live paycheck to paycheck? How many of our elected officials will help them out during their involuntary layoff? Add to that another estimated 70,000 construction workers idled by stop work orders on various FAA-funded projects. They’ll all collect unemployment, thus adding to the cost of doing business and the cost of government. The 74,000 laid off will also skew the jobless numbers, which will affect stocks and other aspects of the economy.
The previous FAA reauthorization expired 22 July. There has been no long-term (meaning 2-4 years) for the FAA since 2007. Meanwhile, some airlines have raised ticket prices, pocketing the previous tax amounts the government is not, presently, collecting. Do you suppose they’ll lower prices when the taxes come back on line? If you do, just start sending your checks to me—it’s more productive than just burning your cash.
At issue in the debate are, essentially, two fundamental aspects. The most publicized is the Essential Air Service (EAS) subsidy, which pays airlines to provide commercial service to largely remote areas. In Michigan, that affects 8 airports with EAS subsidies:
This FAA bill funded the EAS for two-and-a-half years. So that would be stable funding for two-and-a-half years rather than a few months at a time. I think it’s a good program and I’m all for it. As far as I was concerned, it was a vote for the program.
So, let me see. Benishek votes against the FAA reauthorization, but it’s really a vote for the Essential Air Service program. Reminds me of “These are not the droids you’re looking for.” Is anyone else confused by this? That said, however, the travel distances to “non-essential” air service facilities seems to justify ending this taxpayer subsidy. Heck, I live in metro Detroit and it takes me about 45 minutes to get to Detroit Metro. Suck it up and drive an hour to another airport.
Interestingly, Rep. Justin Amash (R-MI-03), a Tea Party freshman from Grand Rapids, broke party lines and voted against HR 638. He’s the only Michigan representative that didn’t vote with his party. Apparently, he was opposed to the general fund subsidy, according to Amash’s Facebook post:
[Justin Amash] just voted no on H R 658, FAA Reauthorization and Reform Act. The bill authorizes FAA activities through 2014. Under the bill, the authorized FAA spending level is flat-lined at the FY 2008 level for FY 2012-2014. That is a savings of $495 million per year over current spending. Even so, the bill relies on subsidies from the general fund to cover about 25% of total costs. The bill passed 223-196. |
After seven years, Republicans have finally released their health care legislation. Now their bill can be compared side-by-side with the Affordable Care Act based on how it affects enrollees’ pocketbooks — including both premiums and out-of-pocket costs for care.
The bill does not measure up well: For all but the youngest individuals, it increases both overall costs and the risk of a financially devastating event.
Republicans will argue that by cutting back insurance standards, their bill would lower premiums — because people can choose to buy less coverage than the ACA currently requires. But premiums are only one expense that enrollees have to worry about. First, the level of tax credits affects how much enrollees would actually pay for those premiums, out of pocket.
Second, the degree of insurance protection affects how much enrollees would pay in deductibles, co-pays, and other forms of cost-sharing. (“Cost-sharing” refers to how the insurance company and the enrollee split the costs of health services.)
We’re presenting an analysis here of the net financial impact of the Republican bill on premiums, after tax credits, plus cost-sharing. We estimate that the bill would increase costs for the average enrollee by $1,542, for the year, if the bill were in effect today. In 2020, the bill would increase costs for the average enrollee by $2,409.
We provide the figure for 2020 because that’s when the Republican tax credits would go into effect; we provide a figure for this year so that readers can get a sense of how the plan might affect their situation were it implemented today. Importantly, the gap between costs under the ACA and under the Republican bill would grow over time.
In general, the impact of the Republican bill would be particularly severe for older individuals, ages 55 to 64. Their costs would increase by $5,269 if the bill went into effect today and by $6,971 in 2020. Individuals with income below 250 percent of the federal poverty line would see their costs increase by $2,945 today and by $4,061 in 2020.
The bill’s key alterations to the framework created by the ACA, explained
The ACA includes three elements that affect the generosity of insurance. First, it requires insurers to cover a minimum share of costs, on average. This minimum “actuarial value” of the plans is set by law at 60 percent. Second, the act provides premium tax credits that are linked to the cost of a plan that covers 70 percent of costs, on average (the so-called silver plans). As the price of those plans rise, so does the tax credit.
Third, the ACA reduces cost-sharing levels — that is, it provides another kind of subsidy — for lower-income individuals with income from 100 percent to 250 percent of the federal poverty level. The combined effect of these elements is that, for non-group policies under the ACA, the weighted average share of costs covered by insurers is about 75 percent.
The Republican bill unveiled last night would remove these elements. It would eliminate the minimum required actuarial value; eliminate cost-sharing reductions for lower-income individuals; and provide flat tax credits by age unrelated to any plan’s cost. These tax credits are for the most part also unrelated to people’s income, but they start to phase out for individuals with income above $75,000. The combined effect of these changes is that the bill would dramatically reduce the generosity of insurance and sharply increase deductibles and other out-of-pocket costs.
The Republican bill would also relax the limit on how much insurers can charge older individuals (a practice known as “age rating”). Currently, the ACA prohibits insurers from charging older individuals premiums that are more than three times greater than premiums for younger individuals. Under the Republican bill, insurers could charge premiums for older individuals that are as much as five times greater. Therefore, obviously, premiums for older individuals would go up, those for younger individuals would go down.
Lastly, the Republican bill would eliminate the individual mandate. Instead, if individuals have a gap in coverage greater than 63 days, they would face a penalty equal to 30 percent of premiums for 12 months.
How we estimated costs
We previously published an analysis of the Republican plan using the tax credit levels prescribed in legislation sponsored by Secretary of Health and Human Services Tom Price when he was a member of Congress. For this analysis, we used the same methodology and altered parameters and assumptions as explained below.
We used the tax credit levels specified in the Republican bill: $2,000 for individuals up to age 30; $2,500 for individuals age 30 to 39; $3,000 for individuals age 40 to 49; $3,500 for individuals age 50 to 59; and $4,000 for individuals over age 60. These tax credits phase out for individuals with income above $75,000 and for those filing a joint return with income above $150,000. (In our analysis, we treated households with at least two adults as joint filers.)
As stated above, we first applied these tax credits to premiums in 2017 and then to premiums in 2020, the year the credits would take effect. To estimate premiums in 2020, we inflated premiums using National Health Expenditure (NHE) projections. For comparison with the ACA, we adjusted the ACA’s subsidy amounts using Congressional Budget Office estimates and NHE projections.
Over time, the value of the new tax credits under the Republican bill would erode significantly. That’s because they are indexed to grow with consumer inflation plus 1 percentage point, which is much slower than the rate medical costs are actually growing. Under the ACA, by contrast, tax credits grow in lockstep with premiums for “silver” plans, and costs are capped as a percentage of income.
The ACA’s tax credit structure would help protect enrollees from premium increases from 2017 to 2020; under the Republican plan, enrollees would pay a greater share of premiums each year.
Whenever tax credit levels exceed premiums, we assumed that the excess could be deposited in health savings accounts to reduce cost-sharing levels, as specified in the Republican bill.
We assume that under the Republican bill the average actuarial value would fall to 50 percent; all things considered, plans would cover only half of health care costs. That’s because the Republican bill would encourage enrollment in “catastrophic” plans with high deductibles. The insurance industry pegs the actuarial value of such catastrophic plans at 50 percent. In addition, a recent analysis by the Urban Institute estimated that about half of people, under the Republican system, could use their tax credits to buy a plan with an actuarial value of a mere 47 percent.
Our assumption of a 50 percent actuarial value is actually generous to the Republican bill. Even though the bill repeals the minimum actuarial value, it does not repeal limits on out-of-pocket costs or essential health benefits. Using the 2018 actuarial value calculator, mathematically plans could not have an actuarial value much below 58 percent with these constraints.
The plan would lead to a sicker pool of enrollees
We assume that the Republican bill’s replacement for the individual mandate would cause some degree of adverse selection. In other words, the change in incentives would likely lead disproportionately sicker individuals to enroll in coverage, driving up premiums.
Younger, healthier individuals may not be sufficiently motivated by the “continuous coverage” requirement, and modest penalty for violating it, to sign up for coverage to avoid an abstract penalty if they happen to get sick sometime in the unforeseeable future. If they do miss the open enrollment period, they would effectively be locked out of the market. Sicker individuals, on the other hand, would do absolutely everything they could to sign up and avoid a gap in coverage.
What’s more, the late enrollment penalty would be far lower than the additional premium insurers would charge to many sicker individuals if they were able to do so. So it would be a bargain for many individuals to wait until they get sick to enroll in coverage.
In the absence of the individual mandate, CBO estimates that adverse selection would increase premiums by 20 percent. We assume that the Republican bill’s replacement for the individual mandate would have at least some effect, but that it would not be as effective as the mandate. We assumed the shift to a continuous coverage model would increase premiums by 10 percent.
We found significant cost increases both for individuals and for families
Although premiums would be lower under the Republican bill, this decrease would be offset by an increase in cost-sharing. Once the differences in tax credits are accounted for, the bill would increase costs significantly. On top of this, shifting consumer spending from premiums to cost-sharing would greatly increase financial risk. (If you’re now paying 50 percent of your costs, instead of 25 percent, a big hospital bill could be devastating.)
We reported above the results for individuals. For families, the Republican bill would increase costs by $2,243 if the bill were in effect today. For families with a head of household age 55 to 64, the bill would increase costs by $7,604. For families with income below 250 percent of poverty, the bill would increase costs by $6,228.
These cost increases would explode by 2020. We estimate that the Republican bill would increase costs for families by $4,274. For families with a head of household age 55 to 64, the bill would increase costs by $10,591. For families with income below 250% percent of poverty, the bill would increase costs by $9,024.
There may be a reason why Republicans took so many years to reveal their health care plan: It is easier to attack an imperfect existing system than to improve it. Under examination, the Republican bill clearly does not compare favorably with the ACA. As many have pointed out, and as the CBO score will clearly show, the Republican bill would cause millions of people to lose their coverage — but it would also increase costs significantly for those who remain insured.
David Cutler is the Otto Eckstein Professor of Applied Economics at Harvard University. John Bertko is the chief actuary for Covered California, the state’s health insurance exchange. Topher Spiro is the vice president for health policy at the Center for American Progress. Emily Gee is a health economist at the Center for American Progress.
The Big Idea is Vox’s home for smart, often scholarly excursions into the most important issues and ideas in politics, science, and culture — typically written by outside contributors. If you have an idea for a piece, pitch us at thebigidea@vox.com. |
971 F.Supp. 440 (1997)
Charla J. KRAHEL, Plaintiff,
v.
OWENS-BROCKWAY GLASS CONTAINER, INC., a Delaware corporation, and a division of Owens-Illinois, Inc.; Owens-Illinois, Inc., a Delaware corporation; Local 3112 Glass Molders Pottery Plastics & Allied Workers Union; Glass Molders Pottery Plastics & Allied Workers International Union, Defendants.
Civil No. 96-1280-AS.
United States District Court, D. Oregon.
March 13, 1997.
*441 *442 Judy Danelle Snyder, Cynthia Halse Stutsman, Hoevet & Snyder PC, Portland, OR, for Charla J. Krahel.
Christine Kitchel, Stoel Rives, Portland, OR, Lee Ann Huntington, Stephen M. Hankins, Morgenstein & Jubelirer, San Francisco, CA, for Owens-Brockway Glass Container Inc., Owens Illinois Inc.
Gene B. Mechanic, Goldberg Mechanic & Stuart, Portland, OR, Carl S. Yaller, Glass Molders Pottery Plastics & Allied Workers Int'l Union, Media, PA, for Local # 12 Glass Molders, Pottery, Plastics & Allied Workers Union, Glass, Pottery, Plastics & Allied Workers Int'l Union.
OPINION
ASHMANSKAS, United States Magistrate Judge:
Plaintiff Charla Krahel brings this action against defendants Owens-Brockway Glass Container, Inc., and its parent Owens-Illinois, Inc. (collectively "Owens"), and against Local 112 of the Glass Molders Pottery Plastics & Allied Workers Union ("Local 112") and its parent Glass Molders Pottery Plastics & Allied Workers International Union (collectively "Union").
Owens has moved to dismiss (or in the alternative to stay) the action on grounds the Collective Bargaining Agreement ("CBA") between Owens and the Union contains a mandatory grievance and arbitration procedure. Owens has also moved to dismiss all claims against the parent Owens-Illinois for failure to state a claim, to strike the claims for damages in excess of the cap established by the 1991 Civil Rights Act and to dismiss the sixth claim for negligence. Plaintiff has conceded the motion to dismiss the negligence claim, so I will not address it further.
BACKGROUND
I acknowledge that the parties have very different versions of the facts in this case and the inferences to be drawn from those facts. For purposes of these motions, however, the factual allegations of the complaint are generally presumed to be true and plaintiff is entitled to the benefit of all reasonable inferences from those facts.[1] Plaintiff is an employee of defendant Owens-Brockway Glass. Plaintiff is also a member of defendant Local 112, which represents certain employees of Owens. There is a collective bargaining agreement ("CBA") between the Union and Owens. Plaintiff was employed by Owens for over five years as a carton assembler and bulk pack operator. In September 1989, plaintiff applied for an apprentice electrician position with Owens. There were 36 applicants for the position. Plaintiff was the only female applicant. Plaintiff scored higher than all other applicants on the qualifying test, but she was not selected for the apprentice electrician position. Instead, the position was offered to Phil Huddleston. Mr. Huddleston is now Vice-President of Local 112, though it is unclear from the pleadings whether he also held that position in September 1989. The selection committee was composed of three members of Local 112 and three members of the Owens' management team. Plaintiff was designated as the runner-up. When Huddleston was unable to accept the position for personal reasons, plaintiff was awarded the apprenticeship by default.
Plaintiff was scheduled to take her state electrician's examination in November 1993. In October 1993, Local 112 agent Dan Benson and Owens' plant manager Mark Recker sought to dissuade plaintiff from taking the examination as scheduled. They told plaintiff they didn't believe she was ready to take *443 the exam and advised her to extend her apprenticeship for another six months. Plaintiff discussed the matter with a representative of the state licensing agency, who advised her that the apprenticeship could not be extended without approval by the agency and that plaintiff would be dropped from the apprenticeship program unless she sat for the November examination. Plaintiff took and passed the November 1993 examination.
After passing the examination, plaintiff applied for a day shift position. Plant manager Recker told plaintiff's supervisor that plaintiff "will never see straight days." Male employees with lesser seniority were assigned to the day shift, but plaintiff was not permitted to work the day shift during Recker's tenure as plant manager. Recker was reassigned to a different Owens facility in April 1995, after which plaintiff was allowed to work the day shift.
For more than six years beginning around the time she was awarded the apprenticeship position and continuing through the date the complaint was filed plaintiff was ostracized by the male employees, most or all of whom were members of Local 112. They refused to sit near her in the breakroom and joked about that behavior. Plaintiff repeatedly was told that the male employees did not like her and did not want to work with her. A nude centerfold of a woman was posted in Owens' shop area with plaintiff's name written across the breast. An obscene drawing of a woman was found in the men's restroom at Owens with plaintiff's name written by the picture. Plaintiff was told that she was a "birth defect" and referred to as that "fucking cunt."
The male journeymen who supervised plaintiff deliberately placed her in the dirtiest jobs and joked about making sure plaintiff got dirty. She was told, "You won't last a month", "You won't want to get dirty", and "You'll be afraid of breaking your nails." Some of the male employees, including an agent of Local 112, told plaintiff that she was incompetent and that all she did was sit in the office on her ass. A journeyman mechanic, who is a member of Local 112, told plaintiff "There ain't no damn female who is ever going to be [my] equal."
According to the complaint, the discriminatory treatment did not subside with the passage of time, but instead persisted. In April 1996, a drawing was posted in plaintiff's work area depicting plaintiff and her sister, whom she had been training, with the caption "the dumb training the stupid." Derogatory comments about plaintiff were written on machines where she works. Plaintiff believes that some of her equipment was sabotaged to make it appear that she was not competently performing her job.
In March 1996, Swede Lindholm, President of Local 112, stated that plaintiff did not know what her license entailed. Around the same time, another Local 112 agent commented that plaintiff was unable to perform her job duties without one of the men "holding [plaintiff's] hand." A Local 112 agent told a new employee whom plaintiff was assigned to train that "it must be a real put-down to be trained by a woman." Plaintiff's welding skills were criticized and it was proposed that she be required to become a certified welder. No similar requirement has been imposed upon any male electrician at this Owens facility.
On numerous occasions between 1990 and 1996 plaintiff complained to her supervisors and crew leaders about the manner in which she was being treated, but was told that there was nothing Owens could do about the situation.[2] In March 1996, when plaintiff complained about being called a "fucking cunt," plaintiff's supervisor took her complaint to Local 112's president, Swede Lindholm, and vice-president, Phil Huddleston. Their response was to criticize plaintiff's job performance.
In April 1996, plaintiff filed a complaint against Owens with the Oregon Bureau of Labor and Industries ("BOLI") and the EEOC, alleging sexual harassment and unlawful employment practices. In May 1996, plaintiff passed the Owens' management profile *444 test and applied for a management position for which she was qualified. The position was given to a male employee from outside Owens' Portland facility. In June 1996, plaintiff and five male employees at Owens' Portland facility were selected for a journeyman training program. The following week, there was an unsuccessful attempt to mediate plaintiff's claims against Owens. The EEOC and BOLI both issued "right to sue" letters. One week later, plaintiff was informed by Owens that she could not participate in the training program. Plaintiff subsequently filed additional complaints against Local 112 and Owens with BOLI and the EEOC, and received "right to sue" letters.
Plaintiff has asserted claims against Owens and the Union for violation of Title VII and ORS 659.030(1)(b). These claims appear to be premised on a hostile work environment theory. Plaintiff also has asserted state and federal law claims against Owens for unlawful retaliation (after she filed her Title VII claim with BOLI and EEOC). Finally, plaintiff has asserted claims against all defendants for "negligence" in failing to train its personnel concerning compliance with laws and regulations prohibiting sexual harassment and gender-based discrimination.[3]
Mandatory Arbitration and Grievance Procedure
The Owens defendants have moved to dismiss plaintiff's claims on grounds the collective bargaining agreement between Owens and the Union establishes a mandatory grievance procedure, which culminates in binding arbitration, for resolving all disputes. Owens cites the following language in Article 32 of the CBA:
Section 1. The Company and the Union will comply with all laws preventing discrimination against any employee because of race, color, religion, sex, national origin, age, handicap, or veteran status.
Section 2. This Contract will be administered in accordance with the applicable provisions of the Americans with Disabilities Act. Before taking action relevant to this Section, the Company will meet with the Local Union, and both parties will have sufficient opportunity to express their opinions regarding an anticipated action.
Section 3. Any disputes under this Article as with all other Articles of this Contract shall be subject to the grievance procedure.[4]
I
Whether an employer and labor union may agree between themselves to arbitrate or otherwise limit an employee's civil rights claims has long been the subject of controversy. In Alexander v. Gardner-Denver Co., 415 U.S. 36, 94 S.Ct. 1011, 39 L.Ed.2d 147 (1974), an employee was discharged, allegedly on account of his race. The collective bargaining agreement expressly provided "that there shall be no discrimination against any employee on account of race, color, religion, sex, national origin, or ancestry," and further provided that "[n]o employee will be discharged, suspended or given a written warning notice except for just cause." As in the instant case, the CBA in Alexander established a mandatory four-step grievance procedure culminating in binding arbitration.
The plaintiff in Alexander asserted a grievance, went to arbitration with the company, and lost. He then filed suit against the employer. The district court dismissed on grounds the action was barred by the binding arbitration clause in the CBA. The Supreme Court disagreed. Title VII was designed to supplement rather than supplant, existing laws and institutions relating to employment discrimination. An individual *445 does not forfeit his private cause of action if he first pursues his grievance to final arbitration under the nondiscrimination clause of a collective-bargaining agreement. Id. at 48-49, 94 S.Ct. at 1019-20. In a unanimous decision, the Court also rejected the suggestion that the employee's right to bring a Title VII action had been waived by the arbitration clause in the CBA:
To begin, we think it clear that there can be no prospective waiver of an employee's rights under Title VII. It is true, of course, that a union may waive certain statutory rights related to collective activity, such as the right to strike. These rights are conferred on employees collectively to foster the processes of bargaining and properly may be exercised or relinquished by the union as collective-bargaining agent to obtain economic benefits for union members. Title VII, on the other hand, stands on plainly different ground; it concerns not majoritarian processes, but an individual's right to equal employment opportunities. Title VII's strictures are absolute and represent a congressional command that each employee be free from discriminatory practices. Of necessity, the rights conferred can form no part of the collective-bargaining process since waiver of these rights would defeat the paramount congressional purpose behind Title VII. In these circumstances, an employee's rights under Title VII are not susceptible of prospective waiver.
Id. at 51-52, 94 S.Ct. at 1021 (internal citations omitted.). The Court observed that an employee may waive his rights as part of a settlement agreement. However, in determining the effectiveness of any such waiver a court would have to determine that the employee's consent to the settlement was voluntary and knowing. In no event can the submission to arbitration of a claim under the nondiscrimination clause of a collective-bargaining agreement constitute a binding waiver with respect to an employee's rights under Title VII. Id. at 52 n. 15, 94 S.Ct. at 1021 n. 15.
The Alexander court also expressed concern regarding the different procedures followed in labor arbitration, the comparative inexperience by labor arbitrators in civil rights litigation, the potential for conflicts between Title VII and the CBA, and the limited remedies that might be awarded by an arbitrator pursuant to the CBA. Id. at 56-58, 94 S.Ct. at 1023-25. Finally,
A further concern is the union's exclusive control over the manner and extent to which an individual grievance is presented. In arbitration, as in the collective-bargaining process, the interests of the individual employee may be subordinated to the collective interests of all employees in the bargaining unit. Moreover, harmony of interest between the union and the individual employee cannot always be presumed, especially where a claim of racial discrimination is made. And a breach of the union's duty of fair representation may prove difficult to establish. In this respect, it is noteworthy that Congress thought it necessary to afford the protections of Title VII against unions as well as employers.
Id. at 58 n. 19, 94 S.Ct. at 1024 n. 19. The Court concluded that "the federal policy favoring arbitration of labor disputes and the federal policy against discriminatory employment practices can best be accommodated by permitting an employee to pursue fully both his remedy under the grievance-arbitration clause of a collective-bargaining agreement and his cause of action under Title VII. The federal court should consider the employee's claim de novo. The arbitral decision may be admitted as evidence and accorded such weight as the court deems appropriate." Id. at 60, 94 S.Ct. at 1025.
Eighteen years later, the Supreme Court granted certiorari to decide the validity of an arbitration clause in an individual contract, as opposed to a collective bargaining agreement. In Gilmer v. Interstate/Johnson Lane Corp., 500 U.S. 20, 111 S.Ct. 1647, 114 L.Ed.2d 26 (1991), the plaintiff was a registered securities representative who, in the course of registering with the New York Stock Exchange ("NYSE"), signed an agreement to arbitrate any disputes arising out of his employment or termination of employment. Plaintiff was later terminated, allegedly on account of his age, and brought an action in federal court for violation of the *446 Age Discrimination in Employment Act ("ADEA").
The Supreme Court held that Gilmer was bound by the arbitration agreement he had signed. The court emphasized that Gilmer was not foregoing any of his substantive legal rights under ADEA, but merely submitting those claims for resolution in an arbitral, rather than a judicial, forum. Id. at 26, 111 S.Ct. at 1652. So long as Gilmer could effectively vindicate those rights in the arbitral forum, the purpose of the statute would not be frustrated. Id. at 28, 111 S.Ct. at 1653. The Court observed that under the NYSE arbitration rules the arbitrator had authority to award the same relief to Gilmer as could be obtained in a court of law. Id. at 32, 111 S.Ct. at 1655. The Court rejected Gilmer's concerns about the fairness of the arbitration proceedings, finding that the particular rules employed by the NYSE were adequate. Id. at 30-32, 111 S.Ct. at 1654-55. The Court also rejected Gilmer's contention that he had not voluntarily signed the arbitration agreement, noting that Gilmer was an experienced businessman. Id. at 33, 111 S.Ct. at 1655-56.
Gilmer might be viewed as a "sea change," rejecting the views expressed in Alexander and giving the court's blessing to coerced arbitration of all individual civil rights claims. However, the Gilmer Court gave mixed signals. On the one hand, it rejected the "mis-trust of the arbitral process" expressed in Alexander. On the other hand, the Court disclaimed any intention to overrule the holdings in Alexander v. Gardner-Denver and its progeny, Barrentine v. Arkansas-Best Freight System Inc., 450 U.S. 728, 101 S.Ct. 1437, 67 L.Ed.2d 641 (1981) and McDonald v. West Branch, 466 U.S. 284, 104 S.Ct. 1799, 80 L.Ed.2d 302 (1984):
In holding that the employee [in Alexander v. Gardner-Denver] was not foreclosed from bringing the Title VII claim, we stressed that an employee's contractual rights under a collective-bargaining agreement are distinct from the employee's statutory Title VII rights:
"In submitting his grievance to arbitration, an employee seeks to vindicate his contractual right under a collective-bargaining agreement. By contrast, in filing a lawsuit under Title VII, an employee asserts independent statutory rights accorded by Congress. The distinctly separate nature of these contractual and statutory rights is not vitiated merely because both were violated as a result of the same factual occurrence."
We also noted that a labor arbitrator has authority only to resolve questions of contractual rights. The arbitrator's "task is to effectuate the intent of the parties" and he or she does not have the "general authority to invoke public laws that conflict with the bargain between the parties." By contrast, "in instituting an action under Title VII, the employee is not seeking review of the arbitrator's decision. Rather, he is asserting a statutory right independent of the arbitration process." We further expressed concern that in collective-bargaining arbitration "the interests of the individual employee may be subordinated to the collective interests of all employees in the bargaining unit."
Barrentine and McDonald similarly involved the issue whether arbitration under a collective-bargaining agreement precluded a subsequent statutory claim. In holding that the statutory claims were not precluded, we noted, as in Gardner-Denver, the difference between contractual rights under a collective-bargaining agreement and individual statutory rights, the potential disparity in interests between a union and an employee, and the limited authority and power of labor arbitrators.
There are several important distinctions between the Gardner-Denver line of cases and the case before us. First, those cases did not involve the issue of the enforceability of an agreement to arbitrate statutory claims. Rather, they involved the quite different issue whether arbitration of contract-based claims precluded subsequent judicial resolution of statutory claims. Since the employees there had not agreed to arbitrate their statutory claims, and the labor arbitrators were not authorized to resolve such claims, the arbitration in those cases understandably was held not to preclude subsequent statutory actions. Second, because the arbitration in those *447 cases occurred in the context of a collective-bargaining agreement, the claimants there were represented by their unions in the arbitration proceedings. An important concern therefore was the tension between collective representation and individual statutory rights, a concern not applicable to the present case. Finally, those cases were not decided under the FAA, which, as discussed above, reflects a "liberal federal policy favoring arbitration agreements."
Id. at 34-35, 111 S.Ct. at 1656-57 (internal citations omitted).
In the years since Gilmer was decided, the Ninth Circuit has enforced arbitration agreements that were part of an individual employment contract, while carefully distinguishing cases in which the arbitration clause was part of a collective bargaining agreement. See Mago v. Shearson Lehman Hutton, Inc., 956 F.2d 932, 935 (9th Cir.1992); Prudential Ins. Co. v. Lai, 42 F.3d 1299 (9th Cir.1994).
Controlling case law from the Supreme Court and this Circuit thus holds that an employee's right to a judicial forum for his or her Title VII claims cannot be waived by a binding arbitration clause inserted in a collective bargaining agreement. Owens essentially is asking this court to declare those precedents void. The question is whether there is any basis for doing so.
Owens first cites a number of cases, from this and other circuits, which enforced arbitration agreements in an individual employment contract. See, e.g., Mago, 956 F.2d at 935; Prudential Ins., Co., 42 F.3d 1299. However, in none of those cases was the arbitration clause contained in a collective bargaining agreement. Consequently, these cases merely follow the Gilmer/Alexander dichotomy established by the Supreme Court. They do not repudiate Alexander.
Next, Owens contends that the 1991 Civil Rights Act overruled Alexander, citing the following language in the Act:
Where appropriate and to the extent authorized by law, the use of alternative means of dispute resolution, including ... arbitration, is encouraged to resolve disputes arising under the Acts or provisions of Federal law amended by this title.
Pub.L. 102-166, § 18. The Ninth Circuit has expressly rejected Owens' contention that this language abrogates the holding in Alexander. Prudential Ins. Co., 42 F.3d at 1304-05. The Circuit cited language from the House Report on the bill which expressly disclaimed any intent to overrule Alexander:
The committee emphasizes ... that the use of alternative dispute resolution mechanisms is intended to supplement, not supplant, the remedies provided by Title VII. Thus, for example, the committee believes that any agreement to submit disputed issues to arbitration, whether in the context of a collective bargaining agreement or in an employment contract, does not preclude the affected person from seeking relief under the enforcement provisions of Title VII. This view is consistent with the Supreme Court's interpretation of Title VII in Alexander v. Gardner-Denver Co., 415 U.S. 36 [94 S.Ct. 1011, 39 L.Ed.2d 147] (1974). The committee does not intend for the inclusion of this section to be used to preclude rights and remedies that would otherwise be available.
HR Rep. No. 40(I), 102nd Cong., 1st Sess., reprinted in 1991 USCCAN 549, 635. Had Congress desired to abrogate the holding in Alexander, it could have done so expressly in a single sentence: "A collective bargaining agreement may provide for binding arbitration, in lieu of any judicial remedy, for disputes arising under the Acts or provisions of Federal law amended by this title." Instead, Congress chose to adopt weaker language that left Alexander intact. In the very same bill, Congress expressly overruled several other Supreme Court precedents. Congress clearly knew how to take such action when it desired.
Finally, Owens cites a recent opinion from the Fourth Circuit, Austin v. Owens-Brockway Glass Container Inc., 78 F.3d 875 (4th Cir.), cert. den., ___ U.S. ___, 117 S.Ct. 432, 136 L.Ed.2d 330 (1996), which held that a binding arbitration clause in a collective bargaining agreement is sufficient to bar an employee from pursuing a Title VII or ADA claim in the courts. I find the Austin court's *448 analysis unpersuasive. Austin cites Gilmer and the 1991 Civil Rights Act amendment for the proposition that arbitration is encouraged. However, both those authorities expressly disclaim any intent to overrule Alexander with regard to arbitration clauses in collective bargaining agreements. Austin offers no other basis for concluding that Alexander has been abrogated. This glaring omission has been noted by other courts. See Pryner v. Tractor Supply Co., 927 F.Supp. 1140, 1145-46 (S.D.Ind.1996) (the fatal flaw in Austin is its failure to fully consider the prior holding of Alexander v. Gardner-Denver); Bush v. Carrier, 940 F.Supp. 1040, 1045-46 (E.D.Tex.1996) (declining to follow Austin); Bynes v. Ahrenkiel Ship Management, (U.S.), Inc., 944 F.Supp. 485 (W.D.La.1996) (same); Buckley v. Gallo Sales Co., 949 F.Supp. 737, 743 (N.D.Cal. 1996) (declining to follow Austin and concluding that the Ninth Circuit would do the same); Hill v. American National Can Co., 952 F.Supp. 398 (N.D.Tex.1996) (declining to follow Austin).[5]
The Austin court cited several post-Gilmer cases in which arbitration clauses were enforced, but each of those cases concerned a clause in an individual employment contract such as the one at issue in Gilmer. None of the cases relied upon by Austin concerned an arbitration clause inserted in a CBA. The vast majority of reported post-Gilmer decisions have concluded that Alexander v. Gardner-Denver still controls in the circumstances presented here. See, e.g., Tran v. Tran, 54 F.3d 115 (2d Cir.1995), cert den., ___ U.S. ____, 116 S.Ct. 1417, 134 L.Ed.2d 542 (1996); E.E.O.C. v. Board of Governors, 957 F.2d 424, 431 n. 11 (7th Cir.), cert den., 506 U.S. 906, 113 S.Ct. 299, 121 L.Ed.2d 223 (1992); Buckley, 949 F.Supp. at 742-43; Bynes, 944 F.Supp. 485; Bush, 940 F.Supp. at 1045-46; Pryner, 927 F.Supp. at 1145-46; Hill, 952 F.Supp. 398; Humphrey v. Council of Jewish Federations, 901 F.Supp. 703, 709-10 (S.D.N.Y.1995); DiPuccio v. United Parcel Service, 890 F.Supp. 688, 692-93 (N.D.Ohio 1995); Jackson v. Quanex Corp., 889 F.Supp. 1007, 1010-11 (E.D.Mich.1995); Randolph v. Cooper Indus., 879 F.Supp. 518 (W.D.Pa.1994); Block v. Art Iron, Inc., 866 F.Supp. 380, 385-87 (N.D.Ind.1994); Griffith v. Keystone Steel Wire Co., 858 F.Supp. 802, 804 (C.D.Ill.1994); Claps v. Moliterno Stone Sales Inc., 819 F.Supp. 141, 147 (D.Conn.1993). But cf. Brummett v. Copaz Packing Corp., 954 F.Supp. 160 (S.D.Ohio 1996) (following Austin); Jessie v. Carter Health Care Center, Inc., 930 F.Supp. 1174 (E.D.Ky.1996)(same); Bright v. Norshipco, 951 F.Supp. 95 (E.D.Va. 1997)(same, though the court is in the Fourth Circuit and thus is bound by the decision in Austin).
The judges in this District have adhered to Alexander v. Gardner-Denver. See Schmidt v. Safeway, Inc., 864 F.Supp. 991, 995 (D.Or.1994)(opinion by Judge Panner); James v. James River Paper Co., CV 94-142-ST (D Or 1994) (findings and recommendations issued by Magistrate Judge Stewart on June 29, 1994 and adopted by Judge Jones on July 26, 1994).
Admittedly, there is some incongruity between the holdings in Alexander and Gilmer. As a practical matter, an arbitration clause inserted in a personal employment contract may be no more "voluntary" than one inserted in a collective bargaining agreement. Arbitration clauses such as the one in Gilmer are, for the average employee, not the product of bargaining but a non-negotiable adhesion contract. Consent to the arbitration clause is the price for obtaining or retaining employment. Nonetheless, the Gilmer Court elected to distinguish Alexander rather than overrule it, and Congress left that holding intact.
There also is some logic to Owens' assertion that the Title VII claims concern other employees and their relationship with each other and with their employer, and thus the Title VII claims cannot be viewed in isolation. However, that is true of all cases in which individual rights are at issue. For instance, one person's right to a smoke-free workplace may come at the expense of another *449 employee's right to smoke on the job. Owens also contends that resolution of plaintiff's claims may impact the collective bargaining agreement. There is the potential for some overlap; a claim that an employee was wrongly terminated or not promoted on account of race, gender, or other forbidden grounds may well implicate the terms of a collective bargaining agreement which establishes a grievance procedure to resolve claims for wrongful termination or refusal to promote. Claims relating to discrimination in job assignments, shifts, seniority, and working conditions may also implicate matters that are the subject of the collective bargaining agreement. On the other hand, Alexander does not preclude requiring an employee to first pursue her grievances before bringing an action; it merely holds that the grievance procedure is not the exclusive remedy and an adverse decision in that forum does not preclude filing a Title VII action.
Defining the balance between individual rights and the policies reflected in federal labor law is ultimately a political decision that Congress must make. In Alexander, the Supreme Court offered its interpretation of the balance that Congress has struck. In the years since, Congress has acquiesced in that decision. Consequently, it remains the law of the land. Congress or the Supreme Court may overrule Alexander, but this court is bound by controlling precedent in the absence of intervening changes in the law. See Rodriguez de Quijas v. Shearson/American Express, Inc., 490 U.S. 477, 484, 109 S.Ct. 1917, 1921-22, 104 L.Ed.2d 526 (1989) (where a Supreme Court precedent has direct application in a case, yet may rest on reasons rejected in some other line of decision, the lower courts must follow the case which directly controls, leaving to the Supreme Court "the perogative of overruling its own decisions"); Ackerley Communications of the Northwest, Inc. v. Krochalis, 108 F.3d 1095, 1099 (9th Cir.1997).
II
Even in the absence of controlling precedent, I would likely reach the same result in this particular case. Laws prohibiting discrimination on account of factors such as race, gender, national origin, religion, and disability are designed to protect the rights of minorities or other groups whom Congress has determined require special protection. The same is true of laws forbidding sexual harassment. There is an inherent tension between these laws and a rule that would permit the majority to waive or compromise the very laws that were intended to protect the rights of the minority. The fear is that during the collective bargaining process, a union that is to cite one possible example overwhelmingly white, male, and able-bodied, may be all too willing to compromise the special protections that are afforded to women, minorities, or persons with disabilities. The majority of union members may not perceive any personal benefit from laws that protect only a minority, or may in some cases be openly hostile to the changes mandated by those laws.[6] The employer also has a powerful incentive to incorporate in a collective bargaining agreement terms that limit its potential liability under the civil rights laws.
A further concern is that the union and its membership may themselves be the target of a Title VII action. Cf Woods v. Graphic Communications, 925 F.2d 1195, 1200-03 (9th Cir.1991) (union may be liable under Title VII for refusing to process grievances of black members alleging racial discrimination, and acquiescing in racially discriminatory work environment); Local Union No. 12, United Rubber Workers v. N.L.R.B., 368 F.2d 12 (5th Cir.1966) (union allegedly refused to process any grievances by black members concerning segregated plant facilities). In the instant case, most of the offensive conduct allegedly was perpetrated by employees of Owens who are members and officers of Local 112, including its President and Vice-President. The defendants include *450 Local 112 and the parent International Union. In essence, the defendants have contracted amongst themselves to waive plaintiff's rights and to submit plaintiff's claims against them to binding arbitration. Defendants now ask this court to enforce that agreement against plaintiff.
A related matter is the efficacy of the grievance and arbitration procedure. At my request, the parties submitted supplemental briefing on these issues.[7] Because this motion to dismiss is directed at the court's jurisdiction to hear this case, as opposed to the merits of the complaint, the court may properly consider certain materials outside the complaint such as the collective bargaining agreements.[8]Winter, 900 F.2d at 1324; Roberts, 812 F.2d at 1177. The court may also resolve factual disputes regarding jurisdictional matters to the extent they are separable from the merits of the controversy. Id.
Owens and the Union defendants agree that the CBA provides for a four-step grievance procedure. The employee initiates a grievance by presenting it to his or her foreman and shop steward "within three (3) working days from the date the grievance arises." If the grievance is not resolved in Step 1, the employee and Shop Steward may refer the matter to the Local 112 Business Committee for investigation. If the Business Committee elects to pursue the grievance, it must present the grievance to the employee's department head within seven days. If the Business Committee is dissatisfied with the response, the Committee and the International Representatives of the Union have seven more days in which to jointly present the grievance to the Owens' plant manager.[9] If the grievance still has not been resolved to the Union's satisfaction, the fourth step is a conference between the International President of the Union and the Vice President of Human Resources for Owens. Finally, either the Union or Owens may request binding arbitration of the dispute. The arbitrators are selected by Owens and the Union, and follow the Voluntary Labor Arbitration Rules of the American Arbitration Association. The arbitrator has no power to add to, subtract from, or modify the terms of the CBA.
While this procedure may work well for ordinary labor disputes, there are a number of unique problems in applying these procedures to the Title VII and state law claims at issue here. First, with the exception of the initial decision to present a grievance, it is the Union and Owens that are adjusting the grievance, the Union and Owens that decide whether a grievance has been satisfactorily resolved, the Union and Owens that decide whether to elevate a grievance to the next step or allow it to die, the Union and Owens that decide whether to refer the grievance to arbitration, the Union and Owens that select the arbiters, and the Union and Owens that participate in and control the arbitration process. CBA, Articles 26 and 27. See also Griffin v. International Union, United Auto., Aerospace and Agr. Implement Workers of America, 469 F.2d 181, 183 (4th Cir. 1972) (an individual employee has no absolute right to insist that his grievance be pressed through any particular stage of the contractual grievance procedure; union may choose to process only those grievances that it concludes will justify the expense and time involved in terms of benefitting the membership at large.)
It is also the Union membership and officers who, along with Owens, are accused of violating plaintiff's Title VII rights. That presents a serious conflict of interest. If the *451 threat of legal action was looming on the horizon, the Union and Owens might still have a powerful incentive to resolve the problem in order to preclude a lawsuit. Once that threat is eliminated, the situation is reversed. The Union and Owens would both have incentive to let the claims quietly die.
Owens argues that if the employee is dissatisfied with the Union's representation, he or she may bring a separate action against the Union for breach of the duty of fair representation. The Supreme Court found that argument unpersuasive because such a claim may be difficult to prove. Alexander v. Gardner-Denver, 415 U.S. at 58 n. 19, 94 S.Ct. at 1024 n. 19. It is analogous to ignoring a clear conflict of interest on the part of an attorney because his client can always bring an action for malpractice. In some cases the client could choose to knowingly waive the conflict, but here the plaintiff is given no option: she must accept the Union as her representative without regard to any conflict of interest.
Owens and the Union also contend that 29 U.S.C. § 159(a) allows plaintiff to pursue a grievance independently of the Union. That section states, in relevant part, that:
[A]ny individual employee or a group of employees shall have the right at any time to present grievances to their employer and to have such grievances adjusted, without the intervention of the bargaining representative, as long as the adjustment is not inconsistent with the terms of a collective-bargaining contract or agreement then in effect [and further providing that] the bargaining representative has been given opportunity to be present at such adjustment.
While § 159(a) gives plaintiff a right to "present" her grievances to her employer, it apparently does not compel Owens to meet with plaintiff, let alone to take any action on her grievances. See Broniman v. Great Atlantic & Pacific Tea Co., 353 F.2d 559, 562 (6th Cir.1965) (§ 159(a) preserves the employee's right to approach the employer individually, but does not require the employer to accept the invitation or to adjust the grievance); Black-Clawson Co. v. International Ass'n of Machinists, Lodge 355, Dist. 137, 313 F.2d 179 (2d Cir.1962) (same); Malone v. United States Postal Service, 526 F.2d 1099, 1106-07 (6th Cir.1975); Local Union No. 12, United Rubber Workers of America v. N.L.R.B., 368 F.2d 12, 18 n. 8 (5th Cir.1966) ("substantial doubt exists concerning the extent of the employee's `right' to compel his employer to comply with the grievance and arbitration provisions in the bargaining contract when his union refuses to represent him"); Serra v. Pepsi-Cola General Bottlers Inc., 248 F.Supp. 684, 686 (N.D.Ill.1965); Ostrofsky v. United Steelworkers of America, 171 F.Supp. 782, 791-92 (D.Md.1959). But cf Hughes Tool Co. v. N.L.R.B., 147 F.2d 69, 73 (5th Cir.1945) (the right to "present" a grievance includes the right to fully prosecute a grievance through all stages and appeals); Donnelly v. United Fruit Co., 40 N.J. 61, 190 A.2d 825, 835 (N.J.1963) (if union is not properly representing employee, he may intervene in arbitration proceedings and obtain independent representation, and is not bound by the actions of the union in disposing of his grievance.)
In their responses to this court's questions, Owens and the Union agreed that plaintiff could not pursue arbitration on her own. Only the Union and Owens may request arbitration of a grievance. Owens again suggests that if the Union wrongly refused to pursue the grievance or failed to properly represent her, plaintiff could bring an action against the Union for breach of its duty of fair representation. However, that is rarely a satisfactory answer. Alexander, 415 U.S. at 58 n. 19, 94 S.Ct. at 1024 n. 19. It requires the plaintiff to litigate and win a "case within a case"; the plaintiff must show that the union acted arbitrarily or in bad faith in its handling of the grievance and must also prove that, but for the Union's misconduct, she likely would have prevailed on her grievance. See Chauffeurs, Teamsters & Helpers, Local No., 391 v. Terry, 494 U.S. 558, 564, 110 S.Ct. 1339, 1344, 108 L.Ed.2d 519 (1990); Vaca v. Sipes, 386 U.S. 171, 192-93, 196-98, 87 S.Ct. 903, 917-18, 919-21, 17 L.Ed.2d 842 (1967) (plaintiff must do more than show he would have prevailed on his grievance; he must also prove arbitrariness *452 or bad faith on the part of the union in processing his grievance and prove that his damages were caused by the union's conduct); Dushaw v. Roadway Express, Inc., 66 F.3d 129, 132 (6th Cir.1995) (plaintiff cannot recover from either union or employer unless he proves both breach of the CBA by the employer and breach of the duty of fair representation by the union which substantially affected the outcome of the grievance proceeding); Deboles v. Trans World Airlines, Inc., 552 F.2d 1005, 1019-20 (3d Cir. 1977) (union not liable for breach of duty of fair representation absent proof of that the breach directly damaged person to whom the duty was owed.)
There is, of course, precedent for such dual claims in "hybrid § 301" actions where the employee brings an action against the employer for breach of the collective bargaining agreement along with an action against the union for breach of its duty of fair representation. See, e.g., Clayton v. International Union, United Automobile, Aerospace & Agricultural Implement Workers of America, 451 U.S. 679, 101 S.Ct. 2088, 68 L.Ed.2d 538 (1981); Vaca, 386 U.S. at 186, 87 S.Ct. at 914-15; Dushaw, 66 F.3d 129. In such cases, however, the rights in question arise under the collective bargaining agreement, which also establishes the exclusive remedy for violations of that agreement. Ordinarily there would be no recourse to the courts. Consequently, it is incumbent upon the employee to establish the existence of extraordinary circumstances that justify invocation of a judicial remedy.
To the extent an employee's rights arise under a collective bargaining agreement and are created by that agreement, it may be appropriate for those rights to be vindicated solely through the grievance procedures established by that agreement. Cf Republic Steel Corp. v. Maddox, 379 U.S. 650, 652-53, 85 S.Ct. 614, 616-17, 13 L.Ed.2d 580 (1965) (individual employee wishing to assert contract grievances must first attempt to use the contract grievance procedure agreed upon by employer and union as the mode of redress); Smith v. Evening News Ass'n, 371 U.S. 195, 200, 83 S.Ct. 267, 270, 9 L.Ed.2d 246 (1962)(rights of individual employees arising from a CBA are often inextricably intertwined with union interests and therefore may not be pursued by a private state law action, but are subject to the provisions of federal labor law).
However, the rights at issue here were not created by the collective bargaining agreement, but by Congress. They do not arise from the contract. There was no consideration for the employer's promise to follow the civil rights laws, for that duty already existed. These rights are not subject to negotiation. They cannot be bargained away by the Union in return for an extra twenty-five cents an hour in wages or two additional days of sick leave. Nor is a union authorized to compromise an employee's civil rights for the good of the bargaining unit as a whole.
It has also been suggested that by agreeing to arbitration the employee does not forfeit any substantive rights, but simply trades one forum for another. Gilmer, 500 U.S. at 26, 111 S.Ct. at 1652. While that may have been true of the specific arbitration agreement at issue in Gilmer, that does not appear to be the case here. In a judicial forum, plaintiff would have an absolute right to pursue her Title VII claims. She would not need the Union's blessings to pursue her claims, nor could her claims be involuntarily dismissed by the Union. Her cause would be decided by a jury or a federal judge, not a panel selected exclusively by the defendants. Plaintiff would be at liberty to retain counsel of her own choosing and to present her own case, whereas according to Owens' reply brief plaintiff would be represented during the grievance and arbitration procedure by the Union or by an attorney representing the Union. It is indeed an unusual set of facts were the plaintiff is represented in litigation by the co-defendant's attorney.
In addition, the CBA requires that all grievances be presented within three days from the date the grievance arises. By contrast, the statute of limitations in a Title VII action is 300 days, 42 U.S.C. § 2000e-5(e)(1), and evidence of earlier incidents may be admissible to prove a continuing violation. Varner v. National Super Markets, Inc., 94 F.3d 1209, 1214 (8th Cir.1996). Admittedly, there is some merit to a rule that requires *453 claims to be promptly asserted so the problem does not fester. The purposes of Title VII would not necessarily be undermined by a policy of nipping the misconduct in the bud, rather than allowing the injury to compound, and awarding damages later. However, that policy has already been implemented in large part by the comparatively brief statute of limitations for Title VII claims when compared to the limitations periods for ordinary tort or contract claims. The CBA effectively overrides the 300-day statute of limitations established by Congress and replaces it with a three-day statute of limitations. That is a material alteration. A three-day statute of limitation may be suitable for the types of claims that commonly arise under a CBA; it is not necessarily suited to a Title VII claim predicated upon maintenance of a hostile work environment, or for many sexual harassment claims. In such cases, it may not be a particular isolated act that gives rise to the claim, but a pattern of conduct.
A further consideration is the remedies that would be available to plaintiff under the CBA. Under Title VII, an employee may recover compensatory and punitive damages as well as attorney fees. However, the CBA provides that the "arbitrator shall have no power to add to, subtract from, or modify the terms of this Contract ..." The question, then, is what remedies are authorized by the contract.
In response to the court's questions, the Union has suggested that an arbitrator has authority to award some compensatory damages under the label of "make whole." However, the examples cited by the Union appear to be limited to economic damages and would not authorize an award of non-economic damages. There are some Ninth Circuit cases that seem to allow a labor arbitrator to award punitive damages, at least in the absence of any contractual provision limiting that authority. Goss Golden West Sheet Metal, Inc. v. Sheet Metal Workers Inter. Union, Local 104, 933 F.2d 759 (9th Cir. 1991); Pullman Power Prods. Corp. v. Local 403, 856 F.2d 1211 (9th Cir.1988) (over a strong dissent from Judge Beezer, who maintained that settled Ninth Circuit law forbids an award of punitive damages by a labor arbitrator absent express authorization of such awards in the CBA.)[10]
However, a careful reading of those cases discloses that the Circuit merely applied an extremely deferential standard of review and deferred to the arbitral panel's interpretation of its own powers. Goss Golden West, 933 F.2d at 764 ("we cannot say that ... the agreement would not even arguably include the power to make an award of punitive damages.") That is a far cry from affirmatively holding that the arbitrators who would hear plaintiff's claim are authorized to award punitive damages. Moreover, as the Union acknowledges, there is a split among the circuits on this issue, with some circuits holding that labor arbitrators have no authority to award punitive damages.[11] At best it remains an unsettled issue, absent any contract language expressly conferring such authority.
*454 Owens suggests that the provisions and remedies of Title VII are incorporated by reference in the contract, hence, the arbitrator would have the power to award any remedy that could be awarded by a court, including compensatory and punitive damages. That is certainly one plausible interpretation of the contract. However, that interpretation is not binding upon the arbitral panel and this court would have only limited authority to review the arbitrator's contrary holding. United Paperworkers International Union v. Misco, Inc., 484 U.S. 29, 38, 108 S.Ct. 364, 371, 98 L.Ed.2d 286 (1987) ("as long as the arbitrator is even arguably construing or applying the contract and acting within the scope of his authority, that a court is convinced he committed serious error does not suffice to overturn his decision.") The same holds true for the suggestion that the arbitrator might still consider plaintiff's claims notwithstanding her failure to present a grievance within three days of the incident in question. That is one potential interpretation of the contract, but unless it is the only permissible reading that interpretation would not be binding upon the arbitral panel.
In the end, I cannot say with any degree of certainty that the contractual remedies are substantially equivalent to the remedies that would otherwise be available to plaintiff in a court of law, or that plaintiff could "effectively vindicate" her Title VII rights under the procedures established by the CBA. Cf Gilmer, 500 U.S. at 26, 28, 111 S.Ct. at 1652, 1653. That is a further reason for holding that plaintiff's claims are not barred by the arbitration clause in the CBA.[12]
III
In the alternative, Owens asks the court to stay this action while plaintiff exhausts her remedies under the grievance procedure, including (presumably non-binding) arbitration. This question was not definitively addressed in Alexander, since the employee had invoked the grievance and arbitration procedures and filed suit only after failing to obtain the desired relief.
I have serious concerns about the efficacy of the grievance and arbitration procedures in this case, particularly when the Union and Owens are both defendants. However, there are also important considerations that favor requiring an employee to first attempt to resolve the matter by way of the established grievance procedure before resorting to the courts. See, e.g., Republic Steel, 379 U.S. at 653, 85 S.Ct. at 616-17. In Alexander v. Gardner-Denver, the Court observed that:
"[T]he federal policy favoring arbitration of labor disputes and the federal policy against discriminatory employment practices can best be accommodated by permitting an employee to pursue fully both his remedy under the grievance-arbitration clause of a collective-bargaining agreement and his cause of action under Title VII. The federal court should consider the employee's claim de novo. The arbitral decision may be admitted as evidence and accorded such weight as the court deems appropriate."
415 U.S. at 60, 94 S.Ct. at 1025. The Court thus sought to address some of the concerns that Owens has raised regarding the overlap between Title VII claims and issues that may be the subject of the collective bargaining agreement. Therefore, I will stay this action and require plaintiff to first pursue the grievance and arbitration remedies available to her under the CBA. In the event that plaintiff's worst fears regarding that procedure materialize, she still has resort to the courts.
Exhaustion may prove futile and the parties may be back before this court several months from now. Nonetheless, I conclude that it is a necessary step in order to minimize any friction between the vindication of individual statutory rights and the federal labor policies that favor the collective bargaining process. Indeed, had plaintiff *455 promptly lodged grievances, instead of allowing the matter to fester, it might have been possible to avoid some of the problems that later developed. There also is some merit to having grievances addressed, at least at the initial stages, by those who are most familiar with the participants and the issues involved. For instance, while it is possible that Recker and Benson were discriminating against plaintiff because of her gender, I cannot preclude the possibility that plaintiff's gender had nothing to do with their actions and they genuinely believed that she would benefit from additional training before taking the examination.
Given the advanced status of the grievances here, the parties may mutually agree to forego the initial grievance stages and proceed directly to arbitration. Since plaintiff will not be required to accept the decision of the arbitrator as final, the same rule will apply to defendants. Non-binding arbitration may appear to be a waste of time, but it may also provide a preview of the likely result of any litigation and enhance the prospects for settlement.[13]
Motion to Strike Claims for Damages in Excess of Cap
Owens also moves to strike plaintiff's prayer for damages in excess of the cap established by the Civil Rights Act of 1991. 42 U.S.C. § 1981a(b)(3) provides that:
The sum of the amount of compensatory damages awarded under this section for future pecuniary losses, emotional pain, suffering, inconvenience, mental anguish, loss of enjoyment of life, and other nonpecuniary losses, and the amount of punitive damages awarded under this section, shall not exceed, for each complaining party ... $300,000.
The complaint demands that Owens pay compensatory damages of $300,000 and also punitive damages of $300,000. Owens correctly asserts that the $300,000 limit is for compensatory and punitive damages combined hence plaintiff cannot recover more than that sum. See Kimzey v. Wal-Mart Stores, Inc., 107 F.3d 568 (8th Cir.1997) ("Title VII provides that the upper limit on an award including punitive and compensatory damages in a case such as this is $300,000.")
However, that does not preclude plaintiff from making such a demand in her complaint. The jury could conceivably award $300,000 in compensatory damages and no punitive damages, or $20,000 in compensatory damages and $280,000 in punitive damages. Plaintiff is, therefore, entitled to plead $300,000 in compensatory damages and also $300,000 in punitive damages.[14]
Owens also protests that plaintiff seeks $300,000 in damages for the underlying Title VII claim, and an additional $300,000 in damages on her claim that Owens illegally retaliated against her for asserting the Title VII claim. Owens contends that the $300,000 limit was intended to limit the total recovery on all of plaintiff's Title VII claims against her employer and she may not circumvent that limit by pleading multiple claims alleging separate violations of Title VII by the same defendant.
I agree with Owens' analysis of the statute. Plaintiff may not recover twice from Owens for the alleged violations of Title VII. I do not believe that a one-recovery rule "irrationally diminishes the consequences [to the employer] of retaliating against an employee who has complained of or resisted discrimination," as plaintiff suggests. A $300,000 cap upon damages is certainly adequate to seize the employer's attention. The employer will not have a license to retaliate without fear of consequences, for it is by no means certain *456 that the award in the underlying case would exhaust the entire $300,000 cap. Indeed, there are cases where the employer has prevailed on the underlying sexual harassment claim only to then be found liable for retaliating against the employee for having filed the claim. See, e.g., Iannone v. Frederic R. Harris Inc., 941 F.Supp. 403 (S.D.N.Y.1996).[15]
However, that possibility also counsels against granting Owens' motion to strike plaintiff's prayer for $300,000 in damages on her retaliation claim. Rather, the appropriate time to address the damage cap is during post-trial motions, assuming that this case progresses to that stage.
Motion to Dismiss Owens-Illinois
Defendant Owens-Ilinois seeks dismissal of the claims against it. Plaintiff has not alleged any conduct by Owens-Illinois, which is the parent corporation of defendant Owens-Brockway. Ordinarily a parent corporation is not liable for the Title VII violations of its wholly owned subsidiary. Watson v. Gulf & Western Industries, 650 F.2d 990, 993 (9th Cir.1981). Plaintiff correctly observes that there are limited exceptions to that rule. However, plaintiff has offered no basis for this court to find that any of the exceptions is applicable here. Nor does there appear to be any pressing need for plaintiff to find such an exception in this case. Owens has stipulated that its Owens-Brockway subsidiary has more than 500 employees for purposes of evaluating its Title VII liability.[16] Owens has also represented to the court that the Owens-Brockway subsidiary has over one billion dollars in assets, in excess of one hundred million dollars in net equity, and is more than capable of paying any judgment that might be rendered in this case. In reliance upon those representations, I grant the motion to dismiss defendant Owens-Illinois.
At oral argument, plaintiff suggested that she was concerned with discovery and, in particular, the right to obtain documents that were in the possession of the parent corporation. The federal discovery rules would seem to provide ample means for plaintiff to obtain documents in the possession of defendant Owens-Ilinois that relate to this case. That is not a valid basis to retain Owens-Illinois as party to this case. If a problem arises during discovery, the court will address it at that time.
CONCLUSION
Owens' motion (# 17-1) to dismiss this action on grounds that arbitration is the sole remedy available to plaintiff is DENIED. Owens' alternative motion (# 17-2) to stay this action pending exhaustion of remedies is GRANTED. The results of the arbitration will not bar subsequent judicial action unless the parties otherwise agree. Owens' motion (# 17-3) to strike the prayer for damages in excess of the statutory cap is DENIED with leave to renew such motion post-trial. Owens' motion (# 17-4) to dismiss the Sixth Claim for negligence is GRANTED. Owens' motion (# 17-5) to dismiss defendant Owens-Illinois is GRANTED. Owens' Request for Judicial Notice (# 19-1) is DENIED as moot.
NOTES
[1] There are limited exceptions for jurisdictional allegations and similar matters, where the court may consider some materials outside the complaint and may resolve certain factual disputes to the extent they are separable from the merits of the controversy. Winter v. California Medical Review, Inc., 900 F.2d 1322, 1324 (9th Cir.1990); Roberts v. Corrothers, 812 F.2d 1173, 1177 (9th Cir.1987.)
[2] There is some suggestion that plaintiff did not personally witness certain incidents, and her supervisors told plaintiff they could not rely upon hearsay. However, that is not entirely clear in the complaint.
[3] Plaintiff has conceded the motion to dismiss the negligence claim against Owens. The Union did not move to dismiss, so the negligence claim against the Union remains in this case.
[4] The CBA does not expressly say that all Title VII claims are subject to binding arbitration to the exclusion of judicial remedies. It merely says that "disputes under this Article ... shall be subject to the grievance procedure." Article 26 is entitled "Grievance Procedure". The arbitration clause is in Article 27. However, arbitration clauses in collective bargaining agreements tend to be broadly construed. See Mitchell v. Hercules, Inc., 410 F.Supp. 560 (S.D.Ga.1976). My resolution of other issues in this case makes it unnecessary to decide this question.
[5] Owens also suggests that there are important differences between the language of the arbitration clause at issue here and the one in Alexander, that warrant departing from the holding in that case. I disagree.
[6] I do not mean to imply that this is necessarily true of the defendant Union. On the contrary, the supplemental briefing suggests that there may be a substantial number of female members in Local 112, including shop stewards and members of the union's Business Committee. Nonetheless, the potential that individual civil rights will be subordinated is a significant concern that cannot be gainsaid.
[7] Thoughtful responses were received from the Owens and Union defendants. Plaintiff's counsel declined the opportunity to brief these issues.
[8] Defendants' request for judicial notice of the collective bargaining agreement is, therefore, moot. However, I question whether the terms of a collective bargaining agreement between two private parties satisfies FRE 201(b)(2) (court may take judicial notice of facts "capable of accurate and ready determination by resort to sources whose accuracy cannot reasonably be questioned.") Rather, this language appears to contemplate judicial notice of facts such as the mileage between Portland and Seattle, or the height of Mount Hood.
[9] During most of the time period addressed by the complaint, the plant manager was Mark Recker. Notably, Recker is named in the complaint as one of the leading protagonists. That raises some questions about the efficacy of steps one through three of the grievance procedure.
[10] The Supreme Court's recent decision in Mastrobuono v. Shearson Lehman Hutton Inc., 514 U.S. 52, 115 S.Ct. 1212, 131 L.Ed.2d 76 (1995), is not dispositive of this question. It was not a labor arbitration case, and the arbitration rules designated in the contract expressly authorized an award of punitive damages.
[11] There is a longstanding reluctance to award punitive damages in labor cases. See, e.g., Local 127, United Shoe Workers of America v. Brooks Shoe Mfg. Co., 298 F.2d 277, 284 (3d Cir.1962) (Biggs, concurring) ("It is the general policy of the federal labor laws ... to supply remedies rather than punishment.") In part, that may be because punitive damages are ordinarily not available in an action for breach of a contract. However, the aversion to punitive damages in labor cases appears to extend far beyond that. See International Bro. of Electrical Workers v. Foust, 442 U.S. 42, 52, 99 S.Ct. 2121, 2127-28, 60 L.Ed.2d 698 (1979) (denying punitive damages); Association of Flight Attendants v. Horizon Air Indus., Inc., 976 F.2d 541, 551 (9th Cir.1992) (citing this policy as rationale for denying award of attorney fees to prevailing party); Moore v. Local Union 569, IBEW, 989 F.2d 1534, 1542 (9th Cir.1993); United Transportation Union Local 74 v. Consolidated Rail Corp., 881 F.2d 282 (6th Cir.1989); Williams v. Pacific Maritime Ass'n, 421 F.2d 1287, 1289 (9th Cir.1970); Atwood v. Pacific Maritime Ass'n, 432 F.Supp. 491, 498 (D.Or.1977) (all concluding that there was no right to punitive damages). But cf Woods v. Graphic Communications, 925 F.2d 1195, 1204-05 (9th Cir.1991) (awarding punitive damages against union for racial discrimination against member).
[12] Plaintiff has argued that membership in the union was mandatory, she did not vote in favor of the collective bargaining agreement, and she did not knowingly and voluntarily waive her Title VII rights. Whether plaintiff personally voted for the agreement or read it is of no consequence. Rather, such questions are subsumed within the larger question of whether a union may consent to arbitration of claims by its members for violation of their civil rights.
[13] Nothing I have said in this opinion precludes the parties from agreeing to other methods for resolving this case, including arbitration on terms acceptable to all parties that address the concerns plaintiff has expressed regarding the existing arbitration procedure.
[14] Several courts have held that granting a pretrial motion to strike a prayer for damages in excess of the statutory cap would violate the express language of 42 U.S.C. § 1981a(c)(2):
"If a complaining party seeks compensatory or punitive damages under this section the court shall not inform the jury of the [damage cap] limitations ..."
Johnson v. Metropolitan Sewer Dist., 926 F.Supp. 874, 876 (E.D.Mo.1996); Haltek v. Village of Park Forest, 864 F.Supp. 802, 807 (N.D.Ill.1994).
[15] At oral argument, plaintiff suggested that a plaintiff might file a Title VII claim, which is resolved, after which the employer would have nothing to lose by subsequently retaliating against the plaintiff. Without deciding the issue, since it is not presented here, the scenario described by plaintiff would seemingly give rise to a separate claim. Resolution of the first claim would not waive any claims the plaintiff might have for subsequent Title VII violations.
[16] Owens' reply brief used the number "over 300 employees". Reply Brief at 15. The court assumes this was a typographical error the statute establishes a cap of $300,000 in damages from an employer with more than 500 employees and that Owens-Brockway intended to stipulate that it has over 500 employees for purposes of 42 U.S.C. § 1981a. Owens should immediately advise the court if it has a different understanding of the stipulation.
|
Introduction {#s0001}
============
Dopamine (DA) regulation of neural circuit function is ubiquitously observed across species. Acting through D1 and D2 classes of G protein-coupled receptors (GPCRs), DA broadly regulates synaptic transmission in the central nervous system (CNS) through modulation of presynaptic neurotransmitter release and postsynaptic response \[[@cit0092]\]. In particular, DAergic modulation of synaptic output from interneurons, through the activation of D2 receptors, modulates circuit function in a wide range of neurobiological functions, from fundamental homeostatic processes to higher order neural function. For example, in the freshwater pond snail *Lymnaea stagnalis*, rhythmic DAergic inhibition of respiratory interneuron output is key to mediating aerial respiration behaviour \[[@cit0088],[@cit0075]\]. In the mammalian brain, DAergic D2 receptor-dependent inhibition of neurotransmitter release from interneurons in the striatum \[[@cit0021],[@cit0023],[@cit0053]\] and amygdala \[[@cit0010],[@cit0019],[@cit0072]\] are critically involved in motor control and associative learning. Therefore, understanding the mechanisms underlying D2 receptor-mediated DAergic inhibition of interneuron synaptic output is of particular physiological significance.
Activation of D2 receptors inhibited voltage-gated Ca^2+^ current (*I*~Ca~) in both *L. stagnalis* \[[@cit0004]\] and mammalian \[[@cit0099],[@cit0016],[@cit0074]\] interneurons. As activity-induced Ca^2+^ influx is a key determinant of presynaptic vesicle release \[[@cit0104]\], this likely contributes to DAergic inhibition of interneuron synaptic output. D2 receptor-mediated inhibition of voltage-gated Ca^2+^ channels occurs through both voltage-dependent and -independent mechanisms \[[@cit0015],[@cit0015],[@cit0060]\]. The voltage-dependent mechanism involves direct binding between the G-protein βγ subunit and the α1 subunit of voltage-gated Ca^2+^ channels \[[@cit0020],[@cit0037],[@cit0079],[@cit0101]\], which results in reduction of the peak current amplitude and slowing of current activation kinetics \[[@cit0071],[@cit0002],[@cit0005],[@cit0031]\]. The voltage-dependence stems from the ability of a strong depolarization to induce unbinding of the Gβγ subunit and relieve part of the inhibition \[[@cit0005],[@cit0013],[@cit0030],[@cit0042],[@cit0057]\]. In contrast, the slower and longer-lasting voltage-independent inhibition can be mediated through a variety of mechanisms, including regulation of voltage-gated Ca^2+^channel surface expression levels through direct interaction with GPCRs \[[@cit0060]\], involvement of the Gα subunit \[[@cit0051]\], soluble second messenger cascades \[[@cit0049],[@cit0038]\] and kinase activation \[[@cit0080],[@cit0015],[@cit0025]\]. However, whether D2 receptor-mediated inhibition of voltage-gated Ca^2+^ channels leads to synaptic suppression in interneurons remains unclear.
The central pattern generator network that gives rise to the aerial respiration behaviour in the mollusk *Lymnaea stagnalis* provides a well-characterized and highly tractable model for examining DA-mediated regulation of voltage-gated Ca^2+^ channels and synaptic output in interneurons. This circuit consists of the DAergic pacemaker neuron RPeD1 and the follower interneurons VD4 and IP3i \[[@cit0096]\]. DAergic input from the RPeD1 to the follower cells is necessary for rhythmic network activity of the CPG, as when VD4 and IP3i are cultured together in the absence of the RPeD1, pulsatile application of DA elicited a series of alternating bursts similar to that exhibited by the intact three-interneuron network both *in vivo* and *in vitro* \[[@cit0088]\]*.* In a well-established *in vitro* soma-soma synapse model \[[@cit0034]\], VD4 forms an excitatory cholinergic synapse with its postsynaptic target LPeD1 \[[@cit0045],[@cit0097],[@cit0098]\]. The soma-soma synapse between VD4 and LPeD1 allows direct access to both pre- and post-synaptic compartments for electrophysiological, pharmacological, and imaging studies. Furthermore, DA receptors, G protein subunits and Cav2 channels have been well-characterized in the *L. stagnalis* CNS. Both D1- and D2-like receptors have been identified in *L. stagnalis* central neurons \[[@cit0026],[@cit0048]\]. The effects of DA on the VD4 and IP3i are shown to be mediated through D2-like receptors, as the effects can be blocked only by the D2 receptor antagonist, sulpiride \[[@cit0068],[@cit0069]\].
In this study, we employed the VD4 to LPeD1 synapse model to study the endogenous mechanisms underlying DAergic modulation of voltage-gated Ca^2+^ channels and synaptic output in interneurons. We found that DA not only inhibits *I*~Ca~ in the VD4 through both voltage-dependent and independent pathways, but also suppresses synaptic vesicle release downstream of voltage-gated Ca^2+^ channel-conducted Ca^2+^ influx.
Materials and methods {#s0002}
=====================
Sequence alignment and phylogenetic analysis {#s0002-0001}
--------------------------------------------
Nucleotide sequences of the *L. stagnalis* CNS transcriptome assembly \[[@cit0082]\] were retrieved from the European Nucleotide Archive (<https://www.ebi.ac.uk/ena>) (accession numbers FX180119- FX296473). Open reading frames (\>100 amino acids) were identified using TransDecoder v5.0.2 \[[@cit0044]\] to form the predicted protein-coding sequence set.
Protein sequences of vertebrate orthologs of D2 subfamily receptors, G protein subunits and Cav2 channels were retrieved from UniProt \[[@cit0091]\] ([Table 1](#t0001){ref-type="table"}). For each protein, sequences of the orthologs were aligned via MUSCLE \[[@cit0029]\] to create a profile HMM (HMMER v3.1b1) \[[@cit0028]\] that was then used to query the predicted protein-coding sequences of the *L. stagnalis* CNS transcriptome (cut-off E-value:1e-5). The top hit was searched against the Nr database using BLAST \[[@cit0001]\] to confirm protein identity. The *L. stagnalis* sequences were aligned with their respective vertebrate orthologs using MUSCLE and analyzed in MEGA7 (Kumar et al., 2016) to find the best-fit model and construct the phylogenetic tree with 500 bootstrap replicates. Functional protein domains were identified according to UniProt annotations. Table 1.Accession numbers of proteins used to construct profile HMM and sequence alignments.GeneHumanNon-human primateRatMouseVertebrate fish*Lymnaea*Cav2.1O00555H2NXR5P54282P97445F8W3Z0FX182534Cav2.2Q00975H2PU57Q02294O55017A0A146UZM5 DRD2P14416H2NFB8P61169P61168Q8AWE0 DRD3P35462H2P9P0P19020P30728Q6DGJ2FX186271DRD4P21917H2NCB0P30729P51436Q5DJ15 GNAOP09471H2NQY0P59215P18872F8W442FX182600GNAI1P63096Q5RAD4P10824B2RSH2Q7T3D3 GNAI2P04899H2QMN4P04897P08752Q6TNT8FX180365GNAI3P08754H2PZK9P08753Q9DC51A9JTC8 Gβ~1~P62873Q5R5W8P54311P62874Q6PH57FX180485Gγ~2~P59768Q5R7U4NP_001244278.1P63213Q15KE4FX191281
Animals {#s0002-0002}
-------
Freshwater pond snails, *L. stagnalis*, obtained from an inbred culture at the Free University, Amsterdam, were raised and maintained in aquaria at the University of Toronto. All animals used were kept in water at room temperature (20--22°C) on a 12 hr light/dark cycle and fed lettuce twice a week (Monday and Friday) and Purina Trout Chow once (Wednesday). One- to two-month-old snails with shell length of 10--15 mm were used in all experiments.
Dissection {#s0002-0003}
----------
All animals were dissected under sterile conditions. Snails were anaesthetized for 10 minutes in ∼10% (v/v) Listerine in water. The anaesthetized snails were then de-shelled with fine curved forceps and pinned to a black silicone rubber--based dissection dish containing normal snail saline (NSS) (mM: 51.3 NaCl, 1.7 KCl, 4.1 CaCl2, and 1.5 MgCl2, 5.0 HEPES, pH adjusted to 7.9 with NaOH). A dorsal midline incision was made to expose the CNS, including the central ring and the buccal ganglia from under the buccal mass. The CNS was subsequently removed from the animal using fine dissection scissors and immediately placed in the antibiotic-containing solution (ACS): NSS containing 50 mg/mL gentamycin (Sigma, ON, Canada).
Cell culture {#s0002-0004}
------------
Conditioning medium (CM) was prepared by incubating 8-12 acutely isolated central ring ganglia in 6 ml defined medium (DM) (mM: serum-free 50% (v/v) Liebowitz L-15 medium (GIBCO, NY, USA) containing 40.0 NaCl, 1.7 KCl, 4.1 CaCl2, 1.5 MgCl2, 5.0 HEPES, 10 glucose, 1.0 L-glutamine, 20-mg/mL gentamycin, pH adjusted to 7.9 with NaOH) in glass Petri dishes pre-coated with Sigmacote (Sigma) for 72 hrs, as described previously \[[@cit0081],[@cit0034],[@cit0089]\]. The resulting 1X CM was frozen in polypropylene tubes at −20°C until required. Subsequently, the brains were then rewashed in ACS and then re-incubated in DM for another 3--5 days to produce 2X CM. A further session of washing and re-incubating for another week produced 3X CM.
For cell isolation, the central ring ganglia were treated with trypsin (Type III, 3 mg/mL, Sigma) dissolved in NSS for 20 min to weaken the outer glial sheath surrounding the central ganglia. The brains were then treated with trypsin inhibitor (3 mg/mL, Sigma) dissolved in NSS for 18 min. Upon completion of digestion, the ganglia were then placed in CM on a black silicone rubber based dissection dish. The connective tissue sheath surrounding the neuronal ganglia was removed using fine forceps. The VD4 and LPeD1 neurons were identified by colour and size in the visceral ganglia and left pedal dorsal ganglia, respectively. Gentle suction via a 2mm fire-polished pipette (World Precision Instruments, FL, USA) that was coated with Sigmacote (Sigma) was used to isolate the identified neurons. The neurons were subsequently plated onto a poly-L-lysine coated glass bottom culture dish filled with pre-prepared CM.
For single cell configuration, acutely isolated VD4 neurons were plated in culture dishes independently from one another for 24 hrs prior to testing. To culture synaptic pairs, acutely isolated VD4 and LPeD1 neurons were plated in culture dishes in close proximity to each other to allow for direct contact between respective neurites. Neurons were kept in culture for 24 hrs to allow for synaptic formation prior to experiments. The formation of the synapse was confirmed by electrical analysis through noting the existence of a postsynaptic response correlated to presynaptic electrical stimulation.
Electrophysiology {#s0002-0005}
-----------------
As previously described electrophysiological recordings were performed under current clamp mode \[[@cit0034],[@cit0033],[@cit0039]\], or voltage-clamp mode \[[@cit0033],[@cit0052],[@cit0065]\], using an Axopatch 700A amplifier (Axon Instruments, CA, USA) connected to an analog-to-digital interface Digidata 1322 that was linked to a personal computer running pClamp9 (Axon Instruments) \[[@cit0039],[@cit0065]\]. Recording pipettes were pulled using a Flaming-Brown micropipette puller (Model P-87, Sutter Instruments, Novato, CA, USA. The data were filtered at 1 kHz (-3 dB) using a 4- pole Bessel filter and digitized at a sampling frequency of 2 kHz. Data was analyzed using Clampfit version 9.2 (Axon Instruments). All curve fittings were carried out using Origin 7 (OriginLab, MA, USA).
Whole-cell (ruptured) patch-clamp recordings {#s0002-0006}
--------------------------------------------
Pipettes were filled with whole cell recording pipette solution (mM: 29 KCl, 2.3 CaCl2, 2 MgATP, 0.1 GTP-Tris, 11 EGTA, 10 HEPES, pH adjusted to 7.4 with KOH) (series resistances ∼1 -- 2 MΩ). Whole cell recordings were carried out in modified NSS (mM: 10 CaCl2, 45.7 TEA-Cl, 1 MgCl2, 10 HEPES, 2 4-AP, pH adjusted to 7.9 with TEA-OH). Dopamine (DA) (Catalogue \#62-31-7, Sigma) was applied via perfusion in the bath solution. Based on previous report that the maximum effective dose of DA on VD4 interneurons is 100 µM \[[@cit0004]\], we had chosen 10 µM DA for all experiments, unless noted otherwise, to ensure consistency of response.
For voltage step experiments, currents were elicited by stepping from the holding potential to the test potential of +30mV for 50 ms. A prepulse protocol was applied consisting of a holding potential of −70 mV which first stepped to a depolarization of +80 mV for 10 ms, then to test voltage of +30mV for 50 ms separated by an inter-pulse voltage of −70 mV for 5 ms ([Figure 7A](#f0007){ref-type="fig"}). To generate the current-voltage (IV) curve, the holding potential was set to −70 mV and 50 ms depolarizing steps from −40 mV to +100mV with a +5mV interval was used. The IV relation was generated from peak inward current using a Boltzmann fit (I=G\*(V-Vrev)\*(1-(1/(1+exp((V-Vh)/S))))).
To generate the AP waveform (APW), single VD4 neurons were current clamped via a sharp intracellular pipette in NSS bath solution to evoke and record APs endogenous to those neurons. Positive current was injected at levels to induce and maintain an AP train at 2Hz. This frequency was chosen because it represents a sustainable firing rate composed of single APs. The averaged AP profile showed a threshold voltage of −29 mV, an overshoot voltage of +35mV, and half width of 4.5 ms ([Figure 6A](#f0006){ref-type="fig"}). Experiments conducted using the APW was controlled using pClamp9. The APW was flanked with the holding potential of −70 mV. Data acquisition was filtered at 1 kHz (-3 dB) using a 4- pole Bessel filter and digitized at a sampling frequency of 2 kHz. Leak currents were subtracted via P/N leak subtraction protocol using 4 positive subsweeps from a holding level of −70 mV. Data was analyzed using Clampfit version 9.2. All curve fittings were carried out using Origin 7.
Simultaneous pre- and post-synaptic monitoring of VD4-LPeD1 synaptic transmission {#s0002-0007}
---------------------------------------------------------------------------------
To study synaptic transmission between the VD4 and LPeD1 neurons, a dual clamp protocol was used ([Figure 4B](#f0004){ref-type="fig"}). The presynaptic cell was current clamped via the intracellular sharp electrode and the postsynaptic cell was simultaneously voltage clamped via the patch electrode. Prior to testing, the presynaptic neuron was kept hyperpolarized to −70 mV by negative current injection to prevent any unwanted firing of APs. During testing, APs were induced by positive current injection to depolarize the neuron just past its firing threshold. A 5s long 1 Hz current pulse train was used to elicit five APs. Postsynaptic responses were detected as excitatory postsynaptic currents (EPSCs). The existence of a functional synapse was confirmed when an EPSC was correlated with a presynaptic AP. All recordings were carried out in NSS bath solution.
Ratiometric FURA-2 Ca^2+^ imaging {#s0002-0008}
---------------------------------
Intracellular Ca^2+^ (\[Ca^2+^\]~i~) was measured using a FURA-2 ratiometric Ca^2+^ imaging system, as described previously \[[@cit0033]\]. For intracellular sharp recording experiments, the cell-permeant AM-FURA-2, was used. The cells were incubated with 10 μM AM-FURA-2 (Molecular Probes, OR, USA) for 30 minutes and washed out with recording solution three times prior to imaging. The experiments were carried out in the dark to prevent photobleaching of the dye. The cells were stimulated with simultaneous intracellular recording, and the corresponding FURA-2 fluorescence signal was excited at 340 and 380 nm wavelengths generated by UV light from a 100W Hg/Xe-arc lamp, alternately passed through 340 and 380 nm excitation filters using a high speed random monochromator controlled by Image Pro 5 (Photon Technology International). The fluorescence signal, generated after the excitation light, was reflected via a 430 nm dichroic mirror, passed through a 530 nm long-pass emission filter, and detected and digitized by an intensified charged-coupled device (ICCD) camera (Photon Technology International) in Image Pro 5. Signal acquisition was done in hi-speed acquisition mode using a 10 ms exposure time per excitation wavelength at 8x8 binning. Intensity of fluorescent signals detected at 340 and 380 nm were then processed to floating point images before being used to generate Poenie-Tsien ratio intensity images. These images were used for all FURA-2 analyses.
For voltage clamp experiments, the cell impermeant FURA-2 penta-potassium salt was loaded into neurons through the patch pipette by inclusion in the pipette solution. A final concentration of 100 µM FURA-2 penta-potassium salt was used and allowed to dialyze into the neuron after establishing a seal and rupture.
FM1-43 imaging of vesicle release {#s0002-0009}
---------------------------------
Levels of vesicle release were monitored using the styryl dye N-(3-Triethylammoniumpropyl)-4-(4-(Dibutylamino) Styryl) Pyridinium Dibromide (FM1-43) (Molecular Probes). This water-soluble dye fluoresces when it binds to a lipid-rich membrane and has been commonly used to visualize synaptic vesicles following endocytotic processes. FM1-43 dye (4 µM) was added to culture dishes and allowed to equilibrate for 5 minutes. To load the dye, neurons were induced to fire APs by intracellular sharp electrode current injection. Two 5s current pulses separated by 30s were used, which caused endocytosis of the FM1-43 dye. Any dye that was not endocytosed was subsequently washed away by exchanging NSS bath solution once every 5 minutes for a total of three washes. The experiments were carried out in the dark to prevent photobleaching of the dye. Exocytosis of FM1-43 dye and subsequent destaining of dye was achieved by either electrical stimulation or ionomycin application. Electrical stimulation of vesicle release was performed using intracellular electrodes to inject current pulses into FM1-43 loaded neurons, to cause unloading of dye. The current injection protocol consisted of three current injection pulses of 5s each separated by 30s, which was controlled by pClamp9 software. Ionomycin stimulation of vesicle release was performed by rapid bath exchange of 2 μM ionomycin dissolved in NSS bath solution onto neurons.
Imaging of FM1-43 fluorescence was acquired simultaneously with the above mentioned stimulus protocols. FM1-43 fluorescence signal was excited at 488 nm wavelength generated by UV light from a 100 W Hg/Xe-arc lamp, alternately passed through a 488nm excitation filter, which was controlled by Image Pro 5. Emitted light was passed through a band pass filter 510 nm--560 nm and detected and digitized by an intensified charged-coupled device (ICCD) camera in Image Pro 5. Signals were sampled at 0.5Hz using a 300 ms exposure time and 4×4 binning.
Fluorescent intensities in single neurons were analyzed using the averaged fluorescence from the entire soma. In synaptically paired neurons, fluorescence intensities were taken from three regions: (i) presynaptic contact site (CS), (ii) presynaptic non-contact site, (iii) postsynaptic non-contact site ([Figure 4E](#f0004){ref-type="fig"}).
Data analysis and statistics {#s0002-0010}
----------------------------
Unless otherwise stated, data are presented as the mean ± s.e.m. Statistical analyses were carried out using SigmaStat 3.0 (Jandel Scientific, IL, USA). Differences between mean values from each experimental group were tested using a paired t-test for two groups or one-way analysis of variance (ANOVA, Holm-Sidak or Tukey method) followed by Holm-Sidak post-hoc test for multiple comparisons. Differences were considered significant if *p* \< 0.05.
Results {#s0003}
=======
Identification and phylogenetic analyses of *L. stagnalis* orthologs of D2-like receptors, G protein subunits and Cav2 channels {#s0003-0001}
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We first examined the *L. stagnalis* CNS transcriptome \[[@cit0082]\] to characterize the conservation of genes involved in DAergic regulation of Cav2 channels in central neurons. Whereas the D2-like subfamily of receptors in vertebrates is known to include three isoforms, D2, D3 and D4 receptors, we found that the *L. stagnalis* CNS expresses a single D2-like receptor ([Figure 1](#f0001){ref-type="fig"}) in which the two agonist bindings sites show partial sequence similarity with vertebrate D2-4 receptors. Consistent with previous reports \[[@cit0062],[@cit0061]\], we observed that *L. staganalis* Gαi ([Figure 2](#f0002){ref-type="fig"}A) and Gαo ([Figure 2B](#f0002){ref-type="fig"}) subunits share high degrees of sequence identity with their vertebrate counterparts, with complete conservation of the four guanine nucleotide binding sites required for GTP binding. Similarly, the seven WD repeat domains in the single *L. stagnalis* Gβ protein ([Figure 2C](#f0002){ref-type="fig"}), which are implicated in protein-protein interaction \[[@cit0063]\], are nearly identical to those in vertebrate Gβ~1~ orthologs. Greater sequence divergence was observed in the single *L. stagnalis* Gγ isoform as compared to vertebrate Gγ~2~ orthologs ([Figure 2D](#f0002){ref-type="fig"}). Finally, sequence analyses of the *L. stagnalis* Ca~V~2 (*L*Ca~V~2) channel ortholog Ca~V~2, demonstrate that two of the three Gβ~1~γ~2~ binding sites, one in the N-terminus cytoplasmic tail and another in the I-II linker region, on vertebrate Ca~V~2.1 and Ca~V~2.2 channels that are essential for G protein-mediated voltage-dependent regulation of Cav2 channels \[[@cit0102]\] are conserved in considerable degrees in L Ca~V~2. Taken together, these findings demonstrate *L. stagnalis* to be a conserved model for examining the fundamental mechanisms of G protein-mediated DAergic modulation of Ca~V~2 channels in the CNS. Figure 1.Protein sequence alignment and phylogenetic tree of the D2-like receptor in *L. stagnalis.* *A*, Amino acid sequence comparisons of the two agonist bindings sites between the single *L. stagnalis* D2-like receptor and the three isoforms of the D2-like subfamily of DA receptors in selected vertebrate species. Conserved and similar sequences in alignments are colored as black and grey boxes, respectively. *B*, Phylogenetic analysis was conducted by the Maximum Likelihood method using the JTT+G+I model. Bootstrap value from 500 replicates are shown next to each node. The scale bars indicate the estimated evolutionary distance in the units of the number of amino acid substitutions per site. Figure 2.Protein sequence alignment and phylogenetic tree of G protein subunits in *L. stagnalis*. *A-B*,Amino acid sequence comparisons of the four nucleotide binding sites in the single *L. stagnalis* Gαi and Gαo orthologs with the vertebrate Gαi isoforms GNAI1-3 (A1) and Gαo (B1), respectively. As all four sites are identical across GNAI1-3 isoforms in human, chimpanzee, rat, mouse and zebrafish, only one instance is shown for simplicity. Phylogenetic analysis was conducted by the Maximum Likelihood method using the JTT+G model for Gαi (A2) and the LG+G model for Gαo (B2). *C*, Amino acid sequence comparisons of the seven WD repeat regions (WD1-7) of the single isoform *L. stagnalis* Gβ and vetebrate orthologs of Gβ~1~ (C1). Phylogenetic analysis was conducted by the Maximum Likelihood method using the WAG model (C2). *D*, Amino acid sequence comparisons of the single *L. stagnalis* Gγ isoform and vetebrate orthologs of Gγ~2~ (D1). Phylogenetic analysis was conducted by the Maximum Likelihood method using the LG model (D2). Conserved and similar sequences in alignments are colored as black and grey boxes, respectively. Bootstrap value from 500 replicates are shown next to each node. The scale bars indicate the estimated evolutionary distance in the units of the number of amino acid substitutions per site.Figure 2.(Continued).Figure 2.(Continued).
DA inhibits synaptic output of the VD4 {#s0003-0002}
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VD4 and LPeD1 were acutely isolated and cultured for 24 hours to allow for soma-soma synapse formation prior to testing, as previously described by \[[@cit0034]\]. Only pairs adopting the soma-soma synapse morphology were selected for recordings ([Figure 4A](#f0004){ref-type="fig"}). To test the effects of DA on synaptic transmission between the VD4 and LPeD1, postsynaptic responses to presynaptic APs were examined using dual-clamp recordings ([Figure 4B](#f0004){ref-type="fig"}). As it has previously been shown that 10 µM DA nearly abolishes all evoked action potential firing activity in VD4 interneurons \[[@cit0004]\], we employed 1 µM DA here to ensure sufficient VD4 synaptic output and detectable LPeD1 post-synaptic response. Indicative of the formation of an excitatory synapse between VD4 and LPeD1, recordings showed a one-to-one correlation between presynaptic APs and EPSCs ([Figure 4C](#f0004){ref-type="fig"}). As commonly observed, the first EPSC from the train of five APs had a larger amplitude than the remaining four APs. We noted that DA affected the properties of the AP train, however did not change the first AP of the train. We thus compared the first EPSC elicited by the first AP, before and after DA application. We found that DA resulted in a 37.8% reduction in peak amplitude of the first EPSC (no DA: −126.15 ± 7.97 pA; DA: −78.46 ± 10.38 pA, n = 4, *p* \< 0.05) ([Figure 4D](#f0004){ref-type="fig"}). Inhibition of synaptic transmission by DA was reversed by washing with NSS bath solution (−101.33 ± 9.67 pA, n = 4).
We next sought to determine whether the DA-mediated reduction in EPSC amplitude was due to changes in vesicle release from the VD4, using the fluorescent styryl dye FM1-43 to visualize synaptic vesicle exocytosis ([Figure 4E](#f0004){ref-type="fig"}). FM1-43 labelled synaptic pairs show intensified labelling at the presynaptic side of the contact site (CS) before (left panel) and after (right panel) simulation ([Figure 4E](#f0004){ref-type="fig"}), indicating the location of the presynaptic recyclable vesicle pool. Exocytosis of FM1-43 labeled vesicles was elicited by a 5s burst of APs induced presynaptically. DA application resulted in a 70.2% (no DA: −4.7 ± 0.8 a.u.; DA: −1.4 ± 0.4 a.u.; n = 5; *p* \< 0.05) reduction in FM1-43 destaining, which could be rescued by 36.2% after wash with NSS bath solution (-3.0 ± 0.6 a.u., n = 5; [Figure 4F](#f0004){ref-type="fig"}). Fewer vesicles situated at the pre- and postsynaptic non-contact sites (non-CSs) were released in response to evoked APs and their release was insensitive to DA ([Figure 4F](#f0004){ref-type="fig"}). Taken together, these findings indicate that DA inhibited synaptic output of the VD4 through suppression of vesicle release.
DA inhibits *I*~Ca~ in the VD4 {#s0003-0003}
------------------------------
Activity-induced Ca^2+^ influx is a key determinant of presynaptic vesicle release. We first confirmed and expanded upon earlier findings by \[[@cit0004]\]. that 10 µM DA indeed inhibited the amplitude of *I*~Ca~ in the VD4 ([Figure 5A](#f0005){ref-type="fig"} and [B](#f0005){ref-type="fig"}), without affecting its activation properties ([Figure 5C](#f0005){ref-type="fig"}). However, as a non-physiological square wave (SW) protocol was used to evoke *I*~Ca~, the physiological relevance of the observed inhibition by DA was unclear. Therefore, as shown in [Figure 6A](#f0006){ref-type="fig"}, we employed pre-recorded VD4 AP waveforms (APW) as the voltage clamp command to examine the effect of the same concentration of DA on intracellular Ca^2+^ dynamics during neuronal activity. We then compared the *I~Ca~* peak amplitude induced by either APW ([Figure 6B](#f0006){ref-type="fig"}) or SW ([Figure 6C](#f0006){ref-type="fig"}) in response to 10 μM DA. We found that DA reduced the average peak amplitude of APW-evoked *I*~Ca~ by 36.9 ± 9.01% (n = 4) ([Figure 6B](#f0006){ref-type="fig"}), which was comparable with the extent of DA-mediated reduction observed in *I*~Ca~ elicited by a SW voltage step to peak APW amplitude (+30 mV) (36.10 ± 5.03%, n = 6; p\>0.05) ([Figure 6C](#f0006){ref-type="fig"}). The 10 µM DA-induced reduction of I~Ca~ evoked by SW or APW DA was consistent, as summarized in [Figure 6D](#f0006){ref-type="fig"}. Clearly, DA inhibited Ca^2+^ influx evoked by neuronal activity in the VD4.
Prepulse depolarization facilitates *I*~Ca~ in the presence of DA {#s0003-0004}
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Next, we sought to investigate the mechanisms underlying DAergic inhibition of *I*~Ca~ in the VD4. GPCR-mediated inhibition of presynaptic voltage-gated Ca^2+^ channels, via the liberated Gβγ subunit, can be detected using a prepulse depolarization that causes unbinding of the Gβγ subunit from the channel and disinhibition of *I*~Ca~ \[[@cit0047],[@cit0054]\] ([Figure 7A](#f0007){ref-type="fig"}). We found that DAergic inhibition of *I*~Ca~ (36.10 ± 5.03%, n=5) in the VD4 was significantly reduced by prepulse depolarization (26.95 ± 3.41%, n=5, *p* \< 0.05) ([Figure 7B](#f0007){ref-type="fig"} and [C](#f0007){ref-type="fig"}). The prepulse had no effect on *I*~Ca~ in the absence of DA ([Figure 7B](#f0007){ref-type="fig"} and [C](#f0007){ref-type="fig"}). These findings suggest that DAergic inhibition of *I*~Ca~ in the VD4 involved Gβγ-dependent signalling.
DA inhibits ionomycin-induced synaptic vesicle release from the VD4 {#s0003-0005}
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Several studies have shown that neuromodulators can also inhibit presynaptic vesicle release in neurons independently of their effects on Ca^2+^ dynamics, such as through direct G protein-dependent interaction with the exocytic machinery \[[@cit0070],[@cit0011],[@cit0012],[@cit0040],[@cit0041],[@cit0078],[@cit0093],[@cit0100]\]. To investigate the possibility that DA also modulates VD4 synaptic release downstream of Ca^2+^ influx, we employed the ionophore ionomycin to mediate Ca^2+^ entry into the cell independently of voltage-gated Ca^2+^ channels \[[@cit0018]\]. Upon addition of ionomycin, the linear relationship between extracellular Ca^2+^ concentration and FURA-2 imaging of intracellular Ca^2+^ concentration indicated that the source of the Ca^2+^ influx is from the extracellular bath ([Figure 8A](#f0008){ref-type="fig"}). First, we confirmed that ionomycin-induced Ca^2+^ influx was sufficient to trigger vesicle release by monitoring intracellular Ca^2+^ concentration and vesicle release using FURA-2 fluorescence and FM1-43 destaining, respectively ([Figure 8B](#f0008){ref-type="fig"}). We observed that ionomycin caused a rapid influx of Ca^2+^ that then reached an equilibrium level and remained constant. In parallel, FM1-43 fluorescence traces showed two components: a rapid exponential decrease in fluorescence directly after ionomycin application, followed by a slow linear decay in fluorescence. Finally, we examined the effects of DA on ionomycin-induced vesicle release. Interestingly, exogenous DA was still able to attenuate ionomycin-induced vesicle release in the VD4 by 66.9% (no DA: 221.2 ± 35.6 a.u., n = 6; DA: 73.3 ± 11.5 a.u., n = 4; *p* \< 0.05) ([Figure 8C](#f0008){ref-type="fig"} and [D](#f0008){ref-type="fig"}). Taken together, these results indicate that DA also inhibited VD4 synaptic output via voltage-gated Ca^2+^ channel-independent mechanisms.
Discussion {#s0003-0006}
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In this study, we examined the effects of DA on *I*~Ca~ and vesicle release in a well-characterized molluscan interneuron synapse model. We demonstrated for the first time that DAergic inhibition of synaptic output is mediated through both voltage-dependent and -independent inhibition of voltage-gated Ca^2+^ channels, and voltage-gated Ca^2+^ channel-independent suppression of vesicle release.
The DAergic system in *L. stagnalis* {#s0003-0007}
------------------------------------
In mammalian neurons, DA broadly regulates neurotransmission through activation of a family of GPCRs, which are divided into two major classes based on their structural, pharmacological, and signalling properties: D1 and D5 receptors belong to the subfamily of D1-like receptors, whereas D2, D3, and D4 receptors are grouped into the D2-like receptor class. Both D1/3- and D2/4-like receptors have been identified in *L. stagnalis* based on their pharmacological properties, albeit with differing sensitivities to various agonists and antagonists as compared to their vertebrate counterparts \[[@cit0086],[@cit0003],[@cit0048],[@cit0069],[@cit0094]\]. The D1- and D2-like receptors in *L. stagnalis* exhibit differential expression patterns, with the former present on growth cones and the latter on the soma \[[@cit0026]\]. The effects of DA on the VD4 are shown to be mediated by D2-like receptors, as it has been shown that the effets of both synaptically released DA from the RPeD1 and exogenously applied dopamine on the VD4 can be blocked *only* by sulpiride, a D2 receptor antagonist \[[@cit0068]\]. Indeed, DAergic inhibition of *I*~Ca~ in the VD4 \[[@cit0004]\] is consistent with observations of D2 receptor effects in mammalian CNS \[[@cit0074],[@cit0016],[@cit0050],[@cit0073]\]. While the downstream targets and signaling mechanisms of D2-like receptors in *L. stagnalis* remain unclear, previous studies \[[@cit0062],[@cit0061]\]; Knol *et al.*, 1995) and our sequence analyses of G protein subunits ([Figure 2](#f0002){ref-type="fig"}) in the *L. stagnalis* CNS have demonstrated that they are highly homologous to their vertebrate counterparts. Taken together, *L. stagnalis* provides a conserved model for studying DAergic regulation of interneuron function.
There are several potential limitations to the cultured VD4 interneuron electrophysiological experimental model employed in studies thus far, including our current report, in recapitulating the physiological conditions of DAergic modulation of interneurons in *L. stagnalis*. As the VD4 likely receives pulsatile DAergic input from the presynaptic rhythmically active pacemaker neuron RPeD1 \[[@cit0085],[@cit0088]\], the bath-applied tonic DA treatment may not fully mimick the effects of phasically released DA on VD4 membrane and synaptic properties *in vivo.* While the sensitivity of cultured VD4 interneurons to bath-applied DA has been characterized \[[@cit0004]\], it is yet unclear what range of DA concentrations act on the VD4 interneuron *in vivo*.
Voltage-dependent and independent inhibition of *I*~Ca~ by DA {#s0003-0008}
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Activity-induced Ca^2+^ influx is a key determinant of presynaptic vesicle release \[[@cit0104]\]. A reduction in the amount of Ca^2+^ influx through voltage-gated Ca^2+^ channels at the active zone would efficiently reduce the probability of synaptic vesicle fusion and therefore neurotransmission \[[@cit0058],[@cit0046]\]. Previous studies have reported that DAergic inhibition of synaptic output in interneurons is associated with reductions in *I*~Ca~ in mammalian interneurons \[[@cit0099],[@cit0016]\]. In this study, we confirmed and expanded upon the findings of \[[@cit0004]\]. by demonstrating that DA inhibits voltage-dependent Ca^2+^ influx elicited by physiologically relevant stimuli, i.e. action potential waveforms, in the VD4. These findings suggest that DA likely inhibits activity-induced Ca^2+^ influx in the presynaptic terminal that is required for neurotransmitter release.
Prepulse facilitation of VD4 *I*~Ca~ in the presence of DA indicates that this inhibition is mediated in part through voltage-dependent G-protein--mediated inhibition, which is shown to be mediated through direct binding of membrane-delimited Gβγ to cytoplasmic regions of the α1 subunit of Ca~V~2 family of voltage-gated Ca^2+^ channels, resulting in delay of the activation kinetics and a depolarizing shift in the activation voltage of the channel \[[@cit0027],[@cit0005],[@cit0031],[@cit0036],[@cit0047],[@cit0054],[@cit0103]\]. In this study, we observed only a reduction in *I*~Ca~ amplitude without changes in its activation kinetics. As the effects of Gβγ-mediated inhibition are shown to be dependent on the Ca~V~ β subunit subtype \[[@cit0017],[@cit0032]\], this may in part be due to differences in the *L. stagnalis* and mammalian Ca~v~ β subunit properties. A previous study reported that the *L. stagnalis* Ca~V~2 ortholog, *L*Ca~V~2, does not exhibit prepulse facilitation when co-expressed in HEK-293T cells with rat orthologs of the Ca~V~2 channel accessory subunits α2δ1 and β1b and G protein subunits β1 and γ2 \[[@cit0051]\]. As protein-protein interaction between LCa~V~2 and rat Gβ1γ2 was not directly confirmed in the study, and given the sequence divergence we observed between *L. stagnalis* and vertebrate Gβ ([Figure 2C](#f0002){ref-type="fig"}), Gγ ([Figure 2D](#f0002){ref-type="fig"}), and Ca~V~2 channel Gβγ binding sites ([Figure 3](#f0003){ref-type="fig"}), the discrepancies between our findings may be attributable in part to non-canonical associations between LCa~V~2 and mammalian Gβγ protein. In addition, endogenous factors present in *L. stagnalis* neurons but absent in HEK-293T cells may also be required for the G protein-mediated voltage-dependent regulation of LCa~V~2 channels observed in this study. Figure 3.Protein sequence alignment and phylogenetic tree of the Cav2 channel in *L. stagnalis*. *A*, Amino acid sequence comparison of the Gβγ binding sites on the single *L. stagnalis* Cav2 channel isoform, LCav2, N-terminus cytoplasmic tail (*A1*) and I-II linker region (*A2-3*) with vertebrate orthologs of Cav2.1 and Cav2.2. Conserved and similar sequences in alignments are colored as black and grey boxes, respectively. Gaps are denoted by dashes. *B*, Phylogenetic analysis was conducted by the Maximum Likelihood method using the JTT+G model. Bootstrap value from 500 replicates are shown next to each node. The scale bars indicate the estimated evolutionary distance in the units of the number of amino acid substitutions per site. Figure 4.DA inhibits vesicle release from VD4 interneurons. *A*, DIC image of a soma-soma synaptic pair. VD4 and LPeD1 were isolated and placed in culture for 24 hours to allow for soma-soma synapse formation. *B*, Schematic of the dual-clamp configuration to simultaneously monitor pre- and post-synaptic activity in synaptically paired VD4 and LPeD1. *C*, Representative traces of simultaneous pre-synaptic action potentials (APs) recoreded from VD4 cell and excitatory post-synaptic currents (EPSCs) recorded from LPeD1 cells, before (left) and after (right) DA application. *D*, Summary of the amplitude of the first EPSCs recorded from LPeD1 cells, before (Ctrl), during (1 µM DA) and after (Wash) dopamine application. *E*, Representatives of FM1-43 imaging showing distribution of FM1-43 staining with high intensity at the cell-contact region (arrow, CS), as well as the sites of non-contact site (white dashed line ovals) at the pre- (Pre Non-CS, VD4 cell) and post-synaptic cells (Post non-CS, LPeD1 cell) respectively. FM1-43 labelling before (left panel) and after (right panel) action potential stimuli in VD4 cells. The reduction in fluorescence intensity at CS indicates the presynaptic vesicle release. *F*, Summary of the changes in FM1-43 signal at the different regions indicated in *E*, showing DA inhibits vesicle release from the VD4 at the CS, but not at non-CSs. The patterns of the bars showing the sites of the images were taken, and the sequence of the bars with different background color shows the recording conditions, in order of control (first bar, white), 1 uM DA (second bar, grey) and wash (third bar, white), at indicated sites where fluorescent intensities were taken. \**p* \< 0.05. Figure 5.DA inhibits *I*~Ca~ in VD4 interneurons. *A*, Whole cell voltage clamp recordings were performed in VD4 interneurons to characterize the effects of DA on *I*~Ca.~ Representative traces of *I*~Ca~ elicited by SW voltage steps in the VD4 before (left) and after (right) DA application. *B*, Representative IV relationship of peak *I*~Ca~ before and after DA application, and after washout. *C*, Representative activation curves of *I*~Ca~ before and after DA application. Figure 6.DA inhibits action potential waveform (APW)-evoked *I*~Ca~ in VD4 interneurons~.~ *A*, To mimic physiologically relevant neuronal activity, APs recorded from a VD4 interneuron were used to elicit *I*~Ca~ in whole cell voltage-clamped cultured VD4 interneurons. Upper panel: APWs recorded from VD4 cells were used as the stimulus protocol. Lower panel: the inward I~Ca~ recorded in response to each APW stimulus. *B*, Representative traces of APW-evoked *I*~Ca~ in the absence or presence of DA. *C*, Representative traces of *I*~Ca~ evoked by a square-waveform (SW) voltage step from the resting membrane potential of −70 mV to +30 mV, the APW peak amplitude (+30mV), in the absence or presence of DA. *D*, Comparable reductions are observed in SW- and APW-evoked *I*~Ca~ in the presence of DA. \* *p* \< 0.05. Figure 7.Prepulse facilitation of *I*~Ca~ in VD4 interneurons in the presence of DA. *A*, The prepulse protocol employed in whole cell voltage clamp recordings of VD4 interneurons. *B*, Representative traces of *I*~Ca~ evoked by the test pulse without (solid line) and with (dashed line) a prepulse, in the absence or presence of DA. *C*, Significant recovery of *I*~Ca~ by prepulse depolarization is observed only in the presence of DA. *\* p* \< 0.05. Figure 8.DA inhibits vesicle release from VD4 interneurons downstream of Ca^2+^ influx. *A*, Ionomycin-evoked Ca^2+^ influx in the VD4 interneuron, as measured by averaged FURA-2 signal from four proximal-membrane regions (inset), is proportional to extracellular Ca^2+^ concentration (\[Ca\]~o~). *B*, Ionomycin-induced Ca^2+^ influx, as measured by FURA-2 signal (grey), is sufficient to induce vesicle release, as indicated by FM1-43 destaining (black). *C*, Representative FM1-43 destaining curve upon ionomycin application (arrow) in the absence (filled) or presence (open) of DA. *D*, Ionomycin-induced vesicle release from VD4 interneurons is significantly reduced in the presence of DA. \* *p* \< 0.05.
The depolarizing prepulse relieved only ∼30% of DAergic inhibition of *I*~Ca~ in the VD4 in our study, suggesting that DA also inhibited *I*~Ca~ through a voltage-independent mechanism. G protein-mediated voltage-independent inhibition of LCa~V~2 in the VD4 has been reported to be mediated through the Gα subunit and increases in cAMP levels, with a slow time course on the scale of minutes \[[@cit0051]\]. Slow but persistent voltage-independent G protein-mediated inhibition of voltage-gated Ca^2+^ channels has also been well-documented in mammalian neurons \[[@cit0009],[@cit0006],[@cit0007],[@cit0022],[@cit0056],[@cit0066],[@cit0083],[@cit0087],[@cit0102]\] and shown to be mediated by a variety of mechanisms, including regulation of Ca~v~ surface expression levels through direct interaction with GPCRs \[[@cit0059],[@cit0060]\] and phosphatidylinositol 4,5-bisphosphate (PIP~2~) depletion \[[@cit0049],[@cit0038]\] and kinase activation \[[@cit0080],[@cit0025]\].
Parallel activation of voltage-dependent and independent inhibition of voltage-gated Ca^2+^ channels has been hypothesized to allow for fine-tuning of intracellular Ca^2+^ levels and activity-dependent plasticity \[[@cit0066],[@cit0014],[@cit0051],[@cit0076],[@cit0095]\]. The relative ratio between voltage-dependent and -independent modes of inhibition in chick sensory neurons is shown to be critically dependent on intracellular Gβγ concentration \[[@cit0064]\]. Activation of D2 receptors induces both voltage-dependent and -independent inhibition of the N-type voltage-gated Ca^2+^ channels in HEK-293T cells \[[@cit0060]\] and differentiated NG108-15 cells \[[@cit0015]\]. Consistent with the previous reports, our findings demonstrated DA effects are mediated by both voltage-dependent and -independent inhibition. It is likely that the synaptically released DA level onto interneurons varies, and thus can differentially modify interneuron intracellular Ca^2+^ dynamics and synaptic output, thereby inducing cellular and circuit-wide plasticity.
DAergic inhibition of vesicle release downstream of Ca^2+^ influx {#s0003-0009}
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In neurons and secretory cells, GPCRs can inhibit vesicle release in parallel with changes in *I*~Ca~ \[[@cit0070],[@cit0018],[@cit0024],[@cit0077],[@cit0084]\]. This inhibition can occur through direct binding of the Gβγ subunit to the C-terminus of the SNARE protein SNAP-25, thereby displacing synaptotagmin and preventing vesicle exocytosis \[[@cit0040],[@cit0093],[@cit0105]\]. Gβγ is also known to interact with several other proteins involved in synaptic vesicle release, including syntaxin, VAMP, CSP and synaptotagmin \[[@cit0055]\]. Binding of Gβγ to these proteins may alter their function and/or interaction with other proteins in the exocytic machinery, thereby inhibiting vesicle release downstream of Ca^2+^ influx \[[@cit0090]\]. While no direct interaction between G protein and presynaptic proteins have been reported in *L. stagnalis*, they are shown to be homologous in structure and function to their vertebrate counterparts ([Figure 2](#f0002){ref-type="fig"}) \[[@cit0062],[@cit0061]\]; Knol *et al.*, 1995; \[[@cit0035],[@cit0043]\]. Here we employed the ionophore ionomycin to induce Ca^2+^-dependent synaptic release independently of voltage-gated Ca^2+^ channel activation, as it has been shown in hippocampal neurons that ionomycin-induced synaptic release is unaffected by the voltage-gated Ca^2+^ channel blocker Cd^2+^ \[[@cit0018]\]. We demonstrated that DA inhibits vesicle release from VD4 interneurons downstream of activity-induced Ca^2+^ influx. Our finding suggests that *L. stagnalis* may serve as an easily tractable model in which to elucidate the molecular mechanisms of G protein-mediated modulation of synaptic release.
Potential functional significance of redundant mechanisms of DAergic inhibition of synaptic transmission in interneurons {#s0003-0010}
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In this study, we provide the first demonstration that inhibition of *I*~Ca~ and direct inhibition of synaptic vesicle release all contribute to DAergic presynaptic inhibition in interneurons. It may be hypothesized that whereas the Gβγ subunit-mediated voltage-dependent inhibition allows for rapid activity-dependent regulation of synaptic transmission, the voltage-independent inhibition of *I*~Ca~ and direct inhibition of vesicle release machinery may allow for more persistent and nuanced inhibition of interneuron synaptic output \[[@cit0066],[@cit0014],[@cit0051],[@cit0076],[@cit0095]\]. Indeed, strong but modifiable inhibition of the VD4 activity may be integral to respiratory control in *L. stagnalis*. In the context of the respiratory CPG network, the VD4 controls the muscles that close the pneumostome \[[@cit0089]\]. Increased firing of the RPeD1 neuron, which results in increased DA release onto VD4, coincides with opening of the pneumostome and initiation of the inspiration phase \[[@cit0088]\]. Therefore, complete inhibition of VD4 output during this phase is likely crucial to prevent interruption of inspiration and thus generating normal rhythmic respiration behaviour. In addition, the capacity for activity-dependent plasticity in the VD4 response to DA, endowed by voltage-dependent inhibition of voltage-gated Ca^2+^ channels, may be important for the well-documented hypoxia and learning-induced modulation of CPG activity and aerial respiration behaviour in *L. stagnalis* \[[@cit0067],[@cit0008]\].
Conclusion {#s0003-0011}
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In this study, we provide the first demonstration that DA suppresses synaptic output of a molluscan respiratory interneuron through both voltage-dependent and -independent inhibition of *I*~Ca~, and voltage-gated Ca^2+^ channel-independent inhibition of synaptic vesicle release. In future studies, the relative sensitivity and function of each pathway and any potential interactions between them will be further investigated to expand our understanding of the fundamental mechanisms that shape interneuron function and neuronal network dynamics.
Disclosure of potential conflicts of interest
=============================================
No potential conflicts of interest were disclosed.
Acknowledgments
===============
This work was supported by an operating grant from the National Sciences and Engineering Research Council of Canada to HSS (RGPIN-2016-04574) and ZPF (RGPIN-2014-06471). ND was a recipient of Canadian Graduate Studentship of NSERC (NSERC-CGS-D). The funder had no role in study design, data collection and analysis, decision to publish or preparation of the manuscript.
Author contributions
====================
ZPF conceived and designed research, DL performed experiments; DL & ND analyzed data and prepared figures; ND, DL, HSS, ZPF interpreted results of experiments and wrote the manuscript.
[^1]: These authors contributed equally to this work.
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If you frequent comic conventions, there's a good chance you've spotted the iconic banner of the Wuvable Oaf at one point or another. The large hairy, naked wrestler wearing nothing more than pink underwear with a cat's face in front, his scary eyes glaring and taunting you to come over through shear intrigue and curiosity. Or fear. Creator Ed Luce has the Wuvable Oaf collected hardcover coming out from Fantagraphics this month, collecting the first five years of his wildly entertaining comic. The wuvable creator was on hand at WonderCon this past weekend and was nice enough to sit down and answer a few of my oafish questions.
Cameron Hatheway: Tell me all about Wuvable Oaf. How did it all begin? What makes him so wuvable?
Ed Luce: Well he started out actually as a paper doll design. I was asked to contribute to a paper doll themed show, and the core of the character, the most recognizable image of him is completely naked but has a little pair of underwear on with a cat face on the front of it. So that was the blank doll, and he's scary looking obviously, he has pink eyes and this grill of pink teeth, a heavy beard and he's hairy. All his outfits around him were The Smiths t-shirts, or a onesie pajama pants with cats crawling all over it, or a powdered blue jogging suit. So the Wuvable Oaf concept was kind of set up there.
I moved up to San Francisco after that and started to go to comic book shows and had a lifelong interest in comics, but never thought I could make one, until I went to the Alternative Press Expo and discovered the Prism Comics booth there. Prism Comics is a non-profit LGBT organization that supports queer comic creators. And I was paging through, and I thought, "This is great! I didn't know this existed," but I didn't see a character whose story I felt reflected my own experience. You know the best way to create something is to fill a vacuum or create something that you want to see. That's kind of how the Oaf was born, I just said, "You know, I'm sick of seeing these big heavy guys either be the villains in comics, or the butts of a lot of jokes, without any kind of telling their story from their point of view." I am not a big guy, but I know a lot of big guys. The character was influenced by a lot of my friends, so he's kind of an amalgam of a lot of my friends. If you're a student of comics, you can see him making a lot of references to Nancy; Sluggo from the Nancy comics, Bluto from the Popeye comics, he's kind of that type but he's been given the center stage, so that's the heart of the comic.
CH: How much of yourself did you put into Oaf? For instance, are you a retired professional wrestler? How many cats do you own?
EL: I call it "exaggerated autobio." My life is not that interesting in of and itself, like from a memoir standpoint, but I think my perspective is. There are a lot of nuggets of truth in the comic, especially from my dating experience. The dynamic in the comic is of this big, oafish guy, who kind of likes smaller guys. That's been kind of my dating dynamic, prior to meeting my partner of course. But I always say the Oaf is me on the inside, I'm not physically that size but he's kind of the guy that my mom raised, the "mama's boy." He's very friendly, a people pleaser. The Eiffel character, his sort of primary love interest, is more physically me. He's smaller and also the negative side of my personality, like all the pettiness and jealously and all of that. They kind of are represented in these two characters. And when they get together it becomes this weird, almost self-portrait, like a comic conceptual self-portrait. So that part of it is very much me. But also as I said, a lot of the characters are based on friends, and again I know a lot of big guys who I base the characters on them.
I do have one cat. A lot of people see the comic and think I'm a cat hoarder, and I'm not! The cats ended up in the comic because I had ended a long-term relationship when I moved to San Francisco, and we had cats, and I didn't want to break them up too, so I left them with my Ex and I just miss my cats. They kind of also are fun to play off of the big scary guy; the cute kitties and the big scary guy, there's a nice tension that kind of develops. And I think people are just also attracted to cats. That was a nice byproduct of what I put out there. To a certain degree you try to control, and you put out a message, and you think you know how people are going to react. But when you put something out into the world, that's what's great about art, it gets picked-up and turned into something else by the feedback and peoples reaction to it. The cats have definitely become a big part of the storyline. I've given them their own storyline, a lot of their part in the book is just me trying to explain their weird behavior, the kind of unknowable feline psychology works its way into the book. I only have one cat strangely enough. We waited several years before we got that one. She's one cat, but has many personalities, so I think she's a legion, a split-personalities of cats in one cat, so one is enough for me.
CH: Can we expect to see a plush doll line of the cats stuffed with your body hair?
EL: Oh god no! I don't think I have strength. My partner is fairly furry but he doesn't grow his hair back as quickly as the Oaf does. I mean I've looked at merchandising for toys and things like that. When I make merchandise, I'm more of make what I would buy, so I don't own a lot of stuffed animals. But I have gotten into the figure market a little bit. I'm lucky enough to have a collaborator in Erik Erspamer, he's a Phoenix based sculptor and he's been making figures for me. The stuffed doll thing, maybe somewhere down the line we could get into licensing and doing that, I would love to—
CH: Like maybe one of those WWE Brawlin' Buddies!
EL: Yeah totally! We could do that, I'm just a licensing agreement away.
CH: What's the reception been like in the LGBT community? Are people fans of the character, or feel like he's putting bears in a negative light?
EL: I would say I made this character for this bear community. He's never called a "bear" in the comic, I feel like I avoided labels, I didn't even want to use the words "gay" or "queer" or "bear" anywhere in the book because I think it's all really obvious. And in that sense its left it open for everybody even outside of the gay community to appreciate it, but really it's a valentine to that group, and I never expected anybody outside of that to appreciate it. They've hung with me, I haven't really gotten any kind of criticism from the gay community. It's interesting especially in the last couple weeks the big book has come out from Fantagraphics, it seems like my queer audience is there, it's devoted, but it's almost being eclipsed by a straight audience now. Especially at this show, so many guys have come up and said, "That's me! You're ripping-off my life story!" Jokingly, but they really respond to the kind of hyper masculinity of it, I think there's a lot of body positivity that comes out of this character. Big hairy guys are not always well-received in mainstream pop culture, but people see him and they're like, "Oh it's a celebration of me. I don't have to feel weird and awkward about being big and hairy and maybe a little sweaty, maybe take up a little too much space," so it does, it sort of celebrates that type.
It's interesting you should mention has there been any kind of criticism or critique from the gay community, there hasn't from the gay community at large from the audience, but I do feel, and not to focus on the negative, but occasionally I get critiques from other queer comics creators that my comic isn't "gay enough." That it doesn't have enough explicit sex or nudity in it. I made a decision really early on that I love that in other people's work, I like Tagame, and Jiraiya, there are definitely people who are really good at doing that, but I wanted the focus of my book to be elsewhere and I think some great creators think that explicit sex and gay comics have to go together—
CH: And it just might not be your cup of tea.
EL: It's not. I had an art career as a painter for years and I did really kind of more explicit illustration in painting works, so when I got to this project, it's a pop medium. I wanted it to be accessible to that large audience. It seems to have been as I've said, as a pleasant side-effect, it's working. Not just a lot of straight guys but women like the character, and the cats, and the story. If I've received any kind of negativity, occasionally I'll get "sex positive," that kind of academic term gets thrown at me a little bit, and although my book doesn't have sex in it, it's not "sex positive," but there are some sexual situations in there but I think they're more—I call them "situational erotics," they're more incidental exposures. I call it "The Galifianakis Factor." In a lot of his films he's naked and it's meant to gross-out one part of the audience, but I know a large part of the audience also finds it endearing, so I kind of work that angle a lot in my comics too.
CH: You made him bearable.
EL: Exactly, pun intended.
CH: You have the Wuvable Oaf hardcover coming out this month from Fantagraphics. What's it like to finally have the result of years' worth of blood, sweat & tears in your hands? Any special features in the back?
EL: It's exciting. It's really fulfilling. I've been buying Fantagraphics books since I was a teenager, so to kind of fit into that echelon of creators—I'm not trying to be arrogant or brag, but when they send the checks out, in the corner it's got a Jaime Hernandez drawing and it says, "We publish the world's greatest cartoonists," so I can't quite get my head around that, to be kind of considered in that league, and I'm certainly not, but to be welcomed into that family has been certainly great. And again I did not expect these comics, these are the first comics I've ever made, to reach such a wide audience, so there's a little hesitation and I'm a little freaked out by how big the audience has potentially become for this. Just because I sort of see things in the art, mistakes I may have made that nobody else can see.
But other than that to finally get everything collected, there are dozens of comics represented in this, the first five years of my work. It's been great, Fantagraphics did a beautiful job with the hardcover, putting it together. They put their full faith and backing into it, from a promotional standpoint as well. There's not a lot of new work in there, they specifically wanted to collect everything I've done before because it's been hard to get your hands on it until now, but I think the feature that some of the editors were most excited about was the back portion of the book is all profiles on each of the characters based on the Marvel Universe Handbook that used to come out in the '80s. It's totally in that format, and I'm excited about that too because it allows a little window to the history of the characters that I can't get at in the main storyline. They have fake superpowers and all that sort of stuff. I think when people at shows like this, WonderCon being a sort of superhero venue, they open that book and sort of see how that's influenced my work. You may not think that as an indie artist that I was influenced by Marvel and DC, but that's what I bought from the get go. That kind of aspect of it is I think good bonus material.
CH: Going back to the check really quick, do you have that laminated just in case anyone has a critique for you? Do you just whip it out and point to the corner?
EL: [Laughter] No I definitely kept them. I haven't done anything with them yet, but I definitely took a picture of it and posted it with my address blurred out. I think that definitely upset some of my friends and fellow creators, but it is what it is.
CH: Music plays a big part in the comic. If you ever decide to retire from comics, can we expect to see you form the band Ejaculoid and tour the country?
EL: You know, Ejaculoid exists already. I've released three singles, actual music singles, from friends of mine that are in the bands Limp Wrist and Talk Is Poison, they're in a band called Needles and they've recorded as though they are Ejaculoid. We've released three singles on vinyl, and have digital downloads that accompany it. I actually then had a couple other bands expand those songs and do covers of them for another project called Oafanthology which is other artists and creators like Tom Neely and Johnny Ryan drew my characters, and it made sense to them to release a record version of that with covers songs. Harassor is a Los Angeles black metal band, they did a full-on black metal version of the song, and Author & Punisher is sort of a doom industrial sort of one man band, and they also did a cover of the song as well. Yeah I've already started releasing music under the name. I don't think I'd ever form a band, I'm not musically inclined at all so I would avoid that. That might bring a negative light onto my project, but I'm really open-minded to working with musicians to continue to record music.
CH: Any other projects you're currently working on, or is it just Wuvable Oaf and world domination?
EL: I'm really committed to Wuvable Oaf at this point, especially touring behind the book. We're going all over the place in the next three months including London, England, which I'm really excited about. And Canada. I'm looking forward to kind of pushing him as far as I can. After that, I have subsequent storylines, it picks up with issue five, so it'll be a different Oaf. I think of Oaf as a type—it's not necessarily the titular character, it's also a type of guy. There's another character in the book, Smusherrrr, my best friend is writing that story arc because the character is based on him. We'll be exploring another corner of the Oaf Universe, the "Oafiverse" as I call it. I mean I'm always open to continue to work on things. I was a part of the Henry & Glenn Forever project, so I did a story in that, and I always sort of contribute little things to that, Henry Rollins and Glenn Danzig in a domestic partnership. Kind of the ultimate in fan-fiction. I've been doing alternate covers for other artists at Image and things like that. I'll always been working on the Oaf, that's my main project, my main platform to talk about everything I'm interested in, so definitely Oaf for the foreseeable future.
Special thanks to Ed for taking time out of his busy schedule during WonderCon to talk all-things Wuvable Oaf with me. You can find more of his work at his website or follow him on Twitter.
Cameron Hatheway is a reviewer and the host of Cammy's Comic Corner, an audio podcast. You can pitch him on a Wuvable Cammy plush on Twitter @CamComicCorner. |
---
abstract: |
We use topological methods to prove a semicontinuity property of the Hodge spectra for analytic germs defined on an isolated surface singularity. For this we introduce an analogue of the Seifert matrix (the fractured Seifert matrix), and of the Levine–Tristram signatures associated with it, defined for null-homologous links in arbitrary three dimensional manifolds. Moreover, we establish Murasugi type inequalities in the presence of cobordisms of links.
It turns out that the fractured Seifert matrix determines the Hodge spectrum and the Murasugi type inequalities can be read as spectrum semicontinuity inequalities.
address:
- 'Institute of Mathematics, University of Warsaw, ul. Banacha 2, 02-097 Warsaw, Poland'
- 'A. Rényi Institute of Mathematics, 1053 Budapest, Reáltanoda u. 13-15, Hungary.'
author:
- Maciej Borodzik
- András Némethi
title: The Hodge spectrum of analytic germs on isolated surface singularities
---
[*Dedicated to Joseph Steenbrink*]{}
Introduction
============
In a series of articles [@BN; @BN2] (see also [@BNR; @BNR2]) the authors developed a topological method to prove the semicontinuity of the Hodge spectrum in low dimensions, which originally was obtained by purely Hodge theoretical methods (that is, by algebraic or analytic machinery). This topological method worked successfully for local plane curve singularities, or for two-variable complex polynomials (for the mixed Hodge structure at infinity). It was even possible to compare the spectrum at infinity with local spectra of singular points of a fixed fiber of a polynomial map. The approach used only topological, not analytic, arguments; the idea was that upon using the polarization properties of the mixed Hodge structure, the spectrum was characterized by the Levine–Tristram signatures of the Seifert form. Next, in the presence of a deformation, using the corresponding topological cobordism one proved a Murasugi type inequality valid for the Levine–Tristram signatures. This inequality was reinterpreted as a spectrum semicontinuity property.
Having these results, it was natural to ask if these method can be generalized to germs $g:(X,0)\to (\C,0)$ defined on an arbitrary isolated surface singularities $(X,0)$; in fact, this question was asked explicitly by J. Steenbrink at the meeting in Lille in 2012 during a presentation of the first author.
The point is that a possible generalization was obstructed seriously already at its starting point: if the link $M$ of $(X,0)$ (which is an oriented 3–manifold) is not a rational homology sphere, then one cannot associate with the link of $g$, $L_g\subset M$, a Seifert form, and all the linking theory of cycles in $M$, intensively used in the previous cases, was missing.
There is also a second warning. Although in the literature there are a few different proofs for the semicontinuity property of [*hypersurface*]{} singularities (see [@St; @Var; @Var2]), in this general context the semicontinuity was not even formulated, and it is not so clear what would be a possible Hodge theoretical proof for it. In this general case even the computation of the spectrum in concrete examples might create problems, hence we lack even key examples.
The goal of the present note is to surmount all these difficulties, and to propose and prove a possible semicontinuity inequality. Since in the classical case of hypersurfaces, the semicontinuity of the spectrum had several strong applications (mostly as obstructions for deformations), we expect that the present results will also find their applications regarding deformations of these more general objects.
The main novelty is the definition of the [*fractured Seifert form*]{}, defined on the subspace $\ker(H_1(\S)\to H_1(M))$ of $H_1(\S)$ ($\S$ being the Milnor fiber of $g$). Moreover, we establish for this new object all the important properties of the classical Seifert form, and its relation with monodromy and intersection forms. In this presentation we use intensively the language of hermitian variation structures of [@Nem2].
For this fractured Seifert form we can consider the analog of the Levine–Tristram signatures, and we prove Murasugi type inequality in the presence of a cobordism. Furthermore, one of the main results shows that the fractured Seifert form determines the Hodge spectrum, hence, as in the old case, the Murasugi type inequalities for the signatures provide semicontinuity properties for the spectrum.
Unless specified otherwise, the homologies usually mean homologies with rational coefficients. For a set $A$, the symbol $|A|$ denotes the cardinality. All the manifolds are assumed to be oriented.
Hermitian variation structures – Generalities {#S:HVS}
=============================================
Hermitian Variation Structures (in short HVS) were introduced in [@Nem2] as a way to encode the ‘homological Milnor package’ of the Milnor fibration. It turns out that they can be used to connect knot theory with Hodge theory via the Seifert form of the link. This approach was exploited in [@BN]: in this language, the Levine–Tristram signatures for links correspond to the spectrum of a HVS.
Review of hermitian variation structures {#s:reviewHVS}
----------------------------------------
First recall the definition of a HVS. In contrast with e.g. [@BN] or [@BN2] we will deal with non-simple variation structures as well.
\[def:HVS\] [@Nem2] For a fixed sign $\ef=\pm 1$, an *$\ef$–hermitian variation structure* consist of a quadruple $(U;b,h,V)$, where
- $U$ is a complex linear space;
- $b\colon U\to U^*$ is an $\ef$–hermitian endomorphism;
- $h\colon U\to U$ is an automorphism preserving $b$;
- $V\colon U^*\to U$ is an endomorphism.
These objects should satisfy the following compatibility relations: $$V\circ\, b=h-I\text{ and }{\overline{V}}^*=-\ef V\circ\, {\overline{h}}^*
\ \ \ \ \ \mbox{(`Picard--Lefschetz' formulae)}.$$ Here ${\overline{\cdot}}$ denotes the complex conjugate and $\cdot^*$ the duality.
In our applications in the next sections we shall always choose the sign $\ef=-1$. Sometimes we refer to the *dimension* of a HVS as the dimension of the underlying linear space $U$. The prototype of a HVS is provided by a Milnor fibration of an isolated hypersurface singularity $(\C^{m+1},0)\to (\C,0)$: $U$ is the middle homology $H_m(F)$ of the fiber, $b$ the intersection form on it, $h$ the monodromy, and $V$ is the variation operator, see Section \[ss:clas\]. In this case $\ef=(-1)^m$.
If $V$ is an isomorphism, then we say that the HVS is *simple*. In such a case $V$ determines $b$ and $h$ completely by the formulae $h=-\ef V({\overline{V}}^*)^{-1}$ and $b=-V^{-1}-\ef {{\overline{V}}^*}^{-1}$. If $V$ fails to be an isomorphism, then necessarily $1$ must be an eigenvalue of $h$.
If $b$ is an isomorphism, we say that the HVS is [*non-degenerate*]{}. Then $V=(h-I)b^{-1}$, hence the HVS is completely determined by the underlying *isometric structure* $(U;b,h)$, see [@Nem2 Remark 2.6a] and [@Milnor-forms] for the definition of the isometric structure.
Examples of HVS
---------------
Here we shall follow closely [@Nem2; @BN] (some sign conventions differ from [@Nem2]). For $k\ge 1$, $J_k$ denotes the $(k\times k)$–Jordan block with eigenvalue $1$.
\[ex:mv2k\] For $\lambda\in\mathbb{C}^*\setminus S^1$ and $k\ge 1$, the quadruple $${\mathcal{V}}_{\lambda}^{2k}=\left(\mathbb{C}^{2k};\left(\begin{matrix}0&I\\\ef I&0\end{matrix}\right),\left(\begin{matrix}\lambda J_k&0\\ 0&(1/\bar{\lambda})\cdot {J_k^*}^{-1}\end{matrix}\right),\left(\begin{matrix}0&\ef(\lambda J_k-I)\\ (1/\bar{\lambda})\cdot {J_k^*}^{-1}-I&0\end{matrix}\right)\right)$$ defines a simple and non-degenerate HVS. Moreover, ${\mathcal{V}}_{\lambda}^{2k}$ and ${\mathcal{V}}_{1/\bar{\lambda}}^{2k}$ are isomorphic.
\[ex:mvlambda\] For any $k\ge 1$ there are precisely two non-degenerate $\epsilon$–hermitian forms (up to a real positive scaling), denoted by $b^k_\pm$, such that $${\overline{b}}^*=\ef b\text{ and }J_k^*bJ_k=b.$$ By convention, the signs are fixed by $(b^k_{\pm})_{1,k}=\pm i^{-m^2-k+1}$, where $\epsilon=(-1)^m$. The entries of $b$ satisfy: $b_{i,j}=0$ for $i+j\leq k$ and $b_{i,k+1-i}=(-1)^{i+1}b_{1,k}$. According to this, for $\lambda\in S^1$, there are up to an isomorphism two non–degenerate HVS with $h=\lambda J_k$. These are $${\mathcal{V}}^k_{\lambda}(\pm 1)=\left(\mathbb{C}^k;b^k_{\pm},\lambda J_k,(\lambda J_k-I)(b^k_\pm)^{-1}\right).$$ The structures are simple for $\lambda\not=1$, otherwise not.
\[ex:mvtilde\] For $k\ge 1$ there are two degenerate simple HVS with $h=J_k$. They are $$\widetilde{{\mathcal{V}}}^k_1(\pm 1)=\left(\mathbb{C}^k;\widetilde{b}_\pm,J_k,\widetilde{V}_{\pm}^k\right),
\ \ \ \mbox{where} \ \ \
\widetilde{b}^k_\pm=\left(\begin{matrix} 0 & 0\\ 0&b^{k-1}_\pm \end{matrix}\right).$$ The entries of $V^{-1}$ satisfy: $(V^{-1})_{i,j}=0$ for $i+j\geq k+2$, $(V^{-1})_{i,k+1-i}=
\pm (-1)^{i+1} i^{-m^2-k}$. For $k=1$ this is $\widetilde{{\mathcal{V}}}^1_1(\pm 1)=(\mathbb{C},0,I, \pm i^{m^2+1})$.
We use the following uniform notation for the above simple structures: $$\label{eq:wk}
{\mathcal{W}}^k_\lambda(\pm 1)=\begin{cases}
{\mathcal{V}}^k_\lambda(\pm 1)&\text{if $\lambda\in S^1\sm\{1\}$}\\
\widetilde{{\mathcal{V}}}^k_1(\pm 1)&\text{if $\lambda=1$.}
\end{cases}$$
Classification of simple HVS
----------------------------
In [@Nem2] the second author proved that each simple variation structure is a direct sum of indecomposable ones.
\[p:classification\] A simple HVS is uniquely expressible as a sum of indecomposable ones up to ordering of summands and up to an isomorphism. The indecomposable pieces are ${\mathcal{W}}^k_\lambda(\pm 1)$ (for $k\ge 1$, $\lambda\in S^1$) and ${\mathcal{V}}^{2k}_\lambda$ (for $k\ge 1$, $0<|\lambda|<1$).
Hence, for each [*simple*]{} HVS, say ${\mathcal{V}}$, there exists a collection of numbers $p^k_\l(u)$ (with $k\ge 1$, $\l\in S^1$, $u=\pm 1$) and $q^k_\l$ (with $k\ge 1$ and $0<|\l|<1$) such that $$\label{eq:decomp}
{\mathcal{V}}=\bigoplus_{\substack{0<|\lambda|<1\\ k\geqslant 1}} q^k_\lambda\cdot {\mathcal{V}}^{2k}_\lambda
\oplus
\bigoplus_{\substack{|\lambda|=1\\ k\geqslant 1, \ u=\pm 1}} p^k_\lambda(u)\cdot {\mathcal{W}}^{k}_\lambda(u),$$ where the symbol $m\cdot{\mathcal{V}}$ denotes a sum of $m$ copies of the structure ${\mathcal{V}}$.
If a HVS is not simple, then a direct sum decomposition of the monodromy $h$ (e.g. its Jordan block decomposition) does not imply the existence of splitting of the whole structure.
\[ex:nonsplit\] Consider $$b=\bp 0&0&1\\0&0&0\\-1&0&0\ep, \hspace{5mm}
h=\bp 1&0&0\\0&1&1\\ 0&0&1\ep, \hspace{5mm}
V=\bp 0& 1 & 0\\ 1&0&0\\ 0&0&0\ep$$ These matrices define a $(-1)$–HVS, which is indecomposable.
Nevertheless, the next splitting holds (to see it, write $V$ as a block matrix and use the assumptions).
\[lem:split\] Let ${\mathcal{V}}=(U;b,h,V)$ be a HVS. Assume that $U=U_1\oplus U_2$ such that both $b$ and $h$ have block decomposition $b=b_1\oplus b_1$ and $h=h_1\oplus h_2$ with $b_1$ non-degenerate. Then $V=V_1\oplus V_2$ as well, hence ${\mathcal{V}}$ decomposes as a direct sum ${\mathcal{V}}_1\oplus {\mathcal{V}}_2$ of HVS’s.
\[rem:matrices\] Regarding our identities we use the following matrix notations.
Assume that in the vector spaces $V$ and $W$ we fixed the bases $\{\xi_i\}_i$, respectively $\{\zeta_j\}_j$. Then a morphism $A:V\to W$ is represented by the matrix ${\bf A}=\{A_{ij}\}_{ij}$, where $A(\xi_i)=\sum_jA_{ji}\zeta_j$. (This means that $(A_{11} \cdots A_{1n})$ is the first line.) (In other words, if ${\bf v}$ is the column vector representing $v\in V$ (i.e. it has entries $\{v_i\}_i$, where $v=\sum_i v_i\xi_i$), then $A(v)$ is represented by the column vector ${\bf A}\cdot {\bf v}$.) Any base $\{\xi_i\}_i$ in $V$ determines a dual base $\{\xi_j^*\}_j$ in $V^*=\operatorname{Hom}_{\R}(V,\R)$ via $\xi_j^*(\xi_i)=\delta_{ji}$, where $\delta_{ji}$ is the Kronecker symbol. If $A:V\to V$ is a morphism, then its dual $A^*:V^*\to V^*$ has matrix representation ${\bf A^*}={\bf A}^t$. Similarly, if $B:V\times V\to \R$ is a bilinear form, then it is represented by the matrix ${\bf B}=\{B_{ij}\}_{ij}$, where $B_{ij}:=B(\xi_i,\xi_j)$. (This means that $B(v,w)$ in matrix calculus is given by ${\bf v}^t\cdot
{\bf B}\cdot {\bf w}$.) Furthermore, if $b:V\to V^*$ is defined by $b(v)=B(v,\cdot )$, then the identities $B_{ik}=B(\xi_i,\xi_k)=b(\xi_i)(\xi_k)=\sum_jb_{ji} \xi_j^*(\xi_k)=b_{ki}$ show that ${\bf B}={\bf b}^t$.
Spectrum and signature of a real simple HVS {#s:specHVS}
-------------------------------------------
Let ${\mathcal{V}}$ be a simple HVS defined over the real numbers. For simplicity we will also assume that the coefficients $q^k_\lambda$ in the decomposition are all zero. In the sequel we define the [*spectrum*]{} $\operatorname{Sp}$ and the [*signature*]{} of ${\mathcal{V}}$. For more details regarding this subsection, see [@BN].
\[def:spectrum\] The [*spectrum*]{} is a finite set of real numbers from the interval $(0,2]$ with integral multiplicities such that any real number $\alpha$ occurs in $\operatorname{Sp}$ precisely $s(\alpha)$ times, where $$s(\alpha)=\sum_{n=1}^\infty\sum_{u=\pm1}\left(\frac{2n-1-u(-1)^{\lfloor \alpha\rfloor}}
{2}p^{2n-1}_\lambda(u)+np^{2n}_\lambda(u)\right), \ \
(e^{2\pi i\alpha}=\lambda).$$
\[def:signatureofHVS\] The *signature* of ${\mathcal{V}}$ is the map $\s_{{\mathcal{V}}}\colon S^1\sm\{1\}\to\Z$ given by $$z\mapsto\textrm{signature of}\left((1-z)V+(1-{\overline{z}})V^t\right).$$
The spectrum and the signature are related, cf. [@BN Corollary 4.15].[^1]
\[lem:sigandspec\] Let $x\in[0,1]$ be such that $\{x,1+x\}\cap \operatorname{Sp}=\emptyset$. Let $z=e^{2\pi ix}$. Then $$\begin{aligned}
|\operatorname{Sp}\cap (x,x+1)|&=\frac12(\dim U-\sigma(z))\\
|\operatorname{Sp}\setminus [x,x+1]|&=\frac12(\dim U+\sigma(z)).\end{aligned}$$
This lemma will allow us to use topological methods developed in Section \[S:fracturedd\] (namely, cobordism) to study semicontinuity of the spectrum.
Links in $3$-manifolds {#S:fracturedd}
======================
In this section we study links in oriented closed $3$-manifolds. Our approach depends on several choices, for example, choices of the Seifert surface. However, in the applications in singularity theory, there will always be a natural choice, dictated by singularity theory.
Fractured linking number {#ss:fracturedlink}
------------------------
Let $M$ be a closed connected oriented $3$-manifold. Let $\alpha,\beta\subset M$ be two disjoint one-dimensional cycles. If $M\cong S^3$, the linking number $\operatorname{lk}(\alpha,\beta)\in\Z$ is a well-defined number. We refer to [@Rol Chapter V.D] for various equivalent definitions. In this section we extend the definition for arbitrary 3-manifold $M$, but for special 1-cycles.
Assume that $[\alpha]=[\beta]=0$ in $H_1(M;\Q)$. Then there exists a 2-chain $A$ such that $\p A=\alpha$. We denote the algebraic intersection number of $A$ and $\beta$ in $M$ by $A\cdot\beta$ (which counts intersection points with signs provided that $A$ and $\beta$ are in general position). If $A$ and $A'$ are two different 2-chains such that $\p A=\p A'=\alpha$, then $A\cdot\beta=A'\cdot\beta$. Indeed, the cycle $A\cup -A'$ defines an element in $H_2(M;\Q)$. Then $(A\cup -A')\cdot \beta$ as an intersection product in $M$, is zero, since $[\beta]=0\in H_1(M)$.
\[def:clk\] We define the [*fractured linking number*]{} $\operatorname{flk}(\alpha,\beta)$ as $A\cdot\beta\in\Q$, where $\partial A=\alpha$. (By the above discussion it is independent of the choice of $A$.)
If $M$ is a 3-manifold, one has a linking form on the torsion part of its first homology with values in $\Q/\Z$. Our construction is different: it assigns an element from $\Q$ to any two disjoint rationally null-homologous cycles. By choosing its name ‘fractured linking number’ (instead of ‘linking number’) we emphasize the difference and avoid confusions.
As the classical linking number, the fractured linking number is symmetric too.
\[lem:fractured\] For any two disjoint null-homologous cycles $\alpha,\beta$ on $M$ we have $\operatorname{flk}(\alpha,\beta)=\operatorname{flk}(\beta,\alpha)$.
It is enough to prove the statement for $\alpha$ and $\beta$ integral cycles. Let $A$, $B$ be surfaces such that $\p A=\alpha$, $\p B=\beta$, and $A$ and $B$ intersect transversely. Then $A\cap B$ is an oriented cobordism between $A\cap\p B$ and $\p A\cap B$. This proof extends to the level of chains as well.
In the classical case, one has another definition of the linking pairing. Namely, given two disjoint 1-cycles $\alpha,\beta\subset S^3=\p B^4$, one takes two 2-chains $A,B$ in the ball $B^4$ such that $\p A=\alpha$ and $\p B=\beta$. Then $\operatorname{lk}(\alpha,\beta)=A\cdot B$. We extend this result in a way that we allow an arbitrary four manifold instead of $B^4$, but we need to impose additional conditions on the chains $A$ and $B$.
\[lem:AcdotB\] Assume that $W$ is a four manifold such that $\p W=M$. Let $\alpha,\beta$ be two disjoint null-homologous 1-cycles in $M$. Then for any 2-chains $A,B\subset W$ such that $\p A=\alpha$, $\p B=\beta$ and $[A]=[B]=0\in H_2(W,M;\Q)$ we have $$\operatorname{flk}(\alpha,\beta)=A\cdot B.$$
First we show that $A\cdot B$ does not depend on the specific choice of $A$ and $B$. To this end, assume that we have a 2-chain $A'$ such that $\p A'=\alpha$ and $[A']=0\in H_2(W,M;\Q)$. Then $A\cup -A'$ is an absolute cycle in $W$ so it represents a class $[A-A']\in H_2(W)$ and $(A\cup -A')\cdot B=[A-A']\cdot [B]$, where the last product is the intersection pairing $H_2(W)\times H_2(W,M)\to\Q$. But this is zero since $[B]=0$. Thus $A\cdot B$ is well-defined.
By picking concrete $A$ and $B$ we will show that $A\cdot B=\operatorname{flk}(\alpha,\beta)$. To this end, choose a collar $M\times[0,1)\subset W$, such that $M\times\{0\}$ is identified with $M=\p W$. Let $C$ be a 2-chain in $M$ such that $\p C=\beta$. We define $B$ as $C$ with its interior pushed slightly inside $M\times[0,1/2]$. Clearly $[B]=0\in H_2(W,M;\Q)$. Let $A$ be arbitrary 2-chain satisfying the hypothesis of the lemma. We isotope $A$ so that $A\cap (M\times[0,1])=\alpha\times[0,1]$. Then, by construction, all the intersection points of $A\cap B$ correspond to the intersections of $\alpha$ with $C$.
The condition that $A$ and $B$ represent $0\in H_2(W,M)$ is essential, even if $M$ is the 3-sphere. For example, consider $\C^2$ with coordinates $x,y$ and let $M=\{|x|^2+|y|^2=1\}$, $W_0=\{|x|^2+|y|^2\le 1\}$. Let $A_0=\{x=0\}$, $B_0=\{y=0\}$ and put $\alpha=A_0\cap M$, $\beta=B_0\cap M$. Then $\operatorname{lk}(\alpha,\beta)=1$, as is the algebraic intersection number of $A_0$ with $B_0$.
But now we can define $W$ as $W_0$ blown up in the origin and $A$, $B$ as the strict transforms of $A_0$ and $B_0$ respectively. Then $A\cap B=\emptyset$, but still we have $\p A=\alpha$, $\p B=\beta$. Of course, $A$ and $B$ do not represent $0$ in $H_2(W,M)$.
We end up this subsection with an alternative construction of the fractured linking number. Let $\alpha$ and $\beta$ be disjoint cycles in $M$, which represent $0\in H_1(M;\Q)$. Assume that $\alpha$ can be represented by a simple closed loop. Then $\beta$ defines an element in $H_1(M\sm\alpha;\Q)$, which is mapped to $0$ by the map $H_1(M\sm\alpha)\to H_1(M)$. We have $$U:=\ker (H_1(M\sm\alpha;\Q)\to H_1(M;\Q))\cong\Q$$ and there is a canonical choice of the isomorphism, such that the oriented meridian of $\alpha$ goes to $1$. Then we can define $\operatorname{flk}(\alpha,\beta)$ to be the class $[\beta]\in \Q$. We leave it as an exercise to check that the two definitions are in fact equivalent.
Links and fractured Seifert matrices
------------------------------------
\[def:link1\] A *link* $L$ in an oriented connected 3-manifold $M$ is a disjoint union of embedded oriented circles $K_1\sqcup\dots\sqcup K_n$ in $M$. A *Seifert surface* of a link $L\subset M$ is a [*connected oriented surface*]{} $\S\subset M$ such that $\p\S=L$, and the interior of $\S$ is disjoint from $L$.
If such surface exists, we know that $[L]=0\in H_1(M;\Z)$. Conversely, if $[L]=0\in H_1(M;\Z)$, the arguments of [@Er] or [@BNR2] guarantee the existence of $\S$. However, in the present paper, all the links that we shall consider will have a Seifert surfaces.
Let $\S$ be a Seifert surface for a link $L$ and $j:\S\hookrightarrow M$ be the inclusion map. We set $$\label{eq:V0}
\vs=\ker\big(j_*\colon H_1(\S;\Q)\to H_1(M;\Q)\big).$$ For any $\beta\in \vs$ let $\beta^+$ be the cycle $\beta$ pushed slightly off $\S$ in the positive normal direction. Obviously, $[\beta^+]=0\in H_1(M;\Q)$.
\[def:csp\] The *fractured Seifert pairing* $S\colon \vs\times \vs\to \Q$ for $\S$ is defined by $(\alpha,\beta)\mapsto \operatorname{flk}(\alpha,\beta^+)$. A *fractured Seifert matrix* is a rational square matrix of size $\dim \vs$ such that in some basis of $\vs$ the fractured Seifert pairing is represented by $S$.
Usually we shall not make a distinction between a Seifert pairing and a Seifert matrix, see Remark \[rem:matrices\].
In general, $S$ is not $\pm$-symmetric, nevertheless Lemma \[lem:fractured\] implies the following.
\[lem:disjoint\] If $\alpha,\beta\in \vs$ and $\alpha$ is disjoint from $\beta$, then $S(\alpha,\beta)=\operatorname{flk}(\alpha,\beta)$. In particular, if $\alpha_1,\dots,\alpha_k\in\vs$ are pairwise disjoint, then $S$ restricted to the subspace spanned by $\alpha_1,\dots,\alpha_k$ is symmetric.
In this paper we assume that all the links satisfy the following additional assumptions.
\[def:link\]
- A link will be called 0–link if all component are (rational) null-homologous: $[K_j]=0\in H_1(M;\Q)$ for any $j=1,\dots,n$, and if $L$ admits a Seifert surface.
- A 0–link is called [*special*]{} if $\operatorname{flk}(K_i,K_j)>0$ for all $i\not=j$.
Consider the fractured linking matrix $\{{\mathcal L}(K_i,K_j)\}_{i,j}$ associated with a [*special*]{} link $L$. Here, ${\mathcal L}(K_i,K_j):=\operatorname{flk}(K_i,K_j)$ for $i\not=j$, while ${\mathcal L}(K_i,K_i)$ is determined by the imposed identities ${\mathcal L}(\sum_iK_i,K_j)=0$ for any $j$.
\[lem:nondeg\] If $L$ is special, then ${\mathcal L}$ is negative semi-definite with 1-dimensional null space generated by $\sum_iK_i$.
(Cf. [@Neu-inv Sec. 3]) If $R=\sum_ir_iK_i$, then ${\mathcal L}(R,R)=-\sum_{i<j} (r_i-r_j)^2\operatorname{flk}(K_i,K_j)$.
Fibred links and monodromy {#s:fibred}
--------------------------
Our goal in this section is to study the fractured Seifert matrix associated to a fibred link. Understanding a decomposition of a fractured Seifert matrix with respect to generalized eigenspaces of the monodromy operator will lead us to a decomposition of HVS defined for a fibred link.
We begin with the following definition.
\[def:hs\] We shall refer to an open book decomposition $(M,L,p)$ with binding $L$ and projection $p\colon M\sm L\to S^1$ simply as a *fibred link*. We define its (canonical) *Seifert surface* $\S$ as the page $p^{-1}(1)$. The *monodromy* diffeomorphism (well defined up to an isotopy) will be denoted by $\hs\colon\S\to\S$. (Notice that since we consider $L$ to be an oriented link, we require that $p$ restricted to the oriented meridians $\mu_1,\ldots,\mu_n$ of components of $L$ is an *orientation preserving* diffeomorphism.)
For any $t\in[0,1]$, set $\S_t=p^{-1}(e^{2\pi it})$ with $\S=\S_0$. Since $p$ is locally trivial, there exist a smooth family of diffeomorphisms $\hst\colon\S\stackrel{\cong}{\longrightarrow}\S_t$ induced by trivialization over $[0,t]$, such that $\hs_0$ is the identity and $\hs_1=\hs$ is the monodromy. These diffeomorphisms are also well defined only up to isotopy. Let $h\colon H_*(\S;R)\to H_*(\S;R)$ be the homological monodromy induced by $\hs$ for any coefficient ring $R$.
In the usual definition of the Seifert matrix, to any cycle $\beta\in H_1(\S)$ we associate $\beta^+$ (‘the push off of $\beta$ in the positive direction’). In the case of the above fibred situation, we set $\beta^+=\hs_{1/2}\beta$. This is common in singularity theory too, see e.g. [@AGV; @Zol].
The Wang sequence of the fibration $p\colon M\sm L\to S^1$ is $$\label{eq:wang}
\ldots \to H_1(\S)\to H_1(M\sm L)\stackrel{h-I}{\longrightarrow} H_1(M\sm L)\stackrel{q}{\to} H_0(\S)\to\ldots$$ The map $q$ is the following: a cycle $\alpha\in H_1(M\sm L)$ in general position with respect to $\S$ is mapped to $(\alpha\cdot\S)$ times the generator of $H_0(\S)\simeq \Z$. Since $q(\mu_i)=1$, $q$ is onto.
Let $L$ be a special fibred link. Let $j\colon\S\hookrightarrow M$ be the inclusion. We define $$U_\partial :=\ker\big(
\overline{j_*}:H_1(\S)/{\rm im}(h-I)\to H_1(M)\big),$$ where $\overline{j_*}$ is induced by $j_*$. Later on we shall define a lift of $\vb$ to a subspace of $H_1(\S)$.
Let $\mu_i$ be the oriented meridian of $K_i$ in $M$. We have the following commutative diagram, $$\label{eq:newdiagram}
\xymatrix{&&0\ar[d]&&\\
&&\Q\langle\mu_i\rangle_{i=1}^n\ar^m[d]\ar^{{\overline{m}}}[dr]&&\\
0\ar[r]&\vb\ar[r]\ar^{{\overline{j}}_*}[dr]&H_1(M\sm L)\ar[r]\ar^r[d]&H_0(\S)\cong\Q\ar[r]&0\\
&&H_1(M)\ar[d]&&\\
&&0&&
}$$ where the horizontal exact sequence is induced by (\[eq:wang\]). The map $m$ is induced by inclusions of meridians, the map $r$ is induced by inclusion. The diagonal maps are compositions.
\[lem:new\]
- The vertical line of is a short exact sequence.
- The map ${\overline{m}}$ is given by $\sum q_i\mu_i\mapsto\sum q_i\in H_0(\S)$, hence it is onto.
- The map ${\overline{j}}_*$ is onto. Furthermore $\dim\vb=n-1$ and $\vb\cong\{\sum q_i\mu_i \colon \sum q_i=0\}$.
<!-- -->
- Use $H_2(M, M\setminus L)=\Q\langle \mu_i\rangle _{i=1}^n$ and the fact that $H_2(M)\to H_2(M,M\setminus L)$ is trivial due to the fact that each $[K_i]=0$.
- is clear, the map ${\overline{m}}$ sends a meridian to $M\sm L$ and $q$ sends it further to $1$, for each meridian intersects $\S$ precisely once.
- surjectivity of ${\overline{j}}_*$ follows from (b) and diagram chasing. The rest is clear.
The intersection form $\alpha \cdot_\S\beta $ on $H_1(\S)$ has the following compatibility properties. (Part (b) is the analogue of a Picard–Lefschetz formula from singularity theory.)
\[lem:new2\] Assume that $L$ is a special fibred link and $\alpha=(h-I)\gamma$ for some $\gamma\in H_1(\S;\Q)$. Then $\alpha\in U^\Sigma$. Moreover, the following hold.
- If $\beta\in\ker(h-I)$ then $\alpha\cdot_\S\beta=0$.
- If $\beta\in \vs$ then $\operatorname{flk}(\alpha,\beta^+)= \gamma\cdot_\S\beta.$
- Denote the homology classes in $H_1(\S)$ determined by the boundary components by $\{K_i\}_{i=1}^n$ (subject to the single relation $\sum_i K_i=0$). Let ${\mathcal K}$ be the subspace of $H_1(\S)$ generated by these components. Then ${\mathcal K}\cap \operatorname{im}(h-I)=0$, hence ${\mathcal K}$ injects to $H_1(\S)/{\rm im}(h-I)$ with image exactly $U_\partial$.
The first statement follows from Wang exact sequence, which shows that the class of $\alpha$ is zero already in $H_1(M\setminus L)$.
- $\gamma\cdot_\S\beta=h\gamma\cdot_\S
h\beta=(\gamma+\alpha)\cdot_\S\beta=\gamma\cdot_\S\beta+\alpha\cdot_\S\beta$, since $\cdot_\S$ is $h$-invariant.
- Consider $A=\bigcup_{t\in[0,1]}\hst \gamma$. The boundary of $A$ is $h\gamma-\gamma$, which is homologous to $\alpha$. Hence $\operatorname{flk}(\alpha,\beta^+)=A\cdot\beta^+$. We can assume that $A$ is in general position with respect to $\beta^+=h^\S_{1/2}\beta$. $$A\cdot\beta^+=(A\cap\S_{1/2})\cdot_{\S_{1/2}}\beta^+=
\hs_{1/2}\gamma\cdot_{\S_{1/2}}\hs_{1/2}\beta=\gamma\cdot_\S\beta.$$
- Set $R=\sum_ir_iK_i=(h-I)\gamma$. Then by part (b) $\operatorname{flk}(R,K_j)=\gamma\cdot_\S K_j=0$. Hence, by Lemma \[lem:nondeg\], $R=0$ in $H_1(\S)$. Since each $K_j$ is zero-homologous, ${\mathcal K}$ injects in $U_\partial$. Since these spaces have the same dimension, they are isomorphic.
In the sequel we will not make distinction between ${\mathcal K}$ and $U_\partial$, we think about $U_\partial$ as the [*kernel of the intersection pairing on $H_1(\S)$*]{}, that is $\vb$ is regarded as a subspace of $\vs$.
Consider the generalized eigenspace decomposition of $h$ $$\label{eq:firstdecomp}
H_1(\S;\Q)=\vn\oplus\ve,$$ corresponding to eigenvalue $\neq 1$, respectively $=1$. Both subspaces $\vn$ and $\ve$ are monodromy invariant and orthogonal with respect to $\ \cdot_\S\ $.
\[cor:fromwang\]
- The subspace $\vn$ belongs to $\vs$. Furthermore $\ve\cap \vs=\vi\oplus\vb$, where $\vi=\ve\cap\operatorname{im}(h-I)$.
- The monodromy $h$ preserves the direct sum decomposition $$\label{eq:v0-decomp}
\vs=\vn\oplus\vi\oplus\vb.$$
- The components in (\[eq:v0-decomp\]) are pairwise orthogonal with respect to the intersection form $\ \cdot_\S \ $.
- The restriction of the intersection form on $\vn$ is non-degenerate.
For (a) use Wang exact sequence, Lemma \[lem:new\] and part (c) of Lemma \[lem:new2\]. Part (b) is clear. Next, we prove (c). The kernel of the intersection form, $\vb$ is orthogonal to everything. Next, $\vi\perp \vn$, since $\ve\perp \vn$. For (d), take $\alpha$ from the kernel of $\cdot_\S|\vn$. Then $\alpha\in \ker(\cdot_\S)$, hence $\alpha\in U_\partial$. But $U_\partial\cap \vn=0$.
\[prop:sisinv\] For the fractured Seifert pairing $S$ the following facts hold.
- $S$ is monodromy invariant, i.e. $S(h\alpha,h\beta)=S(\alpha,\beta)$ for any $\alpha,\beta\in \vs$,
- $S$ satisfies $S(\alpha,\beta)=S(h\beta,\alpha)$,
- $S$ satisfies $S(\alpha,\beta)=S(\beta,\alpha)=0$ for $\alpha\in\vn$ and $\beta\in\vi\oplus\vb$, and
- $S$ has block structure with respect to the decomposition .
<!-- -->
- The monodromy $\hs$ extends to an automorphism of $M$, still denoted by the same $\hs$. We clearly have $\operatorname{flk}(\alpha,\beta^+)=\operatorname{flk}(\hs\alpha,(\hs\beta)^+)$. Hence $S(\alpha,\beta)=S(h\alpha,h\beta)$.
- We have $S(\alpha,\beta)=\operatorname{flk}(\alpha,\beta^+)=\operatorname{flk}(\alpha^+,\hs\beta)=\operatorname{flk}(\hs\beta, \alpha^+)=
S(h\beta,\alpha)$.
- Take $\gamma\in \vn$ such that $(h-I)\gamma=\alpha$. Then $S(\alpha,\beta)=\gamma\cdot_\S\beta=0$ by Corollary \[cor:fromwang\]. Similarly, $S(\beta,\alpha)=S(h\alpha,\beta)=S(\alpha,h^{-1}\beta)=\gamma\cdot_\S h^{-1}\beta=0$.
- By part (c) it is enough to ensure that $S$ has block structure on $\vi\oplus\vb$. Let $\alpha
=(h-I)\gamma\in\vi$ and $\beta\in\vb$. Then $S(\alpha,\beta)=\gamma\cdot_\S\beta=0$.
Corresponding to part (d) of Proposition \[prop:sisinv\], we write ${S_{\neq 1}}$, ${S_{\operatorname{im}}}$ and ${S_\partial}$ for the fractured Seifert pairing restricted to $\vn$, $\vi$ and $\vb$ respectively.
Non-degeneracy of $S$. Simple fibred links
------------------------------------------
In this subsection we give sufficient conditions for the fractured Seifert matrix of a fibred link to be non-degenerate.
\[prop:Si-nondeg\]
- ${S_{\neq 1}}$ and ${S_\partial}$ are non-degenerate.
- If $\vi \subset \ker(h-I)$, then ${S_{\operatorname{im}}}$ is non-degenerate as well.
We begin with (a). Since $h-I$ is invertible on $\vn$ and the intersection pairing on $\vn$ is non-degenerate, the statement follows from Lemma \[lem:new2\](b). The non-degeneracy of ${S_\partial}$ is built in our assumptions: Lemma \[lem:disjoint\] together with Definition \[def:link\] and Lemma \[lem:nondeg\] show that ${S_\partial}$ is actually a negative definite symmetric matrix. We note, that in the statement of Lemma \[lem:nondeg\], we use the word ‘negative semi-definite’, but on $\vb$ this 1-dimensional null–space of the fractured linking form is killed by Lemma \[lem:new\](c).
We continue with (b). Recall that by Lemma \[lem:new2\] we have $\vb \cap\vi=0$. Set ${\overline{\ve}}:=\ve/\vb$. Then $\vi$ projects isomorphically to a subspace of $\overline{\ve}$. Let $\alpha_1,\dots,\alpha_k$ be linearly independent elements in $\vi$, such that their representatives form a basis in $\vi/\vb$. Let us choose $\beta_1,\dots,\beta_k$ in $\ve$ such that $(h-I)\beta_j=\alpha_j$. Let $\vbb$ be the space spanned by $\beta_1,\dots,\beta_k$. Clearly $\vbb\to\vbb/\vi$ is an isomorphism. Finally, take a subspace $\vf$ of $\ve$ such that $$\label{eq:vfix}
\ve=\vf\oplus\vi\oplus\vb\oplus\vbb,$$ and such that $\vf$ is $h$–invariant. This is possible because the assumption guarantees that there are no Jordan block of size 3 or larger and $\vbb\oplus\vi$ corresponds to Jordan blocks of size $2$.
We have $\vi\oplus \vf\subset \ker(h-I)$, so by Lemma \[lem:new2\](a) $\vi\perp (\vi\oplus \vf)$. On the other hand, the induced intersection form on $\vi\oplus\vf\oplus\vbb$ is non-degenerate, this follows from the fact that the kernel of the intersection form on $\ve$ is exactly $\vb$, see Corollary \[cor:fromwang\](c). We conclude that the block matrix $\{\alpha_i\cdot_\S\beta_j\}_{i,j}$ should be non-degenerate. But by Lemma \[lem:new2\](b) this is the matrix of ${S_{\operatorname{im}}}$ in the basis $\alpha_1,\dots,\alpha_k$.
The subspaces $\vbb$ and $\vf$ of $\ve$ that were defined in the above proof, will be important in Section \[s:vf\]. Their definition depends on various choices, in Section \[s:vf\] we will put additional conditions on $\vbb$ and $\vf$.
The assumption that $\vi\subset \ker(h-I)$ is equivalent to the absence of Jordan blocks of size $3$ or larger of eigenvalue $1$ in the Jordan block decomposition of $h$. This always holds if $L$ is a graph link in a graph manifold (see e.g. [@EN]). More generally, if in the Nielsen–Thurston decomposition of $h$ there are no pseudo–Anosov pieces, then $h$ cannot have Jordan blocks of size larger than $2$ (with whatever eigenvalue) by [@FM Corollary 13.3].
\[def:simple\] A special fibred link $(M,L,p)$ is called *simple* if the monodromy has no Jordan block of size more than 2 with eigenvalue $1$.
\[cor:simple\] The fractured Seifert matrix of a simple fibred link is non-degenerate.
Complementary space to $\vs$ {#s:vf}
----------------------------
Assume that $L$ is a simple fibred link. Let us consider the space $\vf $ in the proof of Proposition \[prop:Si-nondeg\]. Since the intersection form on $\vi\times \vbb$ is non-degenerate we can choose $\vf$ (by adding vectors from $\vi$ to base elements of the original $\vf$) such that $\vbb\perp \vf$ too and $\vf$ still remains $h$-invariant. Decomposition has the property that the space $\vf$ is orthogonal to $\vi\oplus\vb\oplus\vbb$, $\vi\perp\vi$, and $\ker(h-I)=\vf\oplus \vi\oplus \vb$. On $\vf\oplus \vi\oplus \vbb$ the intersection from is non-degenerate. Then automatically one also has the following result.
\[cor:vfnondeg\] The intersection form of $H_1(\S)$ restricted to $\vf\times\vf$ is non-degenerate, and $\vf$ is even dimensional.
Decomposition \[eq:vfix\] together with Corollary \[cor:fromwang\] gives also $$\label{eq:complement}
H_1(\S)=\vs\oplus\vbb\oplus\vf.$$
To conclude this section let us write a corollary to Lemma \[lem:new\](c).
\[cor:dimvs\] For any special fibred link (not necessary simple) we have $$\dim\vs=\dim H_1(\S)-\dim H_1(M).$$
Lemma \[lem:new\](c) tells that ${\overline{j}}_*$ is onto, hence $H_1(\S)\to H_1(M)$ is onto, and $\vs$ is defined as the kernel of this map.
Cobordisms and signatures
=========================
Cobordisms of links
-------------------
We begin with the following definition.
Fix two links $L_0\subset M_0$ and $L_1\subset M_1$ as in \[def:link1\]. A *cobordism of links* connecting $(M_0,L_0)$ and $(M_1,L_1)$ is a pair $(W,Y)$, where $W$ is a 4-manifold and $Y\subset W$ is a surface, such that $\p W=-M_0\sqcup M_1$, $\p Y=-L_0\sqcup L_1$.
A cobordism will be called *standard* if $W\cong M_0\times[0,1]$.
Compatibility with Seifert surfaces of links is formulated as follows.
\[def:Seifertcobordism\] Let $(M_0,L_0)$ and $(M_1,L_1)$ be two links and $\S_0,\S_1$ Seifert surfaces respectively for $(M_0,L_0)$ and $(M_1,L_1)$. A pair $(W,\O)$ is a *Seifert cobordism* between links $(M_0,L_0)$ and $(M_1,L_1)$ and their Seifert surfaces $\S_0$ and $\S_1$ if
- $W$ is a 4-manifold with boundary $-M_0\sqcup M_1$;
- $\O$ is a 3-manifold with corners;
- $\S_0:=\O\cap M_0$ and $\S_1:=\O\cap M_1$ are the Seifert surfaces for $L_0=\p\S_0$ and $L_1=\p\S_1$;
- $\p\O=\S_0\cup Y\cup\S_1$, where $Y\subset W$ and $\p Y=-L_0\cup L_1$.
\[rem:iswsmooth\] The condition that $W$ is a manifold might be slightly relaxed. More precisely, we can allow $W$ to be singular away from $\p W\cup\O$. For example, we can assume that there exists a finite number of points $w_1,\dots,w_s\in W\sm(\partial W\cup \O)$ such that $W\sm\{w_1,\dots,w_s\}$ is a smooth manifold. In fact, in the applications we do not use the smoothness of $W$. On the other hand, the smoothness of $\O$ is exploited by its Poincaré duality.
We wish to study, how the fractured Seifert matrices does change under the Seifert cobordism. The situation is standard in the classical case. To simplify the notation, we shall first restrict ourselves to the case when $M_1$, $L_1$ and $\S_1$ are empty. The manifolds $M_0$, $L_0$ and $\S_0$ will be denoted by $M$, $L$, $\S$. The inclusions $\S\hookrightarrow\O$, $\S\hookrightarrow M$ and $(\O,\S)\hookrightarrow(W,M)$ will be denoted by $i$, $j$, resp. $k$.
Let $\vnu\subset \vs$ be the space of those elements $\alpha\in\ker i_*$ for which there exists $A\in H_2(\O,\S;\Q)$ such that $\p A=\alpha$ and $k_* A=0$ (see diagram (\[eq:funddiagram\])).
\[prop:thenullspace\] Let $\alpha,\beta\in \vnu$. Then, $S(\alpha,\beta)=0$.
Let $B^+$ be the cycle $B$ pushed off $\O$ in the positive normal direction. Obviously $\p B^+=\beta^+$ and $B^+$ is a zero element in $H_2(W,M;\Q)$. By Lemma \[lem:AcdotB\] we have $\operatorname{flk}(\alpha,\beta^+)=A\cdot B^+$. But $A\subset\O$ and $B^+$ is disjoint from $\O$.
Next we search for a bound for $\dim \vnu$. We will need the following diagram $$\label{eq:funddiagram}
\xymatrix{
\ & H_2(\O,\S)\ar[r]^{\p}\ar[d]_{k_*} &
H_1(\S)\ar[r]^{i_*}\ar[d]_{j_*} & H_1(\O)\ar[d]\\
0\to\operatorname{coker}(H_2(M;\Q)\to H_2(W;\Q))\ar[r]^(0.7){l_*} & H_2(W,M)\ar[r]^{\p'} & H_1(M)\ar[r]^{a_*} & H_1(W),
}$$ (where the rows are long exact sequences of pairs) and the next terminology as well.
The *irregularity* of the Seifert cobordism $(W,\O)$ is $$\label{eq:irr}
\operatorname{Irr}_2:=\dim\operatorname{coker}\big(H_2(M;\Q)\to H_2(W;\Q)\big).$$ (The subscript $2$ suggests that the irregularity is related to the map on the second homologies. Later, in a more specific case, we shall also introduce $\operatorname{Irr}_1$.)
We have the following estimates.
$$\begin{aligned}
(a) \hspace{1cm} & \dim \vnu\ge \dim(\ker i_*\cap \ker j_*)-\operatorname{Irr}_2\\
(b) \hspace{1cm} & \dim(\ker i_*\cap\ker j_*)\ge\dim\ker i_*-\dim\ker a_*.\end{aligned}$$
\(a) Since $\vnu=\p(k_*^{-1}(0))$ and $\ker i_*\cap\ker j_*=\p(k_*^{-1}(\ker \p'))$, one has $$\dim (\ker i_*\cap \ker j_*)/\vnu\leq \dim(k_*^{-1}(\ker \p')/k_*^{-1}(0)
=\dim \ker \p'.$$
\(b) $0\to \ker i_*\cap\ker j_*\to \ker i_*\stackrel{j_*}{\longrightarrow} \ker a_*$ is exact.
We remark that $\dim\ker a_*$ does not depend on the cobordism of the link itself (that is, on $L,\ \S,\ \Omega$), but only on $M$ and $W$. Finally, we estimate $\dim\ker i_*$.
\[lem:poinc\] One has the following estimate $$\dim\ker i_*\ge b_1(\S)-\frac12b_1(\S\cup Y).$$
Decompose $i_*$ as $H_1(\S)\stackrel{b_*}\longrightarrow H_1(\S\cup Y)
\stackrel{c_*}{\longrightarrow}H_1(\O)$. Then $$\dim\ker i_*-\dim\ker b_*=\dim (\operatorname{im}b_*\cap \ker c_*)\ge
\dim \operatorname{im}b_*+\dim\ker c_*-b_1(\S\cup Y).$$ Clearly, $\dim\ker b_*+\dim (\operatorname{im}b_*)=b_1(\S)$. As $\S\cup Y=\p\O$ and $\O$ has dimension three, by the Poincaré duality arguments one gets $\dim\ker c_*= b_1(\S\cup Y)/2$.
Now we combine our last three statements.
\[cor:bound\] If $(W,\O)$ is a Seifert cobordism such that $(M_1,L_1,\S_1)=\emptyset$, then $\vs$ contains the subspace $\vnu$ of dimension at least $$b_1(\S)-\frac12 b_1(Y\cup\S)-\operatorname{Irr}_2-\dim\ker a_*$$ on which the Seifert form identically vanishes.
We will use Corollary \[cor:bound\] to control the fractured signatures, which we now define.
Fractured signatures
--------------------
\[def:fracturedsig\] Let $(M,L)$ be a special link, $\S$ its Seifert surface, and $S$ the fractured Seifert pairing on $\vs$. The *fractured signature* is a function $\s\colon S^1\sm\{1\}\to\Z$ defined as $$z\mapsto \textrm{signature}((1-z)S+(1-{\overline{z}})S^t).$$ The *fractured nullity* is a function $n \colon S^1\sm\{1\}\to\Z$ defined as $$z\mapsto \dim\ker ((1-z)S+(1-{\overline{z}})S^t).$$
Here $\cdot^t$ denotes the transpose (in the matrix notation), or simply $S^t(\alpha,\beta)=S(\beta,\alpha)$.
If $S$ is non-degenerate then $n(z)=0$ for almost all values of $z$. Furthermore, if $(M,L)$ is fibred and $\S$ is a fiber, then $\s$ is a piecewise constant function with possible jumps only at roots of the characteristic polynomial of the monodromy $\Delta(z):=\det(h-I\cdot z)$. Indeed, by Proposition \[prop:sisinv\](b) one has the identity $(1-z)S+(1-{\overline{z}})S^t=(1-{\overline{z}})S(h^{-1}-I\cdot z)$.
Fractured signatures are motivated by cobordisms: the next Theorem \[thm:signatures\] is at the core of the present article. To prove it, we start with the following standard fact from linear algebra.
\[lem:lagrang\] If $\vnu\subset \vs$ is a subspace such that for $\alpha,\beta\in \vnu$ we have $S(\alpha,\beta)=0$, then for all $z\in S^1\sm\{1\}$: $$|\s(z)|\le \dim \vs-2\dim \vnu+n(z).$$
The next main result is the starting point in proving our semicontinuity results.
\[thm:signatures\] Let $(W,\O)$ be a Seifert cobordism of links $(M_0,L_0)$ and $(M_1,L_1)$. Then for all $z\in S^1\sm\{1\}$ we have $$\begin{gathered}
|\s_0(z)-\s_1(z)|\le \dim \vs_0+\dim \vs_1-2b_1(\S_0)-2b_1(\S_1)+
b_1(Y\cup\S_0\cup\S_1)+2\operatorname{Irr}_2+\\+2\dim\ker(H_1(M_0\cup M_1)\to H_1(W))+n_0(z)+n_1(z),\end{gathered}$$ where $\vs_j=\ker(H_1(\S_j)\to H_1(M_j))$ and $\S_j=\O\cap M_j$ is the Seifert surface of $L_j$ ($j=0,1$).
We define $(M,L)=(M_1\cup -M_0,L_1\cup -L_0)$. Let also $\S=\S_1\cup-\S_0$. Then the fractured signatures of $L$ are $\s(z)=\s_0(z)-\s_1(z)$ and the nullities satisfy $n(z)=n_0(z)+n_1(z)$. Indeed, if $S_0$ and $S_1$ are fractured Seifert matrices for $(M_0,L_0)$ and $(M_1,L_1)$, respectively, then $S_1\oplus -S_0$ is a fractured Seifert matrix for $S$. The theorem is now a direct consequence of Corollary \[cor:bound\] and Lemma \[lem:lagrang\].
Hermitian variation structures associated with a simple fibred link {#s:chvs}
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In this section we will associate with a simple fibred link two HVSs. One of them is given by the fractured Seifert matrix, the other by the classical variation map. We prove that they determine each other.
The ‘fractured’ and ‘mended’ HVS for simple fibred links {#ss:chvs}
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Let $(M,L,p)$ be a simple fibred link. Let $\S$ be its Seifert surface, $h\colon H_1(\S)\to H_1(\S)$ the monodromy, $b$ the hermitian intersection form on $H_1(\S)$, and $S\colon \vs\times \vs\to\C$ the fractured Seifert pairing.
\[def:fracturedHVS\] The *fractured hermitian variation structure* associated to the simple fibred link $L$ is the structure ${{\mathcal{V}}_{\frct}}=(\vs;b|_{\vs},h|_{\vs},(S^{t})^{-1})$ (defined already over $\Q$).
By Lemma \[lem:new2\](b) and Proposition \[prop:sisinv\](b) (and using the last line of Remark \[rem:matrices\] too) one checks that the above system forms a HVS. Since $(S^t)^{-1}$ is invertible, cf. Proposition \[prop:Si-nondeg\], ${{\mathcal{V}}_{\frct}}$ is simple.
According to the direct sum $\vs:=\vn\oplus\vb\oplus\vi$ (cf. Section \[s:fibred\]) the fractured HVS decomposes into a direct sum ${{\mathcal{V}}_{\frct}}:={{\mathcal{V}}_{\neq 1}}\oplus{{\mathcal{V}}_{\partial}}\oplus{{\mathcal{V}}_{\operatorname{im}}}$ of HVS as well. This follows from the Splitting Lemma \[lem:split\], since the pair $(b|_{\vs},h|_{\vs})$ admits a direct sum decomposition, and $b|_{\vs}$ is non-degenerate on ${{\mathcal{V}}_{\neq 1}}\oplus{{\mathcal{V}}_{\operatorname{im}}}$, cf. Corollary \[cor:fromwang\]. The components are the following.
- The quadruple ${{\mathcal{V}}_{\neq 1}}=(\vn;{b_{\neq 1}},h|_{\vn},({S_{\neq 1}}^t)^{-1})$ (the natural restrictions on $\vn$);
- On $\vb$ the $h|_{\vb}$ is trivial and $b|_{\vb}= 0$. Hence ${{\mathcal{V}}_{\partial}}=(\vb;0,I,({S_\partial}^t)^{-1})$. By Lemma \[lem:nondeg\] $({S_\partial}^t)^{-1}$ is negative definite, thus ${{\mathcal{V}}_{\partial}}=(n-1)\cdot {\mathcal{W}}^1_1(+1)$.
- On $\vi$ the form $b|_{\vi}$ is $0$ (by Lemma \[lem:new2\](a)) and $h|_{\vi}$ is the identity (since $L$ is simple). Thus ${{\mathcal{V}}_{\operatorname{im}}}=(\vi;0,I,({S_{\operatorname{im}}}^t)^{-1})$. In particular, $\vi$ is a union of copies of ${\mathcal{W}}^1_1(+1)$ and ${\mathcal{W}}^1_1(-1)$.
Although the operators $b$ and $h$ of ${{\mathcal{V}}_{\frct}}$ can be extended to (the intersection form and monodromy on) $H_1(\S,\C)$, the extension of $(S^t)^{-1}$ is not immediate.
Nevertheless, we wish to define such an extension, however the extension will fail to be simple. First, we introduce a HVS on $\vf$ (see Section \[s:vf\]).
\[def:fixext\] The structure ${{\mathcal{V}}_{\fix}}$ on $\vf$ is the HVS structure determined by non-degenerate isometric structure $(\vf;b|_{\vf},h|_{\vf})$ (cf. Corollary \[cor:vfnondeg\]).
Note that $h$ is the identity, $V=0$, and $b|_{\vf}$ is fully antisymmetric. Hence ${{\mathcal{V}}_{\fix}}$ is a direct sum of $\frac12\dim\vf$ copies of ${\mathcal{V}}^1_1(+1)\oplus {\mathcal{V}}^1_1(-1)$.
\[def:mended\] The *mended* HVS associated with a simple fibred link, denoted by ${{\mathcal{V}}_{\mend}}$, is a direct sum ${{\mathcal{V}}_{\mend}}:={{\mathcal{V}}_{\partial}}\oplus{{\mathcal{V}}_{\neq 1}}\oplus{\mathcal{V}}'\oplus{{\mathcal{V}}_{\fix}}$, where ${\mathcal{V}}'$ is constructed from ${{\mathcal{V}}_{\operatorname{im}}}$ by replacing each summand ${\mathcal{W}}^1_1(\pm 1)$ of ${{\mathcal{V}}_{\operatorname{im}}}$ by a copy of ${\mathcal{V}}^2_1(\pm 1)$.
It is straightforward that the operator $h$ of ${{\mathcal{V}}_{\mend}}$ is the monodromy $ H_1(\S)\to H_1(\S)$, the form $b$ of ${{\mathcal{V}}_{\mend}}$ is the intersection form of $\S$, and the restriction of ${{\mathcal{V}}_{\mend}}$ on $\vs$ is ${{\mathcal{V}}_{\frct}}$. The operator $V$ of ${{\mathcal{V}}_{\mend}}$ is zero on $\vf\oplus U_B$, which is exactly the kernel of $V$. This space is isomorphic to $H_1(M;\C)$, since $j_*:H_1(\S)\to H_1(M)$ is onto, cf. Lemma \[lem:new\](c).
The form of the above extensions is motivated by Theorem \[th:mendfib\].
The ‘classical’ homological variation structure on $H_1(\S)$ {#ss:clas}
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Fix a fibred link $(M,L,p)$ and consider the fibration $p:M\setminus L\to S^1$ with fiber $\Sigma=p^{-1}(1)$. Let $\hs:\S\to\S$ be the geometric monodromy as in Definition \[def:hs\]. We can assume that $\hs|_{\partial \S} $ is the identity (this is how usually we recover $M$ from $\hs$).
The [*variation map*]{} $\operatorname{Var}:H_1(\S,\partial\S)\to H_1(\S)$ is given by $[x]\mapsto [\hs(x)-x]$ for any relative cycle $x$ of $(\S,\partial \S)$, see e.g. [@Lo]. After identifying $H_1(\S,\partial\S)$ with the dual of $H_1(\S)$ we obtain the [*homological (real) VHS associated with the fibration $p$*]{}, ${\mathcal{V}}_{{\rm fib}}:=(H_1(\S); b,h, \operatorname{Var})$, where $b$ and $h$ are the intersection form and the algebraic monodromy. (${\mathcal{V}}_{{\rm fib}}$ is defined already over $\Z$.)
It is known that when $M$ is a $\Q$– or $\Z$–homology sphere, then $\operatorname{Var}= (S^t)^{-1}$ (over $\Q$ or $\Z$ respectively). This fact is generalized in the next statement.
\[th:mendfib\] ${\mathcal{V}}_{{\rm fib}}={{\mathcal{V}}_{\mend}}$. Moreover, ${\mathcal{V}}_{{\rm fib}}$ determines the fractured Seifert form $S$, while $S$ and the integer $n$ (the number of components of $L$) determine ${\mathcal{V}}_{{\rm fib}}$ as well.
Let us write $\widetilde{U}:= \vi\oplus U_B$. Note that the monodromy $h$ and the intersection form $b$ on $U=H_1(\S)$ have block decomposition according to the direct sum decomposition $U=U_{\not=1}\oplus \vf\oplus \widetilde{U}\oplus \vb$. Since the kernel of $b$ is exactly $\vb$, by Lemma \[lem:split\] the whole ${\mathcal{V}}_{{\rm fib}}$ splits into ${\mathcal{V}}_{\not=1}\oplus {\mathcal{V}}_{fix}\oplus \widetilde{{\mathcal{V}}}\oplus {{\mathcal{V}}_{\partial}}$.
Consider now the homological exact sequence of the pair $(M,\S)$. In the presence of the open book decomposition $p$, the boundary operator $\partial: H_2(M,\S)\to H_1(\S)$ can be identified with $\operatorname{Var}:H_1(\S,\partial \S)\to H_1(\S)$. Hence, one has the exact sequence (see also [@Ste (2.6)(b)]) $$\label{ex:VAR}
0\to H_2(M)\to H_2(\S,\partial \S)\stackrel{\operatorname{Var}}{\longrightarrow} H_1(\S)\to H_1(M)\to 0.$$ This has several consequences. First, $\operatorname{im}\operatorname{Var}=U^\S$. Hence, if $\alpha\in H_1(\S,\partial \S)$ and $\beta\in U^\S$, and $\alpha(\beta)$ denotes the pairing (duality) $H_1(\S,\partial\S)\otimes H_1(\S)=
U^*\otimes U\to \R$, then $S(\operatorname{Var}\alpha,\beta)$ is well-defined, and, in fact, it equals $\alpha(\beta)$ (whose proof is analogous to the proof of \[lem:new2\](b)). In matrix notations, $ \alpha(\beta)=S^t(\operatorname{Var}\alpha)(\beta)$, hence $S^t\cdot \operatorname{Var}$ is the identity whenever $S$ is well-defined. In particular, $\operatorname{Var}$ extends $(S^t)^{-1}$ from $U^\S$ to $U$.
The extension is special: by (\[ex:VAR\]) the rank of the kernel of $\operatorname{Var}$ is $\dim H_1(M)$ which equals $\dim (\vf\oplus U_B)$ (cf. the end of \[ss:chvs\]), the complementary space of $U^\S$ in $U$.
Since $b|_{\vf}$ is non-degenerate on $\vf$, it determines the HVS, hence this component agrees with the extension \[def:fixext\] of ${{\mathcal{V}}_{\mend}}$. Finally, the extension from $\vi$ to $\widetilde{U}$ with the imposed kernel property mentioned above, imposes the modification ${\mathcal{W}}^1_1(\pm 1) \,\mapsto \, {\mathcal{V}}^2_1(\pm 1)$ from \[def:mended\]. This ends the proof of the identity ${\mathcal{V}}_{{\rm fib}}={{\mathcal{V}}_{\mend}}$.
Let us recall the type of the blocks of $({{\mathcal{V}}_{\mend}})_{=1}$. ${{\mathcal{V}}_{\fix}}$ is a direct sum of $\frac12\dim\vf$ copies of ${\mathcal{V}}^1_1(+1)\oplus {\mathcal{V}}^1_1(-1)$, ${{\mathcal{V}}_{\partial}}=(n-1)\cdot {\mathcal{W}}^1_1(+1)$, while $\widetilde{{\mathcal{V}}}$ has (say) $c_{\pm}$ copies of ${\mathcal{V}}^2_1(\pm 1)$.
Since all these types are different, it is easy to delete the extended part: ${{\mathcal{V}}_{\fix}}$ is deleted, ${{\mathcal{V}}_{\partial}}$ is preserved, while $\oplus_\pm\,
c_{\pm}\cdot {\mathcal{V}}^2_1(\pm 1)$ is modified into $\oplus_\pm \,c_{\pm}\cdot {\mathcal{W}}^1_1(\pm 1)$ (the restriction to $\vi=\operatorname{im}(h|_{\vi}-1)\subset \widetilde{U}$). Hence, ${\mathcal{V}}_{{\rm fib}}$ determines $S$.
Conversely, the matrix $S$ itself almost determines ${\mathcal{V}}_{{\rm fib}}$. The only missing data is to know, how to separate the sum $n-1+c_+$ (which is determined from $S$) into two pieces $n-1$ and $c_+$.
Isolated complex analytic surface singularities {#S:NSS}
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Links in isolated surfaces singularities {#s:milnor}
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Let $(X,0)$ be a complex analytic isolated surface singularity (germ). We fix an embedding of $(X,0)$ into some $\C^N$. The *link* of $(X,0)$ is the oriented 3-manifold $M$ obtained as the intersection $X\cap S^{2N-1}_\e$, where $S^{2N-1}_\e$ is a sphere of sufficiently small radius $\e$ and centered at $0$. The diffeomorphism type of $M$ does not depend on the choice of the embedding and on the radius of the sphere [@LDT; @Lo; @Milnor-book].
Assume that $g\colon (X,0)\to(\C,0)$ is the germ of an analytic function, which determines an isolated singularity $(\{g=0\},0)\subset (X,0)$. If $\e$ is sufficiently small, then the intersection $L_g:=M\cap\{g=0\}$ is transverse.
The pair $L_g\subset M$ is called the *link* of the germ $g$ at $0$.
For a germ $g$ as above one defines two fibrations. The first one is the [*Milnor fibration*]{} (see [@Milnor-book] when $X$ is smooth and [@Ham] in the general case).
\[prop:MilnorOnM\] The map $\arg g\colon M\sm L_g\to S^1$ defines an open book decomposition of $(M,L_g)$.
In parallel, let $\eta>0$ be sufficiently small, $D_\eta\subset\C$ be the disk of radius $\e$ centre $0$, and $B_\e \subset\C^N$ be the $\e$–ball around $0$. Then one has the [*tube filtration*]{} (see [@LDT3]):
\[prop:MilnorOnB\] The map $g\colon (g^{-1}(D_\eta\setminus 0)\cap B_\e)\to D_\eta
\sm 0$ is a locally trivial fibration.
\[prop:equiv\] [@Milnor-book; @LDT; @CSS] The fibrations $\arg g$ of \[prop:MilnorOnM\] and the restriction of the fibration of \[prop:MilnorOnB\] to $S^1=\partial D_\eta$ are equivalent. In particular, their fibres are diffeomorphic and the monodromy maps coincide.
Take $\Sigma:=(\arg g)^{-1}(1)\subset M $ to be the Seifert surface of $L_g$ and denote the components of $L_g$ by $K_1,\ldots, K_n$. For the pair $\S\subset M$ we will use all the notation of sections 2 and 3.
The following result proves that $L_g\subset M$ is a 0–link in the sense of Definition \[def:link\].
\[lem:nullhomog\] Each component $K_i$ of $L_g$ represents $0\in H_1(M;\Q)$.
In general it is not true that there exist analytic germs $g_i:(X,0)\to (\C,0)$ ($1\leq i\leq n$), such that the link of $g_i$ is $K_i\subset M$. However, if we allow to modify the analytic structure supported on the topological type of $(X,0)$ (that is, if we keep the pair $(M,L_g)$ up to an isotopy, but we change the analytic structure into some $(X_i,0)$), then such a germ $g_i:(X_i,0)\to (\C,0)$ exists; see [@NP], or page 3 of [@NNP]. Then the Milnor fiber $\Sigma_i\subset M$ of $g_i$ satisfies $\p\Sigma_i=K_i$.
\[lem:vbneg\] $L_g$ is special fibred in the sense of Definition \[def:link\]. In particular, the form $\operatorname{flk}$ on $\vb$ is negative definite (cf. Lemma \[lem:nondeg\]).
We need to show that $\operatorname{flk}(K_i,K_j)>0$ for any $ i<j$. By resolution of singularities, the pair $g^{-1}(0)\subset X$ has an embedded resolution, hence the pair $L_g\subset M$ has a plumbing representation, where each $K_i$ is represented by an arrowhead. Let $\Sigma_i$ be the Seifert surface of $K_i$ provided by the Milnor fiber of $g_i:(X_i,0)\to (\C,0)$ (identified topologically, cf. the proof of Lemma \[lem:nullhomog\]). If the arrowhead associated with $K_j$ is supported by the vertex $v_j$, then $\operatorname{flk}(K_i,K_j)=\S_i\cdot K_j$ is exactly the multiplicity of the germ $g_i$ along the exceptional divisor marked by $v_j$. This is a positive integer (which can be identified combinatorially from the plumbing graph of $(M,L_g)$).
Finally, we verify that $L_g$ is simple in the sense of Definition \[def:simple\].
\[prop:monod\] The eigenvalues of monodromy $h$ are roots of unity, and $h$ does not have any Jordan blocks of size $\ge 3$.
The fibred link $(M,L_g,\arg g)$ is a simple fibred link.
In particular, its fractured HVS ${\mathcal{V}}_{{\rm frct}}$ and the mended HVS ${{\mathcal{V}}_{\mend}}$ are well-defined, and ${{\mathcal{V}}_{\mend}}={\mathcal{V}}_{{\rm fib}}$. The analyticity implies one more restriction for them. It is the generalization of [@Neu-inv (3.2)] (valid for plane curves and $\lambda\not=1$), [@Nem2 6.14] (valid for arbitrary hypersurfaces and $\lambda\not=1$).
\[prop:twist\] For any eigenvalue $\lambda$ the block ${\mathcal{V}}^2_\lambda(-1)$ does not appear in ${\mathcal{V}}_{{\rm fib}}$.
Consider first the case $\lambda=1$. Using the terminology of [@EN Sec. 13], the twist of the monodromy is nonpositive. This follows similarly as in [@EN], since it involves only local computation regarding local analytic germs of type $f(x,y)=x^ay^b$ with $a,b$ positive integers and $(x,y)\in (\C^2,0)$ corresponding to the edges of an embedded resolution graph. This means, that if $\alpha\in H_1(\S,\partial \S)$ then $\alpha(\operatorname{Var}\alpha)$ should be nonpositive (here we use for $\alpha(\beta)$ the notation of the proof of Theorem \[th:mendfib\], regarding the pairing $(\alpha,\beta)\in H_1(\S,\partial\S)\otimes H_1(\S)$). Since $\alpha(\beta)=S(\operatorname{Var}\alpha,\beta)$ (cf. the proof of \[th:mendfib\]) we get that $\alpha(\operatorname{Var}\alpha)= S(\operatorname{Var}\alpha,\operatorname{Var}\alpha)$. Let us consider ${\mathcal{V}}^2_1(\pm 1)$. It is the structure $$\Big( \C^2;\, \bp 0&\mp 1\\ \pm 1 & 0\ep, \bp 1&1\\ 0&1\ep, \bp \mp 1& 0\\ 0&0\ep\Big).$$ Suppose ${\mathcal{V}}^2_1(\pm 1)$ is a summand of ${\mathcal{V}}_{{\rm fib}}$, let $\alpha$ be in $\C^2$ corresponding to ${\mathcal{V}}^2_1(\pm 1)$, then $\operatorname{Var}\alpha$ is a vector of type $(a,0)$ for some $a\in\C$ and then $\alpha(\operatorname{Var}\alpha)=\mp a^2$. This is nonpositive for any $\alpha$ if and only if from $\mp$ we take the minus sign.
In the literature, there is another test for the sign of the twist which works uniformly for any $\lambda$. In [@Neu-inv] the notations are the following: Neumann’s $L$ is our $S^t$, while his $S$ is our $b^t$. (This can be verified by identifying his identities with ours from Definition \[def:HVS\].) Then, for any $\lambda$, an $N$–root of unity, the test from pages 228–229 from [@Neu-inv] requires that $S(\alpha, (h^N-1)\alpha)$ is nonpositive. This, in our language, means that $b^t_\pm(J_2-1)$ must have on the diagonal nonpositive entries (where $b_\pm$ is the $b$–operator of ${\mathcal{V}}^2_\lambda(\pm1)$, or of ${\mathcal{V}}^2_1(\pm1)$ given above). By a computation, $b^t_\pm(J_2-1)={\tiny \bp 0& 0\\ 0& \mp1\ep}$, hence in $\mp1$ only the $-$ sign is allowed.
\[rem:graph\] As a corollary of Proposition \[prop:twist\], the components ${{\mathcal{V}}_{\fix}}\oplus {{\mathcal{V}}_{\partial}}\oplus \widetilde{{\mathcal{V}}}$ of $({\mathcal{V}}_{{\rm fib}})_{=1}$ (generalized eigenspace for $\lambda=1$) are the following: ${{\mathcal{V}}_{\fix}}$ is a direct sum of $\frac12\dim\vf$ copies of ${\mathcal{V}}^1_1(+1)\oplus {\mathcal{V}}^1_1(-1)$, ${{\mathcal{V}}_{\partial}}=(n-1)\cdot {\mathcal{W}}^1_1(+1)$, and $\widetilde{{\mathcal{V}}}$ is a direct sum of $\dim \vi$ copies of ${\mathcal{V}}^2_1(+ 1)$. All these ranks can be read from the dual embedded resolution graph of $(M,L_g)$.
Indeed, if $\Gamma$ is the (abstract) dual resolution graph of $(X,0)$, let $c(\Gamma)$ be the number of independent cycles in $\Gamma$ (that is, the first Betti number of the topological realization of $\Gamma$), and let $g(\Gamma)$ be the sum of all genus decorations of the vertices. Then, by [@NS], $c(\Gamma)=\dim \vi$ (which equals the number of $2\times 2$-Jordan blocks with eigenvalue one), and $\dim \vf=2g(\Gamma)$. In particular, all these numbers are independent of the choice of the germ $g$ (that is, of the choice of the link $L_g$). Moreover, $\dim H_1(M)=2g(\Gamma)+c(\Gamma)$.
On the other hand, $n$ obviously is the number of arrowheads of the graph of $(M,L_g)$.
Regarding the notations of the proof of Theorem \[th:mendfib\], in this analytic case $c_-=0$, and $c_+=c(\Gamma)$. Hence $({\mathcal{V}}_{{\rm frct}})_{=1}$ consists of $n-1+c(\Gamma)$ copies of ${\mathcal{W}}^1_1(+1)$. Hence, the last statement of Theorem \[th:mendfib\] can be reformulated also as follows: $S$ and $c(\Gamma)$ determine ${\mathcal{V}}_{{\rm fib}}$.
In particular, if $\Gamma$ is a tree, then $S$ and ${\mathcal{V}}_{{\rm fib}}$ determine each other.
Mixed Hodge Structures on the vanishing (co)homology of $g$ {#ss:MHS}
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If $g$ is an isolated hypersurface singularity (in any dimension) then the cohomology of its Milnor fiber carries a mixed Hodge structure by the work of Steenbrink and Varchenko. The structure is compatible with the monodromy action (the semisimple and the nilpotent parts are morphisms of type $(0,0)$ and $(-1,-1)$ respectively), and has several polarization properties induced by the intersection and variation forms. Steenbrink and Varchenko considered also the associated spectrum, which are rational numbers $\alpha$, one number for each eigenvalue $\lambda=e^{2\pi i\alpha}$ of the monodromy, such that the choice of $\alpha$ reflects the position in the Hodge filtration of the corresponding eigenvector.
The more general case when $(X,0)$ is a space germ with an isolated singularity, and $g:(X,0)\to (\C,0)$ is an analytic function germ which also defines an isolated singularity, is treated in [@Ste]. In this case, if $\dim (X,0)=2$, then the spectrum $\operatorname{Sp}_{{\rm MHS}}$ is situated in the interval $(0,2]$ (or shifted to $(-1,1]$, but here we prefer the first version). For precise definitions and particular cases see the articles of Steenbrink and Varchenko in the present bibliography (e.g. [@Stee (5.3)] or [@Stsp]), and also their references.
In fact, the (co)homologies of the link $M$ itself carry mixed Hodge structure as well (see e.g. [@Ste]). For example, if $\dim
(X,0)=2$, then $\dim\operatorname{Gr}^W_{-1}H_1(M)=2g(\Gamma)$ and $\dim\operatorname{Gr}^W_0H_1(M)=c(\Gamma)$ (in $H^1(M)$ the weights are $+1$ and $0$). The Hodge numbers for $H_1(M)$ are $h_{-1,0}=h_{0,-1}=g(\Gamma)$ and $h_{0,0}=c(\Gamma)$. Moreover, the natural geometric exact sequences (like (\[ex:VAR\])) are compatible with MHS (see e.g. the proof of Theorem \[th:specs\]).
If $H_1(M,\Q)=0$ then $\operatorname{Sp}_{{\rm MHS}}$ is symmetric with respect to 1, see [@SSS]. Hence, in this case $\operatorname{Sp}_{{\rm MHS}}\subset (0,2)$. However, in general, $\operatorname{Sp}_{{\rm MHS}}\cap\Z$ fails to be symmetric, see below.
In our approach, one can consider the fractured HVS ${\mathcal{V}}_{{\rm frct}}$ and its spectrum $\operatorname{Sp}_{{\rm frct}}\subset (0,2]$ determined from ${\mathcal{V}}_{{\rm frct}}$ as in Section \[s:specHVS\].
\[th:specs\]
- $\operatorname{Sp}_{{\rm MHS}}\setminus \Z = \operatorname{Sp}_{{\rm frct}}\setminus \Z$. In particular, they are both symmetric with respect to 1. Hence $\operatorname{Sp}_{{\rm frct}}$ is also symmetric.
- In $\operatorname{Sp}_{{\rm MHS}}$ the spectral number 2 appears with multiplicity $c(\Gamma)+g(\Gamma)$, while 1 with multiplicity $c(\Gamma)+g(\Gamma)+n-1$.
- All integral spectral numbers of ${\mathcal{V}}_{{\rm frct}}$ are concentrated at 1 with multiplicity $c(\Gamma)+n-1$.
- The spectrum $\operatorname{Sp}_{{\rm MHS}}$ coincides with the spectrum of ${\mathcal{V}}_{{\rm fib}}$ (hence also with the spectrum of ${\mathcal{V}}_{{\rm mend}}$, by Theorem \[th:mendfib\]).
- In particular, $\operatorname{Sp}_{{\rm MHS}}=\operatorname{Sp}_{{\rm frct}} + g(\Gamma)\cdot \{1,2\}+ c(\Gamma)\cdot \{2\}$.
Here all the spaces are considered with complex coefficients. As the monodromy preserves the decomposition $H_1(M)=\vn\oplus\vf\oplus\vb\oplus(\vbb\oplus\vi)$, the spectrum of MHS is a union of contributions on $\vn$, $\vf$, $\vb$ and $\vbb\oplus\vi$. On $\vn\oplus\vf$ the intersection form is non–degenerate, so the polarization property of the MHS (as in [@Nem2 Section 6]) shows that the spectrum of the MHS agrees with the spectrum ${\operatorname{Sp}_{\neq 1}}\cup{\operatorname{Sp}_{\fix}}$. This shows (a). Notice that $\vf$ is the sum of the same amount of copies of blocks with different polarizations (signs), hence ${\operatorname{Sp}_{\fix}}$ is a union of the same amount of copies of $\{1\}$ and $\{2\}$.
On $\vi\oplus\vbb$, the monodromy is the union of two–dimensional Jordan blocks with eigenvalue 1. Each Jordan block corresponds to either ${\mathcal{V}}^2_1(1)$, or ${\mathcal{V}}^2_1(-1)$, but the contribution of both structures to the spectrum is the same: each contributes with $\{1,2\}$. Indeed, the nilpotent monodromy operator shifts the Hodge filtration by $-1$; in particular $\vi$ contributes with spectral numbers 1 and $\vbb$ with 2.
The contribution of $\vb$ to $\operatorname{Sp}_{\operatorname{MHS}}$ follows from an extension of the argument in [@SSS Theorem 2.1] (the term $(\#\mathcal{A}-1)(0,1)$ in that article corresponds to the element $(n-1)\cdot\{1\}$ in $\operatorname{Sp}_{\operatorname{MHS}}$). The above discussion (see also Remark \[rem:graph\]) shows that $\operatorname{Sp}_{\operatorname{MHS}}$ agrees with the spectrum of ${\mathcal{V}}_{{\rm fib}}$. So (b) and (d) are also proved.
\(c) For $\lambda=1$ we have only blocks of type ${\mathcal{W}}^1_1(+1)$ (cf. Proposition \[prop:twist\]); then use Definition \[def:spectrum\].
Part (e) is a consequence of (a)–(d) and the comparison of ${{\mathcal{V}}_{\frct}}$ with ${\mathcal{V}}_{{\rm fib}}$ in Remark \[rem:graph\].
An alternating way to check the Hodge types of the blocks $\vb$ and $\vf\oplus \vbb$ is via exact sequences. There are two main exact sequences (usually written in cohomology and compact support cohomology), both of them being sequences of mixed Hodge structures, see [@Ste (2.6)(a)-(b)]. The first, written in our language, is $$0\to \C\to H_1(\partial \Sigma)\to (H_1(\Sigma))_1\stackrel{j}{\to}(H_1(\Sigma,\partial \Sigma))_1\to H_1(\partial \Sigma)\to \C\to 0,$$ where (by duality) $j$ can be identified with our $b_1$. In particular, the kernel of $b_1$ (hence $\vb$ too) supports a mixed Hodge structure, as the link of the curve singularity $X\cap \{f=0\}$. For dimensional reason it supports only one Hodge type, which is the same as for curves sitting on surface singularities with rational homology sphere links, or even as for plane curve singularities. Hence they have the same type of spectrum contributions, namely 1.
To identify the term $\vf\oplus \vbb\simeq {\rm coker}({\rm Var})$ we consider the ‘variation exact sequence’: $$0\to H_2(M)\to H_1(\Sigma,\partial \Sigma)\stackrel{{\rm Var}}{\longrightarrow}H_1(\Sigma)\to H_1(M)\to 0$$ and use the Hodge types of $M$, cf. Section \[ss:MHS\].
We emphasize again that $\operatorname{Sp}_{{\rm frct}}$ can be connected with the signatures of ${\mathcal{V}}_{{\rm frct}}$ by Lemma \[lem:sigandspec\]. They agree with the signatures of the Seifert form because of the following lemma.
\[lem:signature\] The fractured signature of the link $L_g$ (defines via the Seifert matrix, cf. Definition \[def:fracturedsig\]) is equal to the signature of ${\mathcal{V}}_{{\rm frct}}$ (cf. Definition \[def:signatureofHVS\]).
Note that $V=(S^t)^{-1}$. But then we have $$S\left((1-z)V+(1-{\overline{z}})V^t\right)S^t=(1-z)S+(1-{\overline{z}})S^t,$$ hence the two forms $(1-z)V+(1-{\overline{z}})V^t$ and $(1-z)S+(1-{\overline{z}})S^t$ are congruent. Their signatures coincide.
Deformations of singularities {#s:notation}
-----------------------------
In this section we establish notation, which will allow us to formulate and prove Theorem \[thm:semic\].
A *deformation* of an isolated singularity $g_0:(X,0)\to (\C,0)$ is a complex 3-dimensional variety $\X\subset\C^{N}\times D$ (where $D$ is a small disk in $\C$ centered at the origin) together with an analytic function $G\colon\X\to\C$ and a projection $\pi\colon\X\to D$ such that:
- $\pi$ is a flat morphism;
- for $t\in D$, the inverse image $X_t:=\pi^{-1}(t)$ is a surface with isolated singularities;
- the function $g_t=G|_{X_t}$ has only isolated singularities;
- the central fiber $X_0$ has a single singularity $x_0$ and $g_0$ is regular away from $x_0$.
Given such a deformation, let us choose a small ball $B_0\subset\C^{N}$ and put $S_0=\p B_0$. Suppose that the ball is such that $X_0\cap S_0$ is the link $M_0$ of the singularity $x_0\in X_0$. Shrinking $B_0$ if necessary, we can assume that $g_0^{-1}(0)\cap S_0$ is the link of singularity of $g_0$ at $x_0$. We shall denote this link by $L_0$.
(-6,-3)(6,3) (2.5,2.5)(2,2)(1,0)(0,0)(2.7,2.7) (2.5,-2.5)(2,-2)(1,0)(0,0) (3,2.5)(2.5,2)(2.1,1.3)(1.8,1.2)(3.2,2.7) (1.8,1.2)(2.1,1.1)(1.5,0)(1,0) (3,-2.5)(2.5,-2)(2.1,-1.3)(1.8,-1.2) (1.8,-1.2)(2.1,-1.1)(1.5,0)(1,0) (1,0)[0.07]{} (1.8,1.2)[0.07]{} (1.8,-1.2)[0.07]{} (2.4,1.8)(2.2,1.6)(2.15,1.4)(1.95,1.35) (1.85,1.05)(1.85,0.9)(1.5,0.17)(1.3,0.1) (2.4,-1.8)(2.2,-1.6)(2.15,-1.4)(1.95,-1.35) (1.85,-1.05)(1.85,-0.9)(1.5,-0.17)(1.3,-0.1) (2,0.5)
(1.9,1.3)[0.04]{} (1,0)[0.3]{}(1.2,0.35) (1.8,1.2)[0.2]{}(2.2,1.2) (1.8,-1.2)[0.2]{}(2.2,-1.2) (0,0)[3]{}(3.2,0)
Let now $t\in D\sm\{0\}$ be sufficiently small. Then $X_t\cap S_0\cong M_0$. Furthermore, by choosing $t$ small enough we can guarantee that $(X_t\cap S_0,g_t^{-1}(0)\cap X_t\cap S_0)\cong (M_0,L_0)$ as pairs. Let $x_1,\dots,x_k$ be the critical points of $g_t$ on $X_t$. (If $x\in X_t$ is a singular point of $X_t$ and $g_t(x)=0$, then $x$ has to be considered as a critical point of $g_t$.) Let $B_1,\dots,B_k$ be small pairwise disjoint balls near $x_1,\dots,x_k$ such that $B_i\subset B_0$ and the pair $(M_i,L_i):=(\p B_i\cap X_t,\p B_i\cap X_t\cap g_t^{-1}(0))$ is the link of the singularity of $g_t$ at $x_i$. Finally let $$W={\overline{B_0\cap X_t\sm(B_1\cup\cdots \cup B_k)}}.$$ Then $W$ is a cobordism between a disjoint union $M_1\cup\cdots \cup M_k$ and $M_0$. In general, $W$ can have a finite number of singular points: these are all those singular points of $X_t$ where $g_t$ does not vanish. See Figure \[fig:deform\].
Let us consider the map $\arg g_t\colon W\to S^1$. This is a surjection and let us pick a regular value $\delta$ such that $\O:=\arg g_t^{-1}(\delta)$ omits all the singular points of $W$. We have the following observation.
For any $i=0,\dots,k$ the intersection $\O\cap\p B_i$ is the Seifert surface $\S_i$ for $L_i$ cut out by its Milnor open book.
Let $Y={\overline{\p\O\sm\bigcup_{i=0}^k\S_i}}$. Observe that $Y=g_t^{-1}(0)\cap W$. Let also $Z=Y\cup\S_1\cup\dots\cup\S_k$. (This has some ‘corners’ along $\partial Y$, but they can be smoothed.)
\[lem:Zisdiffeo\] The manifold $Z$ is diffeomorphic to a Seifert surface $\S_0$.
By Proposition \[prop:equiv\], $\S_0\cong g_0^{-1}(\delta)\cap B_0$ if $\delta\in\C\sm\{0\}$ is sufficiently small. Then, since $t$ is sufficiently close to $0$, $\S_0\cong g_t^{-1}(\delta)\cap B_0$. Now $$g_t^{-1}(\delta)\cap B_0=\big(g_t^{-1}(\delta)\cap W\big)
\cup\bigcup_{i=1}^k \big(g_t^{-1}(\delta)\cap B_i\big).$$ Applying Proposition \[prop:equiv\] again, we have $g_t^{-1}(\delta)\cap B_i\cong\S_i$. On the other hand, since $\delta$ is very small and $g_t^{-1}(0)$ has no singular points, we have $Y=g_t^{-1}(0)\cap W\cong g_t^{-1}(\delta)\cap W$.
Semicontinuity of ${\operatorname{Sp}_{\frct}}$ {#s:semic}
-----------------------------------------------
Given the notation introduced in Section \[s:notation\] we are ready to formulate and prove the next semicontinuity result regarding the spectrum. ${\operatorname{Sp}_{\frct}}^i$ denotes the spectrum associated with the corresponding local fractured HVS, $i=0,\ldots, k$.
\[thm:semic\] If $s\in[0,1]$ is such that $z=e^{2\pi is}$ is not an eigenvalue of the monodromy of $L_0$, then $$\begin{aligned}
|{\operatorname{Sp}_{\frct}}^0\cap(s,s+1)|\ge& \sum_{i=1}^k|{\operatorname{Sp}_{\frct}}^i\cap(s,s+1)|-\operatorname{Irr}_2-\operatorname{Irr}_1\\
|{\operatorname{Sp}_{\frct}}^0\sm[s,s+1]|\ge& \sum_{i=1}^k|{\operatorname{Sp}_{\frct}}^i\sm[s,s+1]|-\operatorname{Irr}_2-\operatorname{Irr}_1,\end{aligned}$$ where $$\operatorname{Irr}_1=\dim\ker(H_1(M_0\cup M_1\cup\dots\cup M_k)\to H_1(W))-\sum_{i=1}^k b_1(M_i).$$
The pair $(W,\O)$ is a Seifert cobordism of links $(M_0,L_0)$ and $(M_1,L_1)\sqcup\dots\sqcup(M_k,L_k)$. For $i=0,\dots,k$, let $\s_i(z)$ denotes the fractured signature of the link $L_i$. Suppose first that $z$ is chosen so that $z$ is not an eigenvalue of the monodromy of any $h_i$. Since the links $(M_0,L_0)$,…,$(M_k,L_k)$ are simple fibred, we have $n_0(z)=n_1(z)=\dots=0$.
Theorem \[thm:signatures\] applied in this situation yields
$$\begin{gathered}
\left|\sum_{i=1}^k\s_i(z)-\s_0(z)\right|\le
\sum_{i=1}^k(\dim \vs_i-2b_1(\S_i))+b_1(\p\O)+\dim \vs_0-2b_1(\S_0)+\\
+2\operatorname{Irr}_2+2\dim\ker(H_1(M_0\cup M_1\cup\dots\cup M_k)\to H_1(W)).\end{gathered}$$
Here $\vs_i=\ker(H_1(\S_i)\to H_1(M_i))$ and $\dim\vs_i$ is the size of the fractured Seifert matrix for $M_i$. Therefore $\dim \vs_i-2b_1(\S_i)=-\dim \vs_i-2b_1(M_i)$. On the other hand, by Lemma \[lem:Zisdiffeo\], we have $\p\O\cong\S_0\cup\S_0$, hence $b_1(\p\O)=2 b_1(\S_0)$. We obtain.
$$\label{eq:firstsemic}
\begin{split}
&\left|\sum_{i=1}^k\s_i(z)-\s_0(z)\right|+\sum_{i=1}^k\dim \vs_i-\dim \vs_0\le\\
&\le 2\operatorname{Irr}_2+2\dim\ker(H_1(M_0\cup M_1\cup\dots\cup M_k)\to H_1(W))-2\sum_{i=1}^k b_1(M_i).
\end{split}$$
The proof now follows from Lemma \[lem:sigandspec\]. It remains to deal with the case where $z$ is an eigenvalue of $h_j$ for some $j>0$. This is done by choosing $z'$ sufficiently close to $z$ and using the result for $z'$. The argument is as in [@BNR Section 4.1], we omit here the details.
Special cases of Theorem \[thm:semic\]
--------------------------------------
Theorem \[thm:semic\] is stated in a rather general form, $X_t$ might have many singular points, $W$ itself is allowed to be singular. Sometimes it is more convenient to have some special cases. We begin with the following lemma
We have $$\operatorname{Irr}_1+\operatorname{Irr}_2=\dim H_2(W,M)-\sum_{i=1}^k b_1(M_i),$$ where $M=\p W=M_0\sqcup M_1\sqcup\dots\sqcup M_k$.
By the long exact sequence of the pair $(W,M)$ we obtain $$\dim\operatorname{coker}(H_2(M)\to H_2(W))+\dim\ker(H_1(M)\to H_1(W))=\dim H_2(W,M).$$
\[prop:irr=0\] Suppose that $M_0\cong M_1$ are rational homology cobordant and $M_2\cong\dots\cong M_k\cong S^3$. Suppose additionally that $W$ is built from a rational $H$–cobordism (that is the inclusions $M_0\hookrightarrow W'$ and $M_1\hookrightarrow W'$ induce isomorphism on rational homologies) $W'$ between $M_0$ and $M_1$ by removing $k-1$ balls, then $\operatorname{Irr}_1+\operatorname{Irr}_2=0$.
Clearly $H_2(W',M)\cong H_2(W,M)$. Furthermore $\dim H_2(W,M)=b_1(M_0)=b_1(M_1)$. The statement follows by definition.
If $\X$ is a trivial deformation, that is $X_t\cong X_0$, then $\operatorname{Irr}_1+\operatorname{Irr}_2=0$.
We can choose $M_1$ to be equal to $M_0$. Then $W$ is obtained from $M_0\times [0,1]$ by removing a finite number of 4-balls; these balls are neighbourhoods of the critical points of $g_t$ on $g_t^{-1}(0)$. Thus $W$ satisfies the assumptions of Proposition \[prop:irr=0\].
Semicontinuity results for ${\operatorname{Sp}_{\operatorname{MHS}}}$
---------------------------------------------------------------------
Using Theorem \[th:specs\](e) we can now deduce semicontinuity property for ${\operatorname{Sp}_{\operatorname{MHS}}}$ from Theorem \[thm:semic\]. For $i=0,1,\ldots,k$ let $c_i$ and $g_i$ be the quantities $c(\Gamma)$ and $g(\Gamma)$ corresponding to $M_i$, as in Remark \[rem:graph\]. That is $c_i$ is the number of independent cycles in the graph $\Gamma_i$ representing the link $M_i$, while $g_i$ is the sum of all genus decorations of the vertices. Let us set $$\Delta_1=c_0-\sum_{i=1}^kc_i, \ \ \ \ \
\Delta_2=c_0+g_0-\sum_{i=1}^k(c_i+g_i).$$ Then one has the following result.
\[thm:semic-MHS\] If $s\in[0,1]$ is such that $z=e^{2\pi is}$ is not an eigenvalue of the monodromy operator of $L_0$, then $$\begin{aligned}
|{\operatorname{Sp}_{\operatorname{MHS}}}^0\cap(s,s+1)|\ge& \sum_{i=1}^k|{\operatorname{Sp}_{\operatorname{MHS}}}^i\cap(s,s+1)|-\operatorname{Irr}_2-\operatorname{Irr}_1+\Delta_1\\
|{\operatorname{Sp}_{\operatorname{MHS}}}^0\sm[s,s+1]|\ge& \sum_{i=1}^k|{\operatorname{Sp}_{\operatorname{MHS}}}^i\sm[s,s+1]|-\operatorname{Irr}_2-\operatorname{Irr}_1+\Delta_2.\end{aligned}$$
Suppose $s\in(0,1)$. We use the fact that $|({\operatorname{Sp}_{\operatorname{MHS}}}^i\sm{\operatorname{Sp}_{\frct}}^i)\cap(s,s+1)|=c_i$ and $|({\operatorname{Sp}_{\operatorname{MHS}}}^i\sm{\operatorname{Sp}_{\frct}}^i)\sm(s,s+1)|=c_i+g_i$, which follows from Theorem \[th:specs\](d).
If $s=0$ or $s=1$, then the assumptions imply that $1$ is not an eigenvalue of the monodromy operator of $L_0$, in particular, neither 1 nor 2 are in ${\operatorname{Sp}_{\operatorname{MHS}}}^0$. By Remark \[rem:graph\] we infer that $c_0=g_0=0$, hence $\Delta_1,\Delta_2\le 0$. Clearly, ${\operatorname{Sp}_{\operatorname{MHS}}}^i\cap(0,1)={\operatorname{Sp}_{\frct}}^i\cap(0,1)$, so the first inequality holds if $s=0,1$. If $s=0$, we have ${\operatorname{Sp}_{\operatorname{MHS}}}^i\sm[0,1]={\operatorname{Sp}_{\frct}}^i\sm[0,1]\cap (g_i+c_i)\cdot\{2\}$, so the second inequality in that case follows from the case $s\in(0,1)$. As ${\operatorname{Sp}_{\operatorname{MHS}}}^i\sm[1,2]={\operatorname{Sp}_{\frct}}^i\sm[1,2]$ and $\Delta_2\le 0$, we infer that the second inequality holds for $s=1$ as well.
As a corollary, we prove the semicontinuity in the case of Proposition \[prop:irr=0\].
Under the assumptions of Proposition \[prop:irr=0\], for instance if $X_t\cong X_0$, we have $\Delta_1=\Delta_2=0$. Thus for any $s\in[0,1]$ such that $e^{2\pi i s}$ is not an eigenvalue of the monodromy operator of $L_0$ we have $$\begin{aligned}
|{\operatorname{Sp}_{\operatorname{MHS}}}^0\cap(s,s+1)|\ge& \sum_{i=1}^k|{\operatorname{Sp}_{\operatorname{MHS}}}^i\cap(s,s+1)|\\
|{\operatorname{Sp}_{\operatorname{MHS}}}^0\sm[s,s+1]|\ge& \sum_{i=1}^k|{\operatorname{Sp}_{\operatorname{MHS}}}^i\sm[s,s+1]|.\end{aligned}$$
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[^1]: This is Corollary 4.4.9 in the arxiv version of [@BN].
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Introduction
============
Since the introduction of the concept of burnout by [@ref-15] ([@ref-15]), this syndrome is becoming an important topic in psychological and educational research ([@ref-23], [@ref-23]; [@ref-30], [@ref-30]). An expanding body of research examining the relationship between teaching stressful situations and burnout have found that teachers tend to report higher levels of occupational-related stress and burnout than many other human service professionals ([@ref-30], [@ref-30]). According to [@ref-29] ([@ref-29]), burnout syndrome is characterized by three primary dimensions: (1) feelings of emotional exhaustion and being emotionally drained by intense contact with students; (2) depersonalization or negative, cynical attitudes toward students; and (3) a sense of lack of personal accomplishment or of ineffectiveness and low competence in one's work. This syndrome has been repeatedly described as being the result of a significant accumulation of chronic work-related stress ([@ref-28], [@ref-28]). In identifying important sources of teacher burnout, [@ref-32] ([@ref-32]) included a wide diversity of stressors such as students' misbehaviours and discipline problems, students' poor motivation for work, role conflict and role ambiguity, and pressure and criticisms from parents, among others. All these factors have been associated with the development and maintenance of teacher burnout ([@ref-9], [@ref-9]; [@ref-24], [@ref-24]). In addition, the high levels of stress experienced by teachers and costly mental health-related problems have also been found to contribute to the growing retention problems within the school setting ([@ref-36], [@ref-36]).
However, teaching professionals do show marked individual differences in their responses to different teaching stressors, ranging from minor psychological symptoms and mild anxiety to burnout as the more severe negative affective experience ([@ref-4], [@ref-4]). Individual differences constructs are believed to increase the likelihood that conditions related to the stressful situation will be effectively addressed or resolved and higher levels of such skills will lead to lower reported burnout ([@ref-25], [@ref-25]). Consistent with this view, researchers in the field of individual differences have shown interest in examining mechanisms that might explain what individual factors predispose teachers to burnout ([@ref-1], [@ref-1]; [@ref-9], [@ref-9]).
One dimension that has gained growing attention in the field of individual differences as a person-related psychological resource is the people ability to deal effectively with affective information, often referred to as emotional competence (or emotional intelligence) ([@ref-31], [@ref-31]; [@ref-10], [@ref-10]). Some authors prefer the use of the more generic and neutral "emotional competence" term when are used self-report measures similar to those used in this study ([@ref-10], [@ref-10]; [@ref-18], [@ref-18]). Emotional competence (EC) is regarded here as an affect-related skill, which refers to the ability to understand, manage, and express the social and emotional aspects of life in ways that enable one to coping with stressful and emotionally laden situations ([@ref-22], [@ref-22]). In recent years, studies and theories have emphasized that EC has an impact on adaptive functioning at school ([@ref-21], [@ref-21]), even in the prediction of prosocial classsroom climate and teacher burnout ([@ref-7], [@ref-7]; [@ref-33], [@ref-33]).
Several authors have proposed that EC is a personal coping resource that allows teachers to manage and cope successfully with external and internal demands in a stressful workplace ([@ref-5], [@ref-5]; [@ref-21], [@ref-21]). According to [@ref-41] ([@ref-41]), it is believed that emotionally competent individuals are better adjusted than their less skilled counterparts due to the former having access to their own feelings and being able to manage their negative states even when emotionally aroused by challenging situations. Likewise, [@ref-7] ([@ref-7]) suggested that the integrated operation of these emotional competencies might render teachers less vulnerable to teacher burnout, since they might gain better access to the healthy information and action tendency within emotions, and use the information to make sense of their reactions to stressors as well as to guide adaptive action. In fact, EC has been considered to be particularly relevant to work behaviour in teachers because abilities to manage relationships and to show interpersonal sensibility when needed are the prerequisites for improving increasing classroom management ([@ref-16], [@ref-16]). Consistent with this assumption, accumulating empirical research has shown that EC might explain unique variance of both attitudinal and behavioural work outcomes ([@ref-17], [@ref-17]; [@ref-18], [@ref-18]). Having high EC is one of these personal resources that might act as a protector factor, reducing the effects of teacher work strain ([@ref-6], [@ref-6]; [@ref-20], [@ref-20]).
Although EC appears to be negatively related to burnout, the mechanisms by which EC affects burnout are not clear. [@ref-41] ([@ref-41]) have listed several underlying mechanisms which might play a mediating role in the EC--occupational-related stress link, suggesting the levels of perceived stress as an underlying process. Given the emerging evidence of a link between EC and burnout ([@ref-6], [@ref-6]; [@ref-20], [@ref-20]; [@ref-33], [@ref-33]), and the well-established connections between high perceived stress and burnout ([@ref-28], [@ref-28]), it is probable that part of the influence of EC on burnout occurs through the mediating effect of perceived stress. However, although these factors are reported to be correlated with each other in the literature, such a proposition has not been empirically evaluated. Also, the relative strength of the direct and indirect relations between EC and burnout is unclear. Therefore, there are some reasons to believe that EC may show influence the risk of burnout symptoms through perceived stress. Stress is conceptualized as an experience resulting from an imbalance between demands and resources or as taking place when pressure exceeds one's perceived ability to cope ([@ref-27], [@ref-27]). Relevant to the current study, results of previous research suggest that teachers confused about their emotional knowledge abilities and with no confidence in their own emotional regulation abilities are unlikely to feel in control of stressful situations, showing generally higher perceived stress ([@ref-6], [@ref-6]; [@ref-20], [@ref-20]). When these individuals maintain higher stress levels, there is the potential for them to increase the risk of becoming burned out on the job. On the contrary, it is tentative to think that teachers who are high on emotional competence would also experience as though they have more control over their stressful environment because they can confer sense and manage their negative moods more adaptively ([@ref-41], [@ref-41]). In fact, several researchers have found evidence that EC are negatively associated with experience of stress ([@ref-12], [@ref-12]; [@ref-16], [@ref-16]), supporting its utility as an individual characteristic that helps shape subjective interpretations of stressful daily events. These positive effects of EC on perceived stress may result in reduced levels of burnout. Likewise, EC might influence the manner in which a teacher views and reacts to stressful events and experience of stress which, in turn, may reduce levels of burnout symptoms. Hence, the assessment of perceived stress as a potential mediator of the link between EC and teacher burnout symptoms seems to be warranted.
Additionally, a variety of socio-demographic factors has been associated with symptoms of burnout, including age, sex and grade level taught ([@ref-30], [@ref-30]). In order to ensure that our findings would not be confounded with these predictive dimensions, respondents's age, gender, and grade level taught were used as control variables in our proposed mediation model of perceived stress on the link between EC and burnout.
In summary, a large body of literature deals with the prediction of different indicators of teacher burnout. One of this predictor may be the way in which people identify and manage one's own feelings and those of others. However, rather little is known about the mechanisms that interlink EC, perceived stress and burnout in teachers. Beyond the mere associations among these dimensions, this study will examine whether there is a mediation effect to gain more insight into possible mechanisms of the development of teacher burnout and of protective resource factors. Although the theoretical assumption of mediation of perceived stress on the interplay between EC and burnout has been proposed by authors ([@ref-41], [@ref-41]), one finds hardly any formal tests of mediation in the available literature. One valuable exception is the preliminary work of [@ref-13] ([@ref-13]) who examined the relationship of perceived emotional intelligence, stress, and burnout in a sample of high school teachers using the TMMS (i.e., Trait Meta-Mood Scale) to predict teacher burnout and the mediating role of stress. In short, they found partial support for the idea that perceived stress mediated the influence of TMMS dimensions on specific subscales of teacher burnout. However, as authors have pointed out, TMMS only evaluates intrapersonal emotional process, but this does not preclude the importance of interpersonal dimensions not measured by TMMS. Besides, other important socio-demographic dimensions such as sex, age and grade taught level, which are related to stress and teacher burnout, were not controlled for. Finally, the sample was composed of only high school teachers which limits the extent to which the findings can be generalized. Future research with a heterogenous sample of grade level teachers, using more comprenhensive EI measures and controlling for classic socio-demographics factors related to teacher burnout is needed to confirm the usefulness and validity of these findings. In light of the above considerations, the purpose of the present study was to examine the role of perceived stress as a mediator in the relationship between EC and teacher burnout. We hypothesized that more emotionally competent teachers would experience less stress, and this reduction in stress might account for their decreased experience of symptoms of teacher burnout, even when controlling for salient background characteristics.
Methods
=======
Participants
------------
The study used a cross-sectional survey with incidental sampling. The original sample, who participated voluntarily and anonymously in the study, consisted of 494 teachers (334 female and 160 male). The responses provided by five participants were dropped from the study because they were incomplete. The final sample comprised 489 teachers (330 females and 159 males) from fifteen autonomous regions in Spain: Andalusia (*n* = 165); Galicia (*n* = 80); Madrid (*n* = 71); Castile-La Mancha (*n* = 46); Castile and León (*n* = 11); Cantabria (*n* = 25); Valencia (*n* = 17); Navarra (*n* = 15); Extremadura (*n* = 11); Aragón (*n* = 11); Canary Islands (*n* = 9); Asturias (*n* = 9); Balearic Islands (*n* = 8); Ceuta (*n* = 6) and La Rioja (*n* = 5). The mean age was of 39.90 years (SD = 9.49 years). One hundred and three were elementary teachers (males = 14; females = 89) who taught pupils from 3-to-5 year-olds; 243 intermediate teachers (males = 77; females = 166) who taught students from 6-to-11 year-olds; 135 secondary teachers (males = 66; females = 69) who taught students from 12-to-17 year-olds and eight teachers with unreported grade level taught. A total of 81.8% of the teachers worked in state schools and 17.2% worked in private schools that receives public funds. Teaching experience ranged from one month to 38 years (*M* = 4.22 years; SD = 7.85 years).
Materials
---------
### Wong and Law Emotional Intelligence Scale (WLEIS; [@ref-26], [@ref-26])
To evaluate EC we used the WLEIS. The scale consists of 16 items relating to self-emotional appraisal (SEA), other emotional appraisal (OEA), use of emotion (UOE) and regulation of emotion (ROE). The items are scored on a 7-point Likert-type scale (1 = totally disagree to 7 = totally agree). The scale has shown adequate internal consistency and evidence of validity ([@ref-26], [@ref-26]). As in previous studies, we combined the subscales into a global EC measure since we were more interested in the overall EC construct than in each of its dimensions ([@ref-38], [@ref-38]; [@ref-40], [@ref-40]). The WLEIS was translated from English into Spanish using the method of back-translation. In our sample, the Cronbach's alpha for total EC was 0.89.
### Perceived Stress Scale (PSS; [@ref-11], [@ref-11])
This is a 14-item measure of self-appraised stress. Respondents are asked to rate the frequency during the last month with which they have been in situations they consider stressful. Frequency is rated across a 5-point Likert-type scale ranging from 0 (never) to 4 (very often). We used the Spanish version of this scale ([@ref-35], [@ref-35]). In our sample, the reliability was 0.75.
### Maslach Burnout Inventory (MBI; [@ref-29], [@ref-29])
This scale consists of 22 items scored on a 7-point frequency scale from 0 (never) to 6 (daily) and comprises three sub-scales: Emotional Exhaustion, which describes feelings of being emotionally overextended and exhausted by one's work; Depersonalization, which describes an unfeeling and impersonal response towards recipients of one's care or service; and Personal Accomplishment, which describes feelings of competence and successful achievement in one's work with people ([@ref-29], [@ref-29]). We used the most widely used Spanish version of MBI, which has shown adequate psychometric properties in occupational population ([@ref-37], [@ref-37]). In this study, Cronbach's alpha for Emotional Exhaustation was 0.90; for Depersonalizaton was 0.72 and for Personal Accomplishment was 0.83.
Procedures
----------
Participants were recruited through the help of Psychopedagogy students (UNED) and psychology students at University of Málaga. These students received instructions from the teaching staff regarding how to administer the questionnaire correctly. The data were collected as part of a project, participating in a research study on emotions and well-being at work. Most importantly, participants were fully informed about the voluntary basis of participation; they were also informed that questionnaires were completed anonymously. Thereafter, they provided informed consent. Once the questionnaires were completed, the students returned them to the teaching staff for statistical processing. The study protocol was approved as part of the project PSI2012-38813 by the Research Ethics Committee of the University of Malaga.
Results
=======
Descriptive statistics
----------------------
Descriptive statistics (e.g., means, standard deviations, skewness and kurtosis) alpha coefficients for the study variables are presented in [Table 1](#table-1){ref-type="table"}.
10.7717/peerj.2087/table-1
###### Descriptives, internal reliabilities and correlations for all study measures.
*M* SD Skewness Kurtosis *α* 1 2 3 4 5
----------------------------- ------ ------ ---------- ---------- ----- ------------------------------------------- ----------------------------------------- ------------------------------------------- ------------------------------------------- ----
1\. Emotional competence 5.25 .69 --0.54 0.15 .89 --
2\. Perceived stress 1.19 .64 0.41 0.08 .75 --.47[^\*\*^](#table-1fn1){ref-type="fn"} --
3\. Emotional exhaustion 2.06 1.24 0.56 --0.25 .90 --.38[^\*\*^](#table-1fn1){ref-type="fn"} .45[^\*\*^](#table-1fn1){ref-type="fn"} --
4\. Depersonalization .84 1.02 1.53 2.48 .72 --.32[^\*\*^](#table-1fn1){ref-type="fn"} .27[^\*\*^](#table-1fn1){ref-type="fn"} .52[^\*\*^](#table-1fn1){ref-type="fn"} --
5\. Personal accomplishment 4.78 .84 --.99 .96 .83 .55[^\*\*^](#table-1fn1){ref-type="fn"} --.34[^\*^](#table-1fn2){ref-type="fn"} --.42[^\*\*^](#table-1fn1){ref-type="fn"} --.40[^\*\*^](#table-1fn1){ref-type="fn"} --
**Notes.**
*p* \< 0.01.
*p* \< 0.05.
Mahalanobis' distance was computed to determine if multivariate outliers occurred in the dataset. One participant was found to be outlier (*p* \< .001), being removed from the dataset. Pearson product--moment correlation coefficients were used to specify the relationship between the variables. Scores on all the factors, except for depersonalization, are normally distributed, as indicated by skewness and kurtosis. Therefore, for depersonalization that showed high kurtosis, Spearman correlations were computed. In general, all relationships among EC, stress and burnout symptoms were statistically significant. Thus, perceived stress scores were significantly and positively related to emotional exhaustation and depersonalization and negatively associated with personal accomplishment.
Mediation analysis
------------------
According to the general guidelines offered by [@ref-3] ([@ref-3]) for establishing evidence for a proposed mediation model, four conditions need to be satisfied. First, the predictor (EC) needs to be related to the outcome (burnout subscales). Second, the predictor must be related to the hypothesized mediator (perceived stress). Third, the mediator must be related to the outcome when controlling for the predictor. Fourth, the effect of the predictor on the outcome must be reduced when the effect of the mediator is controlled. As recommended by [@ref-34] ([@ref-34]), bootstrap analysis, a non-parametric sampling procedure, was used to test the significance of the indirect effects. Bootstrapping is an approach that resamples the original sample size from the data multiple times and does not rely on the assumption that data are normally distributed. Current analyses utilized 5,000 bootstrap resamples to generate 95% confidence intervals. The indirect effect is significant at *p* \< .05 if zero is not included in the 95% confidence interval for that indirect effect. We conducted a set of path analyses to test separately the potential role of perceived stress as a mediator between EC and each burnout subscale including sex, age, and grade taught level as covariates in the analyses.
Perceived stress as a mediator between EC and teacher emotional exhaustation
----------------------------------------------------------------------------
We conducted a series of regressions to test for a mediation effect of perceived stress on the relationship between EC and teacher emotional exhaustion controlling for sex, age and grade taught level in the first step. As seen in [Table 2](#table-2){ref-type="table"}, after controlling for teachers background characteristics, in the second step EC was regressed on emotional exhaustion, accounting for 14% of the variance in this burnout dimension. In the third step, emotional exhaustation was simultaneously regressed on background characteristics, EC and perceived stress. When perceived stress was entered into the equation, the beta weight from EC dropped from --.37 to --.22, but it remained significant.
10.7717/peerj.2087/table-2
###### Regression models predicting the three teacher burnout symptoms from emotional competence and perceived stress controlling for sex, age and grade taught level.
Predictor Emotional exhaustion Depersonalization Personal accomplishment
-------------------- ---------------------- ------------------- ------------------------------------------- ----------------------------------------- ----- ------- ------------------------------------------- ----------------------------------------- ----- ------- ------------------------------------------- -----------------------------------------
**Step 1** .04 6.23 .03 4.30 .04 5.61
Sex .06 --.10[^\*^](#table-2fn1){ref-type="fn"} --.00
Age .19[^\*\*^](#table-2fn2){ref-type="fn"} .04 --.08
Grade taught level .02 .09 --.16[^\*\*^](#table-2fn2){ref-type="fn"}
**Step 2** .18 24.42 .14[^\*\*^](#table-2fn2){ref-type="fn"} .13 17.45 .10[^\*\*^](#table-2fn2){ref-type="fn"} .35 60.89 .31[^\*\*^](#table-2fn2){ref-type="fn"}
Sex .05 --.10[^\*\*^](#table-2fn2){ref-type="fn"} --.00
Age .16[^\*\*^](#table-2fn2){ref-type="fn"} .02 --.04
Grade taught level .00 .07 --.13[^\*\*^](#table-2fn2){ref-type="fn"}
EC --.37[^\*\*^](#table-2fn2){ref-type="fn"} --.33[^\*\*^](#table-2fn2){ref-type="fn"} .56[^\*\*^](#table-2fn2){ref-type="fn"}
**Step 3** .27 32.89 .09[^\*\*^](#table-2fn2){ref-type="fn"} .15 16.47 .02[^\*\*^](#table-2fn2){ref-type="fn"} .36 51.12 .01[^\*\*^](#table-2fn2){ref-type="fn"}
Sex .03 --.11[^\*\*^](#table-2fn2){ref-type="fn"} .01
Age .14[^\*\*^](#table-2fn2){ref-type="fn"} .01 --.03
Grade taught level --.00 .07 --.13[^\*\*^](#table-2fn2){ref-type="fn"}
EC --.22[^\*\*^](#table-2fn2){ref-type="fn"} --.25[^\*\*^](#table-2fn2){ref-type="fn"} .50[^\*\*^](#table-2fn2){ref-type="fn"}
Perceived stress .34[^\*\*^](#table-2fn2){ref-type="fn"} .16[^\*\*^](#table-2fn2){ref-type="fn"} --.12[^\*\*^](#table-2fn2){ref-type="fn"}
**Notes.**
*p* \< .05.
*p* \< .01.
By using the SPSS macro provided by [@ref-34] ([@ref-34]), the indirect effect of perceived stress was estimated to lie between --.38 and --.19 with 95% confidence (bootstrap coefficient = --.27), as you can see in [Table 3](#table-3){ref-type="table"}. Because zero was not in the 95% confidence interval, the findings suggested that the indirect effect through perceived stress was significantly different from zero at *p* \< .05, supporting the view that perceived stress partly mediated the relation between EC and emotional exhaustation controlling for sex, age and grade taught level.
10.7717/peerj.2087/table-3
###### Indirect effects of emotional competence on burnout symptoms, through perceived stress and controlling for background characteristics.
Model[^a^](#table-3fn1){ref-type="fn"} *Estimated*[^b^](#table-3fn2){ref-type="fn"}*coefficient* *SE* 95% CI
---------------------------------------------- ----------------------------------------------------------- ------ -------- -------
Emotional competence-emotional exhaustation --.29 .04 --.38 --.19
Emotional competence-depersonalization --.11 .03 --.19 --.05
Emotional competence-personal accomplishment .06 .02 .02 .12
**Notes.**
In the presence of perceived stress as a mediator, and the covariates of, sex, age, and grade taught level.
Estimated using bias corrected and accelerated bootstrapping, with 5,000 samples.
Perceived stress as a mediator between EC and depersonalization
---------------------------------------------------------------
Next, EC was regressed on depersonalization (*b* = − .32, *p* \< .001), accounting for 10% of the variance in this burnout dimension even controlling for background characteristics. In the third step, depersonalization was simultaneously regressed on background characteristics, EC and perceived stress. As [Table 2](#table-2){ref-type="table"} shows, when perceived stress was included in the model, there was a decrease in EC influence on depersonalization (the beta weight dropped from --.33 to --.25). The indirect effect was significant (bootstrap coefficient = --.11), with a 95% confidence interval of --.18 to --.04, supporting the view that perceived stress partly mediated the relation between EC and depersonalization (see [Table 3](#table-3){ref-type="table"}).
Perceived stress as a mediator between EC and personal accomplishment
---------------------------------------------------------------------
Finally, we conducted a series of regressions to test for a mediation effect of perceived stress on the relationship between EC and personal accomplishment. In the first step, we controlling for background characteristic, grade taught level was a significant predictor of the variance in this burnout dimension. In the second step, EC was found to be a significant predictor of personal accomplishment, accounting for 31% of the variance in this burnout symptom. In the last step, perceived stress was added to the model, explaining an additional 1% of the variance in this burnout subscale. As [Table 2](#table-2){ref-type="table"} shows, when perceived stress was included in the model, there was a decrease in EC influence on personal accomplishment (the beta weight dropped from .56 to .50). The indirect effect was significant (bootstrap coefficient = .06), with a 95% confidence interval of .02 to 0.11, supporting the view that perceived stress is also a partial mediator in the link between EC and personal accomplishment (see [Table 3](#table-3){ref-type="table"}).
Discussion
==========
This study expands on previous research literature on EC and teacher burnout ([@ref-7], [@ref-7]; [@ref-20], [@ref-20]; [@ref-33], [@ref-33]) by examining direct and indirect relations between EC, perceived stress and burnout in a sample of teachers. Our underlying reasoning was that EC may work through to the reduction of perceived stress, which in turn would promote lower levels of teacher burnout independently of sex, age and grade taught level.
There is accumulating empirical evidence that deficits in emotional abilities are directly related to high levels of burnout ([@ref-13], [@ref-13]; [@ref-33], [@ref-33]). Consistent with these findings, our research did provide evidence that EC was correlated with both perceived stress and burnout symptoms. Specifically, teachers who report being poor emotionally at perceiving and managing emotions also tend to report feeling exhausted more often and being more cynical about their work and about students whom they work with, and a more reduced sense of personal accomplishment. One explanation for these findings is that teaching professionals' skills at effectively managing emotional challenges are characterized by more constructive thought patterns, and teachers find it easier to catch and to identify faulty appraisals and correct maladapted construals in the workplace ([@ref-41], [@ref-41]). In addition, it is possible that teachers who are more emotionally competent would also feel that they have more control over their stressful environment because they can confer sense and manage their negative moods associated with stress more adaptively.
Similarly, in line with earlier studies, our correlational data found that greater perceived stress scores were related in the expected direction to higher levels of burnout symptoms ([@ref-28], [@ref-28]). Specifically, greater perceived stress was significantly associated with greater emotional exhaustion and depersonalization and lower feelings of personal accomplishment. The present study found some preliminary support for the idea that perceived stress mediated the influence of EC on specific subscales of teacher burnout, suggesting a complex process. The mediation analyses revealed that perceived stress partially mediated the relations between EC and all burnout symptoms. The results of this study might point to one plausible explanation for the association between EC and burnout as being related to the reduced perceptions of stress experienced by teachers with high EC. In general, increasing EC in teachers may reduce the risk of job burnout both directly and indirectly by reducing the experience of stress. Emotionally competent teachers may reduce be better equipped to engage with and successfully manage stressful school situations, which in turn would lead to lower symptoms of emotional exhaustation and depersonalization and higher personal accomplishment. More research is needed to examine the underlying mechanism by which teachers with high EC reduce their levels of stress, either identifying and avoiding potentially stressful contexts or interpreting stressful conditions at work in a less stressful way.
Nevertheless, these findings may be valuable not only for developing theoretical models and for understanding better the link between EC and occupational stress ([@ref-41], [@ref-41]), but also for developing more effective stress intervention programmes for teachers ([@ref-9], [@ref-9]). Based on our results, it is suggested that EC might play an important role in the process of certain responses to job stress in teachers. In terms of intervention implications, teachers could be taught how to employ specific emotional strategies for managing stress; this in turn might help them to reduce their feelings related to teacher burnout. In this sense, our data support the idea that programmes to prevent burnout involving the enhancement of EC might be useful to facilitate an increased perception of self-appraisal in teaching work. Besides, whereas therapeutic efforts to increase EC may reduce symptoms burnout, perceived stress appears to be an important aspect of burnout in teachers, so it is also of great importance to help teachers who are vulnerable for burnout to provide specific strategies for reducing negative moods provoked by stress. Cognitive behavioral therapy has been shown to be an effective way of reducing work-related stress, even more than the other intervention types ([@ref-39], [@ref-39]). Further research will determine whether EC interventions, either alone or in conjunction with other stress management interventions such as cognitive behavioral therapies, will enhance psychological outcomes for the classic symptoms of teacher burnout ([@ref-14], [@ref-14]). Future work should also be addressed to the positive pole of burnout, work engagement ([@ref-2], [@ref-2]), to determine when and under what circumstances EC work better for increasing individuals' positive and fulfilling attitude toward work in teachers.
Finally, several limitations of the current study should be mentioned. First, although our data provide preliminary evidence for the mediation model proposed, due to data being collected in a single wave of measurement it is impossible to determine the directionality of any causal relationships between variables. A closer examination of the nature of this relationship should be performed using prospective studies. Second, self-reported measures of EC may not reflect actual emotional ability. To address this issue, further studies might consider the inclusion of other approaches complementary to the use of self-report for measuring EC, such as peer reports or performance measures, which provide valuable information about people's emotional reactions in the work sphere. Finally, it is important to underline that our participants were based on a purposive sampling and, hence, their representativeness is questionable.
Despite these limitations, it appears that EC may have an important place in the educational psychologist's repertoire of occupational well-being and may suggest possible avenues for improving future stress management programs to assist distressed teachers. Although school climate factors are considered to be one of the prominent causes of teacher burnout ([@ref-1], [@ref-1]; [@ref-19], [@ref-19]), our results, in line with prior studies, support the importance of individual differences with regard to EC in the development of teacher burnout. While organization-focused interventions in educational settings are important in preventing burnout, the findings of this study provide some evidences that educational settings should pay more attention to the development of protective personal resources taking into account the perspective of interaction between personal characteristics and contextual variables in teaching ([@ref-1], [@ref-1]; [@ref-9], [@ref-9]).
Finally, as high stress levels and poor EC continually rank as the most prominent causes why teachers become dissatisfied with the profession and end up leaving their positions ([@ref-8], [@ref-8]), paying more attention to the development of these personal resources might help teachers employ EC in their professional and personal relationships and contribute to greater positivity at work ([@ref-16], [@ref-16]; [@ref-20], [@ref-20]). Future research could examine this issue by training people in EC and observing how such training impacts on teacher burnout symptoms over time. Elucidating which protective resource factors contribute most to a better subjective well-being at work, and how to develop these aspects, is a promising approach to the enhancement of teaching skills and merits serious attention.
Supplemental Information
========================
10.7717/peerj.2087/supp-1
###### Raw data
######
Click here for additional data file.
10.7717/peerj.2087/supp-2
###### Mahalanobis
######
Click here for additional data file.
We would like to give our heartfelt thanks to all the teachers who participated in this study.
Additional Information and Declarations
=======================================
The authors declare there are no competing interests.
[Lourdes Rey](#author-1){ref-type="contrib"}, [Natalio Extremera](#author-2){ref-type="contrib"} and [Mario Pena](#author-3){ref-type="contrib"} conceived and designed the experiments, performed the experiments, analyzed the data, contributed reagents/materials/analysis tools, wrote the paper, prepared figures and/or tables, reviewed drafts of the paper.
The following information was supplied relating to ethical approvals (i.e., approving body and any reference numbers):
Comité ético de experimentación de la Universidad de Málaga.
The following information was supplied regarding data availability:
The raw data has been supplied as [Supplemental Information](#supplemental-information){ref-type="supplementary-material"}.
|
/*
* Copyright 2004, 2011 Freescale Semiconductor.
*
* SPDX-License-Identifier: GPL-2.0+
*/
/*
* mpc8541cds board configuration file
*
* Please refer to doc/README.mpc85xxcds for more info.
*
*/
#ifndef __CONFIG_H
#define __CONFIG_H
/* High Level Configuration Options */
#define CONFIG_BOOKE 1 /* BOOKE */
#define CONFIG_E500 1 /* BOOKE e500 family */
#define CONFIG_CPM2 1 /* has CPM2 */
#define CONFIG_MPC8541 1 /* MPC8541 specific */
#define CONFIG_MPC8541CDS 1 /* MPC8541CDS board specific */
#define CONFIG_SYS_TEXT_BASE 0xfff80000
#define CONFIG_PCI
#define CONFIG_PCI_INDIRECT_BRIDGE
#define CONFIG_SYS_PCI_64BIT 1 /* enable 64-bit PCI resources */
#define CONFIG_TSEC_ENET /* tsec ethernet support */
#define CONFIG_ENV_OVERWRITE
#define CONFIG_FSL_LAW 1 /* Use common FSL init code */
#define CONFIG_FSL_VIA
#ifndef __ASSEMBLY__
extern unsigned long get_clock_freq(void);
#endif
#define CONFIG_SYS_CLK_FREQ get_clock_freq() /* sysclk for MPC85xx */
/*
* These can be toggled for performance analysis, otherwise use default.
*/
#define CONFIG_L2_CACHE /* toggle L2 cache */
#define CONFIG_BTB /* toggle branch predition */
#define CONFIG_SYS_MEMTEST_START 0x00200000 /* memtest works on */
#define CONFIG_SYS_MEMTEST_END 0x00400000
#define CONFIG_SYS_CCSRBAR 0xe0000000
#define CONFIG_SYS_CCSRBAR_PHYS_LOW CONFIG_SYS_CCSRBAR
/* DDR Setup */
#define CONFIG_SYS_FSL_DDR1
#define CONFIG_SPD_EEPROM /* Use SPD EEPROM for DDR setup*/
#define CONFIG_DDR_SPD
#undef CONFIG_FSL_DDR_INTERACTIVE
#define CONFIG_MEM_INIT_VALUE 0xDeadBeef
#define CONFIG_SYS_DDR_SDRAM_BASE 0x00000000 /* DDR is system memory*/
#define CONFIG_SYS_SDRAM_BASE CONFIG_SYS_DDR_SDRAM_BASE
#define CONFIG_NUM_DDR_CONTROLLERS 1
#define CONFIG_DIMM_SLOTS_PER_CTLR 1
#define CONFIG_CHIP_SELECTS_PER_CTRL (2 * CONFIG_DIMM_SLOTS_PER_CTLR)
/* I2C addresses of SPD EEPROMs */
#define SPD_EEPROM_ADDRESS 0x51 /* CTLR 0 DIMM 0 */
/*
* Make sure required options are set
*/
#ifndef CONFIG_SPD_EEPROM
#error ("CONFIG_SPD_EEPROM is required by MPC85555CDS")
#endif
#undef CONFIG_CLOCKS_IN_MHZ
/*
* Local Bus Definitions
*/
/*
* FLASH on the Local Bus
* Two banks, 8M each, using the CFI driver.
* Boot from BR0/OR0 bank at 0xff00_0000
* Alternate BR1/OR1 bank at 0xff80_0000
*
* BR0, BR1:
* Base address 0 = 0xff00_0000 = BR0[0:16] = 1111 1111 0000 0000 0
* Base address 1 = 0xff80_0000 = BR1[0:16] = 1111 1111 1000 0000 0
* Port Size = 16 bits = BRx[19:20] = 10
* Use GPCM = BRx[24:26] = 000
* Valid = BRx[31] = 1
*
* 0 4 8 12 16 20 24 28
* 1111 1111 1000 0000 0001 0000 0000 0001 = ff801001 BR0
* 1111 1111 0000 0000 0001 0000 0000 0001 = ff001001 BR1
*
* OR0, OR1:
* Addr Mask = 8M = ORx[0:16] = 1111 1111 1000 0000 0
* Reserved ORx[17:18] = 11, confusion here?
* CSNT = ORx[20] = 1
* ACS = half cycle delay = ORx[21:22] = 11
* SCY = 6 = ORx[24:27] = 0110
* TRLX = use relaxed timing = ORx[29] = 1
* EAD = use external address latch delay = OR[31] = 1
*
* 0 4 8 12 16 20 24 28
* 1111 1111 1000 0000 0110 1110 0110 0101 = ff806e65 ORx
*/
#define CONFIG_SYS_FLASH_BASE 0xff000000 /* start of FLASH 8M */
#define CONFIG_SYS_BR0_PRELIM 0xff801001
#define CONFIG_SYS_BR1_PRELIM 0xff001001
#define CONFIG_SYS_OR0_PRELIM 0xff806e65
#define CONFIG_SYS_OR1_PRELIM 0xff806e65
#define CONFIG_SYS_FLASH_BANKS_LIST {0xff800000, CONFIG_SYS_FLASH_BASE}
#define CONFIG_SYS_MAX_FLASH_BANKS 2 /* number of banks */
#define CONFIG_SYS_MAX_FLASH_SECT 128 /* sectors per device */
#undef CONFIG_SYS_FLASH_CHECKSUM
#define CONFIG_SYS_FLASH_ERASE_TOUT 60000 /* Flash Erase Timeout (ms) */
#define CONFIG_SYS_FLASH_WRITE_TOUT 500 /* Flash Write Timeout (ms) */
#define CONFIG_SYS_MONITOR_BASE CONFIG_SYS_TEXT_BASE /* start of monitor */
#define CONFIG_FLASH_CFI_DRIVER
#define CONFIG_SYS_FLASH_CFI
#define CONFIG_SYS_FLASH_EMPTY_INFO
/*
* SDRAM on the Local Bus
*/
#define CONFIG_SYS_LBC_SDRAM_BASE 0xf0000000 /* Localbus SDRAM */
#define CONFIG_SYS_LBC_SDRAM_SIZE 64 /* LBC SDRAM is 64MB */
/*
* Base Register 2 and Option Register 2 configure SDRAM.
* The SDRAM base address, CONFIG_SYS_LBC_SDRAM_BASE, is 0xf0000000.
*
* For BR2, need:
* Base address of 0xf0000000 = BR[0:16] = 1111 0000 0000 0000 0
* port-size = 32-bits = BR2[19:20] = 11
* no parity checking = BR2[21:22] = 00
* SDRAM for MSEL = BR2[24:26] = 011
* Valid = BR[31] = 1
*
* 0 4 8 12 16 20 24 28
* 1111 0000 0000 0000 0001 1000 0110 0001 = f0001861
*
* FIXME: CONFIG_SYS_LBC_SDRAM_BASE should be masked and OR'ed into
* FIXME: the top 17 bits of BR2.
*/
#define CONFIG_SYS_BR2_PRELIM 0xf0001861
/*
* The SDRAM size in MB, CONFIG_SYS_LBC_SDRAM_SIZE, is 64.
*
* For OR2, need:
* 64MB mask for AM, OR2[0:7] = 1111 1100
* XAM, OR2[17:18] = 11
* 9 columns OR2[19-21] = 010
* 13 rows OR2[23-25] = 100
* EAD set for extra time OR[31] = 1
*
* 0 4 8 12 16 20 24 28
* 1111 1100 0000 0000 0110 1001 0000 0001 = fc006901
*/
#define CONFIG_SYS_OR2_PRELIM 0xfc006901
#define CONFIG_SYS_LBC_LCRR 0x00030004 /* LB clock ratio reg */
#define CONFIG_SYS_LBC_LBCR 0x00000000 /* LB config reg */
#define CONFIG_SYS_LBC_LSRT 0x20000000 /* LB sdram refresh timer */
#define CONFIG_SYS_LBC_MRTPR 0x00000000 /* LB refresh timer prescal*/
/*
* Common settings for all Local Bus SDRAM commands.
* At run time, either BSMA1516 (for CPU 1.1)
* or BSMA1617 (for CPU 1.0) (old)
* is OR'ed in too.
*/
#define CONFIG_SYS_LBC_LSDMR_COMMON ( LSDMR_RFCR16 \
| LSDMR_PRETOACT7 \
| LSDMR_ACTTORW7 \
| LSDMR_BL8 \
| LSDMR_WRC4 \
| LSDMR_CL3 \
| LSDMR_RFEN \
)
/*
* The CADMUS registers are connected to CS3 on CDS.
* The new memory map places CADMUS at 0xf8000000.
*
* For BR3, need:
* Base address of 0xf8000000 = BR[0:16] = 1111 1000 0000 0000 0
* port-size = 8-bits = BR[19:20] = 01
* no parity checking = BR[21:22] = 00
* GPMC for MSEL = BR[24:26] = 000
* Valid = BR[31] = 1
*
* 0 4 8 12 16 20 24 28
* 1111 1000 0000 0000 0000 1000 0000 0001 = f8000801
*
* For OR3, need:
* 1 MB mask for AM, OR[0:16] = 1111 1111 1111 0000 0
* disable buffer ctrl OR[19] = 0
* CSNT OR[20] = 1
* ACS OR[21:22] = 11
* XACS OR[23] = 1
* SCY 15 wait states OR[24:27] = 1111 max is suboptimal but safe
* SETA OR[28] = 0
* TRLX OR[29] = 1
* EHTR OR[30] = 1
* EAD extra time OR[31] = 1
*
* 0 4 8 12 16 20 24 28
* 1111 1111 1111 0000 0000 1111 1111 0111 = fff00ff7
*/
#define CONFIG_FSL_CADMUS
#define CADMUS_BASE_ADDR 0xf8000000
#define CONFIG_SYS_BR3_PRELIM 0xf8000801
#define CONFIG_SYS_OR3_PRELIM 0xfff00ff7
#define CONFIG_SYS_INIT_RAM_LOCK 1
#define CONFIG_SYS_INIT_RAM_ADDR 0xe4010000 /* Initial RAM address */
#define CONFIG_SYS_INIT_RAM_SIZE 0x4000 /* Size of used area in RAM */
#define CONFIG_SYS_GBL_DATA_OFFSET (CONFIG_SYS_INIT_RAM_SIZE - GENERATED_GBL_DATA_SIZE)
#define CONFIG_SYS_INIT_SP_OFFSET CONFIG_SYS_GBL_DATA_OFFSET
#define CONFIG_SYS_MONITOR_LEN (256 * 1024) /* Reserve 256 kB for Mon */
#define CONFIG_SYS_MALLOC_LEN (128 * 1024) /* Reserved for malloc */
/* Serial Port */
#define CONFIG_CONS_INDEX 2
#define CONFIG_SYS_NS16550
#define CONFIG_SYS_NS16550_SERIAL
#define CONFIG_SYS_NS16550_REG_SIZE 1
#define CONFIG_SYS_NS16550_CLK get_bus_freq(0)
#define CONFIG_SYS_BAUDRATE_TABLE \
{300, 600, 1200, 2400, 4800, 9600, 19200, 38400,115200}
#define CONFIG_SYS_NS16550_COM1 (CONFIG_SYS_CCSRBAR+0x4500)
#define CONFIG_SYS_NS16550_COM2 (CONFIG_SYS_CCSRBAR+0x4600)
/* Use the HUSH parser */
#define CONFIG_SYS_HUSH_PARSER
#ifdef CONFIG_SYS_HUSH_PARSER
#endif
/* pass open firmware flat tree */
#define CONFIG_OF_LIBFDT 1
#define CONFIG_OF_BOARD_SETUP 1
#define CONFIG_OF_STDOUT_VIA_ALIAS 1
/*
* I2C
*/
#define CONFIG_SYS_I2C
#define CONFIG_SYS_I2C_FSL
#define CONFIG_SYS_FSL_I2C_SPEED 400000
#define CONFIG_SYS_FSL_I2C_SLAVE 0x7F
#define CONFIG_SYS_FSL_I2C_OFFSET 0x3000
#define CONFIG_SYS_I2C_NOPROBES { {0, 0x69} }
/* EEPROM */
#define CONFIG_ID_EEPROM
#define CONFIG_SYS_I2C_EEPROM_CCID
#define CONFIG_SYS_ID_EEPROM
#define CONFIG_SYS_I2C_EEPROM_ADDR 0x57
#define CONFIG_SYS_I2C_EEPROM_ADDR_LEN 2
/*
* General PCI
* Memory space is mapped 1-1, but I/O space must start from 0.
*/
#define CONFIG_SYS_PCI1_MEM_VIRT 0x80000000
#define CONFIG_SYS_PCI1_MEM_BUS 0x80000000
#define CONFIG_SYS_PCI1_MEM_PHYS 0x80000000
#define CONFIG_SYS_PCI1_MEM_SIZE 0x20000000 /* 512M */
#define CONFIG_SYS_PCI1_IO_VIRT 0xe2000000
#define CONFIG_SYS_PCI1_IO_BUS 0x00000000
#define CONFIG_SYS_PCI1_IO_PHYS 0xe2000000
#define CONFIG_SYS_PCI1_IO_SIZE 0x100000 /* 1M */
#define CONFIG_SYS_PCI2_MEM_VIRT 0xa0000000
#define CONFIG_SYS_PCI2_MEM_BUS 0xa0000000
#define CONFIG_SYS_PCI2_MEM_PHYS 0xa0000000
#define CONFIG_SYS_PCI2_MEM_SIZE 0x20000000 /* 512M */
#define CONFIG_SYS_PCI2_IO_VIRT 0xe2100000
#define CONFIG_SYS_PCI2_IO_BUS 0x00000000
#define CONFIG_SYS_PCI2_IO_PHYS 0xe2100000
#define CONFIG_SYS_PCI2_IO_SIZE 0x100000 /* 1M */
#ifdef CONFIG_LEGACY
#define BRIDGE_ID 17
#define VIA_ID 2
#else
#define BRIDGE_ID 28
#define VIA_ID 4
#endif
#if defined(CONFIG_PCI)
#define CONFIG_MPC85XX_PCI2
#define CONFIG_PCI_PNP /* do pci plug-and-play */
#undef CONFIG_EEPRO100
#undef CONFIG_TULIP
#undef CONFIG_PCI_SCAN_SHOW /* show pci devices on startup */
#define CONFIG_SYS_PCI_SUBSYS_VENDORID 0x1057 /* Motorola */
#endif /* CONFIG_PCI */
#if defined(CONFIG_TSEC_ENET)
#define CONFIG_MII 1 /* MII PHY management */
#define CONFIG_TSEC1 1
#define CONFIG_TSEC1_NAME "TSEC0"
#define CONFIG_TSEC2 1
#define CONFIG_TSEC2_NAME "TSEC1"
#define TSEC1_PHY_ADDR 0
#define TSEC2_PHY_ADDR 1
#define TSEC1_PHYIDX 0
#define TSEC2_PHYIDX 0
#define TSEC1_FLAGS TSEC_GIGABIT
#define TSEC2_FLAGS TSEC_GIGABIT
/* Options are: TSEC[0-1] */
#define CONFIG_ETHPRIME "TSEC0"
#endif /* CONFIG_TSEC_ENET */
/*
* Environment
*/
#define CONFIG_ENV_IS_IN_FLASH 1
#define CONFIG_ENV_ADDR (CONFIG_SYS_MONITOR_BASE + 0x40000)
#define CONFIG_ENV_SECT_SIZE 0x40000 /* 256K(one sector) for env */
#define CONFIG_ENV_SIZE 0x2000
#define CONFIG_LOADS_ECHO 1 /* echo on for serial download */
#define CONFIG_SYS_LOADS_BAUD_CHANGE 1 /* allow baudrate change */
/*
* BOOTP options
*/
#define CONFIG_BOOTP_BOOTFILESIZE
#define CONFIG_BOOTP_BOOTPATH
#define CONFIG_BOOTP_GATEWAY
#define CONFIG_BOOTP_HOSTNAME
/*
* Command line configuration.
*/
#include <config_cmd_default.h>
#define CONFIG_CMD_PING
#define CONFIG_CMD_I2C
#define CONFIG_CMD_MII
#define CONFIG_CMD_ELF
#define CONFIG_CMD_IRQ
#define CONFIG_CMD_SETEXPR
#define CONFIG_CMD_REGINFO
#if defined(CONFIG_PCI)
#define CONFIG_CMD_PCI
#endif
#undef CONFIG_WATCHDOG /* watchdog disabled */
/*
* Miscellaneous configurable options
*/
#define CONFIG_SYS_LONGHELP /* undef to save memory */
#define CONFIG_CMDLINE_EDITING /* Command-line editing */
#define CONFIG_AUTO_COMPLETE /* add autocompletion support */
#define CONFIG_SYS_LOAD_ADDR 0x2000000 /* default load address */
#if defined(CONFIG_CMD_KGDB)
#define CONFIG_SYS_CBSIZE 1024 /* Console I/O Buffer Size */
#else
#define CONFIG_SYS_CBSIZE 256 /* Console I/O Buffer Size */
#endif
#define CONFIG_SYS_PBSIZE (CONFIG_SYS_CBSIZE+sizeof(CONFIG_SYS_PROMPT)+16) /* Print Buffer Size */
#define CONFIG_SYS_MAXARGS 16 /* max number of command args */
#define CONFIG_SYS_BARGSIZE CONFIG_SYS_CBSIZE /* Boot Argument Buffer Size */
/*
* For booting Linux, the board info and command line data
* have to be in the first 64 MB of memory, since this is
* the maximum mapped by the Linux kernel during initialization.
*/
#define CONFIG_SYS_BOOTMAPSZ (64 << 20) /* Initial Memory map for Linux*/
#define CONFIG_SYS_BOOTM_LEN (64 << 20) /* Increase max gunzip size */
#if defined(CONFIG_CMD_KGDB)
#define CONFIG_KGDB_BAUDRATE 230400 /* speed to run kgdb serial port */
#endif
/*
* Environment Configuration
*/
/* The mac addresses for all ethernet interface */
#if defined(CONFIG_TSEC_ENET)
#define CONFIG_HAS_ETH0
#define CONFIG_ETHADDR 00:E0:0C:00:00:FD
#define CONFIG_HAS_ETH1
#define CONFIG_ETH1ADDR 00:E0:0C:00:01:FD
#define CONFIG_HAS_ETH2
#define CONFIG_ETH2ADDR 00:E0:0C:00:02:FD
#endif
#define CONFIG_IPADDR 192.168.1.253
#define CONFIG_HOSTNAME unknown
#define CONFIG_ROOTPATH "/nfsroot"
#define CONFIG_BOOTFILE "your.uImage"
#define CONFIG_SERVERIP 192.168.1.1
#define CONFIG_GATEWAYIP 192.168.1.1
#define CONFIG_NETMASK 255.255.255.0
#define CONFIG_LOADADDR 200000 /*default location for tftp and bootm*/
#define CONFIG_BOOTDELAY 10 /* -1 disables auto-boot */
#undef CONFIG_BOOTARGS /* the boot command will set bootargs*/
#define CONFIG_BAUDRATE 115200
#define CONFIG_EXTRA_ENV_SETTINGS \
"netdev=eth0\0" \
"consoledev=ttyS1\0" \
"ramdiskaddr=600000\0" \
"ramdiskfile=your.ramdisk.u-boot\0" \
"fdtaddr=400000\0" \
"fdtfile=your.fdt.dtb\0"
#define CONFIG_NFSBOOTCOMMAND \
"setenv bootargs root=/dev/nfs rw " \
"nfsroot=$serverip:$rootpath " \
"ip=$ipaddr:$serverip:$gatewayip:$netmask:$hostname:$netdev:off " \
"console=$consoledev,$baudrate $othbootargs;" \
"tftp $loadaddr $bootfile;" \
"tftp $fdtaddr $fdtfile;" \
"bootm $loadaddr - $fdtaddr"
#define CONFIG_RAMBOOTCOMMAND \
"setenv bootargs root=/dev/ram rw " \
"console=$consoledev,$baudrate $othbootargs;" \
"tftp $ramdiskaddr $ramdiskfile;" \
"tftp $loadaddr $bootfile;" \
"bootm $loadaddr $ramdiskaddr"
#define CONFIG_BOOTCOMMAND CONFIG_NFSBOOTCOMMAND
#endif /* __CONFIG_H */
|
1. Introduction {#sec1-materials-13-02521}
===============
Sulfamethoxazole (SMZ) is one of the numerous antibiotics belonging to the sulfonamide family. SMZ is used widely as an antibacterial agent in drugs for infectious diseases, animal-derived food, and aquatic environments \[[@B1-materials-13-02521],[@B2-materials-13-02521]\]. As SMZ cannot be eliminated effectively through common water or food treatment processes, there is a probability of an excess amount of SMZ entering the human body. After prolonged exposure to low concentrations of antibiotics, the human body is bound to suffer from a resistance reaction \[[@B3-materials-13-02521],[@B4-materials-13-02521]\]. This risk renders it necessary to determine the SMZ content in pharmaceutical formulations as well as to test residues of SMZ, which should not exceed the regulatory limit in drinking water or in food originating from animals, such as eggs, milk, and meat \[[@B5-materials-13-02521]\]. Therefore, various SMZ detection methods including spectrophotometry \[[@B6-materials-13-02521]\], electrochemical methods \[[@B7-materials-13-02521],[@B8-materials-13-02521]\], LC/MS \[[@B9-materials-13-02521]\], HPLC \[[@B10-materials-13-02521],[@B11-materials-13-02521]\], solid-phase extraction \[[@B12-materials-13-02521]\], and voltammetry \[[@B13-materials-13-02521]\] have been developed.
Recently, fluorescence sensing has attracted the interest of researchers for chemical and biological applications, because they both overcome some of the drawbacks of the other detection methods and are also rapid, convenient, simple, non-polluting, and highly sensitive \[[@B14-materials-13-02521],[@B15-materials-13-02521]\]. Various fluorescence sensors have been prepared based on GQDs, which are optical materials possessing outstanding characteristics such as stable photoluminescence, good water dispersity, chemical stability, good biocompatibility, and low toxicity \[[@B16-materials-13-02521],[@B17-materials-13-02521]\]. Nevertheless, these GQD-based fluorescence sensors have a significant drawback of low selectivity \[[@B18-materials-13-02521]\]. With our experience in developing fluorescence methods, we addressed this limitation by combining GQDs and a highly selective molecularly imprinted polymer (MIP) \[[@B19-materials-13-02521],[@B20-materials-13-02521],[@B21-materials-13-02521]\]. Recognition using MIP is a technology that is used to analyze samples based on a mechanism that is similar to enzyme--substrate action \[[@B22-materials-13-02521],[@B23-materials-13-02521]\]. Therefore, with combined MIP technology, the selectivity of a GQDs-based sensor would be improved significantly. In recent years, SMZ fluorescence sensors replied on MIP have been reported \[[@B2-materials-13-02521],[@B24-materials-13-02521],[@B25-materials-13-02521]\]. They have emerged as powerful techniques not only because of their strong selectivity but also due to their simplicity, easy-preparation and inexpensive cost, when compared with other SMZ sensing methods which require expensive instruments and complex operating processes \[[@B26-materials-13-02521],[@B27-materials-13-02521],[@B28-materials-13-02521],[@B29-materials-13-02521]\].
In particular, we synthesized GQDs coated with a silica MIP (denoted as GQDs\@SMIP). First, GQDs were prepared from citric acid monohydrate by a thermal process. Subsequently, the GQD surface was modified with APTES, a precursor for silica layer growth, to form GQD-APTES. Next, GQDs\@SMIP was fabricated via the sol-gel polymerization of the GQD-APTES complex (as the fluorescent material), SMZ (as the template), APTES (as the functional monomer), TEOS (as the crosslinker), and ammoniacal solution (as the catalyst). SMZ was imprinted on GQDs\@SMIP through a non-covalent attachment and could be easily removed by a washing process. After the removal of SMZ, cavities with a shape similar to that of the SMZ structure were left in the polymer, which could recognize and rebind SMZ molecules. Thus, the obtained GQDs\@SMIP could serve as a novel material for SMZ detection. [Scheme 1](#materials-13-02521-sch001){ref-type="scheme"} clearly demonstrates the preparation method and application in SMZ sensing of GQDs\@SMIP. In this work, we introduced the SMZ analysis in phosphate buffer saline (PBS) by employing GQDs\@SMIP. Presently, we are continuing to develop this method for analyzing the various real samples such as human serum, blood sample, drinking water, and food originated from animals.
2. Experimental Details {#sec2-materials-13-02521}
=======================
2.1. Materials {#sec2dot1-materials-13-02521}
--------------
All chemical substances were obtained from Sigma--Aldrich (St. Louis, MO, USA) and used without further purification. The chemicals include citric acid monohydrate (CA) (CAS: 5949-29-1), NaOH (CAS: 1310-73-2), ethanol (CAS: 64-17-5), APTES (CAS: 919-30-2), TEOS (CAS: 78-10-4), NH~4~F (CAS: 12125-01-8), NH~4~OH (CAS: 1336-21-6), SMZ (CAS: 723-46-6), sulfadiazine (CAS: 63-35-9), sulfamerazine (CAS: 127-79-7), sulfamethazine (CAS: 57-68-1), sulfasalazine (CAS: 599-79-1), sulfapyridine (CAS: 144-83-2), and phosphate buffer saline (PBS) (pH = 9). Deionized (DI) water (pH = 7) (CAS: 7732-18-5) was utilized in all the experiments.
2.2. Instruments and Measurements {#sec2dot2-materials-13-02521}
---------------------------------
Photoluminescence (PL) spectra were recorded using a QuantaMaster TM 50 PTI spectrofluorometer from Photon Technology International (Kyoto, Japan). Transmission and Scanning electron microscopy (TEM and SEM) images were collected using FEI microscope (Tecnai, F30S-Twin, Hillsboro, OR, USA) and a field-emission scanning electron microscope (Hitachi S-4700, Hitachinaka, Ibaraki Prefecture, Japan), respectively. Fourier-transform infrared (FTIR) spectra were recorded using a Nicolet 6700 spectrometer from Thermo Scientific (Waltham, MA, USA). Powder X-ray diffraction (XRD) patterns of GQDs\@SMIP were recorded on an automated Rigaku D/max 2200 X-ray diffractometer with monochromatic Cu *Kα* radiation (Tokyo, Japan). X-ray photoelectron spectroscopy (XPS) was measured by an X-ray photoelectron spectrometer (PHI 5000, Chigasaki, Kanagawa Prefecture, Japan). The zeta potential was performed on electrophoretic light scattering (Photal Otsuka Electronics, ELS 8000, Osaka, Japan).
2.3. Synthesis of GQDs and APTES-Modified GQDs {#sec2dot3-materials-13-02521}
----------------------------------------------
First, 2 g of CA was taken in a small beaker and heated to 200 °C in an oven. The CA melted, yielding an orange liquid after 30 min. Next, the resulting liquid was dropped into a solution of NaOH (10 mg/mL; 100 mL) and stirred vigorously for 3 h. Finally, the obtained GQD sample was dialyzed using a dialysis bag (MCWO: 1000 Da) for 72 h to obtain pure GQDs.
To synthesize APTES-modified GQDs, 1.5 mL of APTES was dropped to 20 mL of pure GQDs solution (6.85 mg/mL in water solvent). The solution was stirred at 40 °C for 30 min and then cooled to room temperature. The prepared APTES-modified GQDs were purified using petroleum ether, then dispersed in ethanol.
2.4. Synthesis of GQDs\@SMIP and silica non-molecularly imprinted polymer (GQDs\@SNIP) {#sec2dot4-materials-13-02521}
--------------------------------------------------------------------------------------
GQDs\@SMIP was formed through a sol--gel polymerization method. First, adding 25 mg of SMZ to 5 mL of ethanol under stirring. Subsequently, 12 mL of the suspension of APTES-modified GQDs in ethanol (volume ratio is 1:1), 2.4 mL of TEOS, and 3.6 mL of APTES were added to the mixture. Next, adding 0.6 mL of a catalytic solution prepared from 2 g of NH~4~F, 23 mL of NH~4~OH, and 100 mL of H~2~O. The mixture was stirred at 25 °C for 30 min. Then, the mixture was centrifuged to recover the product, which was washed with anhydrous ethanol. The SMZ template in the composites was eliminated by washing with methanol until no absorbance peak of SMZ in the washing solvent was obtained. Next, the composites were dried in an oven at 50 °C.
GQDs\@SNIP was synthesized in the same manner without adding the SMZ template.
2.5. SMZ detection {#sec2dot5-materials-13-02521}
------------------
First, adding 0.1 g of GQDs\@SMIP to 100 mL of PBS (pH = 9) under vigorously stirring to prepare a stock solution. Next, a series of 5 mL volume of the stock solution and variety amounts of an SMZ solution were serially dropped into cuvettes. Various mixtures with a final concentration of SMZ of 0, 1, 3, 5, 10, 20, 30, 40, 50, 60, 80, 100, 120, and 140 µM were obtained. The solutions were shaken and then incubated at room temperature for 90 min before fluorescence measurements.
2.6. Selectivity {#sec2dot6-materials-13-02521}
----------------
To determine the selectivity of GQDs\@SMIP to SMZ, the effect and interferences of other substances belonging to the sulfonamide family such as sulfadiazine, sulfamerazine, sulfamethazine, sulfasalazine and sulfapyridine were investigated.
3. Results and Discussion {#sec3-materials-13-02521}
=========================
3.1. Characterization of GQDs\@SMIP {#sec3dot1-materials-13-02521}
-----------------------------------
Fluorescence spectroscopy was applied for characterizing the optical properties of GQDs\@SMIP. The fluorescence spectra ([Figure 1](#materials-13-02521-f001){ref-type="fig"}) shows the maximum emission peak of GQDs is placed at 455 nm, whereas the fluorescence emission maxima of the GQDs\@SNIP and GQDs\@SMIP red-shifted to 462 and 464 nm, respectively, under the excitation wavelength of 370 nm. This can be explained based on charged Si‒O groups on the surfaces of GQDs\@SNIP and GQDs\@SMIP. These groups might produce an electric field, which causes the recombination of trapped charged carriers and dangling bonds at the particle surfaces. This led to a change in the position of the emission peak \[[@B30-materials-13-02521],[@B31-materials-13-02521],[@B32-materials-13-02521]\].
Moreover, [Figure 1](#materials-13-02521-f001){ref-type="fig"} shows that GQDs\@SMIP can be a good material for SMZ sensing. After the SMZ elimination, the fluorescence intensity of GQDs\@SMIP increased sharply and when it was recombined with SMZ, the intensity decreased significantly. This is a fundamental characteristic for selective and effective SMZ detection.
The TEM and SEM images in [Figure 2](#materials-13-02521-f002){ref-type="fig"} show the morphologies and size of the GQDs and GQDs\@SMIP. [Figure 2](#materials-13-02521-f002){ref-type="fig"}A reveals that GQDs were mono-dispersedly synthesized with a narrow size distribution of 2.7 to 5 nm and an average size of 4.1 nm. In the high-resolution (HR) TEM image (inset of [Figure 2](#materials-13-02521-f002){ref-type="fig"}B), the crystal structure of the GQDs is apparent, with a lattice parameter of 0.152 nm, which is associated with the graphitic diffraction planes \[[@B33-materials-13-02521],[@B34-materials-13-02521]\]. The TEM image of GQDs\@SMIP ([Figure 2](#materials-13-02521-f002){ref-type="fig"}C) displays that the average diameter of GQDs\@SMIP is 459 nm, whereas the SEM image ([Figure 2](#materials-13-02521-f002){ref-type="fig"}D) indicates the average diameter to be 522 nm. Therefore, there is quite good agreement between the TEM and SEM outcomes. Moreover, these results indicate that SMIP might contain many small particles of GQDs.
We further characterized GQDs\@SNIP and GQDs\@SMIP by FTIR spectroscopy. In [Figure 3](#materials-13-02521-f003){ref-type="fig"}A, the spectrum of GQDs\@SMIP (before washing) presents main characteristic peak in the range of 3050--2800 cm^−1^, which may be assigned to the C‒H, O‒H stretching of the carboxylic acid and hydroxyl groups, or N‒H stretching belonging to amine groups. Further, a peak positioned at 1560 cm^−1^, which occurs owing to the HN‒CO bonding vibrations; a peak located at 1297 cm^−1^ results from the vibration of the O=S=O group, which is a part of the SMZ molecule, and a peak at 1017 cm^-1^ occurs due to the stretching vibrations of the Si‒O group. The FTIR spectrum of GQDs\@SMIP (after washing) contains all the peaks belonging to GQDs\@SMIP (before washing) except for the peak of the O=S=O group, which confirms that SMZ molecules were completely extracted out of the GQDs\@SMIP composite. Therefore, after the removal of SMZ, the spectrum of GQDs\@SMIP (washed) is extremely similar to that of GQDs\@SNIP.
The XRD patterns ([Figure 3](#materials-13-02521-f003){ref-type="fig"}B) of both GQDs\@SNIP and GQDs\@SMIP only show a broad peak at \~21°, which could be attributed to the amorphous silica phase (JCPDS No. 29-0085). This result indicates the presence of silica polymer layer in the nanocomposites. Although the TEM image shows a crystalline structure of GQDs ([Figure 2](#materials-13-02521-f002){ref-type="fig"}B), their size is significantly small as compared to the size of the silica layer; therefore, no specific peak of GQDs was observed in the XRD pattern.
The XPS profile of GQDs\@SMIP ([Figure 4](#materials-13-02521-f004){ref-type="fig"}A) presents five typical peaks at 529, 397, 282, 150, and 106 eV, correlating with O1s, N1s, C1s, Si2s, and Si2p, respectively. The weight percentages of C, N, O, and Si were analyzed to be 37.16%, 7.05%, 36.62%, and 19.17%, respectively. In [Figure 4](#materials-13-02521-f004){ref-type="fig"}B, the C1s peak can be de-convoluted into three peaks located at 284.4, 285.6, and 287.8, corresponding to C‒C/C=C, C‒O/C‒N/C‒Si, and C=O bonds, respectively, which originate from the sp^2^ graphitic structure \[[@B35-materials-13-02521]\] and several carboxyl, hydroxyl, amine, and Si-containing groups belonging to GQDs\@SMIP which were further confirmed by O1s, N1p, and Si2p spectra. The O1s spectrum ([Figure 4](#materials-13-02521-f004){ref-type="fig"}C) was de-convoluted into three characteristic peaks including those of O‒C at 532.4 eV, O‒Si at 532 eV, and O=C at 531.5 eV. The N1s spectrum ([Figure 4](#materials-13-02521-f004){ref-type="fig"}D) was de-convoluted into two specific peaks corresponding to N‒H at 400.2 eV and N‒Si at 398.8 eV. The Si2p spectrum ([Figure 4](#materials-13-02521-f004){ref-type="fig"}E) was de-convoluted into a peak at 102.2 eV assigned to the Si‒N bond, and peaks located at 102.7 eV were ascribed to Si‒O and Si‒C bonds.
3.2. SMZ Sensing {#sec3dot2-materials-13-02521}
----------------
We investigated the effect of pH, which is a vital parameter which influences the fluorescence stability of GQDs\@SMIP and the fluorescence response of GQDs\@SMIP to SMZ. [Figure 5](#materials-13-02521-f005){ref-type="fig"}A indicates that the fluorescence intensity of GQDs\@SMIP is low in strongly acidic or basic solutions. In the pH range of 6 to 9, the intensity reached the maximum value and remained stable. In the presence of SMZ ([Figure 5](#materials-13-02521-f005){ref-type="fig"}B), the intensity of GQDs\@SMIP was strongly quenched at pH values between 7 and 9. It is well-established that if the pH is excessively low or high, the imprinted silica shell can hydrolyze and the template cavities can be destroyed \[[@B2-materials-13-02521],[@B36-materials-13-02521],[@B37-materials-13-02521]\]; this affects the stability as well as the ability of the GQDs\@SMIP template to recognize the target analyze. Based on these results, we realized that a pH in the range of 7 to 9 is suitable for SMZ detection. In particular, the pH of 9 is optimum for the investigation of SMZ sensing.
The fluorescence intensities of GQDs\@SNIP and GQDs\@SMIP were quenched in the presence of SMZ ([Figure 6](#materials-13-02521-f006){ref-type="fig"}). This occurred because of hydrogen bonding interaction between SMZ molecules and the amine groups acting as binding sites on the surfaces of GQDs\@SNIP and GQDs\@SMIP \[[@B18-materials-13-02521],[@B30-materials-13-02521]\]. However, there was a key difference in the quenching responses of GQDs\@SNIP and GQDs\@SMIP to SMZ. Clearly, the quenching degree of GQDs\@SMIP was more pronounced than that of GQDs\@SNIP. Particularly, [Figure 6](#materials-13-02521-f006){ref-type="fig"}A,B (insets) shows that the GQDs\@SMIP fluorescence intensity quenched sharply corresponding to increasing in SMZ amount from 0 to 140 µM, whereas that of GQDs\@SNIP decreased insignificantly. More precisely, in the existence of 140 µM SMZ, the intensities of GQDs\@SMIP and GQDs\@SNIP at the same concentration of 5 mg/mL were quenched by 53% and 33%, respectively. The presence of specific imprinted cavities in GQDs\@SMIP to recognize SMZ led to stronger adsorption of the SMZ template to it. Therefore, SMZ molecules were observed to bind to GQDs\@SMIP more strongly, which caused a strong fluorescence quenching effect. In addition, SMZ is known to be a good hole or electron acceptor \[[@B38-materials-13-02521]\], and an electron transfer process might occur after the entry of SMZ into the imprinted cavities; this is confirmed by a change in the zeta potential of the GQDs\@SMIP suspension from −14.75 to −9.08 mV after the addition of SMZ (140 µM). This process also contributes to the quenching phenomenon. The calibration curve in [Figure 6](#materials-13-02521-f006){ref-type="fig"}A (inset) clearly demonstrates the quenching effect of SMZ on the GQDs\@SMIP fluorescence intensity. The intensity decreased steadily and significantly corresponding to the increase in SMZ concentration up to 100 µM. No notable change occurred with further increase because all imprinted cavities might have been filled with SMZ molecules. In the range of SMZ concentration (C~M~) 1 to 100 µM, a good linear relationship was found with the equation, *I*/*I*~0~ = 1 − 0.00555 C~M~ and a correlation coefficient (R^2^) of 0.99537. The experiment was repeated thrice and the result is expressed as the average ± standard deviation. Moreover, the limit of detection (LOD) was determined to be approximately 1 µM. [Table 1](#materials-13-02521-t001){ref-type="table"} shows the result comparison of our fluorescence method with other currently presented methods. It is clear to see that our simple fluorescence approach gives the similar results to that of the others which require expensive instruments and complicated operating process. This is a remarkable advantage of our fluorescence technique using GQDs\@SMIP for SMZ detection.
3.3. Selectivity {#sec3dot3-materials-13-02521}
----------------
To verify the specificity of GQDs\@SMIP to SMZ, the fluorescent responses of the composite in the presence of five potentially interfering structural analogs belonging to the sulfonamide group were investigated. The chemical structures of sulfadiazine, sulfamerazine, sulfamethazine, sulfasalazine, and sulfapyridine are shown in [Figure 7](#materials-13-02521-f007){ref-type="fig"}A. GQDs\@SMIP contains imprinted cavities, which are specific in shape and size to absorb the SMZ used as the template for imprinting; as other analogues could not be embedded in these cavities, they did not produce remarkable variations in the fluorescence intensity of GQDs\@SMIP. However, further adding of SMZ makes the fluorescence of the system decreased significantly ([Figure 7](#materials-13-02521-f007){ref-type="fig"}B). It may be inferred that the GQDs\@SMIP exhibits excellent selectivity in SMZ detection. The experiment was repeated thrice and the result is expressed as the average ± standard deviation.
4. Conclusions {#sec4-materials-13-02521}
==============
We produced GQDs\@SMIP via a sol-gel polymerization method. Characterization using fluorometry, TEM, SEM, FTIR, XRD and XPS confirmed that the synthesis approach was successful. Moreover, applying SMZ as a template for the imprinting process resulted in specific absorption cavities for SMZ in the polymeric layer. This imprinting technique combined with fluorescence detection aided us in developing a sensor that is not only effective in SMZ detection, but also has enhanced sensitivity and selectivity. Particularly, the obtained results show that the fluorescence of GQDs\@SMIP was quenched with an increase in SMZ concentration over a wide range with a low LOD. This quenching response was not clearly observed with other analogs belonging to the sulfonamide group. With these remarkable features, the GQDs\@SMIP sensor can potentially be applied in biomedical systems and environments.
Investigation, T.H.L.; Methodology, H.J.L.; Formal analysis, J.H.K.; Writing---review & editing, S.J.P. All authors have read and agreed to the published version of the manuscript
This research was supported by Basic Science Research Capacity Enhancement Project through Korea Basic Science Institute (National research Facilities and Equipment Center) grant funded by the Ministry of Education (Grant No. 2019R1A6C1010016).
The authors declare no conflict of interest.
Figures, Scheme and Table
=========================
{#materials-13-02521-sch001}
{#materials-13-02521-f001}
{#materials-13-02521-f002}
{#materials-13-02521-f003}
{#materials-13-02521-f004}
{#materials-13-02521-f005}
{#materials-13-02521-f006}
{#materials-13-02521-f007}
materials-13-02521-t001_Table 1
######
Comparison of SMZ detection for different methods.
Method Linear Range LOD Reference
--------------------- ---------------- ---------- -------------------------------
**Electrochemical** 0.2--1.4 µM 0.05 µM \[[@B39-materials-13-02521]\]
**Electrochemical** 0.8--170 µM 0.8 µM \[[@B40-materials-13-02521]\]
**Electrochemical** 2.4--23.6 µM 0.81 µM \[[@B26-materials-13-02521]\]
**Electrochemical** 10--100 µM 0.144 µM \[[@B27-materials-13-02521]\]
**Ultrasound** 0.78--19.74 µM 0.23 µM \[[@B41-materials-13-02521]\]
**Voltammetry** 0.05--70 µM 0.01 µM \[[@B42-materials-13-02521]\]
**Our method** 1--100 µM 1 µM
|
---
abstract: |
Exact ground-state properties are presented by combining the diagonalization in the Fock space (and taking [*all*]{} hopping integrals and [*all*]{} two-site interactions) with the [*ab initio*]{} optimization of the Wannier functions. Electrons are essentially localized for the interatomic distance $R \sim 2.0$ Å for $s$-like states, when the quasiparticle mass is divergent. The momentum distribution [*dispersion*]{} is proposed to define the localization [*order parameter*]{}. Dimerization and zero-point energies are also discussed. The method provides convergent results for $N\geq 8$ atoms.\
\
PACS Nos. 71.10.Fd, 71.15.Fv, 31.25.Nj
address: |
Marian Smoluchowski Institute of Physics, Jagiellonian University, ulica Reymonta 4,\
30-059 Kraków, Poland\
author:
- Jozef Spałek and Adam Rycerz
date: 'June 4, 2001'
---
[2]{}
One dimensional systems range from organic metals [@jero] to quantum rings and wires [@jaca], and to nanotubes [@mint]. In their description the role of the long-range Coulomb interaction is crucial because of reduced dimensionality, for which the charge screening becomes less effective [@ovch]. The existing exact solutions of the parametrized models with inclusion of intersite interactions [@ovch; @stra] prove the existence of the metal-insulator transition for the half-filled-band case, in contradistinction to the corresponding Hubbard-model solution [@lieb], for which the system is insulating even for an arbitrarily small Coulomb repulsion. The existence of such metal-insulator the transition has been also discussed [@daul] within the density-matrix renormalization group (DMRG) method when the second-neighbor hopping is included. A separate question concerns the appearance of the Tomonaga-Luttinger behavior [@emer] in the metallic state, for which some evidence has been gathered [@dard]. In brief, the search for a proper description of those systems as quantum liquids (and their instabilities) is one of the basic problems in the physics of low-dimensional systems.
In the above theoretical analysis \[1-8\] the solutions have been disscussed as a function of the microscopic parameters, which are not easy to measure. Therefore, one assumes that they should be determined first from a separate single-particle approach. In following this route one must avoid counting twice the interaction, as discussed carefully in the papers implementing the LDA+U [@anis] and SIC [@temm] methods. We have proposed [@spapo] a new method in which the single-particle (Wannier) wave functions are allowed to relax in the correlated state and thus are determined by optimizing the exact ground state energy obtained from the diagonalization in the Fock space. In other words, we treat properly the interactions first due to their strongly nonperturbative nature and then readjust the single-particle functions $\{w_i({\bf r})\}$ by setting Euler equation for them, which plays the role of the renormalized wave equation for a particle in the correlated ground state. In such approach the problem of double counting the interaction does not arise [*at all*]{}. Additionally, we include [*all*]{} the hopping integrals and [*all*]{} two-site interactions to make the solution more complete. The method is executable on a desktop server for the number of atoms $N\leq 12$. What is probably the most remarkable formal feature of these calculations is that the electronic correlations make the wave function more tightly bound to the atoms and thus limiting the interaction range. In effect, the results are converging very fast for $N\geq 8$ atoms meaning that the [*optimized*]{} Wannier functions and the interaction parameters are relevant at most up to the [*third*]{} neighbors. The results are detailed below and to the best of our knowledge they represent the first analysis of the strong correlation effects as a function of the lattice parameter within the exact acount of both the interaction and the wave function [*without limiting the range of either the hopping processes or the two-site interactions*]{}. The obtained results show that the method is particularly useful for accurate studies of electronic correlations in quantum dots and rings.
The nature of the electron momentum distribution [@carmelo] $n_{k\sigma}\,\equiv\,<a_{k \sigma}^{\dagger}\,a_{k \sigma}>$ is shown in Fig. 1 for $N=10$ atoms (we use the periodic boundary conditions). For the interatomic distance $R=3a_0$, where $a_0$ is the $1s$ Bohr radius (setting the length scale), this is essentially the Fermi-Dirac function with a tail extending to the Brillouin zone boundary. The smearing out of the distribution with increasing $R$ suggests that the electronic states transform from itinerant to localized states, as exemplified for $R=R_c\approx 3.929$. The continuous line represents the parabolic fit of the same type for both $k\leq k_F$ and $k\geq k_F$. A natural question to be dealt with is whether the Fermi ridge disappearance at $R=R_c$ is reflected in any singularity in other properties.
To distinguish quantitatively between those states we plot in Fig. 2, the following basic quantities (as a function of $R$) defined in both itinerant and localized states: (i) the site spin magnitude $\theta_M\equiv (4/3)\left<{\bf S}^2_i\right>$, where ${\bf S}_i\,=\,(S_{i}^{+},\,S_{i}^{-},\,S_{i}^{z})\,
=\,(a_{i \uparrow}^{\dagger}\,a_{i \downarrow},\,
a_{i \downarrow}^{\dagger}\,a_{i \uparrow},\, (n_{i \uparrow}\,-\,
n_{i \downarrow})/\,2)$ is the electron spin on site $i$, (ii) the spin correlation function $\theta_{AF}=-\left<{\bf S}_i\cdot{\bf S}_{i+1}\right>$, and (iii) $\theta_{MI}=4{\sigma}^2\left\{n_{k\sigma}\right\}$, where ${\sigma}^2\left\{n_{k\sigma}\right\}$ is the dispersion of the statistical distribution defined as: $${\sigma}^2\left\{n_{k\sigma}\right\}=
\frac{1}{2N}\sum_{k\sigma}n_{k\sigma}^2-
\left(\frac{1}{2N}\sum_{k\sigma}n_{k\sigma}\right)^2.$$ The averages are for the ground state, which is determined via an exact diagonalization in the Fock space. The quantity ($\theta_M\,=\,1\,-\,2\,<n_{i \uparrow}\,
n_{i \downarrow}>$) takes the value ($1/2$) in the ideal gas limit and approaches unity in the atomic limit, where we have a Pauli spin on each atom. $\Theta_{AF}$ approaches the value ($3/4$) for the singlet configuration of atomic spins, whereas $\sigma^2\left\{n_{k\sigma}\right\}$ acquires the value $1$ in the gas limit ($n_{k \sigma}\,=\,\Theta\,(\mu\,-\,\epsilon_{k})$) and vanishes for an even momentum distribution ($n_{k \sigma}\,=\,1/2$), when the particle position is sharply defined on atom, i.e. for the localized electron states characterized by atomic states. Thus, the quantity $\theta_{MI}$ plays the role of [*the order parameter*]{} for this [*crossover behavior*]{}, since it clearly distinguishes between the complementary momentum and position representations of the system quantum states. From Fig. 2 it follows that for $R/a_0=5$ all three parameters acquire (within $5\%$) their asymptotic values for purely atomic states.
The analysis of metal-insulator transition induced by electron-electron interaction started with the works of Mott [@mott] and Hubbard [@hubb]. The first of them introduced the critical carrier concentration for the transition to take place in a discontinuous manner, whereas the second introduced the critical bandwidth to interaction ratio (of the order of unity). Our method of approach can be used to relate the above criteria, as we discuss next. Namely, to relate our method to the original ideas of Mott and Hubbard, we have plotted in Fig. 3 the ratio of bandwidth $W \equiv 2 |\sum_{j(i)} t_{ij}|$, where $t_{ij}$ is the hopping integral between the neighbors $\left<ij\right>$ (calculated through the relation $t_{ij}=\left<w_i\right|H_1\left|w_j\right>$ for the basis $\left\{w_i\right\}$ optimized in the correlated state and for full single-particle potential in $H_1$), to the effective short range Coulomb interaction $U-K$, where $U=\left<w_iw_i\right|V_{12}\left|w_iw_i\right>$ and $K=\left<w_iw_{i+1}\right|V_{12}\left|w_iw_{i+1}\right>$. The value $W/\left(U-K\right)=1$ marked in this figure represents roughly the dividing line between metallic and Mott insulating states for three-dimensional systems [@hubb]. This point, achieved for $R\approx 2.7a_0$, does not reflect any characteristic point for our system. Instead, the localization is practically achieved for the distance about twice as large, as is the size of the atomic states composing the Wannier function [@spapo] (characterized by the quantity ${\alpha}^{-1}$, see the inset), which nears its atomic value for the $s$-like state. Again, the results for $N=8$ and $N=10$ are very close to each other; this is the reason why we have shadowed the areas between the corresponding curves in both Figs. 2 and 3.
On the basis of Figs. 2 and 3 we can estimate the localization threshold for our system. The corresponding Mott criterion [@mott], generalized to $d$ dimensions takes the form $n_c^{1/d}a_H\approx 0.2$, where $n_c$ is the carrier concentration, and $a_H$ is the size of the states at the localization threshold. In our situation of neutral chain: $n_c=1/R$, and $a_H={\alpha}^{-1}$ so that for $R\approx 5a_0$ this criterion takes the form $\left(a_0/R\right)\left({\alpha}^{-1}/a_0\right)\approx 0.95/5\approx 0.2$, a suprisingly close value to that of Mott (which reflects the long-range nature of the Coulomb interaction). Thus, our results provide a support for the Mott criterion rather than for the Hubbard one [@hubb]. In other words, the [*metallicity*]{} extends well beyond the $W=U$ limit and this must be caused by the inclusion of more distant hopping processes. One may also say that the Mott-criterion universality originates from the long-range nature of the interaction, which imitates the higher-lattice dimensionality.
Hence, the conclusion [@lieb] about the universality of the insulating state for the Hubbard chain does not extend to the $1d$ models with a realistic account of the electronic structure. This conclusion is very important also because it removes one of the main objections against using the itinerant (or even effective mass) states for quantum dots [@jaca].
We can determine directly the effective mass at the Fermi level. Namely, the calculated band mass $m_{F}$ is about $40\%$ enhanced near the localization threshold. The quasiparticle mass $m^{\star}_{F}$ is found from the relation $m^{\star}_{F} = (\Delta n_{k_{F}})^{-1} m_{F}$, where the first factor is the usual Fermi-liquid $Z^{-1}$ enhancement (the discontinuity at the Fermi level marked in Fig.1). The results are shown in Fig. 4. A clear critical behavior is detected: $m^{\star}_{F} = A |R - R_{c}|
^{-\gamma}$, with $A = 10.2, R_{c} = 3.92$, and $\gamma = 4/3$. This quantum critical behavior is obtained, since we emulate the discrete distribution $n_{k}$ with a continuous parabolic interpolation when determining $\Delta n_{k_F}$. The localization threshold $R_{c}$ is about $10\%$ higher for $N=8$. It is tempting to speculate that with the increasing $N\rightarrow\infty$ the Mott and the Hubbard criteria for $R_{c}$ may coalesce. The masses near $R = R_{c}$ are huge and reach those known only for heavy-fermion compounds.
The one-dimensional systems are unstable with respect to the dimerization [@jero]. We have determined the ground state energy of such a state on the same level of precision as above and have additionally minimized it with respect to the amplitude of the lattice distortion. In Fig. 5 (bottom) we have compared the energy contribution $\Delta E$ due to the dimerization with that due to the zero-point motion (top). Both the dimerization amplitude and $\Delta E$ are strongly reduced for $R/a_0 >5$, a feature inevitably connected with the long-range nature of Coulomb interactions, which drives the system towards spatially periodic state (the Mott insulating state on the lattice replaces the Wigner-crystal state [@emer] for the electron gas). Therefore, our results and conclusions above should remain intact for longer chains. Additionally, the zero-point energy overcomes the dimerization energy for a light (hydrogen) chain and has been estimated in the following manner.
In the harmonic approximation, the phonons have energy $\omega_k=2\left(C/M\right)^{1/2}\sin\left(\pi k/N\right)$, where $M$ is ionic mass, and the elastic constant is calculated by a numerical differentiation $C=N^{-1}{\partial}^2E_G/\partial R^2$. Formally, these formulae are valid only if the energy has an absolute minimum. Here we assume that the system is closed in a box of length $NR$ and thus the global repulsive interaction between the atoms (the situation with $\partial E_G/\partial R < 0$ for given $R$) is balanced out by the environment. Also, as the k=0 mode is a Goldstone mode, we include only the modes with $k \neq 0$. The phononic contribution to the ground state energy (in the atomic units) is then $$\Delta E_G^{\rm ph}=\left(\frac{2m}{M}\right)^{{\frac{\scriptstyle 1}{\scriptstyle 2}}}
\left(\frac{1}{N}\frac{{\partial}^2 E_G}{\partial R^2}\right)^{{\frac{\scriptstyle 1}{\scriptstyle 2}}}
\sum^{N-1}_{k=1}\sin\left(\frac{\pi k}{N}\right),$$ where $m$ is the bare electron mass. On the basis of the relation for the $k$-th mode $\left(1/2\right)M\omega_k\left(\Delta R_k\right)^2=\hbar\omega_k/2$, where $\left(\Delta R_k\right)^2$ is the mode contribution to the zero-point vibrations, we can easily estimate the total amplitude $\left(\Delta R\right)^2$, which in the atomic units has the form $$\left(\Delta R\right)^2= \frac{1}{N}\left(\frac{m}{2M}\right)^{{\frac{\scriptstyle 1}{\scriptstyle 2}}}
\left(\frac{1}{N}\frac{{\partial}^2E_G}{\partial R^2}\right)^{-{\frac{\scriptstyle 1}{\scriptstyle 2}}}
\sum_{k=1}^{N-1}\frac{1}{\sin\left(\pi k/N\right)}.$$ In the $N\rightarrow\infty$ this result give $\left(\Delta R\right)^2\sim\log N$, providing the dynamical lattice instability in one dimension. At the localization threshold (i.e. for $R/a_0\approx 5$) and for $N=8$, we have that $\Delta R\approx 0.12$, a substantial. By comparison, the shift due to the dimerization is $\approx 0.06$ . Also, the [*Peierls distorted state*]{} extends to the localized state (up to $R\,\approx\,6.5\,a_{0}$).
In summary, we have determined the microscopic criteria for the [*transition*]{} from the itinerant to the localized states in a one-dimensional system of a finite size and have illustrated those findings on the example of a correlated quantum ring. The new method of optimizing the single-particle wave functions in the correlated state [@spapo] proves thus valuable in the exact treatment of nanoscopic systems. We have calculated all the properties as a function of the lattice parameter. The work was supported by KBN Grant No. 2PO3B 092 18.
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|
When speech becomes suspicious: the FBI's "communities against terrorism"
Submitted by sosadmin on Mon, 02/13/2012 - 12:30
The FBI wants you to know that paying with cash, being concerned about your privacy (or as the FBI calls it, your "privacy"), and taking an "unusual" interest in surveillance or security procedures are all suspicious activities that could be linked to terrorism.
Last week, Public Intelligence posted a file containing a number of FBI "Communities Against Terrorism" cheat sheets, which contain information about supposed terrorism risk indicators, directed at various groups of people or private entities. Among the categories are:
construction sites
electronics stores
hobby shops
hotels and malls
internet cafés
entertainment facilities
martial arts and paintball activities
mass transportation and
"sleepers" -- or "otherwise persons who camouflage their involvement in terrorist activity or planning by attempting to fit in with others in our society."
(That last bit is awfully strange, isn't it? You'd assume that anyone bent on committing acts of terrorism would want to camouflage their involvement with that activity, no?)
You might think: great! The FBI is reaching out to communities and businesses, doing due diligence to ensure that many different communities in the United States have the information they need to protect themselves and their surroundings from those who would do them harm. And indeed, some of the FBI's advice to businesses and the public make sense. For example, when advising farm store suppliers about things to watch out for, the FBI lists a number of chemicals that might be used to manufacture a bomb, and advises that shop owners ask for identification whenever people purchase those materials.
But the cheat sheets go well beyond commonsense advice, and encroach directly on our rights to freedom of speech and freedom from government intrusion into our private lives. We've talked for a long time about the FBI's classification of commonplace activities like taking notes or photography as "suspicious activities," and these sheets repeat those mistakes. But there are three other trends in these documents that warrant particular concern.
First is the notion that Muslims are a dangerous enemy within; second is the conflation of unpopular speech or dissent with terrorism; and third is the notion that if we are concerned with privacy, we are somehow suspicious.
How to spot a "sleeper"
There is ample evidence to suggest that the FBI has made Muslims its enemy number one in the agency's anti-terrorism work. A cursory glance at its dedicated resources, investigations, surveillance, and personnel training reveals an obsession with Muslims and Islam that does not match reality. As a recent terrorism study showed, the threat from radical Muslims to the United States is "minuscule" and shrinking every year, but you wouldn't know it by listening to the FBI.
Here are some choice segments from the document. Judge for yourself whether or not you think the FBI is specifically targeting Muslims, absent any evidence that Muslims are more dangerous to the US than any other group of people.
Equating unpopular speech with propensity for criminal activity
As you can see in the example cited above, the FBI not only inappropriately targets Muslims and Islam, but also suggests that expressing "fury at the West," "excusing violence against Americans on the grounds that American actions provoked the problem," or harboring "conspiracy theories about Westerners" are "attitude indicators" that should raise red flags.
But if that's true, many of us are in for an FBI investigation into our unpopular speech. Here are a series of quotes from high profile public people, including a GOP presidential candidate, that raise alarm given the FBI's above cited criteria.
Do these comments warrant the FBI digging into the speakers' personal lives in order to find out if they are dangerous terrorists? If you hear someone say things like this on television, should you immediately pick up the phone and call the FBI tips line?
1. On US actions and the notion that violence against Americans can be provoked by American actions:
We're under great threat because we occupy so many countries. We're in 130 countries. We have 900 bases around the world. We're going broke. The purpose of al-Qaeda was to attack us, invite us over there, where they can target us. And they have been doing it. They have more attacks against us and the American interests per month than occurred in all the years before 9/11. But we're there, occupying their land. And if we think that we can do that and not have retaliation, we're kidding ourselves.
That was GOP presidential candidate and Congressperson Ron Paul. I wonder how large his FBI file is.
2. On "fury at the West":
This was just simple murder…America is the big evil. We are just a small mouthful in front of America.
That was a Senator from Pakistan, a close ally of the United States and one of the top recipients of US State Department and military aid, speaking after suspected CIA agent Raymond Davis killed two Pakistanis in broad daylight in that country.
3. On "conspiracy theories about Westerners":
[9/11] couldn’t possibly have been done the way the government told us.”
That was Judge Andrew Napolitano, a libertarian who until last week had a very popular FOX Business television program.
Don't hold your breath for the FBI to initiate terrorism prosecutions of any of the above people. Perhaps advocating "extreme" ideology is only really a problem when you are Muslim.
Don't cover your computer screen or use encryption: that's suspicious
The FBI is concerned about unpopular, "anti-US" speech, but it is also concerned about how speech is protected. Or rather, the agency thinks it is suspicious if you try to protect your communications or data from its -- or hackers' -- prying eyes.
Do you care about your privacy online? Are you concerned about the fact that the government can now routinely, warrantlessly subpoena access to your most intimate information, including your real-time credit card and travel information, your cell phone data, and your IP address?
Do you encrypt any of your internet data, like your email or your instant messaging? Do you use Tor, or another service that helps prevent the tracking of your physical location online?
Are you a journalist? A lawyer? A businessperson? Does your line of work require that you keep confidential sources, or that you ensure that your client's information is not disclosed to anyone, including hackers or government spies?
Or maybe you are just an ordinary person who doesn't want your credit card information to be scooped up by hackers at an internet cafe. Maybe you don't want your ex-partner, who is a computer expert, to be able to snoop into your unencrypted email.
In short: there are literally thousands of legitimate reasons for us to want to maintain some privacy online. But to the FBI, all of that is so much nonsense. Your interest in online privacy is suspect, says its "Communities Against Terrorism" documents. And if you own an internet cafe or an electronics shop, the FBI wants your help in ratting out those among us who take some precautionary measures to protect ourselves online and in the digital world.
The "Communities Against Terrorism" documents repeatedly reference paying with cash, being "overly concerned about privacy," and expression of so-called "anti-US" sentiments as grounds for suspicion. But the documents particular to electronics stores and internet cafes are especially interesting, because they directly assault the notion that privacy has intrinsic value.
In other words, if you are interested in trying to protect yourself from the government's all-seeing digital surveillance eye, you are suspicious. Given the woefully inadequate statutory protections against improper government spying that allow for serious violations of our privacy, taking precautionary measures like those listed above may be your only hope of escaping the digital surveillance matrix.
But if you try to escape, beware: ironically enough, doing so may make you a target. |
"Previously on Justified..." "This is supreme bullshit." "You do know that we're not allowed to shoot people on sight anymore?" "I'm gonna reassign you." "Eastern District of Kentucky." "I don't wanna go back there." " Still got family here in Kentucky?" " Ex-wife here." "Next time I see you, I'm gonna..." "Fire in the hole!" "How well did you know Boyd Crowder?" "Boyd and I dug coal together when we were 19." "Did you know Boyd's brother?" "The girl he married, Ava." "She ended the union last night with a.30-06." "I had a crush on you from the time I was 12 years old." "...that you get out of Harlan County by tomorrow noon" " or I'm gonna come looking for you." " Now you're talking." "I guess I just never thought of myself as an angry man." "Honestly, you're the angriest man I have ever known." "Looks like it hurts." "Why, yes, Raylan." "Thank you for noticing." "Somebody shot me in the chest the other day." "You getting something for the pain?" "Well, I can goose it as needed, but I've been holding off." "I was hoping that you'd stop by." "I wanted my mind clear and my mouth not all full of rubber when I saw you." "Let's hear it." " What do you think I'm gonna say, Raylan?" " I wouldn't know." "You know, if Ava hadn't come in that room and distracted me with that rifle, you think I could have got you first?" " I don't know." " Well, it don't matter." "The real question is, why didn't you kill me?" "Did you miss my heart on purpose?" "No." "I was aiming to kill." "That's the way I was taught." "Sometimes you don't hit the bull's-eye." "No, I suppose not." "But, you see, I have this belief, this conviction that it wasn't just an accident and that, I was wondering if the fact that we were friends, if that played any part." "Then last night I woke up, and I knew why you didn't kill me." "I was laying here in pain, in awful pain." "But I didn't hit the pump because I knew it wasn't just pain from a gunshot wound." "It was something deeper." "It was a pain from my very soul." "And I realized that, well, I couldn't any more blame you for my situation here than a farmer could blame his neighbor for a hailstorm." "A hailstorm being an act of God." "That's right, Raylan." "Me shooting you was an act of God?" "Well, God was acting through you, Raylan, through your gun, to get my attention, to set me on a new course." "Now, I know not yet what his will for me is, but I have faith." "I have faith that the path will be illuminated before me as I need it to be." "For even through this searing pain, I am at peace." "For I am born again in the eyes of the Lord, Raylan." "And I wanted to thank you for playing your part." "Now, if you will excuse me," "I must tend to the needs of the flesh." "You understand?" "Raylan?" "Did you come all the way out here just to see me?" "What do you think?" "Initial here, here, and here." "Stand up." "How come?" "We're gonna play pin-the-tail-on-the-donkey." "Just stand up." "Come through and stand on the feet." "You got your feet on backwards?" "Turn around." "Just checking you for visible injury." " All's I see is the nose." " Which I got when he hit me with a shotgun barrel for no good reason." " Is that how you remember it?" " You should thank him." "That nose's the only reason you got to spend two days here instead of going straight to Big Sandy." "Hey, careful with the teeth." "You got any more Marshals in the car?" " Task force is undermanned, just me." " Want to put him in leg irons?" "I think I can handle Mr. Crowe." "Marshals drive Lincolns now?" "Or is this confiscated?" "Yeah, I had a Town Car myself one time when I was down visiting Cousin Dale in Florida, till I sold it for parts and went to work at Disney's." "You know what I tried out for?" "To play Goofy..." "Mickey Mouse's friend." "Only, you had to water-ski." "I couldn't get the hang of that, so they put me selling ice cream." "But Disney's got a lot of Negroes and homosexuals working there," " so I came back home." " If you're gonna talk," "I'm gonna put you in the trunk, and I'll drive myself." "You grew up in Harlan, huh?" "I grew up in Corbin." "You ready for this?" "My dad has never been outside of Kentucky." "Whole life, never been closer to the border than Parisville, where he is now." "You know, we're gonna be going by there." "If we was to get off on Route 9, we could stop by and see him." "It wouldn't be more than a few miles out of our way." "What do you say to that?" "Not much, huh?" "Your old dad's never crossed the state lines, but he's been up to Manchester, hasn't he?" "He's seen the inside of the Kentucky State Prison." "You got an uncle who came out of there, and another did his time in McCreary." "I think we'll skip seeing any of your kin this trip." " My uncles are both dead." " By gunshot, huh?" "You understand how I see your people?" "Put one on your left wrist." "Now snap the other one to the wheel." "To the wheel, Chinatown." "Let's go." "I can't drive handcuffed to the damn steering wheel." "You'll get the hang of it." "Now drive." "You gonna report what I did?" "I don't take what you did personally, you understand?" "Want to lean on you." "Or wish you get any more time than you deserve." "But what you'll have to do now is ride the rap, as they say." "It's all anybody has to do." "Let's go." "Come on down, fellas." "All right." "Next." "Where the hell did they get these stupid costumes, anyway?" "Shit." "Well, this is an embarrassment." "Piss and moan all you please, Cooper." "This is what they want to see." ""Hey, Martha, look." "They're making fun of themselves."" "They eat that shit up." "All a part of what sells the CDs." "Of which we don't get one red cent." "Now, you want out, buddy, you just say the word." "We'll be out here, playing parties, eating good food, looking at pretty women." "You can be back at the tiers, making yourself another chess set out of cardboard, huh, Henry?" "I heard that." "And if they wanted suit and ties, we'd be wearing suit and ties." "All right." "Let's head on out." "Free Bird!" "Hell, these horses live better than most people I know." "Hey, Price, you're not eating?" "No, Henry." "You have at it." "Hey, Henry, I got to take a leak." "Coop's already in the Porta-Potty." "Use a tree." "Hell, Henry, now, that ain't civilized." "You're back on." "We're gonna start with the cake and Happy Birthday." "Price, let's go." "We got to get back out there." "Come on, Henry." "I really got to drain it." "Come on, Cooper!" "Let's go!" " Hey, Henry." "What do you want to do?" " You walk them out." " I'll bring these two." " All right." "Come on, Coop." "They want to do Happy Birthday now." "Coop!" "Stand over there." "Coop, open this door." " Open this door!" "Come on, Coop!" " Hey, Henry, watch this." " Hello, Art." " Where are you?" " Just heading back." " How far are you from the prison?" "Not far." "Just passed through Parisville." "Well, I want you to go back." "They had a breakout." " No shit." " There was a bluegrass convict band that was playing a birthday up near Parisville, and the bass player and the drummer decided to make a run for it, so I need you to go back up to Big Sandy and," "you know, check their cells, see what you can find." "I sent a couple of deputies up to Parisville." "And get this, the bass player was about to be released in 3 months after a 15-year stretch." "You got some names?" "They couldn't have gotten very far." "See what you can find out." " Evening." " Evening." "You..." "You need help with something?" "No, I'm just looking for some road food." "There's no way in hell you're gonna be able to draw and fire before your head comes off." " I could get him." " Fine with me." " What?" " Set your weapon down on the ground, please, sir." "And your backup." "Kick them back this way." "On your belly." "Hands on your neck." "See, I told you." "Turn the light on, we'll get us a car." " Got us some more guns, too." "Give me one." " Oh, no." " You're gonna run." " What?" "As far and as fast as you can, 'cause I swear to you, if I ever see you again, I'll kill you." "But we just busted out of the damn joint together." "You got five seconds." "What is this, a joke?" "Shit!" "All right." "You can sit up." "Wallet, ID, keys, hand them over." " What are you, state police?" " US Marshal." "Marshal?" "Like in Gunsmoke?" "More like The Fugitive." ""Deputy US Marshal Raylan..." ""Givens."" "I knew a fella up in Manchester named Givens, Arlo Givens." "Any relation?" "I suppose there's still some." "He's my father." "No shit." "And here you've become a US Marshal." " How'd that go down with him?" " I wouldn't know." "Now take your handcuffs out and cuff your hands behind your back." "So, you Cooper or Price?" "I'm one of them." "Fine." "I'll wait and find out tomorrow when your picture's in the paper." "My name is Douglas Cooper." "Glad to meet you." " You didn't care so much for Price, huh?" " Get on your feet." "What was he in for?" "His real crime?" "Being a lousy drummer." "He's not incompetent." "The man could play a paradiddle, but he's showy, has no sense of time." "How can you tell there's a bad drummer at your door?" " I don't know." "How?" " The knock speeds up." "Nice." "You a musician?" "No, just someone who likes music." "Yeah, and shitty jokes." "Come on." "Let's go." " And what were you in for, Mr. Cooper?" " I expect you know that already." "Fifteen years is a long time for one bank job." "Well, the thing is, a fella died as a direct result." "Foreseeable circumstances." "But, honestly, if you hire a moron for a driver, it's foreseeable." "You taking my badge and my car to get past any roadblocks, huh?" "And your hat." "Good night, deputy." "Good night, Mr. Cooper." "Well..." "Shit." "Come in." "Come in." "Now, let me get this straight." "He took your gun..." "Sorry, two guns." "Your badge, your car, and your hat." " He take anything else?" " Not that I can remember." "He didn't rape you, did he?" "We found your car at the airport, which means that Cooper either left town or he wants us to think that he left town." "We found this in the trunk." "That look familiar?" " You didn't find any guns, did you?" " No." "Sorry." "The dogs chased Price into a culvert, and then Rachel talked to him." "She and Tim can bring you up to speed." "All right." "Raylan, just a second." "Shut that door." "I got a call this morning from AUSA David Vasquez." "Wants to talk to you about your shooting Boyd Crowder." "Well, what's there to talk about?" "He pulled first." "There was a witness." "But, you see, 10 days ago, you shot a man in Miami." "Put it like this." "If you was in the first grade and you bit somebody every week, they'd start to think of you as a biter." "He also wants Ava to come up to Lexington to talk about it." " Well, fine with me." " Which part?" "The part about her talking to Vasquez or the part about her coming up to Lexington?" " Raylan, you can't sleep with her." " I know." " Raylan..." " I won't." "You starting to regret me coming here?" "Not yet." "Price says the only reason why he helped Cooper escape is because Cooper promised him a lot of money." "Which could be from his last job." "He got away with $180,000." "Never recovered." "Tell me about the dead driver." "He was a Mensa candidate named Drew Baxter." "A few hours after the robbery, Cooper and Baxter headed out of town." "Baxter's driving." "They get pulled over for a traffic violation." "Baxter decides to floor it." "Hilarious hijinks ensue." "Baxter drives head-on into a tree, goes through the windshield, and into the afterlife." "And it all fell under commission, so Cooper got charged with his murder." "So, why is he breaking out with only three months left on his bit?" "I mean, has he got a daughter getting married or a granddaughter graduating school?" "No kids, and his mother and father passed." "He was married when he went inside." "Younger woman, one-time exotic dancer, named Shirley Kelso." "Didn't divorce until five years ago." "Still lives in town." "I thought I'd go have a word." "I'm gonna take a team and check acquaintances." "I'm gonna go with him." "Nothing against acquaintances, but one-time-exotic-dancer Shirley sounds a little more fun." "What the hell did you say to him?" "I'll catch up with you at the car." " Hello, Winona." " What did you say to Gary?" "I believe I said, "Hi, Gary."" " Why?" "Why did he say I said?" " He didn't." "Just he didn't sleep the rest of that night, and the next morning, he was still shaking." "And every night since then, he checks the windows, and he checks the doors, and then he checks them again." "I don't know." "Winona, does Gary spook easy?" "What are you implying?" "You wouldn't be startled if somebody broke into your home in the middle of the night?" "I'm not implying anything." "I heard you got jumped by an old convict." "Does 55 still seem old to you?" "Are you gonna shoot him if you catch him?" "All right, look, I won't show up unannounced anymore." "You won't show up at all anymore." "Art tells me you were a sniper with the Rangers." "Yeah, I was." "What's the longest you ever had to watch a target?" "Three days." "Shitty little village outside Kandahar." "You watch a man that long, you can get to know him better than his wife does." "How he reads the paper, picks his nose, what glass he likes for tea, what one for milk..." "If he jerks off, what he looks at when he does." "If he's nice to the dog when no one's around." "What's the trick to something like that?" "Keeping your focus?" "Well, they told us to come up with stories about ourselves and the target." " What do you mean, "stories"?" " Well, nothing elaborate." "Imagine taking Shirley to the movies, watching Price is Right, eating takeout Chinese." "They eventually stopped that, the business with the stories." "Why is that?" "They found some folks get so involved in the tales they're telling themselves, they grow to like the target." "And when they got the green light, they couldn't pull." "That ever happen to you?" " Is that her?" " Looks like it." "US Marshals." "Shirley Kelso?" "You think he's here?" "You're welcome to look around." "Who's this?" "They're with the Marshals." "I'm guessing they're looking for my ex." "My cousin Dupree." "He's staying with me till he gets on his feet in construction." " Y'all want a beer or something?" " Yeah, love one." " Pabst, Schlitz, Mickey's..." " It was a joke." " We can't have a beer." " Well, I don't want your job, then, do I?" "Either of you seen or heard from Douglas Cooper?" "You mean since he broke out or since ever?" "Since last night." "No, and I swear to you, you give me a card or a number and he turns up, you'll be the first person I call." "Marrying him was the biggest mistake of my life." "You stayed married to him till five years ago." "There were tax advantages." "Any idea why he'd bust out with just a few months left on his bit?" "None at all." "I mean, you ask me, he's long gone." "I mean, there is nothing for him here." "When's the last time you saw him?" "Before the divorce, yeah." "What do you think?" "Sure made a big deal about running down her ex-husband." "Of course, that might have been for Dupree's benefit." "You don't think they're cousins?" "Maybe, maybe not." "Either way, she's banging him." "That's got to suck." "To break out of prison, expecting a blissful marital reunion." "I got to think, no matter how long you've been divorced, seeing your old lady shack up with someone else is gonna annoy the shit out of you." "If Cooper does show up, you sure as hell won't call the number on that Marshal's card." "Oh, yeah?" "Well, Coop might not be so happy to see us, you know?" "Who gives a shit?" "He's the only one who knows which house to go into." "It doesn't matter." "I hope he shows up." "I'm glad you feel that way." "Sit down." "Take a seat right there." "How'd you pick the houses?" "I saw reports on the TV in prison about somebody breaking into houses in Riverbrook, tearing up the floors." "Now, I know you haven't found the money yet." "I knew that the minute I saw this shit hole." "How did you pick the houses?" "You told me you hid the money in a house under construction in a development, and I just figured out it had to be Riverbrook." "Picked the houses at random?" "Well, you always said your lucky number was 3-2-3, so we went for houses with 3-2-3 in the address." "Y'all sleeping together?" "We're cousins!" "Well, from all the lotions, condoms, and devices I saw sitting on your nightstand, it's clear you're sleeping with somebody." "Well, it ain't like we're first cousins or anything." "There's no need to hide it from him." "He already knows." "There was one device, kind of a vibrating thing with ball bearings going all around, making it wobble all over." "That's Randy Rabbit." "It's our best seller." "If I'd known you wanted something like that, I'd have got it for you back in the day." "I was 22 when you went in." "You were the first man I ever slept with." "I didn't know what I wanted." "Hey, we can all have a real interesting conversation later about the merits of various sex toys, but right now, maybe we ought to focus on how we're gonna get you out from under the eyes of that Marshal." "And what's all this "we" shit?" "I'm just here to make sure you hadn't already found the money." "Yeah, but we can help." "We got tools." "We got pry bar, a Sawzall." "Fine." "I'll take 'em." "How you gonna get out?" "You know they got Marshals watching." "I'll wait till after dark, and I'll sneak out back." "You're gonna walk to Riverbrook?" "I got a car." "I'll steal one." "You know, you just leave us, what's gonna stop us from just calling the Marshal?" "Good point." "Maybe I'll just kill you." "I'm not gonna kill you." "And you aren't gonna call that Marshal and get sent away for all them burglaries you've done." " You know how to bypass burglar alarms?" " I do." "Burglar alarms that have come along in the last 15 years?" "Fiber optics, net-based?" "I was an alarm installer before." "How do you think we got in and out of all those houses without getting caught?" "All right." "You're in." " All right." " 10%." " Shirley, too." "We're a team." " Fine." "But you share the 10%." "Now, why don't you run out on the porch and sit down for a spell and keep an eye on that Marshal." "Cousin Dupree?" "Yeah, I'll do that." "I know you must be angry, but I swear I kept my knees together for 10 years after you went in." "Finally, I realized I had to live." "Baby, I understand that." "Frankly, I'm surprised you hadn't gone after my money before now." "Well, we only went after it now 'cause we had to." "Folks in Riverbrook, they've been remodeling instead of selling 'cause of the downturn, and we just didn't want someone to stumble on it." "That's all." " That was the reason, huh?" " Yeah." "Nothing to do with me getting out in three months." "I told Dupree about it a couple months ago, and he knows alarms and all, and he just thought we should try it." "You know, Dupree has ambitions, plans." " For what, a chain of dildo stores?" " Not just dildos." "Ava." "I told the manager I was your girlfriend." "I'm not being presumptuous and saying that I am." "I just wanted to surprise you." "And you did." "I can't sleep with you, Ava." "Now look who's being presumptuous." "I know about the assistant attorney who wants to talk to you." "I can't be getting amorous with a witness in a shooting I was involved in." " Couldn't we just make out a little?" " No." "You want me to drive back to Harlan?" "You can stay." "I could always sleep on the floor." "Well, it's your bed." "I'll take the floor." "Can we just put on a little music and dance?" "Do you know why the Pentecostals don't have sex standing up?" "It could lead to dancing." "People talk about cars having a new-car smell." "This car has an "old car somebody died in" smell." " You had a car somebody died in." " You mean Baxter?" "Technically, he died outside the car, when he hit the tree." "No, I'm not talking about Baxter." "I'm talking about the red car." "My Lord." "That '71 Valiant." "I called it the Rocket." "The Rocket." "That's right." "He told me he got it cheap 'cause the old guy who owned it died in it and no one wants to buy a dead man's car." "And I kept joking maybe it was haunted." "And then we went for a drive in the country, you know, windows down, breathing in the night air." "And all of a sudden I hear this moaning sound, this..." "You know, like a ghost." "And I about shit a brick." "And this one can't stop laughing." "And then he shows me a tape recorder under the seat playing him sounding like a ghost." "Can you believe that?" "Y'all want to keep jawing about the old days, or y'all want stay on the money train?" "What address are you looking for?" "I'm not." "When I stashed the money, these houses were still being built." "They didn't have addresses." "Then what are you looking for?" "You were onto something with my lucky number, 3-2-3." "But it's not in the address." "Are you gonna tell us or not?" "All right." "The first thing they built out here was that school we passed back yonder." "Now, that was my starting point." "I took the third right and the second left, and the third house on the right, 3-2-3." "Which puts it right here." "No burglar alarm." "Apparently, I didn't need your help after all." "About as much as we needed your car-stealing skills." "Well, I stole one." "Could have rented one faster, and it wouldn't have smelled like a grave." " Keep it up, and your 10% is gonna be 5%." " Whatever you say, old man." "You guys want to argue, or you want to find some money?" "Come on, Martha Stewart." "Just drop that." " Here we go." "Right here." " I'm coming." "Maybe you counted wrong." "I counted right." "Maybe you counted wrong 15 years ago." "I didn't count wrong, not then, not now." "The only possibilities are some other folks found the money and are long gone or that school got up and moved somehow." " Now, which do you think is more likely?" " Let me get this straight." "After all this time, you don't have any idea where that money is?" " No, I guess I don't." " Well," "I guess we don't really need you then, after all, do we?" "Come on." "Let's go." "I'm sorry." "You were gone so long, I just couldn't wait." "I'm sorry." "You look good, Coop." "Come on!" "We've got some shit to do." " Do you know where the money is?" " Well, I do now." "Where are you going?" "I ain't getting in that shit heap again." "We get the money, we'll take ourselves another car." "Ain't nobody gonna stop us." "Now, come on." " Raylan?" " I think I know where Cooper's money is." "Come on, baby." "We're gonna get that money, I'm gonna buy you anything you want." "Shit." "Got to ask." "Why the hat?" "Honestly," "I tried it on one time, and it fit." "Oh, shit!" "You don't do exactly as I say, you're gonna get two in the chest and one in the head!" "You boosted a Gremlin?" "Oh, hell, with all the alarms and stuff they got on cars these days, that's all I could get." "I tried to get a Mustang." "So, what happened?" "They take the money and run?" "No." "There wasn't any." "Well, why'd they shoot you?" "I don't know." "I don't care." "I thought I broke out 'cause of the money, but then I saw Shirley." "Well, maybe Dupree figured out where the money is." "Well, I don't see how." "I told him either the money was here and somebody found it and took off or that school up and moved." "Yeah, I knew where the money was in relation to the school." "Which one?" "We passed two driving around." "Oh, shit." "Fifteen years is a long time." "I told you we shouldn't have taken the money." " You enjoyed it just as much as I did." " Shut up!" " How'd you find it?" " Well," "Mr. "I'm too cheap to hire a plumber" tried to put in a new dishwasher and flooded the entire place, and then we had to replace the floor." "Oh, yeah, I'm an idiot." "But if it wasn't for me, we never would have found the money." "And we wouldn't be sitting here now!" "Where was all your second-guessing when you got your new boobs?" "You enjoyed them a hell of a lot more than I ever did!" "They're very nice." " Thank you." " Shut up!" "Now, I want what's left of the money right now, or I start shooting." " There is none." " I'll start with you." "No!" "No!" "He's telling the truth." "After the boat and the car and my boobs and the TVs, it's all gone." "Man." "He's got them tied to chairs." "We take the back." "Rachel and Raylan, you take the front." " You got a story for Cousin Dupree?" " Yeah." "But it's pretty simple." "If he does anything out of line, I get to shoot him." "That's a good story." " How much those shoes run you?" " Seven hundred." "$700 for a pair of shoes?" "They're alligator." "Got your alligator's attention?" "We'll get you every last cent we have!" "Just please don't shoot anymore!" "My foot!" "Shirley, untie the woman." "She might could take us to the bank." "Okay." "No." "Shit." "Stop." "The banks ain't open this hour." "Shit!" "Let me think." "US Marshals." "I was wondering if I could come inside." "No, you can't come inside!" "Dupree, this isn't your home." "Mr. Lonner, may I come inside?" "God, yes!" "Come inside!" "Hey, you ain't calling the shots here." "Just coming inside to explain things to you." " There ain't nothing to explain." " Ten seconds." "Huh?" "Dupree, can you just keep your gun down for 10 seconds?" "I can tell you both what's what." "You can see my hands." "All right?" " All right." " All right." "You mind standing where I can see you?" "Now I'm gonna give you a choice." "You won't like it, but it's real simple." "If you raise your gun again, you're dead." "Aim at the family, you're dead." "If you move too fast from where you're standing, dead." "In fact, I'd say dropping your weapons and putting your hands behind your head's the only viable option, but that's your choice." " Well, we got guns and hostages here." " I see that." "Do you really think you can draw and fire before one of us pulls the trigger?" "This ain't about me." "This is about Deputy Tim Gutterson, sniper in the Afghan War." "Well, I don't see him." "You got a little sniper in your pocket?" "Well, he's out back, across the street there." "He bullshitting?" "Well," "I see cars and people." "I don't see a sniper." "No, no, no, no." "He's there, or I wouldn't be here." "Where's the light switch for this room?" "Now, Dupree, I know that wasn't on the list, but..." "Where's the goddamn light switch?" " On the wall, by your friend." " Shirley, find that switch." " Shirley..." " On the count of three, flip the switch." " Shirley, don't do it." " One, two, three!" "Why'd you turn the light back on?" "He had no need to shoot my husband." "Initial here, here, and here." "Going solo again?" "Another deputy in the car." " Learned your lesson?" " Until I forget." "Stand up, walk through." "Put your feet on the feet." "You know the drill." " How's the gut?" " Well, they tell me my plumbing's okay, but every which way I move hurts." "I think we're good." "Did you find the money?" "The couple in the house found it." "They enjoy it?" "They bought a lot of stuff." " Have you seen Shirley?" " I'm sorry, I haven't." "I know she's in custody." "But she helped you guys nail Dupree, right?" "That ought to count for something." "She's still gonna pull some time." "Maybe we'll get out about the same time." "Maybe." "Maybe." "Man." "She looked good." |
/*
Fraise version 3.7 - Based on Smultron by Peter Borg
Written by Jean-François Moy - jeanfrancois.moy@gmail.com
Find the latest version at http://github.com/jfmoy/Fraise
Copyright 2010 Jean-François Moy
Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.
*/
#import "FRAStandardHeader.h"
#import "FRATextView.h"
#import "FRALayoutManager.h"
#import "FRATextMenuController.h"
#import "FRAProjectsController.h"
#import "FRABasicPerformer.h"
#import "FRAToolsMenuController.h"
#import "FRAFileMenuController.h"
#import "FRALineNumbers.h"
@implementation FRATextView
@synthesize colouredIBeamCursor, inCompleteMethod;
- (id)initWithFrame:(NSRect)frame
{
if (self = [super initWithFrame:frame]) {
FRALayoutManager *layoutManager = [[FRALayoutManager alloc] init];
[[self textContainer] replaceLayoutManager:layoutManager];
[self setDefaults];
}
return self;
}
- (void)setDefaults
{
inCompleteMethod = NO;
[self setTabWidth];
[self setVerticallyResizable:YES];
[self setMaxSize:NSMakeSize(CGFLOAT_MAX, CGFLOAT_MAX)];
[self setAutoresizingMask:NSViewWidthSizable];
[self setAllowsUndo:YES];
[self setUsesFindPanel:YES];
[self setAllowsDocumentBackgroundColorChange:NO];
[self setRichText:NO];
[self setImportsGraphics:NO];
[self setUsesFontPanel:NO];
[self setContinuousSpellCheckingEnabled:[[FRADefaults valueForKey:@"AutoSpellCheck"] boolValue]];
[self setGrammarCheckingEnabled:[[FRADefaults valueForKey:@"AutoGrammarCheck"] boolValue]];
[self setSmartInsertDeleteEnabled:[[FRADefaults valueForKey:@"SmartInsertDelete"] boolValue]];
[self setAutomaticLinkDetectionEnabled:[[FRADefaults valueForKey:@"AutomaticLinkDetection"] boolValue]];
[self setAutomaticQuoteSubstitutionEnabled:[[FRADefaults valueForKey:@"AutomaticQuoteSubstitution"] boolValue]];
[self setFont:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextFont"]]];
[self setTextColor:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextColourWell"]]];
[self setInsertionPointColor:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextColourWell"]]];
[self setBackgroundColor:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"BackgroundColourWell"]]];
[self setAutomaticDataDetectionEnabled:YES];
[self setAutomaticTextReplacementEnabled:YES];
[self setPageGuideValues];
[self updateIBeamCursor];
NSTrackingArea *trackingArea = [[NSTrackingArea alloc] initWithRect:[self frame] options:(NSTrackingMouseEnteredAndExited | NSTrackingActiveWhenFirstResponder) owner:self userInfo:nil];
[self addTrackingArea:trackingArea];
NSUserDefaultsController *defaultsController = [NSUserDefaultsController sharedUserDefaultsController];
[defaultsController addObserver:self forKeyPath:@"values.TextFont" options:NSKeyValueObservingOptionNew context:@"TextFontChanged"];
[defaultsController addObserver:self forKeyPath:@"values.TextColourWell" options:NSKeyValueObservingOptionNew context:@"TextColourChanged"];
[defaultsController addObserver:self forKeyPath:@"values.BackgroundColourWell" options:NSKeyValueObservingOptionNew context:@"BackgroundColourChanged"];
[defaultsController addObserver:self forKeyPath:@"values.SmartInsertDelete" options:NSKeyValueObservingOptionNew context:@"SmartInsertDeleteChanged"];
[defaultsController addObserver:self forKeyPath:@"values.TabWidth" options:NSKeyValueObservingOptionNew context:@"TabWidthChanged"];
[defaultsController addObserver:self forKeyPath:@"values.ShowPageGuide" options:NSKeyValueObservingOptionNew context:@"PageGuideChanged"];
[defaultsController addObserver:self forKeyPath:@"values.ShowPageGuideAtColumn" options:NSKeyValueObservingOptionNew context:@"PageGuideChanged"];
[defaultsController addObserver:self forKeyPath:@"values.SmartInsertDelete" options:NSKeyValueObservingOptionNew context:@"SmartInsertDeleteChanged"];
lineHeight = [[[self textContainer] layoutManager] defaultLineHeightForFont:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextFont"]]];
}
- (void)observeValueForKeyPath:(NSString *)keyPath ofObject:(id)object change:(NSDictionary *)change context:(void *)context
{
if ([(NSString *)context isEqualToString:@"TextFontChanged"]) {
[self setFont:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextFont"]]];
lineHeight = [[[self textContainer] layoutManager] defaultLineHeightForFont:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextFont"]]];
[[FRACurrentDocument valueForKey:@"lineNumbers"] updateLineNumbersForClipView:[[self enclosingScrollView] contentView] checkWidth:NO recolour:YES];
[self setPageGuideValues];
} else if ([(NSString *)context isEqualToString:@"TextColourChanged"]) {
[self setTextColor:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextColourWell"]]];
[self setInsertionPointColor:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextColourWell"]]];
[self setPageGuideValues];
[self updateIBeamCursor];
} else if ([(NSString *)context isEqualToString:@"BackgroundColourChanged"]) {
[self setBackgroundColor:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"BackgroundColourWell"]]];
} else if ([(NSString *)context isEqualToString:@"SmartInsertDeleteChanged"]) {
[self setSmartInsertDeleteEnabled:[[FRADefaults valueForKey:@"SmartInsertDelete"] boolValue]];
} else if ([(NSString *)context isEqualToString:@"TabWidthChanged"]) {
[self setTabWidth];
} else if ([(NSString *)context isEqualToString:@"PageGuideChanged"]) {
[self setPageGuideValues];
} else if ([(NSString *)context isEqualToString:@"SmartInsertDeleteChanged"]) {
[self setSmartInsertDeleteEnabled:[[FRADefaults valueForKey:@"SmartInsertDelete"] boolValue]];
} else {
[super observeValueForKeyPath:keyPath ofObject:object change:change context:context];
}
}
- (void)insertNewline:(id)sender
{
[super insertNewline:sender];
// If we should indent automatically, check the previous line and scan all the whitespace at the beginning of the line into a string and insert that string into the new line
NSString *lastLineString = [[self string] substringWithRange:[[self string] lineRangeForRange:NSMakeRange([self selectedRange].location - 1, 0)]];
if ([[FRADefaults valueForKey:@"IndentNewLinesAutomatically"] boolValue] == YES) {
NSString *previousLineWhitespaceString;
NSScanner *previousLineScanner = [[NSScanner alloc] initWithString:[[self string] substringWithRange:[[self string] lineRangeForRange:NSMakeRange([self selectedRange].location - 1, 0)]]];
[previousLineScanner setCharactersToBeSkipped:nil];
if ([previousLineScanner scanCharactersFromSet:[NSCharacterSet whitespaceCharacterSet] intoString:&previousLineWhitespaceString]) {
[self insertText:previousLineWhitespaceString];
}
if ([[FRADefaults valueForKey:@"AutomaticallyIndentBraces"] boolValue] == YES) {
NSCharacterSet *characterSet = [NSCharacterSet whitespaceAndNewlineCharacterSet];
NSInteger index = [lastLineString length];
while (index--) {
if ([characterSet characterIsMember:[lastLineString characterAtIndex:index]]) {
continue;
}
if ([lastLineString characterAtIndex:index] == '{') {
[self insertTab:nil];
}
break;
}
}
}
}
- (NSRange)selectionRangeForProposedRange:(NSRange)proposedSelRange granularity:(NSSelectionGranularity)granularity
{
if (granularity != NSSelectByWord || [[self string] length] == proposedSelRange.location || [[NSApp currentEvent] clickCount] != 2) { // If it's not a double-click return unchanged
return [super selectionRangeForProposedRange:proposedSelRange granularity:granularity];
}
NSInteger location = [super selectionRangeForProposedRange:proposedSelRange granularity:NSSelectByCharacter].location;
NSInteger originalLocation = location;
NSString *completeString = [self string];
unichar characterToCheck = [completeString characterAtIndex:location];
NSInteger skipMatchingBrace = 0;
NSInteger lengthOfString = [completeString length];
if (lengthOfString == proposedSelRange.location) { // To avoid crash if a double-click occurs after any text
return [super selectionRangeForProposedRange:proposedSelRange granularity:granularity];
}
BOOL triedToMatchBrace = NO;
if (characterToCheck == ')') {
triedToMatchBrace = YES;
while (location--) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == '(') {
if (!skipMatchingBrace) {
return NSMakeRange(location, originalLocation - location + 1);
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == ')') {
skipMatchingBrace++;
}
}
NSBeep();
} else if (characterToCheck == '}') {
triedToMatchBrace = YES;
while (location--) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == '{') {
if (!skipMatchingBrace) {
return NSMakeRange(location, originalLocation - location + 1);
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == '}') {
skipMatchingBrace++;
}
}
NSBeep();
} else if (characterToCheck == ']') {
triedToMatchBrace = YES;
while (location--) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == '[') {
if (!skipMatchingBrace) {
return NSMakeRange(location, originalLocation - location + 1);
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == ']') {
skipMatchingBrace++;
}
}
NSBeep();
} else if (characterToCheck == '>') {
triedToMatchBrace = YES;
while (location--) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == '<') {
if (!skipMatchingBrace) {
return NSMakeRange(location, originalLocation - location + 1);
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == '>') {
skipMatchingBrace++;
}
}
NSBeep();
} else if (characterToCheck == '(') {
triedToMatchBrace = YES;
while (++location < lengthOfString) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == ')') {
if (!skipMatchingBrace) {
return NSMakeRange(originalLocation, location - originalLocation + 1);
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == '(') {
skipMatchingBrace++;
}
}
NSBeep();
} else if (characterToCheck == '{') {
triedToMatchBrace = YES;
while (++location < lengthOfString) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == '}') {
if (!skipMatchingBrace) {
return NSMakeRange(originalLocation, location - originalLocation + 1);
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == '{') {
skipMatchingBrace++;
}
}
NSBeep();
} else if (characterToCheck == '[') {
triedToMatchBrace = YES;
while (++location < lengthOfString) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == ']') {
if (!skipMatchingBrace) {
return NSMakeRange(originalLocation, location - originalLocation + 1);
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == '[') {
skipMatchingBrace++;
}
}
NSBeep();
} else if (characterToCheck == '<') {
triedToMatchBrace = YES;
while (++location < lengthOfString) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == '>') {
if (!skipMatchingBrace) {
return NSMakeRange(originalLocation, location - originalLocation + 1);
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == '<') {
skipMatchingBrace++;
}
}
NSBeep();
}
// If it has a found a "starting" brace but not found a match, a double-click should only select the "starting" brace and not what it usually would select at a double-click
if (triedToMatchBrace) {
return [super selectionRangeForProposedRange:NSMakeRange(proposedSelRange.location, 1) granularity:NSSelectByCharacter];
} else {
NSInteger startLocation = originalLocation;
NSInteger stopLocation = originalLocation;
NSInteger minLocation = [super selectionRangeForProposedRange:proposedSelRange granularity:NSSelectByWord].location;
NSInteger maxLocation = NSMaxRange([super selectionRangeForProposedRange:proposedSelRange granularity:NSSelectByWord]);
BOOL hasFoundSomething = NO;
while (--startLocation >= minLocation) {
if ([completeString characterAtIndex:startLocation] == '.' || [completeString characterAtIndex:startLocation] == ':') {
hasFoundSomething = YES;
break;
}
}
while (++stopLocation < maxLocation) {
if ([completeString characterAtIndex:stopLocation] == '.' || [completeString characterAtIndex:stopLocation] == ':') {
hasFoundSomething = YES;
break;
}
}
if (hasFoundSomething == YES) {
return NSMakeRange(startLocation + 1, stopLocation - startLocation - 1);
} else {
return [super selectionRangeForProposedRange:proposedSelRange granularity:granularity];
}
}
}
-(BOOL)isOpaque
{
return YES;
}
- (void)insertTab:(id)sender
{
BOOL shouldShiftText = NO;
if ([self selectedRange].length > 0) { // Check to see if the selection is in the text or if it's at the beginning of a line or in whitespace; if one doesn't do this one shifts the line if there's only one suggestion in the auto-complete
NSRange rangeOfFirstLine = [[self string] lineRangeForRange:NSMakeRange([self selectedRange].location, 0)];
NSInteger firstCharacterOfFirstLine = rangeOfFirstLine.location;
while ([[self string] characterAtIndex:firstCharacterOfFirstLine] == ' ' || [[self string] characterAtIndex:firstCharacterOfFirstLine] == '\t') {
firstCharacterOfFirstLine++;
}
if ([self selectedRange].location <= firstCharacterOfFirstLine) {
shouldShiftText = YES;
}
}
if (shouldShiftText) {
[[FRATextMenuController sharedInstance] shiftRightAction:nil];
} else if ([[FRADefaults valueForKey:@"IndentWithSpaces"] boolValue] == YES) {
NSMutableString *spacesString = [NSMutableString string];
NSInteger numberOfSpacesPerTab = [[FRADefaults valueForKey:@"TabWidth"] integerValue];
if ([[FRADefaults valueForKey:@"UseTabStops"] boolValue] == YES) {
NSInteger locationOnLine = [self selectedRange].location - [[self string] lineRangeForRange:[self selectedRange]].location;
if (numberOfSpacesPerTab != 0) {
NSInteger numberOfSpacesLess = locationOnLine % numberOfSpacesPerTab;
numberOfSpacesPerTab = numberOfSpacesPerTab - numberOfSpacesLess;
}
}
while (numberOfSpacesPerTab--) {
[spacesString appendString:@" "];
}
[self insertText:spacesString];
} else if ([self selectedRange].length > 0) { // If there's only one word matching in auto-complete there's no list but just the rest of the word inserted and selected; and if you do a normal tab then the text is removed so this will put the cursor at the end of that word
[self setSelectedRange:NSMakeRange(NSMaxRange([self selectedRange]), 0)];
} else {
[super insertTab:sender];
}
}
- (void)mouseDown:(NSEvent *)theEvent
{
if (([theEvent modifierFlags] & NSAlternateKeyMask) && ([theEvent modifierFlags] & NSCommandKeyMask)) { // If the option and command keys are pressed, change the cursor to grab-cursor
startPoint = [theEvent locationInWindow];
startOrigin = [[[self enclosingScrollView] contentView] documentVisibleRect].origin;
[[self enclosingScrollView] setDocumentCursor:[NSCursor openHandCursor]];
} else {
[super mouseDown:theEvent];
}
}
- (void)mouseDragged:(NSEvent *)theEvent
{
if ([[NSCursor currentCursor] isEqual:[NSCursor openHandCursor]]) {
[self scrollPoint:NSMakePoint(startOrigin.x - ([theEvent locationInWindow].x - startPoint.x) * 3, startOrigin.y + ([theEvent locationInWindow].y - startPoint.y) * 3)];
} else {
[super mouseDragged:theEvent];
}
}
- (void)mouseUp:(NSEvent *)theEvent
{
[[self enclosingScrollView] setDocumentCursor:[NSCursor IBeamCursor]];
}
- (NSInteger)lineHeight
{
return lineHeight;
}
- (void)setTabWidth
{
// Set the width of every tab by first checking the size of the tab in spaces in the current font and then remove all tabs that sets automatically and then set the default tab stop distance
NSMutableString *sizeString = [NSMutableString string];
NSInteger numberOfSpaces = [[FRADefaults valueForKey:@"TabWidth"] integerValue];
while (numberOfSpaces--) {
[sizeString appendString:@" "];
}
NSDictionary *sizeAttribute = [[NSDictionary alloc] initWithObjectsAndKeys:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextFont"]], NSFontAttributeName, nil];
CGFloat sizeOfTab = [sizeString sizeWithAttributes:sizeAttribute].width;
NSMutableParagraphStyle *style = [[NSParagraphStyle defaultParagraphStyle] mutableCopy];
NSArray *array = [style tabStops];
for (id item in array) {
[style removeTabStop:item];
}
[style setDefaultTabInterval:sizeOfTab];
NSDictionary *attributes = [[NSDictionary alloc] initWithObjectsAndKeys:style, NSParagraphStyleAttributeName, nil];
[self setTypingAttributes:attributes];
}
- (void)drawRect:(NSRect)rect
{
[super drawRect:rect];
if (showPageGuide == YES) {
NSRect bounds = [self bounds];
if ([self needsToDrawRect:NSMakeRect(pageGuideX, 0, 1, bounds.size.height)] == YES) { // So that it doesn't draw the line if only e.g. the cursor updates
[pageGuideColour set];
[NSBezierPath strokeRect:NSMakeRect(pageGuideX, 0, 0, bounds.size.height)];
}
}
}
- (void)setPageGuideValues
{
NSDictionary *sizeAttribute = [[NSDictionary alloc] initWithObjectsAndKeys:[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextFont"]], NSFontAttributeName, nil];
NSString *sizeString = [NSString stringWithString:@" "];
CGFloat sizeOfCharacter = [sizeString sizeWithAttributes:sizeAttribute].width;
pageGuideX = (sizeOfCharacter * ([[FRADefaults valueForKey:@"ShowPageGuideAtColumn"] integerValue] + 1)) - 1.5; // -1.5 to put it between the two characters and draw only on one pixel and not two (as the system draws it in a special way), and that's also why the width above is set to zero
NSColor *color = [NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextColourWell"]];
pageGuideColour = [color colorWithAlphaComponent:([color alphaComponent] / 4)]; // Use the same colour as the text but with more transparency
showPageGuide = [[FRADefaults valueForKey:@"ShowPageGuide"] boolValue];
[self display]; // To reflect the new values in the view
}
- (void)insertText:(NSString *)aString
{
if ([aString isEqualToString:@"}"] && [[FRADefaults valueForKey:@"IndentNewLinesAutomatically"] boolValue] == YES && [[FRADefaults valueForKey:@"AutomaticallyIndentBraces"] boolValue] == YES) {
unichar characterToCheck;
NSInteger location = [self selectedRange].location;
NSString *completeString = [self string];
NSCharacterSet *whitespaceCharacterSet = [NSCharacterSet whitespaceCharacterSet];
NSRange currentLineRange = [completeString lineRangeForRange:NSMakeRange([self selectedRange].location, 0)];
NSInteger lineLocation = location;
NSInteger lineStart = currentLineRange.location;
while (--lineLocation >= lineStart) { // If there are any characters before } on the line skip indenting
if ([whitespaceCharacterSet characterIsMember:[completeString characterAtIndex:lineLocation]]) {
continue;
}
[super insertText:aString];
return;
}
BOOL hasInsertedBrace = NO;
NSUInteger skipMatchingBrace = 0;
while (location--) {
characterToCheck = [completeString characterAtIndex:location];
if (characterToCheck == '{') {
if (skipMatchingBrace == 0) { // If we have found the opening brace check first how much space is in front of that line so the same amount can be inserted in front of the new line
NSString *openingBraceLineWhitespaceString;
NSScanner *openingLineScanner = [[NSScanner alloc] initWithString:[completeString substringWithRange:[completeString lineRangeForRange:NSMakeRange(location, 0)]]];
[openingLineScanner setCharactersToBeSkipped:nil];
BOOL foundOpeningBraceWhitespace = [openingLineScanner scanCharactersFromSet:whitespaceCharacterSet intoString:&openingBraceLineWhitespaceString];
if (foundOpeningBraceWhitespace == YES) {
NSMutableString *newLineString = [NSMutableString stringWithString:openingBraceLineWhitespaceString];
[newLineString appendString:@"}"];
[newLineString appendString:[completeString substringWithRange:NSMakeRange([self selectedRange].location, NSMaxRange(currentLineRange) - [self selectedRange].location)]];
if ([self shouldChangeTextInRange:currentLineRange replacementString:newLineString]) {
[self replaceCharactersInRange:currentLineRange withString:newLineString];
[self didChangeText];
}
hasInsertedBrace = YES;
[self setSelectedRange:NSMakeRange(currentLineRange.location + [openingBraceLineWhitespaceString length] + 1, 0)]; // +1 because we have inserted a character
} else {
NSString *restOfLineString = [completeString substringWithRange:NSMakeRange([self selectedRange].location, NSMaxRange(currentLineRange) - [self selectedRange].location)];
if ([restOfLineString length] != 0) { // To fix a bug where text after the } can be deleted
NSMutableString *replaceString = [NSMutableString stringWithString:@"}"];
[replaceString appendString:restOfLineString];
hasInsertedBrace = YES;
NSInteger lengthOfWhiteSpace = 0;
if (foundOpeningBraceWhitespace == YES) {
lengthOfWhiteSpace = [openingBraceLineWhitespaceString length];
}
if ([self shouldChangeTextInRange:currentLineRange replacementString:replaceString]) {
[self replaceCharactersInRange:[completeString lineRangeForRange:currentLineRange] withString:replaceString];
[self didChangeText];
}
[self setSelectedRange:NSMakeRange(currentLineRange.location + lengthOfWhiteSpace + 1, 0)]; // +1 because we have inserted a character
} else {
[self replaceCharactersInRange:[completeString lineRangeForRange:currentLineRange] withString:@""]; // Remove whitespace before }
}
}
break;
} else {
skipMatchingBrace--;
}
} else if (characterToCheck == '}') {
skipMatchingBrace++;
}
}
if (hasInsertedBrace == NO) {
[super insertText:aString];
}
} else if ([aString isEqualToString:@"("] && [[FRADefaults valueForKey:@"AutoInsertAClosingParenthesis"] boolValue] == YES) {
[super insertText:aString];
NSRange selectedRange = [self selectedRange];
if ([self shouldChangeTextInRange:selectedRange replacementString:@")"]) {
[self replaceCharactersInRange:selectedRange withString:@")"];
[self didChangeText];
[self setSelectedRange:NSMakeRange(selectedRange.location - 0, 0)];
}
} else if ([aString isEqualToString:@"{"] && [[FRADefaults valueForKey:@"AutoInsertAClosingBrace"] boolValue] == YES) {
[super insertText:aString];
NSRange selectedRange = [self selectedRange];
if ([self shouldChangeTextInRange:selectedRange replacementString:@"}"]) {
[self replaceCharactersInRange:selectedRange withString:@"}"];
[self didChangeText];
[self setSelectedRange:NSMakeRange(selectedRange.location - 0, 0)];
}
} else {
[super insertText:aString];
}
}
- (NSMenu *)menuForEvent:(NSEvent *)theEvent
{
NSMenu *menu = [super menuForEvent:theEvent];
NSArray *array = [menu itemArray];
for (id oldMenuItem in array) {
if ([oldMenuItem tag] == -123457) {
[menu removeItem:oldMenuItem];
}
}
[menu insertItem:[NSMenuItem separatorItem] atIndex:0];
NSEnumerator *collectionEnumerator = [[FRABasic fetchAll:@"SnippetCollectionSortKeyName"] reverseObjectEnumerator];
for (id collection in collectionEnumerator) {
if ([collection valueForKey:@"name"] == nil) {
continue;
}
NSMenuItem *menuItem = [[NSMenuItem alloc] initWithTitle:[collection valueForKey:@"name"] action:nil keyEquivalent:@""];
[menuItem setTag:-123457];
NSMenu *subMenu = [[NSMenu alloc] init];
NSMutableArray *array = [NSMutableArray arrayWithArray:[[collection mutableSetValueForKey:@"snippets"] allObjects]];
[array sortUsingSelector:@selector(localizedCaseInsensitiveCompare:)];
for (id snippet in array) {
if ([snippet valueForKey:@"name"] == nil) {
continue;
}
NSString *keyString;
if ([snippet valueForKey:@"shortcutMenuItemKeyString"] != nil) {
keyString = [snippet valueForKey:@"shortcutMenuItemKeyString"];
} else {
keyString = @"";
}
NSMenuItem *subMenuItem = [[NSMenuItem alloc] initWithTitle:[snippet valueForKey:@"name"] action:@selector(snippetShortcutFired:) keyEquivalent:@""];
[subMenuItem setTarget:[FRAToolsMenuController sharedInstance]];
[subMenuItem setRepresentedObject:snippet];
[subMenu insertItem:subMenuItem atIndex:0];
}
[menuItem setSubmenu:subMenu];
[menu insertItem:menuItem atIndex:0];
}
return menu;
}
- (IBAction)save:(id)sender
{
[[FRAFileMenuController sharedInstance] saveAction:nil];
}
- (void)updateIBeamCursor
{
NSColor *textColour = [[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextColourWell"]] colorUsingColorSpaceName:NSCalibratedWhiteColorSpace];
if (textColour != nil && [textColour whiteComponent] == 0.0 && [textColour alphaComponent] == 1.0) { // Keep the original cursor if it's black
[self setColouredIBeamCursor:[NSCursor IBeamCursor]];
} else {
NSImage *cursorImage = [[NSCursor IBeamCursor] image];
[cursorImage lockFocus];
[[NSUnarchiver unarchiveObjectWithData:[FRADefaults valueForKey:@"TextColourWell"]] set];
NSRectFillUsingOperation(NSMakeRect(0, 0, [cursorImage size].width, [cursorImage size].height), NSCompositeSourceAtop);
[cursorImage unlockFocus];
[self setColouredIBeamCursor:[[NSCursor alloc] initWithImage:cursorImage hotSpot:[[NSCursor IBeamCursor] hotSpot]]];
}
}
- (void)cursorUpdate:(NSEvent *)event
{
[colouredIBeamCursor set];
}
- (void)mouseMoved:(NSEvent *)theEvent
{
if ([NSCursor currentCursor] == [NSCursor IBeamCursor]) {
[colouredIBeamCursor set];
}
}
- (void)performFindPanelAction:(id)sender
{
[super performFindPanelAction:sender];
}
// A workaround for Radar ID 5663445 (the complete menu disappears too soon)
//- (void)complete:(id)sender
//{
// inCompleteMethod = YES;
// [super complete:sender];
// inCompleteMethod = NO;
//}
@end
|
Tom Nook
Tom Nook, known in Japan as , is a fictional character in the Animal Crossing series who operates the village store. He first appeared in the Nintendo 64 game Dōbutsu no Mori, released in Europe and North America on the Nintendo GameCube as Animal Crossing. Nook sells a house to the player at the beginning of each title in the series, giving a set mortgage for them to pay and offering to upgrade it after the mortgage is paid off. He has made several appearances in the Super Smash Bros. series as well. Nintendo's Treehouse localization members Rich Amtower and Reiko Ninomiya have argued that, in spite of his perceived greed, he is a nice person due to taking the risk of hiring someone who was new to the town.
Concept and characteristics
Tom Nook is based on the tanuki, the raccoon dog. Although he is considered to be greedy by 1UP.com, Rich Amtower and Reiko Ninomiya, members of Nintendo's Treehouse localization team, disagreed; describing him as a nice person. Amtower described him as "that first boss you ever had", adding that, "despite him being all business and not always having the time for pleasantries, Nook isn't a bad person; because he hired someone new to town. Due to that involving risk, it shows generosity". Ninomiya agreed, and both felt that Nook's greed is diminished by the city's price index compared to that of his shop. Amtower jokingly alludes to an "anti-Nook bias" several times throughout the interview with 1UP.com.
Appearances
Dōbutsu no Mori (2001, Nintendo 64)
Animal Crossing 2001, GameCube)
Animal Crossing: Wild World (2005, Nintendo DS)
Dōbutsu no Mori (film) (2006)
Animal Crossing: City Folk (2008, Wii)
Animal Crossing: New Leaf (2012, Nintendo 3DS)
Animal Crossing: Happy Home Designer (2015, Nintendo 3DS)
Animal Crossing: Amiibo Festival (2015, Wii U)
Animal Crossing: Pocket Camp (2017, mobile)
Animal Crossing: New Horizons (2020, Nintendo Switch)
Role in the series
Tom Nook first appears in the Nintendo 64 title Dōbutsu no Mori (ported to the Nintendo GameCube as Animal Crossing in non-Japanese regions) as the town's main shop owner and continues his job in the next two installments. Nook's role in the series remained virtually unchanged from 2001 until 2012 with the release of Animal Crossing: New Leaf. In addition to being the main shop owner, Nook will also sell the player a house at the beginning of the game for around 19,800 bells (in game currency). Because the player will only have 1000 bells in his or her pocket, Nook will request that the player work in his shop for a bit to pay off some of the debt. The chores Nook assigns you to do are meant for the player to get used to the controls of the game. After planting flowers, writing letters, and talking to villagers the player is sent off to do whatever they want, but have to pay the remaining amount of their mortgage on their own. Each time a mortgage payment is completed Nook will upgrade or add on to the players house, each time putting the player more and more into debt to Nook, with the last addition being the most costly.
Nook's store also goes through three upgrades and changes throughout the game. The time of the upgrade depends on how many bells are spent in the store. Eventually his humble "Nook's Cranny" shack-like store with basic tools and very little objects to buy will become "Nookington's Department Store" - a large, two story building with a wide variety of items for purchase. It is in this expansion that the player meets his two nephews, Tommy and Timmy, who run the second floor of the store. In every game, no matter what upgrade the store is on, the items in the store will be changed everyday. This means that no two days will ever have the exact combination of items for sale.
In Animal Crossing, at the end of the month Nook will host a raffle with rare items to win. This was not continued in any sequel.
In Wild World, with the Nookington's expansion the player meets Harriet, a poodle who will do the player's hair for 3000 bells.
In City Folk, Harriet has moved her shop to the city. With the Nookington's expansion, Nook will randomly ask the player a series of questions. How the player answers could change the store to a former appearance.
Nook returns in Animal Crossing: New Leaf. Instead of being the local shop owner, Nook is now in charge of "Nook's Homes" and instead sells things to upgrade the exterior of the players house. He also will expand the player's house for a price, which increases with each expansion. His nephews now run the town shop by themselves.
Nook makes a minor appearance in Animal Crossing: Pocket Camp with the player being able to purchase him to put in their camp for 250 Leaf Tickets (Only available for purchase 45 days after starting the game).
In other media
Tom Nook has made several minor appearances in the Super Smash Bros. series of video games; appearing as various collectibles in Super Smash Bros. Melee and Super Smash Bros. Brawl. as well as a background character on the Smashville stage, which is based on the Animal Crossing series. Tom Nook's shop music also features in Super Smash Bros. Brawl as part of "Town Hall and Tom Nook's Store". Tom Nook has also been featured in several promotional items, including plush toys.
Reception
Tom Nook has received mixed reception since his appearance in Animal Crossing. IGN listed him as the ninth most-wanted character to appear in Super Smash Bros. Brawl. They describe him as devious, diabolical, and sinister, commenting that while he may not be a good fighter due to being from a video game without any fighting, they would enjoy seeing him get beaten up. Another article by IGN compares a talking baton given to the protagonist of Major Minor's Majestic March to Nook, calling it the second only to Nook in annoyance. GameSpy listed Tom Nook as one of their favourite bosses; editor Brian Altano specified that he passionately loves to hate Nook, stating that while he provides appreciated services to the small village, he keeps his reality grounded in that he lives in Nook's town, not his own. UGO.com ranked him the fifth best Animal Crossing character, stating that while Mr. Resetti was an irritant, Tom Nook was a jerk. They added that they love to hate him, jokingly suggesting that he was a "kingpin".
In spite of the negative reception, Tom Nook has received some positive reception. In author Katherine Isbister's book, "Better game characters by design: a psychological approach", she cites Tom Nook as an example of a mentor character, one who indirectly helps players. GamesRadar also listed him as one of the 25 best new characters of the decade, stating that he has earned his place amongst the hearts of gamers and people on the Internet as both a viral meme and a deceptively devious character. In 2012, GamesRadar ranked Tom Nook as the 80th best villain in video games in their 2013 "Top 100", saying despite raccoons are "stripy, furry and cute", "Tom Nook can go to Hell." That same year, Complex placed him as the 49th coolest video game villain of all time.
Game-studies scholar Ian Bogost described Nook as central to Animal Crossing's effective depiction of the economics of consumption and debt:
None of the townsfolk ever appear in Tom Nook's shop... In contrast, the player participates in a full consumer regimen; he pays off debt, buys goods, and sells goods. Tom Nook buys goods, which he converts to wealth. ... While the player spends more, Nook makes more. By condensing all of the environment's financial transactions into one flow between the player and Tom Nook, the game proceduralizes the redistribution of wealth in a manner even young children can understand. Tom Nook is a kind of condensation of the corporate bourgeoise.
Parody and analysis
Tom Nook has been satirized in several articles, often compared to a mob boss or kingpin or otherwise a bad person. IGN listed him among the top 100 video game villains, suggesting that Tom Nook has a nice face, but the "cold, dead heart of a megalomaniac whose sole desire is to make a quick bell". Fellow IGN editor Patrick Kolan described Nook as the Animal Crossing equivalent of Al Swearengen, a pimp from the 1800s, due to his business sense, as well as both the character's position and disposition. Tom Nook has also been personified as a devious character, as well as a gangster, including an issue of the web comic VG Cats, which depicts him roughing up the player's character for his rent money. He has also appeared in the web comic PvP, in which Tom and Rowan threaten to destroy the player's home for owing 500,000 bells. In a satirical article written by GamesRadar, they suggest that the cast of Animal Crossing, most importantly Tom Nook, were setting the player up into a "furry cult". GameSpy listed Tom Nook as a video game character who would be disliked in real life, stating that he is annoying in the video games, and would be terrifying if he was a landlord in real life. 1UP.com editor Jeremy Parish, in his review of Animal Crossing: Wild World, he makes a parody documentary of the in-game world. In it, he suggests that Tom Nook's keen business sense allows him to effectively control the village.
References
Category:Animal Crossing characters
Category:Animal characters in video games
Category:Anthropomorphic characters in video games
Category:Fictional businesspeople
Category:Fictional raccoons
Category:Japanese mythology in popular culture
Category:Male characters in video games
Category:Nintendo protagonists
Category:Video game characters introduced in 2001 |
Introduction {#Sec1}
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AMPARs mediate fast excitatory signaling in the brain, and a change in their number or function underlies lasting forms of synaptic plasticity^[@CR1],[@CR2]^. At many central synapses the time course of the excitatory postsynaptic current reflects the rapid deactivation of AMPARs following fast neurotransmitter clearance from the cleft^[@CR3]--[@CR5]^. AMPAR desensitization, where the channel closes while glutamate remains bound, is also important in shaping transmission, especially during periods of high-frequency synaptic input^[@CR6]^ or when glutamate clearance is slow^[@CR7],[@CR8]^. In this situation, AMPAR-mediated responses are depressed and AMPARs must recover from desensitization before they can be re-activated^[@CR8]--[@CR10]^. Thus, the balance between AMPAR desensitization and recovery influences the amplitude, duration, and frequency of neuronal responses^[@CR11]^.
AMPARs are homo- or heterotetrameric assemblies of the pore-forming subunits GluA1--4. The activation, deactivation, and desensitization of the receptor is controlled by ligand-binding domains (LBDs) which form a self-contained clamshell-like structure within each of the four subunits^[@CR12],[@CR13]^. Glutamate binds between the upper (D1) and lower (D2) lobes of these structures. Within the resting receptor, LBDs of adjacent subunits form dimers that are linked back-to-back between their D1 domains^[@CR12],[@CR14]^. Following glutamate binding, closure of the LBD clamshell around the agonist causes separation of the D2 domains, applying tension to linkers between the LBDs and the ion channel which opens the gate^[@CR12],[@CR15]--[@CR17]^. This can be followed by desensitization, which is initiated by rupturing of the D1--D1 interfaces, relieving the tension on the pore linkers imposed by glutamate binding, allowing the channel to close^[@CR14],[@CR16],[@CR18],[@CR19]^.
In neurons, AMPARs are intimately associated with numerous classes of auxiliary subunits, which include the transmembrane AMPAR regulatory proteins (TARPs)^[@CR20]^ and germ cell-specific gene 1-like protein (GSG1L)^[@CR21],[@CR22]^. These auxiliary proteins determine many biophysical and pharmacological properties of AMPARs and influence their desensitization^[@CR23],[@CR24]^. The prototypical TARP γ-2 markedly slows the rate of AMPAR desensitization and accelerates recovery from desensitization^[@CR25],[@CR26]^, while TARP γ-8 and GSG1L slow both the entry into and the recovery from desensitization^[@CR21],[@CR22],[@CR27]^. The structures of desensitized complexes, composed of homomeric GluA2 AMPARs with either the prototypical TARP γ-2 or GSG1L, have recently been determined at \~8 Å resolution by cryo-electron microscopy (cryo-EM)^[@CR16],[@CR19]^. The desensitized structures displayed a closed pore, a ruptured D1 interface, and a modest rearrangement (relaxation) of the LBD dimer with closely apposed D2 lobes^[@CR18]^. This contrasts with the more variable LBD structures of GluA2 seen in the absence of auxiliary subunits^[@CR28],[@CR29]^.
Native GluA2 is subject to RNA editing which causes a switch from the genetically encoded glutamine (Q) to an arginine (R) in the selectivity filter; this Q/R editing reduces channel conductance and Ca^2+^ permeability^[@CR30]--[@CR32]^. Structural details of the closed, desensitized, and activated states of auxiliary subunit-associated homomeric GluA2(R) and GluA2(Q) have been well characterized^[@CR16],[@CR17],[@CR19],[@CR33]^. Here we describe striking differences in the functional properties of homomeric GluA2(Q) and GluA2(R) receptors. The edited (R) form displays unusual desensitization and gating behavior when compared with the unedited (Q) form, or indeed any other AMPAR assembly that we have examined^[@CR34]--[@CR38]^. Specifically, we find that GluA2(R) displays a particularly large fractional steady-state current and an anomalous current--variance relationship. When GluA2(R) is expressed with TARPs (γ-2 or γ-8) or with GSG1L we observe similarly anomalous behavior. We suggest that this behavior can be attributed to pore loop arginines preventing desensitization-mediated channel closure of the GluA2(R) assemblies, giving rise to conducting desensitized receptors. Using functional cysteine cross-linking we exploited this phenomenon to gain insight into the structure of desensitized AMPARs in the plasma membrane.
Results {#Sec2}
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Atypical channel behavior of Q/R-edited GluA2 {#Sec3}
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When recording glutamate-evoked currents (10 mM,100 ms, --60 mV) in outside-out patches excised from HEK293 cells expressing homomeric GluA2 with and without γ-2, γ-8, or GSG1L, we observed unexpected differences in the behavior of the unedited (Q) and edited (R) forms (Fig. [1](#Fig1){ref-type="fig"}). Compared with that of the Q-forms, GluA2(R) desensitization was slower (Fig. [1a--c](#Fig1){ref-type="fig"}). The mean differences in the weighed time constants of desensitization (*τ*~w,\ des~) between the R- and Q-forms were 4.53 ms (95% confidence interval, 3.71--5.35) for GluA2 alone, 2.13 ms (95% confidence interval, 0.49--3.90) for GluA2/γ-2, 6.36 ms (95% confidence interval, 2.91--9.65) for GluA2/γ-8, and 2.83 ms (95% confidence interval, 1.28--4.56) for GluA2/GSG1L. This slowing of desensitization by Q/R site editing was accompanied by a striking increase in fractional steady-state current for GluA2, GluA2/γ-2, and GluA2/γ-8 (Fig. [1a, b, d](#Fig1){ref-type="fig"}). The mean differences in *I*~SS~ (% peak) between the R- and Q-forms were 9.2 (95% confidence interval, 6.6--11.1) for GluA2 alone, 33.9 (95% confidence interval, 29.2--38.4) for GluA2/γ-2, and 24.2 (95% confidence interval, 18.5--30.1) for GluA2/γ-8. By contrast, *I*~SS~ was not increased in the case of GluA2/GSG1L (1.43; 95% confidence interval, --0.35; 3.25) (Fig. [1d](#Fig1){ref-type="fig"}). Of note (except for GluA2/GSG1L) Q/R site editing had a much more pronounced effect on the steady-state currents (\~400--600% increase) than on the desensitization time course (\~30--90% slowing).Fig. 1Q/R editing affects the kinetics and variance of GluA2 currents. **a** Representative outside-out patch response (10 mM glutamate, 100 ms, --60 mV; gray bar) from a HEK293 cell transfected with GluA2(Q)/γ-2 (average current, black; five individual responses, grays). Inset: current--variance relationship (dotted line indicates background variance and red circle indicates expected origin). **b** As **a**, but for GluA2(R)/γ-2. Note that the data cannot be fitted with a parabolic relationship passing through the origin. **c** Pooled *τ*~w,des~ data for GluA2 alone (*n* *=* 12 Q-form and 9 R-form), GluA2/γ-2 (*n* *=* 21 and 27), GluA2/γ-8 (*n* *=* 7 and 10), and GluA2/GSG1L (*n* *=* 6 and 13). Box-and-whisker plots indicate the median (black line), the 25--75th percentiles (box), and the 10--90th percentiles (whiskers); filled circles are data from individual patches and open circles indicate means. Two-way ANOVA revealed an effect of Q/R editing (*F*~1,97~ = 111.34, *P* \< 0.0001), an effect of auxiliary subunit type (*F*~3,97~ = 32.3, *P* \< 0.0001) and an interaction (*F*~3,97~ = 2.84, *P* = 0.041). **d** Pooled data for *I*~ss~. Box-and-whisker plots and *n* numbers as in **c**. Two-way ANOVA indicated an effect of Q/R editing (*F*~1,97~ = 129.98, *P* \< 0.0001), an effect of auxiliary subunit type (*F*~3,97~ = 58.30, *P* \< 0.0001), and an interaction (*F*~3,97~ = 58.67, *P* \< 0.0001). **e** Doubly normalized and averaged current--variance relationships (desensitizing current phase only) from GluA2(Q) and GluA2(R) expressed alone (*n* = 12 and 9), with γ-2 (*n* = 19 and 23), with γ-8 (*n* = 7 and 10), or with GSG1L (*n* = 6 and 13). Error bars are s.e.m.s. All Q-forms can be fitted with parabolic relationships passing through the origin, while R-forms cannot. **f** Pooled NSFA conductance estimates for GluA2(Q) alone, GluA2(Q)/γ-2, GluA2(Q)/γ-8, and GluA2(Q)/GSG1L (*n* = 12, 18, 7, and 6, respectively). Box-and-whisker plots as in **c**. Indicated *P* values are from Wilcoxon rank sum tests. Source data are provided as a Source Data file
In order to determine the underlying weighted mean single-channel conductance for the Q- and R-forms of the receptors we used non-stationary fluctuation analysis (NSFA) (Fig. [1a, b, e](#Fig1){ref-type="fig"}). Such analysis typically produces current--variance relationships that can be fitted by a parabolic function which extrapolates to the origin^[@CR36],[@CR37]^. All GluA2(Q) combinations yielded plots with these features. Consistent with previous reports^[@CR37],[@CR38]^, the estimated weighted mean single-channel conductance of GluA2(Q) (16.5 ± 1.3 pS, *n* = 12) (mean ± s.e.m. from *n* patches) was increased by co-expression with γ-2 or γ-8 (to 32.8 ± 2.0 and 34.6 ± 4.8 pS; *n* = 18 and 7, respectively) but reduced by co-expression with GSG1L (to 11.7 ± 1.0 pS, *n* = 6) (Fig. [1f](#Fig1){ref-type="fig"}). The mean differences were 16.3 pS (95% confidence interval, 11.9--20.8), 18.1 pS (95% confidence interval, 10.8--29), and --4.8 pS (95% confidence interval, --7.93 to --2.06). By contrast, NSFA of GluA2(R) receptor combinations produced anomalous current--variance relationships that were right-shifted (Fig. [1b,e](#Fig1){ref-type="fig"}), precluding conventional interpretation. This shift, which was apparent for GluA2(R) alone, was accentuated by expression with TARPs γ-2 or γ-8, but was reduced by co-expression of GSG1L (Fig. [1e](#Fig1){ref-type="fig"}). Such current--variance relationships have not been reported for other AMPAR complexes^[@CR34]--[@CR38]^.
To determine the basis of the anomalous results from NSFA, we focused on GluA2(R)/γ-2, which displayed the most robust expression, the greatest increase in steady-state current, and the most right-shifted current--variance relationship. First, we observed a near identical current--variance relationship for the tandem construct GluA2(R)\_γ-2 (Supplementary Fig. [1a](#MOESM1){ref-type="media"}). This suggests that the anomalous behavior of co-expressed GluA2(R) and γ-2 did not simply reflect the presence of AMPARs with different TARP stoichiometries, and thus heterogeneous channel properties^[@CR39]^. Second, shifted relationships were also seen with GluA2(R)/γ-2 at +60 mV (Supplementary Fig. [1b, c](#MOESM1){ref-type="media"}). As channels would be passing Cs^+^ rather than Na^+^ in this condition, this argues that the phenomenon is independent of both voltage and permeating ion. Third, we obtained anomalous current--variance relationships with the edited form of GluA4 (GluA4(R)/γ-2) (Supplementary Fig. [1d](#MOESM1){ref-type="media"}), indicating that the behavior is not confined to GluA2(R) receptors. Fourth, current--variance relationships derived from deactivation of GluA2(R)/γ-2 (following 1 or 100 ms glutamate exposure; Supplementary Fig. [2a--e](#MOESM1){ref-type="media"}) and from GluA2(R)\_γ-2 or GluA4(R)/γ-2 (following 1 ms glutamate exposure; Supplementary Fig. [2f, g](#MOESM1){ref-type="media"}) also displayed non-parabolic features. Taken together, our results reveal that the behavior of homomeric Q/R-edited AMPARs deviates substantially from that expected.
GluA2(R)/γ-2 receptors display two types of channel opening {#Sec4}
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Stationary fluctuation analysis of GluA2(R) currents in the absence of TARPs has previously yielded an estimated conductance of \~300 fS^[@CR32]^. While single-channel openings of this magnitude would be too small to resolve directly, in some of our GluA2(R)/γ-2 patches containing small numbers of channels, we were able to observe discrete single-channel openings that were in the picosiemens range (Fig. [2a, b](#Fig2){ref-type="fig"}). A histogram of channel amplitudes (pooled from six patches) revealed that openings to a conductance level of 3.5 pS were the most prevalent (Fig. [2c](#Fig2){ref-type="fig"}). The additional peaks above 3.5 pS could reflect either the presence of multiple conductance states, as reported for unedited AMPAR combinations^[@CR26],[@CR32],[@CR40]--[@CR42]^, or multiple concurrent events.Fig. 2GluA2(R)/γ-2 single-channel recordings. **a** GluA2(R)/γ-2 currents from an outside-out patch containing few channels (--60 mV). Forty consecutive applications of 10 mM glutamate (gray bar) are overlaid. **b** Individual responses exhibiting discrete channel openings superimposed on a persistent steady-state current (upper sweeps) or exhibiting only a persistent steady-state component (lower sweeps). Note the decay of the steady-state currents on glutamate removal (gray arrows) is much slower than the closure of resolved channels (black arrow). **c** Histogram of channel conductance for 392 discernible openings from six patches. The histogram is fit with the sum of four Gaussian curves (dashed lines) with a common standard deviation (1.2 pS), revealing four peaks (3.5, 6.9, 10.3, and 14.1 pS)
The resolved openings showed several unusual features. First, despite the steady-state macroscopic current being relatively large (\~40% of the peak current; Fig. [1d](#Fig1){ref-type="fig"}), the majority of resolvable individual openings were present at the onset of the glutamate application (Fig. [2a, b](#Fig2){ref-type="fig"}). Second, while the amplitudes of resolved openings were equivalent to (or larger than) the steady-state current, the recordings contained no sojourns to the baseline; the resolvable openings thus appeared to ride on a low-noise background current (Fig. [2a, b](#Fig2){ref-type="fig"}). Third, throughout the recordings, occasional responses were observed in which the current onset showed no discernible picosiemens openings. Nonetheless, these responses still exhibited the low-noise steady-state current (Fig. [2b](#Fig2){ref-type="fig"}). Fourth, unlike the rapid closure of the resolved picosiemens channel openings, the steady-state current decay that followed agonist removal was slow (and roughly exponential), as might be expected if it reflected the closure of a large number of lower conductance openings (Fig. [2b](#Fig2){ref-type="fig"}). These results suggest that GluA2(R)/γ-2 receptors are capable of generating two distinct types of channel opening---conventional AMPAR openings (with conductances in the picosiemens range) which form the initial phase of the macroscopic response, along with openings of much lower conductance that form the steady-state current. The pattern of channel behavior we observed---predominantly large openings occurring at the onset of the response and predominantly small openings at steady-state---would give rise to a steady-state current with relatively low variance, consistent with the right-shifted current--variance relationships (Fig. [1e](#Fig1){ref-type="fig"}).
GluA2(R) receptors in the absence of auxiliary subunits exhibit detectable chloride permeability (*P*~Cl~/*P*~Cs~ estimated as 0.14, ref. ^[@CR43]^). We asked whether the different classes of channel openings seen with GluA2(R)/γ-2 could have different relative chloride permeabilities. To address this, we applied 100 ms pulses of glutamate and measured the reversal potential of the peak and steady-state currents (comprising mostly large and small openings, respectively) in external solutions containing high (145 mM) or low (35 mM) CsCl^[@CR43]^ (Supplementary Fig. [3](#MOESM1){ref-type="media"}). The expected shift in reversal potential following a switch between these conditions is --30.4 mV for a Cs^+^-selective (Cl^--^ impermeable) channel and +30.1 mV for a purely Cl^--^-selective channel (see Methods). We recorded shifts in reversal potential of --36.0 ± 1.4 and --33.7 ± 2.1 mV for the peak and steady-state currents, respectively (*n* = 7, *P* = 0.100; Supplementary Fig. [3](#MOESM1){ref-type="media"}), suggesting that the different classes of channel opening do not differ in their relative chloride permeability. Indeed, this result suggests that in the presence of γ-2, GluA2(R) receptors mediate negligible Cl^--^ flux.
Low conductance steady-state openings follow desensitization {#Sec5}
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NSFA for both desensitization and deactivation gave current--variance relationships that were not amenable to conventional interpretation. We thus sought to determine whether NSFA of the rising phase of the current (AMPAR activation) could accurately report weighted mean single-channel conductance and, if so, whether this approach might be applicable to GluA2(R)/γ-2. We first confirmed that NSFA of the fast-rising AMPAR activation phase would allow us to estimate accurately the single-channel conductance of unedited GluA2(Q)/γ-2. This yielded a weighted mean conductance of 24.7 ± 4.3 pS, not different from that obtained from the analysis of deactivating current (26.4 ± 3.1 pS; *P* *=* 0.64, paired *t-*test, *n* = 5; Fig. [3a, b](#Fig3){ref-type="fig"}). For GluA2(R)/γ-2 activation (unlike the deactivation phase of the same records) we obtained conventional parabolic current--variance relationships yielding a weighted mean conductance of 3.8 ± 0.5 pS (*n* = 10; Fig. [3c, d](#Fig3){ref-type="fig"}), similar to the most prevalent conductance seen in our single-channel analysis (Fig. [2c](#Fig2){ref-type="fig"}).Fig. 3Estimated weighted mean conductance from NSFA of GluA2(R)/γ-2 activation. **a** Representative GluA2(Q)/γ-2 responses to 1 ms (gray bar) glutamate application (gray traces) with superimposed average (black trace). NSFA was performed on the activation phase (blue highlight; filled blue circles) and deactivation phase (light blue highlight; open blue circles) of the same records, yielding similar estimates of weighted mean conductance. **b** Pooled current--variance plots for the activation and deactivation of GluA2(Q)/γ-2 currents (*n* = 5). Error bars indicate s.e.m. **c** Representative GluA2(R)/γ-2 response to 1 ms glutamate application (as in **a**). NSFA was performed on the activation phase (pink highlight; filled pink circles) and deactivation phase (light pink highlight; open pink circles) of the same records. Current--variance relationship is non-parabolic for deactivation but parabolic for activation. **d** Pooled current--variance plots for the activation and deactivation of GluA2(R)/γ-2 currents (*n* = 8). Error bars indicate s.e.m.
As conventional current--variance relationships could be produced only from GluA2(R)/γ-2 activation and not desensitization (nor indeed from deactivation, during which there is a degree of desensitization) we speculated that desensitization itself may provide the key to our unexpected results. We hypothesized that the conformational rearrangements of the LBDs which normally trigger desensitization might not fully close the ion channel, such that the GluA2(R)/γ-2 receptors could adopt a conducting desensitized state, giving rise to the large fractional steady-state current and the anomalous current--variance relationships. If this were the case, and the shift from large resolvable channel openings to smaller openings was linked to the process of desensitization, a decline in GluA2(R)/γ-2 single-channel conductance (and therefore macroscopic current) would not be expected if desensitization was blocked. In the presence of cyclothiazide, which inhibits desensitization by stabilizing the upper LBD dimer interface^[@CR14]^, we found that GluA2(R)/γ-2 macroscopic currents (10 mM glutamate, 1 s) did not decay (Fig. [4a](#Fig4){ref-type="fig"}). Likewise, if the low-noise steady-state current of GluA2(R)/γ-2 arose from conducting desensitized channels, then we would expect the steady-state current to remain when desensitization was enhanced. To test this idea, we used the point mutation S754D. This weakens the upper LBD dimer interface, accelerating desensitization and reducing steady-state currents of GluA2(Q)^[@CR14]^. For both GluA2(Q)/γ-2 and GluA2(R)/γ-2 the S754D mutation produced a near 20-fold acceleration of desensitization (Fig. [4b, c](#Fig4){ref-type="fig"}) and a greater than twofold slowing of recovery from desensitization (Fig. [4d](#Fig4){ref-type="fig"}). As anticipated, GluA2(Q) S754D/γ-2 produced a negligible steady-state current (Fig. [4b, e](#Fig4){ref-type="fig"}). In marked contrast, GluA2(R) S754D/γ-2 exhibited an appreciable steady-state current (Fig. [4b, e](#Fig4){ref-type="fig"}). The presence of a large steady-state current with GluA2(R)/γ-2 under conditions strongly favoring desensitization is consistent with the view that desensitized channels can conduct.Fig. 4Large steady-state GluA2(R)/γ-2 currents are observed even in conditions favoring desensitization. **a** Representative GluA2(R)/γ-2 current (--60 mV) evoked by 10 mM glutamate (gray bar) in the presence of 50 µM cyclothiazide (green bar). Note the minimal current decay when desensitization is inhibited (for pooled data *I*~SS~/*I*~peak~ = 93.4 ± 1.6%, *n* = 6) (mean ± s.e.m. from *n* patches). **b** Representative glutamate-evoked currents from Q- and R-forms of GluA2 S754D/γ-2. Both forms exhibit very fast desensitization, but the R-form has an appreciable steady-state current. **c** Pooled data showing desensitization kinetics (*τ*~w,des~) for wild-type (wt; *n* = 6 and 5) and mutant (S754D; *n* = 5 and 5) forms of GluA2(Q)/γ-2 and GluA2(R)/γ-2. Box-and-whisker plots as in Fig. [1c](#Fig1){ref-type="fig"}. Two-way ANOVA indicated an effect of Q/R editing (*F*~1,\ 17~ = 10.56, *P* *=* 0.0047), an effect of the mutation (*F*~1,\ 17~ = 43.19, *P* *\<* 0.0001) but no interaction (*F*~1,\ 17~ = 2.63, *P* *=* 0.12). The mean difference between S754D and wild type was --8.1 ms (95% confidence interval, --10.9 to --6.0) for Q and --14.1 ms (95% confidence interval, --20.0 to --9.3) for R. **d** Pooled data (as in **c**) for recovery kinetics (*τ*~w,recov~). Two-way ANOVA indicated no effect of Q/R editing (*F*~1,\ 17~ = 0.13, *P* *=* 0.72), an effect of the mutation (*F*~1,\ 17~ = 31.67, *P* *\<* 0.0001) but no interaction (*F*~1,\ 17~ = 1.65, *P* *=* 0.22). The mean difference between S754D and wild type was 24.1 ms (95% confidence interval, 15.3 to 33.2) for Q and 38.7 ms (95% confidence interval, 23.7 to 53.9) for R. **e** Pooled data (as in **c**) for the fractional steady-state current (*I*~SS~). Two-way ANOVA indicated an effect of Q/R editing (*F*~1,\ 17~ = 65.37, *P* *\<* 0.0001), an effect of the mutation (*F*~1,\ 17~ = 28.37, *P* *\<* 0.0001), and an interaction (*F*~1,\ 17~ = 14.93, *P* *=* 0.0012). The mean difference in *I*~SS~ (% of peak) between S754D and wild type was --7.7 (95% confidence interval, --11.2 to --5.2) for Q and --37.9 (95% confidence interval, --49.2 to --25.8) for R. Indicated *P* values are from Welch *t*-tests. Source data are provided as a Source Data file
A model incorporating conducting desensitized receptors {#Sec6}
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We next considered whether the presence of desensitized receptors able to conduct ions could account quantitatively for our observations. To examine this, we incorporated such states into a modified version of a kinetic scheme we used previously to describe AMPAR/TARP concentration-dependent behaviors^[@CR25],[@CR44]^ (Scheme 1; Fig. [5a](#Fig5){ref-type="fig"}), and attempted to mimic the macroscopic kinetics and NSFA of GluA2(R)/γ-2 by varying the rate constants and conductances. From six patches in which activation, deactivation, and desensitization were all examined, we generated global average waveforms and current--variance plots for each condition (Fig. [5b--d](#Fig5){ref-type="fig"}). The inclusion in our scheme of conducting desensitized states allowed simultaneous modeling of all kinetic and current--variance data.Fig. 5A kinetic scheme including conducting desensitized states can mimic GluA2(R)/γ-2 behavior. **a** Scheme 1 is a modified form of a previously proposed kinetic model^[@CR25],[@CR44]^. States which can conduct are red. Open states (O1--O4) and occupied desensitized states (D1\*--D4\*, D~2~2\*--D~2~4\*) have independent conductances that are occupancy-dependent. **b**--**d** Global averaged GluA2(R)/γ-2 records (top) and variance data (bottom) for desensitization, deactivation, and activation (10 mM glutamate---gray bars). Using a single set of rate constants and conductances, the model closely mimics all six measures (dashed red lines): *k*~1~ = 1.3 × 10^6^ M^--1 ^s^--1^, *k*~−1~ = 350 s^--1^, *α* = 3100 s^--1^, *β* = 1000 s^--1^, *γ*~1~ = 88 s^--1^, *δ*~1~ = 110 s^--1^, *γ*~2~ = 36 s^--1^, *δ*~2~ = 39 s^--1^, *γ*~0~ = 8 s^--1^, *δ*~0~ = 0.48 s^--1^, *k*~−2~ = 870 s^--1^, conductance of fully occupied open state (O4) = 3.9 pS, conductance of fully occupied desensitized state (D4\* and D~2~4\*) = 670 fS. Conductances of partially occupied states were proportional to their occupancy (e.g. O3 = 0.75 × O4, O2 = 0.5 × O4, O1 = 0.25 × O4)
The model yielded estimated conductances of 3.9 pS for the fully open state and 670 fS for the fully occupied desensitized state of GluA2(R)/γ-2. As the steady-state occupancy of desensitized receptors (D1\*--D4\*, D~2~2\*--D~2~4\* combined: 90%) was much higher than that of the open receptors (O1--O4 combined: 6%), the latter contributed just 27% of the steady-state current. The low conductance and high steady-state occupancy of desensitized channels predicted by the model can fully explain the unusually low variance of the large steady-state current and, therefore, the right-shifted current--variance relationship produced from the macroscopic desensitizing current (Fig. [1](#Fig1){ref-type="fig"}). The model indicated that the proportion of current carried by desensitized and non-saturated receptors increased during deactivation (from 11% and 6%, respectively, at the peak, to 25% and 77% at mid-decay). The combination of these factors could explain the rapid fall-off in deactivation variance (Supplementary Fig. [2](#MOESM1){ref-type="media"}). While alternative kinetic schemes remain possible (see Supplementary Discussion), we favor Scheme 1 as the simplest that can account for our experimental findings with homomeric GluA2(R) complexes.
Functional cross-linking of desensitized receptors {#Sec7}
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Recent work on the structural basis of desensitization has shown that the variety of conformations adopted by the desensitized LBD layer is greatly diminished when the full-length AMPAR is co-assembled with auxiliary subunits^[@CR16],[@CR19],[@CR28],[@CR29]^. In the presence of γ-2 the LBD dimers of desensitized GluA2 favor a relaxed dimer conformation, with the upper D1--D1 interfaces ruptured and the lower D2 domains more closely apposed, allowing channel closure^[@CR16]^. We reasoned that conducting desensitized receptors could enable us to determine whether this conformation (previously revealed through crystallography and cryo-EM) can indeed be adopted by AMPARs in the plasma membrane. Specifically, we predicted that if the steady-state current of GluA2(R) reflected ion flow through desensitized receptors in the relaxed dimer conformation, then if trapped in this conformation the receptors should maintain their conductance. To test this, we introduced cysteines at sites on the central axis of the D2--D2 dimer interface, cross-linking of which has previously been shown to inhibit channel opening by trapping the receptor in desensitized-like states. Thus we compared S729C, cross-linking of which permits the relaxed dimer conformation^[@CR16],[@CR18],[@CR45]^, with G724C^[@CR46]^ which we predicted would not accommodate the relaxed dimer conformation when cross-linked (Supplementary Fig. [4](#MOESM1){ref-type="media"}). In each case, we examined the effect of cross-linking on GluA2 currents.
We first simulated currents from wild-type GluA2(R)/γ-2 receptors (Scheme 1), and compared these with simulated currents expected from receptors occupying only desensitized states (Scheme 2; Fig. [6a, b](#Fig6){ref-type="fig"}). These simulations predicted that if cross-linking trapped receptors in the native conducting desensitized state, it would change the glutamate response to a purely non-decaying steady-state current of reduced size.Fig. 6A model with access to only desensitized states predicts behavior of cross-linked GluA2(R) S729C/γ-2. **a** Scheme 2 is modified from Scheme 1 (Fig. [5a](#Fig5){ref-type="fig"}) and assumes that, following cross-linking, the receptor can occupy only desensitized states (excluded states are shown in gray). **b** Simulated responses to 10 mM glutamate (gray bar) using Scheme 1 to mimic the non-cross-linked condition and Scheme 2 to mimic the effect of cross-linking. **c** Representative currents at --60 mV activated by 10 mM glutamate (gray bar) from GluA2(Q) G724C/γ-2 and GluA2(R) G724C/γ-2 in DTT (black) or CuPhen (red). Note that, for both forms, currents are fully inhibited following cross-linking by 10 µM CuPhen. **d** Representative responses from individual patches demonstrate that following cross-linking by 10 µM CuPhen, GluA2(Q) S729C/γ-2 currents are inhibited, while GluA2(R) S729C/γ-2 currents show minimal desensitization and continue to display a large steady-state current, as predicted in **a**. Gray boxes (**b** and **d**) highlight the similarity of modeled currents and recorded GluA2(R) S729C/γ-2 currents
To investigate the functional effects of cysteine cross-linking, and test these predictions, we examined the sensitivity of both unedited and edited GluA2 G724C/γ-2 and S729C/γ-2 receptors to the oxidizing agent CuPhen^[@CR45]^. Application of CuPhen to both editing forms of GluA2 G724C/γ-2 receptors caused rapid inhibition of glutamate-evoked currents, resembling the reported effects of cross-linking on TARP-free receptors^[@CR46]^ (Fig. [6c](#Fig6){ref-type="fig"}; Supplementary Fig. [5a](#MOESM1){ref-type="media"}). The peak and steady-state currents generated by GluA2(Q) S729C/γ-2 were also inhibited by CuPhen (Fig. [6d](#Fig6){ref-type="fig"}; Supplementary Fig. [5b](#MOESM1){ref-type="media"}). By contrast, cross-linking of edited GluA2(R) S729C/γ-2 abolished the peak current, but not the steady-state current (Fig. [6d](#Fig6){ref-type="fig"}; Supplementary Fig. [5b](#MOESM1){ref-type="media"})---a result consistent with the predictions of Scheme 2. Similar results were also seen when GluA2(R) S729C was expressed with γ-8 or GSG1L (Supplementary Fig. [5c](#MOESM1){ref-type="media"}). Overall, these results demonstrate that ion permeation through desensitized channels allows possible LBD conformations of the desensitized wild-type receptor to be probed using functional cross-linking. Of the two LBD conformations we examined, only S729C, which can accommodate the relaxed dimer state when cross-linked, behaved in a manner resembling that of the wild-type desensitized channel.
Antagonist-bound cross-linked GluA2 LBD structures {#Sec8}
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Our functional data demonstrate that cross-linked GluA2(R) S729C/γ-2 receptors retain sensitivity to glutamate, implying that upon agonist binding they can undergo structural change which affects the channel gate. To understand the molecular basis of this, we determined the crystal structure of cross-linked S729C ligand binding cores in apo-like conformations bound to the competitive antagonists NBQX (diffracted to 1.8 Å resolution) or ZK200775 (diffracted to 2.0 Å) (Fig. [7a](#Fig7){ref-type="fig"}; Supplementary Fig. [6](#MOESM1){ref-type="media"}). AMPAR gating is driven by the separation of the D2-M3 linker regions following agonist binding^[@CR12],[@CR16],[@CR17]^. Thus, binding of glutamate is known to increase the distance between the α-carbons of Proline 632 pairs at the base of the D2 lobe of the GluA2 LBD (Fig. [7a](#Fig7){ref-type="fig"})^[@CR12],[@CR15],[@CR47]^. For the cross-linked S729C mutant LBD bound with NBQX (S729C~NBQX~) the Proline 632 separation was 22.8 Å (similar to that seen with S729C~ZK~, 22.6 Å). This is less than the separation we calculate for the glutamate-bound mutant LBD (S729C~glu~, 26.4 Å)^[@CR18]^. The relative separation of Pro632 residues suggests that, despite being constrained by the cross-link, glutamate binding to GluA2(R) S729C can trigger relative movements of the lower LBDs which, in the intact receptor, may induce tension in the M3-D2 linkers sufficient to allow ion flow (Fig. [7b](#Fig7){ref-type="fig"}).Fig. 7Cross-linked S729C LBD structures suggest a model of gating for desensitized GluA2(R). **a** Left, crystal structure of the dimeric GluA2 S729C ligand-binding core in the presence of NBQX, with the upper (D1, pale) and lower (D2, dark) lobes of each monomer (red and blue) distinguished by shading. The structure is viewed perpendicular to the axis between the Cα atoms of Pro632 (magenta spheres). Right, crystal structure of the GluA2 S729C ligand-binding core in the presence of glutamate (S729C~glu~; PDB: 2I3W)^[@CR18]^. The Pro632 separation seen in the presence of glutamate (right) is \>3 Å greater than that seen with NBQX (left). **b** Cartoon representing possible conformations of the GluA2(R) LBD dimer and pore in our functional cross-linking recordings. Non-cross-linked GluA2(R) channels bind glutamate (gray spheres), closing the clamshell LBDs and opening the pore to the full open channel conductance. Desensitization does not fully close the pore. As determined in the presence of γ-2, cross-linking of the G724C mutant (yellow) does not allow the action of agonist binding to be communicated to the pore in any state, and disrupts the normal dimeric conformation of desensitized receptors. Cross-linking of the S729C mutant (yellow) is not compatible with the full open state, but the channel can adopt the normal desensitized conformation, meaning that (as with the non-cross-linked receptor) the pore is not closed
We also crystallized isolated cross-linked G724C LBDs in both the apo-like ZK200775-bound form (G724C~ZK~) and desensitized-like glutamate-bound forms in two different space groups (G724C~glu~ Forms A and B; Supplementary Fig. [7](#MOESM1){ref-type="media"}**)**. As we anticipated, G724C~ZK~ demonstrated reduced Pro632 separation (19.2 Å) compared to the antagonist-bound S729C forms, in keeping with the greater constraints on LBD separation imposed by G724C. However, unlike glutamate-bound S729C^[@CR18],[@CR45]^, neither form of G724C~glu~ adopted a relaxed dimer conformation (Fig. [7b](#Fig7){ref-type="fig"}). Instead they displayed a non-biological conformation, with a large rotation and total loss of the dimer interface which cannot be accommodated within the intact receptor (Supplementary Fig. [7](#MOESM1){ref-type="media"}). Thus, the Pro632 separation in the intact, cross-linked GluA2 G724C receptor could not be meaningfully assessed.
Discussion {#Sec9}
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Our experimental findings have implications for the understanding of AMPAR desensitization. They challenge the idea that the pore of desensitized AMPARs must be fully closed, and provide direct functional evidence concerning the conformation of the LBDs of desensitized receptors. Our NSFA, single-channel measurements and kinetic modeling all support the unexpected conclusion that atypical currents generated by GluA2(R)/γ-2 arise from desensitized receptors that retain around one-sixth of the maximal conductance of open channels. Our data indicate a weak, previously unidentified, coupling between the desensitized LBD and the gate, that is revealed only in Q/R-edited homomers, and is strengthened by TARP association. While a conducting desensitized state has previously been described for a mutant, homomeric, α7 nicotinic acetylcholine receptor^[@CR48]^, to our knowledge such behavior for a ligand-gated ion channel formed from wild-type subunits has not previously been described. The presence of a conducting desensitized state of GluA2(R) provided us with a functional readout to probe the likely arrangement of LBDs within desensitized AMPARs. By comparing currents from GluA2(R)/γ-2, GluA2(R)/γ-8, and GluA2(R)/GSG1L receptors with those from constrained cross-linked cysteine mutants^[@CR18],[@CR46]^, we have established that the relaxed dimer conformation identified in structural studies^[@CR18]^ is indeed representative of desensitized AMPARs within the plasma membrane.
What is the evidence that the steady-state current does indeed arise from desensitized AMPARs? The fractional steady-state glutamate-evoked currents we recorded with GluA2(R)/γ-2 were much larger than those of other AMPAR/auxiliary subunit combinations we have examined previously^[@CR34]--[@CR38]^. While one might reasonably suppose that such a large steady-state current could arise simply from a reduced level of receptor desensitization, a number of the GluA2(R)/γ-2 properties we have identified suggest this is not the case. Importantly, the rates of entry into, and recovery from, desensitization for GluA2(R)/γ-2 were similar to those for GluA2(Q)/γ-2, which had a much smaller steady-state current. Moreover, a reduced extent of desensitization would not give rise to the rightward shift in the current--variance relationships that we observed. By contrast, the presence of a substantial steady-state current of unusually low variance would produce such a shift. Thus, the steady-state current could be generated by low-conductance channels with a high open probability. Furthermore, resolvable (picosiemens) openings were common at the onset of the current, but occurred only rarely during steady-state, supporting the view that these contribute little to the large steady-state component. Finally, AMPAR mutations (S754D and S729C) that enhanced desensitization essentially eliminated steady-state currents of GluA2(Q)/γ-2 receptors, but had much less effect on steady-state currents of GluA2(R)/γ-2 receptors. Consequently, our data suggest that a large fraction of the GluA2(R)/γ-2 steady-state current arises from conducting desensitized channels.
How do our functional data fit with recently published AMPAR structures? Cryo-EM analysis has indicated that the pore diameter at the M3 gate of agonist-bound desensitized GluA2(R)/γ-2 is less than that of the activated receptor^[@CR16]^ and similar to that of the closed (antagonist-bound) receptor^[@CR33]^. Thus, the occurence of conducting desensitized states could be seen to present something of a paradox. The single closed structure for desensitized GluA2(R)/γ-2 (ref. ^[@CR16]^) indicates that open desensitized states were not present under the conditions used for cryo-EM analysis or, if present, were either too heterogeneous to allow reconstruction, or perhaps too similar in structure to closed desensitized states to be classified distinctly. At the same time, although our kinetic and current--variance data could be adequately mimicked by Scheme 1 without the inclusion of closed desensitized receptors, our data do not preclude their existence. For simplicity, we assigned a conductance to all occupied desensitized states, but models including both closed and conducting desensitized states could also broadly reproduce our functional data. Nonetheless, the magnitude of the steady-state current (relative to the peak current) limits how many closed desensitized channels are likely to be present in our recordings. Of note, rapid transitions between these states would be required to account for the absence of clear channel closures from steady state in our single-channel records. Taken together, it is certainly possible that both closed and open desensitized receptors are present in cryo-EM conditions, in which closed desensitized channels might predominate, as well as in our recordings, in which conducting desensitized channels are clearly prevalent.
In our model of GluA2(R)/γ-2 gating, assigning fully occupied desensitized channels a conductance of 670 fS provided a good approximation to both our kinetic and noise data. While currents mediated by GluA2(R), GluA2(R)/γ-8, and GluA2(R)/GSG1L also bore all the hallmarks of conducting desensitized channels, for these combinations the deviations from conventional parabolic current--variance relationships were less dramatic, and the editing-dependent increases in steady-state current were smaller. Furthermore, when co-expressed with γ-8 or GSG1L, cross-linking of the GluA2(R) S729C mutant displayed a smaller residual steady-state current than that seen when it was co-expressed with γ-2. One possible explanation for these differences is that for GluA2(R) receptors the rank-order of desensitized channel conductance is γ-2 \> γ-8 \> no auxiliary \> GSG1L. An alternative possibility is that this reflects the presence of both conducting and non-conducting desensitized states. In this latter scenario, our macroscopic data could be explained by γ-2-associated receptors spending a greater proportion of time than GluA2(R), GluA2(R)/γ-8, or GluA2(R)/GSG1L in conducting desensitized states, relative to closed desensitized states.
Recently, a chimeric AMPAR/KAR construct (ATD and LBD of GluK2 with TM and C-tail of GluA2) has been shown to exhibit a large leak current when co-expressed with TARPs^[@CR49]^. Remarkably, when these chimera/TARP combinations were exposed to glutamate the currents decreased, suggesting that, despite conducting in the absence of agonist, desensitization could still cause closure of the channel^[@CR49]^. The existence of a leak current in the presence of a TARP was taken to indicate that TARPs disrupt the ligand-free closed state of the receptor, leading to spontaneous channel opening. Although we found no evidence that edited GluA2 receptors open spontaneously when expressed with a TARP, the existence of receptors that conduct when desensitized---and the fact that the magnitude of the steady-state current is greatest when γ-2 is present---supports the view that TARPs can also disrupt channel closure in the desensitized state, in a manner that is Q/R-editing-dependent.
How might Q/R site editing render the desensitized GluA2 receptor ion permeable? Of note, in the case of the homologous Q/R-edited kainate receptor GluK2(R), the homomeric receptors are markedly more sensitive to block by *cis*-unsaturated fatty acids than are GluK2(R)/K1(Q) heteromers^[@CR50]^. Structural modeling of the pore loop arginines of the GluK2(R) homomers suggests their side chains project away from the cytoplasm and towards the gate, and the resultant interaction between the pore loop and the M3 helix proximal to the gate is proposed to influence fatty acid pharmacology^[@CR51]^. While the orientation of the arginine side chains in the desensitized state has yet to be resolved, in the activated structure of the GluA2(R)/γ-2 receptor^[@CR16]^ (and in closed heteromeric GluA1/2(R)\_γ-8; ref. ^[@CR27]^) they too project away from the cytoplasm and towards the gate. If such interactions are present in desensitized GluA2(R)/γ-2, these might modify the rearrangement of the channel gate following desensitization, thereby hampering full channel closure. Alternatively, given structural evidence that the Q/R site may act as an additional gate of the receptor^[@CR17]^, charge--charge repulsion between arginines at this site might specifically compromise the constriction at this gate, which may be sufficient, on its own, to account for the ion flow through desensitized channels.
There is general agreement that desensitization-induced AMPAR pore closure is caused by LBD rearrangements which allow the base of the D2 lobes to assume positions similar to those of the apo/inactivated form, thereby releasing the tension exerted by the M3-S2 linkers on the M3 helix caused by glutamate binding^[@CR16],[@CR19]^. In the absence of auxiliary proteins there is considerable heterogeneity in the LBD and ATD layers of desensitized AMPARs^[@CR28],[@CR29]^. However, when associated with γ-2 or GSG1L, AMPAR LBD dimers show increased stability of a single relaxed dimer conformation^[@CR16],[@CR18],[@CR19]^. The fact that GluA2(R) S729C, co-expressed with auxiliary subunits and trapped in the relaxed dimer conformation by cross-linking, exhibited properties consistent with those of wild-type channels, demonstrates that this conformation does indeed mimic the behavior of the native desensitized receptor in the plasma membrane. By contrast, functional cross-linking of a different mutant GluA2(R) G724C/γ-2---which did not assume a relaxed LBD dimer when crystallized---trapped these receptors in a non-conducting state, indicating that this conformation must be distinct from that of native desensitized AMPARs. It is noteworthy that despite the constraint on LBD movement imposed by cross-linking at S729C, the current produced by cross-linked GluA2(R)/γ-2 was glutamate-dependent, suggesting agonist binding produces changes within the constrained LBD layer sufficient to influence the pore. Dimeric Pro632 separation within S729C ligand-binding core crystals in the presence of glutamate^[@CR18]^ is greater than the separation we observed in the presence of competitive antagonists. While this suggests that glutamate binding might exert only a small degree of tension on the LBD-TM linkers within the cross-linked receptors, in the intact receptor (especially in the presence of TARPs that prevent loss of tension due to LBD compression towards the transmembrane domains^[@CR16],[@CR19]^), this might be sufficient to open the gate. However, the Pro632 measure provides only a one-dimensional approximation of a complex three-dimensional process. Future cryo-EM analysis of full-length GluA2 S729C may provide valuable further information on the complex dynamics of desensitized receptors.
Do conducting desensitized states of homomeric GluA2(R) contribute to neuronal or glial signaling? Neurons and glia normally express multiple AMPAR subunit isoforms. When GluA2 is co-expressed with other subunits (in the absence of auxiliary proteins) the formation of GluA2 homomers is strongly discriminated against, in favor of GluA2-containing heteromers^[@CR52],[@CR53]^. Nonetheless, trafficking of homomeric GluA2(R) is enhanced if the receptors are unedited at the secondary (R/G) editing site^[@CR54]^, and we (and others^[@CR55],[@CR56]^) have demonstrated that the presence of γ-2 allows robust heterologous expression of functional GluA2(R) homomers. Of note, glutamate-gated channels with femtosiemens conductance have been detected in cerebellar granule cells^[@CR57]^. Moreover, an immunoprecipitation study that suggested hippocampal AMPARs were predominantly GluA1/2 or GluA2/3 heteromers did not expressly rule out the presence of GluA2 homomers^[@CR58],[@CR59]^. Additionally, functional GluA2(R) homomers can be trafficked to hippocampal synapses by endogenous TARPs following the conditional deletion of the alleles for GluA1 and GluA3 (ref. ^[@CR60]^). Whether, in the presence of multiple GluA subtypes, TARPs facilitate the formation of GluA2(R) homomers remains to be determined. Nevertheless, it is clear from recent cryo-EM analysis of native AMPARs that homomeric GluA2 receptors exist in the brain^[@CR61]^, and our findings suggest that they can conduct even when desensitized.
Methods {#Sec10}
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Heterologous expression {#Sec11}
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We expressed recombinant AMPAR subunits and TARPs (plus EGFP) in HEK293 cells (a gift from Trevor Smart, UCL). These were maintained under standard protocols, as described previously^[@CR25]^. AMPAR subunit cDNAs (rat) were flip splice variants and the GluA2 forms were additionally R/G edited. Point mutations of the GluA2 subunit were produced using standard PCR protocols. Primer sequences are listed in Supplementary Table [1](#MOESM1){ref-type="media"}. AMPAR/TARP combinations were transfected at a cDNA ratio of 1:2. The GluA2_γ-2 tandem consisted of full-length GluA2 and a nine amino-acid linker (GGGGGEFAT) before the start codon of full-length γ-2. Transient transfection was performed using Lipofectamine 2000 (Life Technologies). Cells were split 12--30 h after transfection and plated on glass coverslips in the presence of 50 μM NBQX (2,3-dioxo-6-nitro-1,2,3,4-tetrahydrobenzo\[*f*\]quinoxaline-7-sulfonamide; Tocris-Abcam) to avoid AMPAR-mediated toxicity. Electrophysiological recordings were performed 18--48 h later.
Electrophysiology {#Sec12}
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Patch-clamp electrodes were pulled from borosilicate glass (1.5 mm o.d., 0.86 mm i.d.; Harvard Apparatus) and fire polished to a final resistance of 8--12 MΩ. For outside-out patches the external solution contained 145 mM NaCl, 2.5 mM KCl, 1 mM CaCl~2~, 1 mM MgCl~2~, and 10 mM HEPES, pH 7.3. The internal solution contained 145 mM CsCl, 2.5 mM NaCl, 1 mM Cs-EGTA, 4 mM MgATP, and 10 mM HEPES (pH 7.3 with CsOH) supplemented with 100 µM spermine tetrahydrochloride (Tocris Bioscience). Currents with a risetime \>500 µs were rejected. For chloride permeability experiments, two CsCl based solutions were used---one with high CsCl (145 mM CsCl, 10 mM HEPES, 1 mM CaCl~2~; pH 7.3 with CsOH) and one with low CsCl (CsCl reduced to 35 mM and osmolarity adjusted with glucose). For recordings involving cysteine cross-linking, control and agonist solutions were supplemented with 1 mM DTT to reduce disulfide bonds or 10 µM CuCl and 30 µM 1--10-phenanthroline (CuPhen) to promote disulfide formation^[@CR45]^. The effects of CuPhen were fully reversible by 1 mM DTT. Recordings were made from outside-out patches at 22--25 °C using an Axopatch 200A amplifier (Molecular Devices). Currents were recorded at --60 mV, low-pass filtered at 10 kHz, and digitized at 20 kHz, except for recordings to assess activation noise which were digitized at 100 kHz (Digidata 1440A interface with pClamp 10 software; Molecular Devices). Patches with small responses were filtered at 2 kHz to more readily identify single-channel openings, and digitized at 10 kHz.
Rapid agonist application to excised patches {#Sec13}
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Rapid agonist application was achieved by switching between continuously flowing solutions. Solution exchange was achieved by moving an application tool made from theta glass (Hilgenberg; 2 mm outer diameter, pulled to a tip opening of ∼200 μm) mounted on a piezoelectric translator (Physik Instrumente). At the end of each experiment, the adequacy of the solution exchange was tested by destroying the patch and measuring the liquid-junction current at the open pipette (10--90% rise time typically 150--250 μs).
Data analysis {#Sec14}
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Entry into desensitization (100 ms application of 10 mM glutamate) and current deactivation (1 ms) were fitted with the sum of two exponentials using IGOR Pro 6.35 (Wavemetrics) with NeuroMatic^[@CR62]^ and the weighted time constant (*τ*~w~) calculated. Recovery from steady-state desensitization was measured following a 100 ms equilibrating application of 10 mM glutamate. The recovery of glutamate-activated peak currents was measured following 2--200 ms intervals in control solution.
Records used for single-channel analysis were filtered at 0.5 kHz and individual channel events were selected by eye. Channel openings were analyzed using QuB (ver. 2.0.0.7; <https://qub.mandelics.com>). The amplitude of the resolved openings was measured from the closing transition (final current level to steady-state current). Measured openings (at --60 mV) were binned by conductance and fitted using a multi-peak Gaussian function (IGOR Pro).
NSFA was performed on the decaying phase of currents evoked by 1 or 100 ms applications of 10 mM glutamate (35--300 successive applications), as previously described^[@CR36]^. The variance for each successive pair of current responses was calculated and the single-channel current (*i*) and total number of channels (*N*) were then determined by plotting the ensemble variance (*σ*^2^) against mean current ($\documentclass[12pt]{minimal}
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\begin{document}$$\bar I$$\end{document}$) and fitting with a parabolic function:$$\documentclass[12pt]{minimal}
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\begin{document}$${\mathrm{\sigma }}_{}^2 = i\bar I - \bar I^2/N + {\mathrm{\sigma }}_{\mathrm{B}}^2,$$\end{document}$$where *σ*~B~^2^ is the background variance^[@CR63]^. For NSFA of current activation, records were digitized at a high sampling rate (100 kHz) to ensure sufficient numbers of data points from the average record could be grouped into each of the ten amplitude bins. As alignment of traces on their rising phases (as used for deactivation and desensitization records) led to a distortion of activation noise, analysis was instead performed on unaligned traces (from sections of recording in which the time of the current onset was stable; Spearman Stability Analysis, NeuroMatic).
Experimentally determined shifts in reversal potentials following local exchange from the high to low CsCl solutions were compared to the calculated shifts (for purely Cs^+^-permeable and purely Cl^--^-permeable channels) determined using the equation:$$\documentclass[12pt]{minimal}
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\begin{document}$$V_{{\mathrm{rev}}} = \frac{{RT}}{F}{\mathrm{{ln}}}\frac{{a{\mathrm{Cs}}_{\mathrm{o}} + \left( {{\raise0.5ex\hbox{$\scriptstyle {P_{{\mathrm{Cl}}}}$}\kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {P_{{\mathrm{Cs}}}}$}}} \right)a{\mathrm{Cl}}_{\mathrm{i}}}}{{a{\mathrm{Cs}}_{\mathrm{i}} + \left( {{\raise0.5ex\hbox{$\scriptstyle {P_{{\mathrm{Cl}}}}$}\kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle {P_{{\mathrm{Cs}}}}$}}} \right)a{\mathrm{Cl}}_{\mathrm{o}}}},$$\end{document}$$where *V*~rev~ is the reversal potential measured at the peak or steady-state, *P*~Cl~/*P*~Cs~ is the permeability ratio of chloride relative to cesium and *a*Cs and *a*Cl are the activities of the ions in the intracellular (i) and extracellular (o) solutions^[@CR43]^. *F*, *R*, and *T* have their usual meanings. *a*Cs in the high CsCl solution was extrapolated from tabulated values to be 0.714 (<https://web.archive.org/web/20190228144112/http://www.kayelaby.npl.co.uk/chemistry/3_9/3_9_6.html>). *a*Cs in the low CsCl solution was estimated to be 0.824. This value has a small degree of uncertainty, as the effect of glucose---demonstrated to modestly affect *a*Na in NaCl solutions^[@CR64]^---is unknown. Our chosen value assumes a similar effect of glucose on the activities of both NaCl and CsCl. Seals were formed and patches obtained in the standard NaCl external solution. The two experimental CsCl solutions were applied locally (interleaved) while the bath was continuously perfused with standard external. No correction was applied for liquid-junction potentials.
Kinetic modeling {#Sec15}
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Kinetic simulations and fits were performed in Scilab 5.5.0. (Scilab Enterprises; [https://www.scilab.org](http://www.scilab.org)) using the *Q*-matrix method^[@CR65]^. Rate constants were adapted from our previous model for GluA1/γ-2 (refs. ^[@CR25],[@CR26]^). For each iteration of the rate constants, currents were calculated from the occupancies of all conducting states at given time points multiplied by their unitary current. Noise was calculated using the following equation:^[@CR66]^$$\documentclass[12pt]{minimal}
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\begin{document}$${\mathrm{\sigma }}^2 = i^2Np\left( {1 - p} \right),$$\end{document}$$where *N* is the number of channels of unitary current *i* of open probability *p*. The ensemble variance for a channel with multiple subconductances was calculated as the sum of the variances for each state:$$\documentclass[12pt]{minimal}
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\begin{document}$${\mathrm{\sigma }}^{\mathrm{2}} = N\mathop {\sum }\limits_{{{j}} = 1}^{{k}} \left( {i_{{j}}^2p_{{j}}(1 - p_{{j}})} \right)N,$$\end{document}$$where *k* is the number of conducting states, *j* refers to each conducting state, and *i*~*j*~ and *p*~*j*~ are its unitary current and occupancy respectively. *N* was re-derived from the experimentally measured peak current as well as the peak open probability and conductance of each state for each iteration of the fit. Kinetics and noise of desensitization, deactivation, and activation, across six patches from which all properties could be measured, were normalized, averaged, and fit using Scheme 1 (Fig. [5](#Fig5){ref-type="fig"}). Kinetic data were parsed (to 35 data points) to make computation manageable. While all variables contributed to the model output, certain rates were strongly influenced by particular aspects of the data: *k*~1~---activation kinetics; *k*~−1~---deactivation kinetics; *α*, *β*---activation kinetics, steady-state current, and current--variance relationships; *γ*~1~, *δ*~1~, *γ*~2~, and *δ*~2~---desensitization kinetics and steady-state current; *γ*~0~, *δ*~0~---current--variance relationships and desensitization; open channel conductance---all current--variance relationships; desensitized conductance---current--variance relationship of desensitization. Rate constant *k*~--2~ was constrained by microscopic reversibility.
Expression and purification of ligand-binding cores {#Sec16}
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Cysteine mutants of the GluA2 flop S1S2-binding core with an N-terminal octahistidine tag in the pET22b vector^[@CR12]^ were produced using standard PCR protocol (see Supplementary Table [1](#MOESM1){ref-type="media"}). Following transformation of Origami B cells (VWR; 71408--3), high levels of protein were expressed by induction with 0.5 mM IPTG when the cells had reached OD~600~ \~1.2. The cells were harvested by centrifugation following overnight incubation at 20 °C. Harvested cells were washed once with PBS and resuspended in HisTrap binding buffer (50 mM Tris, pH 8; 150 mM NaCl; 20 mM imidazole; protease inhibitor cocktail (Roche), and 50 µM NBQX to displace glutamate and promote dimerization). Resuspended cells were treated with lysozyme for 30 min at 4 °C and cell membranes were disrupted by sonication and removed by centrifugation. Samples were filtered (0.45 µm) to remove residual cellular debris and loaded onto a HisTrap Column (GE Healthcare) at 4 °C. Protein was eluted using HisTrap elution buffer (50 mM Tris pH 8; 150 mM NaCl; 300 mM imidazole) and aliquots containing the highest concentrations of dimers were pooled for further purification. Parallel reducing and non-reducing SDS-PAGE and Coomassie blue staining established that ligand-binding cores preferentially formed cross-linked dimers with no need for exogenous oxidization. Protein was concentrated using 10 kDa concentrators before exchanging into column buffer (50 mM Tris, pH 8; 150 mM NaCl). Histidine tags were cleaved using thrombin. A final purification step (in column buffer) was performed with a size exclusion column (Superdex 200; GE Healthcare, Little Chalfont, UK). Final purified AMPAR LBDs were concentrated to 2--7 mg ml^--1^.
Protein crystallography {#Sec17}
-----------------------
Crystallization was achieved using sitting drop vapor diffusion at 16 °C. All crystals appeared within 72 h, and were harvested after 1--2 weeks. For each crystal, precipitant solutions, and additives for cryoprotection prior to freezing, differed. GluA2 S729C~NBQX~: 0.1 M tri-sodium citrate pH 5.5, 20% PEG 3000. Supplemented with 15% glycerol for cryoprotection. GluA2 S729C~ZK~/GluA2 G724C~ZK~: 0.2 M ammonium chloride, 20% PEG 3350, 10 µM ZK200775. Supplemented with 15% glycerol for cryoprotection. GluA2 G724C~glu~ Form A: 1 M lithium chloride, 0.1 M citric acid pH 4.0, 20% (w/v) PEG 6000, 30 mM glutamate. Supplemented with 20% glycerol for cryoprotection. GluA2 G724C~glu~ Form B: 0.16 M calcium acetate, 0.08 M sodium cacodylate pH 6.5, 14.4% (w/v) PEG 8000, 20% (v/v) glycerol, 1 mM glutamate. No additives necessary for cryoprotection.
Diffraction data were collected at Diamond Light Source beamlines I04 and I24, and at ESRF ID30B (see Supplementary Table [2](#MOESM1){ref-type="media"}). Diffraction data were initially processed using Xia2 (ref. ^[@CR67]^) and AIMLESS^[@CR68]^. Initial molecular replacement was performed using Phaser^[@CR69]^ and structures were refined using PHENIX^[@CR70]^ and *Coot*^[@CR71]^. Structures G724C~ZK~, S729C~NBQX~, and S729C~ZK~ were solved using the ZK200775-bound wild-type LBD (PDB 3KGC)^[@CR13]^ as the search model. Both forms of G724C~glu~ were solved using the glutamate-bound wild-type LBD (PDB 1FTJ)^[@CR12]^ as the search model. Cysteines were modeled into cryo-EM structures of GluA2(R)/γ-2 in the activated and desensitized forms using PyMOL (The PyMOL Molecular Graphics System, Version 2.0 Schrödinger, LLC), and the separation of the sulfur atoms was determined. The separation of Cα Pro632 atoms in LBD structures was also measured using PyMOL.
Data presentation and statistical analysis {#Sec18}
------------------------------------------
Summary data are presented in the text as mean ± s.e.m. (from *n* patches). Comparisons involving two data sets only were performed using a paired *t-*test or unpaired Welch two-sample *t-*test that does not assume equal variance (normality was not tested statistically, but gauged from quantile--quantile (Q--Q) plots and/or density histograms). Comparisons of multiple conditions were performed using two-sided Welch two-sample *t-*tests with Holm's sequential Bonferroni correction. When comparing Q and R edited forms of AMPARs, analyses were performed using two-way analysis of variance (Welch heteroscedastic *F-*test) followed by pairwise comparisons using two-sided Welch two-sample *t*-tests. Exact *P* values are presented to two significant figures, except when *P* *\<* 0.0001. Statistical tests were performed using R (version 3.3.3, the R Foundation for Statistical Computing, [https://www.r-project.org/](http://www.r-project.org/)) and R Studio (version 1.1.383, RStudio). Independent-samples confidence intervals for the differences between two population means were obtained using a bias-corrected and accelerated (BCa) bootstrap method in R^[@CR72]^. No statistical test was used to predetermine sample sizes; these were based on standards of the field. No randomization was used. A full list of statistical analyses is provided in Supplementary Table [3](#MOESM1){ref-type="media"}.
Reporting summary {#Sec19}
-----------------
Further information on research design is available in the [Nature Research Reporting Summary](#MOESM2){ref-type="media"} linked to this article.
Supplementary information
=========================
{#Sec20}
Supplementary Information Reporting Summary Source Code Source Code
Source Data
**Peer review information** *Nature Communications* thanks Lonnie P Wollmuth, Wei Lu, and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.
**Publisher's note** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
=========================
**Supplementary information** accompanies this paper at 10.1038/s41467-019-12280-9.
This work was supported by the MRC (MR/J002976/1 to S.G.C.-C. and M.F. and MR/J012998/1 to M.F. and S.G.C-C.), the Wellcome Trust (086185/Z/08/Z to S.G.C.-C. and M.F.) and the BBSRC (BB/N015274/1 to M.G.G.). M.G.G. is a Wellcome Trust and Royal Society Sir Henry Dale fellow (104194/Z/14/Z). We thank Ingo Greger for providing the GluA2 LBD expression vector, and Trevor Smart, Duncan Laverty, and Ambrose Cole for assistance with crystallography. We thank Mark Mayer for discussion and for comments on an earlier version of the manuscript.
I.D.C., D.S., T.P.M., M.G.G., M.F. and S.G.C.-C. designed the experiments. I.D.C., D.S. and T.P.M. performed the experiments. I.D.C., D.S., T.P.M., M.G.G., and M.F. analyzed the data. I.D.C., M.G.G., M.F. and S.G.C.-C. interpreted the results. I.D.C. and M.F. prepared the figures. I.D.C., M.F. and S.G.C.-C. wrote the manuscript with input from all authors.
Data supporting the findings of this manuscript are available from the corresponding authors upon reasonable request. The data underlying Fig. [1](#MOESM5){ref-type="media"}c, d, f, [4c--e](#MOESM5){ref-type="media"} and Supplementary Figs [1](#MOESM5){ref-type="media"}c and [2b](#MOESM5){ref-type="media"} are provided as a Source Data file. The coordinate and structure factor data for the GluA2 LBD crystals have been deposited in the Protein Data Bank (PDB) with the following accession codes: S729C~NBQX~, 6FQH; S729C~ZK~, 6FQK; G724C~ZK~, 6FQJ; G724C~glu~ Form A, 6FQG; G724C~glu~ Form B, 6FQI.
Computer code demonstrating example calculations for the current and non-stationary fluctuation analysis presented in Fig. [5](#Fig5){ref-type="fig"} is available from the UCL Research Data Repository: 10.5522/04/8797892.
The authors declare no competing interests.
|
1. Introduction {#sec1-foods-09-00324}
===============
*Saccharomyces cerevisiae* (typically known as baker's yeast) is a single-cell eukaryote that is often utilized in research. *S. cerevisiae* has proven to be an ideal organism for research applications especially after releasing its genome sequence was released to the scientific community \[[@B1-foods-09-00324],[@B2-foods-09-00324]\]. This yeast can be stored, and its genome sequence and translated proteins are similar in action to those of other organisms. Its proteome contains cell cycle and signaling proteins \[[@B3-foods-09-00324]\]. In the past few years, biologically active peptides have been produced in different sources such as food, plants, animals and microorganisms. Many studies have focused on the production, isolation, and purification of the antimicrobial peptides \[[@B4-foods-09-00324]\].
Antimicrobial peptides (AMPs) are small oligopeptides (AMPs) that typically contain 10--100 amino acids, with a net positive charge and an amphipathic structure \[[@B5-foods-09-00324]\]. Antimicrobial peptides have a broad spectrum of inhibition activity against microorganisms such as bacteria, molds, yeasts, parasites, and some viruses. Many living organisms such as microorganisms, invertebrates, and other species belonging to the animal and plant kingdoms produce antimicrobial peptides \[[@B6-foods-09-00324]\]. In addition, bioactive peptides produced during the fermentation process by different microorganisms have been used as antibacterial, antioxidant, antihypertensive, anticancer, and immunomodulatory agents, in addition to containing lipid-reducing properties \[[@B7-foods-09-00324]\]. Several studies have investigated the production of antimicrobial peptides from lactic acid, however, few studies focus on the production of antimicrobial peptides from yeasts in a medium \[[@B7-foods-09-00324],[@B8-foods-09-00324]\].
In previous studies, metabolic compounds of *Saccharomyces boulardii* were separated and examined against 26 bacterial isolates in order to study the compounds' antimicrobial activity. The extracted peptide from *Saccharomyces boulardii* has ben shown to exhibit high inhibition activity toward *Bacillus cereus* \[[@B9-foods-09-00324]\].
It has been reported that some *S. cerevisiae* strains have the ability to produce antimicrobial peptides. Recent studies demonstrated that the isolated *S. cerevisiae* CCMI 885 produced small peptides (\<10 kDa) that exhibit antimicrobial activity against some yeasts such as *Hanseniaspora guilliermondii*, *Torulaspora delbrueckii*, *Kluyveromyces marxianus,* and *Lachancea thermotolerans* \[[@B10-foods-09-00324]\]. The ultrafiltration process with a 10 kDa cut-off was used to extract the antimicrobial peptide from *Candida intermedia* after growth on YPD agar at 28 °C over 7 days. The molecular weight of the peptide was 5 kDa exhibiting an inhibition activity against *Brettanomyces bruxellensis* \[[@B11-foods-09-00324]\].
Several authors have noted alternate strategies for biocontrol, such as the use of peptide-based killer toxins. For example, *Saccharomyces cerevisiae* produces peptide-based killer toxins that are able to inhibit the growth of different species of bacteria \[[@B12-foods-09-00324]\]. Similar results were reported for bioactive peptide production by *S. cerevisiae* CCMI 885 at 30 °C for 48 h. These peptides were used to inhibit the growth of some wine-related yeasts \[[@B8-foods-09-00324]\]. Past research including both in vitro and in vivo studies indicated that *Saccharomyces cerevisiae* inhibited intestinal tract infections from *Bacillus subtilis*, *B. cereus*, *Escherichia. coli*, *Proteus vulgaris*, *Pseudomonas aeruginosa*, *Salmonella typhimurium*, *Salmonella typhi*, *Staphylococcus aureus*, *Yersinia enterocolitica*, and some yeasts such as *Candida albicans* \[[@B13-foods-09-00324]\].
*Saccharomyces cerevisiae* yeast exhibits antibacterial activity against *E. coli*, *Pseudomonas* sp. *Salmonella* sp., *Staphylococcus aureus,* and *Vibrio cholera.* In addition, this yeast strain has antimicrobial activity against other pathogenic bacteria species, yeasts, and molds \[[@B14-foods-09-00324]\]. Many studies have described the effect of these antimicrobial activities on inhibition zones (zones free of growth).
To date, however, very limited information is available about bioactive peptides from *Saccharomyces cerevisiae*. Thus, the aim of this study was to investigate the antimicrobial components from a full extract of *Saccharomyces cerevisiae,* isolate antibacterial peptides, and test their thermostability characteristics which are very important aspect in food production including for sterilization and thermal processes.
2. Materials and Methods {#sec2-foods-09-00324}
========================
2.1. Microbial Strains {#sec2dot1-foods-09-00324}
----------------------
*Saccharomyces cerevisiae* ATCC 36858 was obtained from a local scientific store in Basrah, Iraq. *Bacillus subtilis* ATCC 23857, *E. coli* ATCC 25922, *Klebsiella aerogenes* ATCC 13048, and *Staphylococcus aureus* ATCC 25923 were supplied by the Food Science Department/College of Agriculture/University of Basrah, Iraq and used as indicator strains.
2.2. Antibacterial Peptide Production {#sec2dot2-foods-09-00324}
-------------------------------------
First, 1 mL (6 log cfu/mL) of activated yeast (36 h) was added to 250 mL of glucose yeast peptone broth (GTPB) medium (Himedia, Mumbai, India) and incubated at 20, 25, 30, and 35 °C for 24, 48, 72, and 96 h, respectively. After incubation, *S. cerevisiae* cells were removed by centrifugation at 6000 rpm for 20 min at 4 °C, and the cell free yeast supernatant was filtered with 0.45 µm cellulose acetate membranes (Merck company, Watford, UK) \[[@B9-foods-09-00324]\]. In order to isolate the peptides that were released from the yeast in the medium, the filtered metabolic yeast extract was passed through ultrafiltration membranes with pore sizes of 10 kDa (cut-off 10 kDa, Millipore and Amicon, USA) and then concentrated (100-fold) with 2 kDa (cut-off 2 kDa) membranes. The concentrated metabolic yeast extract was lyophilized by freeze-drying (Heto Lab Equipment, Denmark). Next, 100 mg/mL of lyophilized metabolic yeast was tested against four indicator strains (*Bacillus subtilis* ATCC 23857, *E. coli* ATCC 25922, *Klebsiella aerogenes,* and *Staphylococcus aureus* ATCC 25923) using the agar well diffusion agar method, and then 100 µL of lyophilized peptide was added to the wells (6 mm) in Nutrient agar (Himedia, Mumbai, India). After incubation, the clear zones were measured in millimeters \[[@B15-foods-09-00324],[@B16-foods-09-00324]\].
2.3. Purification of the Antibacterial Peptide from Yeast {#sec2dot3-foods-09-00324}
---------------------------------------------------------
An ÄKTA Pure 25 System (GE Healthcare Life Sciences, Germany) was used to purify the antibacterial peptides from lyophilized metabolic extracts of *S. cerevisiae*. The specific column Superdex 200 (10/300GL) was used with a column volume set at 23.562 mL and a column diameter set at 10 mm with a pressure of 1.5 MPa. The column was filled with agarose and dextran. A 0.5 M acetate phosphate buffer (pH 5.0) at 0.5 mL/min was used for elution, and a 280 nm UV detector was used to determine the isolated peaks \[[@B17-foods-09-00324],[@B18-foods-09-00324]\]. Peak fractions were collected, and the antibacterial activity against two indicator strains (*E. coli* ATCC 25922 and *Staphylococcus aureus* ATCC 25923) was determined.
2.4. Characterization of the Antibacterial Peptide {#sec2dot4-foods-09-00324}
--------------------------------------------------
### 2.4.1. Thermal Stability of the Antibacterial Peptide {#sec2dot4dot1-foods-09-00324}
To determine the thermal stability of the extracted antibacterial peptide from *S. cerevisiae,* 5 mL (10 mg/mL) of the active peptide was heated at 50, 60, 70, 80, 90, 100, 110, and 120 °C for 30 min. The antibacterial activity was estimated by the agar well diffusion agar activity against *E. coli* ATCC 25922 and *Staphylococcus aureus* ATCC 25923. Next, 100 μL of the extracted bioactive peptide was transferred to three wells in a Petri dish containing a Nutrient agar medium. The non-heated bioactive peptide was used as a control sample. The percentage of antibacterial activity was calculated using the following equation: where Ac is the inhibition zone of control sample, and As is the inhibition zone of test sample.
### 2.4.2. pH Stability of the Antibacterial Peptide {#sec2dot4dot2-foods-09-00324}
The lyophilized purified antibacterial peptide from *S. cerevisiae* was dissolved in distilled water at 10 mg/mL and adjusted with 1N NaOH or 1N HCl to different pH values of 2, 3, 4, 5, 6, 7, 8, 9, and 10. After incubation for 24 h at 4 °C and 25 °C, the solutions containing the samples were adjusted to pH 7.0 ± 0.02 with a 0.5 M sodium citrate buffer. The inhibition activity of the peptide was then determined using the agar well diffusion agar method against *E. coli* ATCC 25922 and *Staphylococcus aureus* ATCC 25923. After incubation for 24 h at 37 °C, the percentage of antibacterial activity was calculated \[[@B19-foods-09-00324]\].
### 2.4.3. Molecular Weight of the Antibacterial Peptide {#sec2dot4dot3-foods-09-00324}
The molecular weights of the antibacterial peptide extracted from *S. cerevisiae* were analyzed using sodium dodecyl sulphate with 15% polyacrylamide gel electrophoresis (SDS-PAGE) as described by Judd \[[@B20-foods-09-00324]\]. Then, 1 mg/mL of the antibacterial peptide and standard proteins (α-Lactalbumin 14.4 kDa, Aprotinin 6.5 kDa, Glucagon 3.8 kDa, and Insulin-A 2.5 kDa) (Promega Company, Madison, WI, USA) were dissolved in a phosphate buffer and transferred to a vertical slab chamber (10 cm × 10 cm × 0.6 mm). The gel was run at 50 mA and 50--70V for 3 h. The molecular weight of the extracted antibacterial peptide was determined after the relative mobility (Rm) of the antibacterial peptide and marker proteins were determined per the following equation:
Rm = the traveled distance of the peptide or marker proteins/traveled distance of methylene blue dye
2.5. Mode of Action {#sec2dot5-foods-09-00324}
-------------------
The modes of action (bacteriostatic) of the extracted antibacterial peptide from *S. cerevisiae* were assayed as described by \[[@B10-foods-09-00324]\]. The 6 log cfu/mL cultures of four indicator strains were cultivated into 100 mL of Nutrient broth (Himedia, Mumbai, India). The lyophilized purified antibacterial peptide was added to the indicator strain cultures at a final concentration of 0.01% (*w:v*). The samples and the control sample (without antibacterial peptide) were incubated at 37 °C. Indicator strain suspensions were taken at 3, 6, 12, 18, and 24 h, and the absorbance was measured by spectrophotometry (Sunny UV.7804C, Tokyo, Japan) at OD~600~. The viable bacteria cells were determined on the nutrient agar at various incubation periods \[[@B12-foods-09-00324],[@B21-foods-09-00324]\].
2.6. Statistical Analysis {#sec2dot6-foods-09-00324}
-------------------------
Statistical analyses of the different treatments cited above were conducted using the SPSS Statistics V22.0 (Statistical Package for Social Sciences, San Antonio, TX, USA). An analysis of the variance (ANOVA table) of the data was conducted and means for treatment values were analyzed (*p* ≤ 0.05) with least significant difference (LSD). Differences were considered significant at *p* ≤ 0.05.
3. Results and Discussion {#sec3-foods-09-00324}
=========================
3.1. Optimum Conditions of for Antibacterial Peptides Production {#sec3dot1-foods-09-00324}
----------------------------------------------------------------
Both gram-negative bacteria tested including *E. coli* and *Klebsiella aerogenes* were inhibited by the presence of the antibacterial peptides produced from *Saccharomyces cerevisiae* in all the conditions tested (at the four time points and four different temperatures). This was not the case when testing the other two gram-positive bacteria including *Bacillus subtilis* and *Staphylococcus aureus,* which better tolerated the presence of the antibacterial peptides produced from *Saccharomyces cerevisiae.* This could be explained in part by the presence of cell walls comprised of thick layers of peptidoglycan in the case of Gram-positive bacteria. However, Gram-negative bacteria are known to have cell walls with a thin layer of peptidoglycan. The optimum conditions for the production of active peptides from yeast were 25--30 °C for 48 h, resulting in the highest inhibition towards *E. coli* and *Klebsiella aerogenes*. At 20 °C and 35 °C, the detected antibacterial activity was negligible with no effect against the four indicator strains (*Bacillus subtilis*, *E. coli*, *Klebsiella aerogenes*, and *Staphylococcus aureus*) especially at 24, 72, and 96 h ([Table 1](#foods-09-00324-t001){ref-type="table"}).
3.2. Purification of the Antibacterial Peptide {#sec3dot2-foods-09-00324}
----------------------------------------------
The extracted yeast peptides were passed through super filtration membranes of 10 kDa and 2 kDa and then freeze-dried. For further purification of the antibacterial peptide fractions, an ÄKTA purifier system was employed. Three peaks appeared after the ÄKTA Pure treatment. Fractions of 21--22 mL (peak 2) and 23--25 mL (peak 3) did not show growth inhibition activity against the two tested bacterial strains, while fractions of 16--20 mL (peak 1) showed the highest growth inhibition ([Figure 1](#foods-09-00324-f001){ref-type="fig"}). The yield of the antibacterial peptide was 155 mg/100 mL of the culture medium. The inhibition zones were 24 and 20 mm for *E. coli* ATCC 25922 and *Staphylococcus aureus* ATCC 25923, respectively. Gram-negative bacteria (*E. coli*) appeared to be more sensitive to antibacterial peptide fractions than gram-positive (*S. aureus*) bacteria. These results were in agreement with Fakruddin et al. \[[@B13-foods-09-00324]\] who reported that Gram-negative bacteria were more sensitive to yeast peptides when compared to gram-positive bacteria. The inhibition activity of peptides increased proportionally with the α-helix of hydrophobic C-terminal peptides. This feature may be related to the composition of the amphipathic amino acids that are necessary for binding the bacterial cell membranes \[[@B19-foods-09-00324],[@B22-foods-09-00324]\].
3.3. Characterization of the Antibacterial Peptide {#sec3dot3-foods-09-00324}
--------------------------------------------------
### 3.3.1. Thermal Stability of the Antibacterial Peptide {#sec3dot3dot1-foods-09-00324}
The effect of temperature on the *S. cerevisiae* antibacterial peptide was determined ([Figure 2](#foods-09-00324-f002){ref-type="fig"}). The results showed that the antibacterial peptide from yeast was stable at different temperatures ranging from 50 to 90 °C during 30 min of treatment. Interestingly, an antibacterial activity of 93% and 95% for *E. coli* and *S. aureus* was sustained even at 100 °C during 30 min of treatment. After 120 °C for 30 min, the antibacterial activity of the peptide was 68% and 77% for *E. coli* and *S. aureus*, respectively. This thermostable property makes this antibacterial peptide suitable for use in sterilization and thermal processes. The thermal stability of this small peptide could be related to the nature and chemical structures of such peptides, including the primary protein's structure and with low molecular weight. Similar reports have shown that antibacterial peptides isolated from different microbial sources are able to persist at high temperatures without any change in the antimicrobial activity \[[@B23-foods-09-00324],[@B24-foods-09-00324]\].
### 3.3.2. Effect of pH on the Antibacterial Peptide {#sec3dot3dot2-foods-09-00324}
In order to address the pH properties including dependent and independent effects, the above fragments were estimated for antibacterial activity inhibition against two indicator strains; *E. coli* ATCC 25922 and *Staphylococcus aureus* ATCC 25923. The effects of the pH values on the stability of the antibacterial peptide from *S. cerevisiae* are shown in [Figure 3](#foods-09-00324-f003){ref-type="fig"}. An evaluation of the pH value stability revealed that the antibacterial peptide remained stable after 24 h at 4 °C and 25 °C at pH values ranging from 4.0 to 7.0.
The inhibition activity of the peptide with extreme pH values 2, 3, 8, 9, and 10 against bacterial strains was also tested ([Figure 3](#foods-09-00324-f003){ref-type="fig"}). Similar properties were previously studied for active peptides produced from yeasts, which were easily inactivated by strong acidic and alkaline conditions in different media. These characteristics limit the usage of peptides in food production with acidic and alkaline food. The antibacterial activity of this peptide was evaluated at different pH values at two temperatures (4 °C and 25 °C). The produced peptide was more effective at 4 °C within a pH range from 4 to 7 against the bacterial strains tested when compared to 25 °C. There was no significant difference (p \> 0.05) between samples of *S. aureus* when tested at 4 °C and 25 °C at pH value 2, while there was a significant difference (*p* \< 0.05) between samples of *E. coli* tested under the same conditions. In contrast, a significant difference (*p* \< 0.05) between samples of *S. aureus* and *E. coli* tested at 4 °C and 25 °C at a pH value of 2 was observed. Furthermore, the analysis showed the presence of significant differences (*p* \< 0.05) between samples of *S. aureus* tested at 4 °C and 25 °C at pH value 3. We also observed a significant difference (*p* \< 0.05) between samples of *E. coli* when tested at 4 °C and 25 °C at pH 3. When comparing the two bacterial strains, we observed the absence of any significant difference (*p* \> 0.05) between samples of *S. aureus* and *E. coli* tested at 4°C and pH 3. The presence of significant differences (*p* \< 0.05) between samples of *S. aureus* tested at 4°C at pH 10 were also observed. However, no significant differences (*p* \> 0.05) between samples of *S. aureus* tested at 25 °C and *E. coli* tested at 4 °C at pH value of 10 were observed. Interestingly, the lowest inhibition (%) value was observed in *E. coli* when tested at 25 °C and at pH 10.
Overall, the newly discovered produced peptide possessed high thermal stability and a wide range of pH stability when compared to other peptides produced from microorganisms (e.g., bacteriocins) as described in previous studies \[[@B25-foods-09-00324],[@B26-foods-09-00324]\]. Moreover, antibacterial peptides acting in neutral and acidic environments are expected to provide protection from many unacceptable microorganisms that grow in these environments, contaminating food and causing spoilage \[[@B27-foods-09-00324]\].
### 3.3.3. Molecular Weight of the Peptide {#sec3dot3dot3-foods-09-00324}
The purified antibacterial peptide from active fractions (peak1) was analyzed using SDS-PAGE and showed a single band. The molecular weight of the antibacterial peptide, as determined by relative mobility, was approximately 9770 Da ([Figure 4](#foods-09-00324-f004){ref-type="fig"}), which is similar to the small molecular weight of other isolated peptides from *Klebsiella pneumonia,* as described in previous studies \[[@B28-foods-09-00324]\]. Thus, our results strongly suggest that peak 1 (9770Da) correspond to this peptide and might match the antibacterial activity produced by *S. cerevisiae* and thus be responsible for the bioactive activity shown against the different bacterial strains tested. In this sense, to better understand the role of molecular weight distribution in the inhibition of antibacterial activity of brewer's yeast, a fraction analysis using ultrafiltration with 10 kDa cutoff membranes was performed. The results showed that 3--10 kDa fractions were fundamentally comprised of smaller peptides with biological activity, which is in agreement with past studies that indicated that antibacterial peptides are small peptides \[[@B9-foods-09-00324]\].
3.4. Mode of Action {#sec3dot4-foods-09-00324}
-------------------
The antibacterial peptide effect of *S. cerevisiae* on cell viability (kill time) from four indicator strains is shown in [Figure 5](#foods-09-00324-f005){ref-type="fig"}. The antibacterial peptide reduced the viability of target bacteria compared to the control sample. The antibacterial peptide's efficacy depended on both the concentration of added peptide and exposure time. Additionally, the movement of small peptide and their spread during agar well diffusion appeared 3 h following the addition of the antibacterial peptide with 5.8, 5.5, 5.6, and 5.8 log (cfu/mL) reduction of *B. subtilis*, *E. coli*, *K. aerogenes,* and *S. aureus*, respectively. The statistical analysis of log (cfu/mL) reduction for each bacteria strain was estimated at interval times of 3, 6, 12, 18, and 24 h. The result showed that the antibacterial peptide effect on decreasing the viable cell counts was significant (*p* \< 0.05) between the control samples and all four bacterial strains among the five interval times tested. In contrast, there was no significant difference (*p* \> 0.05) between either Gram-positive strains or Gram-negative strains. In addition, the peptide's inhibition effect on Gram-negative strains was highly significant (*p* \> 0.05) when compared with Gram-positive strains. After 24 h of incubation, the peptide's inhibition effect on Gram-negative strains was high compared with that of Gram-positive strains. The antibacterial peptide caused a decrease in the viable cell counts of gram-negative strains ranging from 2 to 2.3 log. units along the evaluated times in comparison to gram-positive strains which ranged from 1.5 to 1.8 log. units. The kill-time of this peptide was in agreement with that from earlier reports \[[@B29-foods-09-00324],[@B30-foods-09-00324]\]. The mode of action of antimicrobial peptides fundamentally depends on the reaction of bioactive peptides with the membrane of bacteria cells and the cells' internal composition \[[@B31-foods-09-00324]\]. Generally, the antimicrobial peptides were effective due to the electrostatic reaction with the cell membranes. In order to understand the mechanism behind antimicrobial peptides, the results of various methods have suggested that adsorption of bioactive peptides will occur on the bacterial cell membrane, leading to complete damage to the membrane. For example, the brave straw model, aggregate model, carpet model, and toroid pore model are critically considered models of bioactive peptides as antibacterial compounds \[[@B27-foods-09-00324],[@B32-foods-09-00324]\].
4. Conclusions {#sec4-foods-09-00324}
==============
*S. cerevisiae* belongs to the eukaryotic kingdom is nonpathogenic, and due to its long history of use in the production of consumable products such as ethanol, many baked products, and pastries, it has been classified as a generally regarded as safe organism (GRAS). In this study, antibacterial peptide was produced and isolated from *Saccharomyces cerevisiae* (Baker's yeast) by an ultrafiltration process (two membranes with cut-offs 2 and 10 kDa) and purified using the ÄKTA Pure 25 system. The antibacterial peptide activity was then characterized and studied against four bacterial strains. The results showed that the peptide produced by *Saccharomyces cerevisiae* had a molecular weight of 9.77 kDa and exerted inhibition activity against both Gram-negative and Gram-positive bacteria. The produced peptide was more effective at 4 °C within a pH range of 4-7 against the bacterial strains tested when compared to 25 °C, while the lowest inhibition (%) was observed in *E. coli* when tested at 25 °C and at a pH value of 10. In addition, the peptide was thermostable and steady with pH values ranging from 4--7, which is a very important aspect in food production for sterilization and thermal processes. The isolated antibacterial peptide demonstrated its potential as a bio-preservative in food manufacturing. Although the current study isolated a peptide containing a novel bioactive compound from *Saccharomyces cerevisiae*, additional research regarding the amino acid sequence and structure of this antibacterial peptide is warranted.
Investigation, S.T.G.A.-s.; designing and planning the experiments, A.B.A.; Supervision, A.J.A.A.-M.; Methodology, A.K.N.; Writing-review & editing, N.L.; Writing original draft, S.A.I. All authors have read and agreed to the published version of the manuscript.
This research received no external funding.
The authors declare no conflicts of interest.
{#foods-09-00324-f001}
{#foods-09-00324-f002}
{#foods-09-00324-f003}
######
The molecular weight of antibacterial peptide production from *Saccharomyces cerevisiae* was determined by electrophoresis method. (**A**) Sodium dodecylsulfate polyacrylamide gel electrophoresis of standard proteins and the antibacterial peptide. (**B**) Relative mobility of standard proteins and the antibacterial peptide.
{#foods-09-00324-f005}
foods-09-00324-t001_Table 1
######
The optimum conditions for antibacterial peptides produced from Saccharomyces *cerevisiae.*
Strains 24 h 48 h 72 h 96 h
------------------------------------ ------ ------ ------ ------ ---- ----- ----- ----- ---- ---- ---- ---- ---- ---- ---- ----
*Bacillus subtilis* ATCC 23857 \- \- \+ \+ \+ \+ ++ ++ \- \- \+ \+ \- \- \+ \-
*Escherichia coli* ATCC 25922 \+ \+ ++ \+ ++ +++ +++ ++ \+ \+ ++ \+ \+ \+ \+ \-
*Klebsiella aerogenes* ATCC 13048 \+ \+ ++ ++ ++ +++ +++ +++ \+ ++ ++ ++ \+ \+ ++ \+
*Staphylococcus aureus* ATCC 25923 \- \- \+ \+ \+ \+ ++ \+ \- \- \+ \- \- \- \+ \-
Diameter of inhibition zone (mm): +++: 16--20; ++: 12--16; +: 8--12; −:no inhibitory activity (including the 6mm diameter of each well).
|
NOT RECOMMENDED FOR FULL-TEXT PUBLICATION
File Name: 12a0985n.06
No. 11-5902
UNITED STATES COURT OF APPEALS FILED
FOR THE SIXTH CIRCUIT Sep 07, 2012
DEBORAH S. HUNT, Clerk
NATASHA BROOKS; ETHEL BROOKS, dba )
Full Line Maintenance, dba Plumline Dining, )
Tots and Volunteer Temp, )
)
Plaintiffs, )
)
ISAAC BROOKS, Full Line Maintenance, dba )
Plumline Dining, dba Tots and Volunteer Temp, ) ON APPEAL FROM THE UNITED
) STATES DISTRICT COURT FOR
Plaintiff-Appellant, ) THE WESTERN DISTRICT OF
) TENNESSEE
v. )
)
WHIRLPOOL CORPORATION; MAYTAG )
CORPORATION; JANICE PAGE )
HOLLINGSWORTH; GARY )
HOLLINGSWORTH, )
)
Defendants-Appellees. )
)
Before: MARTIN and WHITE, Circuit Judges; ECONOMUS, District Judge.*
PER CURIAM. Isaac Brooks, a pro se Tennessee resident, appeals a district court judgment
dismissing his civil action alleging violations of the Racketeer Influenced and Corrupt Organizations
Act (RICO), 18 U.S.C. § 1961, et seq.; negligent supervision; negligent retention; and breach of
contract.
*
The Honorable Peter C. Economus, United States Senior District Judge for the Northern
District of Ohio, sitting by designation.
No. 11-5902
-2-
In December 2004, Brooks, doing business as Temp Owned Temporary Service (TOTS), a
Tennessee Corporation doing business in Madison County, Tennessee, entered into a service
agreement with Maytag, which was later purchased by Whirlpool Corporation. In 2010, Brooks,
doing business as TOTS, filed a civil action against Whirlpool, Gary Hollingsworth, and Janice
Hollingsworth (husband and wife). Brooks alleged that from 1993 to 2008, he was forced to pay
more than one million dollars to Gary Hollingsworth in kickbacks, which had been demanded by
Janice Hollingsworth, who was a Whirlpool Human Resource Manager, in order to protect Brooks’s
business relationship. Brooks’s amended complaint alleged conspiracy and RICO violations by the
Hollingsworths; negligent supervision and retention by Whirlpool; and breach of contract.
The defendants filed a motion to dismiss the complaint on res judicata grounds. In 2008,
“T.O.T.S., Inc.” had filed a complaint against Whirlpool and Janice Hollingsworth in the Circuit
Court of Madison County, Tennessee, alleging a breach of contract and sought to recover improper
payments. The state court dismissed the action finding that T.O.T.S., Inc. had its corporate charter
revoked in 1998, prior to entering into the service agreement with Whirlpool in 2004. As a result,
T.O.T.S., Inc. could not state a claim for breach of contract because it was conducting business in
violation of state law at the time the contract was allegedly formed. The state court also denied a
request to substitute Brooks as a “real party in interest.” T.O.T.S., Inc. appealed and the Tennessee
Court of Appeals affirmed the trial court’s decision. T.O.T.S. v. Whirlpool Corp., No. W2009-
01855-COA-R3-CV, 2009 WL 4878585, at *4 (Tenn. Ct. App. Dec. 18, 2009).
Brooks filed a response to the defendants’ motion to dismiss asserting that res judicata was
not applicable to the case. After consideration, the district court concluded that Brooks’s federal
complaint was barred by the doctrine of res judicata and dismissed the case.
The doctrine of res judicata includes two kinds of preclusion: “issue preclusion” and “claim
preclusion.” Migra v. Warren City Sch. Dist. Bd. of Educ., 465 U.S. 75, 77 n.1 (1984). Issue
preclusion is when a judgment forecloses “relitigation of a matter that has been litigated and
No. 11-5902
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decided.” Id. “Claim preclusion refers to the effect of a judgment in foreclosing litigation of a
matter that never has been litigated, because of a determination that it should have been advanced
in an earlier suit.” Id.
Under Tennessee law, a party asserting a res judicata defense “must demonstrate (1) that a
court of competent jurisdiction rendered the prior judgment, (2) that the prior judgment was final and
on the merits, (3) that both proceedings involved the same parties or their privies, and (4) that both
proceedings involved the same cause of action.” Young v. Barrow, 130 S.W.3d 59, 64 (Tenn. Ct.
App. 2003). The district court’s judgment is reviewed de novo. Kane v. Magna Mixer Co., 71 F.3d
555, 560 (6th Cir. 1995).
On appeal, Brooks challenges the district court’s findings as to the second, third, and fourth
prongs of Tennessee’s four-part res judicata test. With respect to prong two, Brooks asserts that his
state court suit was dismissed because T.O.T.S., Inc. lacked standing to bring the action. He asserts
that a dismissal for lack of standing is a jurisdictional ruling and does not operate as a judgment “on
the merits.”
Brooks’s argument on this point is unavailing because the state court’s order granting the
defendant’s motion to dismiss, and dismissing the case with prejudice, stated that “the Court finds
that the Plaintiff cannot state a cause of action for breach of contract,” not that the case was being
dismissed for lack of standing. Accordingly, the district court properly concluded that the state
court’s dismissal was an adjudication “on the merits” pursuant to state law. See Dyer v. Intera
Corp., 870 F.2d 1063, 1067 (6th Cir. 1989).
With respect to prong three, Brooks asserts that the state cause of action does not involve the
same parties as the federal cause of action and that he is not a privy of T.O.T.S., Inc. “In the context
of both res judicata and collateral estoppel, the concept of privity relates to the subject matter of the
litigation.” State ex rel. Cihlar v. Crawford, 39 S.W.3d 172, 180 (Tenn. Ct. App. 2000) (citations
No. 11-5902
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omitted). “Privity connotes an identity of interest, that is, a mutual or successive interest to the same
rights.” Id. (citations omitted).
The district court did not err in concluding that Brooks was either the same party or a privy
to the state cause of action. Brooks’s own affidavit, filed in the state court action, avers that
T.O.T.S., Inc. began as a corporation of which he was the original founder and that he continued to
do business as the same entity once the corporate charter expired. Brooks’s allegations as a sole
proprietor of TOTS in the federal cause of action are the same allegations that he made on behalf of
T.O.T.S., Inc. in the state cause of action. Therefore, Brooks is a privy to the subject matter of the
state litigation.
Finally, with respect to prong four, Brooks asserts that the federal case is not the same cause
of action as the state case because the federal case covers a different time frame, names Gary
Hollingsworth as a defendant, and alleges a RICO violation. This argument is unavailing.
Regarding the time frame, Brooks’s federal action alleged no facts that occurred after February 2008,
when he filed the state action. Regarding different claims and defendants, Brooks could have named
Gary Hollingsworth as a defendant or asserted a RICO violation in his state court action, but failed
to do so. Res judicata prohibits re-litigation of all claims that were actually litigated as well as
claims that should have been litigated in a prior action. See Kane, 71 F.3d at 560.
The district court’s judgment is affirmed.
|
Introduction {#s1}
============
Maize plants attacked by herbivorous insects emit volatile organic compounds (VOCs) that attract natural enemies of herbivores (Dicke et al., [@B21]; Turlings et al., [@B50]; Turlings and Wäckers, [@B51]; Arimura et al., [@B2]). In the case of maize plants, the blend of VOCs emitted by caterpillar-damaged plants is typically composed of green leaf volatiles (GLVs, C-6 aldehydes, alcohols, and their esters), nitrogenous, and aromatic compounds, as well as mono, homo and sesquiterpenes (Paré and Tumlinson, [@B39]; D\'Alessandro and Turlings, [@B15]). Among the VOCs that have been identified in these blends, GLVs have received particular attention. They are emitted upon mechanical damage, immediately after feeding on the maize plant begins (Turlings et al., [@B49]), and have been considered important for the innate attraction of parasitoids, as they are emitted in higher amounts by freshly damaged plants than by plants with only old damage (Whitman and Eller, [@B54]; Hoballah and Turlings, [@B28]). Commonly, insect herbivores are repelled by inducible plant volatiles (Bernasconi et al., [@B3]; De Moraes et al., [@B19]; Rostas and Hilker, [@B44]). This is particularly evident for Lepidoptera (De Moraes et al., [@B19]), but this is not true for all herbivores. In particular coleopterans are known to be attracted to previously infested plants (Bolter et al., [@B4]; Landolt et al., [@B37]) and they may be attracted to GLVs as was found for scarab (Hansson et al., [@B24]) and buprestid beetles (de Groot et al., [@B17]), and flea beetles (Halitschke et al., [@B23]).
Interestingly, larval stages of several Lepidoptera are attracted by volatiles emitted by plants that have been damaged by conspecific larvae. This was found for neonates of several Lepidoptera species, including *Ostrinia nubialis* (Hübner) and *Ostrinia furnacalis* (Guenée) (Lepidoptera: Pyralidae) on maize (Huang et al., [@B29]; Piesik et al., [@B40]), *Spodoptera frugiperda* (J. E. Smith) (Lepidoptera: Noctuidae) on maize and cowpea (Carroll et al., [@B7], [@B6]), and *Estigmene acrea* (Drury) (Lepidoptera: Arctiidae) on soybean, tomato, and maize (Castrejon et al., [@B8]). Furthermore, caterpillars adapt their behavior depending on plant VOC emission (Shiojiri et al., [@B45]). This attraction to VOCs emitted by already infested host plants is puzzling, as it will lead to competition and may increase the risk of cannibalism and attack by natural enemies that are attracted to the same volatiles. Cannibalism is common among noctuid larvae, such as *Spodoptera littoralis* (Boisduval) (Abdel Salam and Fokhar. cited in Fox, [@B22]), *S. frugiperda* (Chapman et al., [@B9]), and *Helicoverpa armigera* (Hübner) (Kakimoto et al., [@B30]). The attraction of natural enemies to herbivore-induced volatiles has been shown for numerous tritrophic systems (Dicke et al., [@B21]; Turlings et al., [@B50]; Heil, [@B27]; Dicke and Baldwin, [@B20]; Hare, [@B25]), which makes one wonder why lepidopteran larvae are attracted to the same volatiles. This apparent maladaptive behavior may be explained by a trade-off between risks: in the field harsh weather conditions and attempts to escape parasitoids and predators cause larvae to frequently fall off plants (personal observ.). In order to find back the same plant or new suitable plants the larvae will have to rely on dependable and available VOC signals. Induced VOCs may provide the best cues, as undamaged plants are often virtually odorless (Turlings et al., [@B50]). However, once on a plant, caterpillars may prefer sites with minimal VOC emissions, where it is less likely to encounter competitors and natural enemies.
We therefore hypothesized that caterpillars may initially be attracted to induced VOCs, but once they are on the plant they will feed preferentially in places with low GLV emissions. We tested this for larvae of the noctuid moth *Spodoptera littoralis* (Boisduval). First we confirmed attraction to induced plant volatiles in a four-arm olfactometer and then tested their growth rate as a measure of feeding behavior when they were exposed to GLVs. Previous feeding experiences were also taken into consideration, as larval attraction may be higher for volatiles that are emitted by plant species on which the larvae previously fed (Carlsson et al., [@B5]).
Materials and methods {#s2}
=====================
Plants and insects
------------------
Maize plants (*Zea mays*, cv. Delprim) were grown individually in plastic pots (10 cm high, 4 cm diameter) with commercial potting soil (Ricoter Aussaaterde, Aarberg, Switzerland) and placed in a climate chamber (23°C, 60% r.h., 16:8 h L:D, 50000 lm/m^2^). Maize plants used for the experiments were 10--12 days old and had three fully developed leaves. The evening before the experiments, plants were transferred into glass vessels, as described in Turlings et al. ([@B48]) and kept under laboratory conditions (25 ± 2°C, 40 ± 10% r.h., 16:8 h L:D, and 8000 lm/m^2^). *S. littoralis* larvae were reared from eggs provided by Syngenta (Stein, Switzerland). The eggs were kept in an incubator at 30.0 ± 0.5°C until emergence of the larvae. Subsequently, they were transferred on artificial diet at room temperature (24 ± 4°C).
Olfactometer experiments
------------------------
Two olfactometer experiments were performed with fourth-instar *S. littoralis* larvae. In the first experiment, the attraction of larvae to an *S. littoralis*-infested maize plant vs. healthy maize plant was compared. In the second experiment, the attraction of larvae to a maize plant with fresh (mechanically inflicted) damage was tested against a plant with old (mechanically inflicted) damage. In both experiments, the effect of previous feeding experience (either artificial diet or maize) was compared. All the larvae were initially reared on artificial diet as previously described (Turlings et al., [@B48]). Twenty-four hours before each experiment, 90 larvae were transferred on fresh maize leaves (maize feeding experience), and 90 on artificial diet (artificial diet feeding experience).
Attraction of fourth-instar *S. littoralis* larvae to infested maize plants
---------------------------------------------------------------------------
A four-arm olfactometer (as described in D\'Alessandro and Turlings, [@B14]) was modified to measure the attraction of *S. littoralis* larvae. The olfactometer consisted of a central glass choice arena (Figure [1](#F1){ref-type="fig"}) \[6 cm internal diameter (ID), 5 cm length\] with four arms (15 mm ID, 5 cm length), each with a glass elbow (5 cm length) and an upward connection for a glass bulb (50 ml). To avoid visual distraction of the larvae, a white cardboard cylinder was placed around the central choice arena.
).](fpls-04-00209-g0001){#F1}
The choice arena was connected to four glass bottles. One bottle contained a maize plant (cv Delprim) infested with 15 second-instar *S. littoralis* larvae that had been placed on the plant 16 h before the bioassay. The opposite bottle contained a healthy maize plant. The two remaining bottles remained empty. The position of the odor sources was changed between each experimental day, with the two odor sources always opposite to each other.
Thirty fourth-instar larvae were placed in a small plastic box (2 × 2 × 0.8 cm) with an open top, which was introduced in the center of the choice arena. The larvae would crawl out of the box into the central choice arena and a number of them entered one of the four arms. After 60 min, the number of larvae in each arm was counted. The larvae that did not leave the choice arena after 60 min were considered as having made "no choice" and all the larvae were removed from the olfactometer. Six such releases were done on a given day and this was repeated on 6 different days (*n* = 6).
Attraction of fourth-instar *S. littoralis* larvae to plants with old vs. plants with fresh damage
--------------------------------------------------------------------------------------------------
The same setup as described above was used, with the same experimental procedure, except for the odor sources. Two maize plants were brought to the laboratory 16 h prior to the bioassay. One plant was scratched on the underside of the two oldest leaves, damaging approximately 2 cm^2^, on both sides of the central vein (Hoballah and Turlings, [@B28]). Caterpillar regurgitant, collected as described in Turlings et al. ([@B49]), was applied to the two wounds. Both plants were then placed in a glass bottle and exposed to a carbon-filtered, humidified airflow of 300 ml/min for 15 h. The second plant was then scratched and regurgitant was applied. The two plants were then placed opposite to each other in the olfactometer, leaving two empty bottles between them. The airflow was then increased to 1200 ml/min through each bottle, of which 500 ml/min entered the olfactometer choice chamber. The position of the treatments was changed for each experimental day.
GLV dispensers
--------------
To expose larvae to green leafy volatiles we made dispensers as described by von Mérey et al. ([@B53]). The GLVs were first mixed together in an Erlenmeyer flask (100 mL) placed in ice. The composition of the mixture was 80% cis-3-hexen-1-al \[92.5% purity, (NEAT), Bedoukian Research Inc., USA\]; 10% cis-3-hexen-1-ol (\>98%, GC, Sigma-Aldrich, CH-9471 Buchs, Switzerland); 8% cis-3-hexenyl acetate (\>98%, SAFC Supply Solutions, 3050 Spruce street, St. Louis, MO 63103, USA); and 2% trans-2-hexenol (99%, ACROS Organics, New Jersey, USA). The mix was stored at -70°C until it was used. For the assays, 0.2 mL of the GLV mix was transferred into a 2 mL amber glass vial (11.6 × 32 mm) (Sigma-Aldrich, CH-9471 Buchs, Switzerland) containing clean fiberglass wool. Each vial was sealed with a PTFE/rubber septum pierced by a Drummond 2 μL micro-pipette in black polypropylene cap. This device allowed the constant release of GLVs, and their release rate was calibrated to the amount of GLVs that was found to be released by infested maize plants (*Zea mays* cv Delprim) (von Mérey et al., [@B53]). Control dispensers consisted of glass vials only containing fiberglass wool.
VOC-exposure experiments
------------------------
Three experiments were conducted to measure the effect of VOCs on the growth of *S. littoralis* larvae. In the first experiment, the larvae were exposed to the volatiles of caterpillar-damaged maize plants. In the second experiment, they were exposed to amounts of a blend of synthetic GLVs that fall within the range of what is commonly emitted by a single, caterpillar-infested maize plant (see von Mérey et al., [@B53] for details). In the third experiment, they were exposed to high concentrations of synthetic GLVs. In all three experiments we recorded, besides weight gain, mortality, and pupation of the larvae.
Effect of exposure to VOCs emitted by caterpillar-damaged maize plants on feeding rate of *S. littoralis* larvae
----------------------------------------------------------------------------------------------------------------
Second-instar *S. littoralis* were placed individually inside small plastic boxes (2 × 2 × 1.5 cm) that were covered with fine-meshed nylon tissue, fixed with an elastic band. The larvae were provided a 1 cm^3^ cube of wheatgerm-based artificial diet (Turlings et al., [@B48]), which was changed every second day. Twelve such boxes were placed inside a glass bottle lying on its side, connected at its base with a Teflon tube to the top of an odor source bottle (Figure [2](#F2){ref-type="fig"}; see Turlings et al., [@B48] for details on glass bottles and tubing). Odor source bottles contained either a maize plant infested with fifteen second-instar *S. littoralis* larvae (induced plant, VOCi, replaced with a new infested plant every third day) or an uninfested maize plant (control plant, VOCu, also replaced every third day). The odor source bottle was connected to a four-port air-delivery system (Model VCS-HADS-6AF6C6B; ARS Analytical Research Systems, Gainesville, FL, USA), providing a purified and humidified airflow of 300 ml/min. Two such four-port air-delivery systems were used simultaneously to introduce odors into eight exposure chambers, resulting in 48 larvae for each treatment.
{#F2}
Before placing the larvae inside the plastic boxes, they were weighed on a microbalance (Model MX5, Mettler Toledo, Greifensee, Switzerland). Weighing was repeated at the following time-points after placing the boxes inside the glass bottle: 5, 24, 48, 96, 144, 192, 240, 288, 312, 336, 360, 408, and 432 h. After this time-point, all larvae had pupated or had died and the experiment was terminated.
Effect of exposure to synthetic GLVs on weight gain of *S. littoralis* larvae
-----------------------------------------------------------------------------
The same setup as described above was used for this experiment. In this case, the odor source bottles containing a dispenser built up as follows: a 2 ml amber glass vial (11.6 × 32 mm; Sigma-Aldrich, Buchs, Switzerland) containing 100 mg clean fiberglass wool. The vial was sealed with a PTFE/rubber septum (Sigma-Aldrich, Buchs, Switzerland) pierced with a 2 μl micro-pipette (Drummond, Millan SA, Plan-Les-Ouates, Switzerland). The length of the pipette was calibrated to release a controlled amount of GLVs, similar to the amount emitted by maize plants (cv Delprim). The GLV mixture consisted of 80% (*Z*)-3-hexen-1-al \[92.5% purity, (NEAT), Bedoukian Research, Danbury, CT, USA\], 10% (*Z*)-3-hexenyl-acetate (\<98%, SAFC Supply Solutions, St. Louis, MO, USA), 8% (*Z*)-3-hexenyl-Acetate (≥98%, SAFC Supply Solutions, 3050 Spruce Street, St. Louis, MO 63103, USA), and 2% (*E*)-2-hexenol (99%, ACROS Organics, Geel, Belgium). The same GLV dispenser was kept for the duration of the assay. Control bottles contained no dispenser.
In this experiment, the weighing of the larvae was repeated at 5, 12, 24, 48, 96, 120, and 144 h after placement in the bottles. The experiment was terminated at 144 h because the tests showed that larval weight was not affected by the volatiles at these concentrations.
Effect of exposure to high concentrations of GLVs on weight gain of *S. littoralis* larvae
------------------------------------------------------------------------------------------
In this experiment, larvae were placed individually in a plastic box (7.5 × 6.5 × 5 cm) containing a GLV dispenser (described above), and a piece of diet (2 × 1.5 × 1 cm). The box was closed, in order to increase the concentration of GLVs. As a control, an empty dispenser was placed inside the cage without GLVs inside. There were twelve larvae in each treatment and they were weighed before placing them inside the boxes. They were weighed again after 3, 6, 9, 12, 15, 24, 40, 48, 51, 54, 58, 72, 96, 120, and 168 h.
The larger plastic boxes allowed for more mobility, compared to the cages used in the previous experiments. In order to observe whether the high concentrations of GLV affected larval mobility, we recorded whether the larvae were on the diet or off the diet during the first 8 h of exposure.
Statistical analysis
--------------------
VOC-exposure data were compared using Student\'s *t*-test, provided they met the assumptions of normality (Shapiro-Wilk test) and equal variance (Levene\'s test). Else, a Mann-Whitney test was applied. Both treatments (VOCu and VOCi exposure) were compared at each time-point individually. Data on mortality and pupation of the larvae compared using a one-way analysis of variance (ANOVA). Data was tested with SigmaStat (version 3.5, STATCON, Witzenhausen, Germany). Data on mobility were analyzed in a general linear model (GLM) with binomial distribution (the larvae were observed either on the diet or off the diet) family in R (R Development Core Team, [@B41]). Olfactometer data was analyzed using the software package R (R Development Core Team, [@B41]), in a GLM, allowing to compensate for over-dispersed data, as previously described (D\'Alessandro and Turlings, [@B14]; Tamò et al., [@B46]; Ricard and Davison, [@B42]). This means that any positional biases or effects of the individuals on each other\'s behavior are considered in the model and that calculated statistical differences are solely the result of differential attractiveness of the odor sources.
Results {#s3}
=======
Attraction of fourth-instar *S. littoralis* larvae to induced maize plants
--------------------------------------------------------------------------
The larvae that had fed on maize and the larvae fed on artificial diet were both more attracted toward caterpillar-damaged maize plants than to intact plants (GLM *P* \< 0.001 and *P* \< 0.002, respectively; Figure [3](#F3){ref-type="fig"}). However, the maize-fed larvae were attracted more strongly by the induced plants than the diet-fed larvae (GLM *P* \< 0.005). Maize-fed larvae also displayed an increased responsiveness (80% entering an arm) compared to diet-fed larvae (66%).
{#F3}
Attraction to old vs. fresh damage
----------------------------------
Freshly damaged plants were more attractive to maize-fed larvae (GLM *P* \< 0.003) than plants with older damage (Figure [4](#F4){ref-type="fig"}). Artificial diet-fed larvae did not show a preference between old and fresh damage. This difference in preference between maize-fed and diet-fed larvae was significant (GLM *P* \< 0.001). Also in this case, overall responsiveness of maize-fed larvae (84%) was higher than the responsiveness of artificial diet-fed larvae (62%).
{#F4}
Exposure to VOCs from caterpillar-damaged maize plants
------------------------------------------------------
The larvae that were exposed to the VOCs emitted by caterpillar-damaged maize plants grew more slowly in the early stages of development (Figure [5](#F5){ref-type="fig"}). Initial weight of the larvae was equal across treatments. After 5 h, there was still no difference between the two treatment groups (*P* \< 0.356). However, after 24 h, the larvae exposed to VOCs from damaged plants (VOCi) had gained significantly less weight than the larvae exposed to VOCs emitted by healthy plants (VOCu) (*P* \< 0.030). This difference in growth rate persisted throughout the early weighing time points: 48 h (*P* \< 0.030), 96 h (*P* \< 0.012), 144 h (*P* \< 0.033). After this, both treatment groups displayed similar weight gains until pupation. The weight of the pupae did not differ significantly (*P* \< 0.916). There was also no difference in mortality between the larvae of the two treatment groups (*P* \< 0.839).
{#F5}
Effect of exposure to low concentrations of synthetic GLVs on weight gain of *S. littoralis* larvae
---------------------------------------------------------------------------------------------------
When larvae were exposed to the synthetic volatile blend we measured no difference either in larval weight gain (5 h: *P* \< 0.759, 12 h: *P* \< 0.286, 24 h: *P* \< 0.267, 48 h: *P* \< 0.502, 72 h: *P* \< 0.506, 96 h: *P* \< 0.833, 120 h: *P* \< 0.833, 144 h: *P* \< 0.646), or mortality (0% in both treatments).
Effect of exposure to high concentrations of GLVs on weight gain of *S. littoralis* larvae
------------------------------------------------------------------------------------------
When larvae were exposed to high concentrations of GLVs, such as can be expected to be present in the immediacy of the feeding sites on the maize plants, the larvae were found to gain less weight at the early stages of their development (Figure [6](#F6){ref-type="fig"}). After 3 h (*P* \< 0.514) and 6 h (*P* \< 0.173), there was still no difference between the treatments. After exposure to GLVs for 9 h a strong trend of lower weight gain in GLV-exposed larvae was observed (*P* \< 0.051) and at 12 h the difference between the two treatments was significant (*P* \< 0.025). This difference persisted throughout the early part of the experimental time (15 h: *P* \< 0.036; 24 h: *P* \< 0.027; 40 h: *P* \< 0.031; 48 h: *P* \< 0.030; 51 h: *P* \< 0.033; 54 h: *P* \< 0.039; 58 h: *P* \< 0.038; 72 h: *P* \< 0.047). From 96 h, however, there was no longer a difference in weight gain between the treatments. Interestingly, the mobility of GLV-exposed larvae was slightly increased (*P* \< 0.060), with a significant difference in number of larvae moving in the box after 6 h (*P* \< 0.048). However, at 30 min (*P* \< 0.410), 2 h (*P* \< 0.716), 4 h (*P* \< 0.572), and 8 h (*P* \< 0.423), GLV-exposed and control larvae were equally on the diet and off the diet.
{#F6}
Discussion {#s4}
==========
We show here that *Spodoptera littoralis* caterpillars are attracted to volatiles from maize plants that are under attack by conspecifics. This confirms the findings by Carroll et al. ([@B7], [@B6]), who obtained similar results for a related species, *S. frugiperda*, which was found to be attracted to inducible volatiles emitted from maize and cowpea seedlings. Similarly, neonate larvae of the codling moth, *Cydia pomonella*, are more attracted to apple fruits with other codling moth larvae than to uninfested fruits (Landolt et al., [@B36]). This is somewhat surprising, as these Lepidoptera are not known to aggregate, unlike many Coleoptera, for which both adults and larvae are often attracted to the volatiles of already infested plants (Crowe, [@B12]; Bolter et al., [@B4]; Müller and Hilker, [@B38]; Kalberer et al., [@B31]; Heil, [@B26]; Yoneya et al., [@B55]). It should be noted that in the case of *S. frugiperda*, Carroll et al. ([@B6]) found linalool to be particularly attractive. This terpene alcohol is in fact also released, be it in lesser amounts, by undamaged maize plants, at least in some varieties (Degen et al., [@B16]), and therefore can be a reliable cue for the presence of maize in general. In adult Lepidoptera, however, increased linalool levels decreased oviposition (De Moraes et al., [@B19]; Kessler and Baldwin, [@B32]).
The larval response to herbivore-induced volatiles is in contrast to what is known for adult Lepidoptera, which avoid to oviposit on plants that are already under caterpillar attack (Landolt, [@B35]; De Moraes et al., [@B19]; Kessler and Baldwin, [@B32]; Huang et al., [@B29]). Such avoidance of already infested plants, which is also the case for aphids (Bernasconi et al., [@B3]), is expected, as it reduces the chances of competition and cannibalism, as well as predation and parasitism by natural enemies that are attracted to the same volatiles. Then why are the larvae attracted to volatiles that are indicative of these risks? To answer this it may help to list the potential disadvantages and discuss counter arguments why these may not be as important as potential advantages. The apparent disadvantages are: (1) VOCs emitting plants have mobilized their defenses and should be less suitable for caterpillar development, (2) The VOCs indicate the plants carry other larvae that will compete for the same resource and may even pose a cannibalism risk, (3) The VOCs are attractive to natural enemies of the caterpillars and therefore indicate a higher risk of predation and parasitism.
As for the counter argument, the most obvious reason to use herbivore-induced VOCs is the same as has been argued for the natural enemies (Vet and Dicke, [@B52]), the induced VOCs are emitted in large amounts and are therefore easily detectible and reliable cues for the presence of a host plant. Moreover, the alternative, the avoidance of inducible defenses by opting for healthy plants gives only an advantage for a very short period of time, as maize plants respond very rapidly, within hours, to an attack (Turlings et al., [@B49]). This is particularly true for plants that are neighboring already attacked plants and have their defenses primed in response to the volatiles emitted by the neighbor (Ton et al., [@B47]). This then only leaves the risk of competition and possibly cannibalism. This risk may be minor in light of the possibility of not finding a plant at all and unlike *S. frugiperda*, *S. littoralis* is not cannibalistic, at least not the colony that we used in our experiments. We therefore hypothesized that *Spodoptera* and other larvae of herbivorous insects have adapted to use the readily available and reliable herbivore-induced volatile signals to find host plants despite the risks they will face on these plants, because the likely alternative would be starvation. A similar argument formulated by Carroll et al. ([@B7]) emphasizes the limited range at which caterpillars can forage, as compared to the highly mobile adults. The far less mobile caterpillars, when fallen to the ground, have a high risk of predation and are fully exposed to unfavorable environmental conditions. Getting back on a plant should be high priority and in most cases the same plant will be the closest to crawl on. This may also explain why we found that a previous feeding experience has a significant impact on the attractiveness of the induced maize volatiles. Similar preferences for familiar odors in *S. littoralis* larvae were found by Anderson et al. ([@B1]) and Carlsson et al. ([@B5]) when they studied the caterpillar\'s responses to cotton volatiles. This effect of experience even extends to the adult moth, which prefers to oviposit on the same plant species on which it fed as a larva (Anderson et al., [@B1]). It is also known that caterpillars adapt their feeding physiology to plant diet on which they feed as neonates and will perform worse on an alternative diet (el Campo et al., [@B18]; Zalucki et al., [@B56]), the more reason for the larvae to forage for the same plant species.
Once on an already infested plant, however, caterpillars could lessen the risks of competition/cannibalism, which can be very severe in certain *Spodoptera* species (Chapman et al., [@B9], [@B10]; Richardson et al., [@B43]), but this is not the case for *S. littoralis*. They will also reduce the risk of predation and parasitism by avoiding the most odorous plant parts (Turlings and Wäckers, [@B51]). This notion is tentatively supported by the effects of maize VOCs on caterpillar feeding behavior. *S. littoralis* larvae that were exposed to the VOCs induced by their conspecifics on maize plants were found to feed and grow less than larvae that were not exposed to the VOCs (Figure [3](#F3){ref-type="fig"}). This is indicative of an avoidance of the VOCs, which was only evident at high concentrations. Hence, the results of the current study support our hypothesis that on a plant the caterpillars prefer to commence feeding away from freshly damaged areas, i.e., sites from which large amounts of GLVs are emitted. Yet, alternative explanations should be considered. For instance, the larvae that were exposed to GLVs volatiles might have been attracted and searched for the source of the volatiles and therefore ate less on the diet that they were offered. We can also not exclude a direct (toxic) effect of the volatiles on the larvae.
In summary, we show here that *Spodoptera littoralis* larvae are attracted to the volatiles emitted by plants that are already damaged by conspecific larvae. Although such plants are less suitable for the larvae than undamaged plants, the larvae may simply opt to go for readily detectable signals. The notion that the larvae are attracted to reliable, familiar volatile signals even if it leads them to sub-optimal resources is further supported by the fact that previous experience with the odors enhances their attractiveness. But once they are on the plants they seem to avoid the volatiles and eat less when they detect high concentrations of them. We speculate that by doing so the larvae avoid the parts of the plant with up-regulated defenses, competition/cannibalism, and natural enemies that are attracted to the same volatiles.
An understanding of signals that are of importance for host plant foraging by caterpillars can be of use in the development of pest control strategies. In this context, current focus is on foraging of adults and this has found good use in "push-pull" strategies (Khan et al., [@B34], [@B33]; Cook et al., [@B11]). Similarly, with the right combination of repellent and attractive volatiles, it may be possible to manipulate the foraging of caterpillar such that they are guided away from the crop and toward their demise on trap plants.
Conflict of interest statement
------------------------------
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We thank Matthias Erb for useful comments on the manuscript. Yves Borcard and several students of the University of Neuchâtel reared parasitoids, and Syngenta (Stein, Switzerland) provided *S. littoralis* eggs. This work received support by the Swiss National Science Foundation via the National Center of Competence in Research *Plant Survival*.
[^1]: Edited by: Marcel Dicke, Wageningen University, Netherlands
[^2]: Reviewed by: Anne M. Cortesero, University of Rennes1, France; James Blande, University of Eastern Finland, Finland
|
/*
*
* ***** BEGIN LICENSE BLOCK *****
* Version: MPL 1.1/GPL 2.0
*
* The contents of this file are subject to the Mozilla Public License Version
* 1.1 (the "License"); you may not use this file except in compliance with
* the License. You may obtain a copy of the License at
* http://www.mozilla.org/MPL/
*
* Software distributed under the License is distributed on an "AS IS" basis,
* WITHOUT WARRANTY OF ANY KIND, either express or implied. See the License
* for the specific language governing rights and limitations under the
* License.
*
* The Original Code is Rhino code, released
* May 6, 1999.
*
* The Initial Developer of the Original Code is
* Netscape Communications Corporation.
* Portions created by the Initial Developer are Copyright (C) 1997-1999
* the Initial Developer. All Rights Reserved.
*
* Contributor(s):
* Google Inc.
*
* Alternatively, the contents of this file may be used under the terms of
* the GNU General Public License Version 2 or later (the "GPL"), in which
* case the provisions of the GPL are applicable instead of those above. If
* you wish to allow use of your version of this file only under the terms of
* the GPL and not to allow others to use your version of this file under the
* MPL, indicate your decision by deleting the provisions above and replacing
* them with the notice and other provisions required by the GPL. If you do
* not delete the provisions above, a recipient may use your version of this
* file under either the MPL or the GPL.
*
* ***** END LICENSE BLOCK ***** */
package com.google.javascript.rhino;
import static com.google.common.base.Preconditions.checkNotNull;
import static com.google.common.base.Preconditions.checkState;
import com.google.common.annotations.VisibleForTesting;
import com.google.common.base.Function;
import com.google.javascript.rhino.PMap.Reconciler;
import java.io.Serializable;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.Iterator;
import java.util.Objects;
import java.util.function.BiPredicate;
import javax.annotation.Nullable;
/**
* An immutable sorted map with efficient (persistent) updates.
*
* <p>Uses a hash array mapped trie: http://en.wikipedia.org/wiki/Hash_array_mapped_trie.
*
* <p>This implementation stores the bare minimum in each node: a key (with its hash), value, mask,
* and children. It is also optimized to take maximum advantage of binary operations on shared
* trees. Specifically, {@link #reconcile} avoids recursing into entire subtrees if they are
* identical objects. Null keys and values are not allowed. The implementation special-cases away
* the EMPTY map as soon as possible, using 'null' instead for all the logic (since EMPTY violates
* the invariant that key and value are non-null). Finally, we maintain an invariant that the
* entry with the smallest hash code is always at the root of the tree, which avoids almost all
* extra tree rebuilding during binary operations.
*/
// TODO(sdh): Consider using tricks from https://bendyworks.com/blog/leveling-clojures-hash-maps
// We need a solid way to profile the results to see if it's actually worth the extra code.
public final class HamtPMap<K, V> implements PMap<K, V>, Serializable {
/**
* Number of bits of fan-out at each level. May be anywhere from 1 (a binary tree) to 5 (for a
* fan-out of 32). Anything larger requires using a long for the mask (which is ugly for the
* JavaScript-compiled version), and zero is essentially a linked list. The relevant trade-off is
* that more fan-out means shallower trees, which should lead to quicker look-up times and more
* efficient updates, but less fan-out makes reconcile() and equivalent() more efficient for maps
* that are mostly the same, since bigger common trees can be pruned from the operation.
* Preliminary profiling suggests that for type-checking purposes, all nonzero values are roughly
* comparable.
*/
private static final int BITS = 4;
/** Number of bits to shift off to get the most significant BITS number of bits. */
private static final int BITS_SHIFT = 32 - BITS;
/** Non-null key (exception: empty map has a null key). */
private final K key;
/** Hash of the key, right-shifted by BITS*depth. */
private final int hash;
/** Non-null value (exceptions: (1) empty map, (2) result of pivot, if not found). */
private final V value;
/** Bit mask indicating the children that are present (bitCount(mask) == children.length). */
private final int mask;
/** Non-null array of children. Elements are never reassigned. */
private final HamtPMap<K, V>[] children;
private static final HamtPMap<?, ?>[] EMPTY_CHILDREN = new HamtPMap<?, ?>[0];
private static final HamtPMap<?, ?> EMPTY =
new HamtPMap<>(null, 0, null, 0, emptyChildren());
private HamtPMap(K key, int hash, V value, int mask, HamtPMap<K, V>[] children) {
this.key = key;
this.hash = hash;
this.value = value;
this.mask = mask;
this.children = children;
this.checkInvariants();
}
private void checkInvariants() {
checkState(Integer.bitCount(this.mask) == this.children.length);
for (HamtPMap<?, ?> child : this.children) {
checkNotNull(child);
}
}
/** Returns an empty map. */
@SuppressWarnings("unchecked") // Empty immutable collection is safe to cast.
public static <K, V> HamtPMap<K, V> empty() {
return (HamtPMap<K, V>) EMPTY;
}
/** Returns an empty array of child maps. */
@SuppressWarnings("unchecked") // Empty array is safe to cast.
private static <K, V> HamtPMap<K, V>[] emptyChildren() {
return (HamtPMap<K, V>[]) EMPTY_CHILDREN;
}
@Override
public String toString() {
StringBuilder sb = new StringBuilder().append("{");
if (!isEmpty()) {
appendTo(sb);
}
return sb.append("}").toString();
}
/** Appends this map's contents to a string builder. */
private void appendTo(StringBuilder sb) {
if (sb.length() > 1) {
sb.append(", ");
}
sb.append(key).append(": ").append(value);
for (HamtPMap<K, V> child : children) {
child.appendTo(sb);
}
}
/** Returns whether this map is empty. */
@Override
public boolean isEmpty() {
return key == null;
}
/** Returns an iterable for a (possibly null) tree. */
@Override
public Iterable<V> values() {
if (isEmpty()) {
return Collections.<V>emptyList();
}
return () -> new Iter<>(this, map -> map.value);
}
/** Returns an iterable for a (possibly null) tree. */
@Override
public Iterable<K> keys() {
if (isEmpty()) {
return Collections.emptyList();
}
return () -> new Iter<>(this, map -> map.key);
}
/**
* Retrieves the value associated with the given key from the map, or returns null if it is not
* present.
*/
@Override
public V get(K key) {
return !isEmpty() ? get(key, hash(key)) : null;
}
/** Internal recursive implementation of get(K). */
private V get(K key, int hash) {
if (hash == this.hash && key.equals(this.key)) {
return this.value;
}
int bucket = bucket(hash);
int bucketMask = 1 << bucket;
return (mask & bucketMask) != 0 ? children[index(bucketMask)].get(key, shift(hash)) : null;
}
/**
* Returns a new map with the given key-value pair added. If the value is already present, then
* this same map will be returned.
*/
@Override
public HamtPMap<K, V> plus(K key, V value) {
checkNotNull(value);
return !isEmpty()
? plus(key, hash(key), value)
: new HamtPMap<>(key, hash(key), value, 0, emptyChildren());
}
/** Internal recursive implementation of plus(K, V). */
private HamtPMap<K, V> plus(K key, int hash, V value) {
if (hash == this.hash && key.equals(this.key)) {
return value.equals(this.value)
? this
: new HamtPMap<>(key, hash, value, mask, children);
}
if (compareUnsigned(hash, this.hash) < 0) {
return replaceRoot(key, hash, value);
}
int bucket = bucket(hash);
hash = shift(hash);
int bucketMask = 1 << bucket;
int index = index(bucketMask);
if ((mask & bucketMask) != 0) {
// already a child, so overwrite
HamtPMap<K, V> child = children[index];
HamtPMap<K, V> newChild = child.plus(key, hash, value);
return child == newChild ? this : withChildren(mask, replaceChild(children, index, newChild));
} else {
// insert at index
HamtPMap<K, V> newChild = new HamtPMap<>(key, hash, value, 0, emptyChildren());
return withChildren(mask | bucketMask, insertChild(children, index, newChild));
}
}
private HamtPMap<K, V> replaceRoot(K key, int hash, V value) {
int bucket = bucket(this.hash);
int leafHash = shift(this.hash);
int bucketMask = 1 << bucket;
int index = index(bucketMask);
HamtPMap<K, V>[] newChildren;
if ((mask & bucketMask) != 0) {
newChildren =
replaceChild(children, index, children[index].plus(this.key, leafHash, this.value));
} else {
HamtPMap<K, V> newChild = new HamtPMap<>(this.key, leafHash, this.value, 0, emptyChildren());
newChildren = insertChild(children, index, newChild);
}
return new HamtPMap<>(key, hash, value, mask | bucketMask, newChildren);
}
/**
* Returns a new map with the given key removed. If the key was not present in the first place,
* then this same map will be returned.
*/
@Override
public HamtPMap<K, V> minus(K key) {
return !isEmpty() ? minus(key, hash(key), null) : this;
}
/**
* Internal recursive implementation of minus(K). The value of the removed node is returned via
* the 'value' array, if it is non-null.
*/
private HamtPMap<K, V> minus(K key, int hash, V[] value) {
if (hash == this.hash && key.equals(this.key)) {
HamtPMap<K, V> result = deleteRoot(mask, children);
if (value != null) {
value[0] = this.value;
}
return result != null ? result : empty();
}
int bucket = bucket(hash);
int bucketMask = 1 << bucket;
if ((mask & bucketMask) == 0) {
// not present, stop looking
return this;
}
hash = shift(hash);
int index = index(bucketMask);
HamtPMap<K, V> child = children[index];
HamtPMap<K, V> newChild = child.minus(key, hash, value);
if (newChild == child) {
return this;
} else if (newChild == EMPTY) {
return withChildren(mask & ~bucketMask, deleteChild(children, index));
} else {
return withChildren(mask, replaceChild(children, index, newChild));
}
}
@Override
public HamtPMap<K, V> reconcile(PMap<K, V> that, Reconciler<K, V> joiner) {
HamtPMap<K, V> result =
reconcile(
!this.isEmpty() ? this : null,
!that.isEmpty() ? (HamtPMap<K, V>) that : null,
(k, v1, v2) -> checkNotNull(joiner.merge(k, v1, v2)));
return result != null ? result : empty();
}
/** Internal recursive implementation of reconcile(HamtPMap, BiFunction), factoring out empies. */
private static <K, V> HamtPMap<K, V> reconcile(
@Nullable HamtPMap<K, V> t1, @Nullable HamtPMap<K, V> t2, Reconciler<K, V> joiner) {
if (t1 == t2) {
return t1;
} else if (t1 == null) {
V newValue = joiner.merge(t2.key, null, t2.value);
HamtPMap<K, V>[] newChildren = Arrays.copyOf(t2.children, t2.children.length);
for (int i = 0; i < newChildren.length; i++) {
newChildren[i] = reconcile(null, newChildren[i], joiner);
}
return newValue != null
? new HamtPMap<>(t2.key, t2.hash, newValue, t2.mask, newChildren)
: deleteRoot(t2.mask, newChildren);
} else if (t2 == null) {
V newValue = joiner.merge(t1.key, t1.value, null);
HamtPMap<K, V>[] newChildren = Arrays.copyOf(t1.children, t1.children.length);
for (int i = 0; i < newChildren.length; i++) {
newChildren[i] = reconcile(newChildren[i], null, joiner);
}
return newValue != null
? new HamtPMap<>(t1.key, t1.hash, newValue, t1.mask, newChildren)
: deleteRoot(t1.mask, newChildren);
}
// Try as hard as possible to return input trees exactly.
boolean sameChildrenAs1 = true;
boolean sameChildrenAs2 = true;
// If the hashes are different, we need to keep the lower one at the top.
int hashCmp = compareUnsigned(t1.hash, t2.hash);
K key = t1.key;
int hash = t1.hash;
if (hashCmp < 0) {
// t1.key is missing from t2
t2 = t2.vacateRoot();
sameChildrenAs2 = false;
} else if (hashCmp > 0) {
// t2.key is missing from t1
t1 = t1.vacateRoot();
sameChildrenAs1 = false;
key = t2.key;
hash = t2.hash;
} else if (!t1.key.equals(t2.key)) {
// Hash collision: try to rearrange t2 to have the same root as t1
t2 = t2.pivot(t1.key, t1.hash);
sameChildrenAs2 = false;
}
// Note: one or the other (but not both) tree may have a null key at root.
V newValue =
Objects.equals(t1.value, t2.value)
? t1.value
: joiner.merge(t1.key != null ? t1.key : t2.key, t1.value, t2.value);
int newMask = t1.mask | t2.mask;
sameChildrenAs1 &= (newMask == t1.mask);
sameChildrenAs2 &= (newMask == t2.mask);
@SuppressWarnings("unchecked") // only used internally.
HamtPMap<K, V>[] newChildren =
newMask != 0
? (HamtPMap<K, V>[]) new HamtPMap<?, ?>[Integer.bitCount(newMask)]
: emptyChildren();
int mask = newMask;
int index = 0;
while (mask != 0) {
int childBit = Integer.lowestOneBit(mask);
mask &= ~childBit;
HamtPMap<K, V> child1 = t1.getChild(childBit);
HamtPMap<K, V> child2 = t2.getChild(childBit);
newChildren[index] = reconcile(child1, child2, joiner);
sameChildrenAs1 &= (newChildren[index] == child1);
sameChildrenAs2 &= (newChildren[index] == child2);
if (newChildren[index] != null) {
index++;
} else {
newMask &= ~childBit;
}
}
if (sameChildrenAs1 && t1.value.equals(newValue)) {
return t1;
} else if (sameChildrenAs2 && t2.value.equals(newValue)) {
return t2;
} else if (newValue == null) {
return deleteRoot(newMask, newChildren);
}
return new HamtPMap<>(key, hash, newValue, newMask, newChildren);
}
/**
* Checks equality recursively based on the given equivalence. Short-circuits as soon as a 'false'
* result is found.
*/
@Override
public boolean equivalent(PMap<K, V> that, BiPredicate<V, V> equivalence) {
return equivalent(
!this.isEmpty() ? this : null, !that.isEmpty() ? (HamtPMap<K, V>) that : null, equivalence);
}
/** Internal recursive implementation of equivalent(HamtPMap, BiPredicate). */
private static <K, V> boolean equivalent(
@Nullable HamtPMap<K, V> t1,
@Nullable HamtPMap<K, V> t2,
BiPredicate<V, V> equivalence) {
if (t1 == t2) {
return true;
} else if (t1 == null || t2 == null) {
return false;
}
if (t1.hash != t2.hash) {
// Due to our invariant, we can safely conclude that there's a discrepancy in the
// keys without any extra work.
return false;
} else if (!t1.key.equals(t2.key)) {
// Hash collision: try to rearrange t2 to have the same root as t1
t2 = t2.pivot(t1.key, t1.hash);
if (t2.key == null) {
// t1.key not found in t2
return false;
}
}
if (!equivalence.test(t1.value, t2.value)) {
return false;
}
int mask = t1.mask | t2.mask;
while (mask != 0) {
int childBit = Integer.lowestOneBit(mask);
mask &= ~childBit;
if (!equivalent(t1.getChild(childBit), t2.getChild(childBit), equivalence)) {
return false;
}
}
return true;
}
/**
* Returns the index into the 'children' array for the given bit, which must have exactly one bit
* set in its binary representation (i.e. must be a power of two).
*/
private int index(int bit) {
return Integer.bitCount(mask & (bit - 1));
}
/**
* Returns the child for the given bit, which must have exactly one bit set. Returns null if there
* is no child for that bit.
*/
private HamtPMap<K, V> getChild(int bit) {
return (mask & bit) != 0 ? children[index(bit)] : null;
}
/**
* Perform the hash operation. This is done once per object as it enters the map, then never
* again since the result is passed around internally. We reverse the bits since certain types
* (such as small integers and short strings) have hash codes that only vary in the least
* significant bits, but we use the most significant bits for bucketing in order to maintain
* a canonical structure where the key with the smallest hash is always at the root of the
* tree.
*/
private static int hash(Object key) {
return Integer.reverse(key.hashCode());
}
/** Return the current bucket index from the hash. */
private static int bucket(int hash) {
return hash >>> BITS_SHIFT;
}
/** Return a new hash with the next bucket number shifted off. */
private static int shift(int hash) {
return hash << BITS;
}
/** Unshift the bucket number back onto a hash. */
private static int unshift(int hash, int bucket) {
return (hash >>> BITS) | (bucket << BITS_SHIFT);
}
/** Compare two unsigned integers. */
private static int compareUnsigned(int left, int right) {
// NOTE: JDK 7 does not have a built-in operation for this, other than casting to longs.
// In JDK 8 it's just Integer.compareUnsigned(left, right). For now we emulate it
// by shifting the sign bit away, with a fallback second compare only if needed.
int diff = (left >>> 2) - (right >>> 2);
return diff != 0 ? diff : (left & 3) - (right & 3);
}
/**
* Returns a new version of this map with the given key at the root, and the root element moved to
* some deeper node. If the key is not found, then value will be null.
*/
@SuppressWarnings("unchecked")
private HamtPMap<K, V> pivot(K key, int hash) {
return pivot(key, hash, null, (V[]) new Object[1]);
}
/**
* Internal recursive version of pivot. If parent is null then the result is used for the value in
* the returned map. The value, if found, is stored in the 'result' array as a secondary return.
*/
private HamtPMap<K, V> pivot(K key, int hash, HamtPMap<K, V> parent, V[] result) {
int newMask = mask;
HamtPMap<K, V>[] newChildren = this.children;
if (hash == this.hash && key.equals(this.key)) {
// Found the key: swap out this key/value with the parent and return the result in the holder.
result[0] = this.value;
} else {
// Otherwise, see if the value might be present in a child.
int searchBucket = bucket(hash);
int replacementBucket = bucket(this.hash);
if (searchBucket == replacementBucket) {
int bucketMask = 1 << searchBucket;
if ((mask & bucketMask) != 0) {
// Found a child, call pivot recursively.
int index = index(bucketMask);
HamtPMap<K, V> child = newChildren[index];
HamtPMap<K, V> newChild = child.pivot(key, shift(hash), this, result);
newChildren = replaceChild(newChildren, index, newChild);
}
} else {
int searchMask = 1 << searchBucket;
if ((mask & searchMask) != 0) {
int index = index(searchMask);
HamtPMap<K, V> child = newChildren[index];
HamtPMap<K, V> newChild = child.minus(key, shift(hash), result);
if (!newChild.isEmpty()) {
newChildren = replaceChild(newChildren, index, newChild);
} else {
newChildren = deleteChild(newChildren, index);
newMask &= ~searchMask;
}
}
int replacementMask = 1 << replacementBucket;
int index = Integer.bitCount(newMask & (replacementMask - 1));
if ((mask & replacementMask) != 0) {
HamtPMap<K, V> child = newChildren[index];
HamtPMap<K, V> newChild = child.plus(this.key, shift(this.hash), this.value);
newChildren = replaceChild(newChildren, index, newChild);
} else {
newChildren =
insertChild(
newChildren,
index,
new HamtPMap<>(this.key, shift(this.hash), this.value, 0, emptyChildren()));
newMask |= replacementMask;
}
}
}
return parent != null
? new HamtPMap<>(parent.key, shift(parent.hash), parent.value, newMask, newChildren)
: new HamtPMap<>(key, hash, result[0], newMask, newChildren);
}
/** Moves the root into the appropriate child. */
private HamtPMap<K, V> vacateRoot() {
int bucket = bucket(this.hash);
int bucketMask = 1 << bucket;
int index = index(bucketMask);
if ((mask & bucketMask) != 0) {
HamtPMap<K, V> newChild = children[index].plus(this.key, shift(this.hash), this.value);
return new HamtPMap<>(null, 0, null, mask, replaceChild(children, index, newChild));
}
HamtPMap<K, V> newChild =
new HamtPMap<>(this.key, shift(this.hash), this.value, 0, emptyChildren());
return new HamtPMap<>(null, 0, null, mask | bucketMask, insertChild(children, index, newChild));
}
/** Returns a copy of this node with a different array of children. */
private HamtPMap<K, V> withChildren(int mask, HamtPMap<K, V>[] children) {
return mask == this.mask && children == this.children
? this
: new HamtPMap<>(key, hash, value, mask, children);
}
/**
* Returns a new map with the elements from children. One element is removed from one of the
* children and promoted to a root node. If there are no children, returns null.
*/
private static <K, V> HamtPMap<K, V> deleteRoot(int mask, HamtPMap<K, V>[] children) {
if (mask == 0) {
return null;
}
HamtPMap<K, V> child = children[0];
int hashBits = Integer.numberOfTrailingZeros(mask);
int newHash = unshift(child.hash, hashBits);
HamtPMap<K, V> newChild = deleteRoot(child.mask, child.children);
if (newChild == null) {
int newMask = mask & ~Integer.lowestOneBit(mask);
return new HamtPMap<>(child.key, newHash, child.value, newMask, deleteChild(children, 0));
} else {
return new HamtPMap<>(
child.key, newHash, child.value, mask, replaceChild(children, 0, newChild));
}
}
/** Returns a new array of children with an additional child inserted at the given index. */
private static <K, V> HamtPMap<K, V>[] insertChild(
HamtPMap<K, V>[] children, int index, HamtPMap<K, V> child) {
@SuppressWarnings("unchecked") // only used internally.
HamtPMap<K, V>[] newChildren = (HamtPMap<K, V>[]) new HamtPMap<?, ?>[children.length + 1];
newChildren[index] = child;
System.arraycopy(children, 0, newChildren, 0, index);
System.arraycopy(children, index, newChildren, index + 1, children.length - index);
return newChildren;
}
/** Returns a new array of children with the child at the given index replaced. */
private static <K, V> HamtPMap<K, V>[] replaceChild(
HamtPMap<K, V>[] children, int index, HamtPMap<K, V> child) {
HamtPMap<K, V>[] newChildren = Arrays.copyOf(children, children.length);
newChildren[index] = child;
return newChildren;
}
/** Returns a new array of children with the child at the given index deleted. */
private static <K, V> HamtPMap<K, V>[] deleteChild(
HamtPMap<K, V>[] children, int index) {
if (children.length == 1) {
// Note: index should always be zero.
return emptyChildren();
}
@SuppressWarnings("unchecked") // only used internally.
HamtPMap<K, V>[] newChildren = (HamtPMap<K, V>[]) new HamtPMap<?, ?>[children.length - 1];
System.arraycopy(children, 0, newChildren, 0, index);
System.arraycopy(children, index + 1, newChildren, index, children.length - index - 1);
return newChildren;
}
/** Iterates sequentially over a tree. */
private static class Iter<K, V, O> implements Iterator<O> {
final Deque<HamtPMap<K, V>> queue = new ArrayDeque<>();
final Function<HamtPMap<K, V>, O> transformer;
Iter(HamtPMap<K, V> map, Function<HamtPMap<K, V>, O> transformer) {
this.transformer = transformer;
if (!map.isEmpty()) {
queue.add(map);
}
}
@Override
public boolean hasNext() {
return !queue.isEmpty();
}
@Override
public O next() {
HamtPMap<K, V> top = queue.removeFirst();
for (int i = top.children.length - 1; i >= 0; i--) {
queue.add(top.children[i]);
}
return transformer.apply(top);
}
@Override
public void remove() {
throw new UnsupportedOperationException();
}
}
/** Throws an assertion error if the map invariant is violated. */
@VisibleForTesting
HamtPMap<K, V> assertCorrectStructure() {
if (isEmpty()) {
return this;
}
int hash = hash(key);
for (int i = 0; i < children.length; i++) {
int childHash = hash(children[i].key);
if (compareUnsigned(childHash, hash) < 0) {
throw new AssertionError("Invalid map has decreasing hash " + children[i].key + "("
+ Integer.toHexString(childHash) + ") beneath " + key + "("
+ Integer.toHexString(hash) + ": " + this);
}
children[i].assertCorrectStructure();
}
return this;
}
}
|
2.10.2015
Y'all know I have been longing for a writing community for some time now- people to understand my struggles and to guide me in this new arena. I am pleased to share that I found one of the missing pieces on Instagram. I don't remember how I first found her, but ever since I started following Evelyn A. Lauer I have felt we share the same love for love and the same urge to tell a story about our battle to find it and keep it safe. Each time she publishes something new, I am reaffirmed that I know the character in her story. Evelyn earned her MFA in creative writing at Texas State University, is a Huffington Post blogger, and has just recently finished a memoir. This week she is hosting 7 Days of Love Stories written by guest bloggers on her website. The opportunity to share our story came at a perfect time since I'm currently working on our testimony for Re|Engage, the marriage ministry we hold so dear. I am grateful for my words to be included in her series and can't wait for y'all to read it so you can tell me what you think. My story is one fraught with poor decisions. But that's life, isn't it? And, somehow, I found a love that lasts. Here is our love story (in a word count nutshell)...
It's Together Ever After
The
first night we met I was broken.I was
still technically married at the time but had recently left my then-husband to
chase an old flame, to escape the pain, to make it all clean again.My then-husband was relieved to have the spotlight
positioned over my head instead of his and I was questioning why I had never
thought of divorce as an option before.I
let the old flame blanket me in warmth and I melted into him.
Just as soon as I learned to smile
again and to eat more calories than I drank each day, I started to see I wouldn’t
be able to keep him either.He had just
returned from the service overseas.I
had just escaped war in my own home.He
wanted freedom.I wanted security.Tangling in the sheets kept me entertained,
but it wouldn’t make me stay.I could hear
the cries and feel the wounds of the past seven years creeping up behind me at
night like the clip-clop and clatter of an old horse and buggy chasing me in the
dark.Without the warmth of his bed,
would I have the strength to flip on the lights and ward off the ghosts? And then we met...
1.17.2015
Last Thursday night I was sitting outside of Little Girl's acrobatics class doing some self-prescribed homework with Baby Girl. She wants so badly to be big and capable and worthy. I can't believe she doesn't already know she is beyond capable and worthy but I let her assign herself some homework anyway. As we sat on our favorite wooden bench, dancers and cheerleaders crisscrossing in front of us and almost tripping over our feet, we pulled out the Kumon workbooks I bought at Costco forever ago.
First we worked on uppercase letters, then we moved on to mazes, and finally ended up at connect-the-dots. I began at the number one and ran my forefinger through the white space, encouraging her to follow me and draw a straight, bold line right where I had traced an imaginary one. She drew her marker up in the air and pressed it on the paper. Every few seconds her big brown eyes would glance up from the paper to me for encouragement and I would remind her that she knows what comes after 14. "Keep going baby," I told her. "You're good at this." With each page came new challenges- the lines were on a diagonal, the numbers went into the 20s- and when she started to lose interest or get discouraged, I said, "Don't stop. It's going to look so neat when it's done. Can you tell what it is yet?" The mystery of the end product drew her back in.
Eventually, she developed some new strategies, "What if, instead of a straight line, I made a wavy line from seven to eight? What if I drew a circle around fifteen before I draw a line to sixteen?" At this point I was standing at the window, trying to watch Little Girl's dance. She's the youngest and most inexperienced in the class. I have to watch the routines intently so I know the answers to her questions while she practices during the week. Once I brought my attention back to Baby Girl and noticed what she was doing, I tried to steer her back to straight lines. "Honey, if you draw wavy lines between all the numbers, then the picture won't look right. Try the straight lines again." She went back to the straight lines and when she was done with each picture, she'd prance around the halls, holding the workbook open wide with both hands, singing a song about whatever she had just drawn.
As we drove home my mind kept wandering to the night before and the decision I need to make. I had attended an information session about creative writing classes. I debated not going in the days prior, but I figured the classes were unimposing. Adult education or continuing education classes are just for fun, right? Nothing to worry about. Wrong. These classes are intense. The Writer's Path seems like it is designed to strip you down and then build you back up. I expected that in this process. But I was pretty good at bringing myself down on my own; I didn't think I needed to pay someone else to do it for me.
Daddy issues aside, at sixteen I thrust myself into modeling and spent the first few years making decisions which would reveal, in time, who I could trust and who I could not. I was talking to my mom about all of this yesterday and we were half laughing, half cringing at all the mistakes I made when I first started modeling. The writer's retreats and writing classes I want to do now are very reminiscent of the model camps and model schools I tried when I was younger. I hear that tape playing in my head, chiding me with, "Everyone just wants your money. You're smarter than that." But really, I'm not. I'm not savvy enough in this new industry to know where to put my resources. And the stakes are much higher now with a family that depends on me.
My husband, daughters, and I have been discussing this during breakfast, late at night, in the car, in the bath, and now I'm sharing it with you, wherever you are. I think my husband always knew this was coming and is nothing but supportive. The girls just want to know what the book is about. I don't know where this interest in writing will take me but I am going to pursue it regardless, kind of like Baby Girl's connect the dots workbook.
I am now aware of the dots that brought me here but I'm a little hesitant to trust in which direction I should go. Maybe all the self-prescribed studying I've been doing these past seven months was just drawing a circle around my spot instead of moving onto the next one. Maybe the writing retreats or the Writer's Path will be wavy lines instead of straight ones. I don't know. But I wouldn't have met the people I needed to meet in the modeling world if I never started to take risks. And I'm never going to prance around the halls, singing and holding my book wide open with both hands, if I don't start taking more risks. If only the path I should take was lined out perfectly in front of me, each step clearly numbered, you know?
I plan on making more time to share on the blog this year and I hope you'll stay tuned and let me know what you think. For now, I'll be subtly hinting to my husband by posting on my blog that all he has to say is what I told Baby Girl (and what I'm sure I'll tell Little Girl later when we practice her dance), "Keep going baby. You're good at this."
1.06.2015
December is over. Phew. For me, it is always a test- as if I've been auditing and adjusting skills all year and the considerable demands of the busiest month test my limits. It is the most magical time of the year, right? Yes, only if the matriarchs can keep it together. Let's be honest, ladies. The magic is all up to us, isn't it? I think I fared well this year, better than in the past. Did you survive?
December is a glittering mirage that taunts me. "I can't wait until Christmas," I tell myself in July when we're dehydrated and dreading back-to-school. I love decorating with tiny, blinking lights and shimmery ornaments while Bing Crosby sings in the background. I love drinking hot chocolate while oohing and ahhing at Christmas lights in spirited neighborhoods. And I love cozying up under a blanket with my family to watch Home Alone for the umpteenth time. We look forward to it all year. I was proud of myself this fall for making it through the school's fundraiser, the pumpkin parties, the costumes, the candy, and then Thanksgiving in one piece. But as I was doing the last of the dishes at my parents' house, and I saw Christmas on the horizon, the anticipation of glitter and comfort dissipated. I felt the weight of December descend.
I resent the weight and the stress of December. How horribly ironic that Christmas is a celebration of the Lord sending us His one and only Son, yet our culture has tortured it and twisted it into a month-long, all-consuming army of monsters. I didn't want my family to duck out of any of the wonderful traditions, but I decided to reject the weight that is so closely associated with Christmas. My children's memories of the holiday season shouldn't be dictated by a mommy teetering on the edge of sanity.
The first stop on the normally crazy Christmas train is family drama. I am a relational person by nature. I feel most secure and most loved when surrounded by my family, which is a catch-22 because I come from a broken-three-times-sideways family that has always struggled with mending fences. We fight. But nobody ever wants to clean up. And as soon as we started to coordinate schedules for family meals, church services, and mini-birthday celebrations (one of my sisters and I both have birthdays within the week before Christmas), battle wounds from years ago were suddenly sore again. I even went down the will-he-even-send-a-birthday-card-this-year rabbit hole. Everyone's style varies from issue to issue- some choose to be silent, some choose to be very vocal- but either way, the pain is palpable.
This year I chose not to fight the fight. I chose to be respectfully quiet, peaceful, and humble. (Ok, I did freak out twice, but they were short-lived, well-contained, and two is a major improvement.) I smiled. I sent out Christmas cards anyway. And I prayed for them anyway. I heard someone raise the question last week, "How do I know if I have enemies?" If it's difficult for you to pray for them, then they're probably your enemies. And having an enemy within the blood of your own family is excruciating to maneuver well. If blood is thicker than water, it's far more painful to receive a blood transfusion than it is to drink a glass of water.
Sending out Christmas cards is, therefore, a major portion of the December Test. And the questions one must answer aren't confined to family. We must answer for our friendships as well. Will you send a card to them despite what has happened? Will you delete their address from your book completely? Will you contact them to get their new address since they moved, or not? Several years ago I decided I needed to make new friends, even reach out to some old ones. I have never trusted more than a handful of people at a time. Unknowingly, I had set the bar pretty high for success in these new relationships. Along the way many have not ended well. Discontinuation of the new friendships were mostly justified- square peg, round hole syndrome. But it still makes me sad when a connection is lost. Addressing Christmas cards has always reminded me of the fragility of the human heart. Things can change so quickly. You never know what the year will bring. This Christmas I decided I would intentionally change my attitude and focus on all the love that exists, instead of the void where it does not. I focused on the miracle of Jesus and the miracle of love and connection, instead of the great divisions.
Once I realized I could transform my perspective a bit in terms of my emotions, I was inspired to tackle the staggering logistics of December as well. I wanted to be prepared for surprises. I wanted to make sure I got enough sleep and didn't rely on vices for motivation or escape. And I wasn't going to allow myself to be devoured by worry and stress. So, I did the unthinkable- I quit smoking. (Yes, again.)
My close friends and family know I've been struggling with this for years. Each time I was done nursing my daughters, all it took was one date night and I was smoking at home every night after I tucked the girls into bed. It certainly is the dumbest thing I have ever done- to entertain such a ridiculously destructive habit. Yet I indulged over and over again. And I quit over and over again. This time though, I made it through Christmas, my birthday, and New Year's Eve without giving into another monster that used to prop me up during the holidays. More on that later, but I'm pretty proud of myself. And since I wasn't smoking, I hardly drank during the holidays either. Steady as she goes.
Ever since we became parents, the Christmas season has felt like an interminable acupuncture session gone horribly wrong. Each event, communication, task on the to-do list, and even our hopes were steadily poked and jabbed until the soft spot was eventually punctured. It almost seemed like that was the goal, to strip me down of all my safety barriers and crutches so that in January I could start rebuilding again. And I think I accepted it these past few years. But that's not what I want for myself. And my children definitely deserve more. We all deserve the best of me. And if I'm going to be the best version of myself, I have to be intentional about which side of the fight I'm entrusting with my energy.
January is still a time of rebirth and renewal for me, but on better terms this year. For once, the desperation that drove me to press the reset button was lessened...and lessoned. As I grow each year, I realize it isn't as important to maintain relationships as it is vital to understand each person for their own fears, their own needs. I'm afraid of the haunting pain that comes with losing people, so I grip them tightly. That's exactly why I smoked all those years- to lessen the pain of loss. It's unrealistic to expect life to be painless. It is absolutely possible for me to handle pain, and stress, and worry, and failures differently. I think I passed the December Test this year.
So I'm going to stop trying to warm the cold and to melt the ice. It's not my ice to melt. All I can control is what kind of wife I am to my husband, what kind of daughter or sister I am, and what kind of mother I am to my children. And when we have our own ice to deal with I better be ready and willing to stop focusing on the cold, to stop looking for something to lean on, and to just dig in and make the best of it.
9.24.2014
I've spent the past couple months studying the craft, poring over book after book. I desired to return to my story with a fresh set of skills but I needed time to pump myself up. This past summer I realized I shouldn't be desperately seeking writer friends. I needed to be reading their books. So I did. Their impeccable prose and constant encouragement sent me on a literary high. (Stephen King and Dani Shapiro and I have totally bonded. Too bad for them they have no idea.) I neared the end of Anne Lamott's Bird by Bird on the first leg of our family vacation a few days ago. For weeks I had been coasting along on my new-found confidence, itching to get back to my story, when, riding the Magical Express to Disney World, I read Lamott's last chapter. It made me mad- fire-breathing, spitting-dirt, kick-the-wall-even-though-it-hurts mad. I spent the days on our trip in Wonderland, laughing and smiling until my cheeks hurt. Then we'd tuck the girls in, my husband would fall asleep watching the news, and I would lie in bed with my eyebrows all scrunched up and my lower lip stuck out- angry and pouting in one of the most magical places on earth. A wildfire attacked My Galapagos. I stood witness to all of my work going up in flames.
Most artists and writers are introverts. We want to have a support system and a critique group to touch base with, but we aren't looking for new friends. I'm allowing my inner hermit to take over in this phase of life. My close friends would be hesitant to believe I'm any sort of a wallflower because they've stood witness to decades of shenanigans. But the ones who really know me have always suspected I would rather stay home, no matter how much fun we would have if they could get me to come out and play.
I've been locking myself in myself. In order to tell my story, and hopefully many others, I have to truly know myself. What would your answer be if someone asked you, "Who are you? What is your purpose in life?" Would you even have an answer? I was asked this recently. I told them I would have to get back to them. Even though I know my heart, my habits, and my dreams, I couldn't sum up exactly who I am and had never thought about my purpose in life. The easy answer would've been, "I'm a wife and mother and I like to read and write." But that's just the surface. I don't like living on the surface. It isn't the truth.
I have found many answers these past few months in my reading. Every time I read a new book, I learn more about myself. That's what I love about the written word. I love to connect with people, to tear back the façade, and to get a good look at the bones. Maybe this stems from hiding other people's lies; maybe it stems from hiding my own. Either way, all the dishonesty surrounding me left ravines so deep that the ground on which I stood broke away, and decided I would only focus on the truth, the bones from then on. We are all different structures built on the same set of bones. We all have the same problems, same worries, and same insecurities. The manifestations seem incomparable, but the bones are all the same. I just wish everyone wasn't so hell bent on celebrating the surface.
Back in April, I wrote here about my fears with this memoir. I'm afraid to include other people in my story- people who indisputably changed my future with their choices. They certainly didn't think that by popping in and out of my life that their actions would someday be immortalized in print. My curiosity on protocol caused me to reach out and ask for advice. Thank y'all for lending me your time, for your thoughtfulness, and for guiding me in a new direction. Hearing your feedback, whether encouraging or not, shapes me as a writer because it helps me discover what you want to read. Writing is all for naught if no one will read it. My heart and mind were full and ready to burst after y'all sent me down a new path and I naively bopped along this glorious trail with a literary companion for the next few months. And then the bomb went off.
A monsoon bathed the bus as we headed from the airport to our resort in Disney World. Determined to stay awake and utilize every free moment, I opened my book. I wanted to finish it before we arrived at the hotel and the vacation/marathon began. I had just made it to the last chapter when I read this from Lamott's Bird by Bird, "Libel is defamation by written or printed word. It is knowingly, maliciously saying things about people that cast them in false or damaging light." She went on to explain, "if you lived with a man who had a number of curious personal and professional habits and circumstances that his friends and clients know about, and if these friends can identify this man in your work by these habits and circumstances, you should probably change the details dramatically."
I felt robbed. I felt betrayed. I felt angry. Everywhere I turn, authors are inspiring other writers and dreamers to dig deep, to be unafraid, to tell your story, to be transparent, to not leave anything out. Lamott began on page 3, "The very first thing I tell my students on the first day of a workshop is that good writing is about telling the truth," and continued on page 6 with, "Remember that you own what happened to you." Just kidding. Everyone's going to sue you.
I chose to keep quiet about my torment until I had enough time to sort it all out. The next few nights I sulked, I cursed, and I plotted. My island became immediately engulfed in flames. All I had built, the sprouts I had planted, the towering palms I had been babying, even my favorite spot where I sat to write, had been devoured by the fire. This is my life, I thought. I would not be kept quiet anymore. That was the whole point in writing a book- to silence and expel my demons. Instead, they were consuming me, once again.
Eventually, I wiped the page of my mind clean, lifted my pen of creativity, and sketched an escape hatch smack dab in the middle of the empty white space. Fiction. Write fiction. I stared at the scorched bones left behind, littering my once-beautiful island, and began building again. I have no other choice. This dream won't be joining the rest of my failures in the scrap pile. This dream will be realized. If I have to change all the details, the identifying characteristics, the places, and everything else that lies on the surface, it won't bother me a bit. It won't change my story. The bones are still the same.
8.13.2014
The first day of Kindergarten- it was the moment I had been not-so-secretly looking forward to her entire five years of life. On those endless colicky nights that bled into the mornings, during those chaotic evenings when I wanted to hand everyone a package of Pop-Tarts and send myself to bed at 5:30, after running out of patience and answers when faced with the never-ending list of questions about the world, and especially when she asked me to get out the play-doh or the paints again after I just finished scraping Legos out of the carpet, I held out hope for...the first day of Kindergarten.
My parents, my mom friends with older children, her pediatrician, and even her Sunday school teacher all told me, "Just wait. When she's in Kindergarten it'll get easier! You'll have more time to catch up on all those things you've been setting aside." Their words transported me to my go-to fantasy, the one I had been painting in my head ever since her first indiscernible cry, and I smiled. In this future life of mine, I would saunter through the hallway of my clean house, draw in the aromas of the simmering pan, pat the heads of my content children, and go back to my book to sneak in a few pages before dinner. If only for a moment, I smiled. Life was going to be better. I would eventually get my act together. And it would be wonderful.
We had been preparing her for Kindergarten at every stage. "Oh, look! She is focusing her eyes on me for the first time! Go get the color blocks!" On her first half-birthday I began reading three books to her every night and never stopped. I let her use scissors way before I was comfortable giving her any sharp object and I tried to always say yes to play-doh because I knew it would strengthen the writing muscles in her hands. We took her to the zoo, the aquarium, the arboretum, the museum, the library. We pointed out every leaf on every tree, corrected every behavior that would be unbecoming to classmates, and cringed at the ones we knew the teacher would discover anyway.
Suddenly, we could see kindergarten ahead of us. Teachers were pointing out all the ways our children would be prepared for it at her preschool. Parents were giving us tips through past experiences, blogs, books, and unsolicited advice. Even my Mom's Group brought in speakers with checklists and inside information. Then, the wrench. My husband got cold feet. He started to entertain the idea we keep her home another year. Most of our parent friends in her class had children with late birthdays and it seemed at least half had decided to hold their children back. It was unclear whether their motives were sports or social-skills related, but still, he gave into the pressure. And he tried to convince me.
I panicked. I had this all planned out. We had discussed this plan countless times before and he had entirely agreed until now. How on earth was I going to change his mind? As we stood in the hall one morning, watching her class file upstairs to chapel, he whispered to me, "Wow. I never realized how much taller she is than the rest of her class." Bingo. I nodded and gave a little, "Mmm hmmm. She sure is!" Then I waited. I stayed quiet just long enough so he wouldn't see it coming. One night as we laid in bed watching TV, I nudged, "Honey, you know the biggest problem I see with holding her back? If she's a little bit older than everyone else, and even quite a bit taller, she'll probably be the first to...(ahem)...develop." "What? What do you mean?" Then I went for the jugular, "You know, she might be the first one in her class to get boobs. And, trust me, you never want to be the first girl in your class to get boobs." And just like that, it was over. Off to Kindergarten we went.
Finally, there we were. It was the first day of Kindergarten. I parallel-parked on the street in front of the school. Her sparkling new shoes led her as she floated out of the car and bounced off the pavement, skipping to the door. I followed closely behind, swallowing and blinking in quick succession. I only had to hold it together a few more minutes. I pumped myself up, "Come on. You can do this." She replied, "I know Mama! Come on!!" I signed my name and reached out for her hand. She was already halfway down the hall. She turned back and looked over her shoulder at me, bubbling over with giggles and anticipation. But she didn't slow down. I ran to catch up with her and scooted in the door behind her. A few fake smiles to the parents and a simple kiss on her cheek later, she was all settled in and ready. It was time for me to leave.
Of course I had to pull over and ugly cry on the way home. And of course I walked her to class every day that first week. Every day she smiled and skipped into the classroom. And every day it was time for me to leave. I did really well. She never saw a single tear. She only saw my smile, felt my arms squeezing the air out of her tiny little ribcage, and heard me whisper in her ear the same words I always left her with each morning in preschool, "Good bye. And go fly."
But then, that second Monday, I had to drop her off at the door. I turned the steering wheel and curved my car to the back of the building. I slowed up to the curb. A teacher opened my door and I handed her the Merida backpack she had coveted for so long. Be brave. And I let her walk out the door. I didn't move the car until I saw the school door close behind her, not until the teacher gently waved me ahead. And then I lost it.
I am not ashamed to say I pretty much lost it each and every morning I dropped her off at school the entire year. No, I didn't ugly cry every single morning. Yes, the teachers instantly knew I was nuts. No, they didn't hold it against me. But my heart did drop every time that glittery backpack bravely forged on and then disappeared through that door. When I had to release the brake and drive away, I clutched my heart.
Of course I instantly fell in love with her teacher and knew she was as happy and safe as she could be. Of course she made some incredible friends, blew our minds with her amazing math skills and hunger for science, and took our breaths away each time she finished reading us a new book. Of course she loved every minute of it- story time at the library, field trip to the zoo, field day, crazy hair day, kickball in the gym, tying her shoes for the first time by herself, making her very own fossil in class, singing "Let it Go" the loudest in music class. It was the most magical year.
And then, all too quickly, came...the last day of kindergarten. Graduation. Oh. My heart. No one warned me about graduation! I remember thinking how silly a kindergarten graduation sounded when she was a toddler. Really? So everyone gets a trophy, birthday parties are going to put us in the poor house, and they have a graduation ceremony every time they complete something? Isn't that a bit much? Yes. It is. But it's worth it. Preparing for, and entering, kindergarten is such a "thing" nowadays. Kids have to be much more prepared for kindergarten than we ever did, which means us parents do too.
Only, no one ever told me to prepare myself for the last day of kindergarten. No one told me she would have a different laugh, one I didn't recognize, within the first month of kindergarten. No one warned me that she may bolt out of the car in the morning and run into other people's arms...people I don't know- older students, classmates, art teachers, the school nurse. It doesn't matter. I don't know them. They aren't me. No one told me what would happen to my heart if I happened to be volunteering in the classroom on the very day the school practiced its lockdown drill. No one prepared me for those five minutes of silence, cornered in the bathroom with her sweet teacher, with her class, with her- sharing her teacher's fear.
I never realized all those years I was rushing through our three books before bed, not allowing her to speak whatever was on her mind because I was too tired, that she wouldn't learn to ask questions about the story, the characters, their choices. I wasn't letting her write her own story.
I never could have imagined that, after instructing her to return all uneaten food to her lunchbox so I could see how much she ate when she got home, I would be handed a soggy, dripping mess the first week of school because she saved the rest of her ice cream for me. I didn't know how tired she would be after school- too tired to do all the things I had planned to make up for our lost time together. She had already been to PE and recess. She was too tired to go to the park with me.
I never thought parents of kindergarteners would be inviting my little girl to sleepovers at five years old. I never thought girl drama would begin in kindergarten. I never thought parents of kindergarteners would drop their kids off at birthday parties. And I forgot how much I hate homework. No. Really. I despise it. Yes, I'm grateful to be involved with her studies and to better prepare her for "the real world" but give me a break. Let them be little. And let them be with their families in the few hours they have between school and bedtime. But what do I know? It's been decades since I was in kindergarten. My little girl is my oldest. This is our first time. We both had a lot to learn.
Now she knows how to write her own story, how to add and subtract, that humans and tyrannosaurus rex were never neighbors, that we forgive our friends, that she can do it, that I can do it, that I will always be there for her, and that I will need forgiveness too.
And what did kindergarten teach me? It taught me that I have a lot of letting go to do. It taught that me if I do let go, I allow her to fly. Sometimes she will fall, but mostly she will fly higher than I ever imagined. It taught me that she needs to write her own story. But it also taught me that I don't have to let go all at once. I have time. We still have time. Thank God.
7.13.2014
I had always prided myself on being self-made. I had planned, worked, saved, spent, crossed things off lists, worked, risked, failed, worked, saved, worked some more, and finally felt proud, pleased with my accomplishments. The husband? Check. The children? Check. The family? Check. The friends? Check. The house? Check. The vacations? Check. I grabbed the world by the shirt collar and won. I wasn't given special allowances or much of anyone's good graces. Beyond all odds, I had snatched that elusive, dangling carrot and finally sat down to enjoy it, all the while patting myself on the back. Never mind how I arrived here, right? All that mattered was I won.
Early in my journey, I was faced with betrayal on all fronts, personal, professional, and intimate. I learned at nineteen, and perhaps much earlier, that I could trust no one. Everything everyone had ever said to me became a lie with one truth. I forgave, continued to love, enjoyed life, and lived my own story, but always with a sideways glance and always on alert. Never would I allow myself to be unaware of my surroundings again.
Find me a decade later, and I was relieved to have overcome the most trying years- my twenties. Ah, the gloriously awful twenties that lift you up into the heavens of freedom and slam you back down on the ground of reality, over, and over, and over again until you turn thirty. Then, somehow, you stop taking things so seriously. You stand still, look down at your shoes, and laugh how feverishly you used to click those heels together.
I stood at thirty and smiled at the present, laughed at the past, and snorted at the future. Piece of cake. I had things figured out now. I knew men. I knew women. I knew how to work a situation and I knew when to bow out of one. I knew my strengths. I knew my weaknesses. I knew how to get what I desired. Obviously, my thirties had not yet begun to fight. Although, they quickly caught up.
My relationships started to crumble. First, it was my circle of friends, then it was my family, and finally, my marriage. Don't you worry. I justified it along the way. "Well, if that's what she thinks about me then I don't have time or energy to spend on her. This is just what happens after you become a parent. Your circle gets smaller. If he thinks I'm going to just lay down and let him get away with that- he's dead wrong. If they don't add anything to my life, then I have no use for them in mine. I'm done putting up with it all." And finally, "I don't care what he does. He could get a girlfriend. He could spend all our money. I'm not leaving. This is just how marriage is- tough." Haven't we all bought into the ridiculous phrase, "Respect yourself enough to walk away from anything that no longer serves you, grows you, or makes you happy"?
I had created my own world and was reigning over it with a clenched fist. If someone didn't align themselves with my ideals, they were removed. I judged, rejected, and punished people. Had they done me wrong? Absolutely. Was I hurt? Deeply. Was I any authority? Did I know the secrets of the world and, therefore, possess the knowledge required to reign over a kingdom? Did I know any other way than to answer displeasure with judgment and punishment? No. Absolutely not. And, nope.
So why was I in charge? Who put me in power anyway? I did. I had created my own idol- myself. I convinced myself that I knew all before and all future. I knew what he was thinking, knew what she really meant, and knew what would happen if I didn't defend myself. Life was war. Only, I never noticed I was the only one worshipping the idol I had created. I kept waiting for everyone else to get on board. Eventually, if I stuck to my guns, he would change his mind, she would say she's sorry, and then, but only then, would I let them back into my kingdom.
But Something had been lingering in the distance. Even when I couldn't, or didn't want to, hear Its footsteps gaining ground, I always knew It was there. I heard It the first time he told me he loved me, I saw It the days my daughters were born, I felt It in the breeze that tickled my neck, and I tasted It in the depths of my defeat. But I wouldn't acknowledge It. No, no, no. Someone or something else is not going to get credit for all I've done, for how far I've come.
Then all at once, I gave in. I was desperate for help and tired of clawing for something further. I stopped fighting. I released my fist. I got down on my knees and admitted my inadequacy. How could I have fooled myself into believing that I had it all together without accepting responsibility for the outcome? I had all the answers but I didn't like where my answers had lead me. I had stood up for myself and fought back my whole life. I ended up alone. Yes, I had a wonderful husband and two blossoming little girls, but I was keeping a part of my heart from them. It was time to relinquish control.
Suddenly, and I emphasize suddenly, all the things I had yearned for were fulfilled and then trumped with even more incredible gifts than I ever would've thought to ask for. My demons were falling behind. Little treasures revealed themselves to me under rocks I had never imagined turning over before. Now, I was winning.
I am not self-made. "I praise You because I am fearfully and wonderfully made; Your works are wonderful, I know that full well." Psalm 139:14
7.01.2014
It's no secret that I am passionate about relationships- family, friends, and intimate ones. I've spent the better part of my life asking myself, "Why?", as if I'm any authority. I go 'round and 'round in circles wondering why people make the decisions they do in relationships with me, with others. Do you remember that scene in Sex and the City when Carrie is obsessing about yet another breakup with Big and she's sitting at lunch with the girls reassuring herself that she's got things under control, that she doesn't need to sit on some quack's couch, because she has her girlfriends? To which Samantha replies something like, "Nope. You're too much for us. We've done all we can. You need to get some help." That's me- in a nutshell. I'm obsessive and flawed and hungry to learn more.
Well, the other night, in one of my self-imposed Why-fests, I asked myself yet another daunting question, "Why did me marry me?" I mean, really. Why did he marry me? We're such different animals. But in the beginning we only saw our similarities. That's a funny trick life plays on us. You meet someone you can't believe you spent what felt like eternity without and you play up all the things you have in common. "You like Pat Green?! So do I! You have tropical décor in your home? So do I! You workout but won't give up junk food? Me too!! You drive a Jeep Wrangler? No way! I've always wanted one of those!" It's ridiculous really. Like any of those things matter.
Another ruse most of us comfortably dysfunctional people fall for is that once you find the man of your dreams, all the hard work is over. No more awkward first dates, no more disaster break-ups. Gone are the days you had to put up with that one creepy best friend. Now you can take your head off a swivel and return your focus to one person, instead of darting your eyes at everyone that crosses your path wondering if they're "the one". Let it out. Release that big sigh you've been holding in all these years. You can finally breathe.
When you start to get comfortable- I mean really comfortable, as in muffin-top, clothes on the floor, haven't-cleaned-out-my-car-in-three-weeks, and the-creepy-best-friend-keeps-dropping-in-unannounced comfortable- that's when it all starts. That's when the marriage really begins. Soon enough, you've traveled such a distance, don't quite know how you got there, and you look back over your shoulder. Puzzled, you can't figure out what just happened between point A and B. All you're sure of is the two are nothing alike. And you may ask yourself, "Why did he marry me?"
Couldn't he see all the red flags? Of course, I don't consider my need to reorganize the house every two weeks or that nagging feeling I get when I see an unfortunate begging for money as red flags, but I'm pretty sure he does. We do not agree on labeling bins for the kids' toys and he doesn't give me much cash if we're spending a night in the city (I'm a stay-at-home-mom and I'm cool with it).
So, why did he marry me?! The truth is, he didn't marry me. He married a picture of me. He married the picture of me I was selling. As if standing on a street corner, amidst a bustling art fair, I spotted him and held a beautiful portrait over my head, vying for his attention. Luckily, his neck turned, his feet stopped, and his chin moved forward, head tilting, intrigued. He was instantly seduced by the lines, the colors, the composition. He thought the only flaws in this work of art must be the freckles, especially that one on her lower lip, and he adored them. I kept pointing out the brush strokes, exaggerating how much time it took me to complete this work, explaining that it really is a bargain, and embellishing a story about the girl in the picture. Not too much time passed and he decided he must have this portrait. Something about it resonated with him and he could picture it hanging on his wall so well that it became a part of him. The poor guy didn't even realize the art he so loved was only a glimmer of the starving, lonely, and slightly unstable artist he hadn't noticed holding up the portrait- me.
We are quickly approaching our ten year anniversary. Seven years of marriage, but ten years together. Now I realize the world is all one, big con. Here! Look over here! Buy this! Drink this! Put this on your face! Wear this! Marry this!! But God didn't put us together because we're the same, or even because we're similar in ways. He brought us together with His celestial concoction of magic and logic because we're different. Our differences challenge us both...at all times...in all ways imaginable- at the store, on the phone, in the car, in the bedroom. In areas he would never budge on his own, I am the free-spirited force sent to help release him. Whereas I could blindly follow someone, anyone, into a dark alley trying to help them find their lost kitty cat, he is the one to grab my hand and pull me back, to remind me that I can't trust everyone, and to protect me.
The truth? He married me because a Little Voice in the back of his mind told him to marry me. No, he wasn't entirely sure I was the right choice, and I am entirely sure he has questioned this choice on quite a few occasions, but Something in him was telling him to do it.
We are together because of our differences, because God wanted to alter certain parts of us to make us better. How are we supposed to spread love when we'd rather be selfish, to open our arms when we want to retreat, to follow God instead of renouncing Him if we're all walking around in our comfort zones/protective bubbles/monotony cages? The truth? We can't. We can't change the world by living within the world's standards. We have to think outside the box. We have to be open to new ideas, new solutions, and even to ideas and solutions depicted as too flawed or too perfect in the past. |
Q:
When is incorrect pronoun usage likely to offend people based on gender?
At this point it is pretty well known that the recent issues are related to changes in the CoC regarding the use of pronouns. While the new Code of Conduct won't be available until the 10th of October, the current Code of Conduct says
No bigotry. We don’t tolerate any language likely to offend or alienate people based on race, gender, sexual orientation, or religion — and those are just a few examples. When in doubt, just don’t.
What I am curious about is which, if any, of the following scenarios would be likely to offend or alienate people based on gender (and why)
A long time user states in her profile that her pronoun is "she". A new user leaves a comment using "he".
A long time user states in her profile that her pronoun is "she". Another long time user repeatedly refers to this user as "he" even after being repeatedly corrected.
A long time user states in her profile that her pronoun is "she". Another long time user (userB) refers to this user as "he" and upon being corrected, this user apologizes and says that as a non-native speaker, pronouns cause him difficulty.
A long time user states in zir profile that zir pronoun is "ze". Another long time user repeatedly refers to this user as "he" even after being repeatedly corrected.
A long time user states in zir profile that zir pronoun is "ze". Another long time user (userB) refers to this user as "he" and upon being corrected, userB claims "ze" is incorrect according to his religious beliefs and that he (userB) will not use it, but to avoid misgendering users he will only use user names from now on for all users regardless of pronouns.
A long time user states in zir profile that zir pronoun is "ze". Another long time user (userB) refers to this user as "he" and upon being corrected, userB claims "ze" is incorrect according to his religious beliefs and that he (userB) will not use it, but to avoid misgendering users with a pronoun of "ze", he will only use user names for users with a pronoun of "ze".
A long time user states in zir profile that zir pronoun is "ze". Another long time user (userB) refers to this user as "he" and upon being corrected userB claims "ze" is incorrect according to his religious beliefs and that he (userB) will not use it, but to avoid misgendering users with a pronoun of "ze", he will disengage and not respond to comments or provide answers to users with a pronoun of "ze".
A long time user states in their profile that their pronoun is "they". Another long time user repeatedly refers to this user as "he" even after being repeatedly corrected.
A long time user states in their profile that their pronoun is "they". Another long time user (userB) refers to this user as "he" and upon being corrected userB claims the singular they is not grammatically correct and that he (userB) will not use it, but to avoid misgendering users with a pronoun of "they", he will only use user names for users with a pronoun of "they".
A long time user states in their profile that their pronoun is "they". Another long time user (userB) refers to this user as "he" and upon being corrected userB claims the singular they is not grammatically correct and that he (userB) will not use it, but to avoid misgendering users with a pronoun of "they", he will disengage and not respond to comments or provide answers to users with a pronoun of "they".
A:
I go by the pronoun ‘they’. Here's the gist of how it works:
Pronouns serve a function similar to names and titles; they are personal like names, and they carry social associations with them like titles. Let's see how these can all be used disrespectfully:
If I tell you my name is ‘Iñigo Montoya’ and you make a habit of calling me ‘that brat I taught a lesson to all those years ago’, that's not cool.
If you tell me your pronoun is ‘he’ and I make a habit of calling you ‘she’, that's not cool. By doing that I may be verbally emasculating you and treating you as an effeminate ‘sissy boy’ or implying some other negative connotations about feminine gender roles—which by your pronoun you are clearly not subscribing to.
Conversely, if you're a ‘she’ and I call you ‘he’, I may be verbally suggesting you're too ‘bossy’ or gruff or emotionally incompetent or any of various other negative connotations about masculine gender roles.
Why negative connotations and not positive connotations? If I'm deliberately using the pronoun you asked people not to use, it's not because I'm demonstrating respect for you.
If I'm an attorney in a U.S. court of law, and I keep addressing Judge Amy Berman Jackson by saying ‘But Amy, dude, my client is innocent!’ instead of ‘Your Honor, my client is innocent!’, she's not going to be impressed. She'll be even less impressed if she pokes her head into another courtroom and sees you addressing the judges who present as male with ‘Your Honor’.
In fact, while not technically wrong in a broader sense, it is even disrespectful to address her as ‘Judge’ instead of ‘Your Honor’ in U.S. federal court, and this can be exploited to send judges into fits of apoplexy.
If you go out of your way to categorically object to using pronouns for a certain class of people because you think the way they present themselves in society doesn't match what you think their chromosomes or genitalia are, then:
That's really weird, dude. We're on a forum of pseudonymous strangers on the internet and you're worried about my DNA makeup or thinking about my genitals every time you talk about me?
(FOR THE RECORD: As a vulture, I have a cloaca.)
That's not cool.
If you go out of your way to invent a grammatical rule prohibiting singular ‘they’ (but invariably still allowing singular ‘you’) despite seven centuries of consistent use of the word for singular and plural antecedents since it was introduced into the language—and if you do that just so you can refuse to use my pronoun when referring to me, I have to wonder: wat?
I'm also really tired of that debate no matter how many times you've shared a good smirk among your cis friends over a cocktail about your superior command of English prescriptivism to shut down those social justice warriors trying to regulate your use of language…which you're going do by inventing grammatical rules to regulate our use of language.
I get that English may not be your first language and you may make mistakes with English pronouns. That's cool; I'm happy to help you learn, because I'm here on a Q&A site to exchange ideas and communicate—I'm not here to trip you up. I understand it's different in every language;* it's no big deal if you slip up with English—I might make gaffes in other languages too.
I get that you may not know my pronoun when all you see is my name Squeamish Ossifrage. That's cool; I'm happy to let you know, and it's no big deal if you slip up without knowing.
That said, I don't think it's helpful to litigate in advance what the answer to every abstracted scenario is going to be, and I don't think it would be helpful to enshrine that pre-litigation in a code of conduct. You're giving the impression to everyone I may have to deal with now that there's a complicated system of arbitrary rules they will have to memorize and follow (which, in a certain sense, is true anyway, because that's the nature of human interaction, but this isn't making it easier for anyone). I don't know what the updated code of conduct will say, but I hope it doesn't look like your list of abstracted scenarios together with rulings by the court of meta.se opinion.
* Some languages like Old English have grammatical gender that carries very little in the way of social implications, with a neuter word wif for woman, a feminine word wiht for any creature including a person, and a masculine word mann for person of any sex or social role. Some languages like Thai have what are to English speakers—and even to European languages like French and Spanish—very complicated systems of formality and familiarity that make pronoun avoidance obligatory in certain scenarios for tactful conversation. Some languages distinguish pronouns by spatial position instead of social role.
A:
To directly answer the question, it's complicated and there is a growing body of active research related to this question. A 2019 article, found with a very quick Google Scholar search, concluded:
Those who advocate greater use of gender-neutral and non-binary
language should note that resistance to personal pronouns other than
‘he/him’ and ‘she/her’ appear to be driven not simply by grammatical
prescriptivism, but also by more conservative and binary gender role
attitudes. Given the divergence between generic and specific use of
singular ‘they’, greater acceptance of such language is not driven
just by a greater willingness to ignore grammatical conventions.
Future research in this area should focus on clarifying the
relationship between presciptivist attitudes, personality, and gender
ideology, as well as the degree to which speakers attribute their
grammatical judgements to these factors. Greater awareness of these
factors may inform the strategies adopted by those wishing to
influence linguistic style in public and scholarly venues.
Bradley, E. D. (2019). Personality, prescriptivism, and pronouns. English Today. doi:10.1017/S0266078419000063 (PDF)
In short, simply enumerating a list of options is unlikely to give any insight into the problem.
To comment on the structure of the question itself: the list of options is structured a bit more like a push poll than a research instrument. Furthermore, the way it is written is going to lead to respondent fatigue and invalid conclusions since the respondent may end up annoyed at you for asking questions this way (i.e., wall of text, phrasing assumes familiarity with subject, etc.), which will bias their responses. However, this is a really interesting research question; but a survey instrument to examine it will take a lot of work to get right.
A:
Here's a simple take (which, if I gather correctly, was what Monica got fired but hey I can't be fired): this is a Q&A site which doesn't need pronouns. The only time I feel I need to refer to a person is when I want to specify which answer (or comment) I am reacting to and then I can say "while the answer by @chx(link) is correct, it missed a few points..." and there we go. This entire issue can be sidestepped this easily.
To ratchet it up, not much would be lost if we were to remove the username and profile pic from the answers (which "community wiki" actually does) but keep the karma and badges as a sort of "quality stamp" and perhaps link to the user profile page so that an interesting answer can be followed to other answers.
|
Steve Reeves
Stephen Lester Reeves (January 21, 1926 – May 1, 2000) was an American professional bodybuilder, actor, and philanthropist. He was famous in the mid-1950s as a movie star in Italian-made peplum films, playing the protagonist as muscular characters such as Hercules, Goliath, and Sandokan. At the peak of his career, he was the highest-paid actor in Europe.
From 1959 through 1964, Reeves appeared in a string of sword and sandal movies shot on relatively small budgets and, although he is best known for his portrayal of Hercules, he played the character only twice: in the 1957 film (released in the US in 1959) and its 1959 sequel Hercules Unchained (released in the US in 1960). By 1960, Reeves was ranked as the number-one box-office draw in twenty-five countries around the world.
Early life
Born in Glasgow, Montana, in 1926, Reeves moved to California at age 10 with his mother Goldie Reeves after his father Lester Dell Reeves died in a farming accident. Reeves developed an interest in bodybuilding at Castlemont High School and trained at Ed Yarick's gym in Oakland, California.
After graduating from high school, he enlisted in the United States Army during World War II, and served in the Philippines. After his military service Reeves attended California Chiropractic College in San Francisco.
He reigned as Mr. America of 1947, Mr. World of 1948, and Mr. Universe of 1950. He was contacted by an agent who suggested he go into acting.
Career
Cecil B. de Mille
Reeves moved to New York where he studied acting under Stella Adler, but after arguments he was refunded his tuition. He studied instead at the Theodora Irvin School of the Theatre. He began performing a vaudeville act with a comedian named Dick Burney. One of Cecil B. De Mille's talent scouts saw him and had him tested for Samson and Delilah (1949). Reeves received a seven-year contract with Paramount.
Reeves says de Mille wanted to cast him in the lead role, but told Reeves he had to lose 15 pounds in order to look convincing on-camera. Reeves says he tried to lose the weight and worked on his acting in preparation for the role over three months. Then De Mille told him he was going to give the role to Victor Mature.
Early acting appearances
In 1949 he filmed a Tarzan-type television pilot called Kimbar of the Jungle, and in 1950 became Mr. Universe.
Reeves appeared on television in Stars Over Hollywood in the episode "Prison Doctor" with Raymond Burr. He was one of the athletes in Gentlemen Prefer Blondes (1953) and appeared on the TV series Topper ("Reducing").
In 1954, Reeves had a small supporting role as a cop in the Ed Wood film Jail Bait. It was his first film and earned him his Screen Actors Guild card. "I had a suit on at all times," he later recalled. "I even had a tie. Only took my shirt off once. Those were the days, huh?"
The same year Reeves was in the MGM musical Athena, playing the boyfriend of Jane Powell's character.
These two films are the only ones Reeves made in the United States where his actual voice was used; Reeves acted in Italian-made films for the remainder of his career, where all dialogue and sound effects were added in post-production.
Reeves guest-starred on The George Burns and Gracie Allen Show as the owner of a gym. On December 17, 1954, Reeves guest-starred in the ABC sitcom Where's Raymond?, starring Ray Bolger as Raymond Wallace, a song-and-dance man. Reeves played a well-built office employee whom Wallace sees in the company of Wallace's girlfriend, Susan.
In 1955 Reeves appeared on two Broadway shows, Kismet and The Camp.
Pictures of Reeves' costume test for the lead in Li'l Abner (1959) can be easily found on the web.
He then decided to quit acting and worked for American Health Studios in public relations, opening up fitness studios.
Hercules
In Italy, director Pietro Francisci wanted to make a film about Hercules but could not find anyone suitable to play the role. His daughter recommended Reeves on the basis of his appearance in Athena and Francisci offered him the role and a plane ticket to Italy. Reeves at first did not think he was serious but eventually agreed and flew to Italy to make the film. His fee was $10,000.
Hercules was a relatively low-budget epic based loosely on the tales of Jason and the Argonauts, though inserting Hercules into the lead role.
The film proved popular in Europe. What made it an international sensation was when US distribution rights were bought by Joe E. Levine who spent over $1 million promoting it, turning the film into a major box-office success, grossing $5 million in the United States in 1959. However this did not happen until Reeves had already made four more films in Europe.
The first of these was a sequel to Hercules, Hercules Unchained (1959), again directed by Pietro Francisci. Reeves was paid the same fee, although his wage would double from then on. This film was another huge success, being the third most popular film in Britain in 1960. Nonetheless Reeves would not play Hercules again, despite his identification with the role.
Reeves' third film as star was The White Warrior (1959), based on Hadji Murat, the novel by Leo Tolstoy. He played Hadji Murad, a 19th-century Chechen chieftain who led his warriors in a fight against the invading Russians.
Reeves was then in Terror of the Barbarians playing Emilio, about the Lombard invasion of Italy. American International Pictures bought US rights and retitled it Goliath and the Barbarians (1959), with Reeves' character renamed "Goliath". The film earned $1.6 million in North America during its initial release where it was double billed with Sign of the Gladiator
Injury
Reeves was Glaucus Leto in The Last Days of Pompeii (1959), based on the novel by Sir Edward Bulwer-Lytton. It co-starred Christine Kaufmann and Fernando Rey and was mostly directed by Sergio Leone.
During the filming, Reeves had dislocated his shoulder when his chariot slammed into a tree; he re-injured it while swimming in a subsequent underwater escape scene. The injury would be aggravated by his stunt work in each successive film, ultimately leading to his retirement from filmmaking.
U.S. directors
Reeves followed this with The Giant of Marathon (1959) where he was cast as Pheidippides, the famous wartime messenger of the Battle of Marathon. By now Reeves' success was such that his films would use Hollywood directors: Marathon was directed by Mario Bava and Jacques Tourneur. According to MGM records the film earned $1,335,000 in the US and Canada and $1.4 million elsewhere resulting in a profit of $429,000.
Reeves had a change of pace in Morgan, the Pirate (1960) where he played pirate and self-proclaimed governor of Jamaica, Captain Henry Morgan. Andre De Toth and Primo Zeglio directed.
He then did an "Eastern", The Thief of Baghdad (1961), playing Karim, directed by Arthur Lubin.
In The Wooden Horse of Troy (1961) Reeves played Aeneas of Troy, opposite John Drew Barrymore.
He co-starred with fellow body builder Gordon Scott in Duel of the Titans (1961), playing Romulus and Remus respectively. Sergio Corbucci directed.
Reeves played Randus, the son of Spartacus in The Slave (1962) then reprised his role as Aeneaus in War of the Trojans (1962) aka The Avenger.
Later roles
Reeves played Sandokan in two films, both directed by Umberto Lenzi: Sandokan the Great (1963) and Pirates of Malaysia (1964). By this stage Reeves says his fee was $250,000 a film.
In 1968, Reeves appeared in his final film, a spaghetti Western he co-wrote, titled I Live For Your Death! (later released as A Long Ride From Hell). "I ended up with an ulcer from that," he said later. "That was my last."
Reeves reportedly turned down the James Bond role in Dr. No (1962) because of the low salary the producers offered.
Reeves also turned down the role that finally went to Clint Eastwood in A Fistful of Dollars (1964) because he did not believe that Italians could make a western out of a Japanese samurai film.
George Pal contacted Reeves for the role of Doc Savage in Doc Savage: The Man of Bronze, the first of what was meant to be a film series, but when filming was about to begin a Hollywood writers strike put the film on hold with Reeves and the original director replaced.
Post-acting career
Reeves decided to retire for several reasons: stress, his injury, and the decline in the market for his sort of movies. He had earned enough to retire and moved to his ranch in Oregon, which he purchased from Chandler Knowles.
His last screen appearance was in 2000 when he appeared as himself in the made-for-television A&E Biography: Arnold Schwarzenegger Flex Appeal.
Other interests
A biography, Steve Reeves – One of a Kind, was published in 1983 by Milton T. Moore.
In 1991, Chris LeClaire began writing and researching Reeves' life and career. LeClaire lived and worked for Reeves at his Valley Center, California horse ranch during the summers of 1993 and 1994 while writing Worlds To Conquer, The Authorized Biography Of Steve Reeves. LeClaire conducted more than one-hundred hours of taped interviews with Reeves up until the actor's death in the spring of 2000.
In 1994, Reeves, with long-time friend and business partner George Helmer, started the Steve Reeves International Society. In 1996, it incorporated to become Steve Reeves International, Inc.
In 2003, Helmer co-authored Steve Reeves – His Legacy in Films, and in 2010, Steve Reeves' Hercules Cookbook. In 2014, he published a Reeves biography, A Moment in Time – The Steve Reeves Story. Helmer is also the executor of the Reeves' estate, exclusive owner to the rights of Reeves' name and image, and considered by many as the authority on Reeves.
Some doubt exists as to whether Steve Reeves ever gave authorization or approval to any biographer.
Reeves wrote the book Powerwalking,
and two self-published books, Building the Classic Physique - The Natural Way,
and Dynamic Muscle Building. (Note that George Helmer published a revised and updated edition of the Powerwalking book in 2013.)
Freelance writer Rod Labbe interviewed Reeves, and the article appeared in Films of the Golden Age magazine, summer 2011. It was conducted in 1997 and was the last extensive interview Steve Reeves did.
Personal life
Later in his life, Reeves bred horses and promoted drug-free bodybuilding. The last two decades of his life were spent in Valley Center, California. He bought a ranch with savings from his film career and lived there with his second wife, Aline, until her death in 1989.
Death
On May 1, 2000, Reeves died from a blood clot after having had surgery two days earlier. He died at Palomar Hospital in Escondido, California, where his second wife had also died.
In popular culture
In the 1973 British musical stage production The Rocky Horror Show, and its 1975 film counterpart The Rocky Horror Picture Show, Dr. Frank N. Furter introduces himself to Brad and Janet with the song Sweet Transvestite. The lyrics include, "Or if you want something visual/That's not too absymal/We can take in an old Steve Reeves movie".
Filmography
(in parentheses the original movie title)
Gentlemen Prefer Blondes (1953) as Olympic Team Member (uncredited)
Jail Bait (1954, Hollywood film directed by Ed Wood Jr.) as Lieutenant Bob Lawrence
Athena (1954, Hollywood film directed by Richard Thorpe) as Ed Perkins
Hercules (1958, released in Italy in 1958, released in U.S.A. in 1959) (Le fatiche di Ercole / The Labors of Hercules) as Ercole (Hercules)
Hercules Unchained (1959, released in USA 1960) (Ercole e la regina di Lidia / Hercules and the Queen of Lydia) as Hercules
The White Warrior (1959, directed by Riccardo Freda) (Hadji Murad il Diavolo Bianco / Hadji Murad, The White Devil) as Agi / Hadji Murad, the White Warrior
Goliath and the Barbarians (1959) (Il terrore dei barbari / Terror of the Barbarians) as Emiliano (a.k.a. "Goliath")
The Last Days of Pompeii (1959) (Gli ultimi giorni di Pompei / The Last Days of Pompeii) as Glaucus Leto
The Giant of Marathon (1959) (La battaglia di Maratona / The Battle of Marathon) as Phillipides
Morgan, the Pirate (1960) (Morgan, il pirata/ Morgan, the Pirate) as Henry Morgan
The Thief of Baghdad (1961) (Il Ladro di Bagdad) as Karim
The Trojan Horse (1961) (La guerra di Troia/ The Trojan War) as Aeneas
Duel of the Titans (1961) (Romolo e Remo / Romulus and Remus) as Romulus
The Slave (1962) (Il Figlio di Spartaco / Son of Spartacus) as Randus – son of Spartacus
The Avenger (1962) (La leggenda di Enea / The Legend of Aeneas) (also released as The Last Glory of Troy; it is a sequel to The Trojan Horse) as Enea / Aeneas
Sandokan the Great (1963, directed by Umberto Lenzi) (Sandokan, la tigre di Mompracem/ Sandokan, the Tiger of Mompracem) as Sandokan
Pirates of Malaysia (1964, directed by Umberto Lenzi) (a.k.a. Sandokan, the Pirate of Malaysia, a.k.a. Pirates of the Seven Seas; this is a sequel to Sandokan the Great) as Sandokan
A Long Ride from Hell (1968, spaghetti western directed by Camillo Brazzoni, produced and co-written by Steve Reeves) (I Live for Your Death!) as Mike Sturges (final film role)
See also
List of male professional bodybuilders
References
Further reading
Chapman, David. "On The Cover: Steve Reeves", Hardgainer, November 1992.
Moore, Milton Jr. "STEVE REEVES - One of a Kind (An Authorized and Approved Reeves Biography)", 1983.
Helmer, George. "A Moment in Time - The Steve Reeves Story", 2014
Dowling, Dave and Helmer, George. "STEVE REEVES - His Legacy in Films", 2003
LeClaire, Christopher. Steve Reeves Biography "WORLDS TO CONQUER – The Authorized Biography Of Steve Reeves", * , First Edition December 1999, Second Edition 2017.
External links
Steve Reeves Biography The Authorized Biography of Steve Reeves'' by Chris LeClaire, Paperback 1st Edition 1999, 2nd Edition 2017
Steve Reeves International Society
How Steve Reeves Trained by John Grimek, Muscular Development November, 1964
The Many Faces of Hercules at Brian's Drive-In Theater
Reeves gallery and Reeves movie related articles
Category:1926 births
Category:2000 deaths
Category:20th-century American male actors
Category:American bodybuilders
Category:American expatriates in Italy
Category:American male film actors
Category:American male television actors
Category:American military personnel of World War II
Category:Deaths from cancer in California
Category:Deaths from lymphoma
Category:Expatriate male actors in Italy
Category:Male actors from California
Category:Male actors from Montana
Category:People associated with physical culture
Category:People from Glasgow, Montana
Category:Professional bodybuilders |
VAT news
Removal of Low Value VAT Exemption for Imports
Elizabeth Wilson7 December 2016No comments
As part of the European Commission’s measures to improve the VAT environment for e-commerce businesses, the EC has set out their plans to take action against VAT fraud committed by businesses outside the EU by proposing to remove the low value VAT exemption on imports. Currently, small consignments and packages valued at €22 or less can be exempted from VAT on their way in to the EU. The Commission have decided that this low value exemption will be scrapped as the current system “is open to massive fraud and abuse”, and creates “major distortions against EU business”.
According to the Commission, under current rules EU businesses are put at a “clear disadvantage since unlike their non-EU competitors, they are liable to apply VAT from the first eurocent sold”, and high-value items such as smartphones and tablets are “consistently undervalued or wrongly described in the importation paperwork”. It is estimated that around 150 million parcels are imported into the EU under this VAT exemption every year, all of which will become liable to VAT following last Thursday’s announcement.
The low value consignment concession was originally introduced by the EU in 1983 with the aims of reducing the administrative burden on EU Member States customs authorities as well as speeding up the delivery of lower value goods. The boom in e-commerce over the past 20 years has led to a dramatic increase of imports into the EU, and it is claimed that thousands of smaller non-EU retailers have taken advantage of the VAT exemption by mislabelling or undervaluing higher value goods. In 2014, the EU Commission projected that Member States were missing out on €5 billion of VAT revenues, €1 billion of which was attributed to VAT foregone from the concession.
Criticism of the low value exemption on imports is not a recent phenomenon. Almost a decade ago, online retailers such as Amazon and Play.com began to exploit this VAT exemption by shipping lower value items such as CDs and DVDs to the UK from the Channel Islands (a non-EU territory in the English Channel). In the UK, HMRC took action on the Low Value Consignment Relief on goods being shipped from the Channel Islands as it was believed to be costing the UK as much as £110 million per year in tax revenues and was also blamed for the closure of high street retailers such as Virgin Megastore, Woolworths and Zavvi. The UK government came under significant pressure to clamp down on this VAT avoidance and eventually removed the exemption for Channel Islands territories in 2012.
According to the Commission’s press release, a recent study based on real purchases has suggested that 65% of all consignments from non-EU countries were non-compliant with EU VAT rules. It is clear that such high levels of non-compliance will have distorted the EU marketplace and given non-EU businesses an advantage over their competitors within the EU. So, going forward import VAT will be applied to all goods reaching EU borders from non-EU territories. EU businesses should therefore benefit from being on a “level playing field” as non-EU businesses will now also have to incorporate import VAT into their pricing.
Additionally, registration in the VAT One Stop Shop will be available to ‘trustworthy’ traders from outside the EU. This is predicted to cut VAT compliance costs for non-EU businesses as traders will be able to designate an EU intermediary (such as a market place, courier, postal operator or customs agent) to deal with VAT-related compliance. Non-EU businesses will therefore not have to worry about registering in each Member State where they import as this is prohibitively expensive and understanding all the VAT rules can get extremely complicated. Businesses will also benefit from having an easier way to pay and distribute VAT payments across the various Member States.
Clearance of small consignments from trusted non-EU traders who register with the VAT One Stop Shop will benefit from simplified customs procedures. Consignments valued up to €150 will no longer be stopped at customs for VAT clearance and VAT collection for these goods will be managed separately on a self-assessment basis. Non-EU traders or their intermediaries will need to provide advance information on consignments in order to benefit from the simplification of the One Stop Shop. They will also need to keep records of supplies so that tax assessments can take place and if traders abuse the scheme they will be excluded and will need to make customs declarations for each consignment on importation.
The European Commission’s aims are indeed a step in the right direction and should be welcomed, however there are perhaps some fundamental issues that scrapping the low value exemption will not fix in one fell swoop.
Despite removing the exemption, businesses will still be able to undervalue or wrongly label products in order to pay as little import VAT as possible, thus still undercutting EU businesses. With the removal of the exemption, what is to stop a business still deliberately acting fraudulently? With the removal of the exemption, the importer will always be paying VAT, but an abusive importer may want to minimize his VAT liability.
The Commission appear to be replacing one import VAT regime with another that is potentially even more susceptible to VAT fraud as the €150 threshold for small consignments may be even more tempting for non-EU businesses to devalue expensive goods. For example, a smartphone can more conceivably be “under” valued at €149 than €22. It is true that VAT will still be collected and paid to Member States on these items but this new rule presents an opportunity for businesses to pay less VAT by devaluing expensive items to below the €150 threshold.
For example, if a business currently sells items to UK consumers for €200 + VAT @ 20%, but decides to devalue his goods to €150 knowing they will not get stopped at customs, there is a potential lost VAT revenue of €10 per item sold. So, under this measure, the VAT gap of lost VAT revenues may actually increase as there is a greater scope for more expensive items to be devalued to around or below the €150.
Furthermore, a lot of the Commission’s statement places an emphasis on ‘trust’ and helping ‘trustworthy’ businesses. However, ‘trust’ is a subjective term and it could be argued that these new implementations are not targeting the businesses that are most likely to commit VAT fraud and therefore non-compliance is just as likely to occur. So, how can the European Commission ensure each Member State regulates the new rules to the same strict degree and applies the same principles to ‘trustworthy’ businesses?
In order to counter some of these issues outlined above, we believe the Commission could go a step further by introducing measures such as the following:
Increasing the pressure on the EU intermediaries (parcel carriers, customs agents, etc.) to make sure their customers are importing correctly: the intermediary is in the EU and can be more easily reprimanded for fraudulent or abusive behaviour of their customers. This could be by way of extension of the fiscal representation schemes currently in operation in a number of EU countries or the introduction of a Fulfilment House Due Diligence Scheme similar to that being introduced in the UK.
Imposing harsher penalties for those caught deliberately abusing the system: this may act as a deterrent for those thinking about acting fraudulently or not complying with the rules. The ultimate deterrent would be barring a business from importing and selling in the EU.
A less likely option would be to request from importers, say, a 2-year bond/deposit that is refunded in full at the end of the period, or partially refunded to the trader each quarter after they have filed their One Stop Shop VAT Return.
The most obvious measure is to carry out tougher inspections of products and importation paperwork, and encourage better cooperation and coordination between Member States and their governmental agencies.
As mentioned above, the EU Commission’s proposal should be welcomed as it does start to address the problems facing EU e-commerce businesses in dealing with the low value consignment exemption. It should also hopefully generate extra tax revenues for EU Member States as well as help improve the competitiveness of EU businesses against non-EU importers.
However, there is still some way to go before the problems of VAT fraud, non VAT-compliance and the distortions in competition for EU businesses come close to being completely eradicated. |
**2 + o + m*w**4 + d*w**3 + c*w and give m.
-12
Express ((3*g - 2*g + g)*(-4*g + 4*g - g) + 5 - 5 + g**2)*(6110 + 88*g - 6110) in the form c*g + m*g**3 + r + x*g**2 and give m.
-88
Rearrange -161 - 27*o + 161 to y*o + w and give y.
-27
Rearrange 2*w + 5*w**4 + w**3 + 3 - 3 to the form j*w**3 + i + h*w**2 + s*w**4 + z*w and give s.
5
Express -2*a - 13*a + a in the form r + v*a and give v.
-14
Rearrange -3 + 3 + 63*a - 84*a to o + x*a and give x.
-21
Express -46*v + 2*v**4 + v**3 + v**4 + 44*v + 1 - 2*v**4 as y*v + g*v**3 + u*v**4 + h + x*v**2 and give g.
1
Express -31 + 5*j**2 + 8*j**2 - 24*j**2 + 10*j**2 in the form w + g*j**2 + i*j and give g.
-1
Express 9*r**4 + 70*r - 141*r + r**4 - 4*r**3 + 73*r + 2 in the form c + a*r**3 + n*r**4 + b*r**2 + o*r and give o.
2
Express (2*j**3 - 2*j**3 + 2*j**3)*(-4*j - j + 0*j + (j + 0*j - 2*j)*(-4 + 4 + 2)) in the form r*j + z*j**2 + b*j**4 + f*j**3 + w and give f.
0
Rearrange 108*z**2 - 109*z**2 + 67*z**2 to the form b + a*z + y*z**2 and give y.
66
Rearrange (1 - 1 + 23*x)*(x + x + 0*x) to g*x**2 + n + o*x and give g.
46
Rearrange -9*c**2 + 6*c**2 - 3 + 9 + 4 to the form d + v*c + n*c**2 and give n.
-3
Rearrange 7*i**2 - 9*i**3 + 8*i**3 + 3*i**3 + i + 4*i**2 to the form h*i**2 + v*i + y*i**3 + p and give h.
11
Rearrange 3*h**4 + 2*h**3 - 168 + 81 + 2*h**2 + 85 to q*h**4 + g*h**3 + c*h**2 + r + o*h and give r.
-2
Rearrange (m - 2*m - 4*m)*(-3 + 2 - 1) to the form v + f*m and give f.
10
Express (-j + j + 2*j**3)*(-j + 3*j - 3*j) + 3*j - 3*j + 5*j**4 + (0 + 0 + j)*(0 + 2*j**3 + 0) in the form i + k*j**3 + o*j**2 + c*j + m*j**4 and give m.
5
Rearrange -140*d**3 + 0 + 139*d**3 + 19*d**2 + 0 to the form z*d + n + p*d**3 + v*d**2 and give v.
19
Rearrange -2*z**3 + 2*z + 3*z - 8*z to the form a*z**2 + i + p*z**3 + x*z and give p.
-2
Rearrange (0*g**2 + 2*g**2 - g**2)*(2 - 3 - 1)*(156*g**2 - 178*g**2 + 104*g**2) to the form a*g + p*g**3 + k + q*g**2 + u*g**4 and give u.
-164
Rearrange -23*w**2 + 46*w**2 - 19*w**2 to y*w**2 + a + l*w and give y.
4
Rearrange 5*t**4 - 6*t - 2*t**2 + 2*t**3 - t + 0*t - 2*t**4 to the form a*t**3 + c*t**4 + z*t + f + m*t**2 and give m.
-2
Rearrange (3 - 4 + 0)*(3 + 1 - 1)*((7*y - 2*y + y)*(4 - 4 - 2) - 3*y - 2*y + 3*y) to the form t*y + g and give t.
42
Express 52 + 0*m + 11*m - 13*m as v*m + q and give v.
-2
Rearrange -6*j + 3*j**3 + 2*j - 2*j**3 to k*j**3 + t*j + d + y*j**2 and give k.
1
Rearrange (-10 - 1 + 1)*(-13*c**2 + 13*c**2 - 7*c**4) to the form l*c + h*c**4 + a*c**2 + y + w*c**3 and give h.
70
Rearrange 16*h + 11*h - 6*h + 1 to the form i + n*h and give n.
21
Rearrange j**3 + 2 + 0*j**4 - 7*j**2 + 11*j**2 + j**4 to f*j**2 + k*j + v + a*j**3 + s*j**4 and give v.
2
Express x**2 - 4*x**2 + 19*x**2 as q + d*x + j*x**2 and give j.
16
Rearrange -2 - b**3 + 2 + (-2*b + 2*b + b**2)*(0 - 2*b + 0) - 2*b**3 - 3*b + 3*b - 205*b**2 + b + 26*b**3 + 205*b**2 to j*b + o*b**3 + h*b**2 + z and give j.
1
Express (-j**2 + 22*j - 22*j + 2)*(6*j**2 - 3*j**2 - 10 + 6) as d*j**3 + m + p*j**4 + k*j + i*j**2 and give i.
10
Express (5*i**2 + 6*i**3 - 5*i**2)*(-9 + 6 + 0) in the form v*i**2 + a + z*i**3 + l*i and give z.
-18
Express 2*t + 3 - 2*t + 16*t - 6 in the form w + r*t and give w.
-3
Express 15*c + 3 - 1 - 2 in the form y*c + z and give y.
15
Express (-a - a + 0*a)*(7 - 2*a - 7)*(0 - 2 + 0) in the form i + c*a + b*a**2 and give b.
-8
Express -16*t**2 - 8*t - 1 + 17*t**2 - 3*t in the form c*t + z + p*t**2 and give z.
-1
Rearrange -4*y + 0*y + 5*y + 0*y + y - 2*y - 2 + 2 + 2*y + (3*y + 2*y - 4*y)*(2 - 4 + 3) + 5 - 5 + 5*y to the form i + v*y and give v.
8
Rearrange 22 - 36 + 114*o**3 + 16 to w*o**3 + m*o**2 + j + y*o and give w.
114
Express (6*d**2 - 13*d**2 + 4*d**2)*(1 + 1 - 4 - d**2) as m*d**2 + p*d + c*d**3 + o + y*d**4 and give m.
6
Express -20717*w**3 - 2*w**4 + 3*w**2 + 3*w + 20717*w**3 - 2 in the form b*w**2 + i + s*w + k*w**3 + z*w**4 and give k.
0
Express (-1 + 2*u + 1)*(-u + 2*u + u) + 3 - 2*u**2 - 3 + u**2 - 20*u**2 + u**2 in the form r + p*u + f*u**2 and give f.
-16
Rearrange (-3 + 3 + z)*(-6 - 27 - 8)*(-3 + 3 + 2) to the form h + b*z and give b.
-82
Rearrange (-3 + 0 + 1)*(-7 + 2 + 3)*(1 + 86*d + 2 - 88*d) to n*d + i and give n.
-8
Rearrange -13*u + 24 + 24 - 47 + (2*u - u + 0*u)*(2 + 1 + 0) to the form g + w*u and give w.
-10
Rearrange (-2*f - f**3 + 2*f + (-3*f - 3*f + 4*f)*(2*f**2 - 5*f**2 + 2*f**2))*(14 - 1 + 8) to the form d*f + g*f**2 + a + l*f**3 and give l.
21
Rearrange 2*d + d - 2*d + 1 - 1 - 2*d + (-9*d - 6*d + 5*d)*(-4 + 5 - 4) to u*d + g and give u.
29
Rearrange 8*h + 2*h + 0*h - h to p*h + d and give p.
9
Express 14 - 19*d**2 + 1 - 15 as m + g*d**2 + h*d and give g.
-19
Express (-1 + 1 - 2)*(-2*j - 3 + 3 + (-10 + 6 - 21)*(-4*j + 4*j + 2*j)) as u*j + r and give u.
104
Rearrange -19 + 54 - u - 23 to p*u + k and give p.
-1
Express (w - 2*w - 5*w)*(-2 + 1 - 2) - 2 + 2 - w + (0 + 5 - 3)*(-2*w + 6*w - 2*w) + (7*w - 3*w - 2*w)*(0 + 2 - 3) + 0 - 2*w + 0 in the form f + x*w and give x.
17
Express -8 - 5 + 2 + 33*p - 32*p in the form t*p + z and give t.
1
Rearrange 7 - 7 + 9*h**2 to l*h**2 + j + q*h and give l.
9
Express -6*k**2 + 14 - 14 as g*k + v + w*k**2 and give w.
-6
Rearrange (2 - 5 + 4)*(12 - 12 - 4*d)*(-3 - 2 + 11) to the form f + s*d and give s.
-24
Rearrange (3 - 4 + 2)*(2*f - 2 + 2)*(-7*f**2 + 5*f**2 - 12 + 3*f**2) to the form x*f + k + l*f**2 + t*f**3 and give t.
2
Express -3*m**2 + m**4 - 8 + m**4 - 4*m**2 + 6 in the form u*m**2 + t*m**3 + f*m + h + c*m**4 and give t.
0
Express ((-2 + 5 - 1)*(-2*o + 6*o - 3*o) - o - 1 + 1)*(-1 - 3 + 3)*(-4*o + 1900*o**2 + o - 1858*o**2) as c*o**3 + d*o + x + z*o**2 and give z.
3
Rearrange -l**4 + l - l + (3*l**3 - l**3 - 4*l**3)*(-4 + 4 + 2*l) - 5*l**4 + 32*l**4 + 19*l**4 to the form q*l + c + p*l**2 + v*l**4 + x*l**3 and give x.
0
Rearrange 9*f**2 - 10*f**2 + 2*f + 2*f**3 - 8*f**3 to the form o*f**3 + i*f + r + x*f**2 and give o.
-6
Express -k - 2 + 2 - 4*k as a*k + x and give a.
-5
Express (s**3 - 3*s + 3*s)*(-1 + 1 - 2*s) - 9*s**2 + 3*s**2 + 331*s - 332*s - 3*s**4 in the form n*s + j*s**3 + l + y*s**2 + g*s**4 and give y.
-6
Rearrange -3*f + 8*f**2 + 4*f + 2*f - f to the form r*f**2 + p*f + s and give p.
2
Rearrange 2*x**2 + x**2 + 2*x**2 + (-x + 3*x - 3*x)*(5*x - 3*x + 5*x) to the form h + q*x + s*x**2 and give s.
-2
Express (-4 + 12*r**2 + 4)*(1 + 3 - 3) in the form x*r + n + w*r**2 and give w.
12
Rearrange (8 + 12 - 9)*(-m + m - m)*(0 - 3 + 5)*(-3*m - m**2 + 3*m) to the form l*m + x + a*m**3 + b*m**2 and give l.
0
Rearrange (2 - 2 - 2*k)*(2*k**3 + 0*k + 0*k) - 2*k**2 + k**4 + 3*k**2 - 2*k**4 to the form q*k**2 + j*k**3 + t*k**4 + c*k + d and give q.
1
Express ((6*v - 4*v - v)*(2 + 1 - 5) + (2*v + 0*v - v)*(-2 - 1 + 4) - v + v - 2*v)*(1 - 1 - v**3) as c + f*v**4 + a*v**3 + j*v**2 + h*v and give f.
3
Rearrange (0*f - 2*f + f)*(-12 + 17 + 0) to c + t*f and give c.
0
Rearrange 144 + 148 - 5*n - 301 to the form d*n + g and give g.
-9
Express f**2 - 5*f**3 + 0*f**3 + 3*f + 4*f**3 - 2*f**4 in the form s + w*f**4 + u*f**3 + b*f**2 + k*f and give b.
1
Rearrange -6*i + 4 + 5*i + 2*i - 2*i to the form t + d*i and give t.
4
Rearrange 2*z + 2 - 3*z**3 + 0*z**3 - 12*z + 8*z to the form u + m*z**2 + n*z + k*z**3 and give u.
2
Express (-2*b**2 + 5*b**2 - b**2)*(-365 + b + 365 + b**2) in the form s*b**3 + l + r*b + t*b**4 + u*b**2 and give t.
2
Express (-1 + 1 + u**2)*(-u - 14*u - 11*u) - 4*u**3 + 6*u**3 + 0*u**3 + 3*u**3 + u**3 - 2*u**3 in the form h*u**3 + q*u**2 + s + i*u and give h.
-22
Express 0*c + c - 4*c + 2*c as w + u*c and give u.
-1
Rearrange (-1 + 2 + 0)*(105 - 114 + 2*c**2 - 3*c**2) to the form l*c**2 + t*c + i and give l.
-1
Rearrange -9*t - 510 + 510 to p + x*t and give x.
-9
Express (-x + 0 + 0)*(-305*x**3 + 610*x**3 - x**2 - 227*x**3) in the form n*x**3 + d*x + g*x**4 + s*x**2 + i and give g.
-78
Rearrange (-q**3 + 4*q**3 - 5*q**3)*(-q - q - q) to the form v + g*q**2 + x*q**3 + c*q**4 + f*q and give c.
6
Express (-2 - 2 - 3)*(2*j + 1 - 1) in the form w + o*j and give o.
-14
Rearrange 8*o**3 - o**2 - 12*o + o**2 - 6*o**3 to m*o**3 + g*o**2 + i*o + z and give i.
-12
Express 17*s**2 - 37*s**2 + 24*s**2 as v + j*s + u*s**2 and give u.
4
Express 9*n + 0*n**2 + 3*n**4 + 69*n**3 - 68*n**3 + n**2 - 2*n**4 in the form g*n**2 + z*n + |
package org.dynmap.bukkit.helper.v116_2;
import java.lang.reflect.Field;
import java.lang.reflect.InvocationTargetException;
import java.lang.reflect.Method;
import java.util.ArrayList;
import java.util.HashMap;
import java.util.IdentityHashMap;
import java.util.List;
import org.bukkit.Bukkit;
import org.bukkit.Chunk;
import org.bukkit.ChunkSnapshot;
import org.bukkit.Location;
import org.bukkit.Server;
import org.bukkit.World;
import org.bukkit.WorldBorder;
import org.bukkit.entity.Player;
import org.dynmap.DynmapChunk;
import org.dynmap.Log;
import org.dynmap.bukkit.helper.BukkitMaterial;
import org.dynmap.bukkit.helper.BukkitVersionHelperCB;
import org.dynmap.bukkit.helper.BukkitVersionHelperGeneric;
import org.dynmap.bukkit.helper.BukkitWorld;
import org.dynmap.bukkit.helper.v116_2.MapChunkCache116_2;
import org.dynmap.renderer.DynmapBlockState;
import org.dynmap.utils.MapChunkCache;
import org.dynmap.utils.Polygon;
import net.minecraft.server.v1_16_R2.BiomeBase;
import net.minecraft.server.v1_16_R2.BiomeFog;
import net.minecraft.server.v1_16_R2.Block;
import net.minecraft.server.v1_16_R2.BlockFluids;
import net.minecraft.server.v1_16_R2.BlockRotatable;
import net.minecraft.server.v1_16_R2.IBlockData;
import net.minecraft.server.v1_16_R2.IRegistry;
import net.minecraft.server.v1_16_R2.Material;
import net.minecraft.server.v1_16_R2.MinecraftServer;
/**
* Helper for isolation of bukkit version specific issues
*/
public class BukkitVersionHelperSpigot116_2 extends BukkitVersionHelperGeneric {
private Field watercolorfield;
public BukkitVersionHelperSpigot116_2() {
Class biomefog = getNMSClass("net.minecraft.server.BiomeFog");
watercolorfield = getPrivateField(biomefog, new String[] { "c" }, int.class);
}
/**
* Get block short name list
*/
@Override
public String[] getBlockNames() {
int cnt = Block.REGISTRY_ID.a();
String[] names = new String[cnt];
for (int i = 0; i < cnt; i++) {
IBlockData bd = Block.getByCombinedId(i);
names[i] = IRegistry.BLOCK.getKey(bd.getBlock()).toString();
Log.info(i + ": blk=" + names[i] + ", bd=" + bd.toString());
}
return names;
}
private IRegistry<BiomeBase> reg = null;
private IRegistry<BiomeBase> getBiomeReg() {
if (reg == null) {
reg = MinecraftServer.getServer().aX().b(IRegistry.ay);
}
return reg;
}
private Object[] biomelist;
/**
* Get list of defined biomebase objects
*/
@Override
public Object[] getBiomeBaseList() {
if (biomelist == null) {
biomelist = new Object[1024];
for (int i = 0; i < 1024; i++) {
biomelist[i] = getBiomeReg().fromId(i);
}
}
return biomelist;
}
/** Get ID from biomebase */
@Override
public int getBiomeBaseID(Object bb) {
return getBiomeReg().a((BiomeBase)bb);
}
public static IdentityHashMap<IBlockData, DynmapBlockState> dataToState;
/**
* Initialize block states (org.dynmap.blockstate.DynmapBlockState)
*/
@Override
public void initializeBlockStates() {
dataToState = new IdentityHashMap<IBlockData, DynmapBlockState>();
HashMap<String, DynmapBlockState> lastBlockState = new HashMap<String, DynmapBlockState>();
int cnt = Block.REGISTRY_ID.a();
// Loop through block data states
for (int i = 0; i < cnt; i++) {
IBlockData bd = Block.getByCombinedId(i);
String bname = IRegistry.BLOCK.getKey(bd.getBlock()).toString();
DynmapBlockState lastbs = lastBlockState.get(bname); // See if we have seen this one
int idx = 0;
if (lastbs != null) { // Yes
idx = lastbs.getStateCount(); // Get number of states so far, since this is next
}
// Build state name
String sb = "";
String fname = bd.toString();
int off1 = fname.indexOf('[');
if (off1 >= 0) {
int off2 = fname.indexOf(']');
sb = fname.substring(off1+1, off2);
}
Material mat = bd.getMaterial();
DynmapBlockState bs = new DynmapBlockState(lastbs, idx, bname, sb, mat.toString());
if ((!bd.getFluid().isEmpty()) && ((bd.getBlock() instanceof BlockFluids) == false)) { // Test if fluid type for block is not empty
bs.setWaterlogged();
}
if (mat == Material.AIR) {
bs.setAir();
}
if (mat == Material.LEAVES) {
bs.setLeaves();
}
if ((bd.getBlock() instanceof BlockRotatable) && (bd.getMaterial() == Material.WOOD)) {
bs.setLog();
}
if (mat.isSolid()) {
bs.setSolid();
}
dataToState.put(bd, bs);
lastBlockState.put(bname, (lastbs == null) ? bs : lastbs);
Log.verboseinfo(i + ": blk=" + bname + ", idx=" + idx + ", state=" + sb + ", waterlogged=" + bs.isWaterlogged());
}
}
/**
* Create chunk cache for given chunks of given world
* @param dw - world
* @param chunks - chunk list
* @return cache
*/
@Override
public MapChunkCache getChunkCache(BukkitWorld dw, List<DynmapChunk> chunks) {
MapChunkCache116_2 c = new MapChunkCache116_2();
c.setChunks(dw, chunks);
return c;
}
/**
* Get biome base water multiplier
*/
@Override
public int getBiomeBaseWaterMult(Object bb) {
try {
return (int) watercolorfield.get(((BiomeBase)bb).l());
} catch (IllegalArgumentException e) {
} catch (IllegalAccessException e) {
}
return 0xFFFFFF;
}
/** Get temperature from biomebase */
@Override
public float getBiomeBaseTemperature(Object bb) {
return ((BiomeBase)bb).k();
}
/** Get humidity from biomebase */
@Override
public float getBiomeBaseHumidity(Object bb) {
return ((BiomeBase)bb).getHumidity();
}
@Override
public Polygon getWorldBorder(World world) {
Polygon p = null;
WorldBorder wb = world.getWorldBorder();
if (wb != null) {
Location c = wb.getCenter();
double size = wb.getSize();
if ((size > 1) && (size < 1E7)) {
size = size / 2;
p = new Polygon();
p.addVertex(c.getX()-size, c.getZ()-size);
p.addVertex(c.getX()+size, c.getZ()-size);
p.addVertex(c.getX()+size, c.getZ()+size);
p.addVertex(c.getX()-size, c.getZ()+size);
}
}
return p;
}
// Send title/subtitle to user
public void sendTitleText(Player p, String title, String subtitle, int fadeInTicks, int stayTicks, int fadeOutTIcks) {
if (p != null) {
p.sendTitle(title, subtitle, fadeInTicks, stayTicks, fadeOutTIcks);
}
}
/**
* Get material map by block ID
*/
@Override
public BukkitMaterial[] getMaterialList() {
return new BukkitMaterial[4096]; // Not used
}
@Override
protected void loadNMS() {
// Not needed
}
@Override
protected String getNMSPackage() {
Server srv = Bukkit.getServer();
/* Get getHandle() method */
try {
Method m = srv.getClass().getMethod("getHandle");
Object scm = m.invoke(srv); /* And use it to get SCM (nms object) */
return scm.getClass().getPackage().getName();
} catch (Exception x) {
Log.severe("Error finding net.minecraft.server packages");
return null;
}
}
@Override
public void unloadChunkNoSave(World w, Chunk c, int cx, int cz) {
Log.severe("unloadChunkNoSave not implemented");
}
private String[] biomenames;
@Override
public String[] getBiomeNames() {
if (biomenames == null) {
biomenames = new String[1024];
for (int i = 0; i < 1024; i++) {
BiomeBase bb = getBiomeReg().fromId(i);
if (bb != null) {
biomenames[i] = bb.toString();
}
}
}
return biomenames;
}
@Override
public String getStateStringByCombinedId(int blkid, int meta) {
Log.severe("getStateStringByCombinedId not implemented");
return null;
}
@Override
/** Get ID string from biomebase */
public String getBiomeBaseIDString(Object bb) {
String s = ((BiomeBase)bb).toString();
if (s != null) {
String[] ss = s.split("\\.");
return ss[ss.length-1];
}
return null;
}
}
|
Erald Kolasi received his PhD in physics from George Mason University in 2016.
People tend to think of capitalism in economic terms. Karl Marx argued that capitalism is a political and economic system that transforms the productivity of human labor into large profits and returns for those who own the means of production.1 Its proponents contend that capitalism is an economic system that promotes free markets and individual liberty.2 And opponents and advocates alike most often measure capitalism’s impact in terms of wealth and income, wages and prices, and supply and demand.
However, human economies are complex biophysical systems that interact with the wider natural world, and none can be fully examined apart from their underlying material conditions. By exploring some fundamental concepts in physics, we can develop a better understanding of how all economic systems work, including the ways that the energy-intensive activities of capitalism are changing humanity and the planet.
This article will explain how the fundamental features of both our natural and economic existence depend on the principles of thermodynamics, which studies the relationships between quantities such as energy, work, and heat.3 A firm grasp of how capitalism works at a physical level can help us understand why our next economic system should be more ecological, prioritizing long-run stability and compatibility with the global ecosphere that sustains humanity.
Such an understanding requires a glance at some central concepts in physics. These include energy, entropy, dissipation, and the various rules of nature that bind them together. The central features of our natural existence, as living organisms and as human beings, emerge from the collective interactions described by these core physical realities. Although these concepts can be difficult to define without reference to specific models and theories, their general features can be outlined and analyzed to reveal the powerful intersection between physics and economics.
The exchange of energy between different systems has a decisive influence on the order, phase, and stability of physical matter. Energy can be defined as any conserved physical property that can produce motion, such as work or heat, when exchanged among different systems.4 Kinetic energy and potential energy are two of the most important forms of energy storage. The sum of these two quantities is known as mechanical energy.5 A truck speeding down the highway packs a good amount of kinetic energy—that is, energy associated with motion. A boulder teetering at the edge of a cliff has great potential energy, or energy associated with position. If given a slight push, its potential energy transforms into kinetic energy under the influence of gravity, and off it goes. When physical systems interact, energy is converted into many different forms, but its total quantity always remains constant. The conservation of energy implies that the total output of all energy flows and transformations must equal the total input.
Energy flows among different systems represent the engine of the cosmos, and they happen everywhere, so often that we hardly notice them. Heat naturally flows from warmer to colder regions, hence our coffee cools in the morning. Particles move from high-pressure areas to low-pressure areas, and so the wind starts to howl. Water travels from regions of high potential energy to regions of low potential energy, making rivers flow. Electric charges journey from regions of high voltage to regions of low voltage, and thus currents are unleashed through conductors. The flow of energy through physical systems is one of the most common features of nature, and as these examples show, energy flows require gradients—differences in temperature, pressure, density, or other factors. Without these gradients, nature would never deliver any net flows, all physical systems would remain in equilibrium, and the world would be inert—and very boring. Energy flows are also important because they can generate mechanical work, which is any macroscopic displacement in response to a force.6 Lifting a weight and kicking a ball are both examples of performing mechanical work on another system. An important result from classical physics equates the quantity of work to the change in the mechanical energy of a physical system, revealing a useful relationship between these two variables.7
Although energy flows can produce work, they rarely do so efficiently. Large macroscopic systems, like trucks or planets, routinely lose or gain mechanical energy through their interactions with the external world. The lead actor in this grand drama is dissipation, defined as any process that partially reduces or entirely eliminates the available mechanical energy of a physical system, converting it into heat or other products.8 As they interact with the external environment, physical systems often lose mechanical energy over time through friction, diffusion, turbulence, vibrations, collisions, and other similar dissipative effects, all of which prevent any energy source from being converted entirely into mechanical work. A simple example of dissipation is the heat produced when we rapidly rub our hands together. In the natural world, macroscopic energy flows are often accompanied by dissipative losses of one kind or another. Physical systems that can dissipate energy are capable of rich and complex interactions, making dissipation a central feature of the natural order. A world without dissipation, and without the interactions that make it possible, is difficult to imagine. If friction suddenly disappeared from the world, people would slip and slide everywhere. Our cars would be useless, as would the very idea of transportation, because wheels and other mechanical devices would lack any traction with the ground and other surfaces. We would never be able to hold hands or rock our babies. Our bodies would rapidly deteriorate and lose their internal structure. The world would be alien and unrecognizable.
Dissipation is closely related to entropy, one of the most important concepts in thermodynamics. While energy measures the motion produced by physical systems, entropy tracks the way that energy is distributed in the natural world. Entropy has several standard definitions in physics, all of them essentially equivalent. One popular definition from classical thermodynamics states that entropy is the amount of heat energy per unit of temperature that becomes unavailable for mechanical work during a thermodynamic process.9 Another important definition comes from statistical physics, which looks at how the microscopic parts of nature can join to produce big, macroscopic results. In this statistical version, entropy is a measure of the various ways that the microscopic states of a larger system can be rearranged without changing that system.10 For a concrete example, think of a typical gas and a typical solid at equilibrium. Energy is distributed very differently in these two phases of matter. The gas has a higher entropy than the solid, because the former’s particles have far more possible energy configurations than the fixed atomic sites in solids and crystals, which have only a small range of energy configurations that will preserve their fundamental order.11 We should emphasize that the concept of entropy does not apply to a specific configuration of macroscopic matter, but rather applies as a constraint on the number of possible configurations that a macroscopic system can have at equilibrium.
Entropy has a profound connection to dissipation through one of the most important laws of thermodynamics, which states that heat flows can never be fully converted into work.12 Dissipative interactions ensure that physical systems always lose some energy as heat in any natural thermodynamic process, where friction and other similar effects are present. Real-world examples of these thermodynamic losses include emissions from car engines, electric currents encountering resistance, and interacting fluid layers experiencing viscosity. In thermodynamics, these phenomena are often considered irreversible. The continuous production of heat energy from irreversible phenomena gradually depletes the stock of mechanical energy that physical systems can exploit. According to the definition of entropy, depleting useful mechanical energy generally implies that entropy increases. Formally stated, the most important consequence of any irreversible process is to increase the combined entropy of a physical system and its surroundings. For an isolated system, entropy continues to rise until it reaches some maximum value, at which point the system settles into equilibrium. To clarify this last concept, imagine a red gas and a blue gas separated by a partition inside a sealed container. Removing the partition allows the two gases to mix together. The result would be a gas that looks purple, and that equilibrium configuration would represent the state of maximum entropy. We can also relate dissipation to the concept of entropy in statistical physics. The proliferation of heat energy through physical systems changes the motion of their molecules into something more random and dispersed, increasing the number of microstates that can represent the macroscopic properties of the system. In a broad sense, entropy can be seen as the tendency of nature to reconfigure energy states into distributions that dissipate mechanical energy.
The traditional description of entropy given above applies in the regime of equilibrium thermodynamics. But in the real world, physical systems rarely exist at fixed temperatures, in perfect states of equilibrium, or in total isolation from the rest of the universe. The field of non-equilibrium thermodynamics examines the properties of thermodynamic systems that operate sufficiently far from equilibrium, such as living organisms or exploding bombs. Non-equilibrium systems are the lifeblood of the universe; they make the world dynamic and unpredictable. Modern thermodynamics remains a work in progress, but it has been used to successfully study a broad spectrum of phenomena, including heat flows, interacting quantum gases, dissipative structures, and even the global climate.13 There is no universally accepted meaning of entropy in non-equilibrium conditions, but physicists have offered several proposals.14 All of them include time when analyzing thermodynamic interactions, allowing us to determine not just whether entropy goes up or down, but also how quickly or slowly physical systems can change on their path to equilibrium. The principles of modern thermodynamics are therefore essential in helping us understand the behavior of real-world systems, including life itself.
The central physical objective of all life forms is to avoid thermodynamic equilibrium with the rest of their environment by continuously dissipating energy, as the physicist Erwin Schrödinger suggested in the 1940s, when he used non-equilibrium thermodynamics to study the key features of biology.15 We may call this vital objective the entropic imperative. All living organisms consume energy from an external environment, use it to fuel vital biochemical processes and interactions, and then dissipate most of the energy consumed back to the environment. The dissipation of energy to an external environment allows organisms to conserve the order and stability of their own biochemical systems. The essential functions of life critically depend on this entropic stability, including functions like digestion, respiration, cell division, and protein synthesis. What makes life unique as a physical system is the sheer variety of dissipation methods that it has developed, including the production of heat, the emission of gases, and the expulsion of waste. This sweeping capacity to dissipate energy is what helps life to sustain the entropic imperative. Indeed, physicist Jeremy England has argued that physical systems in a heat bath flooded with large amounts of energy can tend to dissipate more energy.16 This “dissipation-driven adaptation” can lead to the spontaneous emergence of order, replication, and self-assembly among microscopic units of matter, providing a potential clue into the very dynamics of the origin of life. Organisms also use the energy they consume to perform mechanical work by, for example, walking, running, climbing, or typing on a keyboard. Those organisms with access to many energy sources can do more work and dissipate more energy, satisfying the central conditions of life.
The thermodynamic relationships among energy, entropy, and dissipation likewise impose powerful constraints on the behavior and evolution of economic systems.17 Economies are dynamical and emergent systems compelled to function in certain ways by their underlying social and ecological conditions. In this context, economies are non-equilibrium systems capable of rapidly dissipating energy to some external environment. All dynamical systems gain strength from some energy reservoir, reach peak intensity by absorbing a regular supply of energy, then unravel from internal and external changes that either disrupt vital energy flows or make it impossible to keep dissipating more energy. They can even experience long-term undulations by growing for some time, then shrinking, then growing again, before finally collapsing. Interactions between dynamical systems can produce highly chaotic results, but energy expansions and contractions are the core features of all dynamical systems. The energy consumed by all economic systems is either converted into mechanical work and the physical products derived from that work, or is simply wasted and dissipated to the environment. We can define the collective efficiency of an economic system as the fraction of all energy consumed that goes into creating mechanical work and electrical energy. Economies that increase the amount of mechanical work they generate can produce more goods and services. But however important it may be, mechanical work represents a relatively small fraction of total energy use in any economy; the vast majority of the energy consumed by all economies is routinely squandered to the environment through waste, dissipation, and other kinds of energy losses.
Throughout history, economic growth has depended heavily on people consuming more energy from their natural environments.18 When humans were hunters and foragers, the primary asset that performed mechanical work was the human muscle.19 Our nomadic way of life lasted for some 200,000 years, but underwent significant disruptions after the Ice Age. Over millennia, changing ecological conditions around the world compelled numerous groups to adopt pastoralist and agricultural strategies. Agrarian economies relied heavily on cultivated plants and domesticated animals to help generate surpluses of food and other goods and resources. These agrarian modes of production and consumption dominated human societies for almost ten thousand years, but were eventually replaced by a new economic system. Capitalism emerged and spread through colonial expansion, waves of industrialization, the proliferation of epidemic diseases, genocidal campaigns against indigenous populations, and the discovery of new energy sources.
The global economy has since become an interconnected system of finance, computers, factories, vehicles, machines, and much more. Creating and sustaining this system required a major upward transition in the rate of energy throughput from our natural environments. In our nomadic days, the daily rate of per capita energy consumption was around 5,000 kilocalories.20 By 1850, per capita consumption had risen to roughly 80,000 kilocalories per day, and has since ballooned to about 250,000 kilocalories today.21 From a physics perspective, the fundamental feature of all capitalist economies is an excessive rate of energy consumption focused on boosting economic growth and material surpluses. The collective deployment of capital assets can generate incredible levels of mechanical work, allowing people to produce more, travel great distances, and lift heavy objects, among other tasks. Capitalism is far more energy-intensive than any previous economic system, and it has wrought unprecedented ecological consequences that may threaten its very existence. It remains uncertain how long humanity can sustain capitalism’s energy-intensive activities, but there is no doubt that the fantasy of endless growth and easy profits cannot continue. All dynamical systems must eventually come to an end.
Over the last two centuries, inefficient capitalist economies have unloaded large amounts of energy losses to their natural environments in the forms of waste, chemicals, pollutants, and greenhouse gases. The aggregate effect of all this waste and dissipation has been fundamentally to alter critical energy flows throughout the ecosphere, triggering a major social and ecological crisis in the natural world. This socioecological crisis is still in its early phases, but has already spawned calamities like deforestation, global warming, ocean acidification, and substantial losses in biodiversity.22 Barring revolutionary changes to our socioeconomic system, this crisis will only continue and intensify. As this occurs, accumulating problems in the natural world will threaten the long-term viability of global civilization. The products we dissipate to the environment may be useless to us, but they often serve as energy reservoirs for other dynamical systems. Energy losses often have an amplifier effect on human civilization, meaning their true costs are far greater than may be visible or superficially understood. Consider the unsanitary conditions in cities throughout much of human history. Cities in pre-modern economies were typically filthy, with trash and waste overwhelming many public spaces. Yet these energy losses were a critical source of food and nourishment for a wide variety of other living organisms, especially insects and other small animals that could survive in the midst of human civilization. When these creatures became hosts to deadly diseases, human waste helped to concentrate their numbers in precisely the worst places: high-density areas like cities. As a consequence, epidemic diseases usually generated far larger death tolls than they would have otherwise, with the unimaginable carnage of the Black Death as a primary example.23
Today we face our own versions of this ancient problem, but on a much bigger scale. There are several kinds of gases in the atmosphere, known as greenhouse gases, able to absorb outgoing heat radiation.24 When these gases in the atmosphere trap and emit radiation back to the surface of the planet, large numbers of photons excite the electrons, atoms, and molecules on the surface to higher energy states, in a process called the greenhouse effect. These additional excitations and fluctuations at the microscopic level collectively represent the warmth we experience at the macroscopic level. The greenhouse effect is critical because it makes the Earth warm enough to be habitable.25 Over the last two centuries, however, wealthy and industrialized nations have been reinforcing this natural process by pumping vast amounts of new greenhouse gases into the atmosphere, in turn causing more global warming. This artificial reinforcement of the greenhouse effect has already had profound consequences for our species and others. Thermal excitations from an amplified greenhouse effect often act as a powerful energy reservoir for other dynamical systems and natural phenomena, including storms, floods, droughts, cyclones, wildfires, insects, viruses, bacteria, and algae blooms.26
A warming planet could also reinforce positive feedback mechanisms in the climate capable of inducing even more warming, beyond that already caused by our greenhouse gas emissions. These mechanisms, such as melting sea ice and thawing permafrost, would allow the planet to absorb more solar energy while naturally emitting vast quantities of greenhouse gases.27 The resulting chaos would render any human attempts to mitigate global warming futile. This is precisely what should worry us: the chaos we are unleashing on the planet through the capitalist system will find a way to produce a new kind of order, one that threatens human civilization itself. As capitalism expands, the ecological crisis will worsen. The intensifying dynamical systems of nature will increasingly interact with our civilizations and could severely disrupt the vital energy flows that support social reproduction and economic activities. Regions with high population densities subject to recurring natural disasters are especially vulnerable. Cyclone Bhola killed about 500,000 people when it struck East Pakistan in 1970, triggering a series of massive riots and protests that culminated in a civil war and contributed to the establishment of a new country, Bangladesh.28 Numerous studies have concluded that the worst drought to strike Syria in almost a thousand years was partly responsible for the social and political tensions that culminated in the current civil war.29 The climate is a resilient dynamical system capable of assimilating many different physical changes, but this resilience has its limits, and humanity will be in deep trouble if it keeps trying to transgress them.
These arguments highlight one of the deepest flaws in modern economic theory: it lacks a scientific foundation. Orthodox economic philosophies, from monetarism to the neoclassical synthesis, focus on describing the transient financial features of capitalism, mistaking these for immutable and universal laws of nature. Capitalist economics has largely been transformed into a metaphysical philosophy whose goal is not to provide a scientific foundation for economics, but to produce sophisticated propaganda designed to protect the wealth and power of a global elite. Any scientific explanation of economics must begin with the realization that energy flows and ecological conditions—not any “invisible hand” of the market—dictate the long-term macroscopic parameters of all economies. Important contributions along these lines have come from the field of ecological economics, especially in seminal works by the economists Nicholas Georgescu-Roegen and Herman Daly, but also from the systems ecologist Howard Odum.30 Marx himself incorporated ecological concerns into his economic and political thought.31 The contributions of these and other thinkers revealed that the economic features of the world are emergent properties shaped by underlying physical realities and ecological conditions, making an understanding of these conditions critical to any basic understanding of economics.
Ecological thought differs from the orthodox schools of economics in fundamental ways. Most importantly, ecological theory contends that we can no longer treat waste and dissipative losses as “externalities” and “costs of doing business,” given how important these energy losses can be in shaping the dynamical evolution of economic systems. What mainstream economists call “externalities” include the physical products we dump into the environment—everything from pollutants and plastic trash to toxic chemicals and greenhouse gases. The consequences of extreme energy losses can have a profound effect on the future evolution of dynamical systems. As scientists continually stress, the energy losses from our modern economies are so large and intense that they are starting to fundamentally alter the energy flows of the entire ecosphere, from the reinforcement of the greenhouse effect to the changing chemistry of the oceans. Some of these new concentrations of energy then act as reservoirs that power the formation and operation of other dynamical systems, which often disrupt the normal activities of civilization. Hence the fundamental reason our economic actions cannot be decoupled from the natural world: if the effects associated with our energy losses become powerful enough to destroy the normal functions of our civilizations, then no number of ingenious economic policies will save us from the wrath of nature.
Most people in power today believe we can carefully manage capitalism and prevent the worst effects of the ecological crisis. A popular strain of technological optimism holds that innovation can solve the fundamental ecological problems that humanity faces. Several different solutions have been proposed to fix our ecological woes, from the adoption of renewable energy sources to more outlandish programs like carbon storage and sequestration. All these ideas share the presumption that capitalism itself does not have to change, because technological solutions will always be available to deliver more economic growth and a healthier environment. From Beijing to Silicon Valley, technocapitalists are fond of arguing that capitalism can keep humming along through gains in energy efficiency.32 The ultimate reason why this strategy will fail over the long run is that nature imposes absolute physical limits on efficiency that no extent of technological progress can overcome. The recent breakdown in Moore’s Law because of quantum effects is a notable example.33 Another is the efficiency barrier that the Carnot cycle poses for all practical heat engines.34
But our most pressing concerns have to do with the underlying relationships between technological innovation and economic growth. Faith in technological solutions helps to foster further technological innovation and economic growth, increasing the overall demands placed on the biophysical world and the dissipation associated with the capitalist system. We can examine these relationships by first looking at how people and economic systems respond to efficiency gains. For a sense of whether capitalism can deliver major improvements in efficiency, we need to develop a general theory that explains how the collective efficiency of our economic systems changes over time.
When fuel efficiency improves, we often drive longer distances. When electricity becomes cheaper, we often power more appliances. Even those who proudly save energy at home through recycling, composting, and other activities are more than happy to jump on an airplane and fly halfway around the world for a vacation. People often take savings in one area and exchange them for expenses in another. What we end up doing with efficiency gains can sometimes be just as important as the gains themselves. In ecological studies, this phenomenon is generally known as the Jevons Paradox, which reveals that the intended effects of efficiency improvements do not always materialize.35 First formulated in the mid-nineteenth century by the British economist William Stanley Jevons, the paradox states that increases in energy efficiency are generally used to expand accumulation and production, leading to greater consumption of the very resources that the efficiency improvements were supposed to conserve. Boosting efficiency leads to cheaper goods and services, which encourages more demand and more spending, leading to the consumption of more energy.36 Jevons first described this effect in the context of coal power and steam engines. He observed that efficiency improvements in steam engines had encouraged more consumption of coal in Britain, implying that increased energy efficiency did not actually yield energy savings.
Variations of this paradox are known in economics as the rebound effect. Most economists accept that some versions of the effect are real, but disagree over the size and the scope of the problem. Some believe rebound effects are irrelevant, arguing that efficiency improvements do encourage lower levels of energy consumption in the long run.37 In a comprehensive review of the literature on the subject, the UK Energy Research Centre determined that the most extreme versions of the rebound effect probably no longer apply to developed economies. However, they also argued that large rebound effects across our economies can still occur. They reached the following conclusion: “it would be wrong to assume that…rebound effects are so small that they can be disregarded. Under some circumstances (e.g. energy efficient technologies that significantly improve the productivity of energy intensive industries) economy-wide rebound effects may exceed 50% and could potentially increase energy consumption in the long-term.”38 The fact that significant economy-wide rebound effects are possible should give us pause about the utility of efficiency strategies in combating the ecological crisis and climate change. In fact, this entire argument obscures a more important uncertainty: the problem of whether efficiency improvements can come fast enough to alleviate the worst consequences of the ecological crisis, which are still ahead of us. Given the mechanics and incentives of capitalism, we should beware the current infatuation with efficiency optimism.
To clarify these arguments, we need a theory that explains the role of efficiency in the wider context of technological progress. The rebound effect and the Jevons Paradox focus on understanding how people and economic systems behave in response to efficiency gains. More fundamental, however, is the task of understanding the general evolution of collective efficiencies over long periods of time. The dominant theme of technological innovation throughout history has been the effort to shift the burden of energy use from human muscles to other physical and biological systems, such as animals, machines, and computers. Consider cars, bicycles, airplanes, microwaves, dishwashers, vacuum cleaners, and virtually all the “wonders” of modern life: their central goal is to exploit energy and perform tasks that would normally require the exertion of human muscles. Robots and artificial intelligence have recently become all the rage, ready to swoop in and perform menial tasks that we have no desire to do. The expansion in mechanical output facilitated by technological progress typically leads to more energy-intensive societies where those who control the means of production can generate greater surpluses and profits. Technological innovation under capitalism in particular has boosted the collective amount of mechanical work that economies can generate, and has also ballooned the rate of energy consumption from our natural environments. But it has not fundamentally changed collective efficiencies, implying that higher rates of economic growth have usually been accompanied by larger energy losses.
Economic systems typically use new sources of energy to expand production, consumption, and accumulation, not to fundamentally improve efficiency. From the cultivation of plants and the domestication of animals to the burning of fossil fuels and the invention of electricity, the mastery and discovery of new energy sources has generally produced more energy-intensive societies. Although any economic system may make efficiency gains, these are incidental and secondary to the wider goal of accumulation. The overall efficiency of an economic system is highly inertial, changing at a glacial pace. We see this very process playing out now with greenhouse gas emissions, although the ecological crisis extends far beyond this problem. Political and business leaders have hoped for years that technological progress will somehow deliver both higher rates of economic growth and a sharp reduction in greenhouse gas emissions. Things have not gone according to plan. The year 2017 saw a substantial global rise in harmful emissions, defying even the modest goals of the Paris Agreement.39 Even before that, the United Nations had warned of an “unacceptable” gap between government pledges and the emission reductions needed to prevent some of the worst consequences from climate change.40 The challenges of boosting efficiency are more apparent when we view capitalism on a global scale: although many developed nations have made modest but measurable improvements in their collective efficiencies, these gains have been undercut by developing economies still in the process of industrialization.41 Evidently, substantial changes in the collective efficiency of any economic system rarely materialize in short periods of time. Technological growth under the regime of capitalism will deliver some additional progress on efficiency, but certainly not enough to prevent the worst consequences of the ecological crisis.
One of the best ways to understand the inertia of collective efficiencies is to compare energy efficiencies under capitalism with those of humanity’s nomadic days, more than ten thousand years ago. Recall that human muscles performed most of the work in nomadic societies, and the efficiency of our muscles is roughly 20 percent, perhaps much more under special circumstances.42 For comparison, most gasoline-powered combustion engines have an efficiency of roughly 15 percent, coal-fired power plants come in at a global average of about 30 percent, and the vast majority of commercial photovoltaics are somewhere around 15 to 20 percent.43 All these figures vary depending on a wide array of physical conditions, but when it comes to efficiency, we can safely conclude that the dominant assets of capitalism hardly do better than human muscles, even after three centuries of rapid technological progress. Cost and convenience are the main reasons why technological innovation works this way, emphasizing mechanical output and the scale of production at the expense of efficiency. Large gains in efficiency are extremely difficult to achieve, in both physical and economic terms. From time to time, a James Watt or an Elon Musk comes along with an amazing invention, but such products do not represent the entire economy. The Watt steam engine was a major improvement over previous models, but its thermal efficiency was only 5 percent at best.44 And although Musk’s Tesla motors have a phenomenal operating efficiency, the electricity needed to run them often comes from much more inefficient sources, such as coal-fired power plants. If you drive a Tesla in Ohio or West Virginia, the dirty sources of energy powering it mean that your amazing technological product produces roughly the same carbon emissions as a Honda Accord.45 The collective efficiency of capitalist economies remains relatively low because these economies are interested in growing their profits and production levels, not in making the enormous investments needed for significant improvements in efficiency.
In November 2017, a group of 15,000 scientists from more than 180 nations signed a letter sounding the alarm on the ecological crisis and what awaits us in the future.46 Their prognosis was grim, and their proposals—intentionally or not—amounted to a wholesale repudiation of modern capitalism. Among their many useful recommendations was a call for “revising our economy to reduce wealth inequality and ensure that prices, taxation, and incentive systems take into account the real costs which consumption patterns impose on our environments.” Our fundamental problem is easy to state: modern civilization uses far too much energy. And the solution to this problem is equally easy to state, but very difficult to implement: humanity must reduce the rate of energy consumption that has prevailed in modern times. The best way to drive down that rate is not through messianic delusions of technological progress, but rather by breaking the structures and incentives of capitalism, with their drive for profits and production, and establishing a new economic system that prioritizes a compatible future with our natural world.
Governments and popular movements around the world should develop and implement radical measures that will help to move humanity from capitalism toward ecologism. These measures should include punitive taxes and caps on extreme wealth, the partial nationalization of energy-intensive industries, the vast redistribution of economic goods and resources to poor and oppressed peoples, periodic restrictions on the use of capital assets and technological systems, large public investments in more efficient renewable energy technologies, sharp reductions in work hours, and perhaps even the adoption of mass veganism among industrialized nations that no longer rely on animals for food production. The economic priorities of the ecological project should focus on improving our existing quality of life, not on trying to generate high levels of economic growth to boost capitalist profits. If human civilization is to survive for thousands of years, and not just a few more centuries, then we must drastically scale back our economic ambitions and focus instead on improving the quality of life in our communities, including our community with nature. Rather than trying to dominate the natural world, we should change course and coexist with it.
Notes |
/*
* Copyright 2016 Red Hat, Inc. and/or its affiliates
* and other contributors as indicated by the @author tags.
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package org.keycloak.testsuite.exportimport;
import org.jboss.arquillian.container.spi.client.container.LifecycleException;
import org.junit.After;
import org.junit.Test;
import org.keycloak.admin.client.resource.RealmResource;
import org.keycloak.authentication.requiredactions.WebAuthnRegisterFactory;
import org.keycloak.exportimport.ExportImportConfig;
import org.keycloak.exportimport.dir.DirExportProvider;
import org.keycloak.exportimport.dir.DirExportProviderFactory;
import org.keycloak.exportimport.singlefile.SingleFileExportProviderFactory;
import org.keycloak.models.UserModel;
import org.keycloak.representations.idm.ComponentRepresentation;
import org.keycloak.representations.idm.KeysMetadataRepresentation;
import org.keycloak.representations.idm.RealmEventsConfigRepresentation;
import org.keycloak.representations.idm.RealmRepresentation;
import org.keycloak.representations.idm.RequiredActionProviderRepresentation;
import org.keycloak.representations.idm.UserRepresentation;
import org.keycloak.testsuite.AbstractKeycloakTest;
import org.keycloak.testsuite.Assert;
import org.keycloak.testsuite.arquillian.annotation.AuthServerContainerExclude;
import org.keycloak.testsuite.runonserver.RunHelpers;
import org.keycloak.testsuite.util.UserBuilder;
import java.io.File;
import java.net.URL;
import java.util.Arrays;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.Properties;
import java.util.Set;
import static org.hamcrest.Matchers.equalTo;
import static org.hamcrest.Matchers.is;
import static org.junit.Assert.assertEquals;
import static org.junit.Assert.assertThat;
import static org.junit.Assert.assertTrue;
import static org.keycloak.testsuite.admin.AbstractAdminTest.loadJson;
import org.keycloak.testsuite.arquillian.annotation.AuthServerContainerExclude.AuthServer;
/**
*
*
* @author <a href="mailto:mposolda@redhat.com">Marek Posolda</a>
* @author Stan Silvert ssilvert@redhat.com (C) 2016 Red Hat Inc.
*/
@AuthServerContainerExclude(AuthServer.REMOTE)
public class ExportImportTest extends AbstractKeycloakTest {
@Override
public void addTestRealms(List<RealmRepresentation> testRealms) {
RealmRepresentation testRealm1 = loadJson(getClass().getResourceAsStream("/testrealm.json"), RealmRepresentation.class);
testRealm1.getUsers().add(makeUser("user1"));
testRealm1.getUsers().add(makeUser("user2"));
testRealm1.getUsers().add(makeUser("user3"));
testRealm1.getUsers().add(
UserBuilder.create()
.username("user-requiredOTP")
.email("User-requiredOTP" + "@test.com")
.password("password")
.requiredAction(UserModel.RequiredAction.CONFIGURE_TOTP.name())
.build()
);
testRealm1.getUsers().add(
UserBuilder.create()
.username("user-requiredWebAuthn")
.email("User-requiredWebAuthn" + "@test.com")
.password("password")
.requiredAction(WebAuthnRegisterFactory.PROVIDER_ID)
.build()
);
testRealm1.getSmtpServer().put("password", "secret");
setEventsConfig(testRealm1);
testRealms.add(testRealm1);
RealmRepresentation testRealm2 = loadJson(getClass().getResourceAsStream("/model/testrealm.json"), RealmRepresentation.class);
testRealm2.setId("test-realm");
testRealms.add(testRealm2);
}
@Override
protected boolean isImportAfterEachMethod() {
return true;
}
@Override
public void beforeAbstractKeycloakTestRealmImport() {
removeAllRealmsDespiteMaster();
}
private void setEventsConfig(RealmRepresentation realm) {
realm.setEventsEnabled(true);
realm.setAdminEventsEnabled(true);
realm.setAdminEventsDetailsEnabled(true);
realm.setEventsExpiration(600);
realm.setEnabledEventTypes(Arrays.asList("REGISTER", "REGISTER_ERROR", "LOGIN", "LOGIN_ERROR", "LOGOUT_ERROR"));
}
private void checkEventsConfig(RealmEventsConfigRepresentation config) {
Assert.assertTrue(config.isEventsEnabled());
Assert.assertTrue(config.isAdminEventsEnabled());
Assert.assertTrue(config.isAdminEventsDetailsEnabled());
Assert.assertEquals((Long) 600L, config.getEventsExpiration());
Assert.assertNames(new HashSet(config.getEnabledEventTypes()),"REGISTER", "REGISTER_ERROR", "LOGIN", "LOGIN_ERROR", "LOGOUT_ERROR");
}
private UserRepresentation makeUser(String userName) {
return UserBuilder.create()
.username(userName)
.email(userName + "@test.com")
.password("password")
.build();
}
@After
public void clearExportImportProps() throws LifecycleException {
clearExportImportProperties();
}
@Test
public void testDirFullExportImport() throws Throwable {
testingClient.testing().exportImport().setProvider(DirExportProviderFactory.PROVIDER_ID);
String targetDirPath = testingClient.testing().exportImport().getExportImportTestDirectory()+ File.separator + "dirExport";
DirExportProvider.recursiveDeleteDir(new File(targetDirPath));
testingClient.testing().exportImport().setDir(targetDirPath);
testingClient.testing().exportImport().setUsersPerFile(ExportImportConfig.DEFAULT_USERS_PER_FILE);
testFullExportImport();
RealmResource testRealmRealm = adminClient.realm("test-realm");
ExportImportUtil.assertDataImportedInRealm(adminClient, testingClient, testRealmRealm.toRepresentation());
// There should be 6 files in target directory (3 realm, 3 user)
assertEquals(6, new File(targetDirPath).listFiles().length);
}
@Test
public void testDirRealmExportImport() throws Throwable {
testingClient.testing()
.exportImport()
.setProvider(DirExportProviderFactory.PROVIDER_ID);
String targetDirPath = testingClient.testing().exportImport().getExportImportTestDirectory() + File.separator + "dirRealmExport";
DirExportProvider.recursiveDeleteDir(new File(targetDirPath));
testingClient.testing().exportImport().setDir(targetDirPath);
testingClient.testing().exportImport().setUsersPerFile(5);
testRealmExportImport();
RealmResource testRealmRealm = adminClient.realm("test-realm");
ExportImportUtil.assertDataImportedInRealm(adminClient, testingClient, testRealmRealm.toRepresentation());
// There should be 4 files in target directory (1 realm, 12 users, 5 users per file)
// (+ additional user service-account-test-app-authz that should not be there ???)
File[] files = new File(targetDirPath).listFiles();
assertEquals(4, files.length);
}
@Test
public void testSingleFileFullExportImport() throws Throwable {
testingClient.testing().exportImport().setProvider(SingleFileExportProviderFactory.PROVIDER_ID);
String targetFilePath = testingClient.testing().exportImport().getExportImportTestDirectory() + File.separator + "singleFile-full.json";
testingClient.testing().exportImport().setFile(targetFilePath);
testFullExportImport();
}
@Test
public void testSingleFileRealmExportImport() throws Throwable {
testingClient.testing().exportImport().setProvider(SingleFileExportProviderFactory.PROVIDER_ID);
String targetFilePath = testingClient.testing().exportImport().getExportImportTestDirectory() + File.separator + "singleFile-realm.json";
testingClient.testing().exportImport().setFile(targetFilePath);
testRealmExportImport();
}
@Test
public void testSingleFileRealmWithoutBuiltinsImport() throws Throwable {
// Remove test realm
removeRealm("test-realm");
// Set the realm, which doesn't have builtin clients/roles inside JSON
testingClient.testing().exportImport().setProvider(SingleFileExportProviderFactory.PROVIDER_ID);
URL url = ExportImportTest.class.getResource("/model/testrealm.json");
String targetFilePath = new File(url.getFile()).getAbsolutePath();
testingClient.testing().exportImport().setFile(targetFilePath);
testingClient.testing().exportImport().setAction(ExportImportConfig.ACTION_IMPORT);
testingClient.testing().exportImport().runImport();
RealmResource testRealmRealm = adminClient.realm("test-realm");
ExportImportUtil.assertDataImportedInRealm(adminClient, testingClient, testRealmRealm.toRepresentation());
}
@Test
public void testImportFromPartialExport() {
// import a realm with clients without roles
importRealmFromFile("/import/partial-import.json");
Assert.assertTrue("Imported realm hasn't been found!", isRealmPresent("partial-import"));
addTestRealmToTestRealmReps("partial-import");
// import a realm with clients without roles
importRealmFromFile("/import/import-without-roles.json");
Assert.assertTrue("Imported realm hasn't been found!", isRealmPresent("import-without-roles"));
addTestRealmToTestRealmReps("import-without-roles");
// import a realm with roles without clients
importRealmFromFile("/import/import-without-clients.json");
Assert.assertTrue("Imported realm hasn't been found!", isRealmPresent("import-without-clients"));
addTestRealmToTestRealmReps("import-without-clients");
}
private boolean isRealmPresent(String realmId) {
return adminClient.realms().findAll().stream().filter(realm -> realmId.equals(realm.getId())).findFirst().isPresent();
}
/*
* non-JavaDoc
*
* Adds a testTealm to TestContext.testRealmReps (which are after testClass removed)
*
* It prevents from affecting other tests. (auth-server-undertow)
*
*/
private void addTestRealmToTestRealmReps(String realm) {
testContext.addTestRealmToTestRealmReps(adminClient.realms().realm(realm).toRepresentation());
}
private void testFullExportImport() throws LifecycleException {
testingClient.testing().exportImport().setAction(ExportImportConfig.ACTION_EXPORT);
testingClient.testing().exportImport().setRealmName("");
testingClient.testing().exportImport().runExport();
removeRealm("test");
removeRealm("test-realm");
Assert.assertNames(adminClient.realms().findAll(), "master");
Map<String, RequiredActionProviderRepresentation> requiredActionsBeforeImport = new HashMap<>();
adminClient.realm("master").flows().getRequiredActions().stream()
.forEach(action -> {
requiredActionsBeforeImport.put(action.getAlias(), action);
});
assertNotAuthenticated("test", "test-user@localhost", "password");
assertNotAuthenticated("test", "user1", "password");
assertNotAuthenticated("test", "user2", "password");
assertNotAuthenticated("test", "user3", "password");
assertNotAuthenticated("test", "user-requiredOTP", "password");
assertNotAuthenticated("test", "user-requiredWebAuthn", "password");
// Configure import
testingClient.testing().exportImport().setAction(ExportImportConfig.ACTION_IMPORT);
testingClient.testing().exportImport().runImport();
// Ensure data are imported back
Assert.assertNames(adminClient.realms().findAll(), "master", "test", "test-realm");
assertAuthenticated("test", "test-user@localhost", "password");
assertAuthenticated("test", "user1", "password");
assertAuthenticated("test", "user2", "password");
assertAuthenticated("test", "user3", "password");
assertAuthenticated("test", "user-requiredOTP", "password");
assertAuthenticated("test", "user-requiredWebAuthn", "password");
RealmResource testRealmRealm = adminClient.realm("test");
assertTrue(testRealmRealm.users().search("user-requiredOTP").get(0)
.getRequiredActions().get(0).equals(UserModel.RequiredAction.CONFIGURE_TOTP.name()));
assertTrue(testRealmRealm.users().search("user-requiredWebAuthn").get(0)
.getRequiredActions().get(0).equals(WebAuthnRegisterFactory.PROVIDER_ID));
// KEYCLOAK-6050 Check SMTP password is exported/imported
assertEquals("secret", testingClient.server("test").fetch(RunHelpers.internalRealm()).getSmtpServer().get("password"));
// KEYCLOAK-8176 Check required actions are exported/imported properly
List<RequiredActionProviderRepresentation> requiredActionsAfterImport = adminClient.realm("master").flows().getRequiredActions();
assertThat(requiredActionsAfterImport.size(), is(equalTo(requiredActionsBeforeImport.size())));
requiredActionsAfterImport.stream()
.forEach((action) -> {
RequiredActionProviderRepresentation beforeImportAction = requiredActionsBeforeImport.get(action.getAlias());
assertThat(action.getName(), is(equalTo(beforeImportAction.getName())));
assertThat(action.getProviderId(), is(equalTo(beforeImportAction.getProviderId())));
assertThat(action.getPriority(), is(equalTo(beforeImportAction.getPriority())));
});
}
private void testRealmExportImport() throws LifecycleException {
testingClient.testing().exportImport().setAction(ExportImportConfig.ACTION_EXPORT);
testingClient.testing().exportImport().setRealmName("test");
testingClient.testing().exportImport().runExport();
List<ComponentRepresentation> components = adminClient.realm("test").components().query();
KeysMetadataRepresentation keyMetadata = adminClient.realm("test").keys().getKeyMetadata();
String sampleRealmRoleId = adminClient.realm("test").roles().get("sample-realm-role").toRepresentation().getId();
Map<String, List<String>> roleAttributes = adminClient.realm("test").roles().get("attribute-role").toRepresentation().getAttributes();
String testAppId = adminClient.realm("test").clients().findByClientId("test-app").get(0).getId();
String sampleClientRoleId = adminClient.realm("test").clients().get(testAppId).roles().get("sample-client-role").toRepresentation().getId();
String sampleClientRoleAttribute = adminClient.realm("test").clients().get(testAppId).roles().get("sample-client-role").toRepresentation().getAttributes().get("sample-client-role-attribute").get(0);
// Delete some realm (and some data in admin realm)
adminClient.realm("test").remove();
Assert.assertNames(adminClient.realms().findAll(), "test-realm", "master");
assertNotAuthenticated("test", "test-user@localhost", "password");
assertNotAuthenticated("test", "user1", "password");
assertNotAuthenticated("test", "user2", "password");
assertNotAuthenticated("test", "user3", "password");
assertNotAuthenticated("test", "user-requiredOTP", "password");
assertNotAuthenticated("test", "user-requiredWebAuthn", "password");
// Configure import
testingClient.testing().exportImport().setAction(ExportImportConfig.ACTION_IMPORT);
testingClient.testing().exportImport().runImport();
// Ensure data are imported back, but just for "test" realm
Assert.assertNames(adminClient.realms().findAll(), "master", "test", "test-realm");
assertAuthenticated("test", "test-user@localhost", "password");
assertAuthenticated("test", "user1", "password");
assertAuthenticated("test", "user2", "password");
assertAuthenticated("test", "user3", "password");
assertAuthenticated("test", "user-requiredOTP", "password");
assertAuthenticated("test", "user-requiredWebAuthn", "password");
RealmResource testRealmRealm = adminClient.realm("test");
assertTrue(testRealmRealm.users().search("user-requiredOTP").get(0)
.getRequiredActions().get(0).equals(UserModel.RequiredAction.CONFIGURE_TOTP.name()));
assertTrue(testRealmRealm.users().search("user-requiredWebAuthn").get(0)
.getRequiredActions().get(0).equals(WebAuthnRegisterFactory.PROVIDER_ID));
List<ComponentRepresentation> componentsImported = adminClient.realm("test").components().query();
assertComponents(components, componentsImported);
KeysMetadataRepresentation keyMetadataImported = adminClient.realm("test").keys().getKeyMetadata();
assertEquals(keyMetadata.getActive(), keyMetadataImported.getActive());
String importedSampleRealmRoleId = adminClient.realm("test").roles().get("sample-realm-role").toRepresentation().getId();
assertEquals(sampleRealmRoleId, importedSampleRealmRoleId);
Map<String, List<String>> importedRoleAttributes = adminClient.realm("test").roles().get("attribute-role").toRepresentation().getAttributes();
Assert.assertRoleAttributes(roleAttributes, importedRoleAttributes);
String importedSampleClientRoleId = adminClient.realm("test").clients().get(testAppId).roles().get("sample-client-role").toRepresentation().getId();
assertEquals(sampleClientRoleId, importedSampleClientRoleId);
String importedSampleClientRoleAttribute = adminClient.realm("test").clients().get(testAppId).roles().get("sample-client-role").toRepresentation().getAttributes().get("sample-client-role-attribute").get(0);
assertEquals(sampleClientRoleAttribute, importedSampleClientRoleAttribute);
checkEventsConfig(adminClient.realm("test").getRealmEventsConfig());
}
private void assertAuthenticated(String realmName, String username, String password) {
assertAuth(true, realmName, username, password);
}
private void assertNotAuthenticated(String realmName, String username, String password) {
assertAuth(false, realmName, username, password);
}
private void assertAuth(boolean expectedResult, String realmName, String username, String password) {
assertEquals(expectedResult, testingClient.testing().validCredentials(realmName, username, password));
}
private void assertComponents(List<ComponentRepresentation> expected, List<ComponentRepresentation> actual) {
expected.sort((o1, o2) -> o1.getId().compareTo(o2.getId()));
actual.sort((o1, o2) -> o1.getId().compareTo(o2.getId()));
assertEquals(expected.size(), actual.size());
for (int i = 0 ; i < expected.size(); i++) {
ComponentRepresentation e = expected.get(i);
ComponentRepresentation a = actual.get(i);
assertEquals(e.getId(), a.getId());
assertEquals(e.getName(), a.getName());
assertEquals(e.getProviderId(), a.getProviderId());
assertEquals(e.getProviderType(), a.getProviderType());
assertEquals(e.getParentId(), a.getParentId());
assertEquals(e.getSubType(), a.getSubType());
Assert.assertNames(e.getConfig().keySet(), a.getConfig().keySet().toArray(new String[] {}));
// Compare config values without take order into account
for (Map.Entry<String, List<String>> entry : e.getConfig().entrySet()) {
List<String> eList = entry.getValue();
List<String> aList = a.getConfig().getList(entry.getKey());
Assert.assertNames(eList, aList.toArray(new String[] {}));
}
}
}
private void clearExportImportProperties() {
// Clear export/import properties after test
Properties systemProps = System.getProperties();
Set<String> propsToRemove = new HashSet<>();
for (Object key : systemProps.keySet()) {
if (key.toString().startsWith(ExportImportConfig.PREFIX)) {
propsToRemove.add(key.toString());
}
}
for (String propToRemove : propsToRemove) {
systemProps.remove(propToRemove);
}
}
private void importRealmFromFile(String path) {
testingClient.testing().exportImport().setProvider(SingleFileExportProviderFactory.PROVIDER_ID);
URL url = ExportImportTest.class.getResource(path);
String targetFilePath = new File(url.getFile()).getAbsolutePath();
testingClient.testing().exportImport().setFile(targetFilePath);
testingClient.testing().exportImport().setAction(ExportImportConfig.ACTION_IMPORT);
testingClient.testing().exportImport().runImport();
}
}
|
Toms River NJ Real Estate & Homes for Sale
465 Properties Found
The median home value in Toms River, NJ is $240,000.
This is
higher than
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The national median home value is $209,892.
The average price of homes sold in Toms River, NJ is $240,000.
Approximately 71% of Toms River homes are owned,
compared to 15% rented, while
14% are vacant.
Toms River real estate listings include condos, townhomes, and single family homes for sale.
Commercial properties are also available.
If you like to see a property, contact Toms River real estate agent to arrange a tour today!Learn more about Toms River Real Estate.
View additional info
This gorgeous 4 BR 3 full bathroom ranch home is ready to impress. Looking for a completely updated home? Would you like 2 master suites? Could you use 4 large BRs & 3 full bathrooms? Then this wonderful home is for you. It features beautiful new flooring throughout, recessed lighting, an open layout with new kitchen w/granite countertops, stainless steel appliances & stylish backsplash. The open concept allows for various different layout options. Off the kitchen you'll find a great room with a beautiful fireplace as the focal point. Down the hall are 2 large BRs with an updated full bathroom, as well as a master BR suite with its own updated full bath. The 2nd BR suite is on the other side of the home in its own separate space. The fully fenced in yard completes this great house
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SUPERB 2012 CUSTOM BUILT COLONIAL HOME WITH CEDAR IMPRESSIONS AND STONE SIDING LOCATED ON A CUL-DE-SAC. THIS HOME BOASTS 4 BR'S, 3.5 BATHS ,EAT IN KITCHEN WITH SS APPLIANCES & GRANITE COUNTERTOP,FAMILY ROOM WITH GAS FIREPLACE, LIVING ROOM, DINING ROOM, FINISHED BASEMENT WITH FULL BATH , BUILT IN BAR,BEAUTIFUL YARD BOASTS IN GROUND FIBERGLASS POOL WITH WATERFALL. CALL TODAY FOR PRIVATE VIEWING.
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Fantastic potential here! This waterfront home needs a little love and a vision to recreate the layout to the home of your dreams! There is a newer vinyl bulkhead and the home does not need to be lifted, the big obstacles are taken care of already. Come imagine all it can be with some love and your own vision.
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Shabby chic- waterview living is how to describe this Center hall Colonial. If you ever dreamed of owning a home that offers cool bay breezes, maritime views and the aura of relaxation that the water exudes than this is the place for you. Fishing, crabbing and bird watching are just a few more benefits to reel you in. This home has so many possibilities, make your appointment today and start creating a backdrop for ;your new lifestyle.
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This is an entertainers dream home featuring a huge newer deck and in-ground swimming pool. Located in the highly desirable North Dover section of Toms River, this home has been meticulously well maintained and it shows.
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Welcome to Laurel Chase - This North Dover Townhouse is ready for a new owner. This 3 bedroom 3.5 bath multi level townhouse is such a wonderful opportunity to own in this desirable community. Direct entry garage into foyer, and partially finished lower level with closet and full bath. Main living level has bright kitchen with center island, dining room, living room with gas fireplace and sliders to you back deck. The next level has your master bedroom with walk in closet, on suite bath with double sinks, whirlpool tub and shower, 2 additional bedrooms, full bath and laundry area round out this home.
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Nice family neighborhood, walking distance to shopping, schools, and church. The home originally was a 4 bedroom however the owner took a wall out between 2 bedrooms to make 1 large room and can be put back to original. The original doors are still in place. Also the original attached garage was converted to a finished room off the kitchen to make it a potential 5 bedroom. An Amish made 14x20 detached garage was installed on the right side of the home. A newer outside 2nd floor deck and stairs was built for great access to 2nd floor bedroom overlooking the large built in pool. The pool has a new liner and recently changed to salt water. A large lot with privacy. This home is waiting for a new owner to put their love and taste into it.
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Welcome to Cranmoor Manor! this 4 bedroom, 3 1/2 bath, 2 car garage on the lagoon offers your chance to live on the water. This is property sits on a 65x254 Lot with a boat ramp right in your backyard. This home features tile and wood floors a spiral staircase, a nice size deck, and a large concrete patio for entertaining. This is a must see!
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Terrific home situated on 75ft of wide & deep lagoon in desirable Shelter Cove, minutes to the open Bay. Home features a newer gourmet kitchen w/large breakfast bar, lots of cabinets, Granite & Full appliance package. Bring the outdoors in w the 4 Season room overlooking the water. Spacious Living room. 3 bedrooms & a renovated main bath rounds out the top level. The entire lower level has been renovated to include a ''Summer Kitchen'' 2 more bedrooms, upgraded bath w/slate tiling & a cozy family room with sliders to the yard. Where you can continue the entertaining with a 16X30 In-ground pool, huge patio & built-in Tiki Bar. Perfect Mother/Daughter setup. Garage. Hardwood flooring. Neutral colors. New Central Air, Furnace, Tank-less Hotwater heater, roof to name a few. A Must See!
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Welcome to Huntington Ct. Come see this well kept 4 bedroom 2 1/2 bath home. Pull into the freshly sealed driveway and come on in! The first floor features a living room, dining room, eat in kitchen and den. There is also a laundry room, 1 car garage and 1/2 bath. Upstairs you will find 3 nice size bedrooms, a full bath. You will also find the master suite with full bath and walk in closet upstairs. The home has a full basement. The pull down attic is floored for even more storage. The backyard is fenced in and has a deck for entertaining. Enjoy the warm weather in the heated saltwater pool. Great location! Come take a look. 1 year home warranty included!
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Large 4 bed 3 1/2 bath with den/office home for a large family, Full basement with kitchen and bathroom and exterior door to basement, possibly be a good mother-daughter or in-law suite. Walk-up attic. This home needs a little TLC to bring it back to its former glory priced more than $87,000 less than its assessed value. See it today! Buyer is responsible for all inspections, and/or any township requirements smoke cert,CO. All information regarding this home has been compiled from various sources and is deemed to be reliable but not guaranteed. It is the buyers responsibility to perform due diligence and confirm all information. Sold AS IS This property may qualify for Seller Financing (Vendee).
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Beautifully renovated turnkey ground floor condominium located in the Waters Edge community. Kitchen has following brand new items: high-end Samsung appliances (Fridge, Stove, Range, Dishwasher), tile floor, cabinets, quartz countertops, sink, backsplash, and lighting fixtures. Both full Bathrooms have brand new tile floors, and new vanities/mirrors. Both Bedrooms have brand new carpeting and new bi-fold doors in second bedroom. All Interior doors are brand new (including sliding patio door) and entire condo has brand new floor molding. The dining room and family room have hardwood flooring and a brand new fireplace mantle. Every room has brand new paint job. Community Pool, tennis courts, and childrens play area close to unit.
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Picture perfect COLONIAL w/ a basement and in ground pool sitting at the end of a private CUL DE SAC. SOUNDS like the perfect fit for you! Start enjoying your new home RIGHT AWAY. GREAT curb appeal, great floor plan & being offered at a GREAT PRICE. Wonderful opportunity to purchase a home on a wonderful quiet street, close to major highway, Jersey Boardwalks or a trip to Atlantic City. Formal living room, formal dining room and eat in kitchen. Family room w/ french doors leading to the deck, private yard and in ground pool. 4 bedrooms are all on the 2nd level, updated baths, paint, flooring, fixtures and touches you will love. Finish the basement & create your own space. NEW ROOF, IN GROUND POOL , full appliance package, outdoor gazebo on the deck is also included. ALARM SYSTEM INCLUDED
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Beautifully renovated turnkey ground floor condominium located in the Waters Edge community. Kitchen has following brand new items: high-end Samsung appliances (Fridge, Stove, Range, Dishwasher), tile floor, cabinets, quartz countertops, sink, backsplash, and lighting fixtures. Both full Bathrooms have brand new tile floors, and new vanities/mirrors. Both Bedrooms have brand new carpeting and new bi-fold doors in second bedroom. All Interior doors are brand new (including sliding patio door) and entire condo has brand new floor molding. The dining room and family room have hardwood flooring and a brand new fireplace mantle. Every room has brand new paint job. Community Pool, tennis courts, and childrens play area close to unit.
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Saratoga model with sunroom addition in rear. Gas heat. Central Air. Windows were replaced about 5 years ago. Large living/dining room combination. Eat-in-kitchen with side door out to yard. Master bedroom opens to screened room addition that spans the entire width of house. Full bath with shower. Direct entry garage. Front room can be used as TV room and/or den. Close to shopping, public transportation, shopping, dining, the Garden State Parkway, the Jersey Shore and beaches. Very nice house. Low taxes and monthly maintenance fee. Extra insulation in house--gas under $65 per month on budget plan. Per owner, the highest electric bill for the year was $88.
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New Construction in Water Front Community! Walk into a two story foyer! Hardwood floors and recessed lighting throughout the first floor! Move on to an open floor plan that leads to your living room - dining room. Then to your gorgeous kitchen with white subway tiled back splash and Quartz counter tops plus huge pantry! Kitchen leads to fenced in yard with stamped concrete patio! Upstairs has 3 nice sized bedrooms! Beautiful family bathroom with subway tile in the shower! Laundry on second floor for convenience! Master has breath taking water views from windows or walk out on your balcony for an even better view! A his and hers closet and a master bath with white subway tile and stone floor in shower! Home is above required level so flood insurance is very reasonable!
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I love everything about this house, from the oversized driveway and walkway to the cute front porch. Large living room, huge eat-in kitchen and separate dining room with bonus area. This house sits on a sizable lot with a huge front and back yard with space for all your gardening or fun. Backyard is a private oasis including a raised patio, fenced and tree lined for maximum privacy, an inground pool, plus 2 large storage shed; it is so inviting and has many possibilities. You'll love the Georgetown Section of Toms River close to shopping, schools, the parkway and beach. Great East Toms River Schools! Make an appointment to see this house today. Key Features: Fireplace both gas and wood burning, solar powered hot water heater with electric back-up, master bedroom extends front to back of the house providing views of both front and back yards.
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I love everything about this house, from the oversized driveway and walkway to the cute front porch. Large living room, huge eat-in kitchen and separate dining room with bonus area. This house sits on a sizable lot with a huge front and back yard with space for all your gardening or fun. Backyard is a private oasis including a raised patio, fenced and tree lined for maximum privacy, an in-ground pool, plus 2 large storage shed; it is so inviting and has many possibilities. You'll love the Georgetown Section of Toms River close to shopping, schools, the parkway and beach. Great East Toms River Schools! Make an appointment to see this house today. Key Features:Fireplace - gas and wood burning, solar powered hot water heater with electric back-up, master bedroom has views of front & back
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THIS IS IT!!! Charming, quaint ranch in desirable Toms River neighborhood. Complete with 3 bedrooms , finished basement, lush rock yard and oversized driveway. The airy bright three seasons room is a must see! Original hardwood floors maintained under carpeting throughout. Come see today!!! Sellers are motivated!!! Close to schools, shopping and the beach.
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I love everything about this house, from the oversized driveway and walkway to the cute front porch. Large living room, huge eat-in kitchen and separate dining room with bonus area.This house sits on a sizable lot with a huge front and back yard with space for all your gardening or fun. Backyard is a private oasis including a raised patio, fenced and tree lined for maximum privacy, an in-ground pool, plus 2 large storage shed; it is so inviting and has many possibilities. You'll love the Georgetown Section of Toms River close to shopping, schools, the parkway and beach. Great East Toms River Schools! Make an appointment to see this house today.Key Features: Fireplace both gas and wood burning, solar powered hot water heater with electric back-up, master bedroom extends front to back of the house providing views of both front and back yards.Home Upgrades: Master bath and main bath remodeled in 2018, brand new pool liner, driveway resealed this year, master bedroom carpet and hallway flooring redone in 2018, all window are only 3 years old.
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Welcome to the Cedars. This sought after END UNIT Town home is move in ready. Beautiful private park like setting. This home features an updated kitchen with newer cabinets, wood countertop, SS appliances and laminate flooring. Hardwood floors in dining room & living room. Upstairs has newer laminate flooring. Den features slider leading to balcony overlooking a treed back yard. Den can easily converted to a second bedroom. Washer and dry located on 2nd floor for easy access. Furnace and water heater replaced in the last 5 years. Central air replaced last year. Don't miss out. Come take a look.
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Live at the Jersey Shore in the desirable Bayshore section of Toms River just minutes from beaches and the boardwalk! Build your dream home or rehab the existing home which is completely gutted waiting for you to fix it up. This home sits on a nice 60x100 lot with bay views, surrounded by gorgeous homes in this wonderful waterfront community. Don't miss this opportunity!
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Come see this wonderful, waterfront, beach bungalow! This home has a lovely open floor plan with 3 bedrooms, large living room and garage. Then walk through the French doors to the kitchen and rear den with beautiful water views. Step out the rear slider to an oversized deck
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A masterpiece of design and functionality. Newer, 4000 sq. waterfront 5 bed, 3 1/2 bath home with open floor plan and amazing garage/storage space, all on a massive lot (130x140x75x100). Meticulously landscaped including salt water pool surrounded by elegant paver design. Covered patio and open patio with views of 2 wildlife sanctuaries. Two minutes to Silver Bay/Barnegat Bay, This home is a builder's own and is jam packed with amenities. This very unique trophy property has it all...
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Great move in conditiion! Open floor plan with great flow, kitchen with granite counter tops, stainless steel appliances. Adjacent dining room with sliding doors to covered deck. Master bedroom with updated full bath finished in ceramic tiling. Downstairs features expansive family room with sliding doors leading to fenced in yard. 1/2 bath and laundry room. New amenities throughout. New central AC.
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Last week, the Parliament of Malawi adopted a law that, for the very first time, sets the minimum age of marriage from 16 to 18 years old. The Marriage, Divorce and Family Relations Bill has been hailed as a step forward for Malawi, where 50% of girls are married off before 18. Girls Not Brides spoke to Ephraim Chimwaza, Programme Manager at the Centre for Social Concern and Development (CESOCODE) in Malawi, to find out what needs to happen for this new law to make a real difference on child marriage.
The arrest, release and then rearrest of Meriam Ibrahim is not really about visas, exit stamps and plane tickets, writes Harriet Alexander. Instead it's a potent cocktail of political positioning, religious extremism and family feuding - with a young mother at its centre When rumour of her release from prison first surfaced, we didn't dare to believe it. When it was confirmed by the Sudanese authorities, we began to have real hope.
Dr Raslan Fadl and father of the 13-year-old girl who died during cutting are the first to be prosecuted in Egypt for practice of FGM.
In a landmark case, Dr Raslan Fadl is the first doctor to be prosecuted for FGM in Egypt, where the practice was banned in 2008, but is still widely accepted and carried out by many doctors in private.
Sohair al-Bata'a died in Fadl's care in June 2013, and her family admitted that she had been victim to an FGM operation carried out at their request.
The case was initially dropped after an official medical report claimed that Sohair had been treated for genital warts, and that she died from an allergic reaction to penicillin. But after a campaign by local rights groups and the international organisation Equality Now, as well as an investigation by Egypt's state-run National Population Council (NPC), the country's chief prosecutor agreed to reopen the case – leading to this week's seminal prosecution of both Fadl and Sohair's father.
"It is a very important case," said Hala Youssef, head of the NPC, which had pushed for the case to be reopened. "It's the first time that somebody in Egypt will be prosecuted for this crime, and it should be a lesson for every clinician. The law is there, and it will be implemented."
According to Unicef, 91% of married Egyptian women aged between 15 and 49 have been subjected to FGM, 72% of them by doctors. Unicef research suggests that support for the practice is gradually falling: 63% of women in the same age bracket supported it in 2008, compared with 82% in 1995.
But according to research, FGM still has high support in areas with a lower standard of education, where proponents claim mutilation makes women less likely to commit adultery.
Families living near where Sohair died have not been put off the practice, says Reda Maarouf, a local lawyer involved in the case; they simply go to other doctors.
Sohair's family are reported to oppose her father's prosecution. "It's a cultural problem, not religious," said Vivian Foad, an official who led the NPC's investigation. "Both Muslims and Christians do it. They believe it protects a woman's chastity."
Some Islamic fundamentalists claim FGM is a religious duty, but it is not nearly as widespread in most other majority-Muslim countries in the Middle East. Suad Abu-Dayyeh, Equality Now's regional representative, said: "It's very much rooted in Egypt, but in other Arab countries – in Jordan, in Palestine, in Syria – we don't have it."
There are four main methods of committing FGM, according to theWorld Health Organisation, and Abu-Dayyeh said the practice of removing a girl's clitoris and labia was probably the most common in Egypt.
"It's a very painful procedure and I don't know why they do it. It's the worst one," said Abu-Dayyeh, who visited Sohair's grave in Mansoura, northern Egypt, as part of Equality Now's campaign. "Women will really not feel any pleasure when having sex with their husband. It's criminal."
Foad hopes Egypt's interim government will be more proactive about FGM than the administration it replaced after Mohamed Morsi's overthrow last year. Officially, Morsi's Muslim Brotherhoodclaimed they opposed FGM, but prominent members and allies of the group expressed support for it. "People are entitled to do what suits them," said Azza al-Garf, a female MP from the Brotherhood's political arm, in 2012. Another ultra-conservative MP, Nasser al-Shaker – a member of a Salafi party that was then an ally of the Brotherhood – called for legalisation of FGM, and said it had a religious mandate.
Two years on, Egypt's leadership has been criticised internationally for other human rights abuses, but Foad hopes it will be more progressive than its predecessors on FGM. "Under Morsi, they didn't create a conducive atmosphere through the media, and through education – not only for FGM but all women's issues. Now the government is responding positively, and the media is responding positively."
Abu-Dayyeh said Fadl's prosecution was just the start. The case would count for little unless the doctor was jailed and an anti-FGM awareness campaign reached the country's poorest districts, she said.
"Now you need much more work. And it has to be done far away from Cairo – in the [rural areas] where the practice is very widespread."
GENEVA (6 November 2013) – Flogging women, including for “honour-related offences” amounts to cruel, inhuman and degrading treatment in international law and must stop, two independent UN human rights experts said Wednesday in the wake of recent cases involving women in Sudan.
Egypt is the only country in North Africa where the practise of female genital mutilation remains widespread – despite an official ban and many public information campaigns for women. Anna Kölling reports from Cairo
According to estimates, over 90 per cent of all Egyptian women of childbearing age are affected by genital mutilation. The scale of this practice first became apparent in 1994 with a study conducted on population development and health. Activists have been fighting against female circumcision for decades and, after the popular uprising in early 2011, women's rights once again became a prominent topic in the media. Although women and men have fought side by side on the streets, the rights of women are nevertheless becoming increasingly jeopardised. Ultra-conservative groups, for example, are calling for the lifting of the ban on female circumcision, which was enacted into law in 2008.
DAR ES SALAAM, Tanzania(Thomson Reuters Foundation)--Tanzania is banking on the on-going constitutional review process of marriage laws to stop child marriages, according to a report in the government newspaper Daily News.
The marriage Act of 1971 allows girls as young as 14-years-old to marry with parental consent. On average, two out of five girls are married off before their 18th birthday, putting Tanzania among countries with the highest child marriage rates in the world.
Three European women went on trial in Tunis on Wednesday for holding a topless anti-Islamic protest, and their French lawyer said he was confident they would escape prison despite the threat of jail sentences.
Pauline Hillier and Marguerite Stern from France, and Josephine Markmann from Germany arrived in court around 0930 GMT wearing the traditional Tunisian headscarf, or safsari.
Countless Moroccan women, continue to face abuse and sexual violence at the hands of their husbands. About 6 million women in Morocco are victims of violence, or around one in three. Morocco’s Social Development Minister Bassima Hakkaoui, the only female minister in the country, said last week that she would try to push forward a law protecting women that has been stuck in Parliament for 8 years.
A secular Egyptian woman outlines the disappointments written into the country's new constitution, passed in late December. Women have had only one legal advance since the revolution: prosecuting sex harassment.
The U.S. evangelist and anti-gay crusader's trial begins January 7 in Massachusetts. Lively is being sued for crimes against humanity by the organization Sexual Minorities of Uganda, represented by the Center for Constitutional Rights (CCR).
n order to shine a spotlight on the work of activists worldwide. Every day, for sixteen days, WLUML shared short stories of and about networkers, brave women and girls who against all odds, survive and carry on with the struggle for social justice and equality.
As Mali pursues peace talks and also prepares for war, Malian women insist they should be at the table for both. They argue women are the primary victims of rebel and terrorist groups occupying the north.
LET us go back a little, nearly a year ago, to that earlier attempt to interfere in, and legislate on sexual conduct between consenting adults. Profiting from that experience, I would like to caution – yet again - that it is high time we learnt to ignore what we conveniently designate and react to as ‘foreign interference’. By now, we should be able to restrict ourselves to the a priori position that, as rational beings, we make pronouncements on choices of ethical directions from our own collective and/or majority will, independent of what is described as ‘external dictation’.
It will pass… a draft of a constitution that doesn’t represent Egyptians or their dreams. A draft that did not engage them in the dialogue for change, which passed just two before the referendum, without giving Egyptians the opportunity to discuss it. When the revolution started, Egyptians looked forward to a time where they could evaluate their beliefs and values, discuss them, even change them and reflect it all in a document that recorded the whole process. But this never happened.
On the morning of November 7, 2012, the 5 admins of The Uprising of Women in the Arab World log into Facebook, to find out that one’s account has been blocked for 30 days, another for 3 days, 2 others for 24 hours, and 1 other received a warning notification.
JUBA - Cut off from development by five decades of civil war, South Sudan has the highest maternal mortality rate in the world and high levels of infant mortality and morbidity. Large families struggle to get by in the war-ravaged new nation.
With the help of aid agencies providing family planning services to bolster a fledgling healthcare system, women and families are starting to choose life for the first time.
The Observatory for the Protection of Human Rights Defenders, a joint programme of the International Federation for Human Rights (FIDH) and the World Organisation Against Torture (OMCT), welcomes the vindication of two women humanrights defenders in The Gambia following two years of judicial harassment.
A multi-country study conducted by the World Health Organization (WHO) found that up to 71 percent of women aged 15 to 49 reported physical and/or sexual violence at some point in their lives. Violence against women commonly becomes a vicious cycle in families thus creating generational dysfunction and disease. The complete social framework of society is at risk when we let violence happen in our homes.
Women have played an important role in spurring reform throughout the Middle East and North Africa. But as elections take place and constitutions are drafted, their rights are at risk of being sidelined.
For the first time, a woman is running for the leadership of the political party of the Muslim Brotherhood, Egypt's most powerful Islamist group. Sabah el-Saqari says she wants to increase female participation in politics and even defends a woman's right to run for president, a stance her organization rejects.
But liberals who fear Islamist rule will set back women's rights say her candidacy is just an attempt by the Brotherhood to improve its image.
Following publication of Article 36 of the 'Rights and Duties' section of Egypt's draft constitution, a number of political parties, coalitions and public figures have issued a joint statement expressing their "deep concern" for the draft article's wording, which, they say, could compromise women's historical rights.
Hard living conditions for Syrian refugees in Libya are forcing some families to marry off their daughters to wealthy local men. Syrians say Libyans often knock at their doors asking for especially underage girls, as BBC Arabic's Ahmed Maher reports from Benghazi.
Ahmed Atrash is among hundreds of Syrian refugees in the country's second largest city, Benghazi. He and his family have fled the raging war back home.
For the first time in Egyptian history, a female anchor on state television has covered her hair with a head scarf. Under the Mubarak regime, women were forbidden to wear a head scarf on state television in order to depict a more modern appearance; however, current President Mohammed Morsi, who is supported by the Muslim Brotherhood, has lifted the ban. Thus, women are now allowed to wear a head scarf on state television if they chose to do so.
Following the Libyan revolution, in which women played a crucial part, and the participation of large numbers of female citizens in the July 2012 elections, Libyan women are now looking forward to a partnership and full equality with their male counterparts."Libyan women were instrumental in the country choosing a liberal and progressive government in the recent elections as many of them voted for the winning National Forces Alliance (NFA) of Mahmoud Jibril," said Nadine Nasrat, from the Institute for Democracy and Electoral Assistance (IDEA).
In the run up to next week's Presidential election in Somalia, Zainab M. Hassan writes an open letter to new women parliamentarians asking them to demonstrate collective leadership in their choice of someone to lead a ruined country.
Campaigners in Egypt say the problem of sexual harassment is reaching epidemic proportions, with a rise in such incidents over the past three months. For many Egyptian women, sexual harassment - which sometimes turns into violent mob-style attacks - is a daily fact of life, reports the BBC's Bethany Bell in Cairo.
Last winter, an Egyptian woman was assaulted by a crowd of men in the city of Alexandria.
The Women Human Rights Defenders (WHRD) program is issuing a series of concept papers that aim to introduce the notion of WHRDs: who they are, what they do, and why they should be considered as a distinct group of human rights defenders. The categories of WHRDs analyzed in the concept papers include: vocational women (doctors, nurses, and teachers); students; political candidates; civil society activists; protesters; and workers (industrial and agrarian sectors).
Most Egyptians will come to remember 13 August 2012 as more than just another long hot day of the holy month of Ramadan. Just a few hours before sunset when millions waited eagerly to break their fast, news broke out of a major development in the ongoing power struggle between two main power houses: the generals representing the country's military past, and the political faction seeking to control its future.
In recent years, the international community has begun to place increased attention on girls’ education generating a better understanding of the underlying causes and consequences of the disparities, and an international consensus on the need to address the issue. Much has been done to create awareness and demonstrate that change is not only necessary but also possible.
Egypt's National Council for Women announced on Tuesday a new hotline dedicated to receiving reports of sexual harassment: 08008883888.
The council issued a statement on their Facebook page stating that they are working with the interior ministry to swiftly reinforce the sexual harassment law on thugs and offenders.
Ambassador Mervat Talawy, head of the council, stressed on the importance of reinforcing the law, considering the council a representation of all women in Egypt and pointing to its keenness to preserve the dignity of women.
As documented in a new report from the Enough Project, which ranks electronics firms on their progress in cleaning up their supply chains of conflict minerals, there are glimmers of hope for eastern Congo despite ongoing violence there, which is driven partly by conflict minerals.
"Educate a girl, and you educate a village," an African proverb goes, illustrating the ripple effect of educating women and the role that women play in making a difference in the lives of those around them.
The female wing of a civil rights group is urging women in Togo to stage a week-long sex strike to demand the resignation of the country's president.
Women are being asked to start withholding sex from their husbands or partners as of Monday, said Isabelle Ameganvi, leader of the women's wing of the group Let's Save Togo. She said the strike will put pressure on Togo's men to take action against President Faure Gnassingbe.
Her laugh is infectious, and you’d be forgiven for thinking you were in a high school drama class or a Hollywood hair salon. But this is the Arab world, not Tinseltown. And Miriem Bensalah Chaqroun is no lightweight.
She leads Morocco’s General Confederation of Moroccan Enterprises (CGEM), a giant trade association roughly analogous to the U.S. chamber of Commerce.
Bensalah is also a licensed pilot, a Harley-Davidson rider, a race car driver, a competitive golfer — and a 49-year-old mother of three.
Tunisia has always led gender equality in the Middle East for the past fifty years, with women playing an active role in civil society and enjoying the same legal rights as men. Now, with the old regime overthrown this past spring, many Tunisians are concerned that Al-Nahda, a more conservative Islamic party, will come to power and pull the nation back into the past.
Layla’s life is still in danger. We need you to take action to save her.
Layla Ibrahim Issa is a 23-year old mother who was sentenced to death by stoning by the Mayo court in Khartoum, Sudan. We put out an action alert to support Layla earlier this month, and we extend our thanks to those of you who raised their voices; but Layla is still in prison with her 6-month old child.
The authorities have not yet responded to our demands to immediately repeal the verdict, and stop the planned execution.
Merna Thomas, a twenty-four-year-old activist, heads out for another day of revolution. Armed with brushes and small buckets of paint, her goal today is not the overthrow of a regime, but something perhaps even more daring: to change Egyptian attitudes toward women. On the side of a downtown building, she puts her graffiti skills to work with an illustration of Samira Ibrahim—hailed for bravely speaking out after becoming one of the victims of the infamous virginity tests that Egyptian security forces performed on detained female protesters in 2011. Passersby mumble streams of complaints.
Some 2,000 years ago, during the Nubian period, North Sudan was ruled by women, including Queen Kandaka, famous for her strength. Today, a new generation of Kandakas is taking back the streets and fighting at the frontline of the revolution.
Amnesty International condemns the sentencing of Layla Ibrahim Issa Jumul to death by stoning and calls on the Sudanese government to halt the execution and to reform its criminal law without delay, with the aim to abolish corporal punishment.
Layla Ibrahim Issa Jumul, a 23-year old Sudanese woman, was sentenced to death by stoning for adultery on 10 July 2012 by the Criminal Court of Mayo, in Khartoum, under Article 146 of Sudan’s 1991 Criminal Code.
RABAT, Morocco — When Rkia Bellot’s family sold their communal land in 2004, each of her eight brothers received a share of the proceeds. But Bellot, a single woman, got nothing.
That’s because Bellot’s family land was part of the 37 million acres in Morocco governed by the orf, or tribal law. When this type of family land is sold, the unmarried or widowed women in the family, collectively called the Soulaliyate, often become destitute.
When cows are traded for an unwilling bride, rural Zulu women lose their freedom, and more. Called thwala, the practice is often abused, activists say.
NORTHWEST OF HOWICK, South Africa —
— She was named Democracy in Zulu, at a time when her country had none.
A few years later, the constitution born of the historic South African election that ended apartheid made Nonkululeko "free" and "equal." But the eight cows paid for her as a bride price mean that she is neither.
Tunisian radio journalist Nadia Heddaoui Mabkhout was denied access to the headquarters of RTCI (Radio Tunis Chaîne Internationale), suspended from work and had her radio show cancelled last Friday.
Mabkhout was on her way to host her show Café Noir, recently renamed L’invité du Journal, which is aired on Monday, Wednesday, and Friday from 8:30 to 9am. She was accompanied by her guest, Neziha Rejiba (alias Om Zied), a well-known Tunisian activist and writer.
On 17 June, when a number of female students led a peaceful protest marching from the female dormitories to the male ones at the University of Khartoum, they did not know that they would inspire protests across the country. Many inside Sudan are calling the ongoing protests an “Intifada” — an Arabic word for rebellion or resistance — and there is much truth in that.
On 9 July 2011, when South Sudan became an independent country, Rose Michael, a South Sudanese woman who had lived most of her life in Khartoum, decided to stay in the city where she had a great job and owned a house. But in April 2012, Rose had to leave for Juba after her employer let her go. She planned to return to Khartoum. But then she lost her Sudanese passport and now she can't return because the war has escalated and flights are cancelled.
I write this on the tenth day of the #SudanRevolts tide that has started to sweep Sudan.
Sudan is a land of revolutionaries. They started in the 20th century with the Mahdi revolution against the British occupation and the ruling Egyptian government and today Sudan is revolting against militarization, human rights atrocities, poverty, corruption and fundamentalism.
The run-off for presidency elections in Egypt are this weekend – the first after the ongoing Egyptian revolution. The two candidates were the least expected to be at this stage: Mohamed Morsi, who represents the “political arm” of a group, the Muslim Brotherhood, that sees “Islam is the Solution,” and the other is Ahmed Shafik, who belongs to the Military that has been running Egypt for the last (60) years and still. Every one who is following the progress of events and incidents in Egypt is curious and everyone inside Egypt is worried, even if their decision is to choose one over the other or to boycott the run-off.
In many regards, Safiya Ishaq is an unremarkable 25-year-old. She is excellent at braiding hair but terrible at being on time. She studied fine arts at Khartoum University in Sudan. Not unusual for a student, Ishaq became involved with politics. She joined Girifna, a pro-democracy movement formed in 2009 on the eve of Sudan’s first multiparty elections in more than two decades aimed at mobilizing citizens to vote. Conducting mass voter registration drives, it quickly evolved into a socio-political movement demanding change in Sudan.
Land relations are critical for women's right in Ghana. This is because of the centrality of land as a resource for the livelihoods of the majority of our population, food, water, fuel and medical plants.
Those who control lands and its resources also gain social and political power and authority. As such, women's unequal land rights affect their access to other resources and their economic, social and political status in society.
Now that Algeria has the largest proportion of women lawmakers in the Arab world, workmen at the national assembly building have some urgent modifications to make.
While the men's washroom just outside the debating chamber is clearly marked with the silhouette of a man, there are so far no signs for the women's. On the opening session of the new parliament on May 26, two of the newly elected female members had to ask for directions to the rest-room.
BAMAKO - Strict Sharia, or Islamic religious laws, imposed by the Islamist rebels controlling vast swathes of northern Mali are driving thousands of students out of schools. Dress codes have been imposed, boys and girls are forced to learn separately, and subjects deemed to promote “infidelity” have been struck off the curriculum.
Outraged parents are transferring their children and some students are opting to miss examinations rather than learn under these conditions.
Plan is deeply concerned at new proposals by the Egyptian parliament to reduce the legal age for girls to marry to 14 – just 4 years after a successful campaign increased the age limit to 18.
Early marriage can have a devastating impact on girls’ lives – they are more likely to be forced out of school, live in poverty, have early pregnancies and endure health complications or die during childbirth.
Violence against women demonstrators in Egypt erupted again on Tuesday when a frenzied mob of 200 men sexually assaulted a female protester in Tahrir Square. Then, during a rally on Friday to protest the incident, about 50 women and their male allies were themselves brutalized and chased away by another mob.
I’ve been working to defend children’s rights since way back. Growing up in rural Uganda I was always aware that many of my friends were denied the chance to fulfil their potential.
Eventually you find that very few friends you started school with complete it with you, and when you look back and think why, you realise it is often because their rights weren’t fulfilled – or protected.
Women in remote parts of Morocco are benefiting from a literacy scheme that also teaches civil rights, numeracy and beekeeping.
In a tiny classroom at the Maison de Citoyenneté support centre for the education of rural girls and women in Beni Zuli, an isolated village in Zagora, deep in south-eastern Morocco's Draa Valley, Fatima Kadmire is describing how learning to read and write is transforming her life.
Egypt’s liberal Free Egyptians Party (FEP) declared its support for the calls by women’s rights organizations and NGOs , which called for anti-harassment laws, an Egyptian online news website reported on Monday.
The party said it stands against “the phenomenon of sexual harassment” and called for the passing of a law criminalizing the act, Egypt’s Bikyamasr news website reported.
In Sudan’s conservative society where many believe a woman’s reputation and honor doesn’t belong to her alone, young female activists who are increasingly choosing to be on the frontline in the fight for democracy and human rights. But not without a cost! They have faced more direct physical and sexual assault to deter them from standing up for their rights. “The rape of Safia Ishaq made our female members scared and reluctant to work, they are strong, but this crossed a red line,” said Sarah Faisal, who is affiliated with the youth movement, Girifna that is an Arabic word for “We are Fed Up”. She was referring to the rape ordeal of one the movement’s members last year. Girifna aims at using civil resistance to overthrow the current Sudanese government.
“Al-Azhar, the country’s highest religious institution, intends to prepare a new document to safeguard women’s rights, as enshrined in the Islamic Sharia,” said Ahmed el-Tayyeb, the Grand Sheikh of Al-Azhar.
CAIRO: A number of Egyptian human rights groups have submitted a communication to the Attorney General Abdel Meguid Mahmoud against the Muslim Brotherhood`s political arm, the Freedom and Justice Party (FJP) to investigate the complaints of people in the village of Abu Aziz in the Minya governorate, south of Cairo, over the existence of a large medical convoy organized by the party that wanders streets and does medical examination on people, including female circumcision, or female genital mutilation, in violation of Egyptian law, conventions and treaties signed by Egypt.
Women protesters and rights groups have accused Egyptian troops and prison authorities of sexual assault during the latest crackdown on demonstrations, reviving allegations they are using abuse to intimidate female detainees and protesters.
The charges made on Wednesday added new tension to Egypt's presidential election campaign, just two weeks before the voting.
With a progressive Code of Personal Status, Tunisia is commonly regarded as the Arab world’s most advanced country in terms of women’s rights. Yet sexual harassment exists in Tunisia, too. Unlike in Egypt, sexual harassment has not entered the arena of public discourse in Tunisia, and is often dismissed as a non-issue.
The two women met for the first time last week at a sleek Georgetown hotel, where they were speakers at a glittering charity dinner. They shook hands and hugged across a vast gulf of culture, geography and faith: one a devout Muslim from West Africa with her hair carefully hidden under a tight scarf, the other a gregarious South Asian in a stylish sari and costume earrings.
In many countries of the Middle East, women are wondering what the Arab Spring means for them. Some observers are concerned that the power vacuum will leave the door open for Islamist groups to take power and force changes opposing women’s rights.
Zainah Anwar, a leading Malaysian social activist and intellectual, is not one of them. She is even excited about the prospects that the Arab Spring could have for women.
In conversation with Jessica Horn, a leading Malian women's rights activist identifies the roots of the crisis in Mali, and the opportunistic use of the crisis by Malian and international Islamic fundamentalists to gain a popular foothold in the north of the country.
Join VNC for two events on 21 April 2012, at the AWID Forum in Istanbul, Turkey. We'll be hosting a talk show on "The Nexus between Culture, Gender and Other Identities: Resisting Discrimination and Reclaiming Space", as well as a workshop on "Visioning Cultures Free from Violence: Transnational Advocacy and Communications using Visual Arts and Digital Media". Full details below.
A new online lesbian, gay, bisexual and transgender magazine in Sudan, north Africa, is a first for the country where homosexuality is still punished by death and an opportunity for gay people to start discussing their lives and hopes for the future.
Rainbow Sudan published articles discussing topics including being gay in Sudan, the history of homosexuality in the country, Islam and sexuality, being lesbian and Muslim, poetry and more.
RABAT (Reuters) - Morocco on Thursday said it would amend a law allowing rapists to marry their underage female victims after the suicide of a teenage girl raised doubts about the effectiveness of reforms to women's rights in the country.
Sixteen-year-old Amina El-Filali killed herself last week near the northern city of Larache by swallowing rat poison after a six-month forced marriage to the man who raped her.
Local human rights activists say the law violates women's rights and was created to avoid damage to the reputation of the victim's family.
RABAT, Morocco -- The case of a 16-year-old girl who killed herself after she was forced to marry her rapist has spurred outrage among Morocco's internet activists and calls for changes to the country's laws.
An online petition, a Facebook page and countless tweets expressed horror over the suicide of Amina Filali, who swallowed rat poison on Saturday to protest her marriage to the man who raped her a year earlier.
The 8th of March of every year is a day set aside by the United Nations as International Women’s Day (IWD). It is a day to recognise, celebrate and honour women’s struggles and achievements in the past years and to call attention to other areas of concerns that are critical to women’s life in particular and the society in general.
While the Iranian government authorities attempted to appropriate the Arab spring, claiming it was a continuation of the Iranian revolution of 1979, the events revived popular longing for democratic change in Iran. Ziba Mir-Hosseini tells Deniz Kandiyoti that no movement for change in Iran can afford to ignore women’s aspiration for equality – a lesson that some of the successful elements in the Arab spring may yet have to learn.
The Association for Women's Rights in Development (AWID) is gravely concerned about the reintroduction of the Anti-Homosexuality Bill in Uganda's Parliament on February 7th, 2012. At the bill's reintroduction, the Speaker informed the House that the bill will not need to be considered again by the "Legal and Parliamentary Affairs Committee", thereby making the process faster and raising the possibility of it becoming law.
The Voice of Libyan Women unfortunately reports that regardless of the numerous petitions, demonstrations and alternative drafts suggested by Libyan civil society the Electoral Law passed by the National Transitional Council of Libya on Wednesday, February 8th 2012 does not in any way guarantee any seats for women at all. Nor does it guarantee a minimum of 40 parliamentary seats for women, despite several statements.
LILONGWE - A campaign to stop people buying merchandise from street vendors is gaining momentum in Malawi’s main cities of Lilongwe, Blantyre and Mzuzu after the small-scale traders went on a rampage undressing women and girls wearing trousers, leggings, shorts and mini-skirts.
A group of men gathered around Amira El Bakry in Tahrir Square as she brandished a newspaper photo that shocked many Egyptians. It showed troops dragging a female protester along the street, her robe ripped open to reveal a blue bra and bare midriff.
DAKAR - Human rights campaigners who have been struggling for years to eliminate female genital mutilation (FGM) in West Africa got a boost this week as news emerged that a group of Muslim clerics and scholars in Mauritania had declared a fatwa, or religious decree, against the practice.
CAIRO — At first Samira Ibrahim was afraid to tell her father that Egyptian soldiers had detained her in Tahrir Square in Cairo, stripped off her clothes, and watched as she was forcibly subjected to a “virginity test.”
The Libyan Human Rights Alliance, along with numerous civil society activists and organizations, find the Libyan Draft Election Law released On January 1 2012 by The National Transitional Council to be unreasonable. Within this Draft Law, Article 1 stated that there would in fact be a parliamentary quota for women; however it is quite vague and reads as the quota will be limited to 10%, or 20 out of 200 seats.
26 December 2011 - This year, millions of women have taken to the streets in the Arab world to demand change.
“This year has been eventful in terms of democratisation, the recognition of freedom of expression and people’s empowerment,” said UN Human Rights chief Navi Pillay. “The courage and determination of women involved in the Arab spring should be a source of inspiration for all of us.”
WHEN Secretary of State Hillary Rodham Clinton announced this month that the United States would use diplomacy to encourage respect for gay rights around the world, my heart leapt. I knew her words — “gay people are born into, and belong to, every society in the world”— to be true, but in my country they are too often ignored.
Thousands of women massed in Tahrir Square here on Tuesday afternoon and marched to a journalists’ syndicate and back in a demonstration that grew by the minute into an extraordinary expression of anger at the treatment of women by the military police as they protested against continued military rule.
The United Nations’ Special Rapporteur on Violence Against Women Rashida Manjoo spoke to reporters in Nairobi Friday about her just-concluded mission to Somalia, where she examined the occurrence of gender-based violence there.
It was Pakpema Bleg’s own family who first accused her of practicing witchcraft.
Her nephew had accidentally pricked his finger on a needle, and the finger swelled up with infection. Bleg hadn’t been there. But the next morning, she says, her brother-in-law arrived outside her house. “Witch!” he allegedly bellowed for all her neighbors to hear. “Witch!” Then, her nephew’s older brother began beating her, she says, and soon others in the village joined in.
Women's groups in the Somali town of Galkayo are lobbying the authorities in the self-declared autonomous region of Puntland to enact a law banning female genital mutilation/cutting (FGM/C), saying the practice was becoming widespread. Activists say FGM/C causes serious health problems to the women and is against their religion.
Geneva, Switzerland – On Monday, October 31, 2011, in collaboration with an alliance of Moroccan civil society organizations from diverse regions across the country1, Global Rights, and The Advocates for Human Rights will issue a joint statement to the 47th Session of the United Nations Committee Against Torture (CAT).
A moderate Islamist party claimed victory Monday in Tunisia's landmark elections as preliminary results indicated it had won the biggest share of votes, assuring it will have a strong say in the future constitution of the country whose popular revolution led to the Arab Spring.
WLUML is deeply concerned that the first public act of the Libya's National Transition Committee has been to proclaim on October 23rd, 2011, that henceforth, a number of laws will be considered annulled and that 'sharia law' is to replace them. Libya’s National Transition Committee is an interim government – what it has responsibility for – and what its first action should have concerned, is to put into place a mechanism for elections for the new government after the fall of the Gaddafi regime.
On the eve of the elections in Tunisia that will shape the future of the country and even that of the Arab world as well, Western do-gooders and Islamic fundamentalists hand in hand rejoice in ‘Tunisia’s first free elections’ and its access to ‘ democracy’. The recent history of Iran and Algeria have taught us better… And women in Tunisia watch in horror the rise of Muslim fundamentalists, as a possible replication of the Algerian scenario of 1989 .
On the eve of the elections in Tunisia that will shape the future of the country and even that of the Arab world as well, Western do-gooders and Islamic fundamentalists hand in hand rejoice in ‘Tunisia’s first free elections’ and its access to ‘ democracy’. The recent history of Iran and Algeria have taught us better… And women in Tunisia watch in horror the rise of Muslim fundamentalists, as a possible replication of the Algerian scenario of 1989 .
SARE HAROUNA, Senegal — When Aissatou Kande was a little girl, her family followed a tradition considered essential to her suitability to marry. Her clitoris was sliced off with nothing to dull the pain.
LAI, Chad, 7 September 2011 – A brave mother, Hadjara Oumarou, sat under a tree with her estranged husband, Oumar Sidik, outside their local village courthouse here in Chad’s Tandjilé District. Their 10-year-old daughter Amira (not her real name) sat between them.
They were at the courthouse because Mr. Sidik had sold Amira for the equivalent of $120. When the man who ‘bought’ her visited Ms. Oumarou to demand his bride, she refused to give her up, insisting that she attend school before she marries.
In the same district, a shocking number of young girls have been raped.
(Cairo, 14 September 2011) In its continuing effort to enhance women's role in the Egyptian political sphere and follow the mechanisms and means that guarantee equality in women's representation, ECWR is going to monitor the 2011 Parliamentary and Shoura Elections from a gender perspective. For this purpose, ECWR is preparing its Operation Room that will be in charge of the monitoring and will undertake the following missions:
Two clerics yesterday dismissed doctors and religious leaders opposed to safe abortion as enemies of women rights. The christian and muslim clerics said the abortion debate in Kenya was demeaning to women. “In this society we are all at the mercy of men,” said Rev Timothy Njoya.
CAIRO, September 13, 2011‑Egyptian women currently face numerous threats that will not only destroy the goals of equality, freedom and change voiced in the January revolution, but the advances women have made over the last century.
Because Mrs. Mubarak was extremely active in women’s issues, including the advancement of women’s rights, many Egyptians, especially men, equate women’s rights with the former corrupt dictatorship of Hosni Mubara.
Last December, Tunisians rose up against their dictator, triggering a political earthquake that has sent shockwaves through most of the Middle East and north Africa. Now, Tunisia is leading the way once again – this time on the vexed issue of gender equality.
Kenya has become the latest African country to ban female genital mutilation, with the passing of a law making it illegal to practice or procure it or take somebody abroad for cutting. The law even prohibits derogatory remarks about women who have not undergone FGM. Offenders may be jailed or fined or both.
Members of the Kenyan Women Parliamentary Association said it was a historic day. Linah Kilimo, its chairperson, said the move would improve school attendance. And Sophia Abdi Noor said:
(Beirut) September 6, 2011 ─ Tunisia’s lifting of key reservations to the Convention on the Elimination of All Forms of Discrimination against Women (CEDAW) is an important step toward gender equality, Human Rights Watch said today. The Tunisian government should next ensure that all domestic laws conform to international standards and eliminate all forms of discrimination against women, Human Rights Watch said.
It’s over four months now since the last general elections, but Nigerian women politicians and even stakeholders are yet to recuperate from the shock of its outcome. Unlike previous elections, women vied enmass for various political offices, but few of them got in! As a response to this fall which has also translated into an abysmal reduction in the representation of women in political offices(apart from the ministerial offices), the question of ‘what went wrong?’ has continued to take centre-stage at most women gatherings.
PARIS (TrustLaw) - What links a British-based law firm to an initiative aimed at protecting women in Burkina Faso from accusations of witchcraft?
The answer's global pro bono work.
Earlier this year, a charity caring for older people, HelpAge International, asked Advocates for International Development (A4ID) to help with its work in, among others, Burkina Faso where it's been trying to raise awareness about the plight of women who've fallen victim to witchcraft allegations.
Last year, during the holy month of Ramadan, I was in Tripoli researching the status of women in Libya's society, along with Journalist and Author Natalie Moore. We interviewed women across the spectrum: artists, housewives, teachers, government officials, university students and businesswomen. The stories were later aired on Chicago Public Radio.
DAKAR, 27 July 2011 (IRIN) - Health workers say an apparent rise in contraceptive use in Nigeria stems largely from a willingness by traditional and religious leaders in some regions to use their influence in promoting reproductive health.
In the predominantly Muslim north, where contraceptive use has historically been far lower than the national average, the support of traditional leaders has helped change attitudes in communities where contraception was long regarded as taboo.
The United Nations official leading the fight against sexual violence in times of conflict today voiced concern over reports that women and girls fleeing famine in Somalia were being raped or abducted and forced into marriage by bandits and other armed groups as they tried to reach refugee camps in Kenya.
Imagine living in a community your whole life. Then suddenly, you are accused of witchcraft and told to leave. Or you are sent threatening letters saying you have bewitched a neighbour's child. Or you are attacked and slashed with a machete during the night.
CAIRO, Egypt (WOMENSENEWS)--Despite the stigma attached to divorce, ending a marriage is still relatively easy for Muslim women in Egypt. All they have to do is file paperwork with a family court and the deed is done, as long as they're not seeking alimony or damages from their husbands.
For the country's millions of Orthodox Christians, or Copts, it's been nearly impossible since Pope Shenouda III, the head of one of the most conservative churches in Christianity, forbade divorce except in the case of conversion or adultery three years ago.
Dozens of people participated Saturday in a sit-in in the center of Tunis to warn against "fundamentalism, extremism and violence", AFP noted.
Gathered on the steps of the City Theatre, the participants came following calls on social networks, waving placards saying "no to violence, yes to tolerance," "against any religious extremism", "No to Algeria of the 90s."
The event turned into impromptu happening, dozens of passers-by sit down to discuss the place of Islam in society, freedom of expression or the defense of the Revolution’s gains.
CAIRO, May 30, 2009 (IPS) - As night falls over Egypt’s capital, youth gather along the banks of the Nile where a carnivalesque atmosphere prevails.
Tamer and Mido have taken up positions on the railing next to the river. As a group of veiled teenage girls approaches, the duo works in tandem. Tamer removes the girls’ headscarves with his eyes, while sexually nuanced words roll off Mido’s tongue.
Rape continues to be the most frequently reported serious crime in Liberia. A new multipronged approach is underway to reduce sexual and gender-based violence.
MONROVIA, Liberia (WOMENSENEWS)-- Korlu, a young mother of two, lives on the outskirts of Monrovia, the capital here. A high school dropout, Korlu, who declined to give her last name for safety reasons, says when she was a teen, she became pregnant. "My parents put me out of their house because they couldn't bear the shame of me getting pregnant," she says.
It's not always easy being a female investigative journalist, even in the west. But imagine going to do an interview and not being able to shake hands with the interviewee or indeed even being able to sit in front of him to ask questions.
In Somali culture – I grew up in a Somali family in Kenya – it is wrong to speak and raise an opinion in front of men or even to shake hands with a man of no relation to you. Even travelling for work unaccompanied by a relative is not permitted.
The head of Egypt’s military intelligence has promised Amnesty International that the army will no longer carry out forced ‘virginity tests’ after defending their use, during a meeting with the organisation in Cairo on Sunday.
Major General Abdel Fattah al-Sisi, of the Supreme Council of the Armed Forces (SCAF), discussed the issue with Amnesty International’s Secretary General Salil Shetty months after the organisation publicized allegations of the forced ‘tests’.
Violence against women still is universal, and while it has many roots, especially in cultural tradition and customs, it is gender inequality that lies at the cross-cultural heart of violent practices. Violence against women is deeply embedded in human history and its universal perpetration through social and cultural norms serves the main purpose of reinforcing male-dominated power structures.
UBA (AlertNet) - It took years of pleading before Jane Aketch persuaded her parents to send her to primary school in the dusty bush of South Sudan's Eastern Equatoria state.
Although her parents wanted her to learn how to read and write, like most of the communities in Aketch's home county of Magwi, they did not place particular importance in furthering a girl's education.
KIGALI, 2 June 2011 (IRIN) - A new report has rekindled debate on whether the Rwandan government "betrayed" women who were raped during the 1994 genocide by letting community-based gacaca courts process their cases.
(Cairo, May 10, 2011) A large number of Egyptian women participated in a march entitled "No to sectarian strife" which appeared with its ugly face in the district of Imbaba. They participated in this march to stress the values of citizenship and tolerance and to prevent the strife that has been witnessed in the district and in many different places in Egypt after the revolution.
Some cultural practices are progressive. Others are harmful to women and girls and they perpetuate abuse. These practices relegate women to inferior positions with respect to property, inheritance, marriage and decision making. In most cases, culture is used as an excuse to continue various forms of abuse that promote sexual, physical and psychological harm.
Article XIX Statement: From Morocco to Bahrain, everyday people have taken on the cast iron hold of dictatorships and absolute monarchies resulting in an extraordinary collective awakening that has paved the way for epochal change in the region. The youth movement, which lies at the core of the uprisings, continues to play a prominent role in the pro-democracy and pro-reform demonstrations, which have swept through the region, unabated by government clampdowns or concessions.
In northern Uganda, daughters with limited understanding of HIV/AIDS are married off at young ages into polygamous households still struggling with the legacy of a brutal 16-year civil war. The practice is a recipe for rapid disease transmission.
GULU, Uganda (WOMENSENEWS)--After getting married at 18, Alice Ongom, who is now 45, settled down in Gulu, a northern Ugandan city that was a battleground during the country's intermittent civil war from 1986 to 2003.
Even as the Arab spring unfolds across the region, I learned with profound astonishment that Mr. Jack Persekian, director of the Sharjah Art Foundation, has been dismissed as “punishment” for allowing an artist invited to the Sharjah Biennial total freedom of expression. I am the artist in question. My installation “Maportaliche/Ecritures sauvages” [It has no importance/Wild Writings] has been censored and removed from the Biennial.
In South Asia and sub-Saharan Africa 38% of women marry before they are 18 years old. Child marriages, as defined by UNICEF, the United Nations’ children’s agency, are those undertaken by women under the age of 18 and include unions where a woman and a man live together as if they were married.
"I, a girl, am going down to Tahrir Square and I will stand alone." With these words, Asmaa Mahfouz put out a call on YouTube that went viral, helping to ignite Egypt's revolution. A 26-year-old business management graduate, Mahfouz helped rally Egyptians for the initial Jan. 25 protest, to "say no to corruption, no to this regime." But Mahfouz's activism had its roots in another protest led by another woman.
NEW YORK — Accusations of witchcraft in Africa have gained increasing attention because of the severe impact they can have on the lives of those accused, including imprisonment, deprivation of property, banishment from villages and in some cases physical violence.
The human-rights law program I direct recently partnered with an N.G.O. in Malawi to run a mobile legal-aid clinic focusing on witchcraft cases in two rural communities.
February 6 was unanimously adopted at the International Conference on Zero Tolerance to FGM organized by IAC from February 4 to 6, 2003 in Addis Ababa, Ethiopia. Representatives at the Conference came from 49 countries including 4 First Ladies (from Nigeria , Burkina Faso , Guinea Conakry and Mali ), Ministers, and Parliamentarians. Others included Religious, Community and Youth leaders.
The Violence is Not out Culture campaign condemns the brutal murder on 26 January 2011 of LGBT human rights defender, David Kato, of Uganda and extends its condolences to his colleagues at Sexual Minorities Uganda (SMUG). David was a long term activist for rights based on sexual orientation and gender identity in Uganda, and was a highly respected and admired human rights defender within his community and worldwide.
A growing movement of African Christians are making waves at home and abroad with their ultra conservative interpretations of scripture. Far from a naïve embrace of conventional norms or a faithful embrace of scripture, these interpretations are emerging as clear political choices and are undermining women's rights struggles across the African continent.
(Yaoundé, November 4, 2010) – Cameroonians are attacked by police, politicians, the media, and even their own communities if they are suspected of having sexual relations with a person of the same sex, four human rights organizations said in a joint report released today.
MANSA, 20 December 2010 (IRIN) - The minimum legal age for marriage in Zambia is 18, and parental consent is required if a girl or boy is 16-17. Anyone under 16 is a minor, and defilement of a minor is a serious offence, punishable by imprisonment of up to 25 years. Patricia was 12 when she married John, four years her senior.
(Nairobi) December 15, 2010 -- The arrest of more than 60 Sudanese women's rights activists on December 14, 2010, for peacefully protesting the lashing of a woman by police shows the urgent need to reform Sudan's public order laws and practices, Human Rights Watch said today. The system imposes illegitimate restrictions on a range of personal behavior and public expression and disproportionately targets women, Human Rights Watch said.
LUSAKA (10 December 2010) – In conclusion of her official visit to Zambia the Special Rapporteur of the United Nations Human Rights Council on violence against women, its causes and consequences, Ms. Rashida Manjoo, delivered the following preliminary findings:
More than 1,000 women accused of witchcraft in northern Ghana live in refuges, where they have to pay for protection from the chief who runs them. Yaba Badoe visits a camp in Gambaga and follows two women as they return to their villages. Watch the video.
The most recent report of the Special Rapporteur on violence against women, its causes and consequences on her mission to Ghana, highlights the practice of offering daughters as 'trokosi' to a traditional fetish shrine to ward off the punishment of the gods for crimes or moral wrongdoings committed by a family member.
Francine Nijimbere relies entirely on her mother for basic things like bathing and eating. Her husband cut off her arms up to the elbows in 2004, for failing to give birth to a boy. She was pregnant at the time and lost the baby due to her injuries, which included cuts on her stomach. The man - a soldier - was arrested and later sentenced to life in prison but was recently released following a presidential pardon.
Sanaa Awadkareem was forced into marriage and then disfigured with acid by her estranged husband.
The tragedy of Sanaa Awadalkareem, a victim of a unique case of domestic violence of the worst kind, became a case of public interest when it was highlighted in local and international news articles, first published in Alrayaam newspaper (Sudan) and consequently on Sudanesonline (an electronic news outlet, concerned with issues pertaining to the Sudan; www.sudaneseonline.com).
Shame, violence, abuse, shame - the circle is complete for women of the East as they face a recurring nightmare of the denial of rights and justice.In most cases of violence against women, the role of society and how it perceives these unfortunate women is a crucial factor in the kind of justice they ultimately receive. |
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abstract: 'In this note, we compute the cobordism map on periodic Floer homology induced by elementary Lefschetz fibration.'
author:
- '[Guanheng Chen]{}'
title: An example of cobordism map on PFH
---
Introduction and Main result
============================
Let $\pi: Y \to S^1$ be a surface fibration over a circle and $\omega$ be a closed, fiberwise nondegenerate $2$-form over $Y$. Assume that the fiber of $\pi$ is a connected oriented surface possibly with boundary. The $2$-form $\omega$ gives a splitting of $TY=TY^{vert}\oplus TY^{hor}$, where $TY^{vert}= ker \pi_*$ and $TY^{hor}$ is the orthogonal complement of $TY^{vert}$ with respect to $\omega$. The horizontal lift of the vector field of $\partial_t$ is called Reeb vector field $R$, where $\partial_t$ is coordinate vector field of $S^1$. The periodic orbit of $(Y, \pi, \omega)$ is the closed integral curve of $R$. Fix a homology class $\Gamma \in H_1(Y, \mathbb{Z})$, we can define the periodic Floer homology (abbreviated as PFH) $PFH_*(Y, \omega, \Gamma)$ [@H1]. The definition will be reviewed latter.
Given a Lefschetz firbation $\pi_X: X \to B$ together with a closed, fiberwise nondegenerate $2$-form $\omega_X$ such that $\partial X=Y$ and $\omega_X \vert_Y =\omega$, it is expected that there is a cobordism map $PFH(X, \omega_X): PFH(Y, \omega, \Gamma) \to \Lambda$, where $ \Lambda$ is local coefficient. There are some technical problems to define this map directly using holomorphic curve method. (Cf. section 5.5 of [@H3]) But at least the map can be defined via the isomorphism between PFH and Seiberg Witten cohomology [@LT].
In this note, we define and compute the cobordism map on periodic Floer homology induced by elementary Lefschetz fibration, that is the Lefschetz firbation over a disk with only one singular point. The motivation is as follows. Under certain technical assumptions, [@GHC] defines the cobordism maps on PFH induced by Lefschetz fibration using holomorphic curve method. Except the case that $B$ is a disk, we can always perform a $C^0$ perturbation on $\omega_X$ such that the technical assumptions hold. Therefore, if we want to extend the results in [@GHC] to general case, it is natural to consider the simplest case that $X$ is an elementary Lefschetz fibration. This special case is expected to be a building block in defining cobordism maps on PFH.
Let us clarify the notation we will be using. We always use $\pi_X: X \to D$ to denote the Lefschetz fibration over a disk with only one singular point at origin and the boundary of $X$ is denoted by $Y$. Throughout this note, we assume that the fiber $F$ of $X$ is a closed surface with genus $g(F) \ge 2$ and the vanishing cycle is non-separated, unless otherwise stated. The main result of this note is as follows.
\[thm3\] Fix a degree $Q \ne g(F)-1$, then for a choice of admissible $2$-form $\omega_X$ such that $\int_F \omega_X>Q$ and a generic $\Omega_X$-tame almost complex structure $J$ which is sufficiently close to $ \mathcal{J}_h(X, \omega_X)$, then the cobordism map $PFH(X, \omega_X): PFH_*(Y, \omega, Q) \to \mathbb{Z}$ is well defined. Moreover,
- If $Q > g(F)-1$, then in chain level $$PFC(X, \omega_X)((\Pi_a e_a^{m_a}) e_0^{m_0} e_1^{m_1})=1$$ and $PFC(X, \omega_X)$ maps others else ECH generators to zero. Here $\{a\} $ are refer to critical points of a Morse function $f$ with $\nabla^2 f(a) >0$, $e_a$ is the periodic orbit corresponding to $\{a\}$, and $\{e_i\}_{i=0, 1}$ are the only two degree $1$ periodic orbits of Dehn twist. For the precise definition, please refer to section 4.2.
- If $g(F)-1>2Q$, then $$PFH(X, \omega_X)( e^Q)=1$$ and maps others generators of $PFH(Y, \omega, Q)$ to zero. In this case, $e_0$ and $e_1$ are homologous and $e$ is their homology class.
Since the cobordism map is invariant under blow-up (Cf. Lemma 5.2 of [@GHC]), we have the following corollary.
Let $\{x_i\}_{i=1}^k \subset X$ be finite set of points such that $\pi_X(x_i) \ne \pi_X(x_j)$ for $i \ne j$ and $\pi_X(x_i) \ne 0$ for all $i$. Let $(\pi_X' : X' \to D, \omega_{X'})$ be the blow-up of $X$ at $\{x_i\}_{i=1}^k$. For any $\Gamma_X \in H_2(X, \partial{X}, \mathbb{Z})$, regarded as a homology class in $X'$, then $PFH(X', \omega_{X'}, \Gamma_X) $ satisfies the same conclusion in Theorem \[thm3\].
We have organized the rest of this article in the following way: In section $2$, we review PFH and the definition which will be using. In section $3$, we review the construction of $\pi_X: X \to D$ and compute its singular homology. In section $4$, we describe the periodic orbits on $Y$. In section $5$, a combinatorial formula for ECH index will be deduced. Finally, in section $6$, we show that the cobordism map is well defined and compute it.
Review of ECH index and PFH
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In this section, we have a quick review of the ECH index and periodic Floer homology.
Basic definition
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Let $\pi_W: W \to B$ be a surface fibration over a circle or a Lefschetz fibration. A $2$-form $\omega_W \in \Omega^2(W)$ is called admissible if $d\omega_W=0$ and $\omega_W$ is fiberwise nondegenerate.
Let $(Y, \pi, \omega)$ be a surface fibration over a circle together with an admissible $2$-form, the Reeb vector field $R$ is a section of $TY^{hor}$ such that $\pi_*(R)=\partial_t$. A periodic orbit is a smooth map $\gamma: \mathbb{R}_{\tau} / q \mathbb{Z} \to Y $ satisfying the ODE $\partial_{\tau} \gamma =R \circ \gamma$ for some $q>0$. The number $q$ is called period or degree of $\gamma$. An orbit set $\alpha=\sum_i m_i \alpha_i$ is a finite formal sum of periodic orbits, where $\alpha_i's$ are distinct, nondegenerate, irreducible embedded periodic orbits and $m_i$ are positive integer. An orbit set $\alpha$ is called ECH generator if $m_i=1$ whenever $\alpha_i$ is hyperbolic orbit. Usually we write an orbit set using multiplicative notation $\alpha=\Pi_i \alpha_i^{m_i}$ instead of summation notation. The following definition is useful when we define the cobordism map on PFH.
(Cf. [@H5]) Let $Q>0$ and $\gamma$ be an embedded elliptic orbit with degree $q \le Q$.
- $\gamma$ is called $Q$-positive elliptic if the rotation number $\theta \in (0, \frac{q}{Q}) \mod 1$.
- $\gamma$ is called $Q$-negative elliptic if the rotation number $\theta \in ( -\frac{q}{Q},0) \mod 1$.
Let $(W , \pi_W, \omega_W)$ be a fibered cobordism from $(Y, \pi, \omega)$ to $(Y', \pi', \omega')$, where $(W, \pi_W)$ is a Lefschetz firbation with boundary $\pi_W^{-1}(\partial B)= Y \cup(-Y')$, and $\omega_W $ is an admissible $2$-form which agrees with $\omega$ and $\omega'$ on $Y$ and $Y'$ respectively. The symplectic form on $W$ is defined by $\Omega_W=\omega_W+\pi_W^*\omega_B$, where $\omega_B$ is a large volume form of $B$. We can define the symplectic completion $(\overline{W}, \omega_W)$ by adding cylindrical ends. (See section 2.3 of [@GHC]).
Given orbit sets $\alpha=\Pi_i \alpha_i^{m_i}$ and $\beta=\Pi_j \beta_j^{n_j}$ on $Y$ and $Y'$ respectively, we can define the space of relative homology classes $H_2(W, \alpha ,\beta)$. The typical element is a $2$-chain $Z$ in $W $ such that $\partial Z = \sum_i m_i \alpha_i- \sum_j n_j \beta_j$, modulo the boundary of $3$-chain. $H_2(W, \alpha ,\beta)$ is an affine space over $H_2(W, \mathbb{Z})$. Given $Z \in H_2(W, \alpha ,\beta)$ and fix a trivialization of $\tau$ of $\ker \pi_*$ and $\ker \pi_*'$ over $\alpha $ and $\beta$ respectively, the ECH index is defined by $$I(\alpha, \beta, Z) = c_{\tau}(Z) + Q_{\tau}(Z) + \sum_i \sum\limits_{p=1}^{m_i} CZ_{\tau}(\alpha_i^{p})- \sum_j \sum\limits_{q=1}^{n_j} CZ_{\tau}(\beta_j^{q}),$$ where $c_{\tau}(Z)$ and $Q_{\tau}(Z)$ are respectively the relative Chern number and the relative self-intersection number(Cf. [@H4] and [@H2]), and $CZ_{\tau}$ is Conley-Zehender index. ECH index $I$ only depend on orbit sets $\alpha$, $\beta$ and relative homology class of $Z$.
An almost complex structure $J$ on $\overline{W}$ is called $\Omega_W$-tame if $J$ satisfies the following properties:
1. On the cylindrical ends, $J$ is $\mathbb{R}$-invariant, $J(\partial_s)=R$ and $J $ sends $\ker \pi_*$ to itself along periodic orbit with degree less than $Q$, where $R$ is the Reeb vector field.
2. $J$ is $\Omega_W$-tame.
3. Identify a neighborhood of critical point of $\pi_W$ with the local model, then $J$ agrees with the standard complex structure $J_0$ of $\mathbb{C}^2$.
The space of $\Omega_W$-tame almost complex structures is denoted by $\mathcal{J}_{tame}(W, \omega_W)$. The admissible $2$-form $\omega_W$ gives a decomposition $TW = TW^{hor} \oplus TW^{vert}$ of tangent bundle of $W$, where $TW^{vert}= \ker \pi_{W*}$ and $TW_{w}^{hor}=\{ a \in TW_w \vert \omega_W(a, b)=0 \mbox{ } \forall b \in TW_w^{vert} \}$. Fix a complex structure $j_B$ over base surface $B$, we define a subspace as follows.
$\mathcal{J}_h(W, \omega_W) \subset \mathcal{J}_{tame}(W, \omega_W)$ is the subspace of $\Omega_W$-tame almost complex structures on $\overline{W}$ with the following properties:
1. $J(T\overline{W}^{hor}) \subset T\overline{W}^{hor}$ and $J(T\overline{W}^{vert}) \subset T\overline{W}^{vert}$.
2. Aways from critical points of $\pi_W$, $J \vert_{\ker d\pi_{W}}$ is compatible with $\omega_W$.
3. $(\pi_W)_*$ is complex linear with respect to $J$ and $j_B$.
Let $(\overline{W} , \pi_W, \omega_W)$ be the symplectic completion of $(W , \pi_W, \omega_W)$. Fix a $\Omega_W$-tame almost complex structure $J$, the holomorphic current $\mathcal{C}= \sum d_a C_a$ from $\alpha$ to $\beta$ is a finite formal sum of simple holomorphic curves, in addition, $\mathcal{C}$ is asymptotic to $\alpha$ and $\beta$ respectively in current sense, where $\{C_a\}$ are distinct, irreducible, somewhere injective $J$ holomorphic curves with finite energy $\int_{C_a} \omega_W < \infty$ and $\{d_a\}$ are positive integers. A holomorphic current $\mathcal{C}$ is called embedded if $d_a=1$ for any $a$ and $\{C_a\}$ are pairwise disjoint embedded holomorphic curves. The number $E(\mathcal{C})=\int_{\mathcal{C}} \omega_W =\sum_a d_a \int_{C_a} \omega_W$ is called $\omega_W$-energy. Let $\mathcal{M}_i^J(\alpha, \beta, Z)$ be the space of holomorphic currents from $\alpha$ to $\beta$ with ECH index $I=i$ and relative homology class $Z$.
\[Cf. [@PS], [@PS1]\] A Lefschetz fibration $(\pi_W: W \to B, \omega_W) $ is called nonnegative if at any point $w $ away from the critical point of $\pi_W$, then $\omega_W \vert_{T W_w^{hor}} = \rho(w) (\pi_W^* \omega_B) \vert_{TW_w^{hor}} $ , where $\omega_B \in \Omega^2(B)$ is a positive volume form $\omega_B \in \Omega^2(B)$ and $\rho$ is a nonnegative function.
It is worth noting that if $(\pi_W: W \to B, \omega_W) $ is nonnegative and $J \in\mathcal{J}_h(W, \omega_W) $, then any $J$-holomorphic current $\mathcal{C}$ has nonnegative $\omega_W$-energy.
Definition of PFH
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Now let us return to the definition of PFH. Fix a homology class $\Gamma \in H_1(Y, \mathbb{Z})$ with degree $\Gamma \cdot [F]=Q$, the chain complex $PFC(Y, \omega, \Gamma)$ of PFH is a free moduli generated by the ECH generators with homology class $\Gamma$. Consider the special case that $\overline{W}=\mathbb{R} \times Y$ and $J$ is a generic $\mathbb{R}$-invariant $\Omega_W$-tame almost complex structure, the differential of PFH is defined by $$<\partial \alpha, \beta> = \sum_{Z \in H_{2}(Y, \alpha, \beta)} \left(\# {\mathcal{M}}^J_{1}(\alpha, \beta, Z)/\mathbb{R} \right)$$ In general the sum above is not finite, one need the monotone assumption or introduce the local coefficient.(Cf. [@H1]) The homology of $(PFC(Y, \omega, \Gamma), \partial)$ is called PFH, denoted by $PFH_*(Y, \omega, \Gamma)$. [@HT1] and [@HT2] show that $\partial^2=0$, thus PFH is well defined.
In our case, $(Y, \pi, \omega)$ is a mapping torus of Dehn twisted. By Lemma 5.1 of [@H1], it satisfies the monotone condition. We use $\mathbb{Z}$ coefficient throughout.
Cobordism maps on PFH
---------------------
Let $(W , \pi_W, \omega_W)$ be a fibered cobordism from $(Y, \pi, \omega)$ to $(Y', \pi', \omega')$, it is expected to define the cobordism map in chain level by $$\label{eq2}
<PFC(W, \omega_W) \alpha, \beta >= \sum_{Z \in H_{2}(W \alpha, \beta)} \left(\# {\mathcal{M}}^J_{0}(\alpha, \beta, Z) \right) .$$ However, above formula doesn’t make sense in general due to appearance of holomorphic current with negative ECH index. The reasons are explained in [@H3]. But in our special case, we show that it works. See Theorem \[thm2\] latter.
Elementary Lefschetz fibration
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Review of construction of Elementary Lefschetz fibration
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In this subsection, we review the construction of elementary Lefschetz fibration $(X, \pi_X, \omega_X)$. To this end, we need to review the construction of the exact Lefschetz firbation $(E, \theta_E)$ in [@PS]. Let $\pi: \mathbb{C}_{\textbf{x}=(x_1, x_2)}^2 \to \mathbb{C}$ be the local model of Lefschetz fibration and $\Sigma$ be the union of all vanishing cycle (include $(0,0)$), where $\pi(\textbf{x})=x_1^2 +x_2^2$. Let $T=T^*S^1=\{ (u,v) \in \mathbb{R}^2 \times \mathbb{R}^2: <u, v>=0 \ \ |v|=1\}. $ We identify $T$ with cylinder $\mathbb{R}_x \times (\mathbb{R}_y/\mathbb{Z})$ via $$\label{eq7}
u=ixe^{i2\pi y}, \ \ v=e^{i2\pi y}.$$ Let $T_{\lambda}=\{(x, y) \in \mathbb{R}\times S^1 \vert |x| \le \lambda\}$. Consider the map $$\label{eq9}
\begin{split}
&\Phi: \mathbb{C}_{\textbf{x}}^2 -\Sigma \to \mathbb{C} \times (T-T_0)\\
&\Phi(\textbf{x})=(\pi(\textbf{x}), \sigma_{\frac{t}{2}} (-Im(\hat{\textbf{x}}) |Re(\hat{\textbf{x}})|, Re(\hat{\textbf{x}}) |Re(\hat{\textbf{x}})|^{-1} ) )=(\pi(\textbf{x}), \sigma_{\frac{t}{2}}(\Phi_2(\hat{\textbf{x}}))),
\end{split}$$ where $\sigma_t$ is the geodesic flow on $T^*S^1$, $\Phi_2$ is the second component of $\Phi$ and $\hat{\textbf{x}}= e^{-i\pi {t} }\textbf{x} $ provided that $\pi(\textbf{x}) =re^{2\pi it}$. $\Phi$ satisfies the following properties:
1. $\Phi$ is a diffeomorphism fibered over $\mathbb{C}$.
2. $(\Phi^{-1})^* \theta_{\mathbb{C}^2}=\theta_T - \tilde{R}_r(|x|) dt,$ where $\theta_{\mathbb{C}^2} =\frac{i}{4}\sum_{k=1}^2 (z_k d\bar{z}_k - \bar{z}_k dz_k )$, $\tilde{R}_r(t)= \frac{t}{2} - \frac{1}{4} \sqrt{r^2 + 4 t^2}$ and $\theta_T = xdy$.
Now let us fix a $\lambda >0$ and $\delta>0$, take a cut off function $g$ such that $g(t)=0$ near $t=0$ and $g(t)=1$ where $t \ge \lambda-\delta_0$. Define a 1-form $\mathfrak{r}=\Phi^*(g(|x|) \tilde{R}_r(|x|) dt )$. Define $$E=\Phi^{-1}(D_{\delta} \times (T_{\lambda}-T_0) )\cup (\Sigma \cap \pi^{-1}(D_{\delta})).$$ Alternative, $E=\{ \textbf{x} \in \mathbb{C}^2 \vert |\textbf{x}|^4-|\pi(\textbf{x})|^2 \le 4 \lambda^2, \ \ |\pi(\textbf{x})| \le \delta\}$. $E$ is a manifold with corners, the boundary of $E$ can be divided into vertical boundary $\partial_v E=\pi^{-1}(\partial D_{\delta})$ and horizontal boundary $\partial_h E = \Phi^{-1}(D_{\delta} \times \partial T_{\lambda})$. Let $\theta_E=\theta_{\mathbb{C}^2} + \mathfrak{r}$ and $\omega_E= d\theta_E$ be the admissible $2$-form on $E$. By definition, $\theta_E= \Phi^*( \theta_T + (g(|x| ) -1) \tilde{R}_r(|x|) dt )$. Let $R_r(t) = (1-g(t)) \tilde{R}_r(t)$, then $\theta _E=\Phi^*( \theta_T -R_r(|x|) dt) $.
The symplectic monodromy of $(E, \omega_E)$ is a generalized Dehn twisted $\phi: \pi^{-1}(\delta) \to \pi^{-1}(\delta) $ around $T(0)$, that is $\phi(x, y) =\sigma_{ R_{\delta}'(|x|)} (x, y)$ when $x \ne 0$ and $\phi(0, y)=y\pm \frac{1}{2}$. As a consequence, the vertical boundary $\partial_v E$ is a mapping torus of Dehn twisted.
Let $N(\partial_h E )= D_{\delta} \times ([-\lambda, -\lambda + \delta_0] \cup [\lambda- \delta_0, \lambda]) \times S^1 $ be a neighborhood of the horizontal boundary. Let $(S, \omega_S)$ be a connected symplectic surface with boundary $\partial S =S_1 \cup (-S_1)$. A collar neighborhood of $\partial S $ is identified with $N(\partial S ) = ([-\lambda, -\lambda + \delta_0] \cup [\lambda- \delta_0, \lambda]) \times S^1$. Choose $\omega_S$ such that $\omega_S \vert_{N(\partial S)} = d \theta_T$. Take a trivial symplectic fibration over a disk $(D_{\delta} \times S, \omega_S)$, then $\pi_X: X \to D$ is obtained by gluing $E$ with $D_{\delta} \times S$ via identify $N(\partial_h E)$ and $D_{\delta} \times N(\partial S)$ and $\omega_X$ is obtained by gluing $\omega_E$ and $\omega_S$. The fiber of $X$ is $F=S \cup T_{\lambda}$ and $Y=\partial_v E\cup( S \times S^1)$. According to the construction, $(\pi_X: X \to D, \omega_X)$ is nonnegative.
In the rest of our note, we always assume that $\delta=1$ and denote $R(t)=R_1(t)$. Also, we choose a large $\lambda $ and a suitable cut off function $g$ such that $0 \le R'(|t|)\le \frac{1}{2}$ and $R''(t) \le 0$.
\[lem1\] Given $L>0$, we can always find an admissible $2$-form $\omega_X$ such that $\int_F \omega_X>L$.
Let $\omega_X$ be the admissible $2$-form constructed before. We modify $\omega_X$ such that $\int_F \omega_X >L$, the modification is as follows.
Let $U= ([-\lambda-2\delta_0, -\lambda + \delta_0] \cup [\lambda- \delta_0, \lambda + 2\delta_0]) \times S^1$ be a collar neighborhood of $\partial S $. Take a function $f: S \to \mathbb{R}$ such that only support in $U$ and $f= c_1 $ on $ [\lambda-\delta_0, \lambda+ \delta_0] \times S^1 $ and $f= c_2 $ on $( [ -\lambda-\delta_0, - \lambda +\delta_0] \times S^1 ) $, where $c_1$ and $c_2$ are positive constant. Define $\theta_S' = \theta_S + f dy$, then $\omega_S'=\omega_E$ on $N(\partial S) $ by definition. Thus we can glue $\omega_S'$ with $\omega_E$ as before, the result is still called $\omega'_X$. By Stoke’s Theorem, $$\int_F \omega_X' = \int_F \omega_X + c_1 -c_2.$$ Let take $c_1-c_2>L$, then it suffices for our purpose.
Singular homology of $Y$ and $X$
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In this subsection, let us compute the classical invariant of $X$ and $Y$, where $Y=\partial X$ is mapping torus of the Dehn twisted $\phi$, that is $$\begin{aligned}
Y= \mathbb{R}\times F /(t+ 2\pi, x) \sim (t, \phi(x)).\end{aligned}$$
$H_1(Y , \mathbb{Z})=\mathbb{Z}^{2g(F)}$.
According to the elementary algebraic topology, we have $H_1(Y , \mathbb{Z})= H_0(F , \mathbb{Z}) \oplus Coker\{(1-\phi_*)\vert_{H_1(F, \mathbb{Z})}\}$. Says $\phi$ is a Dehn twisted around curve $a$, then $\phi_*(b)=b+ (a\cdot b) a$ for any $b \in H_1(Y, \mathbb{Z})$. Using this relation, it is easy to check that $ Coker\{(1-\phi_*)\vert_{H_1(F, \mathbb{Z}) }\}=\mathbb{Z}^{2g(F)-1}$.
\[lem2\] $H_2(X, \mathbb{Z})=\mathbb{Z}$, $H_2(X, \partial X, \mathbb{Z}) =\mathbb{Z}$ and $H_1(X, \mathbb{Z})=\mathbb{Z}^{2g(F)-1}$.
It is worth noting that $E$ is a start-shape domain in $\mathbb{C}^2$, in other words, for any $\textbf{x} \in E=\{ \textbf{x} \in \mathbb{C}^2 \vert |\textbf{x} |^4-|\pi(\textbf{x} )|^2 \le 4 \lambda^2, \ \ |\pi(\textbf{x} )| \le \delta\}$, $t \textbf{x} \in E $ for any $0 \le t \le 1$. As a consequence, $E$ is deformation retract to origin. Hence, $H_*(E, \mathbb{Z})=0$ for any $* \ne0$.
Recall that $\partial_h E=D \times \partial T_{\lambda}$ and our $X=E\cup (D \times S)$ is obtained by gluing $E$ and $D \times S$ along $ \partial S$ and $ \partial T_{\lambda}$. By Mayer-Vietoris theorem, we have $$\begin{split}
&H_2(E, \mathbb{Z}) \oplus H_2(D \times S, \mathbb{Z}) \to H_2(X, \mathbb{Z}) \xrightarrow{ \partial_*}H_1(\partial_h E, \mathbb{Z}) \xrightarrow{ (i_*, j_*)} H_1(E, \mathbb{Z}) \oplus H_1(D \times S, \mathbb{Z}) \\
&\to H_1(X, \mathbb{Z}) \xrightarrow{ \partial_*}H_0(\partial_h E, \mathbb{Z}) \to H_0(E, \mathbb{Z}) \oplus H_0(D \times S, \mathbb{Z})\cdots
\end{split}$$ The first term of above sequence is zero, thus $H_2(X, \mathbb{Z}) = Im \partial_*=Ker(i_*, j_*)$. $i_*=0$ because of the vanishing of $H_1(E, \mathbb{Z})$. $j_*$ is equal to the pull forward of the inclusion $\partial S \to S$, so $\ker j_*=\mathbb{Z}[\partial S]$. Therefore $H_2(X, \mathbb{Z})=Ker(i_*, j_*)=\mathbb{Z}$. Obviously the homology class of fiber $F$ is non-trivial and $H_2(X, \mathbb{Z})$ is generated by $[F]$.
By exactness, $H_1(X, \mathbb{Z})=(H_1(S, \mathbb{Z}) / Im(i_*, j_*) ) \oplus Im\partial_*$. By the another short exact sequence $$0 \to Coker \partial_* \to H_0(E, \mathbb{Z}) \oplus H_0(D \times S, \mathbb{Z})\to H_0(X, \mathbb{Z}) \to 0,$$ We know that $Coker \partial_* = \mathbb{Z}$. Hence $Im \partial_*=\mathbb{Z}$. By previous computation, $Ker(i_*, j_*)=\mathbb{Z}$, thus $ Im(i_*, j_*) =\mathbb{Z}$. In conclusion, $H_1(X, \mathbb{Z}) = H_1(S, \mathbb{Z})=\mathbb{Z}^{2g(S)+1} = \mathbb{Z}^{2g(F)-1} $.
To compute $H_2(X, \partial X , \mathbb{Z})$, we use exact sequence $$H_2(Y, \mathbb{Z}) \xrightarrow{ i_*} H_2(X, \mathbb{Z}) \to H_2(X, \partial X , \mathbb{Z}) \xrightarrow{ \partial} H_1(Y, \mathbb{Z}) \xrightarrow{ i_*} H_1(X, \mathbb{Z})$$ Note that the map $ i_*: H_2(Y, \mathbb{Z}) \to H_2(X, \mathbb{Z}) $ is surjective since $i_*[F]=[F]$. Thus $ H_2(X, \partial X , \mathbb{Z}) =Ker\{ i_*: H_1(Y, \mathbb{Z}) \to H_1(X, \mathbb{Z}) \}$. This kernel is $\mathbb{Z}$, because, all the generators in $ H_1(Y, \mathbb{Z}) $ survive under $i_*$ except the vanishing cycle.
Periodic orbit
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In this section, we describe the periodic orbits on $Y$.
Periodic orbits on $\partial_v E$
---------------------------------
Under the diffeomorphism \[eq9\], the admissible $2$-form over $S^1_t \times (T_{\lambda} -T_0)$ is given by $$\omega_E= dx \wedge dy -R'(x) dx \wedge dt$$ when $x>0$, and $$\omega_E= dx \wedge dy +R'(-x) dx \wedge dt$$ when $x<0$. Therefore, the Reeb vector field is $$R=\partial_t +R'(x) \partial_y$$ when $x>0$ and $$R= \partial_t -R'(-x) \partial_y$$ when $x<0$.
At each $x_0$ such that $R'(x_0) = \frac{p}{q}$, the Morse-Bott torus $S_t \times\{x_0\} \times S_y$ is foliated by embedded periodic orbits. Each periodic orbit is of the form $\gamma_{\frac{p}{q}}(\tau)=(\tau, x_0, y_0+ R'(x_0) \tau)=(\tau, x_0, y_0+ \frac{p}{q} \tau)$ if $x_0>0$ and $\gamma_{\frac{p}{q}}(\tau)=(\tau, x_0, y_0- R'(-x_0) \tau)= (\tau, x_0, y_0 +(\frac{p}{q}-1)\tau)$ if $x_0<0$(When $x_0<0$, we write $R'(-x_0)=1-\frac{p}{q} $.), where $\tau \in \mathbb{R}/( q\mathbb{Z})$. The integers $p, q$ here are relative prime.
Given a periodic orbit $\gamma_{\frac{p}{q}}$, we want to find the inverse image $\textbf{x}(\tau)=\Phi^{-1}(\gamma_{\frac{p}{q}})$. The result is summarized in the following lemma.
\[lem16\] Let $x_0 \in [-\lambda, \lambda]$ such that $R'(x_0)=\frac{p}{q}$ and $\gamma_{\frac{p}{q}}$ is the periodic orbit at $x_0$. Let $\textbf{x}(\tau)=(x_1(\tau), x_2(\tau))=\Phi^{-1}(\gamma_{\frac{p}{q}})$, $\tau \in \mathbb{R} /(q \mathbb{Z})$, we have the following two cases. If $x_0 \ge 0$, then $$\label{eq16}
\begin{split}
&x_1= \frac{1}{2} e^{h+iy_0} e^{2\pi i \frac{p}{q} \tau} + \frac{1}{2} e^{-h-iy_0} e^{2\pi i \frac{q-p}{q} \tau }\\
&x_2=- \frac{i}{2} e^{h+iy_0} e^{2\pi i \frac{p}{q} \tau}+ \frac{i}{2} e^{-h-iy_0} e^{2\pi i \frac{q-p}{q}\tau} ,
\end{split}$$ for some constant $h=h(x_0) \ge 0$. If $x_0 \le 0$, then $$\label{eq17}
\begin{split}
&x_1= \frac{1}{2} e^{h-iy_0} e^{ 2\pi i \frac{q-p}{q} \tau } + \frac{1}{2} e^{-h+iy_0} e^{2 \pi i \frac{p}{q} \tau }\\
&x_2=\frac{i}{2} e^{h-iy_0} e^{ 2\pi i \frac{q-p}{q}\tau} - \frac{i}{2} e^{-h +iy_0} e^{2\pi i \frac{p}{q} \tau},
\end{split}$$ for some constant $h=h(x_0)\ge0$. In both cases, $h=0$ if and only if $x_0=0$.
First note that under the identification \[eq7\], the geodesic flow $\sigma_t$ is $\sigma_t(x, y)=(x, y+ t)$ if $x>0$ and $\sigma_t(x, y)=(x, y-t)$ if $x<0$. Let $\textbf{x} \in E$ and $\hat{\textbf{x}}=e^{-i\pi {t}} \textbf{x} =\hat{p} + i\hat{q}$. $\Phi_2(\hat{\textbf{x}})=(u, v) \in T$ can be written as $v= \frac{\hat{p}}{|\hat{p}|} = e^{i2\pi \theta}$ and $u=-\hat{q} |\hat{p}|=\pm |\hat{p}| |\hat{q}| i e^{i 2\pi \theta}$.
If $ \gamma_{\frac{p}{q}}(\tau)=(\tau, x_0, y_0+ \frac{p}{q} \tau)$ and $x_0>0$, then under the identification \[eq7\], $$\sigma_{\frac{t}{2}}(\Phi_2(\hat{\textbf{x}})) = \sigma_{\frac{t}{2}}( -\hat{q} |\hat{p}|, \frac{\hat{p}}{|\hat{p}|} ) =(|\hat{p}| |\hat{q}|, \theta + \frac{t}{2} ).$$ Therefore, $t=\tau$, $\theta = y_0+ \frac{p}{q}\tau - \frac{1}{2} t $ and $x_0=|\hat{p}| |\hat{q}|$. Since $|\hat{p}|^2 -|\hat{q}|^2=1$ and $<\hat{p}, \hat{q}>=0$ and $x_0^2=|\hat{p}|^2 |\hat{q}|^2 $, we can solve $$\label{eq5}
\begin{split}
&|\hat{p}|^2 =\sqrt{x_0^2 + \frac{1}{4}} + \frac{1}{2}\\
&|\hat{q}|^2 =\sqrt{x_0^2 + \frac{1}{4}} - \frac{1}{2}.
\end{split}$$ We can write $|\hat{p}|=\frac{e^h+ e^{-h}}{2}$ and $|\hat{q}|=\frac{e^h-e^{-h}}{2}$. Follows from the definition, $$\begin{split}
&p=\cos( \pi t) \hat{p} -\sin (\pi t ) \hat{q}\\
&q=\sin (\pi t) \hat{p} + \cos ( \pi t) \hat{q}.
\end{split}$$ Using the relation $\frac{\hat{p}}{|\hat{p}|} =e^{i 2\pi\theta}$ and $-\hat{q} |\hat{p}| =i |\hat{q} ||\hat{p}|e^{i2\pi\theta}$, we have $$\begin{split}
&p=\cos( \pi t) \hat{p} -\sin (\pi t ) \hat{q} = e^{i2\pi \theta} \left( \frac{e^h+ e^{-h}}{2} \cos (\pi t) + \frac{e^h -e^{-h}}{2}i \sin (\pi t)\right) = \frac{1}{2} e^h e^{i 2\pi(\theta + \frac{t}{2})} + \frac{1}{2} e^{-h} e^{i 2\pi (\theta - \frac{t}{2})}\\
&q=\sin (\pi t) \hat{p} + \cos ( \pi t) \hat{q}= -ie^{i 2\pi\theta} \left( \frac{e^h- e^{-h}}{2} \cos (\pi t) + \frac{e^h +e^{-h}}{2}i \sin (\pi t) \right) = \frac{i}{2} e^{-h} e^{i 2\pi(\theta - \frac{t}{2})} - \frac{i}{2} e^{h} e^{i2\pi(\theta + \frac{t}{2})}\\
\end{split}$$ Then $$\begin{split}
&x_1= \frac{1}{2} e^h e^{i 2\pi (\theta + \frac{t}{2})} + \frac{1}{2} e^{-h} e^{-i2\pi(\theta - \frac{t}{2})}\\
&x_2=\frac{i}{2} e^{-h} e^{-i 2\pi (\theta - \frac{t}{2})} - \frac{i}{2} e^{h} e^{i2\pi(\theta + \frac{t}{2})}\\
\end{split}$$ Replace $\theta$ by $y_0+ \frac{p}{q}\tau - \frac{1}{2} t $ and $t=\tau$, then we get the result.
For the case that $ \gamma_{\frac{p}{q}}(\tau)=(\tau, x_0, y_0+ (\frac{p}{q}-1) \tau)$ and $x_0<0$, the argument is similar. Under the identification \[eq7\], $$\sigma_{\frac{t}{2}}(\Phi_2(\hat{\textbf{x}})) =\sigma_t( -\hat{q} |\hat{p}|, \frac{\hat{p}}{|\hat{p}|} ) =(-|\hat{p}| |\hat{q}|, \theta -\frac{t}{2} ).$$ Therefore, $t=\tau$, $\theta = y_0+ \frac{p}{q}\tau - \frac{1}{2} t $ and $x_0=-|\hat{p}| |\hat{q}|$. Since $|\hat{p}|^2 -|\hat{q}|^2=1$ and $<\hat{p}, \hat{q}>=0$ and $x_0^2=|\hat{p}|^2 |\hat{q}|^2 $, we can get the same formula (\[eq5\]). We can write $|\hat{p}|=\frac{e^h+ e^{-h}}{2}$ and $|\hat{q}|=\frac{e^h-e^{-h}}{2}$. Using the relation $\frac{\hat{p}}{|\hat{p}|} =e^{i 2\pi \theta}$ and $-\hat{q} |\hat{p}| =-i |\hat{q} ||\hat{p}|e^{i2\pi \theta}$, we have $$\begin{split}
&p= \cos( \pi t) \hat{p} -\sin (\pi t ) \hat{q}= e^{i 2\pi \theta} \left( \frac{e^h+ e^{-h}}{2} \cos (\pi t)- \frac{e^h -e^{-h}}{2}i \sin (\pi t)\right) = \frac{1}{2} e^h e^{i 2\pi (\theta - \frac{t}{2})} + \frac{1}{2} e^{-h} e^{i 2\pi (\theta + \frac{t}{2})}\\
&q=\sin (\pi t) \hat{p} + \cos ( \pi t) \hat{q}= ie^{i 2\pi \theta} \left( \frac{e^h- e^{-h}}{2} \cos (\pi t) - \frac{e^h +e^{-h}}{2}i \sin (\pi t)\right) = \frac{i}{2} e^{h} e^{i 2\pi (\theta - \frac{t}{2})} - \frac{i}{2} e^{-h} e^{i 2\pi (\theta + \frac{t}{2})}\\
\end{split}$$ Then $$\begin{split}
&x_1= \frac{1}{2} e^h e^{-2\pi i (\theta -\frac{t}{2})} + \frac{1}{2} e^{-h} e^{2\pi i(\theta + \frac{t}{2})}\\
&x_2=\frac{i}{2} e^{h} e^{-2\pi i (\theta - \frac{t}{2})} - \frac{i}{2} e^{-h} e^{2\pi i(\theta + \frac{t}{2})}\\
\end{split}$$ Replace $\theta$ by $y_0+ \frac{p}{q}\tau - \frac{1}{2} t $ and $t=\tau$, then we get the result.
We regard the periodic orbit at $x_0=0$ as limit of the periodic orbits at $x \ne 0$ and $x \to 0$, then from \[eq16\] and \[eq17\] , the periodic orbit at $x_0=0$ is $$\begin{split}
&x_1= \frac{1}{2} e^{i 2\pi (-y_0+ \frac{1}{2} \tau )} + \frac{1}{2} e^{i 2\pi(y_0 +\frac{1}{2} \tau )}\\
&x_2=\frac{i}{2} e^{i 2\pi (-y_0 + \frac{1}{2}\tau )} - \frac{i}{2} e^{i2\pi (y_0 + \frac{1}{2} \tau)}\\
\end{split}$$
Perturbation
------------
Near a Morse-Bott torus $S_t \times\{x_0\} \times S_y$, we can use small Morse function to perturb the admissible $2$-form so that there are only two periodic orbits at $x_0$ survives, one is elliptic and the other one is positive hyperbolic, denoted by $e_{\frac{p}{q}}$ and $h_{\frac{p}{q}}$ respectively. (Cf. [@FB]) Fix an integer $Q$, we can arrange that all the periodic orbits with degree less than $Q$ are either $e_{\frac{p}{q}}$ or $h_{\frac{p}{q}}$.
To see the periodic orbits in the trivial part of $Y$. Let $f: S \to \mathbb{R}$ be a small Morse function such that $\nabla f $ is transversal to $\partial S$ and there are critical points $\{p_i\}_{i=0, 1}$ and $\{q_i\}_{i=0, 1}$ on $N(\partial S) $ satisfying $\nabla^2 f(p_i)>0$ and $tr(\nabla^2 f(q_i)) =0$, in addition, there is no other critical point on $N(\partial S)$. We use $f$ to perturb $\omega_S$ by $\omega_S^f =\omega_S -df \wedge dt $, so that the periodic orbits with degree less than $Q$ over $(S \times D, \omega_S)$ only consists of constant orbits at critical points of $f$. We always use $a \in Crit(f)$ to denote the critical point on $S - N(\partial S )$. If $tr(\nabla^2f (a)) \ne 0$, then the corresponding periodic orbit is elliptic, denoted by $e_a$. Moreover, $e_a$ is either $Q$-positive or $Q$-negative. If $tr(\nabla^2f (a))=0$, then the corresponding periodic orbit is positive hyperbolic, denoted by $h_a$. $\{e_i\}_{i=0, 1}$ and $\{h_i\}_{i=0, 1}$ are respectively elliptic orbits and hyperbolic orbits corresponding to $\{p_i\}_{i=0, 1}$ and $\{q_i\}_{i=0, 1}$.
In conclusion, we can arrange that all the periodic orbits with degree less than $Q$ are either $e_{\frac{p}{q}}$ or $h_{\frac{p}{q}}$ or $e_a$ or $h_a$. Keep in mind that the periodic orbits here are either $Q$-positive elliptic or $Q$-negative elliptic or positive hyperbolic.
ECH index
=========
In this section, we deduce a combinatorial formula for the ECH index as in [@H5]. The result is as follows.
\[thm1\] Let $\pi: E \to D$ be the exact Lefschetz fibration defined in section 3.1 and orbits set $\alpha=\Pi_i \gamma_{\frac{p_i}{q_i}}$ satisfying $\frac{p_i}{q_i} \ge \frac{p_j}{q_j}$ for $i \le j$, then the ECH index is $$I(\alpha)= Q+ P(Q-P) - \sum_{i<j} (p_iq_j -p_jq_i) - e(\alpha),$$ where $e(\alpha)$ is the total multilpity of elliptic orbits in $\alpha$, $P=\sum_i p_i$ and $Q=\sum_i q_i$.
Since $H_2(E, \mathbb{Z})=0$, there is an unique element in $H_2(E, \alpha)$. The relative Chern number and relative self-intersection number are denoted by $c_{\tau}(\alpha)$ and $Q_{\tau}(\alpha)$ respectively. We compute the quantities $c_{\tau}$, $Q_{\tau}$ and $CZ_{\tau}$ in Lemmas \[lem9\], \[lem10\] and (\[eq6\]) respectively. Their proof will appear in the upcoming subsection.
We can rewrite the formula for ECH index in the following way. Let $w_j=\sum_{i=0}^j(p_i, q_i)$, then $\mathcal{P}(\alpha)$ to be the convex path in the plane consisting of straight line segments between the points $w_{j-1}$ and $w_j$, oriented so that the origin is the initial endpoint. (Cf. [@H1]) Let $\Lambda_{\alpha}$ be the region in the plane which is enclosed by $\mathcal{P}(\alpha)$ and line segment from $(0,0) $ to $(P, 0)$ and the line segment from $(P,0) $ to $(P, Q)$. The area of $\Lambda_{\alpha}$ is $$2Area(\Lambda_{\alpha}) =PQ -\sum_{i<j} (p_iq_j -p_jq_i).$$ Therefore, the ECH index can be written as $$I(\alpha)= Q+ 2 Area(\Lambda_{\alpha}) -P^2 - e(\alpha).$$
\[lem12\] $I(\alpha) \ge 0$ and equality holds if and only if $\alpha=e_1^m e_0^n$.
Since $0 \le \frac{p_i}{q_i} \le 1$, the triangle determined by $(0, 0)$, $(0, P)$ and $(P, P)$ is inside the region $\Lambda_{\alpha}$. Therefore, $P^2 \le 2 Area(\Lambda_{\alpha})$. By definition, $e(\alpha) \le Q$. Therefore, $I (\alpha) \ge 0$. The equality holds if and only if $Q=e(\alpha)$ and $P^2 = 2 Area(\Lambda_{\alpha})$. The only possibility is that $\alpha=e_1^m e_0^n$.
\[lem4\] Let a be a critical point of $f$ and $C_a =\{a\} \times D$ and $m_a$ be nonnegative integer, then there are the following three possibilities.
- If $\nabla^2f (a)>0$, then the corresponding periodic orbit $e_a$ is elliptic with Conley Zehender index $CZ_{\tau}(e_a)=-1$. In addition, $I(m_a C_a)=0$.
- If $\nabla^2f (a)<0$, then the corresponding periodic orbit $e_a$ is elliptic with Conley Zehender index $CZ_{\tau}(e_a)=1$. In addition, $I(m_a C_a)=2 m_a$.
- Finally, $tr(\nabla^2f (a))=0$, then the corresponding periodic orbit $h_a$ is positive hyperbolic with Conley Zehender index $CZ_{\tau}(h_a)=0$. In addition, $I(m_a C_a)= m_a$.
Obverse that if $tr(\nabla^2f (a)) \ne 0$, then the sign of rotation number of $e_a$ is equal to $-sign( \nabla^2f (a) )$. In conclusion, $e_a$ is $Q$-negative if $\nabla^2f (a) >0$, and $e_a$ is $Q$-positive if $\nabla^2f (a)<0$. Also, it is easy to check that $c_{\tau}(C_a)=1$ and $Q_{\tau}(C_a)=0$, where $\tau$ is the canonical trivialization on $S^1 \times S$. These two ingredients lead to the statements of the Lemma.
Given an orbit set $\alpha=\Pi_i \alpha_i^{m_i}$, we define a reference element ${Z}_{\alpha}=\sum_i m_i[ S_i] \in H_2(X, \alpha)$, where $S_i$ are surfaces defined as follows. If $\alpha_i=\gamma_{\frac{p}{q}}$, then we define a surface $S_i $ to be the image of $u$ in (\[eq3\]) or (\[eq4\]) accordingly. If $\alpha_i$ is constant orbit at critical point $a$ of $f$, then we define a surface $S_i= \{a\} \times D$. It is worth noting that $u$ doesn’t intersect $\{a\} \times D$, thus $$\label{eq15}
I(Z_{\alpha}) = \sum_a \left(I( e_a^{m_a}) + I(h_a^{n_a} ) \right) + I(\Pi_i \gamma_{\frac{p_i}{q_i}}).$$ Since $ H_2(X, \alpha)$ is an affine space over $H_2(X, \mathbb{Z})$, by lemma \[lem2\], any $Z\in H_2(X, \alpha)$ is of the form $Z=Z_{\alpha} +m [F]$. Let us denote $I_m(\alpha)=I(Z_{\alpha} +m [F])$. Therefore, in general we have $$\label{eq14}
I_m(\alpha )= I_0(\alpha)+ 2m(Q+1- g(F)).$$
Trivialization
--------------
Restrict $\Phi$ to the boundary $\partial_v E$, we have trivialization $\Phi : \partial_v E -\Sigma \to S^1_t \times (T_{\lambda }-T_0) = S^1_t \times ( [-\lambda,0)\cup (0 , \lambda] ) \times S^1_y $. The tangent bundle of $T_{\lambda}=[-\lambda, \lambda]_x \times S^1_y$ has a canonical trivialization. Using $\Phi$ to pull back this canonical trivialization, we get a trivialization $\tau$ along the periodic orbits at $x \ne 0$.
Let us write $\partial_v E - \Sigma= \partial_v E^+ \cup \partial_v E^-$ and $\Phi_{\pm} = \Phi \vert_{ \partial_v E^{\pm}}$. $\Phi_+$ and $\Phi_-$ do not match at $\Sigma$ and thus $\Phi$ cannot be extended to whole $\partial_v E$. But $\Phi_+ $ and $\Phi_-$ can extend to $\overline{\partial_v E^{\pm}} $ and give trivializations $\Phi_{+}: \overline{ \partial_v E^+} \to S^1_t \times [0, \lambda]_x \times S^1_y$ and $\Phi_{-}: \overline{ \partial_v E^- }\to S^1_t \times [-\lambda, 0]_x \times S^1_y$ respectively. Using $\Phi_{\pm}$ to pull back the canonical trivialization, hence there are two trivializations $\tau_{\pm}$ along the periodic orbits at $x_0=0$. But there is no difference between using $\tau_+$ and $\tau_-$ when we compute $c_{\tau}, Q_{\tau}, CZ_{\tau}$. So we just same notation $\tau$ to denote one of them.
Conley Zehender index
----------------------
Since $R''(x)<0$, the elliptic orbit $e_{\frac{p}{q}}$ has small negative rotation number with respect to the trivialization $\tau$, i.e. it is $Q$-negative elliptic. As a result, $$\label{eq6}
CZ_{\tau}(e^k_{\frac{p}{q}}) = -1, \ \ \ CZ_{\tau}(h_{\frac{p}{q}}) = 0,$$ for any $k \le Q$.
Relative intersection number
-----------------------------
The main result of this section is the following lemma.
\[lem9\] For $0 \le \frac{p}{q}, \frac{p'}{q'} \le 1$, then $Q_{\tau}(\gamma_{\frac{p}{q}}, \gamma_{\frac{p'}{q'}}) = \min\{ p(q'-p'), p'(q-p)\}$. Assume that $\alpha=\Pi_i \gamma_{\frac{p_i}{q_i}}$ and $\frac{p_i}{q_i} \ge \frac{p_j}{q_j}$ for $i \le j$, then $$Q_{\tau}(\alpha)=P(Q-P) - \sum_{i<j}( p_iq_j -p_jq_i),$$ where $P =\sum_ip_i$ and $Q=\sum_i q_i$.
It is worth noting that $Q_{\tau} $ is quadratic in the following sense, $$Q_{\tau}(\alpha)=\sum_i Q_{\tau}(\gamma_\frac{p_i}{q_i}) + 2\sum_{i<j} Q_{\tau}(\gamma_\frac{p_i}{q_i}, \gamma_\frac{p_j}{q_j}).$$ Turn out it suffices to compute $ Q_{\tau}(\gamma_\frac{p_i}{q_i}) $ and $Q_{\tau}(\gamma_\frac{p_i}{q_i}, \gamma_\frac{p_j}{q_j}).$ The idea to compute $ Q_{\tau}(\gamma_\frac{p_i}{q_i}) $ and $Q_{\tau}(\gamma_\frac{p_i}{q_i}, \gamma_\frac{p_j}{q_j})$ is to express them as intersection number of two surfaces. To this ends, let us define a surface $u: D_z \to E$ which is asymptotic to $\gamma_{\frac{p}{q}}$ as follows. Let $\epsilon_i(r) : [0 , \infty) \to \mathbb{R}$ be cut-off functions such that
- $\epsilon_i(r)$ is support in $r \le 2\delta$.
- When $r \le \delta$, $\epsilon_i(r)$ is independent of $r$ and $ \epsilon_i \ll \delta$.
If $0\le \frac{p}{q}\le\frac{1}{2}$, we define $$\label{eq3}
u(z)=\left( (1+ \epsilon_1)\frac{1}{2}e^{h+iy_0} z^p + (1+ \epsilon_2)\frac{1}{2}e^{-h-iy_0} z^{q-p} + \epsilon_3, -(1+ \epsilon_1)\frac{i}{2}e^{h+iy_0} z^p + (1+ \epsilon_2)\frac{i}{2}e^{-h-iy_0} z^{q-p} \right).$$ If $\frac{1}{2}\le\frac{p}{q} \le 1$, we define $$\label{eq4}
u(z)=\left( (1+ \epsilon_1)\frac{1}{2}e^{h-iy_0} z^{q-p} + (1+ \epsilon_2)\frac{1}{2}e^{-h+iy_0} z^{p} + \epsilon_3, (1+ \epsilon_1)\frac{i}{2}e^{h-iy_0} z^{q-p} - (1+ \epsilon_2)\frac{i}{2}e^{-h+iy_0} z^p \right).$$ Note that these two definitions agree when $\frac{p}{q}=\frac{1}{2}$. By construction and Lemma \[lem16\], as $z $ tends to boundary of $D$, $u$ is asymptotic to $\gamma_{\frac{p}{q}}(\tau)$.
\[lem11\] $u$ satisfies the following properties:
1. For sufficiently small $\epsilon_i$ and $\delta$, then $u$ is embedded except at $z=0$.
2. Let $\frac{p'}{q'} < \frac{p}{q}$ and $v$ be the $\frac{p'}{q'} $-version of \[eq3\] or \[eq4\] accordingly. If $v$ doesn’t involve the zero order term, i.e. $\epsilon_3=0$, then for sufficiently small $\epsilon_i$ and $\delta$, the intersection points of $u$ and $v$ lies in the region $\{0<|z| \le \delta\} \times \{0<|w| \le \delta\} $.
3. The intersection is transversal and the sign of the intersection points are positive.
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1. It is straight forward to check that $u$ is immersion except at $z=0$. Moreover, $u$ is 1-1 onto its image for sufficiently small $\epsilon_i$. To see this, note the the unperturbed version of $u$( $\epsilon_i=0$ ) is 1-1 onto its image, because, $p$ and $q$ are relative prime. By using limit argument and $u$ is immersion, we can deduce the same conclusion for sufficiently small $\epsilon_i$.
2. Let us consider the case that $0 \le \frac{p'}{q'} < \frac{p}{q} \le \frac{1}{2}$. W.L.O.G, assume that $y_0=0$. Let $(z, w) $ be the intersection points of $u$ and $v$. They satisfies the equation $$\begin{split}
&(1+ \epsilon_1)\frac{1}{2}e^h {z}^p + (1+ \epsilon_2)\frac{1}{2}e^{-h} z^{q-p} + \epsilon_3= (1+ \epsilon_4)\frac{1}{2}e^k {w}^{p'} + (1+ \epsilon_5)\frac{1}{2}e^{-k} w^{q' -p'}\\
& -(1+ \epsilon_1)\frac{i}{2}e^h {z}^p + (1+ \epsilon_2)\frac{i}{2}e^{-h} z^{q-p}= - (1+ \epsilon_4)\frac{i}{2}e^k {w}^{p'} + (1+ \epsilon_5)\frac{i}{2}e^{-k} w^{q'-p'}.
\end{split}$$ These are equivalent to $$\label{eq11}
\begin{split}
&(1+ \epsilon_1)e^h {z}^p + \epsilon_3= (1+ \epsilon_4)e^k {w}^{p'} \\
& (1+ \epsilon_2)e^{-h} z^{q-p} + \epsilon_3= (1+ \epsilon_5)e^{-k} w^{q'-p'}.
\end{split}$$ Assume that $0< \epsilon_i \ll \delta \ll1 $, then the solutions to (\[eq11\]) lie inside either $\{|z| , |w| \le \delta\}$ or $\{|z|, |w| \ge c_0^{-1}\}$ for some constant $c_0 \ge 1$ and $c_0^{-1} \gg \delta$. To see this, if $|w| > \delta$, then (\[eq11\]) implies $$\begin{split}
& |z|^p \ge \frac{1}{1+\epsilon_1 } \left((1+ \epsilon_4) e^{k-h}|w|^{p'} -\epsilon_3 e^{-h}\right) \ge c_0^{-1}|w|^{p'}\\
& |z|^{q-p} \le \frac{1}{1+\epsilon_2} \left( (1+ \epsilon_5)e^{h-k}|w|^{q'-p'} +\epsilon_3 e^{h}\right) \le c_0|w|^{q'-p'}.
\end{split}$$ Therefore, $|w|^{pq'-p'q} \ge c_0^{-q}$. Similarly, if $|z| > \delta$, then we can deduce that $|z| \ge c_0^{-1} $. Note that the cases $\{|z| \le \delta, |w| \ge c_0^{-1}\}$ and $\{|w| \le \delta, |z| \ge c_0^{-1}\}$ cannot happen because of (\[eq11\]).
In the case that $|w|, |z| \ge c_0^{-1} >2\delta$, then $\epsilon_i=0$ and (\[eq11\]) become $$\begin{split}
&e^h {z}^p = e^k {w}^{p'} \\
& e^{-h} z^{q-p} = e^{-k} w^{q'-p'}.
\end{split}$$ Take absolute value both side and one can solve that the norm of $|z|$ and $|w|$ only dependent on $p,q , k ,h$. In fact, $$\log|z|= \frac{k-h}{pq'-p'q}q', \ \ \ \log|w|=\frac{k-h}{pq'-p'q}q.$$ Assume that $R'(x_0)=\frac{p}{q}$ and $R'(x_1)=\frac{p'}{q'}$, then $0<x_0< x_1$ because of $R''<0$. By (\[eq5\]), it is easy to check that $k>h$. Then the norm $|z|, |w|>1$, which is not in our domain. Finally, $(0,0)$, $(z, 0)$ and $(0, w)$ cannot be intersection points for suitable choice of $\epsilon_i$. This can be check directly.
For the case that $\frac{1}{2} \le \frac{p'}{q'}< \frac{p}{q} \le1$, we get $$\label{eq12}
\begin{split}
&(1+ \epsilon_1)e^h {z}^{q-p} + \epsilon_3= (1+ \epsilon_4)e^k {w}^{q'-p'} \\
& (1+ \epsilon_2)e^{-h} z^{p} + \epsilon_3= (1+ \epsilon_5)e^{-k} w^{p'}.
\end{split}$$
The same argument can show that the solutions to \[eq12\] lie inside either $\{|z| , |w| \le \delta\}$ or $\{|z|, |w| \ge c_0^{-1}\}$ for some constant $c_0 \ge 1$ and $c_0^{-1} \gg \delta$. If $|w|, |z| \ge c_0^{-1} > 2\delta$, then $\epsilon_i=0$. Take absolute value both side of( \[eq12\]) and one can solve that $$\log|z|= \frac{h-k}{pq'-p'q}(q'), \ \ \ \log|w|=\frac{h-k}{pq'-p'q}(q).$$ Assume that $R'(x_0)=\frac{p}{q}$ and $R'(x_1)=\frac{p'}{q'}$, then $x_0< x_1<0$ because of $R''<0$. By the definition of $h$ and $k$, it is easy to check that $h>k$. Then the norm $|z|, |w|>1$, which is not in our domain. Finally, $(0,0)$, $(z, 0)$ and $(0, w)$ cannot be intersection points for suitable choice of $\epsilon_i$. This can be check directly.
For the case that $ \frac{p'}{q'}< \frac{1}{2}< \frac{p}{q} \le1$, we have $$\label{eq13}
\begin{split}
&(1+ \epsilon_1 )e^h z^{q-p} + \epsilon_3 = (1+ \epsilon_5) e^{-k}w^{q'-p'}\\
& (1+ \epsilon_2 )e^{-h} z^{p} + \epsilon_3 = (1+ \epsilon_4) e^{k}w^{p'}\\
\end{split}$$ The same argument can show that the solutions to (\[eq13\]) lie inside either $\{|z| , |w| \le \delta\}$ or $\{|z|, |w| \ge c_0^{-1}\}$ for some constant $c_0 \ge 1$ and $c_0^{-1} \gg \delta$. If $|w|, |z| \ge c_0^{-1} > 2\delta$, then $\epsilon_i=0$. Take absolute value both side and one can solve that $$\log|z|= \frac{h+k}{pq'-p'q}(q'), \ \ \ \log|w|=\frac{h+k}{pq'-p'q}(q).$$ Again they are not in our domain.
Finally, $(0,0)$, $(z, 0)$ and $(0, w)$ cannot be intersection points for suitable choice of $\epsilon_i$. This can be check directly.
3. In the region $\{0<|z| \le \delta\} \times \{0<|w| \le \delta\} $, $\epsilon_i$ are constant. The statement follows from that the coordinate functions $x_1$ and $x_2$ are holomorphic with respect to $z$ and $w$.
Finally, we consider the case that $\frac{p}{q} =\frac{p'}{q'}$. W.L.O.G, we only consider the case that $x_0>0 $ and $R'(x_0)=\frac{p}{q}< \frac{1}{2}$. The argument for the other cases are the same. Consider $$u(z)=\left( (1+ \epsilon_1)\frac{1}{2}e^h z^p + \frac{1}{2}e^{-h} z^{q-p} + \epsilon_2, -(1+ \epsilon_1)\frac{i}{2}e^h z^p + \frac{i}{2}e^{-h} z^{q-p} \right)$$ and $$v(z)=\left( \frac{1}{2}e^{h+iy_0} w^p + \frac{1}{2}e^{-h-iy_0} w^{q-p} , -\frac{i}{2}e^{h+iy_0} z^p + \frac{i}{2}e^{-h-iy_0} w^{q-p} \right).$$
$u$ and $v$ satisfies the following properties:
1. For sufficiently small $\epsilon_i$ and $\delta$, then $u$ and $v$ are embedded except at $z=0$.
2. Assume that $\epsilon_1 \gg_{\delta} \epsilon_2$ and $y_0$ is generic, then all the intersection points of $u$ and $v$ lies in the region $\{0<|z| \le \delta\} \times \{0<|w| \le 2\delta\} $.
3. The intersection is transversal and the sign of the intersection points are positive.
We only prove the second conclusion. Let $(z, w)$ be the intersection point, then $$\begin{split}
&(1+ \epsilon_1)\frac{1}{2}e^h {z}^p + \frac{1}{2}e^{-h} z^{q-p} + \epsilon_2= \frac{1}{2}e^{h+iy_0} {w}^{p} + \frac{1}{2}e^{-h-iy_0} w^{q -p}\\
& -(1+ \epsilon_1)\frac{i}{2}e^h {z}^p + \frac{i}{2}e^{-h} z^{q-p}= - \frac{i}{2}e^{h+iy_0} {w}^{p} + \frac{i}{2}e^{-h-iy_0} w^{q-p}.
\end{split}$$ Then $$\label{eq10}
\begin{split}
&(1+ \epsilon_1)e^h {z}^p + \epsilon_2= e^{h+iy_0}{w}^{p} \\
& e^{-h} z^{q-p} + \epsilon_2= e^{-h-iy_0} w^{q-p}.
\end{split}$$ If $|z| \ge 2\delta$, then we have $\epsilon_i=0$, $z^p=e^{iy_0}w^{p}$ and $z^q=w^q$. Using polar coordinate, it is easy to check that $\frac{p}{q}= \frac{y_0+ 2\pi k }{2\pi l} $ for some $k, l \in \mathbb{Z}$. For generic $y_0$, this is impossible. Thus there is no intersection points in the region $|z| \ge 2\delta$.
If $\delta \le |z| < 2\delta$, then by (\[eq10\]), we have $$\begin{split}
&(1+ \epsilon_1) |z|^p - e^{-h} \epsilon_2 \le |w|^p \\
&|w|^{q-p} \le |z|^{q-p} + e^{h} \epsilon_2.
\end{split}$$ Hence, $$\begin{split}
(1+ \epsilon_1) |z|^p \le |z|^p \left( 1 + e^h \frac{\epsilon_2}{|z|^{q-p}} \right)^{\frac{p}{q-p}} + e^{-h} \epsilon_2 \le |z|^p + c_0\frac{e^h \epsilon_2}{ |z|^{q-2p} } +e^{-h} \epsilon_2.
\end{split}$$ Therefore, $$\delta^p \epsilon_1 \le c_0 \delta^{2p-q} \epsilon_2.$$ This is impossible provided that we choose $\epsilon_1 =100 c_0 \delta^{p-q} \epsilon_2$. In conclusion, the only possibility is that $0 \le |z| \le \delta$. From (\[eq10\]), it is easy to deduce that $0 \le |w| \le 2 \delta$.
Finally, it is straightforward to check that $ (0,0)$, $(z, 0)$ and $(0, w)$ cannot be intersection points.
For $\frac{p}{q} \ne \frac{p'}{q'}$, then $Q_{\tau}(\gamma_{\frac{p}{q}}, \gamma_{\frac{p'}{q'}} )$ is equal the intersection number of $u$ and $v$. The number is equal to the number of solutions to equations (\[eq11\]) or( \[eq12\]) or( \[eq13\]) which lie inside the region $\{0<|z|, |w|< \delta\}$. Keep in mind that our $\epsilon_i$ are constant in this region rather than functions. According to the theorem of Bernshtein [@DNB], equations (\[eq11\]) or (\[eq12\]) or (\[eq13\]) have total number of $ \max\{ p(q'-p'), p'(q-p)\}$ solutions in $\mathbb{C}^* \times \mathbb{C}^*$. However, there are $|pq'-qp'|$ solutions outside the region $\{0<|z|, |w|< \delta\}$, in fact, the estimates in the proof of Lemma \[lem11\] implies that these solutions lie in the region $\{1\le |z|, |w|\}$. To see this, note that the unperturbed equations (\[eq11\]) or (\[eq12\]) or (\[eq13\]) ($ \epsilon_i=0$) has exactly $|pq'-qp'|$ solutions in the region $\{1< |z|, |w|\}$. By limit argument, the same conclusion holds provided that $\epsilon_i$ small enough. In conclusion, $$Q_{\tau}(\gamma_{\frac{p}{q}}, \gamma_{\frac{p'}{q'}}) = \max\{ p(q'-p'), p'(q-p)\} -|pq'-p'q|= \min\{p(q'-p'), p'(q-p)\}.$$
Note that $Q_{\tau}(e_{\frac{p}{q}}) =Q_{\tau}(h_{\frac{p}{q}}) =Q_{\tau}(e_{\frac{p}{q}}, h_{\frac{p}{q}}) $ with respect to our trivialization, so the relative self intersection number is equal to the number of solutions to (\[eq10\]) in the region $\{0<|z|, |w|< \delta\}$. Again, by Bernshtein’ theorem [@DNB] and the same argument as before, $Q_{\tau}(e_{\frac{p}{q}}, h_{\frac{p}{q}}) = p(q-p)$.
Relative Chern number
----------------------
The main result of this section is the following lemma:
\[lem10\] Let $\alpha =\Pi_i \gamma_{\frac{p_i}{q_i}}$ be an orbit set with $P=\sum_i p_i$ and $Q=\sum_i q_i$, then $c_{\tau} (\alpha)=Q$.
First of all, note that the relative Chern number satisfies the additive property $$c_{\tau}(\alpha)=\sum_i c_{\tau}(\gamma_{\frac{p_i}{q_i}}).$$ Thus it suffices to compute $c_{\tau}(\gamma_{\frac{p}{q}})$.
By definition, $$4x^2=4|\hat{p}|^2|\hat{q}|^2=(|x_1|^2 + |x_2|^2)^2 - |\pi(x_1, x_2)|^2=2|x_1|^2 |x_2|^2 - \bar{x}_1^2 x_2^2 - x_1^2 \bar{x}_2^2.$$
Differentiate both side of above identity, we have $$4xdx=(x_1\bar{x}_2-\bar{x}_1 x_2) (x_2 d \bar{x}_1-\bar{x}_2 dx_1 + \bar{x}_1 dx_2 - x_1d\bar{x}_2).$$ Note that $4x^2 =-(x_1\bar{x}_2-\bar{x}_1 x_2 )^2=4 (Im(x_1 \bar{x}_2))^2$. Along the periodic orbits at $x \ne 0$, we can check that $x=Im(x_1 \bar{x}_2)$. Therefore, $$dx= \frac{i}{2} (x_2 d \bar{x}_1-\bar{x}_2 dx_1 + \bar{x}_1 dx_2 - x_1d\bar{x}_2),$$ along the periodic orbit. In addition, it can be defined along the periodic orbit at $x=0$.
Let $J \in \mathcal{J}_h(E, \omega_E)$ be an almost complex structure such that $J(\partial_x) =\partial_y$ near $1-\delta \le r \le 1$ and $J=J_0$ near the critical point. Therefore, $dx + idy= dx + iJdx {\pm} iR_r' ( \pm x) dt$ near $x \ne 0$ and $1- \delta \le r\le 1$. $T^{1, 0}_J E $ is generated by $$\begin{split}
ds+ idt, \ \ \ \ dx+iJdx {\pm}\frac{R_r'({\pm}x)}{2}(ds +idt).
\end{split}$$ Define a section $\psi= (ds + idt )\wedge ( dx+iJdx \pm \frac{R_r'(\pm x)}{2}(ds +idt)) = \frac{\bar{z}dz}{|z|^2}\wedge ( dx+iJdx )$, where $z = \pi( \textbf{x})$. Near the critical point of $\pi$, $ dx+iJdx = dx+iJ_0dx= -i \bar{x}_2 dx_1 +i \bar{x}_1 dx_2$. Therefore, $$\begin{split}
\psi=\frac{2 \bar{z}}{|z|^2}(x_1dx_1 + x_2 dx_2)\wedge (-i \bar{x}_2 dx_1 +i \bar{x}_1 dx_2) = 2i\bar{z} dx_1 \wedge dx_2.
\end{split}$$ Therefore, we can extend $\psi$ to a section of $T^{2, 0}_J E$ over the whole $E$.
Obviously, $\psi$ is a nowhere vanishing except at $z=0$. Let $u: D \to E$ be the unperturbed version of (\[eq3\]) or (\[eq4\]), $\psi \vert_u$ vanishing at the critical point and the vanishing order is $-q$. Therefore, $c_{\tau}(\gamma_{\frac{p}{q}})=- \#\psi^{-1}(0)=q$.
Energy
------
In this section, we write down a formula for the $\omega_X$-energy and deduce a constraint on the relative homology class. Let $Z_{\alpha} \in H_2(E, \alpha)$, the energy is denoted by $E(\alpha)$. By Stoke’s theorem, $E(\alpha)=\int_{\alpha} \theta_E$. At $x_0 \ge 0$ and $R'(x_0)=\frac{p}{q}$, $$E(\gamma_{\frac{p}{q}}) =\int_0^q \left(x_0R'(x_0) - R(x_0) \right)dt =x_0p -R(x_0 )q .$$ At $x_0 \le 0$ and $R'(-x_0)=1-\frac{p}{q}$, $$E(\gamma_{\frac{p}{q}}) =\int_0^q \left(-x_0R'(-x_0) - R(-x_0) \right)dt =-x_0R'(-x_0)q - R(-x_0 )q = x_0(p-q) - R(-x_0)q.$$ Therefore, $$E(\alpha) = \sum_i \left( |x_i| R'(|x_i|) -R(|x_i|) \right) q_i.$$ By our formula of $R$, it is easy to show that $E(\alpha) \le {Q}$. Note that for critical point $a$ of $f $ and $S=\{a\} \times D$, we have $E(S)=0$. Thus for $Z_{\alpha} \in H_2(X, \alpha)$, we still have $E(\alpha) \le {Q}$.
As the case for ECH index, for $Z_{\alpha}+ m[F] \in H_2(X, \alpha)$, $$E(\alpha + m[F]) = E(\alpha) + m \int_{F} \omega_X.$$ Combine this formula and (\[eq14\]), they satisfy the relation $I(Z_1)-I(Z_2)= c(E(Z_1) -E(Z_2))$ for some constant $c \ne 0$. Thus the cobordism map can be defined over $\mathbb{Z}$-coefficient.
\[lem3\] Given positive integer $Q$, we can choose a suitable symplectic form $\omega_S$ with the following property: For any orbit set $\alpha$ with degree less than $Q$, $J \in \mathcal{J}_h(X, \omega_X)$ and $m<0$, then there is no holomorphic current $\mathcal{C}$ with relative homology class $Z_{\alpha}+ m[F]$.
According to above discussion, $ E(\alpha + m[F]) \le {Q} + m \int_{F} \omega_X. $ By Lemma \[lem1\], we can choose a symplectic form $\omega_S$ such that $\int_{F}\omega_X \gg Q$, then $E(\alpha + m[F]) <0$. However, our $(X, \pi_X, \omega_X )$ is nonnegative, this implies $E(\mathcal{C}) \ge 0 $ for any $J$ holomorphic current. Therefore, the class $Z_{\alpha} + m[F]$ has no holomorphic representative.
\[lem8\] Given an orbits set with degree $Q$, for a suitable choice symplectic form $\omega_S$ and for any $\Omega_X$-tame almost complex structure $J$ which is sufficiently close to $ \mathcal{J}_h(X, \omega_X)$, then the conclusion in Lemma \[lem3\] still holds.
Given $\epsilon_0>0$, then for any almost complex structure $J$ which is sufficiently close to $ \mathcal{J}_h(X, \omega_X)$, we have $E(\mathcal{C}) \ge -\epsilon_0$ for any $J$-holomorphic current. Otherwise, we can find a sequence of $\Omega_X$-tame almost complex structures $\{J_n\}_{n=1}^{\infty}$ and $J_n$-holomorphic currents $\mathcal{C}_n$ such that $J_n \to J_{\infty} \in \mathcal{J}_h(X, \omega_X)$ and $E(\mathcal{C}_n)< -\epsilon_0$. According to Taubes’ Gromov compactness (Cf. Lemma 9.9 of [@H4]and [@H3]), $\mathcal{C}_n$ converges to a $J_{\infty}$ holomorphic current (possibly broken) $\mathcal{C}_{\infty}$, in addition, $E(\mathcal{C}_{\infty}) \le -\epsilon_0<0$, contradict with $J_{\infty} \in \mathcal{J}_h(X, \omega_X)$.
The rest of the argument is the same as Lemma \[lem3\].
Cobordism map
=============
In this section, we show that the definition of \[eq2\] make sense and prove the main theorem.
\[lem6\] Let $C \in \mathcal{M}^J(\alpha, Z_{\alpha} + m[F])$ be an irreducible holomorphic curve and $[\alpha] \cdot [F]=q \le Q$, then the Fredholm index of holomorphic curve is $${\rm{ind}} C = 2g(C)-2 + h(C) + 2q + 4m(1-g(F))+ 2 e_+(C),$$ where $e_+(C)$ is the number of ends at $Q$-positive elliptic orbits and $h(C)$ is the number of ends at hyperbolic orbits.
By Lemma \[lem10\] and adjunction formula, $c_{\tau}(Z_{\alpha}) = q$ and $$c_{\tau}(Z_{\alpha} + m[F]) = q + mc_{1}([F]) =q+2m(1-g(F)).$$
Given a holomorphic curve $C \in \mathcal{M}^J(\alpha)$, define $e_Q(C)$ to be the total multiplicity of all $Q$-negative elliptic orbits in $\alpha$.
\[lem5\] Let $C \in \mathcal{M}^J(Z_{\alpha}+m[F])$ be a simple irreducible holomorphic curve and $[\alpha] \cdot [F]=q \le Q$. Suppose that $g(F)-1>Q $ and $J$ is generic almost complex structure which is sufficiently closed to $\mathcal{J}_h(X, \omega_X)$, then $$2C\cdot C = 2g(C)-2 + {\rm{ind} }C+ h(C) + 2e_Q(C) + 4\delta(C) \ge 0.$$ In addition, if $ {\rm{ind}} C =0$, then $C \cdot C =0$ if and only if $C $ is a special holomorphic plane which satisfies $q=e_Q=1$ and $h(C)=e_+(C)=0$.
Argue by contradiction, assume that $C \cdot C < 0$, then we must have $g(C)=e_Q(C)=\delta(C)=0$. If $h(C)=0$, then $ {\rm{ind} }C$ is even and hence $ {\rm{ind} }C=0$. According to Lemma \[lem6\], we have $$-1+e_+(C) +q+2m(1-g(F))=0.$$ On the other hand, $e_+(C) +q+2m(1-g(F)) <2q- 2mQ $. Keep in mind that $m \ge 0$ because of Lemma \[lem8\]. As a result, $m=0$. ${\rm{ind} }C= 2q-2 + 2e_+(C) =0$ implies that $e_+(C)=0$ and $q=1$. Therefore, $C$ is closed with degree $1$, this is impossible. If $h(C)=1$, then $ {\rm{ind} }C=0$, otherwise $C \cdot C \ge 0$. However, by Lemma \[lem6\], we know that $ {\rm{ind} }C$ is odd, contradiction. In conclusion, $C \cdot C \ge 0$.
Now let us assume that $ {\rm{ind}} C =0$ and $C \cdot C =0$, then we have $\delta(C)=0$ and $$2g(C)-2 + h(C) + 2e_Q(C)=0.$$ If $g(C)=0$, there are two possibilities: $$\begin{split}
& h(C)=0 \ \ and \ \ e_Q(C)=1,\\
&or \ \ h(C)=2 \ \ and \ \ e_Q(C)=0.
\end{split}$$ On the other hand, $ {\rm{ind}} C =0$ and Lemma \[lem6\] implies that $$h(C)+ 2q+2e_+(C) +4m(1-g(F))=2.$$ It is worth noting that $ 2q+2e_+(C) +4m(1-g(F)) <4q-4mQ$ due to our assumption. In either cases, we have $m=0$, otherwise, the left hand side is strictly less then $2$.
In the first case that $h(C)=0$ and $ e_Q(C)=1$, then $2q+2e_+(C) =2$ implies that $q=1$ and $e_+(C)=0$. Consequently, $C$ is a special holomorphic plane with one positive end at a simple $Q$-negative periodic orbit and has no other ends. In the second case, $q+e_+(C) =0 $ implies that $q=0$, this is impossible. If $g(C)=1$, $C\cdot C=0 $ implies that $h(C)=e_Q(C)=0$. By $ {\rm{ind}} C =0$ and Lemma \[lem6\], we have $$2q+2e_+(C) +4m(1-g(F))=0.$$ If $m \ge 1$, then the left hand side is strictly less than zero, contradiction. If $m=0$, then $q=e_+(C)=0$. $C$ is closed curve and $[C]=n[F]$ because of Lemma \[lem2\]. Adjunction formula implies that $C$ cannot have genus $1$, we obtain contradiction too.
\[lem13\] Let $\mathcal{C} \in \mathcal{M}^J(\alpha, Z_{\alpha} + m[F])$ be a holomorphic current and $[\alpha] \cdot [F] =Q$. Suppose that $ Q\ne g(F) -1$, then $I(\mathcal{C}) \ge 0$. Moreover, if $Q>g(F)-1$, then $I=0$ if and only if $m=0$ and the orbits set of the form $\alpha=(\Pi_a e_a^{m_a}) e_0^{m_0} e_1^{m_1}$ , where $a $ is critical point of $f$ with $\nabla^2 f(a)>0$.
If $ Q< g(F) -1$, then the conclusion follows from corollary \[lem5\], Proposition 4.8 of [@H5] and Theorem 4.15 of [@H2], we have $I(\mathcal{C}) \ge 0$.
If $ Q> g(F) -1$, combine (\[eq14\]), ( \[eq15\]), Lemma \[lem4\] and corollary \[lem12\], then we get the result.
Let $u: \overline{D} \to \overline{X}$ be a section which is asymptotic to a periodic orbit with degree $1$. $u$ is called horizontal section if $Im(du) \subset T\overline{X}^{hor}$.
Note that for any $J \in \mathcal{J}_h (X, \omega_X)$, the horizontal section is $J$-holomorphic. The horizontal section is rigidity in the following sense. Assume that $(X, \pi_X, \omega_X) $ is nonnegative, given an orbit set $\alpha$ with degree $1$ and $ C \in \mathcal{M}^J(\alpha)$, if $E(C)=0$, then $C$ is a horizontal section.(Cf. [@PS1])
\[thm2\] Assume that $Q \ne g(F)-1$, then for generic $\Omega_X$-tame almost complex structure $J$ which is sufficiently close to $ \in \mathcal{J}_h(X, \omega_X)$, the cobordism map $$PFH(X, \omega_X)_J : \mathds{A}(X) \otimes PFH_*(Y, \omega, Q) \to \mathbb{Z}$$ is well-defined, where $\mathds{A}(X)=[U]\otimes \Lambda^*H_1(X, \mathbb{Z})$ and $U$ is the U-map (Cf. [@H3]).
To define the cobordism map, let us consider the moduli space $\mathcal{M}_{0}^J(\alpha + m[F])$ and $\mathcal{C}=\sum_k d_k C_k \in \mathcal{M}_{0}^J(\alpha + m[F])$. Due to lemmas \[lem3\] and \[lem8\], we always assume that $m\ge0 $.
Let us firstly consider the case that $Q>g(F)-1$. Choose a generic almost complex structure $J \in \mathcal{J}_h(X, \omega_X)$. Since $Q>g(F)-1$, the element $\mathcal{C} \in \mathcal{M}_0^J(\alpha, Z_{\alpha} + m[F]) $ cannot contain closed component, otherwise $I\ge 2$. (Cf. Lemma 5.7 of [@GHC])
By corollary \[lem13\], $I(\mathcal{C}) \ge 0$ for any holomorphic current. Moreover, then $I=0$ implies that $m=0$ and the orbits set of the form $\alpha=(\Pi_a e_a^{m_a}) e_0^{m_0} e_1^{m_1}$ , where $a $ is critical point of $f$ with $\nabla^2 f(a)>0$. Thus let us assume $\alpha=(\Pi_a e_a^{m_a}) e_0^{m_0} e_1^{m_1}$ and $m=0$. Since $E(\alpha)=0$, the only element in $\mathcal{M}_0^J(\alpha)$ is of the form $\mathcal{C}=\sum_a m_a C_{e_a} + m_0 C_{e_0} +m_1 C_{e_1}$, where $C_{e_*}$ is horizontal section of $\pi_X: \overline{X} \to \overline{D}$. To see this, first note that $E(C_k)=0$ implies that $TC_k \subset T\overline{X}^{hor}$. Thus the ends of $C_k$ agrees with the trivial cylinders. $C_k$ is embedded, thus the ends of $C_k$ can only asymptotic to a simple orbits, either $e_0$ or $e_1$ or $e_a$. $C_k$ agrees with horizontal sections on the ends. However, the intersection of two different embedded holomorphic curves is isolated. Therefore, $C_k$ must be horizontal section.
Therefore, $\mathcal{M}_0^J(\alpha)$ consists of only one element and it automatic compact. Then we define $PFC(X, \omega_X) \alpha=\# \mathcal{M}_0^J(\alpha) $ and $PFC(X, \omega_X) =0 $ otherwise.
To show that it is a chain map, i.e. $PFC(X, \omega_X ) \circ \partial =0 $, it suffices to show that $PFC(X, \omega_X ) \circ \partial \beta=0 $ for ECH generator $\beta$ satisfying $<\partial \beta, \alpha > \ne 0$. Consider $\mathcal{C} =\sum_k d_k C_k \in \mathcal{M}_1^J(\beta, Z_{\beta}+ m[F])$, according to Lemma \[lem4\] and Theorem \[thm1\], (\[eq15\]) and (\[eq14\]), $I_m(\beta)=1$ implies that $m=0$ and $\beta$ doesn’t involve $Q$-positive elliptic orbit. In this case, one can show that $C_k \cdot C_k \ge 0$ and $d_k>1$ only when $C_k$ is the special holomorphic plane with ${\rm{ind}} C_k=h(C_k)=e_Q(C_k)-1=0$. (Cf. Prop 3.16 [@CG]) A broken curve arising as a limit of curves in $\mathcal{M}_1^J(\beta)$ consists of holomorphic curve with $I=1$ in the top level, curve with $I=0$ in the cobordism level, and connectors(Branched cover of trivial cylinder) between them. Make use of the gluing analysis in [@HT1] and [@HT2], $PFC(X, \omega_X ) \circ \partial \beta =0 $. (When we glue the copy of horizontal sections and the $I=1$ curve, we don’t need to insert any connector in between, otherwise, the result cannot have Fredholm index $1$. )
If $Q< g(F)-1$, choose a generic $\Omega_X$-tame almost complex structure which is sufficiently closed to $ \mathcal{J}_h(X, \omega_X)$. By Lemma \[lem2\], we know that closed holomorphic curve has homology class $m[F]$ for $m \ge 0$. However, $I(m[F])<0$, this is impossible for generic $J$. Hence, there is no closed component in $\mathcal{C}.$ According to Prop 4.8 of [@H5] and Corollary \[lem5\], $I(\mathcal{C})=0$ implies that
1. $I(C_k)={\rm{ind}} C_k =0$ and $C_k$ is embedded for each $k$.
2. $C_k \cdot C_l=0$ for each $k \ne l$.
3. 1. If $C_k \cdot C_k >0$, then $d_k=1$.
2. If $C_k \cdot C_k =0$ and $d_k>1$, then $C_k$ is the special holomorphic plane which is asymptotic to a simple $Q$-negative periodic orbit with degree $1$.
Therefore, $\mathcal{C} = \mathcal{C}_0+ \sum_a d_a C_{e_a} + d_1C_{e_1} + d_0 C_{e_0}$, where $\mathcal{C}_0$ is embedded holomorphic current with $I=0$, $C_{e_*}$ is holomorphic plane which is asymptotic to $e_*$ and $e_*$ is $Q$-negative elliptic orbit. One can follow the same argument in Prop 3.14 of [@CG] to show that $\mathcal{M}_{0}^J(\alpha )$ is a finite set. As a consequence, the definition \[eq2\] make sense in this case. Again, make use of the gluing analysis in [@HT1] and [@HT2], we have $PFC(X, \omega_X ) \circ \partial =0 $. Finally, in ether cases, it is not difficulty to extend the cobordism map over ring $\mathds{A}(X)$.
\[Proof of Theorem \[thm3\]\]
- If $Q>g(F)-1$, according to the proof of Theorem \[thm2\], we know that $PFC(X, \omega_X) \alpha=0$ unless that $\alpha=(\Pi_a e_a^{m_a}) e_0^{m_0} e_1^{m_1}$, where $a$ is critical point of $f$ with $\nabla^2 f(a)>0$. Let us assume that this is the case, then there is only one element in $\mathcal{M}_0^J(\alpha)$. According to [@CG], the sign is positive and hence $ \# \mathcal{M}_0^J(\alpha)=1$.
- Now let us consider the second case that $2Q+1<g(F)$. Without loss of generality, we may assume that there is no critical point $\{a\}$ such that $\nabla^2f(a)>0$. By Theorem 5.3 of [@H1] and our assumption, the generators of $PFH(Y, \omega, Q)$ are represented by of orbits set $\alpha = (\Pi_a h_a) \alpha_0$, where $\{a\}$ is saddle point of $f$. Let us assume that the degree of $\Pi_a h_a$ are $q_h$. Then $\alpha_0$ is an orbits set of index $0 \le I_0(\alpha_0) \le 2Q'-1$ and $Q'=Q -q_h$.
By Lemma \[lem4\] and Theorem \[thm1\] and \[eq14\], $$I_m(\alpha)=q_h + I_0(\alpha_0)+ 2m(Q+1-g(F)).$$ By our assumption, $I_m(\alpha) < q_h +I_0(\alpha_0) -2m Q \le 2Q -2mQ$. According to Lemma \[lem8\], we may assume that $m\ge 0$. Therefore, $I_m(\alpha)<0$ unless $m=0$. When $m=0$, $I_0(\alpha)=0$ if and only if $q_+=q_h=I_0(\alpha_0)=0$, i.e. $\alpha= e_0^{m_0} e_1^{m_1} $.
By the automatic transversality theorem [@Wen], for any $J \in \mathcal{J}_h(X, \omega_X)$, the unbranched cover of holomorphic planes in $\mathcal{M}^J_0(\alpha)$ are regular. Therefore, for $J \in \mathcal{J}_{tame}(X, \omega_X)$ which is sufficiently close to $ \mathcal{J}_h(X, \omega_X)$, $\mathcal{M}_0^J(\alpha, {Z}_{\alpha})$ also consist of one element with positive sign.
` E-mail adress: guanheng.chen@adelaide.edu.au `
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The night is dark but the cave yonder is darker.
You tremble at the crumbling entrance, holding your flickering lantern out, keenly aware of the shrilling of the wind and the never-ending pattering of thousands and thousands of tiny feet.
A voice, <i>her</i> voice, crackling and paper-like, floats from within, "Come in. Douse your lantern. They do not take kindly to the harsh light you bring in so willingly".
[[Flee back to safety]]
[[Douse your lantern and enter the lair]]It was a mistake to come.
You turn and run back along the path by the creek, back to the anxiously waiting village, the worried households, the tearful, the sick, the dying.
The villagers ask whether you have brought back a piece of the Spider Mother's magical cloth.
[[Lie to them]]
[[Tell them the truth]]The last thing you see clearly under the light of the full moon is the Spider Mother's writhing hive of grey hair and millions of black eyes staring, tiny bodies motionless for an instant, tiny legs pointing towards you.
Doused into darkness.
The horror.
[[You take a step forward.]] You attempt to smile and lie.
But it is obvious that your hands are empty.
Despair crawls into the groaning beds of the infirm.
Many villagers turn their heads away. You can hear them weeping desperately as they make their way home.
You can also hear...very faintly...
[[...the sounds of tiny feet...]]You try to speak of the fear but the words don't come.
It doesn't matter. They can see it in your eyes.
A young mother wails nearby before dashing back to her sick baby.
Everyone begins to shuffle away, hopelessly and silently.
Without the cloth's magical healing properties, many will not see the sun rise tomorrow.
Perhaps, tomorrow night, they will send someone else, someone brave, to the cave.
[[Perhaps you will try again.->Entrance to the lair]]
[[No, you will never return to that horror.->...the sounds of tiny feet...]]The shame burns.
You turn around and make your way home.
It feels like hundreds of eyes watch you all the way.
You should never have volunteered to go to the Spider Mother's lair.
As you blow out the candle on your bedside table, you notice that very little moonlight is coming through your bedroom window.
You squint at the window.
[[There seem to be cobwebs.]] Very thick cobwebs.
And thousands of very tiny unblinking eyes.
They gleam and you know that they have come for you.
To take you back to the lair.
[[To her.->Entrance to the lair]]In the darkness, you think of the old tales and you pray for her mercy.
No comely wench is she who resides in the lair beside the creek.
Her eyes are pale, the pupils like golden grit, trapped beneath the hardened wrinkles and withered lips.
Her nose is arched, like a cruel bird’s beak, peering imperiously at visitors.
They say she has no eyebrows, no eyelashes, the tiny hairs having fallen off, like the years she has fallen from.
They say Father Time has no hold of her, that she is a demon with spiders for consorts, a seductress who in her youth would ride upon the back of a colossal arachnid.
They speak her name in fear, in awe or in thrall.
<i>The Spider Mother.</i>
[[You continue to creep forward.]]
[[It's not too late to change your mind. Leave the cave.->Flee back to safety]]You can barely make out your boots in the darkness and tread as lightly as you dare.
Her light grey hair is her crown, her throne, the carpet on which one walks, upon entering her domain.
It is alive, that hair. Thin and silver-grey, forever writhing it is, in this fearsome lair.
Because spiders of all sizes and colours live in it, constantly running in and out, scuttling to their webs, dragging their wrapped prey to hidey-holes, all within her mane, so thin yet altogether terribly thick.
Unperceivable order within that dark tangled confusion of silvery hair smiles in the darkness. You find it hard to swallow.
[[She's no fool, this witch.]]Her spider children whisper everything they learn by windowpanes, wall hangings and fireplaces into her prune-like ears.
They bring knowledge of what goes on in the village by the creek, tales of knights and war in distant lands, gossip and intrigue within kings’ courts, secrets Mother Nature makes known only to her miniature offspring.
[[Wisdom unimaginable.]]The twisting passage forces you to find your way carefully by what little light comes from fractured skylights created by the ancient roots of trees above.
Each time you hear a crunch beneath your feet, you flinch.
Tiny feet continue to patter about you.
A sea of glittering black eyes reflects the scant moonlight.
Eventually, you reach the woman with the medicinal knowledge, the woman with wisdom imparted from the whispering rattles of spiders.
[[The Spider Mother.]]You can barely see her.
She rests on her throne of hair and skittering arachnids, slowly weaving the mythical blanket of healing properties.
Best not to lie for the spiders know everything. You lower your head and beg in the darkness.
"Please, oh please, may I have but a snippet of your magical cloth that we may heal the sick child, cure the young dying mother, save the old man who is suffering in his son’s bed, nurse back to health the baby who wastes away in the cradle..."
[[Your list goes on and on.]]A long silence seems to follow your plea.
And then you realise that the spiders are whispering into her shrunken ears. You strain harder to see in the darkness.
The spiders swarm upon her cloth, and <i> click click</i>, they cut away cleanly.
[[One final horror follows.]]You stand, paralysed in the darkness, as hundreds of spiders swarm up your body to pass the woven gift into your sweaty hands.
As swiftly as they came, the tiny invisible hairy legs make their quiet descent.
When you are sure that the last spider has left your legs, you express your thanks and leave as hastily and politely as you dare.
But halfway home along the path, you are ambushed and brought to your knees.
The highwayman asks you to hand over the Spider Mother's cloth and tells you to get more for yourself later.
When you hesitate, he slashes your right forearm. You cry out and drop your lantern.
[[You are unarmed. Hand over the cloth.]]
[[No, the cloth is priceless. It is worth dying for.]]You choose to live. Perhaps you can brave the cave once more.
You hand over the cloth with your left hand and hope that the bandit will be merciful.
[[You were wrong.]]You lick your lips and try to think of a way to disarm the bandit.
It becomes clear to the bandit that you will not hand over the Spider Mother's blessing.
As he raises his blade in anger, you both hear an unearthly roar.
[[It all happens so quickly.]]You raise your arms to defend yourself, but the ugly blade comes down again and again.
As you fall to the blood-stained ground, you hear an unearthly roar.
[[Your vision begins to fade but you try to make sense of what is happening.]]There appears to be a tremendous thrashing, the likes of which you've never seen before, and tree branches are flailing in every direction.
You catch a hellish glimpse of eight colossal eyes flashing in anger from up above, before too many leaves obscure your vision.
The last thing you hear before lose consciousness is the sound of the screaming highwayman being torn into two.
.
.
.
.
.
[[You feel a strange sensation, as if you were being rocked gently in a cocoon. There are little rattling noises. After a while, you open your eyes and get up and realise that you are no longer bleeding or in pain. You are near the mouth of the lair once more.->You take a step forward.]]It takes a moment for the two of you to realise that you are both under the shadow of a colossal beast.
Eight enormous eyes flash in anger, as two hairy gargantuan legs pick up the screaming highwayman.
The creature disappears into the forest as quickly as it came with a tremendous thrashing. Tree branches flailing in the trail it leaves behind slowly come to a still.
[[You slowly realise that you have been clutching the cloth tightly to your chest all this while and get up.]]Gleaming yellow eyes watch you all the way down to the village by the creek, the silently and fearfully and anxiously and then tearfully waiting village.
Wordlessly, you hand over the soft cloth to a village elder, who divides it quickly before handing it out, for it seems to stop thriving upon being separated from its weaver.
Glistening silver and thick, the cloth rapidly thins and is wont to vanish into the air so it must be placed onto the skin of sickly ones quickly, where it appears to melt into the flesh.
You watch the healing.
[[It is both awful and miraculous to behold.]]Like spider legs, the threads come alive and grasp about only to sink their way into the flesh of their patients who are instantly revived. Like corpses saved from the grave, they dance up and rejoice with a most strange agility granted by the spider-blessed cloth.
Someone notices your bloody arm and offers to wash and bandage it. You let yourself be taken away, weary from tonight's horror.
[[You think back to the warnings of the old tales.]]Those who want the cloth for ill use are warned not to ask for it but still, in they go and never do they come out of the dark lair, their cries echoing into the mountains as they receive their punishment from the spiders.
And on her throne of hair, The Spider Mother watches and smiles.
.
.
.
.
.
[[Visit the Spider Mother's lair again, if you dare.->Entrance to the lair]] |
I agree with Cole and Ohanian that the NIRA aborted a promising recovery after July 1933. I disagree with Paul Krugman on this issue. And unlike most Keynesians, I don’t think the recovery from the Great Depression under FDR was very impressive. Much of the recovery was due to productivity growth (until 1941.)
And yet I find myself once again to be very irritated by an argument against the demand-side view put forward by Cole and Ohanian:
The main point of our op-ed, as well as our earlier work, is that most of the increase in per-capita output that occurred after 1933 was due to higher productivity – not higher labor input. The figure [at the link] shows total hours worked per adult for the 1930s. There is little recovery in labor, as hours are about 27 percent down in 1933 relative to 1929, and remain about 21 percent down in 1939. But increasing aggregate demand is supposed to increase output by increasing labor, not by increasing productivity, which is typically considered to be outside the scope of short-run spending/monetary policies.
I originally read this quotation over at MR, and immediately thought; “When has a Keynesian ever argued that there was a robust demand-side recovery from 1933 to 1939?” I’ve read just about everything ever written on the subject, and I’ve never heard that argument made. Instead, Keynesians argue that demand stimulus led to a fast recovery during 1933-37, and then tight monetary and fiscal policies caused a severe relapse in 1938. So why would Cole and Ohanian pick those dates?
As soon as I clicked over to the Stephen Wiliamson post where Tyler found the argument, I immediately knew the answer. Cole and Ohanian present a graph that strongly supports the AD view of the recovery from the Great Depression. Hours worked went from being 27% below normal in 1933, to only 17% below normal in 1937, the cyclical peak. That means an extra 2.5% per year. Using Okun’s Law, I’d guess that gets you about 5% RGDP growth per year. Now the actual rates were substantially higher during 1933-37, as productivity also grew briskly. But the hours worked finding basically follows the predictions of AD models. Even Keynesians believe the economy was still far from full employment in 1937.
Then hours worked plunged between 1937 and 1939, in response to the sharp fall in AD (as measured by NGDP) during 1938. Again, this is perfectly consistent with demand-side explanations of the 1930s. Indeed it’s the standard view. BTW, I happen to think a massive adverse supply-shock also reduced hours worked and output during 1938, so my position is actually intermediate between C&O and the Keynesians. Looking at the entire period from 1929 to 1939, the blue line (hours worked) is highly correlated with changes in AD (i.e. NGDP.)
I think aggregate supply mattered a lot in the Great Depression. But none of the data presented by C&O refutes the argument that demand played a major role in the Depression, indeed it strongly supports that view.
PS. I’d be interested in whether the C&O data include hours worked on government jobs programs. Official government unemployment data from that period is highly inaccurate, as they treat millions of WPA/CCC workers as “unemployed.”
PPS. In case anyone wonders why I view the 1933-37 recovery as disappointing, despite high RGDP growth rates, consider that industrial production grew 57% between March and July 1933, due to dollar devaluation. Then FDR raised nominal wages by 20% in late July, as part of the NIRA. Monthly industrial production data fell immediately, and didn’t regain July 1933 levels until after the NIRA was declared unconstitutional in May 1935. This led to rapid growth in late 1935. Because of the way annual GDP data averages over entire years, the RGDP growth from 1933-35 looks deceptively steady and impressive. It wasn’t.
Update: I just noticed that Matt Yglesias is just as puzzled as I am by their chart.
I have often thought that, had you been magically transported back to 1935, you would have been a major critic of monetary policy at the time. The reason is FDR and the Fed allowed a huge NGDP level short fall from trend to occur during the 1933-1936 recovery. Even on a trajectory basis, they would not achieve a level target for multiple years. For that reason, you might have argued that efforts to raise NGDP, while welcome, were woefully short of what was necessary.
Which begs the question, what is the relationship between an NGDP shortfall and a real recovery? Does a persistent shortfall imply a newly-recessionary or stagnant real economy? Or just one that grows but not at trend? Obviously, 1930’s NGDP growth was above trend, just not at a trajectory that made a level target achievable within a reasonable time frame. Nevertheless, what does that above-trend growth tell us about the meaningfulness of the NGDP level shortfall construct?
BTW, by the same token, Japan’s real per capita growth, while not stellar, is arguably at trend given the country’s aging population and well-known structural issues. Certainly, the country’s employment experience is far superior to ours. How could the economy be growing at anything close trend with such a large, persistent NGDP “gap”? How would economists even determine what “trend” is after such an important demographic shift and persistent deviation from the historical trajectory? Is the concept of an “AD shortfall” supposed to explain such a long-run phenomenon?
David, Wages fell sharply between 1929-33, and hence I don’t think we needed to get back to 1929 NGDP. Fisher suggested going half way back in price terms, as I recall. In my view there was plenty of NGDP for a fast recovery, and the reason the Depression didn’t end quickly (like 1921) was the NIRA.
In my view the natural rate of unemployment in Japan is about 2%, Because of near-zero NGDP growth since 1994 the actual unemployment rate is more like 4% or 5%. That produces a one time reduction in RGDP, but doesn’t affect the long term growth rate–so in that sense I agree with you. But I still think moving up to 2% or 3% trend NGDP growth would give them a one-time boost in jobs, and that this would be quite desirable.
I thought NIRA raised nominal wages. That is, by 1935 nominal wages had recovered much of their previous fall. Thus, the NGDP-adjusted nominal wage was still way above its 1929 level in 1935. Maybe this is your point: NIRA was at fault for high unemployment. However, why not equally blame the Fed for “allowing” the NGDP-adjusted wage to be so high? Wasn’t it under their control? When it comes to real wages, what government policy does, the Fed can undo.
The above reminds me of today’s debate. The “structuralists” argue part of the reason behind high UE is government-induced uncertainty about total future employment costs (i.e. because of the new health care law). You reply to them, “you have a point, but its still the Fed’s fault for keeping NGDP too low.”
“Per capita real GDP was about 27% below trend in 1939, with more than three-quarters of this shortfall due to the continuing depression in labor. Our research indicates that New Deal industrial and labor policies, such as the National Industrial Recovery Act and the Wagner Act (the National Labor Relations Act), were the main reasons. The NIRA, for example, fostered monopoly and raised wages well above underlying worker productivity by a quid pro quo arrangement of relaxing antitrust enforcement in exchange for industry paying substantially higher wages.
In the absence of these policies, we estimate that labor input would have been about 20% higher than it was at the end of the 1930s and would have returned the economy to trend by that time.”
The SAME thing would happen with my Guaranteed Income plan – which Scott supports.
EVERYONE would get a check from the gvt. but they would auctioned off at WHATEVER rate made their labor PROFITABLE to the private sector.
This would:
1) reduce prices on all kinds of things like daycare, or yard work / remodeling in poor neighborhoods. Increasing consumption.
2) increase productivity, the human that Scott wants to talk to would speak English as a first language – because all the telemarketers would be mommies working from home, instead of Indians up all night in New Delhi.
small fun fact: they teach the girls there to speak with a southern drawl because it best covers up their accent. one of the most surreal experiences of my life (and ther ehave been many) was watching an Englishmen teach a roomful of Indian ladies to to say ya’ll.
“I’d be interested in whether the C&O data include hours worked on government jobs programs. Official government unemployment data from that period is highly inaccurate, as they treat millions of WPA/CCC workers as “unemployed.””
It’s a minor point, but I think “officially” they fixed this in the latest Historical Statistics of the U.S.
Cole and Ohanian present a graph that strongly supports the AD view of the recovery from the Great Depression. Hours worked went from being 27% below normal in 1933, to only 17% below normal in 1937, the cyclical peak.
Scott, I think you are here engaging in the same “very misleading” trick that O&C did in their original op ed, for which Krugman, you, and Glasner sent them to the woodshed. In particular, you are giving us endpoints, when if we look at the graph for the entire period, we see the opposite story.
(BTW sorry if I’m missing the whole debate here, but I think this is right…)
O&C in their latest graph are trying to show that wages and total labor hours move in opposite directions, right? So that fits their story that unemployment was because of New Deal policies that drove wage rates above market-clearing levels. (As Krugman just recently reminded us, Keynesians do NOT blame unemployment during the 1930s on wages being too high.)
That view is supported not only by the endpoints of their chart, but in the middle too. Yes, total hours per worker went up, but not when the gold devaluation occurred. Instead it started in 1934, and that was a period when wages were *falling* not rising. From 1933-1934, wage rates spiked (which I guess shows that a devaluation can turn around prices and wages, just like you tell us), but that period also showed total hours per person continuing its downward trend.
And when you get the collapse in hours per worker starting in 1937, that also goes hand in hand with a huge jump in wages.
I agree O&C had some misleading stats in their original piece, but I don’t see how your critique here to this later chart works.
David, No, it is not my argument that The Fed should try to undo the damage from things like the health care law. I think the Fed should focus on keeping NGDP growing at a constant rate, regardless of the supply-side of the economy. If the government is determined to screw up the economy, the Fed cannot and should not try to stop them–it would merely lead to an inflationary spiral.
Morgan, Why link to a misleading article.
Charlie, Thanks for the info.
Bob, I have no problem with their argument about wages, or their claim that Krugman is wrong. I also think Krugman is wrong. I do have a problem when they present misleading data to try to suggest that the evidence is inconsistent with the AD-view of the Depression. In fact employment and AD are highly correlated throughout the Depression, contrary to what they claim. They are attacking an argument that no Keynesian is making. But they imply Keynesians are making that argument.
Their chart has nothing to say about the effect of gold devaluation on hours worked. Nothing. I very much doubt that industrial output could rise 57% in 4 months with no increase in hours–that would be the fastest productivity growth in history.
happyjuggler, That’s a complicated question. It depends how you define monetary policy. If you define monetary stimulus as rising NGDP, then one might argue that monetary stimulus did the job. On the other hand perhaps NGDP rose because of wartime spending in 1940-41. More pro-business policies might have also helped a bit.
Tommy, That’s right, which is why it bugs me that C&O try to suggest otherwise. Bad AS policies explain the slow recovery, but the Depression itself was caused by a big fall in AD. (And then a smaller fall in 1937.)
Their chart has nothing to say about the effect of gold devaluation on hours worked. Nothing.
What do you mean by that? The chart (I think) shows that hours per adult continued to fall, even after the gold devaluation occurred. Are you saying I’m reading the chart wrong, or that no matter what the chart showed, we wouldn’t be able to conclude anything about the effect of an event happening at a certain point in the chart?
Well, I suppose re-hashing the Great Depression through modern-day ideological lenses is inevitable. I am glad Cole/Ohanian were exposed as near-frauds. (No relation btw).
But the example market monetarists should cite is Japan. That way we avoid the ancient battlegrounds and intellectual tugs-of-war over the Great Depression. Which neither side will ever “win” as partisan politics befogs everything.
Market monetarists should talk about today, and Japan. Crickey-Almighty, there is plenty to talk about.
I have a great idea!…lets pay people not to work at all and if they get a part-time job or entry level job to gain experience in a new field and make the 1st step towards independence then we stop all payments to them…this way we can provide extra incentives not to try some new career.
No – because he might just get himself impeached by the wonderful Republican deflationists.
Of course – real actual tax reform – fewer deductions and lower rates, and eliminate the corporate tax – along with credible long term spending reform – now that might well do it – with a little cooperation from the Fed.
The graph shows M1, M2, and manufacturing hours from 1929-Fall of 1930. During this time period, M1 and M2 were fairly consistent with 1929 values while manufacturing output collapsed. All this happened before the first banking panic. Money supply had nothing to do with the collapse in output! Today we see that the CPI is higher than it was in 2007 or 2008 while manufacturing output hasn’t recovered. The data points to a supply shock, not a fall in AD.
Btw, I studied at UCLA and took several classes from Ohanian, so I’d naturally side with him on this one.
I don’t have time to listen to the entire Ohanian talk, but in the part you reference he seems to be blaming “Labor Market Failure” starting in late 1929 as the cause of the Great Depression. It wasn’t AD shortfall or money supply decline. He goes on to explain the “Labor Market Failure” was rising REAL wages starting in late 1929 (as other nominal prices started to fall). He blames price collusion and Hoover’s support for trade association for the rising real wages.
It sounds like he’s arguing that sticky wages during a deflation caused the depression but he refuses to acknowledge sticky wages as a legitimate economic concept. Instead he calls sticky wages “Labor Market Failure” and blames regulation for exacerbating the stickiness.
On your supply shock question: I think there was a supply shock in 2009, but it was caused by the tight money and the subsequent financial crisis. As an example I present into evidence the rig count, which fell almost 60 percent during the financial crisis. This lowered AS, i.e., led to oil shortages early in the recovery at levels of AD lower than the previous peak.
Bob, No, the chart doesn’t show what he claims, because it uses annual data, which is very misleading. Hours soared after the dollar devaluation–as industrial production rose 57% between March and July 1933. Then hours fell sharply after wages were raised 20% in late summer–this is why hours fell slightly in 1934. The effect of devaluation on hours was strongly positive, and the effect of the NIRA was strongly negative.
Thanks Eric, I’m number three!
Ben, Yes, Japan is what we should be worried about.
Morgan, There are billions of articles I don’t link to, do you think I am afraid of all of them?
Gabe, Yes, it’s called unemployment comp.
JimP, Yes, that’s the problem.
John, Money was extremely tight in late 1929 and early 1930. Between October 1929 and October 1930 the monetary base fell at one of the sharpest rates of the whole 20th century. If you are going to talk about the money supply that’s the one to pay attention to. But as you may know I think all monetary aggregates, even the base, are unreliable indicators of policy. We know money was tight because NGDP plunged in 1929-30.
Unemployment benefits supported household income. Lower household income would mean lower spending and lower investment. Let’s not forget household debt to GDP was not far south of 100% in 2009. Not extending benefits would have been a disaster.
Do you really believe that cutting benefits would promote growth and that job openings would magically appear?
By the way according to the BEA NGDP rose 17% in 1934, 11% in 35 and 14% in 36. Don’t expect much do you.
That sounds so incredibly crazy. What if the government had set the minimum wage to $100 an hour? What if they had made it illegal to produce, distribute, or use oil? NGDP would collapse and it would have nothing to do with money being tight or not. This is basically what Cole & Ohanian are arguing and you’re saying it only comes down to money. It’s absurb. Money is a medium of exchange not the fountainhead of economic growth.
I came across this thread a year late while doing some economic history research, and something struck me reading this thread.
How does this NGDP macroeconomic mindset deal with the economic growth spurred by marginal tax cuts. The first historical example came from Andrew Mellon’s marginal tax cuts following the First World War. The second example was LBJ’s passage of the Kennedy tax cuts inspired by Robert Mundell. Finally the Reagan marginal tax cuts coupled with Volcker’s sound money interest rate policy.
Dave, we allow disinflation to accomodate the RGDP boom. We don’t deviate from the NGDP level target. Supply side issues are important too, more important in the long run. But right now NGDP matters more – a lot of the supply-side problems in the US right now are the consequence of demand-side problems, of tight money.
[…] and Ohanian are comprehensively defenestrated in this blog. Hannan isn’t interested in reality and like all right-wingers of his ilk, he exists in the […]
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About
Welcome to a new blog on the endlessly perplexing problem of monetary policy. You’ll quickly notice that I am not a natural blogger, yet I feel compelled by recent events to give it a shot. Read more...
Bio
My name is Scott Sumner and I have taught economics at Bentley University for the past 27 years. I earned a BA in economics at Wisconsin and a PhD at Chicago. My research has been in the field of monetary economics, particularly the role of the gold standard in the Great Depression. I had just begun research on the relationship between cultural values and neoliberal reforms, when I got pulled back into monetary economics by the current crisis. |
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abstract: 'The effect of proximity to a Mott insulating phase on the charge transport properties of a superconductor is determined. An action describing the low energy physics is formulated and different scenarios for the approach to the Mott phase are distinguished by different variation with doping of the parameters in the action. A crucial issue is found to be the doping dependence of the *quasiparticle charge* which is defined here and which controls the temperature and field dependence of the electromagnetic response functions. Presently available data on high-T$_{c}$ superconductors are analysed. The data, while neither complete nor entirely consistent, suggest that neither the quasiparticle velocity nor the quasiparticle charge vanish as the Mott phase is approached, in contradiction to the predictions of several widely studied theories of lightly doped Mott insulators. Implications of the results for the structure of vortices in high-T$_{c}$ superconductors are determined.'
address: |
Center for Materials Theory\
Department of Physics and Astronomy\
Rutgers University\
136 Frelinghuysen Rd, Piscataway NJ 08854
author:
- 'L. B. Ioffe and A. J. Millis'
date: 'Dec 21, 2001'
title: 'D-wave superconductivity in doped Mott insulators'
---
Introduction
============
High-$T_{c}$ superconductors are created by doping an antiferromagnetic ’Mott insulating’ parent material [@Orenstein00]. A Mott insulator is a material which band theory would predict to be metallic but which, because of electron-electron interactions, is insulating [@Imada98]. It is conventional to distinguish the different doping levels as ’overdoped’, ’optimally doped’, and ’underdoped’. Optimal doping is generally defined as the carrier concentration which maximizes the resistively-defined superconducting transition temperature $T_{c}$. Overdoped materials have more added carriers and underdoped materials have fewer. All high-$T_{c}$ materials exhibit behavior which deviates from the ’Fermi-liquid-Migdal-Eliashberg’ theory which describes most metals; however, the deviations grow more pronounced as the doping is reduced towards the Mott insulator, and indeed understanding the physics of the underdoped regime (in other words, of the approach to the Mott insulating phase) has emerged as one of the crucial questions in the high-$T_{c}$ field.
High-$T_{c}$ superconductivity remains a controversial subject [@Orenstein00]. However, there is general agreement that one important phase, which may actually be observed in sufficiently clean materials, is a homogeneous superconducting phase characterized by an energy gap vanishing only along the nodal directions ($p_{x}=\pm p_{y}$ in a material with tetragonal symmetry) and possessing conventional quasiparticle and supercurrent excitations. The low temperature behavior of a d-wave superconductor is described by a general action, which depends on four parameters which are defined below. The behavior of the parameters as the Mott phase is approached is seen to reveal information about the underlying physics of the Mott transition and governs the structure of vortices and thereby the doping dependence of such macroscopic quantities as the upper critical field. In this paper (which is largely a review) we describe the information which may in principle be obtained from the low T properties, summarize the present status of the experimental values of the different parameters, and (although the presently available data are neither fully consistent nor complete) outline the apparent physical implications of the results. Two subsequent papers are planned: one presenting the derivation of the general low temperature action from different microscopic theories and one using it to analyse the vortex properties (in particular $H_{c2}(T)$ and paraconductivity) in more detail.
Specifically, in this paper we consider a homogeneous d-wave superconducting phase, assuming in particular that there is no spontaneously broken time reversal symmetry and there are no other relevant excitations apart from the quasiparticle and phase fluctuations. (We also restrict attention to two dimensional models, but this restriction can easily be lifted if desired). We find that a crucial parameter is what we define as the effective charge of the quasiparticles. This can be determined at low $T$ by relating the observed electronic specific heat and photoemission (which essentially measure the number and velocity of quasiparticles) to the temperature dependence of the London penetration depth (which is related to the ability of these states to carry an electrical current). Different scenarios for the approach to the Mott transition produce striking differences in the variation, with doping, of this charge. In particular, theories involving some form of spin charge separation seem to lead to a vanishing of the quasiparticle charge as the Mott phase is approached. We analyze available data to determine which scenario actually occurs.
One very important feature of a superconductor is the structure of vortices introduced by thermal fluctuations or via a magnetic field. A vortex is characterized by a core, which may be defined in two ways: either via the density of quasiparticle states, which is higher near the core and drops as one moves away from the core region, or via the supercurrent, which varies as $1/r$ far from the core and drops to zero inside the core. In several of the theoretical approaches to the physics of the lightly doped Mott insulator (including the one which seems to best fit the data discussed below), the core size *as defined from the supercurrent* may become very large. This, combined with the behavior of the quasiparticle charge, has remarkable implications for the size of the critical region, for the behavior of the upper critical field $H_{c2}$ and for the physics of the superconductor-insulator transition which must occur as the doping goes to zero. These implications were pointed out in [@Lee96] and will be further analysed by us in a subsequent paper.
The rest of this paper is organized as follows. In section II we present the low energy, long wavelength theory of a d-wave superconductor near a Mott insulator. In Section III we discuss the available experimental evidence concerning the value and doping dependence of the parameters of the theory. Section IV presents the limits of validity of the low energy action we discuss, along with discussion of the physics occurring when these limits are exceeded. A conclusion discusses the physical implications of our formalism and findings. The Appendix gives the details of calculations of the field dependence of the specific heat and superfluid stiffness in the vortex state.
Low Energy Theory
=================
At low temperatures the state of all (even underdoped) superconducting cuprates seems to be a conventional $d_{x^{2}-y^{2}}$ superconductor [@Tseui98; @dinunderdoped; @Shen95]: it is described by the usual low energy degrees of freedom, namely a superconducting phase variable $\phi (r,t)$ and, as will be discussed in more detail below, apparently conventional fermionic quasiparticle excitations[@Taillefer]. Gradients of the phase correspond to supercurrents. Longitudinal supercurrents lead to charge fluctuations which are coupled by the long-ranged Coulomb interaction. Transverse supercurrents are described by a *phase stiffness* $\rho
_{s}$ whose long-wavelength limit may be deduced from measurements of the London penetration depth. In high-$T_{c}$ materials, the low-$T$ limit of $%
\rho _{S}$ is strongly $x$-dependent, vanishing roughly linearly as $%
x\rightarrow 0$. This behavior is understood as a consequence of the suppression of charge fluctuations as the Mott insulating phase is approached, and appears to be related to the decrease of the resistively defined $T_{c}$ as $x\rightarrow 0$. Indeed in the very early days of high-$%
T_{c}$ Uemura and co-workers showed that in underdoped materials the ratio $%
T_{c}(x)/\rho _{s}(T\rightarrow 0,x)$ was essentially $x$-independent [@Uemura89]. At roughly the same time this behavior was shown by a number of workers to follow naturally from theoretical models of superconductivity near a Mott transition [@Kotliar], and later Emery and Kivelson argued that the behavior could be understood in a more model-independent way as a consequence of the unusually small phase stiffness characteristic of high-$%
T_{c}$ materials [@Emery95]. Recently Corson et. al reported direct evidence that in underdoped $Bi_{2}Sr_{2}Cu_{2}O_{8}$ the superconducting transition was indeed of the vortex-unbinding type driven by a small phase stiffness [@Corson98].
At scales less than maximal value of the gap, $\Delta _{0}$, the physics of a two dimensional superconductor with tetragonal symmetry and a $%
d_{x^{2}-y^{2}}$ gap function is described by an effective Lagrangian density $\mathcal{L}$ involving the phase $\phi $ of the superconductor and quasiparticles excited out of the superconducting condensate: $$\mathcal{L=L}_{\phi }+\mathcal{L}_{F}+\mathcal{L}_{mix} \label{L}$$ Here $\mathcal{L}_{F}=\partial _{\tau }-H_{D}$ is the usual Dirac action describing the ’nodal quasiparticles’ excited in the vicinity of the nodes of the d-wave gap function. In a superconductor, the fermionic energy spectrum is given by $E_{p}=\pm \sqrt{\varepsilon _{p}^{2}+\Delta _{p}^{2}}$ with $\varepsilon _{p}$ the energy spectrum of the underlying fermions and $%
\Delta _{p}$ the gap function. For a $d_{x^{2}-y^{2}}$ gap function, $\Delta
_{p}$ vanishes linearly in the four nodes, i.e. for $\overrightarrow{p}\Vert
(\pm \pi ,\pm \pi )$. It is convenient to measure momentum from the fermi point in the nodal direction and to parametrize the fermion dispersion by two velocities: one, $v_{F}$, of the order of the underlying fermi velocity describing motion perpendicular to the direction in which the gap varies, and one, $v_{\Delta }$, describing the opening of the gap and of order $\Delta _{0}/p_{F}$, obtaining $$E_{p}=\sqrt{(v_{F}p_{1})^{2}+(v_{\Delta }p_{2})^{2}} \label{Edirac}$$
We take the fermions to be normal ordered in the basis which diagonalizes $%
H_{D}$ , so the contribution of the negative energy (filled Dirac sea) states is subsumed in the phase Lagrangian density $\mathcal{L}_{\phi }$ which we write as $$\mathcal{L}_{\phi }=\frac{1}{2}\left( \partial _{i}\phi +2ieA_{i}\right)
\ast \rho _{s0}^{ij}(r-r^{\prime })\ast \left( \partial _{j}\phi
-2ieA_{j}\right) \label{Lphi}$$ Here $i$ is a Cartesian direction, $\mathbf{A}$ is the vector potential and we have allowed for non-locality in space so the $\ast $ represents convolution.
The quantity $\rho _{s0}^{ij}$ is a diagonal matrix with dimension of $%
energy/length^{2}$. Its components $\ \rho _{s0}^{xx}(r)=\rho
_{s0}^{yy}(r)\equiv \rho _{s0}(r)$ (we assume tetragonal symmetry) are related, in the absence of quasiparticle excitations, to the conventionally defined superfluid stiffness $\rho _{s}$ (measurable, e.g. from the London penetration depth) by $$\rho _{s}(T=0,H=0)=\int d^{2}r\rho _{S0}(r) \label{rhos}$$ Systems near a Mott transition are characterized by a low density of mobile charges, and we therefore expect that $\rho _{S0}(r)$ has a length dependence set by this low density.
The term $\mathcal{L}_{mix}$ gives the coupling of the phase fluctuations to the nodal quasiparticles; it may be written $$\mathcal{L}_{mix}=\sum_{\alpha ,\sigma ,p,q}\left( \frac{1}{2}\partial _{\mu
}\phi (r)\\
+ieA_{\mu }(r)\right) \cdot e^{iq\cdot r}Z_{p}^{e}\overrightarrow{v}%
_{F}\psi _{p+q/2\alpha \sigma }^{+}\psi _{p-q/2,\alpha \sigma } \label{Lmix}$$ Here $\alpha =1...4$ labels the four nodes of the d-wave state and $Z^{e}$ is a phenomenological constant which we will show below may be thought of as the charge of a superconducting quasiparticle. It may depend on position relative to the node and on the proximity to the Mott transition and will be discussed in more detail below. It has been stated in the literature that one generically has $Z^{e}=1$; but this is now known not to be correct. Eq. $%
\mathcal{L}_{mix}$ is the long wavelength limit of a more general action involving also ’pairbreaking’ terms such as $\psi ^{+}\psi ^{+}$ with coefficients of order $q$.
Physical content
================
The low energy, long wavelength theory is described by four parameters: $%
\rho _{S0}$, $v_{F}$, $v_{\Delta }$ and the quasiparticle charge renormalization $Z^{e}$.. To see how these parameters may be determined experimentally, we integrate out the fermions in the presence of static, slowly varying superflow field and vector potential, which enter via the gauge invariant combination $$\overrightarrow{Q}=\left( \overrightarrow{\nabla }\phi (r,t)-2ie%
\overrightarrow{A}\right) \label{Qdef}$$ and are taken to be slowly varying on the scales set by $\rho _{S}$ and the fermions. We obtain for the two dimensional free energy density $$F_{static}(\overrightarrow{Q})=\frac{1}{2}\rho _{S}^{0}Q^{2}\\-
2T\sum_{\alpha
}\int dEN(E)\ln \left[ 1+\exp [-(E+\frac{1}{2}Z_{p}^{e}\overrightarrow{Q}%
\cdot \overrightarrow{v}_{a})/T\right] \label{Fstatic}$$ where the 2 is for spin, the sum $(\alpha )$ is over the four nodes of the Dirac spectrum and we have introduced the single-node single-spin density of states per unit area $$N(E)=\int \frac{d^{2}p}{\left( 2\pi \right) ^{2}}\delta (E-E_{p})=\frac{E}{%
2\pi v_{F}v_{\Delta }} \label{dos}$$
The specific heat may be obtained by differentiating Eq. \[Fstatic\] twice with respect to $T$ and is $$\frac{C}{T}=\frac{T}{4\pi v_{F}v_{\Delta }}\sum_{\alpha }\int_{0}^{\infty }dx%
\frac{x(x+\frac{Z_{p}^{e}\overrightarrow{Q}\cdot \overrightarrow{v}_{a}}{2T}%
)^{2}}{\cosh ^{2}\left[ \frac{x+\frac{Z_{p}^{e}\overrightarrow{Q}\cdot
\overrightarrow{v}_{a}}{2T}}{2}\right] } \label{C/T}$$ The integral may easily be evaluated numerically for given $Q,T$. Analytical results exist in the limits $Q/T\rightarrow 0$ and $Q/T\rightarrow \infty $. The zero-field specific heat coefficient (per unit area) $C(B=0,T)$ is $$\frac{C(B=0)}{T}=\frac{18\zeta (3)T}{\pi v_{F}v_{\Delta }} \label{C(B=0)/T}$$ while in the high field low-T limit we obtain (after symmetrization) $$\frac{C(Z^{e}vQ>>T)}{T}=\sum_{\alpha =1...4}\frac{\pi Z^{e}}{%
12v_{F}v_{\Delta }}\left| \overrightarrow{Q}\cdot \overrightarrow{v}%
_{a}\right| \label{highq}$$ Averaging Eq \[highq\] over the $Q$-distribution characteristic of a vortex stateleads to the ’Volovik’ prediction [@Volovik] of a $B^{1/2}$ field dependence of the specific heat if $B_{c2}>>B>>B_{c1}$. In principle the result depends on the nature of the vortex state and on the relative angle between the lattice vectors characterizing the vortex lattice (if any) and the directions corresponding to the gap nodes in the superconducting state. We have evaluated the averages and find that the dependence is weak: $$\frac{C(B>\Phi _{0}v_{F}^{2}/T^{2})}{T}=\frac{\pi Z^{e}}{3v_{\Delta }}\left(
\frac{B}{\Phi _{0}}\right) ^{1/2}A \label{Chigh-field}$$ where $A=\pi /2$ for a square vortex lattice with nodal direction aligned with the vortex lattice vector and $A=1.52$ for $45$ degrees misalignment, similarly for a triangular vortex lattice $A=1.7$ with $5\%$ variations as the angle is varied. Some details of the calculation are presented in the Appendix.
Similarly the differential penetration depth is given by differentiating $F$ twice with respect to $Q$ . For an arbitrary current distribution $\rho _{S}$ is a tensor: $$\rho _{S}^{ab}=\rho _{S0}\delta _{ab}-\sum_{\alpha }\frac{TZ^{e2}v_{\alpha
}^{a}v_{\alpha }^{b}}{4\pi v_{F}v_{\Delta }}\int_{0}^{\infty }dx\frac{x}{%
\cosh ^{2}\left[ x+\frac{Z^{e}\overrightarrow{Q}\cdot \overrightarrow{v}_{a}%
}{4T}\right] } \label{rhosgen}$$ where $a,b$ are specific Cartesian directions and $v^{a}$ is the component of $v_{F}$ in the $a$ direction. Eq. (\[rhos(B)\]) describes among other things the nonlinear Meissner effect [@nonlinmeiss]: note however the importance of the charge renormalization factor $Z^{e}$.
In the weak field limit, $\rho _{S}^{ab}=\rho _{S}\delta _{ab}$ with $$\rho _{S}(T)=\rho _{S0}-\frac{\ln (2)Z^{e2}v_{F}}{2\pi v_{\Delta }}T=\rho
_{S0}-\frac{\ln (2)Z^{e2}v_{F}^{2}}{36\zeta (3)}\frac{C(B=0)}{T}
\label{rhos(T)}$$
The factor $Z^{e}$ is essentially the Landau parameter introduced in previous work [@Landaurefs]. Comparison of Eqs. \[C/T\] and \[rhos(T)\] shows why $Z^{e}$ is more appropriately interpreted as the quasiparticle charge renormalization. The usual f-sum-rule (Ferrel-Glover-Tinkham) arguments imply that the change, with temperature, in the condensate fraction is balanced by an increase in the ’normal’ conductivity due to quasiparticles. Now the quasiparticle conductivity is determined by the number of carriers (which follows from the specific heat, which essentially counts excitations) and their velocity, (which may be determined from photoemission). Any remaining discrepancy with the observed $%
d\rho _{S}/dT$ must then be due to their charge, i.e. to the factor $Z^{e}$. .
At large $Q$ and low $T$ we find the current-dependence of the superfluid stiffness to be $$\rho _{S}^{ab}(Q,T=0)=\rho _{S0}\delta _{ab}-\frac{Z^{e3}v_{\alpha
}^{a}v_{\alpha }^{b}}{16\pi v_{F}v_{\Delta }}\sum_{\alpha }\left|
\overrightarrow{Q}\cdot \overrightarrow{v}_{a}\right| \label{rhos(Q)}$$
Calculations similar to those for the specific heat yield, for a vortex lattice with square or triangular symmetry, $\rho _{S}^{ab}=\rho _{S}\delta
_{ab}$ with
$$\rho _{S}(B,T=0)=\rho _{S0}-A\frac{Z^{e3}v_{F}^{2}}{4\pi v_{\Delta }}\sqrt{%
\frac{B}{\Phi _{0}}} \label{rhos(B)}$$
Experimental values
===================
Overview
--------
The important parameters of the theory, $\rho _{S}$, $Z^{e},v_{F},v_{\Delta
} $ may be determined from experiment. Of these, the crucial parameter is $%
Z^{e}$. Unfortunately, the present situation is unclear because different determinations do not agree; also most measurements determine only combinations of the fundamental quantities, so that uncertainties in one propagate into uncertainties in another. In the following sub-sections section we discuss the available data for each of the three parameters, and then in a concluding subsection summarize the results and outstanding questions.
$\protect\rho _{s}$
-------------------
The $T=0$ superfluid stiffness has been reasonably well determined by muon spin rotation experiments [@Uemura89; @Sonier00] and decreases as the Mott insulator is approached. The decrease is apparently roughly proportional to hole doping. We regard this result as well established and we do not discuss it further.
v$_{F}$
-------
Angle-resolved photoemission measurements yield $v_{F}$ [@Damascelli01];. At present the generally accepted value for high-T$_{c}$ materials (both optimal and underdoped) along the zone diagonal and in the superconducting state is[@Schabel98; @Johnson01] $$v_{F}=1.8[eV-A] \label{vf}$$ The velocity apparently increases slightly as doping is decreased. There is general agreement concerning the value and doping independence of the velocity (note that even undoped materials exhibit zone diagonal velocities of approximately this magnitude). We regard this parameter as having been reasonably reliably established.
v$_{\Delta }$
-------------
The parameter $v_{\Delta }$ may be obtained in three ways: from photoemission, from zero-field specific heat, and from thermal conductivity. Each method is subject to uncertainties, as outlined below.
Photoemission investigations of the form of the superconducting gap near the nodes reveal a broadened structure, with a nonvanishing density of states in a small arc around the zone diagonal [@ARPESUD]. This could be an intrinsic effect, indicating a non-d-wave form of the gap function, or it could be due to pairbreaking or other sample and surface imperfections. However, evidence that the gapless arcs have a non-intrinsic origin is provided by penetration depth and thermal conductivity measurements discussed below, so we take this view here. An estimate of $v_{\Delta }$ from photoemission may be obtained by combining the gap maximum value $%
\Delta _{0}$, the standard $\cos (2\theta )$ d-wave form and the arc length from the zone diagonal fermi point to the gap maximum point, which is roughly $\pi /\sqrt{2}b$ with $b$ the lattice constant, leading to $$v_{\Delta }=\frac{2\sqrt{2}b\Delta _{0}}{\pi } \label{vdelta}$$ Estimates for the gap maximum range from $30-40meV$ in optimal $YBCO$ (with the large values in the direction parallel to the chains and the smaller in the direction perpendicular [@Lu01] to $40meV$ in $BSCCO$ [@Mesot99] leading to $$\begin{aligned}
v_{\Delta } &=&0.13[eV-A]\;(BSCCO) \label{vdelvalBSCCO} \\
v_{\Delta } &=&0.09-0.12[eV-A]\;(YBCO) \label{vdelvalYBCO}\end{aligned}$$ Available photoemission evidence [@Mesot99] suggests that $\Delta _{0}$ and therefore $v_{\Delta }$ if anything increase with decreasing doping; suggesting (if we interpret the maximal gap observed in the $(\pi ,0)$ direction as superconducting gap) that $v_{\Delta }$ increases with decreasing doping. These estimates rely on the assumption that everywhere in the zone the observed gap has a superconducting origin. While this assumption has been used by many workers, and appears to be supported by the good argeement between the simple d-wave form and the data of [@Mesot99], diffferent interpretations exist in which the gap in underdoped materials has a non-superconducting origin [@DDW; @Varma99].
Eq. (\[C(B=0)/T\]) shows that measurements of the low temperature specific heat yield the product $v_{F}v_{\Delta }$. Because we regard the value of $%
v_{F}$ as reliable, these measurements yield a value for $v_{\Delta }$. In optimally doped $YBCO,$ specific heat data [@Wang01] yield (in present notations [@conventions]) $$v_{F}v_{\Delta }=0.06\left[ eV-A\right] ^{2} \label{vfvdeltawang}$$ or $$v_{\Delta }=0.033\left[ eV-A\right] \label{vdeltawang}$$
This value is far outside the range of $v_{\Delta }$ suggested by photoemission. The authors of Ref. [@Wang01] suggest that the discrepancy occurs because there are additional contributions to the measured low-field specific heat (for example from chain states) which should not be included in the comparison between the model and data. This idea is consistent with recent microwave conductivity measurements [@Harris01] which find evidence for a large density of gapless excitations associated with the chains. An alternative possibility is that the gap function does not have the simple $\cos (2\theta )$ form often assumed, but instead is less strongly angle dependent near the nodes, so that $v_{\Delta
} $ is not well estimated from the maximum gap value. Reliable measurements of the low temperature specific heat for $BSCCO$ or underdoped $%
YBCO$ are not available.
Thermal conductivity measurements yield values for $v_{F}/v_{\Delta }$ [@Taillefer; @Chiao00; @Tailleferunpub]. These results rely upon a theoretical ’universal limit’ expression for the low temperature limit of a transport coefficient [@Durst00], and upon the assumption that this low temperature limit has been experimentally accessed. Measurements [@Taillefer] yield $v_{F}/v_{\Delta }=19$ for optimally doped BSCCO. For YBCO a strong doping dependence is found. As doping is decreased the ratio drops from about 19 for a presumably slightly overdoped $YBCO_{6.993}$ [@Tailleferunpub]sample to 14 for a putatively optimally doped $YBCO_{6.95}$ [@Chiao00] to 8 for the $60$ phase $YBCO_{6.73}$. [@Tailleferunpub]. These estimates suggest that $v_{\Delta }$ rapidly increases with underdoping. $$\begin{aligned}
v_{\Delta } &=&0.095\;(BSCCO,overdopedYBCO) \label{vdelthermbscco} \\
v_{\Delta } &=&0.13\;(optimally\,doped\,YBCO) \label{vdeltermybco} \\
v_{\Delta } &=&0.2(underdoped\,YBCO)\end{aligned}$$ These data are roughly consistent with the $v_{\Delta }$ inferred from the gap maximum found in photoemission; however one should bear in mind that the increase in $v_{\Delta }$ found as doping is decreased corresponds to a decrease in the value of the ’universal limit’ thermal conductivity. This could arise from an inhomogeneous sample (in which not all of the material is superconducting) or possibly from novel physics (not included in the basic action studied here) suppressing the ability of the quasiparticles in a doped Mott insulator to carry heat.
Z$^{e}$
-------
The crucial quantity $Z^{e}$ appears in combination with $v_{F},v_{\Delta }$ and so values are subject to uncertainties, particularly in the value of $%
v_{\Delta }$.
The temperature dependence of the penetration depth yields the combination $%
\frac{Z_{e}^{2}v_{F}}{v_{\Delta }}$. In YBCO certainly and in other high-$T_c$ materials, probably, the temperature dependence of the penetration depth in the direction transverse to the chains (if any) is only weakly material-dependent, and is linear at low $T$ with the slope given by [@Bonn96; @BSCCO]
$$\begin{aligned}
\frac{d\rho _{S}}{d\left( k_{B}T\right) } &\approx &0.7\hspace{0.11in}%
(YBCO6.6,6.9) \label{drhosdtYBCO} \\
&\approx &0.9\hspace{0.11in}(BSCCO,optimal) \label{drhosdtbscco}\end{aligned}$$
Note that this linearity is inconsistent with the presence of the ”gapless arcs” [@ARPESUD] in the electronic spectrum. From Eq. \[rhos(T)\] we then obtain
$$\frac{Z_{e}^{2}v_{F}}{v_{\Delta }}=6-8 \label{Z2v}$$
The ability to determine $Z^{e}$ by combining penetration depth data with values for $v_{F}$ and $v_{\Delta }$ (obtained for example from thermal conductivity data) was noted by Chiao, Taillefer and co-workers [@Taillefer]; the values obtained from the thermal conductivity data discussed above then yield $$\begin{aligned}
Z^{e} &=&0.7\;(Optimal\,BSCCO;\,Overdoped\,YBCO)\, \label{zebscco} \\
Z^{e} &=&0.8\;(Opt\,imally\ doped\,YBCO) \label{zeoptybco} \\
Z^{e} &=&1\;(60K\,\ YBCO) \label{zeudybco}\end{aligned}$$
The magnetic field dependence of the specific heat yields $\frac{v_{\Delta }%
}{Z_{e}A}$ where $A$ is a constant (discussed above) relating to the current distribution in the vortex lattice. In optimally doped $YBCO,$ high-field specific heat data [@Wang01] yield (in present notations [@conventions]) $$\frac{v_{\Delta }}{Z_{e}A}=0.09\left[ eV-A\right] \label{vdeloverza}$$ Use of our estimate $A\approx 1.7$ [@conventions] and the range quoted above for $v_{\Delta }$ yields $$0.6<Z^{e}<1$$
Recent microwave conductivity measurements [@Harris01] reveal an additional difficulty with the quantitative extraction of $Z^{e}$ in $YBCO$: in this material the deviations from tetragonal symmetry are found to lead to a strong ($\sim 50\%$) variation in the plane conductivity (which can be separated from the chain conductivity) between electric field parallel to the chain direction and antiparallel to it. This anisotropy has not been taken into account in our analysis.
Summary
-------
In summary, at present the experimental status of the parameter values characterizing the superconducting state is not completely satisfactory. The specific heat results for optimal $YBCO$ suggest rather smaller $v_{\Delta }$ values than are found by other measurements, and photoemission and some tunnelling data suggest that $v_{\Delta }$ decreases as doping is reduced, while other measurements including thermal conductivity suggest that it increases. The available data suggest however that the crucial parameter $%
Z^{e}$ is of order unity and is only weakly dependent on doping. Particularly compelling in this regard is the observed weak doping dependence of $d\rho _{S}/dT$, combined with the doping independence of $%
v_{F},$ and the indications that $v_{\Delta }$ increases with decreasing doping. These indications suggest that $Z^{e}$ is of order unity and if anything increases as doping is decreased. Data contradicting this conclusion exist. Further experimental information would be very helpful.
Range of applicability of low energy action
===========================================
Overview
--------
The results presented above constitute the leading temperature and $Q$ dependence about the $T=0,Q=0$ limit because they are nonanalytic in the standard expansion parameters $(T/E_{0})^{2},(v_{F}Q/E_{0})^{2}$ where $%
E_{0} $ is a ’microscopic’ energy scale (for example the BCS gap amplitude $%
\Delta _{0}$). We expect the expansion ceases to hold when the correction terms are of the order of the leading terms and in particular when the corrections to $\rho _{S0}$ are of the order of $\rho _{S0}$.
One source of correction terms are terms of the order of $Q^{4}$ in the phase part of the action. The usual expectation from study of quantum critical points is that these become important when $$\begin{aligned}
Q &\sim &Q^{\phi }=\left( \rho _{S0}/E_{\phi }\right) ^{1/2}/\xi _{0}
\label{Qphi} \\
T^{\phi } &\sim &\rho _{S0} \label{Tphi}\end{aligned}$$ where $E_{\phi },\xi _{0}$ are ’microscopic’ energy and length scales which do not vanish as the Mott phase or other critical point is approached.
Another correction occurs when the fermionic terms become of the order of the leading terms, i.e. when $$T\sim T^{\ast }=\rho _{S0}\left( \frac{v_{\Delta }}{Z_{e}^{2}v_{F}}\right)
\label{Tlim}$$ or $$Q\sim Q^{\ast }=\frac{2\rho _{S0}}{v_{F}}\left( \frac{v_{\Delta }}{%
Z_{e}^{3}v_{F}}\right) \label{Qlim}$$
Roughly, if the fermionic terms determine the limits of validity of the low $%
T,Q$ expansion, then the physics of the nonsuperconducting state is dominated by electrons and is expected to be more or less a conventional metal, whereas if the phase terms set the limits then fermions are irrelevant at the superconducting-non-superconducting critical point and the physics is presumably bosonic.
In general, the limit of validity of the low $T$ low $B$ expansion signals the destruction of the superconducting state. We shall discuss the superconducting non-superconducting transition on the assumption that the physics is strictly two dimensional. While this is a reasonable approximation for high-T$_{c}$ materials, it is important to bear in mind that ultimately a crossover to three dimensional critical behavior will occur and that the parameter controlling the crossover is the inverse of the square of the logarithm of the superfluid stiffness anisotropy $1/\ln
^{2}(\rho _{S\Vert }/\rho _{S\bot })$ which is not extremely small in practice, so although the two dimensional arguments provide reasonable estimates of the energy scales controlling $T_{c}$ and (as discussed below) $%
H_{c2}$, a quantitative application requires some caution.
Thermal fluctuations, zero field
--------------------------------
In a two dimensional material the thermally driven zero-field superconducting-non-superconducting transition is a Kosterlitz-Thouless vortex unbinding transition. It occurs at a $T_{KT}$ satisfying $%
T_{KT}=2\rho _{S}(T_{KT})/\pi $. Because thermal effects can only decrease $%
\rho _{S}$ from its $T=0$ value, the scale $T^{\phi }$ defined in Eq. \[Tphi\] is an upper bound for this transition temperature.
Two kinds of thermal effects occur: fluctuations of the superconducting phase, and quasiparticle excitations. In the absence of a high density of quasiparticle excitations, longitudinal (”spin-wave”) phase fluctuations involve unscreened charge fluctuations and are therefore strongly suppressed by the Coulomb interaction. In the absence of a high density of quasiparticles the only important excitations are vortex-antivortex pairs, whose energetics are governed by the scale $\rho
_{S0}$. (In this regard we worry that the numerical studies of Ref. [@Carlson00] are not quantitatively relevant to superconductors because these studies were based on the classical $XY$ model, so a large contribution from ’spin-wave’ longitudinal excitations is apparently included, whereas one would expect these to be strongly suppressed in an electronic system in which coulomb forces were important). Quasiparticle excitations will reduce $%
\rho _{S}(T)$ from its $T=0$ value. If $\frac{v_{\Delta }}{Z_{e}^{2}v_{F}}<1$ then the limit $T^{\ast }$ set by quasiparticle effects is more stringent. The physics of this limit (which seems to be favored by the data) is simply that thermal quasiparticle excitations reduce $\rho _{S}$ so that the Kosterlitz-Thouless transition occurs at a temperature lower by a factor of $%
F$ than one would guess from $\rho _{S0}$.
Field driven effects: low T
---------------------------
Application of a magnetic field $B>B_{c1}$ produces vortices in the superconducting order parameter. A superconducting vortex consists of a ”core” and a ”far” region. In the far region superconducting excitation spectrum is only weakly perturbed and there is a circulating supercurrent of a magnitude $j_{S}\rho _{S}/r$. As the core region is approached the supercurrent magnitude exhibits a maximum and then decreases and the quasiparticle excitation spectrum fundamentally changes. These two effects are distinct and define two core sizes, $\xi _{curr}$ at which $dj_{S}/dr=0$ and $\xi _{exc}$ at which the excitation spectrum changes. In a conventional superconductor $\xi _{exc}\approx $ $\xi _{curr}=v_{F}/\Delta $. In the high $T_{c}$ context, substantial attention has focused on $\xi _{exc}$ (which is apparently very short [@Renner98]) and on the possibility that the change of the excitation spectrum is not simply a collapse of the superconducting gap (as in conventional materials) but instead involves the appearance of a new form of long range order, for example antiferromagnetism or staggered flux [@Arovas97; @Han00; @Lee01; @Kishine01]. Here we wish to focus on $\xi _{curr}$ which in a lightly doped Mott insulator may be much greater than $\xi _{exc}$. Writing $j_{S}^{a}=\delta F/\delta Q^{a}$ and using Eq \[Fstatic\] leads to $$j_{S}^{a}=\rho _{s0}Q^{a}-\frac{Z_{e}^{3}}{8\pi v_{F}v_{\Delta }}%
\sum_{\alpha }v_{\alpha }^{a}\left( \overrightarrow{v}_{\alpha }\cdot
\overrightarrow{Q}\right) ^{2}\Theta \left( \overrightarrow{v}_{\alpha
}\cdot \overrightarrow{Q}\right) \label{js}$$
Taking $Q$ to be parallel to a gap node and of magnitude $1/r$ we find that the current is maximal at $\xi _{curr}=\frac{v_{F}^{2}Z^{3}}{4\pi \rho
_{S0}v_{\Delta }}$ *provided* that $\xi _{curr}$ is greater than the scale over which $\rho _{S0}$ varies. Eq \[js\] shows again the importance of $\ $ the doping dependence of $Z^{e}$. If (as available data seem to suggest), $Z^{e}$ remains constant and $\rho _{S0}\sim x$ then $\xi
_{curr}\sim x^{-1}$, whereas gauge-theory based models [@Ioffe88] (including, we believe, those discussed in [@Lee96; @Wen98]) lead to $%
Z^{e}\sim x$ so that $\xi _{curr}$ is controlled by the scale dependence of $%
\rho _{S},$ implying $\xi _{curr}\sim x^{-1/2}$. Typical numbers for optimally doped $YBCO$ are $\rho _{S0}\sim 10meV$, $v_{F}/v_{\Delta }\sim 15$, implying $\xi _{curr}[A]\approx 100Z^{3}$, roughly consistent with muon spin rotation data [@Sonier00], although of course uncertainties in $Z$ lead to large uncertainties in the numerical estimates.
The magnitude of $\xi _{curr}$ is important because $H_{c2}$ is essentially the field at which the vortex cores overlap, and for the resistive transition it is natural to use the ’current’ definition of the vortex core size. Essentially this argument was given by Lee and Wen [@Lee96] who were among the first to emphasize the importance, in the high-T$_{c}$ context, of the scale over which the supercurrent varied and (on the assumption that $Z^{e}=1$) concluded that $H_{c2}\sim x^{2}$. Future papers will examine in more detail the assumption that $\xi _{curr}$ is the correct measure of the core size to use in estimating $H_{c2}$, but the plausibility of this claim may be seen for example from Eq. (\[rhos(B)\]) which shows that when field becomes large enough to suppress $\rho _{S}$ by a factor of order unity the intervortex spacing is of the order of $\xi
_{curr}$.
Conclusions
===========
We have presented and compared to data a general theory of low energy properties of a d-wave superconductor. The theory has four parameters: the $%
T=0$, $H=0$ superfluid stiffness $\rho _{S0}$, the velocities $v_{F}$ and $%
v_{\Delta }$ describing the Dirac spectrum of d-wave quasiparticles, and a quantity $Z^{e}$ which expresses the coupling between quasiparticles and phase fluctuations and which we argued should be interpreted as the charge of the nodal quasiparticle. The behavior of these quantities contains information about the physics of the approach to the Mott transition, because different theoretical treatments of doped Mott insulators predict (or assume) quite different variations of these parameters with doping. The behavior of these quantities controls many aspects of the physics: in particular, the size (as defined from the supercurrent distribution) of superconducting vortices.
Two widely discussed theoretical approaches are the Brinkman-Rice-dynamical mean field theory [@Georges96] and the slave boson gauge theory [@Ioffe88] The essential ingredient of the Brinkman-Rice theory is a self-energy $\Sigma $ with a strong frequency dependence and a negligible momentum dependence. This leads to a Mott transition driven by a divergent $%
\partial \Sigma /\partial \omega $ implying $Z^{e}$ independent of $x$ and $%
v_{F}\sim x$. The latter prediction is in apparent contradiction to photoemission data. The essential assumption of the gauge theory approach is that current is carried by a small density of holes doped into a spin liquid environment. The fermionic excitations of the superconducting state are combinations of hole and spin-liquid states and the low density of holes leads to a small charge $Z^{e}\sim x$. In other words, the quasiparticles become more neutral as the Mott insulating phase is approached. One may think of this as a precursor of the ’nodal liquid’ phase discussed in [@Nodal]. This idea also appears to be inconsistent with the available data, although, as emphasized in Section III the available data are not entirely consistent. Further, and perhaps most important, complete information is not yet available for underdoped (especially strongly underdoped) materials. We urge the experimental community to settle the issue of the data consistency, in order to finally establish the relevance of the Brinkman-Rice and gauge theory approaches to the physics of high-T$_{c}$.
Our understanding of the presently available data favors the hypothesis that $Z^{e}$ and $v_{F}$ remain constant as $\rho _{S}\rightarrow 0$,. This result would appear to rule out both the Brinkman-Rice and gauge theory descriptions of the Mott physics of high $T_{c}$ materials, and it is therefore interesting to understand the origin of the discrepancy. One common feature of the two approaches is that in them the Mott physics affects all of the Fermi surface in the same manner, so the reduction in charge stiffness is described by a reduction in velocity or in quasiparticle charge. If neither of these effects occurs, then the reduction in charge stiffness must be driven by a reduction in ’effective fermi surface area’. In other words, it seems likely that in high $T_{c}$ materials the crucial missing ingredient is a large, doping dependent variation of the parameters around the Fermi surface so that all superfluid properties arise from condensation of fermions in a narrow and doping dependent range around the nodal direction.
Consider for example Eq. (\[rhos(Q)\]) which describes the reduction of the $\rho _{S}$ due to depairing of the nodal quasiparticles by a non-zero superflow. A phase gradient of magnitude $Q$ depairs electrons in an angular range $\delta \theta \sim Z^{e}v_{F}Q/v_{\Delta }$. In an underdoped material it seems that $Z^{e}$ remains of order unity while $\rho _{S}$ becomes very small. Eq. (\[rhos(Q)\]) then implies that exciting quasiparticles in a range $\delta \theta \ll \pi /2$ will reduce $\rho _{S}$ to zero, i.e. that all or most of the supercurrent is carried by electrons small patches, of angular size $\delta \theta \sim \rho _{S}v_{\Delta
}/Z^{e}v_{F}^{2}$ centered on the nodal points. Within this picture an interesting question is the behavior of $Z$ for angles $\theta >\delta
\theta $. Because $\rho _{S}$ cannot become negative, the quasiparticles must in some manner decouple from the superfluid fluctuations (i.e $Z^{e}$ must become small in these regions).
There is to our knowledge no microscopic theory of the narrow patch situation described above which is consistent with all data. One possibility is a commensurate long range order which opens a large, doping dependent gap around the antinodal points $(\pi ,0)$ which kills most of the Fermi surface leaving only hole pockets around the diagonals which then acquire a small amplitude superconducting gap. One example of this phenomenon would be the ’d-density wave’ state. Another would be some form of antiferromagnetic or ’stripe’ order. Two crucial consequences of such physics are a broken symmetry (which should be detectable in various spectroscopies) and a small $%
v_{\Delta }$ (determined by the observed $T_{c}$). We think that the available data do not favor this proposal. Crucially, the thermal conductivity measurements suggest that $v_{\Delta }$ increases when doping is decreased. An alternative which is at least qualitatively consistent with the data is preformed (d-wave) pairs which are made mostly from the electrons near $(\pi ,0)$ regions and which do not contribute to any transport. For example, [@Geshkenbein96] proposed a theory in which a large mass in the $(\pi ,0)$ region prevented the gap maximum regions from contributing to transport. We see here that an alternative is a small $Z^{e}$. Unfortunately there is no controlled microscopic theory which yield this physics, although uncontrolled but interesting extrapolations of scaling equations have been argued to lead to this physics [@Furukawa98].
To summarize: elucidation of the experimental support (or lack thereof) for the ’patch picture’ and (assuming it is relevant) clarification of its theoretical basis are two important challenges for the future.
*Acknowledgements:* We thank D. Bonn, P. A. Lee, M. Chiao and L. Taillefer for very helpful discussions and L. Taillefer for sharing unpublished data. We acknowledge support from NSF-DMR-00081075.
Appendix: Current distribution in vortex lattice: H$%
_{c1}<<H<<H_{c2}$
======================================================
Formalism
---------
In the limit $H_{c2}>>H>>H_{c1}$ we have, for the supercurrent distribution, $$\overrightarrow{j}_{s}(r)=\rho _{S}\overrightarrow{Q}(r) \label{jbasic}$$ with $\rho _{S}$ the superfluid stiffness and the gradient of the superconducting phase field given by $$\overrightarrow{Q}(r)=\sum_{i}\frac{\widehat{z}\times \left( \overrightarrow{%
r}-\overrightarrow{r}_{i}\right) }{\left( \overrightarrow{r}-\overrightarrow{%
r}_{i}\right) ^{2}} \label{qvort}$$ The quantity appearing in the expression for the field-induced specific heat for a vortex lattice oriented at angle $\theta $ to the gap node direction is $$C(\theta )=\frac{1}{A_{V}}\int dxdy\left| Q_{x}\cos (\theta )+Q_{y}\sin
(\theta )\right| \label{C}$$ where the integral is over the unit cell of the vortex lattice and $A_{V}$ is the area of this cell. The result has dimension of $length^{-1}$. It is convenient to measure lengths in units of the inter-vortex spacing $a$ and to normalize the result to the square root of the vortex density $%
n_{V}=B/\Phi _{0}$. Thus we write $$C\left( \theta \right) =n_{v}c(\theta ) \label{c}$$ and compute $c(\theta )$ for square and triangular vortex lattices.
Numerical evaluation, square vortex lattice
-------------------------------------------
We consider a square vortex lattice of lattice constant $a$, so the vortices sit at positions $na\widehat{x}+ma\widehat{y}.$ $n_{v}=a^{-2}$. Eq \[qvort\] gives $$\begin{aligned}
Q_{x} &=&n_{V}^{1/2}\sum_{n,m}\frac{(m-y/a)}{\left( n-x/a\right) ^{2}+\left(
m-y/a\right) ^{2}} \label{qxsquare} \\
Q_{y} &=&-Q_{x}(y,x) \label{qysquare}\end{aligned}$$ Consider $Q_{x}$. The sum over $y$ is most conveniently evaluated in Fourier space by writing $\sum_{m}\rightarrow \int du\rho (u)$ with $\rho
(u)=a^{-1}\sum_{m}\delta (y-ma)=\sum_{k}e^{i2\pi ky}$ Substitution gives $$Q_{x}(x,y)=\frac{\pi }{2}n_{V}^{1/2}\sum_{n}\frac{\sin (2\pi y/a)}{\sinh
^{2}(\pi \left( n-x/a)\right) +\sin ^{2}\left( \pi y/a\right) } \label{ysum}$$ The sum on $n$ is rapidly convergent and may easily be evaluated numerically.
We wish to evaluate Eq. \[C\] by integrating over the region $-a/2<x,y<a/2$. This is most conveniently evaluated numerically by inscribing a circle in the unit cell, performing the integral over the circle in polar coordinates (to eliminate the divergence at $r\rightarrow 0$) and then integrating over the remaining regions. This latter integral is over the region $-a/2<y<a/2$; $a/2>\left| x\right| >\sqrt{\frac{a^{2}}{4}-y^{2}}.$ We have performed this integral numerically using Mathematica; results are shown in the Table below.
Triangular lattice
------------------
Lattice vectors $$\begin{aligned}
\mathbf{v}_{1} &=&a\widehat{x} \label{basis1} \\
\mathbf{v}_{2} &=&a\left( \frac{-1}{2}\widehat{x}\mathbf{+}\frac{\sqrt{3}}{2}%
\widehat{y}\right) \label{basis2}\end{aligned}$$ A general lattice vector is then $n\mathbf{v}_{1}+m\mathbf{v}_{2}$. The unit cell is a hexagon with area $3\sqrt{3}a^{2}/8$.
Eq. \[qvort\] then gives, for the component of $\mathbf{j}$ perpendicular to $\mathbf{v}_{1}$ $$\mathbf{Q}_{y}=-\sum_{m,n}\frac{n-\frac{1}{2}m-x}{\left( n-\frac{1}{2}%
m-x\right) ^{2}+\left( \frac{\sqrt{3}}{2}ma-y\right) ^{2}} \label{jxtriang}$$
The sum over $n$ may again be performed–it is just the previous result with $y\rightarrow x+m/2$ and $n-x/a\rightarrow \frac{\sqrt{3}}{2}ma-y$ so that $$Q_{y}(x,y)=\frac{\pi }{2a}\sum_{m}\frac{\sin (m\pi +2\pi x/a)}{\sinh
^{2}(\pi \left( \frac{\sqrt{3}}{2}m-y/a)\right) +\sin ^{2}\left( m\pi /2+\pi
x/a\right) } \label{qytriang}$$ $Q_{x}$ is obtained by computing the component perpendicular to a different basic lattice vector and then combining appropriately.
For the Volovik effect we require $\int_{hexagon}dxdy\left| \mathbf{v\cdot j}%
(x,y)\right| .$ We find this is very well approximated by the integral over the inscribed circle. Results are shown in the Table.
Angle c$_{square}$ c$_{triangle}$
---------- -------------- ----------------
0 $1.5708...$ 1.74
$\pi /8$ 1.55 1.72
$\pi /4$ 1.52 1.71
*Table caption:* Coefficient $c$ defined in Eq \[c\] for square and triangular vortex lattice as function of angle $\theta $ between lattice vector of vortex lattice and nodal direction of d-wave superconducting order parameter.
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|
Monday, September 29, 2014
We look at the economic background to the rioting and looting in Argentina, and the factors which led to the social crisis there
Argentina, the one time darling of the IMF, held up as an example of how a country should stringently adhere to structural adjustment programmes, is presently standing as a shining example of how the capitalist system cannot be made to work in the interest of the majority.
When Economy Minister Domingo Cavallo pegged the Argentinean peso to the dollar ten years ago – on a one-to-one basis – he envisaged that this would end hyperinflation. Three years ago, when neighbouring Brazil devalued its real, this seriously began to upset Argentina's foreign investments and exports, as buyers of Argentinian products found they could get the same next door and far cheaper.
Argentina is now in debt to the tune of $132 billion – attributable largely to far-reaching borrowing carried out during the second term of the Carlos Menem government, prior to the election of President Fernando de la Rua. The effect of the domestic and foreign borrowing was to send domestic interest rates spiralling upwards. As the debt increased, so did the interest rates, which had a knock on effect for many businesses reliant upon credit.
In the 1990s, Menem introduced mass privatisation as a way of increasing economic efficiency. This resulted in many workers being made redundant, with them being surplus to requirements and unprofitable to employ.
So, back in 1999, the Argentinean recession began, a product of Argentina's relative economic inefficiency and the measures taken to tackle it. The recession began increasing in ferocity as domestic demand declined and unemployment increased and, because the government's tax revenues started shrinking, Argentina's burden of debt became all the more heavier.
In November all of Argentina's economic woes came to a head when people, fearful their pesos would be devalued, began hurrying to the banks to exchange them for dollars whilst the one-to-one rate was still in existence. Cavallo, fearful the banks would be drained of money, issued a decree which limited withdrawals to $1000 per person per month. The effect of this was to create mistrust in the government and widespread uncertainty with people rioting and protesting on the streets, with looting reported in many cities.
One week before Christmas the riots had spread to Buenos Aries. The president declared a state of emergency and brought troops onto the streets. But his government offered no remedy for the economic crisis and this only brought larger numbers of protestors back on to the streets within 24 hours, the unemployed being joined by "middle class" professionals – all taking part in the looting. When thousands of protestors congregated in Congress Square, banging pots and pans, the resignation of the president, his economic minister and the entire cabinet was almost immediate. De la Rua was determined to make one impassioned speech before he left, but with an angry crowd having none of it, he was instantly whisked to safety by a helicopter.
Tensions rose. People poured in from outlying districts, blockading motorways and erecting barricades, destroying banks and multinationals, looting supermarkets and fighting with almost 40,000 police who had been drafted into the city. When the violence had subdued, 26 had been killed.
Many Argentineans blame de la Rua for the crisis, citing the fact that he was the president when the crisis was deteriorating more alarmingly – as if he could control the economy! As the economy was controlling him, he had little option but to cut public spending to service debt repayments. De la Rua, however, did enter office foolishly promising to kick-start the economy and end high level corruption yet by early 2000 he had introduced £650 million worth of spending cuts and forced through eight unpopular austerity plans, which included a 13 percent cut in state workers' wages. Just prior to the unrest, the government planned to further cut public spending from £34 billion to £27 billion in a further attempt to service the crushing loan repayments.
The current president is one Eduardo Duhalde, a former left-wing senator and once upon a time investigated for the corruption his predecessor promised to stamp out. At present he plans to freeze the prices charged by foreign-owned utilities companies and put a tax on foreign owned oil companies. To protect the better off from currency devaluation he has offered to convert dollar loans under $100,000 into pesos, at the one-to-one rate – placing a hefty burden on banks, not borrowers – and he has further promised that cash will be set aside for the unemployed. All of which amounts to a timely game plan to placate the more volatile sections of Argentinean society.
Meanwhile, IMF top brass are in Argentina demanding, on behalf of the US and Europe, that the country does not default on its loan obligations. Outside markets are watching events carefully aware of the fact that economic crisis have tended in the past to lead to military coups and all their implications and are now mindful of granting further loans to the region.
There has been much analysis of recent events in Argentina. The general mood is that the IMF is to blame, that its structural austerity programmes are socially and politically unsustainable and that its rule-book needs tearing up. What has not been said is that, like the Argentinean government, the IMF is simply a body trying to make capitalism work. And in this regard they cannot entirely be faulted, because as events in Argentina have revealed, capitalism is working perfectly well, for this is the only way it can work in an anarchic and chaotic manner, negligent and oblivious to the misery and suffering it creates. If a few get rich while millions lose out big style, then this is capitalism working as it only can work. If there is recession followed by boom followed by recession, then capitalism is working healthily. Argentina, therefore, is another example of capitalism functioning normally.
In the April No. of the "Western Clarion," the official organ of the Socialist Party of Canada, the following welcome note occurs :
"Our comrades in Great Britain are having a very strenuous time in face of the present crisis ; but they are nobly upholding the WORKING CLASS POSITION in spite of "Prussian Militarism," and jingoistic sneers.
It is times like these that draw the revolutionists of every country closer together for united action against the COMMON ENEMY ; and may we, in the near future, be united together with the revolutionists of other lands who have expressed the aims and principles of that part of our class, who, realising that they are slaves, express a desire to be free, in an INTERNATIONAL which, founded on the firm rock of PROLETARIAN SCIENCE, shall withstand all the storms that may assail it.”
And in the report of the Dominion Executive Committee of the Socialist Party of Canada, printed in the same journal, the further statement occurs:
"We are all heartily in accord with the attitude of the S.P.G.B., and hope that before long we will be affiliated with them in a new "International.''"
Comrades, a toast! Here's to the coming Socialist International!
ED. COM.
Strange ! The heroes of the British capitalist Press are the German Socialists who are opposing the war, while the British Socialists who are taking a similar course of action are traitors and skunks, according to that same Press. It is quite consistent with the hypocrisy that decorates one man for risking his life for a kitten, and another for butchering his fellow-man.
o o o o o
Two hundred and fifty thousand men must be torn from their homes and families and driven into the Army in order to provide 200,000 officers with servants and grooms. Who said the workers are not slaves ? What, Henderson ? Military necessity ! Ha, ha ! |
# Product Security Committee Oncall
PSC Oncall is a business-hours only oncall. That means you are not expected to
respond to issues outside of your normal daily working hours or on weekends or
holidays. If you are taking vacation or will be unable to perform your oncall
duties, please swap oncalls or find coverage for that week. See [managing oncall
rotation](#appendix-managing-oncall-rotation).
- [Responsibilities](#responsibilities)
- [Triage Workflow](#triage-workflow)
- [HackerOne triage details](#hackerone-triage-details)
- [Incident Response Workflow](#incident-response-workflow)
- [Handoff](#handoff)
- [Appendix: Managing Oncall Rotation](#appendix-managing-oncall-rotation)
- [Adding the rotation to your calendar](#adding-the-rotation-to-your-calendar)
- [Swapping shifts or adding coverage](#swapping-shifts-or-adding-coverage)
## Responsibilities
Daily:
- Triage HackerOne reports ([query](https://hackerone.com/bugs?subject=kubernetes&view=k8s_triage))
- See [HackerOne Workflow](#hackerone-triage-details) for details
- Triage and respond to security@kubernetes.io emails. If needed, create a [security-disclosures issue](https://github.com/kubernetes-security/security-disclosures/issues).
It's a good idea to make sure that someone has responded to all recent threads. Threads are listed on [google groups](https://groups.google.com/a/kubernetes.io/forum/#!forum/security).
- Handle incident response for ongoing issues
- Drive progress on assigned issues ([query](https://github.com/kubernetes-security/security-disclosures/issues/assigned/@me))
- See [incident response](#incident-response-workflow) for details
- Ping incident commander of critical issues
([query](https://github.com/kubernetes-security/security-disclosures/issues?q=is%3Aissue+is%3Aopen+sort%3Aupdated-asc+label%3Aseverity%2Fcritical))
if last update > 2 days ago
Weekly (ideally at the beginning of your shift):
- Ping incident commander of high severity issues
([query](https://github.com/kubernetes-security/security-disclosures/issues?q=is%3Aissue+is%3Aopen+sort%3Aupdated-asc+label%3Aseverity%2Fhigh))
if last update was > 7 days ago
- Ping incident commander of medium severity issues
([query](https://github.com/kubernetes-security/security-disclosures/issues?q=is%3Aissue+is%3Aopen+sort%3Aupdated-asc+label%3Aseverity%2Fmedium))
if last update was > 1 month ago
- Check for new issues in this repository, especially distributor list join requests. Triage, assign or handle new issues, as appropriate.
([query](https://github.com/kubernetes/security/issues))
- Check for new PRs in this repository and address open PRs where possible
([query](https://github.com/kubernetes/security/pulls))
## Triage Workflow
### HackerOne triage details
**1. Assess assigned issues**
The recommended way of reviewing hackerone issues needing triage is to check
over the assigned issues daily:
https://hackerone.com/bugs?subject=kubernetes&view=k8s\_triage
This view tracks issues that are assigned to the Kubernetes Team (PSC), but
don't yet have a bounty awarded, which is a heuristic for whether the report
needs attention.
**1.a. Needs more information or Invalid**
If the report needs more information or is invalid, you can either respond
directly to the reporter (Add comment > All participants), or respond in a
private comment (Team only) and ask (reassign) the H1 Triage team to relay the
message.
**2. Set severity & tier**
Once you've determined that the report is valid and have an understanding of the
impact, set the [severity][] of the issue based on the CVSS score, and set the
tier (custom field) based on the [Kubernetes definition of
tiers](https://hackerone.com/kubernetes) (under "Rewards").
_TODO: Refine the definition of reward tiers._
[severity]: security-release-process.md#severity-thresholds---how-we-do-vulnerability-scoring
**3. File tracking issue**
Every non-public issue that we decide to take action on should get filed as a
GitHub issue in the https://github.com/kubernetes-security/security-disclosures
repo.
From the HackerOne report, you can use the [security-disclosures
bookmarklet][bookmarklet] to copy the relevant information into an issue on
https://github.com/kubernetes-security/security-disclosures/issues. Alternatively,
or when filing from an email report, you can use the [new issue template][], and
fill in the details manually.
Fill in the known details of the template, including:
- Assignee: yourself, or another PSC member who has volunteered to handle this
issue
- Severity: according to the assigned severity score
- CVE: most code vulnerabilities (not infrastructure vulnerabilities) should
have an assigned CVE.
- Original report: link back to the HackerOne report or google groups thread.
- Current status: one of
- planning - preliminary response stages
- development - fix in progress
- embargo - fix complete, sent to distributors under embargo
- released - fix has shipped
- published - vulnerability details have been made public
- Attribution: the original reporter
Once the issue has been created, add the tracking issue as a reference ID on
HackerOne.
[bookmarklet]: https://github.com/kubernetes-security/security-disclosures#hackerone-issue-escalation
[new issue template]: https://github.com/kubernetes-security/security-disclosures/issues/new?template=vulnerability.md
**4. Award bounty**
Once you're confident that we've sufficiently assessed the severity and tier
(try to get an approval from someone else on the committee), it's time to award
the bounty. Note that you _do not_ need to wait until the issue is resolved
before awarding the bounty.
Choose the corresponding amount from the tiered bounty tables on
https://hackerone.com/kubernetes (under "rewards"). Then, scroll down to the
comment box on the report and change the action to "Set award". Enter the
amount, leave a comment if you'd like, and click "Set award". Congratulations,
you've completed triage on this report (continue on to incident response).
## Incident Response Workflow
## Handoff
When your shift ends, you may be the incident commander on one or more ongoing
incidents. If you are already invested in the incident and have the bandwidth
for it, you can continue managing the incident (thanks!), but _you are not
obligated to continue managing the incident!_
If you would like to handoff incident command:
1. Start by **ensuring the tracking issue is up to date** - review the
information in the issue description, and fill in or correct any missing
details.
2. **Leave a comment** to dump any additional context and state you have on the
issue. Make sure to list any open questions or decisions and any pending
action items.
3. Reassign the issue to the next oncall.
Finally, reach out to the next oncall (email, slack, VC, your choice) to make
sure they're aware of the handoff and to answer any questions. _Until they've
explicitly acknowledged the handoff you are still the incident commander!_
## Appendix: Managing Oncall Rotation
### Adding the rotation to your calendar
1. Navigate to the PSC oncall rotation:
https://kubernetes.app.opsgenie.com/settings/schedule/detail/f835cdef-8df9-4ddc-9a39-911cb9e521b5
2. Click "Open calendar" (appears on hover), add to your calendar.
### Swapping shifts or adding coverage
0. Find someone to agree to swap shifts or cover for days you will be
unavailable.
1. Navigate to the PSC oncall rotation:
https://kubernetes.app.opsgenie.com/settings/schedule/detail/f835cdef-8df9-4ddc-9a39-911cb9e521b5
2. Click "Add override", fill in the appropriate details.
- Select the user who will be taking the shift
- Select the PSC rotation
- Enter the dates for the override
_Note: If you're swapping shifts, you'll need to do this twice, once for your
shift and once for the shift you're swapping for._
|
[transforms.remap_nested]
inputs = []
type = "remap"
mapping = """
.a.b = 123
.x.y = 456
.x.z = 789
"""
[[tests]]
name = "remap_nested"
[tests.input]
insert_at = "remap_nested"
type = "raw"
value = ""
[[tests.outputs]]
extract_from = "remap_nested"
[[tests.outputs.conditions]]
"a.b.equals" = 123
"x.y.equals" = 456
"x.z.equals" = 789
[transforms.remap_array]
inputs = []
type = "remap"
mapping = """
.a[0] = 0
.a[1] = "1"
.a[2] = 2.0
.b[2] = "two"
.b[0] = 0
"""
[[tests]]
name = "remap_array"
[tests.input]
insert_at = "remap_array"
type = "raw"
value = ""
[[tests.outputs]]
extract_from = "remap_array"
[[tests.outputs.conditions]]
"a[0].equals" = 0
"a[1].equals" = "1"
"a[2].equals" = 2.0
"b[0].equals" = 0
"b[1].equals" = "<null>"
"b[2].equals" = "two"
[transforms.remap_arithmetic]
inputs = []
type = "remap"
mapping = """
.result_a = .a * .b + .c - .d
.result_b = .a * (.b + .c) - .d
.result_c = .a + .b * .c / .d
.result_d = (.a + .b) * (.c / .d)
"""
[[tests]]
name = "remap_arithmetic"
[tests.input]
insert_at = "remap_arithmetic"
type = "log"
[tests.input.log_fields]
a = 3
b = 7
c = 12
d = 6
[[tests.outputs]]
extract_from = "remap_arithmetic"
[[tests.outputs.conditions]]
"result_a.equals" = 27
"result_b.equals" = 51
"result_c.equals" = 17
"result_d.equals" = 20
[transforms.remap_boolean_arithmetic]
inputs = []
type = "remap"
mapping = """
.result_a = .a + .b > 9
.result_b = .a * .b < 20
.result_c = 1 >= .a / .b
.result_d = .a + .b > .c + .d
"""
[[tests]]
name = "remap_boolean_arithmetic"
[tests.input]
insert_at = "remap_boolean_arithmetic"
type = "log"
[tests.input.log_fields]
a = 3
b = 7
c = 12
d = 6
[[tests.outputs]]
extract_from = "remap_boolean_arithmetic"
[[tests.outputs.conditions]]
"result_a.equals" = true
"result_b.equals" = false
"result_c.equals" = true
"result_d.equals" = false
[transforms.remap_delete_only_fields]
inputs = []
type = "remap"
mapping = """
only_fields(.foo, .bar, .buz.second)
del(.foo.second)
"""
[[tests]]
name = "remap_delete_only_fields"
[tests.input]
insert_at = "remap_delete_only_fields"
type = "log"
[tests.input.log_fields]
"foo.first" = "foo first value"
"foo.second" = "foo second value"
bar = "bar value"
baz = "baz value"
"buz.first" = "buz first value"
"buz.second" = "buz second value"
[[tests.outputs]]
extract_from = "remap_delete_only_fields"
[[tests.outputs.conditions]]
"foo.first.equals" = "foo first value"
"foo.second.exists" = false
"bar.equals" = "bar value"
"baz.exists" = false
"buz.first.exists" = false
"buz.second.equals" = "buz second value"
[transforms.remap_coercion]
inputs = []
type = "remap"
mapping = """
.foo = to_string(.foo)
.bar = to_int(.bar)
.baz = to_float(.baz)
.bev = to_bool(.bev)
.a = to_timestamp(.a)
.b = to_timestamp(.nope, 10)
.c = to_timestamp(.nope, "2020-09-14T12:51:12+02:00")
.d = parse_timestamp(.quix, format = "%d/%m/%Y:%H:%M:%S %z")
"""
[[tests]]
name = "remap_coercion"
[tests.input]
insert_at = "remap_coercion"
type = "log"
[tests.input.log_fields]
foo = 10
bar = "20"
baz = "30.3"
bev = "true"
quix = "19/06/2019:17:20:49 -0400"
a = "2020-09-14T12:53:44+03:00"
[[tests.outputs]]
extract_from = "remap_coercion"
[[tests.outputs.conditions]]
"foo.equals" = "10"
"bar.equals" = 20
"baz.equals" = 30.3
"bev.equals" = true
"a.equals" = "2020-09-14T09:53:44Z"
"b.equals" = "1970-01-01T00:00:10Z"
"c.equals" = "2020-09-14T10:51:12Z"
"d.equals" = "2019-06-19T21:20:49Z"
[transforms.remap_quoted_path]
inputs = []
type = "remap"
mapping = """
.a."b.c" = ."d.e"
"""
[[tests]]
name = "remap_quoted_path"
[tests.input]
insert_at = "remap_quoted_path"
type = "log"
[tests.input.log_fields]
"a.b\\.c" = "bar"
"d\\.e" = "baz"
[[tests.outputs]]
extract_from = "remap_quoted_path"
[[tests.outputs.conditions]]
"a.b\\.c.equals" = "baz"
[transforms.remap_function_arguments]
inputs = []
type = "remap"
mapping = """
.a = to_string(.in)
.b = to_string(value = .in)
.c = to_string(.in, 20)
.d = to_string(.in, default = 20)
.e = to_string(.nope, 20)
.f = to_string(.nope, default = 20)
.g = to_string(value = .in, default = 20)
.h = to_string(value = .in, 20)
.i = to_string(default = 20, .in)
.j = to_string(default = 20, value = .in)
.k = to_string(default = 20, value = .nope)
.l = to_string(default = .other, value = .nope)
"""
[[tests]]
name = "remap_function_arguments"
[tests.input]
insert_at = "remap_function_arguments"
type = "log"
[tests.input.log_fields]
in = 10
other = 30
[[tests.outputs]]
extract_from = "remap_function_arguments"
[[tests.outputs.conditions]]
"a.equals" = "10"
"b.equals" = "10"
"c.equals" = "10"
"d.equals" = "10"
"e.equals" = "20"
"f.equals" = "20"
"g.equals" = "10"
"h.equals" = "10"
"i.equals" = "10"
"j.equals" = "10"
"k.equals" = "20"
"l.equals" = "30"
[transforms.remap_function_upcase]
inputs = []
type = "remap"
mapping = """
.a = upcase(.a)
.b = upcase(.b)
.c.c = upcase(.c.c)
if upcase(.f) == "F" {
.f = "ff"
}
"""
[[tests]]
name = "remap_function_upcase"
[tests.input]
insert_at = "remap_function_upcase"
type = "log"
[tests.input.log_fields]
a = "a"
b = "bbb bb"
"c.c" = "c.c"
f = "f"
[[tests.outputs]]
extract_from = "remap_function_upcase"
[[tests.outputs.conditions]]
"a.equals" = "A"
"b.equals" = "BBB BB"
"c.c.equals" = "C.C"
"f.equals" = "ff"
[transforms.remap_function_upcase_error]
inputs = []
type = "remap"
drop_on_err = true
mapping = """
.a = upcase(.a)
.b = upcase(.b)
"""
[[tests]]
name = "remap_function_upcase_error"
no_outputs_from = ["remap_function_upcase_error"]
[tests.input]
insert_at = "remap_function_upcase_error"
type = "log"
[tests.input.log_fields]
a = "a"
b = true
[transforms.remap_function_downcase]
inputs = []
type = "remap"
drop_on_err = true
mapping = """
.a = downcase(.a)
.b = downcase(.b)
.c.c = downcase(.c.c)
if downcase(.f) == "f" {
.f = "FF"
}
"""
[[tests]]
name = "remap_function_downcase"
[tests.input]
insert_at = "remap_function_downcase"
type = "log"
[tests.input.log_fields]
a = "A"
b = "BBB BB"
"c.c" = "C.C"
f = "F"
[[tests.outputs]]
extract_from = "remap_function_downcase"
[[tests.outputs.conditions]]
"a.equals" = "a"
"b.equals" = "bbb bb"
"c.c.equals" = "c.c"
"f.equals" = "FF"
[transforms.remap_function_downcase_error]
inputs = []
type = "remap"
drop_on_err = true
mapping = """
.a = downcase(.a)
.b = downcase(.b)
"""
[[tests]]
name = "remap_function_downcase_error"
no_outputs_from = ["remap_function_downcase_error"]
[tests.input]
insert_at = "remap_function_downcase_error"
type = "log"
[tests.input.log_fields]
a = "A"
b = 10
[transforms.remap_function_uuid_v4]
inputs = []
type = "remap"
mapping = """
.a = uuid_v4()
if uuid_v4() != "" {
.b = "bar"
}
"""
[[tests]]
name = "remap_function_uuid_v4"
[tests.input]
insert_at = "remap_function_uuid_v4"
type = "log"
[tests.input.log_fields]
b = "foo"
[[tests.outputs]]
extract_from = "remap_function_uuid_v4"
[[tests.outputs.conditions]]
"a.regex" = "(?i)^[0-9a-f]{8}-[0-9a-f]{4}-4[0-9a-f]{3}-[89ab][0-9a-f]{3}-[0-9a-f]{12}$"
"b.equals" = "bar"
[transforms.remap_function_sha1]
inputs = []
type = "remap"
mapping = """
.a = sha1(.a)
if sha1(.b) == "62cdb7020ff920e5aa642c3d4066950dd1f01f4d" {
.b = sha1(.a + .b + "baz")
}
"""
[[tests]]
name = "remap_function_sha1"
[tests.input]
insert_at = "remap_function_sha1"
type = "log"
[tests.input.log_fields]
a = "foo"
b = "bar"
[[tests.outputs]]
extract_from = "remap_function_sha1"
[[tests.outputs.conditions]]
"a.equals" = "0beec7b5ea3f0fdbc95d0dd47f3c5bc275da8a33"
"b.equals" = "6f74c252bb7f19f553115af5e49a733b9ff17138"
[transforms.remap_function_sha1_error]
inputs = []
type = "remap"
drop_on_err = true
mapping = """
.a = sha1(.a)
.b = sha1(.b)
"""
[[tests]]
name = "remap_function_sha1_error"
no_outputs_from = ["remap_function_sha1_error"]
[tests.input]
insert_at = "remap_function_sha1_error"
type = "log"
[tests.input.log_fields]
a = "foo"
b = true
[transforms.remap_function_md5]
inputs = []
type = "remap"
mapping = """
.a = md5(.a)
if md5(.b) == "37b51d194a7513e45b56f6524f2d51f2" {
.b = md5(.a + .b + "baz")
}
"""
[[tests]]
name = "remap_function_md5"
[tests.input]
insert_at = "remap_function_md5"
type = "log"
[tests.input.log_fields]
a = "foo"
b = "bar"
[[tests.outputs]]
extract_from = "remap_function_md5"
[[tests.outputs.conditions]]
"a.equals" = "acbd18db4cc2f85cedef654fccc4a4d8"
"b.equals" = "223cfa6567e4c0599c9a23628bf7a234"
[transforms.remap_function_md5_error]
inputs = []
type = "remap"
drop_on_err = true
mapping = """
.a = md5(.a)
.b = md5(.b)
"""
[[tests]]
name = "remap_function_md5_error"
no_outputs_from = ["remap_function_md5_error"]
[tests.input]
insert_at = "remap_function_md5_error"
type = "log"
[tests.input.log_fields]
a = "foo"
b = true
[transforms.remap_function_now]
inputs = []
type = "remap"
mapping = """
.a = now()
"""
[[tests]]
name = "remap_function_now"
[tests.input]
insert_at = "remap_function_now"
type = "log"
[tests.input.log_fields]
[[tests.outputs]]
extract_from = "remap_function_now"
[[tests.outputs.conditions]]
"a.ends_with" = "Z"
[transforms.remap_function_format_timestamp]
inputs = []
type = "remap"
mapping = """
.a = format_timestamp(to_timestamp(.foo), format = "%+")
"""
[[tests]]
name = "remap_function_format_timestamp"
[tests.input]
insert_at = "remap_function_format_timestamp"
type = "log"
[tests.input.log_fields]
foo = 10
[[tests.outputs]]
extract_from = "remap_function_format_timestamp"
[[tests.outputs.conditions]]
"a.equals" = "1970-01-01T00:00:10+00:00"
[transforms.remap_function_contains]
inputs = []
type = "remap"
mapping = """
.a = contains(.foo, substring = .bar)
.b = contains(.bar, substring = "bar")
.c = contains(.bar, substring = "BAR", case_sensitive = true)
.d = contains(.bar, substring = "BAR", case_sensitive = false)
"""
[[tests]]
name = "remap_function_contains"
[tests.input]
insert_at = "remap_function_contains"
type = "log"
[tests.input.log_fields]
foo = "foo"
bar = "bar"
[[tests.outputs]]
extract_from = "remap_function_contains"
[[tests.outputs.conditions]]
"a.equals" = false
"b.equals" = true
"c.equals" = false
"d.equals" = true
[transforms.remap_function_slice]
inputs = []
type = "remap"
mapping = """
.a = slice(.foo + .bar, 1)
.b = slice(.foo + .bar, 0, 1)
.c = slice(.foo + .bar, start = -2)
.d = slice(.foo + .bar, start = 1, end = -1)
"""
[[tests]]
name = "remap_function_slice"
[tests.input]
insert_at = "remap_function_slice"
type = "log"
[tests.input.log_fields]
foo = "foo"
bar = "bar"
[[tests.outputs]]
extract_from = "remap_function_slice"
[[tests.outputs.conditions]]
"a.equals" = "oobar"
"b.equals" = "f"
"c.equals" = "ar"
"d.equals" = "ooba"
[transforms.remap_function_tokenize]
inputs = []
type = "remap"
mapping = """
.a = tokenize(.a)
.b = tokenize(.b)
"""
[[tests]]
name = "remap_function_tokenize"
[tests.input]
insert_at = "remap_function_tokenize"
type = "log"
[tests.input.log_fields]
a = "217.250.207.207 - - [07/Sep/2020:16:38:00 -0400] \"DELETE /deliverables/next-generation/user-centric HTTP/1.1\" 205 11881"
b = "bar"
[[tests.outputs]]
extract_from = "remap_function_tokenize"
[[tests.outputs.conditions]]
"a.length_eq" = 7
"a[0].equals" = "217.250.207.207"
"a[1].equals" = "<null>"
"a[2].equals" = "<null>"
"a[3].equals" = "07/Sep/2020:16:38:00 -0400"
"a[4].equals" = "DELETE /deliverables/next-generation/user-centric HTTP/1.1"
"a[5].equals" = "205"
"a[6].equals" = "11881"
"b.length_eq" = 1
"b[0].equals" = "bar"
|
It is now well established that putting an infant to sleep on his or her back is the single most important step in reducing the risk of sudden infant death syndrome (SIDS).
Recent research also suggests that a baby's risk for SIDS can be greatly reduced by using a pacifier. Medical research also shows that babies who can satiate their natural sucking reflex sleep better. Experts recommend giving babies a pacifier every time they are placed to sleep. The exact reason that pacifiers reduce the risk of SIDS is not known. One suggestion is that the presence of a pacifier in the mouth may discourage babies from turning over onto their tummy because turning or moving may dislodge the pacifier. Another suggestion is that pacifier use and/or the sucking reflex helps keep the tongue positioned forward, keeping the airways open. Yet another suggestion is that pacifiers stimulate upper airway muscles and saliva production, so using pacifiers may keep babies from falling into a deep sleep, which is protective against SIDS.
One of the factors that has led to a revival in the ancient practice of swaddling is the practice of putting babies to sleep on their backs as this helps to reduce the incidence of SIDS. However, babies tend to sleep better on their tummies than on their backs. Swaddling has been found to assist infants sleep more comfortably on their backs and to assist in easing colic, which also improves sleep. Swaddling is the practice of wrapping infants tightly in a blanket or cloth so that movement of the limbs is restricted.
Medical research has shown that swaddling and sleeping supine (on the back) promotes more efficient sleep, with fewer spontaneous awakenings compared with sleeping supine but unswaddled. Swaddling seems to inhibit each step from sighs through startles to full arousal in the arousal pathway. This results in swaddled babies sleeping longer and being more likely to return to sleep on their own: Swaddling: a systematic review, Bregje E. van Sleuwen, et al, Pediatrics vol 120, number 4, October 2007.
To achieve the benefits of swaddling, infants need to be wrapped sufficiently tight to restrain the limbs and inhibit the movements associated with a full startle reflex, which can wake babies from sleep. The startle reflex is seen in infants from birth to around 6 months of age (some sources indicate it can occur in infants as old as eight months). The startle reflex is a natural reflex that babies are born with, and can be triggered by loud noise or sudden movement. In response to the trigger, the baby throws back his/her head, extends out the arms and legs, cries, then pulls the arms and legs back in. A baby's own cry can trigger the reflex. It can also be triggered during sleep, causing the baby to wake.
Care needs to be taken not to swaddle too tightly because this can compress the chest and make breathing difficult. There is also an increased risk of overheating especially when the head is covered or when there is infection. Improper swaddling can also lead to a risk of hip dysplasia (including hip dislocation) especially when swaddling with the hips and legs in extension and adduction (i.e. drawn toward the midline or sagittal plane of the body).
Other risks associated with swaddling babies includes an increased risk of SIDS when a swaddled infant is placed prone (on his or her front) or able to turn to prone position. The SIDS risk seems to be increased by swaddling with the head covered. There is also a slightly increased risk of acute respiratory infections, which seems to be related to the tightness of swaddling. These are discussed in the systematic review of swaddling referred to above.
Therefore, to swaddle properly and effectively, and to achieve the desired result, the blanket must be snug enough to immobilise the infant's arms, and to a certain degree its legs, but loose enough that it is still comfortable and not increase the risk of hip dysplasia or suppressed respiration.
Many parents and carers experience difficulty with swaddling due to unfamiliarity with swaddling techniques. If not swaddled correctly, the infant often wriggles free of the swaddle thus becoming exposed to a risk of suffocation or SIDS-related issues due to loose bedding and unrestricted positioning of the infant. However, swaddling alone cannot eliminate these risks. This is especially true for infants that are more than around six weeks old, when they are stronger and more active than newborns. Even when swaddled tightly with all limbs securely enclosed, infants can potentially roll, becoming entrapped in the swaddling blanket or trapped face down while still wrapped in the blanket.
To overcome the difficulty faced by parents and carers in learning proper swaddling techniques and to address the problems of improper swaddling, various swaddling suits have been developed. Swaddling suits such as the infant safety suit of WO 2007/098558 (the Snuggo), the Ergococcoon and the Woombi address the problems of wrapping too loosely or too tightly since the degree of wrapping is predetermined by the suit.
As mentioned above, recent evidence shows that sucking on a pacifier is protective against SIDS. In addition, supplemental non-nutritive sucking (that is, sucking in addition to that required for feeding) is known to help to soothe an infant. Researchers have discovered that there is a clear reflex connection between the hand and mouth of a human fetus as early as 12-14 weeks after conception, and that thumb sucking in utero is common. After birth, many infants continue to soothe themselves by sucking on their thumbs or fingers. A newborn's ability to get the hands up to his or her mouth and suck is seen as a positive ability of the infant to organize him or herself in a self-soothing way. This helps establish an infant's ability to independently cope with stress and frustration.
Thus it would be an advantage to have a swaddle suit that overcomes the problems of improper swaddling and also provides an opportunity for non-nutritive sucking. This would improve the calming effect of the swaddling suit, since research that indicates that multiple simultaneous measures such as swaddling and sucking (along with rocking, white noise and other interventions) have an additive calming effect on crying infants: Karp H, Swaddling and excessive crying, Journal of Pediatrics, July 2007, e2. None of the aforementioned swaddling suits facilitates non-nutritive sucking.
None of WO 2007/098558 (the Snuggo), the Ergococcoon or the Woombi provide access to the hands while the infant is swaddled. Movement of the infant's arms in all three of these swaddling suits is restricted to 180 degrees below the shoulder line so the hands are restrained near the body but below the shoulder line, out of reach of the mouth.
U.S. Pat. No. 7,587,769 is a swaddling article including a blanket formed with opposed arm-receiving sleeves that attempts to facilitate non-nutritive sucking by securing a pacifier to the blanket, thus overcoming the problem of pacifiers falling out of an infant's mouth. The blanket incorporates a pacifier retaining structure to retain a pacifier relative to the blanket so that the pacifier is unable to fall away from the blanket. This keeps the pacifier positioned near the mouth when the blanket is wrapped around an infant so it is available for the infant to suck on at will. The pacifier retaining structure includes a flap of fabric secured to the upper edge of the swaddling blanket. The flap is drawn across the region of the baby's mouth.
A disadvantage of the swaddling article of U.S. Pat. No.7,587,769 is that it relies on a pacifier to be secured to the blanket. Another disadvantage is that it essentially extends the blanket across the face (around the mouth region), which can be uncomfortable and covering the face during sleep increases the risk of SIDs. Yet another disadvantage is that the swaddle article is in the form of a modified blanket and so lacks the convenience and advantages of a swaddling suit for example, the risk remains that the swaddle may loosen through movement thus becoming less effective and also posing a suffocation risk.
While research indicates that there are benefits associated with non-nutritive sucking (e.g. pacifier use), it also indicates that pacifier use may be associated with problems including:
interference with breast feeding,
dependence on the pacifier (so the baby cannot sleep without one),
an increased risk of middle ear infections, and
dental problems associated with prolonged use.
Hence, despite the established benefits of pacifier use, many parents choose not to use pacifiers. Further, some infants simply do not take to pacifiers. In any event, so as to minimise interference with breastfeeding, the recommendation is to wait until nursing is going well (usually one month) before offering a pacifier. Thus pacifier use is not suitable for all infants and it would be an advantage to provide a means for non-nutritive sucking that does not rely on pacifier use.
Reflexes are set motor responses to specific sensory stimuli. Newborns have a hand-to-mouth reflex that is a natural instinct to get their hands to their mouths. Research indicates that this ability to access the hands for sucking is important for self-soothing. The hand-to-mouth reflex (along with the startle reflex) is one of a number of primitive reflexes present from birth or earlier. Primitive reflexes are thought to have provided evolutionary advantages to humans.
The somatosensory system is a complex system of receptors and processing centres that produce the senses including touch, motion perception (proprioception) and balance, and spatial perception of body parts (kinesthesia). The tactile or skin senses (that rely on skin sensors for touch and pressure) appear first during fetal development. The vestibular system, which is responsible for movement and balance perception, and the tactile (touch) sensors are highly developed in newborns.
The hand-to-mouth reflex goes with two reflexes that are considered essential to appropriate feeding responses in newborns: the rooting (or search) reflex and the sucking reflex. Both of these reflexes are triggered by a touch (including pressure) stimulus.
The rooting reflex occurs when the infant's cheek or corner of the mouth is touched or stroked. The infant's mouth opens to follow and “root” (search) in the direction of stroking or touch. Rooting helps the baby to become ready to suck. The suckling reflex is triggered by touching the mucous membranes on the inside of the mouth with any object. Both reflexes facilitate nursing.
In the hand-to-mouth reflex, when an infant's cheek is stroked, his or her mouth roots and the arm flexes. After hand and mouth find each other, the infant may suck energetically on the hands.
There is a need for a swaddling suit that does not suffer the disadvantages of a swaddling using a blanket and that effectively swaddles infants by sufficiently restraining movement of the limbs to suppress the startle reflex, yet still affords sufficient movement so that infants can get their hand(s) toward their mouth, so providing the opportunity for non-nutritive sucking without reliance on a pacifier.
U.S. Pat. No. 4,611,353 describes a swaddling garment in which an infant's arms are gently bound in a bent-elbow, hands-up position to inhibit the ability to fling open the arms without restricting arm movement. Binding of the arms in this manner is described as useful for holding a premature infant.
The BabySense Cuddlewrap is a blanket shaped to wrap an infant's arms tightly near to the body and face, again as a means for suppressing jerks of the arms and legs. However, neither the manufacturer of the BabySense Cuddlewrap nor the inventor of garment of U.S. Pat. No. 4,611,353 refer to the benefit of providing access to the hands for non-nutritive sucking while swaddled and neither swaddle addresses this need adequately.
While the swaddle of U.S. Pat. No. 4,611,353 is referred to as a garment, the part of the garment that is responsible for binding the arms in the manner described is two flaps of sufficient length to wrap around the infant and overlap each other, secured in place either by strips of hook and loop fasteners or simply by relying on the length of the flaps. Thus binding of the arms is achieved by a length of fabric in a manner analogous to a blanket. Loosening of the binding is possible with movement/wriggling of the baby—particularly in the embodiment that relies on the length of the flaps to secure the wrapping around the infant or where the hook and loop fastening is not sufficient to restrain loosening of the flaps through wriggling movement of the infant.
Therefore, the risks associated with use of swaddling blankets or cloths remain with both the BabySense Cuddlewrap and the swaddle of U.S. Pat. No. 4,611,353, including:
1. wrapping too tightly so as to suppress respiration;
2. overwrapping the infant in several layers of fabric so as to increase the risk of overheating (particularly as the preferred embodiment of U.S. Pat. No. 4,611,353 also includes a hood);
3. loosening of the swaddle around the upper body will result in excess fabric around the upper body, posing a suffocation risk to the infant;
4. the arms are only restrained so long as the swaddle remains tightly secured around the infant and loosening allows increasing movement of the arms;
5. the swaddle does not facilitate or maintain access to the hands, although access can initially be provided depending on how the hands are positioned when the infant is first swaddled.
Thus both U.S. Pat. No. 4,611,353 and the BabySense Cuddlewrap share many of the disadvantages of swaddling using a blanket, and do not act to secure the hands in position near the face to provide the opportunity for non-nutritive sucking without reliance on a pacifier.
It is an object of the present invention to provide a new or alternative swaddling suit that swaddles infants by restraining movement of the limbs and which overcomes the disadvantages of other swaddling suits by allowing movement of the hand towards the mouth and maintaining the hand in a position relative to the infant's face thereby facilitating non-nutritive sucking. |
Horace Vere, 1st Baron Vere of Tilbury
Horace Vere, 1st Baron Vere of Tilbury (1565 – 2 May 1635) (also Horatio Vere or Horatio de Vere) was an English military leader during the Eighty Years' War and the Thirty Years' War, a son of Geoffrey Vere and brother of Francis Vere. He was sent to the Palatinate by James I in 1620. He was created Baron Vere of Tilbury, and died without a male heir.
Family
Horace Vere, born in 1565, was the fourth son of Geoffrey Vere of Crepping Hall, Essex, a younger son of John de Vere, 15th Earl of Oxford, and Elizabeth Trussell. His mother was Elizabeth Hardekyn (d. December 1615), daughter of Richard Hardekyn (d. 1558) of Wotton House near Castle Hedingham. He had three brothers, John Vere (c. 1558 – 1624) of Kirby Hall near Castle Hedingham, Sir Francis Vere (born c. 1560), and Robert Vere (b. 1562), and a sister, Frances Vere (born 1567), who married, as his second wife, the 'colonial adventurer and author', Sir Robert Harcourt (1574/5 – 1631), of Nuneham on 20 March 1598.
Military career
Anglo Spanish war
Vere left home in 1590 to join his two elder brothers, Robert and Sir Francis, in the Netherlands, commencing his service in the infantry company of the latter during his tenure of office as sergeant-major-general. He was wounded during the assault by English and Dutch soldiers on the fortress of Steenwijk on 5 July 1592, was recommended by his brother for a company at the siege of Groningen in June 1594, and was knighted for his gallantry at the siege of Cadiz in June 1596.
The following year Horace in his brothers absence took command in the field (albeit temporarily) of the English forces in the Netherlands. With Maurice of Orange they took Rheinberg, Meurs, Greonlo, Bredevoort, Enschede, Oldenzaal and Lingen; cities of the Eastern Netherlands that created an important barrier.
He commanded three hundred foot at the battle of Nieuwport under his brother, after whose retirement from the field he helped Sir John Ogle and Sir Charles Fairfax to rally the English vanguard; and at the Siege of Ostend he took a conspicuous part in the repulse of the Spanish assault on 7 January 1602, being stationed (along with Fairfax) at a vital point in the defenses known as the 'Sandhill,' in command of twelve companies. He was badly hurt in the leg by a splinter. Horace then took to the field under his brother again in the Spring of 1602 with Maurice's army, and after Francis was severely wounded in the head during the siege of Grave he then took over as command of English forces there. Early in April 1603 he was dispatched by his brother with a message to the new king.
Upon the retirement of Sir Francis Vere, Sir Horace took his place in the Netherlands, but at first only the senior of the four colonels of the English companies, the others being Ogle, Sir Edward Cecil, and Sir Edward Harwood.
The outset of Sir Horace's individual career in the Dutch States Army was marked by the fall of Ostend on 24 September 1604 to the Spanish general, Ambrosio Spinola. As a makeweight to Ostend, Maurice of Nassau, Prince of Orange meditated the recapture of Sluys. The Spanish general opposed the advance upon the town with a force of two thousand men strongly entrenched at Damme, situated between Sluys and Bruges. This force, under the Spanish general of horse, Velasco, had to be dislodged, a risky operation. Vere won for his command the approbation of the States-General. In July 1604 Spinola was foiled in an attempt to relieve the town, and on 20 August it was surrendered.
Dutch Service
At the battle of Mulheim on 9 October 1605 the cavalry were completely outmanoeuvred, and several of the troops broke. Vere crossed the river with four companies of infantry and kept the Spaniards at bay for over an hour, while the other forces had time to rally and retreat in some order.
The battle of Mulheim was followed by Vere's return to England, and by his marriage in 1607. Two years later came the twelve years' truce between the United Provinces and Spain. In October 1609 Sir Horace succeeded his brother as governor of the Brill. In 1609 he was promised the reversion of the mastership of ordnance, after Lord Carew.
In 1610 he served at the siege of Juliers under Sir Edward Cecil. In 1616 he yielded up the cautionary town of Brielle to the Dutch on the repayment by them of the loans received from England, receiving a life pension of £800 in compensation for his loss of the governorship. Two years later Sir Horace received from Maurice the governorship of Utrecht. He had previously aided the prince in disarming and suppressing the provincial levies, raised on behalf of Johan van Oldenbarnevelt.
Palatinate campaign
In May 1620 James I was being strongly urged by popular opinion to defend the Protestant cause of his son-in-law, Frederick V, Elector Palatine. He allowed Count Dohna, the Palatine envoy, to levy a body of volunteers at his own cost, and to appeal for funds. Dohna, as paymaster, selected Sir Horace Vere, as commander; Buckingham had wanted the post for Sir Edward Cecil, and withdrew support from the expedition.
News arrived of the treaty of Ulm (23 June), between the union of Catholic princes and the League, preparing the way for a catholic invasion of the palatinate, and money came in more rapidly. On 9 July Vere went to Theobalds to take leave of the king, and on 22 July the regiment, 2,200 strong, set sail from Gravesend to the Netherlands, to be escorted south into Germany and to the seat of war by a body of Dutch cavalry. By this time Vere was a professional soldier, even-tempered, brave and popular. The Earl of Essex was one of his lieutenants. Spinola was in the field with one army, Don Luis de Velasco in the way with another.
Vere's plan was to effect a junction with the Protestant force near Mannheim, under the Margrave of Ansbach. He marched through Wesel into the neighbourhood of Coblenz, and then made a detour by a route through the Taunus, on the other side of which, in the valley of the Main River, Spinola made an unsuccessful attempt to cut him off. Vere crossed the Main by a ford, near Frankfurt, and then, by way of Darmstadt and Bensheim (there resting his troops), and proceeded to Worms, where the junction of forces actually took place.
Spinola now adopted Fabian tactics in the hope of wearing the enemy out, until the approach of winter compelled the English and their allies to seek quarters. Vere divided his troops among the three most important strongholds of the Palatinate. He himself occupied Mannheim, Gerard Herbert he stationed in Heidelberg Castle, while Sir John Burroughs undertook to defend Frankenthal.
Early in 1621 the Protestant union was broken up, and the English garrisons had to give up all hope of relief. The English governors were not closely pressed that year. The garrison under Vere at Mannheim received a visit early in 1622 from the dethroned elector, who had promised them a diversion, and who, in conjunction with Mansfelt, had inflicted a momentary check upon the imperialist army under Johann Tserclaes von Tilly at Wiesloch (April). A few weeks later, however, Tilly, having been reinforced by Gonzalez de Cordova, inflicted defeats on the Protestants, and in June the elector had finally to leave Mannheim.
The English garrisons were now surrounded and threatened by a force of imperialists and Spaniards under Tilly, Cordova, and Verdugo. Vere resolved to hold out, though he knew that the military position was hopeless. On 16 September the town of Heidelberg was taken by storm, and the castle surrendered three days later. Sir Gerard Herbert had received a mortal wound during the siege. At Mannheim Vere, with a garrison of fourteen hundred men, without money or supplies, had to defend extensive fortifications. He retired to the citadel, but no extraneous help being forthcoming, he was forced to capitulate at the close of September, and, having marched out with the honours of war, withdrew to The Hague. Vere's defence was commemorated by George Chapman At Frankenthal, Burroughs did not surrender the place to Verdugo until 14 April 1623, and then only in response to direct orders from home.
The courage displayed by Vere against great odds was recognised in England, when the general returned early in February 1623, even if his salary and expenses were never paid in full by the treasury. On 16 February 1623 he was appointed master-general of the ordnance for life, and he became a member of the council of war on 20 July 1624. On the death of his elder brother, John, in the same year he became his residuary legatee, with the reversion of Tilbury and Kirby Hall upon the death of the widow.
Breda and the Brabant campaign
In 1624 Sir Horace Vere travelled once more to The Hague in order to second Prince Maurice in the defence of the fortress of Breda, under siege by Spinola from August. Maurice died on 23 April 1625. The only ways to approach the siege works from outside were by causeways. The new stadtholder, Maurice's brother, Frederick Henry, Prince of Orange, resolved to attempt the causeways, and Vere was selected to conduct this hazardous operation. Taking with him some six thousand men, including three hundred pikemen led by his kinsman, Robert de Vere, 19th Earl of Oxford, Vere started an hour before the dawn on the morning of 13 May 1625. The English marched along the dyke, and after a sharp engagement captured the redoubt. Spinola thereupon sent strong reinforcements to the threatened point, and, incurring a very heavy loss, the English were forced to retire. On his return to England that summer Vere, high in military reputation, was created Baron Vere of Tilbury.
His next enterprise in the Netherlands was in connection with the siege of 's-Hertogenbosch, one of the chief military positions in Brabant, undertaken by Prince Frederic Henry in April 1629. Sir Edward Vere (born ca. 1580), the illegitimate son of Horatio's first cousin Edward, Earl of Oxford, was mortally wounded in the lines on 18 August a few weeks before the place was finally surrendered. A large number of Englishmen who were afterwards distinguished soldiers served under Vere in the trenches at Den Bosch. Among them were: Thomas Fairfax and Philip Skippon, the future organisers of the New Model Army; Jacob Astley, Thomas Glemham, the future royalist generals; Sir John Borlase, and Henry Hexham, the historian of the Dutch wars. Fairfax, Skippon, and George Monck, particularly, were his pupils in the art of war.
The services of the Veres in the Netherlands were closed by the Capture of Maastricht May–August 1632. Vere commanded a powerful brigade, and posted his headquarters opposite the Brussels Gate. Among those killed during the operations were Vere's kinsman, Robert de Vere, 19th Earl of Oxford, while among the wounded were his nephew, Sir Simon Harcourt, and Sir Thomas Holles.
Death
After the surrender of Maastricht, Vere returned to England. While dining with Sir Harry Vane, The Hague envoy and his diplomatic friend, at Whitehall on 2 May 1635, he was seized with an apoplectic fit and died within two hours. He was buried with military pomp on 8 May in Westminster Abbey, where the same tomb serves for him and his brother, Sir Francis.
Marriage and issue
Vere married, in October 1607, Mary Tracy (1581-1671), daughter of Sir John Tracy (d.1591) of Tuddington, Gloucestershire, and widow of William Hoby, by whom she had two children. With his death the barony of Vere of Tilbury became extinct. Vere left five daughters, who were his coheirs:
Elizabeth Vere, who married John Holles, 2nd Earl of Clare, grandfather of the first Duke of Newcastle;
Mary Vere, who married, first, Sir Roger Townshend, Baronet, of Raynham in Norfolk, whence are descended the Marquises of Townshend, and secondly, Mildmay Fane, 2nd Earl of Westmorland;
Catherine Vere, who married, first, Oliver St John (1612/1613–November 1641 or 1642, son of Sir John St John, 1st Baronet, and Anne Leighton) and had Sir John St John, 2nd Baronet in 1648 (died 1657), and, secondly, John Poulett, 2nd Baron Poulett;
Anne Vere, who married Sir Thomas Fairfax (afterwards 3rd Baron Fairfax of Cameron); and
Dorothy Vere, who married John Wolstenholme, eldest son of Sir John Wolstenholme, bart., of Nostell, Yorkshire.
Susana Vere (1619–1623) Died at a young age.
Lady Vere continued to live at Clapton until the death of the widow of Lord Vere's eldest brother, John, when she succeeded to Kirby Hall, where she died on Christmas Eve 1670, aged 90. For a short while in the spring of 1645, after the death of the Countess of Dorset, the king's children, Elizabeth and Henry, Duke of Gloucester, were entrusted to her care. She was much in Parliament's favour; but (despite the handsome allowance) she transferred it to the Earl and Countess of Northumberland.
Vere was a first cousin of Edward de Vere, 17th Earl of Oxford (1550–1604).
Notes
References
Zedlers Universallexicon, vol.47, p. 211
Attribution
Category:1565 births
Category:1635 deaths
Category:English military personnel of the Eighty Years' War
Category:Barons in the Peerage of England
Category:English army officers
Category:People of the Tudor period
Category:16th-century English nobility
Category:17th-century English nobility
Category:English people of the Thirty Years' War
Category:English people of the Anglo-Spanish War (1585–1604)
Horace
Category:People of the Anglo-Spanish War (1625–1630)
Category:Knights Bachelor |
Background
==========
The National Center for Complementary and Alternative Medicine (NCCAM) defines Complementary and Alternative Medicine (CAM) as "medical and health systems, applications and products currently not considered as part of conventional medicine" \[[@B1]\].
An increased interest in CAM is observed among both the general population and health professionals. Despite its rising popularity, CAM has been excluded from conventional medical training for many years, however recently there is a tendency to include it in the medical curricula in some countries \[[@B2]\]. CAM began to draw attention among medical circles in 1990 when it was found that 13.7 billion US dollars were spent on CAM applications and that one in three Americans made use of CAM in 1993 \[[@B3]\]. A follow-up study by the same research group showed that use of alternative medicine increased by 65 % in 1997, with an increase in spending by 45.2 % \[[@B4]\]. It appears that CAM gained increasing popularity among medical trainers and students \[[@B5]-[@B7]\].
Similarly, use of CAM methods has grown in popularity in Turkey. Surveys with patient subgroups have shown that many patients with chronic diseases have used at least one of the CAM methods. Most commonly used methods were herbal treatment, massage and acupuncture, but they shared this information rarely with their primary doctors. Most of these studies indicated that it is important for healthcare professionals to discuss and give counseling about use of CAM to their patients \[[@B8]-[@B16]\].
In 1996, a broad-based panel including medical and nursing schools and representatives from the American Medical Association (AMA), American Academy of Family Practice (AAFP), Association of American Medical Colleges (AAMC), Federation of State Medical Boards, Pew Health Professions Commission, American Medical Student Association (AMSA), and other organizations gathered to make an evaluation on CAM education, and proposed CAM's integration into the curricula by the discipline with its philosophical underpinnings, scientific bases, educational preparation, applications, and evidence concerning its reliability and effectiveness \[[@B17]\]. In some countries, medical curricula already have structured programs on complementary and alternative medicine. Studies about medical students' attitudes toward and knowledge of CAM in several countries usually showed positive attitudes towards and a high level of desire to learn about CAM in medical schools.
In Turkey, practices of CAM vary widely regarding inclusion of CAM in the medical curriculum in the absence of a nationally agreed policy. Also, there are very few studies on students' attitudes toward, knowledge and desire to learn about CAM. Two studies with medical and nursing students were local studies included only one medical school \[[@B18],[@B19]\]. Another study carried out with general practitioners concluded that general practitioners wanted to learn more about CAM, and improve their knowledge \[[@B20]\]. So, there is lack of data at the national level. Therefore, this study aimed to examine knowledge and attitudes towards Complementary and Alternative Medicine among students attending faculties of medicine in Turkey, and find out whether they want to be trained in Complementary and Alternative Medicine.
Methods
=======
A cross-sectional study was carried out between October and December 2010 among medical students. In Turkey, there are 64 medical faculties, of which 54 are public, and a total of 34.869 students were attending these faculties at the end of 2009. Study population included 1st year, 5th year and 6th year medical students. For data collection, all provinces of Turkey were divided into three sub-groups on the basis of economic development level as measured by the State Planning Organization in 2009, and two faculties of medicine were randomly selected from each sub-group. Data were collected from a total of seven faculties of medicine, including six randomly selected faculties and Faculty of Medicine of Yeditepe University where the pilot study was carried out. The number of students required to represent the population of the study was 348 with a 95 % confidence level. For cluster sampling, we targeted to double the number of participants, and data were collected from 1st year, 5th year, and 6th year students attending the Faculties of Medicine in order to be able compare first-year undergraduates with intern students.
Students completed the questionnaires during class hours after obtaining necessary permits from the Faculty administrations. The questionnaire used was prepared by the researcher after review of the relevant international literature, and finalized following a pilot application prior to data collection.
The questionnaire consisted of three parts. The first part consisted of questions on sociodemographic characteristics of the students, such as age and gender. The second part consisted of yes-no questions asking the students whether they were familiar with the sixteen CAM methods that were selected based on a consensus of the study group after screening Turkish websites on CAM ; what they thought about the effectiveness of these methods; whether they would like to be trained in these methods; and whether they will be recommending these methods to their patients in their future professional lives. The third part consisted of 7-point Likert-type items, aiming to identify attitudes towards CAM designed on the basis of the questions used by Furnham in his 2003 study\[7\], after obtaining appropriate permission from the author. The research was approved by the Ethics Committee of Yeditepe University.
Data analysis
-------------
Statistical analyses were performed using SPSS v.19. Descriptive analyses and relevant significance tests were used for comparisons. The level of significance was set at p \<0.05.
Results
=======
Data were collected from a total of 943 medical students from seven faculties of medicine. Of these participants, 413 were female, and 511 were male, and 19 did not identify their gender. The mean age was 20.6 ±2.7 years. The most well known methods among the students were herbal treatment (n = 765, 81.2 %), acupuncture (n = 762, 80.8 %), hypnosis (n = 743, 78.8 %), and manipulative and body-based practices including massage (n = 726, 77 %) and meditation (n = 615, 65.2 %), respectively. Less than 10 % of the participants were familiar with homeopathy, chiropractic, the Alexander Technique, reflexology, shiatsu and chigong. Acupuncture, aromatherapy, herbal treatment and meditation were better known among female participants compared to males (p \< 0.05), and a larger proportion of male participants were more familiar with chiropractic than females (p \< 0.005). A larger proportion of the 5th and 6th year students reported familiarity with bioenergy (p = 0.009), chelation (p = 0.000), neural therapy (p = 0.009), ayurveda (p = 0.023) and homeopathy (p = 0.042) compared to 1st year students. There were no significant differences between the grades in the most well known five methods in the study sample. Table [1](#T1){ref-type="table"} shows distribution of opinions on the effectiveness of the five most well known methods among students, their willingness to be trained in these methods, and future likelihood of recommending them to their patients.
######
Percentage distribution of answers to other questions given by participants who knew about Alternative Medicine Methods (n = 943)
**I know %** **Believe effectiveness %** **I want education %** **I will suggest to my patients %**
----------------------------------- -------------- ----------------------------- ------------------------ -------------------------------------
**Herbal Treatment** 81,2 79,4 66,6 70,6
**Acupunture** 80,8 74,5 61,2 63,4
**Hypnosis** 78,8 63,8 65,8 48,2
**Body work (including massage)** 77 77,8 60,9 66,4
**Meditation** 65,2 63,6 53,8 52,2
The only inter-gender difference in effectiveness was related with the method of meditation, with a larger proportion of the female participants reporting it as an efficient method. A larger proportion of the 1st year students believed that acupuncture, herbal treatment and manipulative and body-based practices including massage were effective methods compared to 5th and 6th year students (p \< 0.005). Opinions on the effectiveness of the remaining methods did not vary by grade.
A larger proportion of female participants reported that they would recommend acupuncture (p = 0.003) and ayurveda (p = 0.019) compared to males, and future likelihood of recommending other methods did not vary by gender. A larger proportion of the 1st year students reported that they would recommend herbal treatment, acupuncture, manipulative and body-based practices including massage, meditation, shiatsu and ayurveda compared to 5th and 6th year students (p \< 0.005); and future likelihood of recommending other methods did not vary by gender. A larger proportion of the female participants expressed their willingness to be trained in acupuncture (p = 0.008) and meditation (p = 0.004) compared to males. Willingness to receive training in other methods did not vary by gender. In all methods except for homeopathy, a larger proportion of the 1st year students reported that they would like to receive training compared to 5th and 6th year students (p \< 0.05).
Overall, attitude towards CAM among the students was positive; they believed that knowledge of CAM would be useful, and current CAM practitioners were not well-trained, and they had to be medically qualified. Overall, students believed that CAM should be taught in medical schools, and doctors should be familiar with CAM treatments, and knowledge of CAM would be useful in their future professional lives. Table [2](#T2){ref-type="table"} shows attitudes with the highest and lowest percentages of agreement.
######
Attitude questions with the highest (mean score \> 5.00) and lowest (mean score \< 3.00) mean scores (n = 943)
**Items** **Mean ± S.D**
---------------------------------------------------------------------- ----------------
All practitioners of CAM should be medically qualified. 5,37 ± 1,85
I am intereseted in exploring new teratment modalities. 5,28 ± 1,80
Women have more tendency to CAM than men. 5,20 ± 1,9
On avarage, practitioners of CAM make less money than other doctors. 2,93 ± 1,86
I beilieve in alternative approaches in health area 2,92 ± 1,85
Most Practitioners of CAM receive a thorough training. 2,88 ± 1,65
Much of CAM is actually dangerous to the health of the patients. 2,88 ± 1,66
Treating a condition using CAM is safer than using modern methods 2,69 ± 1,71
You need to be "gifted" to carry out CAM 2,25 ± 1,61
One person of my family is currently using CAM treatment 2,17 ± 1,9
Students who had a personal interest in CAM; who thought it as an important aspect of medical practice; those who had a family member currently receiving CAM treatment; who thought that modern medicine had limitations of its own; who thought that patients had a right to choose between modern medicine and CAM; and, who thought that spiritual phenomena have an effect on health were of the opinion that CAM modalities should be included in the medical curriculum (p \< 0.005).
Significant inter-gender differences were found in attitudes in relation to five questions only (Table [3](#T3){ref-type="table"}). A larger proportion of the female students compared to male students reported that a doctor should be knowledgable about CAM (p = 0.001), and it would be helpful in their future professional lives (p = 0.015). A larger proportion of male students reported that CAM is more of an art than science (p = 0.026), patients have the right to choose between modern medicine and CAM (p = 0.004), and they believed in alternative approaches to health (p = 0.000). Table [4](#T4){ref-type="table"} shows inter-grade differences in the Likert-type attitude questions: 1st year students had higher mean scores for most of the items, whereas 5th year and 6th year students expressed more agreement with the following statements: CAM is underestimated in the world of medicine; it is effective in the treatment of minor complaints and illnesses only; it is certainly non-scientific and vague; and, use of CAM treatments are actually detrimental for the health of patients (p \< 0.005).
######
Attitudes in which there were significant inter-gender differences
**Men (n = 511)** **Women (n = 413)** **p**
--------------------------------------------------------------------------------------- ------------------- --------------------- ---------
CAM is more art than science (q18) 3,78 ± 1,82 3,51 ± 1,78 0,026\*
A doctor should know CAM methods (q27) 4,46 ± 1,97 4,92 ± 1,75 0,001\*
Knowledge of CAM is needed in my future professionalism. (q28) 4,20 ± 2,03 4,61 ± 2,37 0,015\*
I believe in that patients have right to choose between modern medicine and CAM (q36) 3,79 ± 2,12 3,38 ± 2,03 0,004\*
I believe in alternative approaches in medicine (q37) 3,16 ± 1,96 2,63 ± 1,67 0,000\*
Mann--Whitney U test p values, \*p \< 0,05.
######
Distribution of the Items of the Scale on Attitudes towards Alternative Methods in Medicine by Grade (n = 943)
**ITEMS** **First year** **5. and 6. class** **p**
------------------------------------------------------------------------------------------ ---------------- --------------------- ---------
Mean ± SD Mean ± SD
All practitioners of CAM should be medically qualified. 5,51 ± 1,75 5,15 ± 1,98 0,024\*
On avarage, practitioners of CAM make less money than other doctors. 3,12 ± 1,88 2,70 ± 1,89 0,000\*
CAM has low status within medicine 4,14 ± 1,78 4,57 ± 1,85 0,001\*
CAM is only effective in treating minor complaints. 3,91 ± 1,77 4,48 ± 1,94 0,000\*
CAM is fairly unscientific. 3,09 ± 1,84 3,47 ± 2,05 0,014\*
CAM has advanced considerably in recent years in understanding of illness and diseases 4,16 ± 1,65 3,52 ± 1,8 0,000\*
Practitioners of CAM are more prepared to listen to their patients. 4,56 ± 1,73 4,21 ± 1,86 0,012\*
Patients on CAM hardly ever get better 3,15 ± 1,57 3,84 ± 1,72 0,000\*
Despite considerable research, there are few aplicable results in CAM. 3,85 ± 1,58 4,66 ± 1,80 0,000\*
CAM should be thught in medical school. 4,66 ± 2,00 4,12 ± 2,13 0,000\*
Women have more tendency to CAM than men. 5,93 ± 1,91 5,58 ± 1,70 0,000\*
Most practitioners of CAM receive a thorough training. 3,03 ± 1,65 2,59 ± 1,63 0,000\*
CAM is safer than modern medical treatments 2,76 ± 1,70 2,55 ± 1,72 0,027\*
You need to be "gifted" to carry out CAM 2,38 ± 1,65 2,00 ± 1,51 0,000\*
A surprising number of patients claim its effective at curing their illness. 4,44 ± 165 4,14 ± 1,88 0,027\*
CAM is more cost-effective than modern medicine 3,47 ± 1,70 3,21 ± 1,79 0,020\*
Much of CAM is actually dangerous to the health of patients 2,75 ± 1,58 3,14 ± 1,78 0,003\*
The reason for the success of CAM is mainly due to treating the whole person. 3,73 ± 1,73 3,19 ± 1,72 0,000\*
A doctor should know CAM methods 4,95 ± 1,73 4,13 ± 2,08 0,000\*
Knowledge of CAM is needed in my future professionalism 4,67 ± 2,21 3,83 ± 2,08 0,000\*
I believe that to suggest CAM modalities to their patients is responsibility of doctors. 4,20 ± 1,91 3,22 ± 2,04 0,000\*
I am personally interested in CAM 4,16 ± 2,03 3,53 ± 2,14 0,000\*
CAM is an important part of my professionalism 3,59 ± 1,95 2,80 ± 1,92 0,000\*
CAM is an important part of my culture 3,52 ± 2,01 3,17 ± 1,95 0,013\*
I believe that CAM may have positive effect on general health outcomes 4,25 ± 1,82 3,71 ± 1,84 0,000\*
Mann--Whitney U test p values, \*p \< 0,05.
Discussion
==========
A majority of the medical students in the study population were familiar with some of the CAM methods while some were almost unheard of. Studies on the general population show that among the methods included in this study, herbal treatment, manipulative and body-based practices including massage and acupuncture are the most well known and the most frequently practiced modalities \[[@B8]-[@B16],[@B21]-[@B24]\].
Medical students are also a part of the general population, and it is only natural, especially for 1st year students, to know about the most well-known and most frequently practiced methods among the general population. Fifth and 6th year students were more knowledgeable about the methods that are less known to the study sample compared to 1st year students. None of the medical schools included in the study had a structured CAM training. Thus, it might be the case that 5th and 6th year students learn about less known methods from patients during their clinical practice or through sharing of experiences \[[@B7]\].
Overall, students were more likely to think that methods that they were familiar with were effective, and they were more likely to recommend these methods to their patients in their future professional lives. It was surprising that students expressed their wish to be trained on these methods independent of their familiarity.
There were inter-gender differences in terms of the CAM methods known, opinions on the effectiveness of different methods, methods in which they wanted to be trained, and attitudes towards the methods. Female participants were more familiar with the most well known methods in the whole study group and had more positive attitudes toward CAM.
Previous studies in different countries have also found that female have more positive attitudes towards CAM, and are more likely to use it \[[@B25]-[@B28]\]. As in the whole world, increasingly more female students have been choosing to study medicine than male students in Turkey. We can assume that this gender difference may increase medical students' willingness for training on CAM in the future.
Many studies show that medical students have positive attitudes towards CAM, and they support its inclusion in the medical curricula \[[@B5]-[@B7],[@B29],[@B30]\]. Despite increasing interest in CAM, many faculties of medicine do not provide structured CAM training, and those that do provide it have very different teaching goals and content \[[@B31]-[@B34]\].
Only a few studies were carried out in Turkey on the knowledge and attitude of medical students towards CAM. In 2004, Uzun&Tan found that 64 % of nursing students of all grades reported that CAM could be included in the curriculum, and 62.3 % reported that it could be used in practice.\[19\] Nursing students had generally a more positive attitude than medical students. In a study conducted in 2006--2007 with the participation of medical students and nursing students of all grades at Ege University, Yıldırım *et al*. used questions developed on the basis of literature, and found that 61.3 % of the nursing students and 37.9 % of the medical student thought that CAM should be included in the school curriculum \[[@B18]\]. The difference might have been related to the methodologic differences in nursing and medical schools. Unlike our study representing all regions of Turkey, their study was carried out in a university from the Western part of Turkey, which was reported as one of the limitations of their study by the authors. Another study with general practitioners in Bursa, a city in the western part of Turkey, found that 62.7 % of the practitioners believed that a CAM training should be provided in faculties of medicine \[[@B20]\]. The present study can be considered complementary to these findings, showing that medical students in Turkey believe that CAM should be included in the curriculum, and that knowledge of CAM would be useful in their future professional lives, and doctors should be familiar with CAM methods. Many factors can be involved in shaping attitudes of the students, including environmental and individual factors such as having a family member who receives CAM treatment, having a personal interest in CAM, believing that spiritual phenomena have an effect on health, and belief in a patient's right to choose between modern and alternative medicine. Overall, positive attitudes towards and willingness to receive training in CAM methods declined as the number of years spent in the faculty of medicine increased \[7,35\]. This change of attitude probably results from increased exposure to evidence-based medicine, trainers who act as role models, and personal experiences with the patients.
CAM applications make up a significant portion of health spending, and there is an increasing demand for CAM applications. Medical doctors, even if they are not CAM practitioners themselves and have negative attitudes towards CAM, will from time to time feel the need to be able to provide guidance for their patients and be familiar with CAM methods at least at a minimal level for drug interactions and treatment effects \[[@B32]\]. It seems to be the case that in future medical students will show a more strongly demand to receive training in this field. On the other hand, CAM is a very broad field with many different applications and despite increasing number of scientific research on some methods, not all methods are evidence-based. It is difficult to include all CAM applications into the curriculum, and locate them into the medical programme, and determine the level of training to be provided.
Our study was limited in some respects. Because it had a cross-sectional design, it was not possible to analyze the factors that have an effect on attitudes over time. A different, prospective, and interventional design is required to interpret how current medical education and sociocultural factors have an impact on students' knowledge and attitudes. Although overall response rate was over 93 % and only a few students declined to complete the questionnaire, students with a negative attitude and less familiarity with CAM might have not answered the questionnaire and this may have affected some results. Because of high response rate and achievement to reach to the targeted number of students, we think this bias may have had some effect on overall results.
Conclusions
===========
Majority of the medical students were familiar with the CAM methods widely used in Turkey, and knowledge about the methods which were less frequently used has been increasing with the senior years in the medical faculty, even though these methods are not included in the curriculum. Overall, most students had positive attitudes towards CAM; they wanted to receive training on the subject; and they are likely to recommend CAM methods to their patients in their future professional lives. Currently, none of the medical curricula in Turkey has a structured standard CAM training. With a gradual scientific development and increasing popularity, there appears a need for a coordinated policy in integrating CAM into the medical cirruculum, and expectations of and feedback from medical students should be taken into consideration in setting educational standards.
Competing interests
===================
The authors declare that they have no competing interests.
Authors\' contributions
=======================
HA carried out the design and coordination of the study and data entry and analysis. HA also participated in the sequence alignment and drafted the manuscript. GĐ carried out the data entry and analysis and in the sequence alignment and drafted the manuscript. EK carried out statistics and also conducted data entry. ÇA, SA, ND,GE, CÖ, HAS carried out the study in their regions. OH designed the methodology of the study and performed the statistical analysis. OH participated in its design and coordination and helped to draft the manuscript. All authors read and approved the final manuscript.
Pre-publication history
=======================
The pre-publication history for this paper can be accessed here:
<http://www.biomedcentral.com/1472-6882/12/115/prepub>
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namespace weka.classifiers.rules;
class OneRRule
{
isA Serializable,RevisionHandler;
depend java.io.Serializable;
depend java.util.Collections;
depend java.util.Enumeration;
depend java.util.LinkedList;
depend java.util.ListIterator;
depend java.util.Vector;
depend weka.classifiers.AbstractClassifier;
depend weka.classifiers.Classifier;
depend weka.classifiers.Sourcable;
depend weka.core.Attribute;
depend weka.core.Capabilities;
depend weka.core.Capabilities.Capability;
depend weka.core.Instance;
depend weka.core.Instances;
depend weka.core.Option;
depend weka.core.RevisionHandler;
depend weka.core.RevisionUtils;
depend weka.core.TechnicalInformation;
depend weka.core.TechnicalInformation.Field;
depend weka.core.TechnicalInformation.Type;
depend weka.core.TechnicalInformationHandler;
depend weka.core.Utils;
depend weka.core.WekaException;
/**
* for serialization
*/
static final long serialVersionUID=-3459427003147861443L;
/**
* for serialization
*/
static final long serialVersionUID=2252814630957092281L;
/**
* The class attribute.
*/
private final Attribute m_class;
/**
* The number of instances used for building the rule.
*/
private final int m_numInst;
/**
* Attribute to test
*/
private final Attribute m_attr;
/**
* Training set examples this rule gets right
*/
private int m_correct;
/**
* Predicted class for each value of attr
*/
private final int[] m_classifications;
/**
* Predicted class for missing values
*/
private int m_missingValueClass=-1;
/**
* Breakpoints (numeric attributes only)
*/
private double[] m_breakpoints;
/**
* A 1-R rule
*/
private OneRRule m_rule;
/**
* The minimum bucket size
*/
private int m_minBucketSize=6;
/**
* a ZeroR model in case no model can be built from the data
*/
private Classifier m_ZeroR;
/**
* Returns a string describing classifier
* @return a description suitable for displaying in the explorer/experimentergui
*/
public String globalInfo(){
return "Class for building and using a 1R classifier; in other words, uses " + "the minimum-error attribute for prediction, discretizing numeric " + "attributes. For more information, see:\n\n"+ getTechnicalInformation().toString();
}
/**
* Returns an instance of a TechnicalInformation object, containing detailed information about the technical background of this class, e.g., paper reference or book this class is based on.
* @return the technical information about this class
*/
@Override public TechnicalInformation getTechnicalInformation(){
TechnicalInformation result;
result=new TechnicalInformation(Type.ARTICLE);
result.setValue(Field.AUTHOR,"R.C. Holte");
result.setValue(Field.YEAR,"1993");
result.setValue(Field.TITLE,"Very simple classification rules perform well on most commonly used datasets");
result.setValue(Field.JOURNAL,"Machine Learning");
result.setValue(Field.VOLUME,"11");
result.setValue(Field.PAGES,"63-91");
return result;
}
/**
* Constructor for nominal attribute.
* @param data the data to work with
* @param attribute the attribute to use
* @throws Exception if something goes wrong
*/
public OneRRule(Instances data,Attribute attribute) throws Exception {
m_class=data.classAttribute();
m_numInst=data.numInstances();
m_attr=attribute;
m_correct=0;
m_classifications=new int[m_attr.numValues()];
}
/**
* Constructor for numeric attribute.
* @param data the data to work with
* @param attribute the attribute to use
* @param nBreaks the break point
* @throws Exception if something goes wrong
*/
public OneRRule(Instances data,Attribute attribute,int nBreaks) throws Exception {
m_class=data.classAttribute();
m_numInst=data.numInstances();
m_attr=attribute;
m_correct=0;
m_classifications=new int[nBreaks];
m_breakpoints=new double[nBreaks - 1];
}
/**
* Returns a description of the rule.
* @return a string representation of the rule
*/
@Override public String toString(){
try {
StringBuffer text=new StringBuffer();
text.append(m_attr.name() + ":\n");
for (int v=0; v < m_classifications.length; v++) {
text.append("\t");
if (m_attr.isNominal()) {
text.append(m_attr.value(v));
}
else if (v < m_breakpoints.length) {
text.append("< " + m_breakpoints[v]);
}
else if (v > 0) {
text.append(">= " + m_breakpoints[v - 1]);
}
else {
text.append("not ?");
}
text.append("\t-> " + m_class.value(m_classifications[v]) + "\n");
}
if (m_missingValueClass != -1) {
text.append("\t?\t-> " + m_class.value(m_missingValueClass) + "\n");
}
text.append("(" + m_correct + "/"+ m_numInst+ " instances correct)\n");
return text.toString();
}
catch ( Exception e) {
return "Can't print OneR classifier!";
}
}
/**
* Returns the revision string.
* @return the revision
*/
@Override public String getRevision(){
return RevisionUtils.extract("$Revision: 10153 $");
}
/**
* Classifies a given instance.
* @param inst the instance to be classified
* @return the classification of the instance
*/
@Override public double classifyInstance(Instance inst) throws Exception {
if (m_ZeroR != null) {
return m_ZeroR.classifyInstance(inst);
}
int v=0;
if (inst.isMissing(m_rule.m_attr)) {
if (m_rule.m_missingValueClass != -1) {
return m_rule.m_missingValueClass;
}
else {
return 0;
}
}
if (m_rule.m_attr.isNominal()) {
v=(int)inst.value(m_rule.m_attr);
}
else {
while (v < m_rule.m_breakpoints.length && inst.value(m_rule.m_attr) >= m_rule.m_breakpoints[v]) {
v++;
}
}
return m_rule.m_classifications[v];
}
/**
* Returns default capabilities of the classifier.
* @return the capabilities of this classifier
*/
@Override public Capabilities getCapabilities(){
Capabilities result=super.getCapabilities();
result.disableAll();
result.enable(Capability.NOMINAL_ATTRIBUTES);
result.enable(Capability.NUMERIC_ATTRIBUTES);
result.enable(Capability.DATE_ATTRIBUTES);
result.enable(Capability.MISSING_VALUES);
result.enable(Capability.NOMINAL_CLASS);
result.enable(Capability.MISSING_CLASS_VALUES);
return result;
}
/**
* Generates the classifier.
* @param instances the instances to be used for building the classifier
* @throws Exception if the classifier can't be built successfully
*/
@Override public void buildClassifier(Instances instances) throws Exception {
boolean noRule=true;
getCapabilities().testWithFail(instances);
Instances data=new Instances(instances);
data.deleteWithMissingClass();
if (data.numAttributes() == 1) {
System.err.println("Cannot build model (only class attribute present in data!), " + "using ZeroR model instead!");
m_ZeroR=new weka.classifiers.rules.ZeroR();
m_ZeroR.buildClassifier(data);
return;
}
else {
m_ZeroR=null;
}
Enumeration<Attribute> enu=instances.enumerateAttributes();
while (enu.hasMoreElements()) {
try {
OneRRule r=newRule(enu.nextElement(),data);
if (noRule || r.m_correct > m_rule.m_correct) {
m_rule=r;
}
noRule=false;
}
catch ( Exception ex) {
}
}
if (noRule) {
throw new WekaException("No attributes found to work with!");
}
}
/**
* Create a rule branching on this attribute.
* @param attr the attribute to branch on
* @param data the data to be used for creating the rule
* @return the generated rule
* @throws Exception if the rule can't be built successfully
*/
public OneRRule newRule(Attribute attr,Instances data) throws Exception {
OneRRule r;
int[] missingValueCounts=new int[data.classAttribute().numValues()];
if (attr.isNominal()) {
r=newNominalRule(attr,data,missingValueCounts);
}
else {
r=newNumericRule(attr,data,missingValueCounts);
}
r.m_missingValueClass=Utils.maxIndex(missingValueCounts);
if (missingValueCounts[r.m_missingValueClass] == 0) {
r.m_missingValueClass=-1;
}
else {
r.m_correct+=missingValueCounts[r.m_missingValueClass];
}
return r;
}
/**
* Create a rule branching on this nominal attribute.
* @param attr the attribute to branch on
* @param data the data to be used for creating the rule
* @param missingValueCounts to be filled in
* @return the generated rule
* @throws Exception if the rule can't be built successfully
*/
public OneRRule newNominalRule(Attribute attr,Instances data,int[] missingValueCounts) throws Exception {
int[][] counts=new int[attr.numValues()][data.classAttribute().numValues()];
Enumeration<Instance> enu=data.enumerateInstances();
while (enu.hasMoreElements()) {
Instance i=enu.nextElement();
if (i.isMissing(attr)) {
missingValueCounts[(int)i.classValue()]++;
}
else {
counts[(int)i.value(attr)][(int)i.classValue()]++;
}
}
OneRRule r=new OneRRule(data,attr);
for (int value=0; value < attr.numValues(); value++) {
int best=Utils.maxIndex(counts[value]);
r.m_classifications[value]=best;
r.m_correct+=counts[value][best];
}
return r;
}
/**
* Create a rule branching on this numeric attribute
* @param attr the attribute to branch on
* @param data the data to be used for creating the rule
* @param missingValueCounts to be filled in
* @return the generated rule
* @throws Exception if the rule can't be built successfully
*/
public OneRRule newNumericRule(Attribute attr,Instances data,int[] missingValueCounts) throws Exception {
data=new Instances(data);
int lastInstance=data.numInstances();
data.sort(attr);
while (lastInstance > 0 && data.instance(lastInstance - 1).isMissing(attr)) {
lastInstance--;
missingValueCounts[(int)data.instance(lastInstance).classValue()]++;
}
if (lastInstance == 0) {
throw new Exception("Only missing values in the training data!");
}
double lastValue=0;
LinkedList<int[]> distributions=new LinkedList<int[]>();
LinkedList<Double> values=new LinkedList<Double>();
int[] distribution=null;
for (int i=0; i < lastInstance; i++) {
if ((i == 0) || (data.instance(i).value(attr) > lastValue)) {
if (i != 0) {
values.add((lastValue + data.instance(i).value(attr)) / 2.0);
}
lastValue=data.instance(i).value(attr);
distribution=new int[data.numClasses()];
distributions.add(distribution);
}
distribution[(int)data.instance(i).classValue()]++;
}
values.add(Double.MAX_VALUE);
ListIterator<int[]> it=distributions.listIterator();
ListIterator<Double> itVals=values.listIterator();
int[] oldDist=null;
while (it.hasNext()) {
int[] newDist=it.next();
itVals.next();
if ((oldDist != null) && ((Utils.maxIndex(newDist) == Utils.maxIndex(oldDist)) || (oldDist[Utils.maxIndex(oldDist)] < m_minBucketSize))) {
for (int j=0; j < oldDist.length; j++) {
newDist[j]+=oldDist[j];
}
it.previous();
it.previous();
it.remove();
it.next();
itVals.previous();
itVals.previous();
itVals.remove();
itVals.next();
}
oldDist=newDist;
}
int numCorrect=0;
it=distributions.listIterator();
itVals=values.listIterator();
oldDist=null;
while (it.hasNext()) {
int[] newDist=it.next();
itVals.next();
numCorrect+=newDist[Utils.maxIndex(newDist)];
if ((oldDist != null) && (Utils.maxIndex(newDist) == Utils.maxIndex(oldDist))) {
for (int j=0; j < oldDist.length; j++) {
newDist[j]+=oldDist[j];
}
it.previous();
it.previous();
it.remove();
it.next();
itVals.previous();
itVals.previous();
itVals.remove();
itVals.next();
}
oldDist=newDist;
}
OneRRule r=new OneRRule(data,attr,distributions.size());
r.m_correct=numCorrect;
it=distributions.listIterator();
itVals=values.listIterator();
int v=0;
while (it.hasNext()) {
r.m_classifications[v]=Utils.maxIndex(it.next());
double splitPoint=itVals.next();
if (itVals.hasNext()) {
r.m_breakpoints[v]=splitPoint;
}
v++;
}
return r;
}
/**
* Returns an enumeration describing the available options..
* @return an enumeration of all the available options.
*/
@Override public Enumeration<Option> listOptions(){
String string="\tThe minimum number of objects in a bucket (default: 6).";
Vector<Option> newVector=new Vector<Option>(1);
newVector.addElement(new Option(string,"B",1,"-B <minimum bucket size>"));
newVector.addAll(Collections.list(super.listOptions()));
return newVector.elements();
}
/**
* Parses a given list of options. <p/> <!-- options-start --> Valid options are: <p/> <pre> -B <minimum bucket size> The minimum number of objects in a bucket (default: 6). </pre> <!-- options-end -->
* @param options the list of options as an array of strings
* @throws Exception if an option is not supported
*/
@Override public void setOptions(String[] options) throws Exception {
String bucketSizeString=Utils.getOption('B',options);
if (bucketSizeString.length() != 0) {
m_minBucketSize=Integer.parseInt(bucketSizeString);
}
else {
m_minBucketSize=6;
}
super.setOptions(options);
}
/**
* Gets the current settings of the OneR classifier.
* @return an array of strings suitable for passing to setOptions
*/
@Override public String[] getOptions(){
Vector<String> options=new Vector<String>(1);
options.add("-B");
options.add("" + m_minBucketSize);
Collections.addAll(options,super.getOptions());
return options.toArray(new String[0]);
}
/**
* Returns a string that describes the classifier as source. The classifier will be contained in a class with the given name (there may be auxiliary classes), and will contain a method with the signature: <pre> <code> public static double classify(Object[] i); </code> </pre> where the array <code>i</code> contains elements that are either Double, String, with missing values represented as null. The generated code is public domain and comes with no warranty.
* @param className the name that should be given to the source class.
* @return the object source described by a string
* @throws Exception if the souce can't be computed
*/
@Override public String toSource(String className) throws Exception {
StringBuffer result;
int i;
result=new StringBuffer();
if (m_ZeroR != null) {
result.append(((ZeroR)m_ZeroR).toSource(className));
}
else {
result.append("class " + className + " {\n");
result.append(" public static double classify(Object[] i) {\n");
result.append(" // chosen attribute: " + m_rule.m_attr.name() + " ("+ m_rule.m_attr.index()+ ")\n");
result.append("\n");
result.append(" // missing value?\n");
result.append(" if (i[" + m_rule.m_attr.index() + "] == null)\n");
if (m_rule.m_missingValueClass != -1) {
result.append(" return Double.NaN;\n");
}
else {
result.append(" return 0;\n");
}
result.append("\n");
result.append(" // prediction\n");
result.append(" double v = 0;\n");
result.append(" double[] classifications = new double[]{" + Utils.arrayToString(m_rule.m_classifications) + "};");
result.append(" // ");
for (i=0; i < m_rule.m_classifications.length; i++) {
if (i > 0) {
result.append(", ");
}
result.append(m_rule.m_class.value(m_rule.m_classifications[i]));
}
result.append("\n");
if (m_rule.m_attr.isNominal()) {
for (i=0; i < m_rule.m_attr.numValues(); i++) {
result.append(" ");
if (i > 0) {
result.append("else ");
}
result.append("if (((String) i[" + m_rule.m_attr.index() + "]).equals(\""+ m_rule.m_attr.value(i)+ "\"))\n");
result.append(" v = " + i + "; // "+ m_rule.m_class.value(m_rule.m_classifications[i])+ "\n");
}
}
else {
result.append(" double[] breakpoints = new double[]{" + Utils.arrayToString(m_rule.m_breakpoints) + "};\n");
result.append(" while (v < breakpoints.length && \n");
result.append(" ((Double) i[" + m_rule.m_attr.index() + "]) >= breakpoints[(int) v]) {\n");
result.append(" v++;\n");
result.append(" }\n");
}
result.append(" return classifications[(int) v];\n");
result.append(" }\n");
result.append("}\n");
}
return result.toString();
}
/**
* Returns a description of the classifier
* @return a string representation of the classifier
*/
@Override public String toString(){
if (m_ZeroR != null) {
StringBuffer buf=new StringBuffer();
buf.append(this.getClass().getName().replaceAll(".*\\.","") + "\n");
buf.append(this.getClass().getName().replaceAll(".*\\.","").replaceAll(".","=") + "\n\n");
buf.append("Warning: No model could be built, hence ZeroR model is used:\n\n");
buf.append(m_ZeroR.toString());
return buf.toString();
}
if (m_rule == null) {
return "OneR: No model built yet.";
}
return m_rule.toString();
}
/**
* Returns the tip text for this property
* @return tip text for this property suitable for displaying in theexplorer/experimenter gui
*/
public String minBucketSizeTipText(){
return "The minimum bucket size used for discretizing numeric " + "attributes.";
}
/**
* Get the value of minBucketSize.
* @return Value of minBucketSize.
*/
public int getMinBucketSize(){
return m_minBucketSize;
}
/**
* Set the value of minBucketSize.
* @param v Value to assign to minBucketSize.
*/
public void setMinBucketSize(int v){
m_minBucketSize=v;
}
/**
* Returns the revision string.
* @return the revision
*/
@Override public String getRevision(){
return RevisionUtils.extract("$Revision: 10153 $");
}
/**
* Main method for testing this class
* @param argv the commandline options
*/
public static void main(String[] argv){
runClassifier(new OneR(),argv);
}
}
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This invention relates in general to an electroforming process for using a reusable electroforming mandrel.
The fabrication of hollow articles by an electroforming process is well known. Generally, the articles are fabricated by electrodepositing a metal onto an elongated mandrel which is suspended in an electrolytic bath. The materials from which the mandrel and the electroformed article are fabricated are selected to exhibit a different coefficient of thermal expansion to permit removal of the belt from the mandrel upon cooling of the assembly. In one example of an electroforming arrangement, the mandrel comprises a core cylinder formed of aluminum which is overcoated with a thin layer of chromium and is supported and rotated in a bath of nickel sulfamate. In the process for forming large hollow articles having a large cross sectional area, it has been found that a diametric parting gap, i.e. a gap formed by the difference between the average inside electroformed article diameter and the average mandrel diameter at the parting temperature must be at least 8 mils (200 mm) and at least about 10-12 mils (0.250 mm-300 mm or 0.04-0.06 percent of the diameter of the mandrel) for reliable and rapid separation of the large article from the mandrel. For example, at a parting gap of about 6 mils (0.015 mm), high incidence of both belt and mandrel damage are encountered due to inability to effect separation of the belt from the mandrel. Various different techniques have been developed for forming and removing tubes from electroforming mandrels depending upon the cross sectional area of the electroformed tube.
A process for electroforming hollow nickel articles having a large cross sectional area onto a mandrel is described in U.S. Pat. No. 3,844,906 to R. E. Bailey et al. More specifically, the process involves establishing an electroforming zone comprising a nickel anode and a cathode comprising a support mandrel, the anode and cathode being separated by a nickel sulfamate solution maintained at a temperature of from about 140.degree. F. (60.degree. C.) to 150.degree. F. (65.5.degree. C.) and having a current density therein ranging from about 20 to 50 amps/ft.sup.2 (amps/dm.sup.2), imparting sufficient agitation to the solution to continuously expose the cathode to fresh solution, maintaining this solution within the zone at a stable equilibrium composition comprising:
______________________________________ Total Nickel 12.0 to 15.0 oz/gal (90-112.5 g/l) Halide as NiX.sub.2.6H.sub.2 O 0.11 to 0.23 mole/gal (0.44-0.92 mole/l) H.sub.3 BO.sub.3 4.5 to 6.0 oz/gal (33.7-45 g/l) ______________________________________
electrolytically removing metallic and organic impurities from the solution upon egress thereof from the electroforming zone, continuously charging to the solution about 1.0 to 2.0.times.10.sup.-4 moles of a stress reducing agent per mole of nickel electrolytically deposited from the solution, passing the solution through a filtering zone to remove any solid impurities therefrom, cooling the solution sufficiently to maintain the temperature within the electroforming zone upon recycle thereto at about 140.degree. F. (60.degree. C.) to 160.degree. F. (65.5.degree. C.) at the current density in the electroforming zone, and recycling the solution to the electroforming zone. The thin flexible endless nickel belt formed by this electrolytic process is recovered by cooling the nickel coated mandrel to effect the parting of the nickel belt from the mandrel due to different respective coefficients of thermal expansion.
For metal articles fabricated by electroforming on mandrels having a small cross-sectional area, the process described in U.S. Pat. No. 4,501,646 to W. G. Herbert overcomes difficulties in removing the electroformed article from the mandrel. For example, when the chromium coated aluminum mandrel described in U.S. Pat. No. 3,844,906 is fabricated into electroforming mandrels having very small diameters of less than about 1 inch, metal articles electroformed on these very small diameter mandrels are extremely difficult or even impossible to remove from the mandrel. Attempts to remove the small diameter electroformed article formed by the process described in U.S. Pat. No. 3,844,906 the can result in destruction or damage to the mandrel or the electroformed article, e.g. due to bending, scratching or denting. The entire disclosures of U.S. Pat. No. 3,844,906 and U.S. Pat. No. 4,501,646 are incorporated herein by reference.
Various materials may be utilized as temporary removable coatings from a mandrel. These coatings can be meltable to facilitate removal of an electroformed article thereon. For example, a coating of wax may be utilized as a meltable coating. However, a wax coating must be rendered conductive in order to function as an electroforming surface. The preparation of a conductive wax as well as the reclaiming of the conductive wax for subsequent use can be expensive and require additional processing steps. Moreover, wax is relatively soft and easily damaged during handling.
Japanese patent document No. J59-060702A, published Apr. 6, 1984, discloses a method of electroforming nickel stampers. The method comprises forming a thin reaction film having a low melting point on a base, embossing fine convex patterns on the film to make a master, forming a coating made of gold (alloy) on the master, forming a nickel layer by electrolytic deposition, separating a laminate comprising the gold and nickel from the master and eliminating the residual thin reaction films from the surface of the gold coat to obtain a nickel stamper. A reaction film is preferably made by reactive sputtering and preferably has a composition of TeCH. Residual film may be eliminated using ammonium persulfate. This process requires a reactive sputtering step, an embossing step, a gold deposition step and a special residual film elimination step using ammonium persulfate. The use of reactive sputtering equipment, exotic materials and multiple steps render the process complex and expensive. Moreover, since it appears that a reaction is necessary during sputtering to deposit the composition of TeCH, the deposited reaction film would appears to be unreusable.
Japanese patent document No. J5-8210 187 A relates to the formation of a parting film on the surface of a metal die, plating a layer on the parting film and peeling off the metal die to form a metal body having a configuration reversal to that of the metal die. The parting film is formed from an oxide film obtained by exposing the metal die to oxygen plasma. The oxygen plasma is applied to the surface of a substrate under oxygen pressure of 0.1-1 torr and a Ni film of about 0.2-0.3 mm in thickness is formed. The method is suitable for forming a pattern of highly integrated digital information, a deeply-grooved pattern, etc. in an electroforming process. Since the parting film is formed by the oxygen plasma, it is uniform and adhesive to the substrate. This process requires extremely high temperatures to form a parting layer and requires peeling off the metal die to form a metal body. Such an oxide film is difficult and expensive to make and does not appear to be readily reusable.
In U.S. Pat. No. 4,300,959, a method of electroforming is disclosed in which, for example, nickel and then copper is electroplated onto a wax mandrel coated with a sprayed coating of silver paint. A third layer of nickel is plated onto the copper layer and the wax mandrel is removed. The layered metallic object is heated to a point above the melting point of copper to yield a nickel electroformed object containing copper, nickel alloy. Since the wax substrate is not normally conductive, it is coated with a conductive silver coating which apparently comprises a heterogeneous mixture of silver particles, a binder , and a solvent for the binder so that the coating can be applied by spraying at room temerature to avoid melting the wax mandrel. The process disclosed in this U.S. patent requires the use of a mandrel that must be destroyed. Moreover, since the conductive coating on the wax would contaminate the wax, the coated mandrel constitutes a disposable, not a reusable material. In addition the use of an apparently heterogeneous conductive coating containing particulate material causes perturbations at the electroforming surface. In addition, a wax mandrel is highly vulnerable to surface damage prior to or during electroforming.
In order to reuse electroforming mandrels meeting precise tolerance requirements, the mandrels must be carefully handled to avoid scratching, gouging or otherwise damaging the smooth electroforming surface of the mandrel prior to, during and after each electroforming operation. Deep gouges, for example, may render the mandrel useless because electroformed articles may not be readily removed from the mandrel. Repair of damaged electroformed surfaces is normally impractical. Moreover, deformities in the surface of an electroforming mandrel can carry over to electroformed articles rendering electroformed articles useless for cosmetic reasons or for failing to meet the tolerance requirements for precision applications. |
RUSSO-TURKISH DIVERGENCE (PART II): THE ENERGY DIMENSION
Energy issues figure prominently in the Russo-Turkish relationship. Their impact is not nearly as clear-cut as are the Iranian and Syrian issues. Turkey and Russia have a complex, evolving relationship characterized by mutual dependencies in the oil and gas spheres. As Richard Weitz stated, “Energy relations between Russia and Turkey have long been characterized by overt friendship and subtle competition.”[1]
In the first part of this two-part series of research on Russo-Turkish relations, the authors contended that during 2009-2010, behind the surface of the rhetoric of convergence, there frequently lay strategic divergence between Russia and Turkey. In all those years, Turkish officials and experts described their relations with Russia as being the best ever and said that bilateral harmony featured prominently in the past decade’s international relations. However, Russia and Turkey had already begun to diverge during 2009-2010, and 2011 was a difficult year in Turkey’s relations with Russia in the security sphere. The year 2012 does not look much better.
There is no clear consensus in the academic literature as to how convergent or divergent Russo-Turkish energy interests are. This is the focus of this article. Is there a coherence between Turkey’s energy policy and its general foreign policy? What is a “gas hub”? More academic work in needed in this area, including the consideration of the implications for European and Central Asian energy security and political relations.The years 2009-2010 have seen sudden reversals of fortune in the acute geopolitical rivalries between Nabucco and South Stream. While uncertainty surrounding future demand and financing raised the possibility that neither pipeline ever become a reality, Moscow seemed to be gaining the upper hand. Nabucco was sinking. Turkey’s stance between Nabucco and South Stream was pivotal. Turkey faced difficult choices between two competing and mutually exclusive energy supply routes. The Nabucco and post-Nabucco routes served Western Europe’s interest in reducing its dependency on Russian gas, while South Stream would help Russia strengthen its position as the main energy producer for European and Turkish markets.
The natural disaster in Japan and revolutions in North Africa in the spring of 2011 ignited a new bout of the pipeline rivalry. By the end of 2011, Ankara had a pair of seemingly contradictory gas pipeline deals (both Nabucco and South Stream), which raised very interesting questions about the nature of Turkey’s energy policy. Although both deals may be part of Ankara’s plan to make itself a major energy transit hub, there was something that sounded dissonant about them coming so close together. With the Azeri agreement, Ankara appeared to be taking part in laying the groundwork for an energy corridor that would help Europe reduce its reliance on Russian gas and that would serve as a template for other pipeline projects–including, ideally, a modified version of the troubled Nabucco pipeline plan–that would bring non-Russian resources from the Caspian and the Middle East westward. On the other hand, with the Russian agreement, Ankara was now taking part in a project that many analysts see as designed to undermine Nabucco and the EU’s plans to dilute Gazprom’s influence in the European energy market.
The Russo-Turkish energy relationship is the most intimate aspect of the bilateral connection. Yet the evidence for an erosion of ties seemingly appeared to be contradicted by the December 30, 2011, Russo-Turkish energy agreement. On its face, this accord signals a high degree of amity and cooperation between Moscow and Ankara. If, however, one probes more deeply into both sides’ energy goals and policies, it becomes clear that while this accord does signify positive aspects of the Russo-Turkish relationship, matters are much more complicated than a simple reading of the accord would indicate.
RUSSO-TURKISH ENERGY RELATIONS AND THE “ENERGY HUB” STRATEGY
Turkish elites take it for granted that geography makes Turkey a predestined energy hub for the transit of Eurasian energy through its territory whether concerning the Russian South Stream pipeline, the EU’s Nabucco pipeline, both of these systems, or other alternatives like interconnectors. Beyond that deeply-rooted assumption is the corollary belief that because of this hub status, the more pipelines that traverse Turkey the better–irrespective of their origin.
For Turkey to become not just a transit country but a hub, it must compensate for its own lack of indigenous energy sources, which forces it into what one writer calls a “retroactive” strategy of depending on multiple international players and sources for energy, where Russia plays a major role. As domestic demand and consumption grow sharply, Turkey not only must maintain this large volume of imports traversing its territory, it will have to depend on increasing electric power and therefore most probably imported nuclear power to provide that electricity. Turkey, therefore, uses its geographical position to leverage pipeline rights through its territory in return for commitments to invest in its energy sector, including nuclear power plants, as in Russia’s case.[2] Yet even as it depends on Russia, it must balance that dependence with multiple other sources of energy to avoid excessive economic and/or geopolitical dependence on Moscow. In this context, one can better grasp the myriad complexities and repercussions of Russo-Turkish energy relations and explain the Russo-Turkish energy deal of December 30, 2011, as well as the earlier deal with Azerbaijan in October 2011.
TURKEY AND NABUCCO
For several years, Moscow’s primary economic and geopolitical objective in Southeastern Europe has been to lock down the conditions necessary for the start and then completion of the South Stream gas pipeline. This pipeline will bring Russian and Caspian natural gas to Southeast Europe and then Central Europe, bypassing Ukraine and tying Central Asian gas producers to Russia’s pipeline network for years to come. This project would then all but ensure Ukraine’s lasting dependence on Russia, compromise its independence and that of the key Central Asian gas producers too, and tie Balkan states to Moscow. Hitherto, Turkey had been distinctly cool to South Stream. It got Russian gas through the bilateral Blue Stream pipeline and from multiple other suppliers–Azerbaijan, Iran, etc.
Turkey opposed South Stream, because its original course would have bypassed Turkey and gone through the seabed of the Black Sea to Bulgaria and then Europe. Yet Turkish officials had occasionally argued that Gazprom could join Nabucco, i.e. reinvigorate the Blue Stream pipeline and integrate it to the Nabucco network. While this solution might work for Turkey, it did not satisfy anybody else. In the meantime, Russo-Ukrainian energy relations have steadily deteriorated as Moscow’s power plays have become more overt and insistent and Turkish demand for gas is growing while the Nabucco pipeline remains on the drawing boards.[3]
At the same time, all of Azerbaijan’s natural gas was contracted out to its immediate neighbors: Turkey, Russia, Iran, and Georgia. For this reason, Azerbaijan’s Shah Deniz II gas field on the Caspian Sea was crucial to the Europeans’ energy plans: It was projected to increase Azerbaijan’s output considerably, from roughly 10 bcm currently to 25 bcm, once the field came online, with most of the natural gas from Shah Deniz II available for export. However, the natural gas produced by this field was not expected to come online for years. In fact, it was pushed back to 2017-2018 due to price rows between Azerbaijan and Turkey. As a result, all projects are effectively competing with each other for limited supplies.[4]
Turkey was already buying around 6 bcm of gas from the Shah Deniz I field, for a very good price. It sells half of that gas on to Greece at a much higher price. Eight bcm of gas was expected to come from Azerbaijan’s new Shah Deniz II gas development. Baku and Ankara, however, could not agree on how much Azerbaijani gas should go to Turkey, at what price, and under what conditions. Baku insisted that the old pricing formula needed to be revised. Turkey disagreed. Katinka Barysch, deputy director for the Centre for European Reform in London, contended that the problems with Nabucco were due to Turkey and Azerbaijan. In her analysis, “As long as this issue is not resolved, an agreement on the Shah Deniz II gas looks unlikely. Without that gas, it is hard to see how Nabucco could get under way.”[5]
At the turn of 2010, when Nabucco’s fiasco was discussed far and wide, Azerbaijan began losing its interest in Nabucco. Early in September 2010, during President Medvedev’s visit to Baku, Gazprom and the State Oil Company of the Azerbaijan Republic (SOCAR) signed a contract under which Azerbaijan pledged to double its gas exports to Russia to reach 2 bcm in 2011. In 2010, Russia bought 1 bcm of gas from Azerbaijan compared to .5 bcm in 2009.[6]
In March 2011, as a means to pressure Turkey, Moscow suggested it might give up on South Stream and review alternative means of supplying Europe with gas, notably LNG (liquefied natural gas), because Turkey would not agree to laying down South Stream along the bottom of the Black Sea in its territorial waters.[7] Turkey then decided to give Nabucco a boost by organizing a signing ceremony in Kayseri on June 8, 2011, for Project Support Agreements between the Nabucco companies and the ministries of the transit states, Austria, Hungary, Bulgaria, Romania, and Turkey.[8] The Kayseri deal signaled that after a long period of hesitation, the U.S.- and EU-backed project was at last gaining traction. Meanwhile, in early July 2011, the Bulgarian election brought to power former Sofia mayor Boyko Borisov, who was already on record as wanting to take Bulgaria out of the Russia-led South Stream consortium. Without Bulgaria on board, the South Stream project may well be dead.
At the same time Turkey was pressing Gazprom to cut its prices, warning that Turkey would otherwise end a 25-year-old supply agreement with Gazprom. Turkey’s decision accords with the European and Chinese stance toward Russian gas, which demands lower prices and an end to rigid, multi-year take-or-pay contracts.[9] Energy Minister Taner Yildiz stated that Gazprom’s prices had risen by 39 percent since mid-2009, despite falling demand, as it was tied to long-term take-or-pay contracts. Therefore Turkey had to contain its losses. Ankara clearly felt that it had some leverage with Russia, since under present conditions, it is actually oversupplied with gas.[10] On this basis, Turkey proceeded to show its leverage by making the deal with Azerbaijan in October 2011.
On October 1, 2011, Turkey announced that it would not renew the purchase of Russian gas delivered through the Western Balkan pipeline route after 2012. The official reason was the high price of Russian gas. Since Gazprom would not grant the discounted prices it sought in a depressed market, Turkey annulled the agreement.[11] Russian media and business circles immediately reacted by claiming that this was part of a concerted anti-Russian attack by Europe and Turkey on Russian gas policy.[12] Yet the reality was different and casts a critical light on both states’ policies, as does the subsequent December 2011 agreement.
Turkey already imports about 60 percent of its gas from Russia and therefore worries about strategic over-dependence. Second, Gazprom had rebuffed Turkey’s requests for easing the onerous take-or-pay clauses in their contract, which raises Turkish payments even as imports contract.[13] Meanwhile, Russia has done everything in its power to block any alternative to its domination of Caspian and Central Asian gas flows to Europe, thereby ranging itself squarely in the path of Turkey’s long-standing ambitions to be an energy hub for the distribution of that gas to Europe.[14]
Since Russia has also generally refused to accede to other customers’ requests of price cuts, Turkey signaled that it would no longer depend exclusively on Russian gas and that it had other options. Ankara also responded to its domestic critics’ complaints about the primacy of the state company BOTAS by allowing private importers to assume the contracts with Gazprom in search of better prices.[15] Turkey also hopes for contracts with Egypt, Iraq, the ITGI interconnector from Azerbaijan, as well as Turkmenistan to Romania, Hungary, and Italy, the projected Nabucco pipeline, and possibly hopes to force its way into the newly discovered Eastern Mediterranean gas fields.
Immediately after giving this signal to Russia, Turkey turned to Azerbaijan and signed a major gas deal with it on October 25, 2011. Turkey will get 6 bcm of gas annually from Azerbaijan’s Shah Deniz-II field, recovering what it lost from Russia by its earlier termination of the contract from the Western Balkans pipeline. Turkey will also serve as a transit point for another 10 bcm annual supply of gas to Europe through spare capacities in its pipelines. These accords also envisage building the new Trans-Anatolian Dogalgas pipeline for Azeri gas through Turkey, while the existing line’s operation–which transports Azeri Gas from Shah Deniz-II–should go into effect by 2017 and send gas until 2043.
These agreements ensure that Azeri gas can traverse a dedicated infrastructure to Turkey and then flow to Europe either through the Nabucco pipeline, the Trans-Anatolian pipeline, or through one of the many other alternative pipelines currently under consideration, e.g. the ITGI Interconnector.[16] Moreover, since the announced agreement refers to the new Trans-Anatolian pipeline as carrying an “initial” volume of 16 bcm, this suggests that Azerbaijan hopes to increase its volume to 24 bcm, especially as it projects an estimated annual production of 50 bcm by 2017.[17] Gazprom will thus lose significant revenue, and Russia considerable political leverage, as Azerbaijan is charging a significantly lower price to Turkey than Russia charges and received a side payment to make up the difference between its price and what Gazprom charged. These agreements also resolve all issues of gas transit between SOCAR–Azerbaijan’s company–and BOTAS–Turkey’s state-run energy firm–which have essentially replaced Gazprom with Azerbaijan as gas suppliers.
Finally, and worse for Russia, these accords open the way for Moscow’s greatest fear, namely the southern corridor for gas that the EU is pursuing and by which Turkmen and Azeri gas will (if not also Kazakh gas) bypass Russia, flow directly to Europe, and strike a decisive blow to Gazprom and Moscow’s power over them and Europe. This deal also strikes at the plans for the Nabucco pipeline, since there will be no need for a Turkish sector and the builder of Nabucco need only connect gas from Turkey to Bulgaria to the distribution point of Baumgarten in Austria. In other words, whether or not Nabucco is actually built, Turkey will get Azeri gas, and what it cannot use will then go to Europe. Thus, Ankara is protecting itself against Nabucco’s continued dithering and inability to organize itself, even while insuring a dedicated European gas supply route.[18]
Since 2002, Nabucco has been the only pipeline project for transporting Caspian gas to EU territory. However, the EU’s southern gas corridor now includes a number of other potential projects for delivering gas from the Caspian region to Europe, including ITGI (Turkey-Greece-Italy), White Stream (across the Black Sea from Batumi to Ukraine), and TAP (Trans-Adriatic gas pipeline). Nabucco relied exclusively on Azerbaijani gas for the pipeline’s first stage. The hopes to add gas volumes from northern Iraq proved unrealistic in any usable time-frame.
The European Commission’s efforts notwithstanding, Nabucco lost momentum and, ultimately, credibility in its existing form. The tipping point may be traced to November-December 2011, when several adverse developments converged. The European financial crisis deepened, indefinitely postponing any decisions by lending institutions to finance Nabucco. In addition, the project’s management did not come forth with a long-expected correction to its cost estimates. The Shah Deniz gas producers’ consortium in Azerbaijan could no longer postpone the investment decision in that project’s second phase, which necessitated determining the transportation solution in early 2012. With that clock ticking, Nabucco was seen to be far from ready with the solution. Conversely, the Nabucco project’s planning assumptions outran the slow development of a trans-Caspian solution for Turkmen gas.
Ultimately, British Petroleum and Azerbaijan’s State Oil Company offered in October and December 2011, respectively, transportation solutions to replace Nabucco outright. Prime Minister Erdogan correctly stated in December that Turkey was ready for the construction of Nabucco, but the EU was not.[19]
TURKEY AND SOUTH STREAM
There is also a dimension of Balkan rivalry here. The immediate destination for Russia’s planned South Stream and other existing pipelines are mainly in the Balkans, and Moscow has consistently used its gas weapon to leverage its influence in the Balkans. In Turkey’s case, Moscow played to Ankara’s long-standing ambition to become an energy hub. Ankara also welcomed the opportunity to create a vibrant energy and economic relationship with Russia that accepts large-scale Russian investment in downstream and domestic distribution of energy networks inside Turkey.
Consequently, Moscow eagerly invested in such projects.[20] However, Moscow typically employed the same tactics in Greece and Bulgaria, promising them both that they would become hubs for the distribution of Russian oil and/or gas if they allowed such investment in their domestic energy networks and gave Moscow majority shares in projected oil and gas pipelines through their countries.[21] For example, a Greek analysis observed that relations between Moscow and Athens had improved dramatically after the New Democracy Party won the Greek elections in 2004.
Russian sources soon realized that Prime Minister Konstantinos Karamanlis intended to follow an individual policy bolstering mutual cooperation on issues like arms sales to Greece. Russia fostered a common understanding with Greece on issues in energy and defense, supported Greece on the Cyprus issue, incited it against the United States, and pushed it to overcome Bulgarian reservations about an oil pipeline, the Burgas-Alexandroupolis pipeline. At the same time, Karamanlis publicly embraced the idea that the Burgas-Alexandroupolis oil pipeline and South Stream gas pipeline would turn Greece into an energy hub.[22] Through these mechanisms Russia clearly loosened Greece’s support for unified European policies directed toward Russia.[23]
Russia made the same pitch about becoming an energy hub to Bulgaria. In speaking about the three current Russian projects with Bulgaria, Energy Minister Sergei Shmatko said:
We do not doubt that the implementation of those three projects is exceptionally important for Bulgaria itself. The projects will allow Bulgaria to become a very important energy center in South Europe and a powerful energy transit junction in Europe. I think that Bulgaria’s current leadership, which has in mind the country’s long-range national interests, must excellently understand this.[24]
Of course, should Bulgaria opt to choose other non-Russian alternatives–and this seems quite unlikely given its near total current dependence on Russian energy–Russian Ambassador to Bulgaria Yuri Isakov reminded Sofia that “Russia has other ways of implementing its energy interests.”[25] Likewise, Moscow has told Greece that it has alternatives to it as well. Thus, Moscow has frequently raised the possibility of Romania joining South Stream, a possibility that used to but ultimately did not frighten Bulgaria from leaving the program. Russia has also incited Serbia to join it lest it be left out. Although it appears Romania has definitively rejected participation in South Stream, it is clear that Moscow’s strategy is not just to divide and conquer in Southeastern Europe, but also actively to incite rivalries among Balkan states to make them each feel they will all be energy hubs or simply left out of the game. The reality, however, is that they are merely cutting up the same existing pie and that will probably be insufficient in the future to meet European demands.[26]
The political results of this divide and conquer strategy were quite evident in 2008 as Romanian journalist Cristian Campeanu observed: “Moscow would thus dominate Europe’s energy and political agenda by means of ‘divide and rule’ tactics, as we could see on the occasion of the war in Georgia, when the countries that had lucrative agreements with Gazprom–France, Germany, Italy, and Hungary–claimed to see nuances in something that was simply a brutal Russian aggression.”[27] In that context, Turkey’s deal with Azerbaijan not only told Moscow that Ankara had other alternatives to it but also showed Moscow that it could lose South Stream given Romania’s unwillingness to join, Bulgaria’s retreat from the program, and Turkey’s new-found alternative options to bring Azeri and possibly trans-Caspian gas to Europe. Furthermore, this Turkish-Azeri deal is seen in the West as complementing Nabucco, ensuring that Azeri gas reaches Europe and cementing an overall reconciliation between Ankara and Baku. Not surprisingly Washington also welcomed the deal.[28]
Meanwhile BP is also proposing a new concept and system for transporting Azeri gas to Eastern Europe called the South-East Europe Pipeline (SEEP) that would use existing pipelines while leaving open for the future the option of Turkmen gas reaching Europe. This too would, if implemented, undermine Russia’s South Stream grand design.[29] Ultimately, the accords with Azerbaijan eliminate all legal and political barriers to transporting Azeri gas through Turkey to Europe through any of the potential pipeline alternatives. The consortium operating Azerbaijan’s Shah Deniz-II field can now proceed knowing it has a secure market and pipeline.
In the meantime, Turkey has reduced its current account deficit by an estimated $2 billion annually. The Southern Corridor championed by the United States and the EU can now open without impediments and the way is open for Turkmenistan to supply gas to Europe directly, as it wants to do, rather than through Russia. Moreover, the EU is planning just such a pipeline that would link Turkmenistan to Azerbaijan along the Caspian Sea’s seabed.[30]
Moscow quickly grasped what was at stake and resumed discussions with Turkey. Essentially Moscow retreated somewhat on its refusal to cut the price of gas sold to Turkey in return for Turkey granting permits to Russia to begin work on South Stream in Turkey’s Economic Exclusion Zone (EEZ) in the Black Sea, which is the only way the project can be realized. This gives Moscow the prospects for revitalizing South Stream, as it desperately wanted, and Turkey gets price relief, even though it has consistently failed to take all the gas available from Russia due to the over-subscription of its gas market. In exchange for the permits to begin work in Turkey’s EEZ, Turkey will buy 3 bcm of Russian gas originally slated for take-or-pay (at the earlier higher prices of several years ago). In addition, both sides have agreed to contracts for long-term delivery of gas to Turkey from two sources until 2021 and 2025 at discounted prices.[31]
From Russia’s standpoint, South Stream can go ahead. Moreover, it has now gained considerably more leverage against Ukraine, which is undoubtedly the big loser here. Russia has long been pressing Ukraine for a takeover of its gas pipeline and domestic distribution network. The construction of South Stream has been the stick it uses to frighten Ukraine into believing that if it refuses Moscow, Russia will build South Stream and simply bypass it, leaving it without any gas at all. Therefore, Ukraine has long regarded South Stream as a direct threat to its number one national asset, its gas network.
The deal with Turkey places enormous pressure upon the Ukrainian parliament to legislate a Russian takeover lest Ukraine be totally bypassed by South Stream.[32] In the past, Ukraine had shown interest in building an LNG terminal in Turkey to reduce Russian pressure. Ukrainian Foreign Minister Konstantin Hryschenko had visited Turkey on December 22, 2011, to establish a joint working group on energy cooperation in order to facilitate their common goal of diversification of energy sources. Yet it is not known if Ankara disclosed its negotiations with Moscow to Kiev. [33] Along with this agreement, Moscow has moved up the timetable to start construction of South Stream to 2012. While it is very unclear if the gas is there to supply South Stream or if its supporters can meet the continually escalating costs of the project, Moscow is clearly trying to preempt the entry into force of the EU’s Third Energy Package in March 2013. Time will tell if this deal helps Moscow with that goal. South Stream could turn out to be an enormous bluff to force Ukraine to submit to Moscow. Those, however, are certainly the costs to Ukraine–and possibly Europe–of this Turkish deal in December 2011.[34]
The value of this deal to Russia should not be underestimated. Without South Stream, not only would it lose leverage on Ukraine, but also on trans-Caspian producers. This is especially relevant as the Azeri-Turkish deal opens up more possibilities for them. In that context, Moscow has done everything possible to intimidate Turkmenistan and Azerbaijan from shipping gas directly to Europe and destroying its grand strategic design of monopolizing gas flows to Europe and thus controlling the CIS.[35] To the extent that it loses the power to intimidate and corrupt Europe by exercising near monopoly power on European gas imports, Moscow will lose its most powerful instrument for influencing European politics on a day-to-day basis. Therefore, Moscow is prepared to coerce these states to join its deal to keep them from signing up to the European and Turkish networks.
On October 19, 2011, Turkmenistan’s Foreign Ministry blasted Russia’s politicized objections to the former country’s participation in a Trans-Caspian pipeline (TCP). It stated that such a pipeline was an objective and vital economic interest of Turkmenistan. It further rebuked Moscow for “distorting the essence and gist of Turkmenistan’s energy policy” and announced that the talks with Europe would continue.[36]
Moscow’s response soon followed. On November 15, 2011, Valery Yazev, vice-speaker of the Russian Duma and head of the Russian Gas Society, openly threatened Turkmenistan with the Russian incitement of an “Arab Spring” if it did not renounce its “neutrality” and independent sovereign foreign policy, including its desire to align with Nabucco. Yazev said:
Given the instructive experience with UN resolutions on Libya and the political consequences of their being “shielded from the air” by NATO forces, Turkmenistan will soon understand that only the principled positions of Russia and China in the UN Security Council and its involvement in regional international organizations–such as the SCO (Shanghai Cooperation Organization), CSTO (Collective Security Treaty Organization), and Eurasian Economic Union–can protect it from similar resolutions.[37]
In other words, Turkmenistan should surrender its neutrality and independent foreign policy and not ship gas to Europe, otherwise Moscow will incite a revolution there leading to chaos. Other Russian analysts and officials threatened that if Turkmenistan were to adhere to the EU’s planned Southern Corridor for energy transshipments to Europe that bypass Russia, Moscow would have no choice but to do to Turkmenistan what it did to Georgia in 2008.[38] This campaign represents another example of Russia’s turn toward coercive diplomacy. It not only resembles what is happening in Russian policies toward Ukraine and Belarus, it also complements what has been seen in regard to missile defenses and Syria and what is described below in the case of Cyprus.
At the same time, Turkey’s moves against Gazprom and Moscow in October 2011 were apparently long-planned and therefore part of its larger strategy. The agenda for the meeting with Azerbaijan’s President Ilham Aliyev was kept secret. Turkey had continued to stall on South Stream while Moscow had disregarded Turkish demands for price cuts or for the Samsun-Ceyhan oil pipeline, in this case due to Turkish oil tariffs.[39] Russian sources saw Russia’s deals with European governments and firms over the projected South Stream pipeline and Turkey’s desire to join the EU as driving this “anti-Russian” campaign. In reality, though, the EU has been very divided over South Stream.[40]
Nonetheless, it is clear that as Russian pressure on Ukraine to hand over its gas pipeline network to Moscow grows, Turkey’s dependence on Russian gas becomes more of a liability and increases its one-sided dependence on Russia. At the same time, Moscow thought it could disregard Turkish economic interests, as suggested above. Indeed, Gazprom’s reluctance or even refusal to reduce its prices unless compelled to do so is clearly triggering resistance throughout Europe, including Turkey. Aiding this resistance is the fact that European customers now rely on the appearance of Qatari and Algerian LNG or shale gas. Therefore, Moscow must hope to restore the cuts in deliveries by making deals with private Turkish importers who are ready to negotiate terms or make a deal with Turkey that would then open the way for both private and state-to-state deals. This is indeed what it chose.[41] Yet it is unlikely those Turkish companies will accept the onerous take-or-pay clauses and high prices that feature so prominently in Gazprom’s contracts.
Therefore, the question arises, did Turkey gain or lose from its December 2011 deal with Russia? Ironically, that deal followed hard on the completion of the final accord to build the Trans-Anatolian pipeline with Azerbaijan prompting analysts to speculate just what Turkey had gained (as it is clear what Moscow gained and Kiev lost here) from these two deals. Some observers feel that Moscow called Turkey’s bluff and insisted that South Stream be approved if Turkey wanted to get cheaper gas from Moscow, and that Turkey thus had no choice but to agree.[42]
Vladimir Socor argues that Turkey derives no real benefit from the deal with Russia, as it failed to get Black Sea oil through the Samsun-Ceyhan pipeline, which was not mentioned in the deals with Moscow.[43] Attila Yesilada, an analyst at Global Source Partners, also criticized the deal with Moscow for surrendering the EU to Moscow while apparently giving up on Nabucco (He believes that the deal with Russia also entailed Turkey’s surrender of its position in Nabucco in return for Russian concessions on the take-or-pay clause in Russo-Turkish contracts.). Yet he withheld final judgment, because it is not clear that South Stream is a real project or a means by which to take over Ukraine’s gas network. Since no source of new gas for South Stream has yet been announced, it is by no means certain that it would supplant the existing Ukrainian pipeline. In the latter case, Nabucco is still alive, and the Trans-Anatolian pipeline is feasible. Still, he worries that Turkey may be driven to seek revenge on the EU at the expense of its own and EU interests.[44]
On the other hand, Alex Jackson argues that Turkey’s deal with Russia could actually bolster Nabucco, as the Trans-Anatolian pipeline is going to be built regardless of whether commitments to buy its gas come first. If this pipeline could undercut the demand for South Stream’s product in Europe, South Stream–given its high costs and many uncertainties–may never be built. Then Turkey would get transit rights for gas going to Europe while still holding a binding contract with Russia for discounted gas.[45] Jackson argues that Turkey has played both pipelines off against each other and that this too prompted Putin to move up the construction of South Stream to 2012 in order to preempt the Trans-Anatolian pipeline.[46] Indeed, Turkey and Azerbaijan can argue that they have established a route for Nabucco through Turkey, even if they have not formally signed onto the project. It should, therefore, be easier for Nabucco to scale its pipeline to Turkey’s existing pipeline networks, namely the Trans-Anatolian pipeline and the interconnector to Greece and Italy.[47]
CONCLUSION
The complex Russo-Turkish energy relationship has hitherto been based on friendship and solid commercial interests, whereby Russia sells Turkey huge amounts of gas and oil to the point where about two-thirds of Turkish energy (especially gas) is imported from Russia. Naturally, this situation offers Russia significant benefits beyond the revenue it gains from a steady customer. It also raises for some the specter of excessive Turkish dependence on Russia and its gas. Russia’s ambition to dominate the European–and particular Eastern European (including Turkey)–gas market is quite visible. Yet that ambition conflicts with Turkey’s overwhelming elite consensus to be the gas hub for Eurasia, a consensus based on a belief that geography–if not other factors–foreordain Turkey to enjoy the status of this energy hub.
As a result, elements of rivalry have entered into Russo-Turkish energy relations. Turkey’s desire to escape a one-sided dependence on Russian energy and to advance Azeri interests may have compromised the EU’s Nabucco program, but the Azeri-Turkish deals of late 2011 have put in its place a much more solidly based overland pipeline alternative to Russia’s South Stream proposal, about which there are still many unresolved questions. In other words, Turkey has agreed to be a major conduit and player in a pipeline that by its very nature contradicts and clashes with Russia’s grand design.
Considering the importance of energy to both states’ overall geopolitical ambitions and perspectives, this likely means that there will be a growing disjunction between their policies–even if they strive to maintain the previous status quo. This can already be seen in Cyprus, where Turkish efforts to block Cyprus’ exploration of gas off its coast has led to the appearance of Russian warships in Cyprus and statements of support for it as well as Russian interest in exploring for gas there. Likewise, Moscow’s well-known ambition to dominate the Caucasus exclusively also encompasses Azerbaijan and its energy economy.
These recent events are therefore most likely harbingers of a new trend that may emerge slowly but will nevertheless make its influence felt. Moreover, these tensions will reinforce those chronicled earlier over the fate of Syria’s revolution and concerning missile defenses integrated with the United States and NATO in Turkey. While both sides are probably loath to admit that the good old days of a halcyon relationship are over and will undoubtedly make efforts to retain that relationship, competition between Ankara and Moscow in the Eastern Mediterranean, Caucasus, and over energy is as likely as not to be the order of the day in the near future.
*This work was supported by a National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-327-B00053).
*Younkyoo Kim (Ph.D., Purdue University) is an associate professor at the Division of International Studies, Hanyang University, Seoul, Korea, where he has taught international relations since 2004. Previously, he taught at various colleges in the United States, including DePauw University, Butler University, and Saint Mary’s College. He is the author and co-author of over 30 scholarly articles and monographs, and author or editor of four books, including Russia and the Six-Party Process in Korea (2010), The Geopolitics of Caspian Oil: Rivalries of the U.S., Russia, andTurkey in the South Caucasus (2008), and The Resource Curse in a Post-Communist Regime (2003). His research interests have been focused on issues of energy security and international relations in East Asia and Eurasia.
*Stephen Blank (Ph.D., University of Chicago) is Professor of Russian National Security Studies at the Strategic Studies Institute of the U.S. Army War College in Pennsylvania. Dr. Blank has been Professor of National Security Affairs at the Strategic Studies Institute since 1989. In 1998-2001, he was Douglas MacArthur Professor of Research at the War College. He has published over 700 articles and monographs on Soviet/Russian, U.S., Asian, and European military and foreign policies, testified frequently before Congress on Russia, China, and Central Asia, consulted for the CIA, major think-tanks and foundations, and has chaired major international conferences in the United States and abroad. He has published or edited 15 books focusing on Russian foreign, energy, and military policies and on international security in Eurasia. His most recent book is Russo-Chinese Energy Relations: Politics in Command, London: Global Markets Briefing, 2006. He is also author of Natural Allies? Regional Security in Asia and Prospects for Indo-American Strategic Cooperation (Strategic Studies Institute, U.S. Army War College, 2005). |
5484
1.6452
2103 * -5.9
-12407.7
What is the product of 0.2 and -1.32189?
-0.264378
What is the product of 42764 and -0.3?
-12829.2
-8314 * -2.2
18290.8
4.6*60
276
Product of -0.3 and 0.7753.
-0.23259
2*-0.67996
-1.35992
Product of 1.9297 and 3.8.
7.33286
64 times 14.84
949.76
36052 times 0.5
18026
Calculate 30*-0.4728.
-14.184
What is the product of -0.277 and 0.0613?
-0.0169801
Multiply 3.276 and 1.4.
4.5864
Product of 0.21 and 4995.
1048.95
Calculate 0.7*70.71.
49.497
What is the product of -547 and 0.085?
-46.495
-0.08 * -4.184
0.33472
Work out 5 * -2004.
-10020
Multiply 397.387 and 0.4.
158.9548
Work out -17 * -8468.
143956
-387 times 45
-17415
Multiply 1 and 8440.
8440
Product of 1.3694 and -1.
-1.3694
What is -9254 times -0.3?
2776.2
32410*-6
-194460
-200.775 * 0.01
-2.00775
72*-223
-16056
Multiply 585604 and -5.
-2928020
Calculate 0.1*10.9692.
1.09692
What is 20 times -12.877?
-257.54
119001 * 0.1
11900.1
Multiply -158 and 3380.
-534040
Calculate -13.3*4455.
-59251.5
Product of -0.5 and -0.37255.
0.186275
-0.08 * 43725
-3498
What is the product of -51 and -14.63?
746.13
Product of -1.629 and -68.
110.772
What is -0.4 times 0.490906?
-0.1963624
Product of 446872 and 0.3.
134061.6
What is 168409 times 1?
168409
-30.3 times 0.48
-14.544
Multiply 10 and 0.0057.
0.057
Product of 31.6687 and 0.2.
6.33374
What is -9494 times 10?
-94940
What is -0.1 times 44539?
-4453.9
-0.08*2.344
-0.18752
11789 * -2
-23578
What is the product of 0.04 and 0.3343?
0.013372
Multiply -9 and 26.956.
-242.604
Multiply 0.06 and 55763.
3345.78
3790*-551
-2088290
Multiply -0.3 and 148.311.
-44.4933
0.8 times 1602
1281.6
Work out -283395 * -0.2.
56679
1*176337
176337
What is the product of -19258 and 106?
-2041348
4 times -534.09
-2136.36
What is the product of -0.5 and -54.63?
27.315
Product of 8 and 116.967.
935.736
Multiply -2265 and -138.
312570
Multiply 11005 and -2.7.
-29713.5
6 * -0.191
-1.146
-35385*8
-283080
Calculate -43*0.843.
-36.249
Multiply -1312 and 0.66.
-865.92
What is 4 times -15236?
-60944
What is 2032.351 times -0.3?
-609.7053
Work out -474758 * 3.
-1424274
Calculate 18168*-17.
-308856
0.135*-20.483
-2.765205
-88.63 * -0.09
7.9767
Product of -10173 and 122.
-1241106
-0.1 * -362.8
36.28
What is the product of -8 and 2511.4?
-20091.2
Multiply 67 and -224.
-15008
Work out -0.4 * -0.1042.
0.04168
Work out 0.09 * -0.2434.
-0.021906
11724*0.7
8206.8
0.016881 times 0.4
0.0067524
1.228 times -162.6
-199.6728
0.07 * -38309
-2681.63
What is the product of 427 and -0.499?
-213.073
Product of -0.3 and 0.109726.
-0.0329178
Calculate 1.6*-290009.
-464014.4
Multiply -0.11 and 0.1106.
-0.012166
0.0013*1.02
0.001326
-9838 times -2.74
26956.12
Multiply 0.87 and -25.
-21.75
-5489592*-0.5
2744796
What is 42 times -1942?
-81564
Multiply 0.05 and 15769.6.
788.48
Multiply -0.2 and -0.3488.
0.06976
Calculate -1*-67169.
67169
What is 0.5 times -5.8935?
-2.94675
Calculate -2*12749.
-25498
Multiply 5.82 and 0.07.
0.4074
Work out -0.16 * -31027.
4964.32
Product of -5 and -414157.
2070785
2.88 times 43
123.84
0.06*-0.211468
-0.01268808
What is -9.539 times -40.4?
385.3756
3 * -53279
-159837
Work out 3464159 * 0.1.
346415.9
What is -5 times -7293?
36465
What is -1010.23 times -0.3?
303.069
Calculate -71428*-0.1.
7142.8
What is 21 times 493?
10353
What is -0.02 times 1725?
-34.5
Product of 3 and 56.
168
Product of -4028 and 758.
-3053224
0.4 * 251856
100742.4
Work out 87 * -18.
-1566
What is the product of 42732 and 0.2?
8546.4
What is the product of -0.19 and 8341?
-1584.79
What is 0.4 times 1.0195?
0.4078
What is the product of 0.624 and 93?
58.032
-942 * -4
3768
What is the product of 1990.9 and -32?
-63708.8
What is -8830 times 24?
-211920
Calculate -10064.44*-4.
40257.76
0.00685 * 0.3
0.002055
Product of 0.242178 and -0.5.
-0.121089
-2*44437
-88874
Product of -25 and 4666.
-116650
Product of 2.073 and 1540.
3192.42
28022*0
0
What is -6 times 4.0967?
-24.5802
Product of 653 and -0.37.
-241.61
What is the product of -0.008 and 41?
-0.328
Multiply -0.1 and 9268.
-926.8
Multiply -0.82 and -1.1247.
0.922254
Calculate -165*-55.5.
9157.5
Product of 84 and -319.
-26796
Multiply 0.5 and 20639.
10319.5
Product of 0.3 and -163.81.
-49.143
What is 0.072 times -4169?
-300.168
What is -0.2 times 52795?
-10559
-0.1 * -2.5153
0.25153
Multiply 4 and 71.2833.
285.1332
92.56 times 0.08
7.4048
213515 * -3
-640545
Work out -31 * -732.
22692
Product of -0.0372756 and -0.3.
0.01118268
Product of -60.18 and -0.02.
1.2036
1.4 * 7642
10698.8
What is -212 times 290?
-61480
Multiply -0.26 and 16221.
-4217.46
Calculate 0.59578*0.07.
0.0417046
Multiply 1054 and 24.
25296
Work out -25486 * -0.1.
2548.6
Work out 2796.289 * 0.3.
838.8867
Multiply 0.2 and 50591.
10118.2
Calculate -336602*-2.
673204
Multiply 3 and 276823.
830469
Calculate -0.2306*10.
-2.306
Product of 93712 and 0.5.
46856
7*-776.641
-5436.487
-0.3*-0.0902474
0.02707422
0.05 times 11799
589.95
Product of -354.5 and 0.63.
-223.335
Product of -882 and -12.2.
10760.4
-0.2756*-0.8
0.22048
65.981 * -0.2
-13.1962
-4.05 times -18
72.9
0.09241*-5.3
-0.489773
Work out 0.4518 * -3.
-1.3554
-46 times 8.58
-394.68
Work out 132 * -0.234.
-30.888
What is -0.0221 times 0.3?
-0.00663
-18*203.6
-3664.8
Work out -1.52 * 1.3749.
-2.089848
Calculate 0.55*464.8.
255.64
What is the product of -39.3 and 1044?
-41029.2
Work out 5 * 8080.
40400
0.1103 * 2808
309.7224
-11*-5742
63162
What is the product of -298 and 2567?
-764966
Multiply 34326 and -98.
-3363948
Product of -263461 and 0.
0
Work out -74 * 0.82.
-60.68
0.1111 * -0.04
-0.004444
1109.56 * -3
-3328.68
Work out -2 * -1231.
2462
Calculate -23143.41*5.
-115717.05
Calculate 0.111*-9.
-0.999
Work out -41 * -472.
19352
Product of -0.022364 and 86.
-1.923304
-0.212227 times -0.1
0.0212227
3 * -12.091
-36.273
14.9*0.023
0.3427
-8765*-4
35060
What is the product of 0.0548 and 14.2?
0.77816
What is 18.6 times 64.1?
1192.26
Multiply 1.738 and 0.0061.
0.0106018
27.9 times 0.074
2.0646
What is the product of 911 and -0.1354?
-123.3494
0.7 * 0.6093
0.42651
Product of 2 and -0.000004.
-0.000008
Multiply -330 and -941.
310530
Multiply -3.4 and -0.355.
1.207
-0.59*-5086
3000.74
Calculate -4*-4415.
17660
11.846 times 12
142.152
18.33 times 0.8
14.664
-0.3 * 22482
-6744.6
50.5*-0.032
-1.616
Work out -40828.9 * 4.
-163315.6
What is -82 times 48047?
-3939854
What is the product of -5.5 and -100?
550
Product of 9685 and -0.007.
-67.795
-3313 times -0.008
26.504
5599 * 0.13
727.87
11 * -25295
-278245
-0.03 * -14941
448.23
What is the product of -80700 and -0.4?
32280
Work out 0.5 * -17631.1.
-8815.55
Calculate 0.4*-129937.
-51974.8
2 * -0.09209
-0.18418
1048 times -0.04
-41.92
-5 times -12285
61425
Product of -0.2 and 66178.
-13235.6
-0.4*-7464
2985.6
Work out -36189 * 0.4.
-14475.6
Multiply 3 and 0.42864.
1.28592
-4*119.747
-478.988
Multiply 9.17 and -2.5.
-22.925
3 times -242.42
-727.26
-0.2637*-1.3
0.34281
Work out -3 * -413.3.
1239.9
Work out 0.7712 * -82.
-63.2384
-1.077375*4
-4.3095
Work out 0.04559 * 0.8.
0.036472
What is -0.0358 times -1375?
49.225
-1267 times 0.135
-171.045
20601 times -22
-453222
Multiply -479 and -490.7.
235045.3
What is 0.38 times 12.32?
4.6816
-0.3025*3.81
-1.152525
Multiply 0.0777 and -3.5.
-0.27195
46*179.1
8238.6
What is the product of -4 and -27121.1?
108484.4
-1.81 * -229
414.49
12259 times 6
73554
Work out 11 * -6.8373.
-75.2103
-78683 times -0.1
7868.3
Work out -75481 * 3.
-226443
-0.040372*-4
0.161488
Work out 0.9 * -650.
-585
-682618 * -0.5
341309
Product of 1682 and 2.33.
3919.06
Product of 43281 and -0.2.
-8656.2
What is the product of -7420 and 4.54?
-33686.8
What is the product of -45.53 and 1.6?
-72.848
What is the product of 0 and 28.94?
0
Multiply -75 and -5327.
399525
-0.5269 times 0.01
-0.005269
What is the product of -0.123 and -680?
83.64
What is -178 times -6858?
1220724
Multiply -5 and 1662.82.
-8314.1
Calculate 0.042069*-0.16.
-0.00673104
What is the product of -0.4 and -78.8584?
31.54336
What is the product of -48205 and 0?
0
Multiply 1.03521 and 0.1.
0.103521
Calculate 15.3*98.7.
1510.11
What is the product of -0.01 and -0.24?
0.0024
Multiply -0.9642 and 0.28.
-0.269976
Product of -1.2 and -7578.
9093.6
0.4*-75.2642
-30.10568
What is the product of 115 and 0.303?
34.845
|
The trouble with Checked Exceptions (C# architect) - davedx
http://www.artima.com/intv/handcuffs.html
======
gioele
The crux of the question:
> Bill Venners: But aren't you breaking their code in that case anyway, even
> in a language without checked exceptions? If the new version of foo is going
> to throw a new exception that clients should think about handling, isn't
> their code broken just by the fact that they didn't expect that exception
> when they wrote the code?
> Anders Hejlsberg: No, because in a lot of cases, people don't care. They're
> not going to handle any of these exceptions. There's a bottom level
> exception handler around their message loop. That handler is just going to
> bring up a dialog that says what went wrong and continue. The programmers
> protect their code by writing try finally's everywhere, so they'll back out
> correctly if an exception occurs, but they're not actually interested in
> handling the exceptions.
> The throws clause, at least the way it's implemented in Java, doesn't
> necessarily force you to handle the exceptions, but if you don't handle
> them, it forces you to acknowledge precisely which exceptions might pass
> through. It requires you to either catch declared exceptions or put them in
> your own throws clause. To work around this requirement, people do
> ridiculous things. For example, they decorate every method with, "throws
> Exception." That just completely defeats the feature, and you just made the
> programmer write more gobbledy gunk. That doesn't help anybody.
~~~
paol
Exactly. I think the 2 key failings of the checked exception idea (there are
others, but not as important) are
1) Precise exception specifications leak implementation details. This will
bite you badly, e.g., when you want to change the implementation from under a
published API.
2) The times when we only care that some exception occurred _vastly outnumber_
the times when we care about the exact types of exceptions that may occur.
Checked exceptions don't add any value to the common case, in fact they make
it worse, because generic exception handlers tend to live many levels up the
call stack from where exceptions are thrown(1), and therefore they "aggregate"
large amounts of code that that can collectively throw a huge range of
exceptions. If you were to carry around detailed "throws" clauses, they would
be a mile long.
The funny thing is, all solutions that solve the problems created by checked
exceptions do so by subverting the mechanism one way or another. So you're
better off without checked exceptions in the first place.
I've always been interested in this discussion because it's one of those cases
where an idea seems very good on paper, only to turn out quite bad in
practice.
(1) This observation is what makes exceptions such a useful mechanism in the
first place.
~~~
bunderbunder
There is one part of the idea that I'd like to salvage, though, and that's
having some clear documentation right there in the code about what kinds of
exceptions I can expect to see a procedure throw.
At the very least it'd be useful for when I'm wearing my "DLL author" hat,
since it'd give me an easy way to look through the public interface and make
sure exceptions won't be causing unrighteous leakage of implementation details
for the end-user. I'd rather not put users in a situation where they have to
look at the framework source in order to interpret an exception. It's kind of
irritating when that happens.
I think it's really not something that should require special language
statements, though. A static analyzer should be able to automatically figure
it out.
------
philbarr
As a long time Java programmer, who has been writing C# for the last year and
a half, I think leaving out checked exceptions from C# may have been a bad
idea. What they've done is to identify that checked exceptions are a pain in
many cases and simply removed them without providing a proper replacement.
This particular quote demonstrates what I mean:
"To work around [the need to declare what you intend to do with each
exception] people do ridiculous things. For example, they decorate every
method with, "throws Exception." That just completely defeats the feature, and
you just made the programmer write more gobbledy gunk. That doesn't help
anybody."
Ok, so what you did instead was to effectively put "throws Exception" on every
method by default. You actually implemented the workaround you've just
criticised into the language?
And what's the effect of this - whenever you call a method in an API, you have
no idea what could go wrong with it, so you can't write code to handle it. It
wouldn't be so bad if a method's potential exceptions were documented, but
they _never_ are. So you end up in a situation where you just code for the
simple "happy case", run it, see what breaks, put some exception handling in
(for just Exception) where you can, run it again, etc. It's a dreadful way to
write code.
I'm not saying Java's checked exceptions were great - far from it - but C#'s
"solution" is terrible. The number of times you end up with a NullException
because some method failed somewhere deep in your code and something else
didn't get initialised is unreal. If you don't believe me, try working with
Sharepoint for a few minutes, and that's Microsoft code.
[edit - spelling]
~~~
pohl
_Ok, so what you did instead was to effectively put "throws Exception" on
every method by default._
That implicit throws clause was already there in any language that contains
unchecked exceptions for things like dereferencing a null pointer, or
assertions, etc. So, no, that's not what removing checked exceptions does.
Personally, I'm a big fan of Guava's Throwables class. The java I write these
days transmutes all checked exceptions into unchecked wrappers at any API
boundary that tries to force them on me. And, no, this doesn't mean I'm only
coding for the happy case. Rather, I'm choosing where and how to handle the
sadness.
~~~
lsd5you
It depends what standards you hold the library to. Null pointer exceptions and
other runtime exceptions are can be treated as errors - something which needs
fixing in the code, rather than something that can be handled. A world of
difference.
~~~
pohl
And that is still the case with the Guava Throwables strategy, which only
effects how checked exceptions are propagated.
------
ZitchDog
I have thought quite a bit about checked vs unchecked exceptions and come to
the realization that there is a fundamental philosophical problem that checked
exceptions can never overcome.
The idea with checked exceptions are that they should be used for errors which
the caller should be forced to handle. But this property is entirely dependent
on the context the function is being called from! For example, if the user is
specifying a filename for a file, I should be expected to catch the error and
display feedback to the user. However, if I just wrote the file to disk 5
seconds ago, I shouldn't be forced to trap the error!
The crux of the problem is this: the severity and recoverability of an error
is known only by the caller of the function, not the function itself. Checked
exceptions attempt to foist this information into the function itself, where
it is unknowable and generally inaccurate. Checked exceptions are a misfeature
if I ever saw one.
~~~
scott_s
I agree with the C# designers' reason that checked exceptions are not a good
idea, but I don't agree with yours. In other words, your argument is different
than theirs, and I don't agree with it. (Although I still agree with your
conclusion.)
_The crux of the problem is this: the severity and recoverability of an error
is known only by the caller of the function, not the function itself._
I agree with that statement, but not that it is the crux of the problem with
checked exceptions. That statement is an argument for general error reporting
- it need not even be exceptions. Simply, the function that encountered the
error does not know what to do about it, so it must report it on up the stack.
We could just as easily accomplish that with error return values - I'm not
saying we _should_ , just that I think your argument is too generic to support
your conclusion.
_Checked exceptions attempt to foist this information into the function
itself, where it is unknowable and generally inaccurate._
And that I actually disagree with. Checked exceptions require that the calling
function _acknowledge_ that an error has occurred, it does not require the
calling function to _handle_ the error. The calling function could easily
catch the exception and rethrow it, or just add the exception to its own
throws clause.
The C# designers' argument is that what I described is generally what people
want to do, so why not just make it the default? That default is unchecked
exceptions.
~~~
ZitchDog
_Checked exceptions require that the calling function acknowledge that an
error has occurred_
But why do they require the client to acknowledge the error? Better stated,
why would one use a checked exception versus an unchecked? The general wisdom
(and perhaps this is where I'm mistaken) is that checked exceptions generally
indicate a more recoverable error. This is why checkedness doesn't belong in
the function itself: it's an indication to the caller of the error's
recoverability, which is completely unknowable.
~~~
scott_s
Note that I was not arguing _for_ checked exceptions. Rather, I was arguing
that your argument does not support your conclusion.
With that said, I think it may be reasonable to say "You may be able to
recover from a missing file, but no one can help you if this pointer is null."
It's the difference between a logic error in the program (null pointer
exception, array out of bounds exception) and configuration errors (missing
file, lost connection). Checked exceptions are typically explicitly thrown by
the called function; unchecked exceptions are typically encountered because
the called function itself had an error. In other words, checked exceptions
are when the called function recognizes an error, and throws it up to its
caller.
So, I am able to distinguish them myself. But I'd still rather not have
checked exceptions. The mentality of "acknowledge all errors" makes more sense
in the error-code model, as seen in C programs. In that case, if you don't at
least check for and report all possible errors that can arise from calling a
function, then they will _never_ get reported, and your program will silently
be wrong.
~~~
ZitchDog
_Note that I was not arguing for checked exceptions._
Right, I understand that. And I was merely pointing out a flaw in your
argument against my argument.
_You may be able to recover from a missing file, no one can help you if this
pointer is null_
My argument (which you seem to be doing a great job of ignoring) is that this
distinction is completely unreasonable. As the calling function, I am passing
in the pointer, therefore I am the only one who can know whether the null
pointer is a recoverable issue! Consider the ArrayOutOfBoundsException -
perhaps the array bounds are passed in from the user interface, and the error
should be trapped and reported to the user. This checked / unchecked
distinction is simply nonsensical from the called function's point of view.
_Checked exceptions are typically explicitly thrown by the called function;
unchecked exceptions are typically encountered because the called function
itself had an error_
This is not typical, is not how you are using them in your examples, and also
makes no sense. What is the difference between encountering a particular error
within a function or a sub function? What if the logic in the function is
later extracted into a subfunction?
~~~
scott_s
I'm sorry if you feel that I'm ignoring your distinction. I'm not trying to
ignore it, but argue that I think we _can_ distinguish between "likely
recoverable" and "likely not recoverable" for _most_ cases. Nothing prevents
you from catching unchecked exceptions. So if you know that you're passing in
a may-be-null-pointer-and-it's-okay, then you can do an unusual thing and
catch that exception. I agree that we can't classify all exceptions as
recoverable or not recoverable from inside the called function, with full
accuracy. But I disagree that we can't make reasonable guesses that will be
true in most cases.
The function may encounter an error but it is not the caller's fault - that's
what I mean by "the called function itself has an error."
~~~
ZitchDog
Sure, we _could_ guess at all sorts of things from within a function. We
_could_ guess that the function is running from a terminal, and simply print
the result of the function to stout. Hell, we could guess what the caller is
going to do with the result of our function and just do that instead! Why even
have a caller at that point?
Of course I'm using hyperbole to point out the absurdity of making this
distinction, which on the surface may seem reasonable. The fact is, however,
the fewer assumptions a function makes about it's calling context, the better.
The whole point of functions is that they are to be reused in ways the author
may not have intended. The checkedness of an exception is an assumption about
the calling context of a function which should not exist.
------
AndrewDucker
I am _very_ glad that C# does not have checked exceptions. Anders is
completely correct in that the vast majority of the time individual methods do
not handle specific exceptions, they just roll things back and pass the
exception up the way. Adding exception attributes in all of these places would
be a massive pain.
~~~
thebluesky
In my experience many C# programmers simply fail to add much exception
handling code at all because the compiler doesn't force them to. The net
result is code which breaks in spectacular fashion when the first unexpected
condition is met.
Checked exceptions are a nuisance (I'm actually glad Scala doesn't enforce
them vs Java), but often leads to inexperienced C# devs writing very fragile
apps.
With C# you have to examine docs and source to identify exceptions which could
be thrown. Many programmers don't bother, leading to things breaking. In Java
the compiler forces you to think about it. I'm not in favour of checked
exceptions, but the arguments against them tend to be a bit simplistic.
~~~
jsolson
> In my experience many C# programmers simply fail to add much exception
> handling code at all because the compiler doesn't force them to.
Still better than:
try {
// Do broken stuff
} catch (Exception e) {
throw new RuntimeException(e); // TODO: Add a domain-specific runtime exception so we can actually catch this
}
I find this or something like it[0] spread across every Java codebase I find
myself mired in, and I read a _lot_ of Java these days (much to my dismay, but
so it goes).
[0]: Actually, that's not fair. Most people don't bother to include the TODO.
~~~
Roboprog
You meant to say "catch (Throwable e)", right? But, yeah, I've had to write
that block too many times.
Throwable will catch Errors as well as Exceptions, such as when a constructor
called from a dependency injection framework fails. It's kind of irked me for
a while that I had to know that. I would have rather had "catch" work on
_anything_ , with the option to check the class and rethrow once in a great
while. That is, in the few places where the error checking/logging actually
belongs (as stated in the article, with which I obviously agree).
There is indeed great irony in Java code littered with catches, which then
falls out and kills the main loop without logging anything. (I recently had to
diagnose such a case in a system at work over the phone -- sure enough, that's
exactly what was coded)
~~~
sixcorners
You are not supposed to, and don't need to, catch Errors. The only exceptions
you need to worry about as far as checked exceptions go are classes that
inherit from Exception but not RuntimeException.
------
philf
> You end up having to declare 40 exceptions that you might throw. And once
> you aggregate that with another subsystem you've got 80 exceptions in your
> throws clause. It just balloons out of control.
What he completely ignores is the possibility to wrap exceptions to either
aggregate them or to convert them into unchecked exceptions.
~~~
paol
But that's exactly one of the main points of the detractors of checked
exceptions (of which I'm one): the only sane way of working with it is to
subvert it.
Whether you convert the throws clause to a common supertype (which very soon
converges to the base type Exception), or wrap everything in a
RuntimeException, you are effectively emulating a language without checked
exceptions. So what was the point in the first place?
~~~
specialist
"the only sane way of working with it is to subvert it."
Perhaps.
In my projects, I use wrapped exceptions to convert "what blew up" exceptions
into "what to do about it" exceptions. A poor man's event routing. For
example, I wrote an ETL workflow thingie that would retry, reset, restart,
backoff (throttle) depending on what was failing.
I'd be totally game for pre declaring what exceptions your code will catch,
harkening back to the days of "on message do this" type programming. Then the
compiler can tell verify that all the thrown exceptions get caught by
somebody.
Meanwhile, I've never had a problem with checked exceptions.
Methinks the real cause of angst over checked exceptions are all these
mindless frameworks, APIs, libraries, strategies, design patterns, aspects,
inversion of common sense, injection of nonsense, etc.
The complexity borne of the manner in which Spring, JPA, Hibernate, connection
pooling, aspects, MVC, blah blah blah attempt to hide, obfuscate, decouple,
mystify, pseudo architect "solutions" ... well, it's just insane.
Someone upthread off-handedly noted the irony of declaring all these
exceptions only to have the main event loop eat an exception without any
logging. Story of my life. Debugging silent death failures really, really
sucks.
Which is why I work as "close to the metal" as possible and worry not about
unchecked exceptions.
------
kbd
For old articles, please put a date in the title. In this case, (2003).
~~~
AndrewDucker
If it was something that was time-dependent, I'd agree, but in the case of an
interview talking about the design of two languages in current use,it's
timeless.
~~~
sirclueless
That's all the more reason to put the date there. It signals an article that
is relevant today despite being almost ten years old. The argument is
considerably more impressive when you realize that it happened ten years ago
and is still relevant, but I didn't know it was a timeless classic until I saw
this comment thread.
------
Uchikoma
Checked exceptions are fine.
The problem is, that they are not composable and most languages have no
syntactic sugar for dealing with them as Monads.
Other checked error mechanisms like Either or are much easier to manage.
I do hope e.g. Java sometimes in the future gets syntactic sugar to deal with
checked exceptions as Monads.
------
lenkite
The Java Programming Language's checked exception feature is fundamentally
broken. All newer Java specifications have acknowledged this and utilize un-
checked exceptions.
~~~
tomjen3
All but one (and arguably the most important) Android.
Android is full of brand new checked exceptions.
And I do what I always do with checked exceptions:
catch (e) {
throw new RuntimeExeception(e);
}
(you can't keep adding throws clauses because the compiler won't let you add
them if the interface you implement can't handle them).
------
rvkennedy
I have long wondered about the syntax of exceptions - if it was:
void function()
{
try:
function_body...
catch(Exception e):
finally:
}
By leaving the function body in the same indentation as it would be without
exception handling, this might help to make the code a little more readable
than:
void function()
{
try
{
function_body...
}
catch(Exception e)
{
}
finally
{
}
}
~~~
ajitk
My mind parsed the first code block as a mix of Python and C. IMO, the later
would be more readable since it involves parsing only one rule that the eye is
already used.
~~~
udp
It reminds me more of C, where labels and goto are often used for error
handling (labels using the same `:` syntax).
~~~
ajitk
Now that you you mention labels, I see the similarity to C. I might have been
influenced by OP's reference to use _indentation_ to make code more readable
instead of using braces.
------
bokchoi
I tend to agree that Java's checked exceptions are annoying (hello
SQLException). However, when I used C# I was annoyed that the VS intellisense
and the C# generated documentation didn't tell me what exceptions might
actually be thrown! In practice this meant just not handling anything at all.
~~~
darrenkopp
That's because the developer didn't put the exception into the documentation.
But at the same time you really shouldn't rely on that because something down
the line could throw an exception that isn't covered in the documented
exceptions.
------
viraptor
The thing that really annoys me about checked exceptions is that
map/reduce/fold like functions throw anything by definition. Basically as soon
as you allow any general type function as a parameter, you need to mark
yourself as throwing everything.
That is really limiting in some scenarios.
------
dscrd
Exceptions are a bad idea. Even in the more saner languages such as python,
they tend to obfuscate needlessly.
~~~
je42
so you prefer to decentralize your exception handling code ? how do you scale
that ?
~~~
dscrd
The problem is that when exceptions are available, people will start using
them for non-exceptional things and (the worst case) basic control flow.
Case in point from a popular framework, Django: the standard way of getting an
object from the DB via the ORM is Class.objects.get. This method either
returns a single object or raises on exception if there are zero rows in the
db or another exception if there are two or more rows. It may also raise other
kinds of exceptions.
Now, it's clear that having zero rows is not very exceptional, and even >1 is
somewhat debatable. Note especially that this is not just some weekend project
by a nobody, it is a framework that is widely used and respected.
~~~
Ingaz
>> and (the worst case) basic control flow. I call it "java-way goto"
I can't agree about Class.objects.get - method must return exactly one row by
known pk value.
So it perfectly sane to raise exception for zero rows.
Class.objects.filter is working the way you want.
~~~
dscrd
Except that get accepts as parameters non-unique non-primary fields too.
I have every reason to believe that the Django devs are capable people who
thought about this and landed on this specific usage with a clear rationale...
but it still is a misuse of error handling capabilities of a language. And a
sort of misuse that everyone else does sometimes as well.
|
Background
==========
Analyzing the effects of genes and/or environmental factors on the development of complex diseases is a great challenge from both the statistical and the computational perspectives. Calle et al. \[[@B1],[@B2]\] recently developed the model-based multifactor dimensionality reduction (MB-MDR) technique, which tackles association and interaction analysis by assigning genotype cells to different risk categories. This method is also applicable to one-dimensional screening. Currently, the MB-MDR approach uses permutation testing to assess significance \[[@B3]\], thereby also correcting for multiple testing. An additional major problem arises when associations between a trait of interest and rare variants are targeted. In this context, it is unclear which of the family-based or population-based designs will be more advantageous. Also, traditional regression methods break down because parametric assumptions are hardly fulfilled for rare variants \[[@B4]\]. In this paper, we explore the utility of several methods, both parametric and nonparametric, to test for or model genetic associations using population-based and family-based data from Genetic Analysis Workshop 17 (GAW17).
Methods
=======
Data set and quantitative trait association analysis
----------------------------------------------------
The data provided by GAW17 include a subset of genes grouped according to pathways that had sequence data available in the 1000 Genomes Project. Effect sizes for coding variants within these genes were assigned using PolyPhen and SIFT predictions of the likelihood that the variant would be deleterious. Two hundred replicates were generated. Our analyses involve the quantitative trait Q1, which was simulated as a normally distributed phenotype. Furthermore, we restrict attention to the available single-nucleotide polymorphisms (SNPs) on chromosome 4 (944 in total). All simulated singular SNP effects (SNPs C4S1861, C4S1873, C4S1874, C4S1877, C4S1878, C4S1879, C4S1884, C4S1887, C4S1889, and C4S1890 in the *KDR* gene and C4S4935 in the *VEGFC* gene) are assumed to be additive on the quantitative trait scale, such that each copy of the minor allele increases or decreases the mean trait value by an equal amount. In addition, values of Q1 were simulated to be higher in smokers, and the listed variants in the *KDR* gene were involved in *KDR*-smoking interaction effects on the trait. There are 944 markers in 81 genes on chromosome 4. The sample size for both population- and family-based data is 697 with family data comprising 8 families with 202 founders and 3 offspring generations. The founders were randomly sampled from the unrelated individuals data set, and genotypes of offspring were sampled using Mendelian inheritance. It should be noted that genetic information is the same for all replicates; only phenotype and smoking status differ.
For the family data, we compare the performance of the MB-MDR approach (family-based, FAM-MDR) to the association test (PBAT) screening \[[@B5]-[@B7]\] (version 3.61), whereas for unrelated individuals we compare the MB-MDR approach to penalized regression (the penalized package in R, v. 2.9). Power is estimated on the basis of rejection of the null hypothesis for the SNP under investigation, whereas the family-wise error rate (FWER) is estimated on the basis of rejection of the null hypothesis for any of the SNPs with no effect. In addition, we reevaluated power and FWER by collapsing rare variants in the genes of chromosome 4.
In the following subsections, we briefly describe the main characteristics of the approaches we consider in this comparative study.
MB-MDR modeling
---------------
The MB-MDR technique for one dimension involves three steps. First, each marker's genotype cells are assigned to one of three categories---high risk (H), low risk (L), or no evidence (O)---on the basis of the result of association tests (*t* tests) on each of the individual cells versus all other cells with the response variable, using a liberal *p*-value threshold of 0.1 \[[@B3]\]. If this threshold is not attained for whatever reason, the cell is labeled O. Next, an association test is performed with the new predictor variable *X* in {H, L, O} on the outcome variable. Association with the trait is investigated by testing H versus L \[[@B3]\] using a *t* test. In the last step, permutation-based step-down max *T* adjusted *p*-values \[[@B8]\] with 999 replicates are computed to assess significance over all considered marker sets, theoretically ensuring control of FWER at 5%. We also implement the step-down min *P* procedure \[[@B8]\], based on 999,999 replicates.
The MB-MDR approach has been adapted to accommodate family-based study designs and uses principles of genome-wide rapid association using mixed model and regression \[[@B9]\]. In particular, the MB-MDR approach for families (FAM-MDR \[[@B10]\]) first involves performing a polygenic analysis using the complete pedigree structure. Then MB-MDR (for unrelated individuals) is applied to familial correlation-free residuals obtained from the polygenic modeling.
Family-based association testing for family-based designs
---------------------------------------------------------
The PBAT screening approach of Van Steen et al. \[[@B7]\] is adopted to identify the top 10 most powerful genotype-phenotype combinations and to independently test these using the family-based association test (FBAT) statistic \[[@B6]\]. To be more in line with our MB-MDR analyses, we report results of the dominant genetic model rather than the additive genetic model. Family 7 was split into nuclear families for better handling by PBAT. Type I errors are Bonferroni controlled.
Penalized regression for population-based designs
-------------------------------------------------
To select the 10 most interesting predictors for Q1, we also apply a least absolute shrinkage and selection operator (LASSO) penalized regression \[[@B11]\]. We decrease the penalizing parameter *λ* with a precision of 0.001 to obtain at least 10 (nonzero) markers in the model, to be in line with PBAT screening. However, sometimes a few more markers were selected (maximum of 12). The covariates Sex, Age, and Smoke are fixed and unpenalized in the regression model. We repeated this analysis for each replicate to obtain a screening technique for the main effects. After this screening procedure, the selected markers were put in a linear regression model to test for association with Q1, again fixing Age, Sex, and Smoke in the model. *P*-values are Bonferroni corrected for the number of markers in the data.
Gene-based collapsing method
----------------------------
Following Li and Leal \[[@B12]\] for discrete traits and Morris and Zeggini \[[@B13]\] for quantitative traits, we collapsed variants with a minor allele frequency (MAF) less than 0.01 within each gene into a single variable coded 0 for absence and 1 for presence of at least one variant allele in an individual. The reported MAFs were evaluated using all individuals separately within each considered study design.
Results
=======
Additional file [1](#S1){ref-type="supplementary-material"} presents estimated power levels for association of important main effects with Q1 using the aforementioned methods. We observe that the MB-MDR approach for unrelated individuals has some power (0.14 for max *T* and 0.34 for min *P*) to find C4S1878, the marker with the largest MAF (0.16), but also elevated FWER estimates (0.13 and 0.50, respectively). With penalized regression, the highest power is achieved for markers C4S1884 (MAF = 0.02) and C4S1877 (MAF \< 0.001), irrespective of whether a gene-collapsing method was adopted or not. However, these results are downplayed by the inflation of the corresponding FWER (\>0.3). PBAT exhibits extremely high power (0.94) to detect C4S4935 (MAF \< 0.001) but also has an extreme FWER of 0.895. When a correction is made for the presence of linkage, interestingly, PBAT's power drops to 0 and its FWER drops to 0.015. On the other hand, the FAM-MDR approach has only limited power (0.18 for max *T* and 0.17 for min *P*) to detect C4S4935 but keeps the FWER under control.
A graphical representation of the relation between error rates for nonfunctional markers and the corresponding markers' MAFs is given in Figure [1](#F1){ref-type="fig"}.
{#F1}
Finally, collapsing rare variants increases the estimated power of the MB-MDR approach on unrelated individuals, both for the common variants C4S1878 (0.375 for max *T* and 0.38 for min *P*) and C4S1884 (0.205 for max *T* and 0.155 for min *P*) on the *KDR* gene and for the collapsed variable obtained from the rare variants on the *KDR* gene (0.355 for max *T* and 0.47 for min *P*). For the FAM-MDR analysis for families, collapsing increases the power to detect the variant C4S4935 on the *VEGFC* gene (0.275 for max *T* and 0.345 for min *P*). FWER for unrelated individuals remains high, whereas for family data FWER is under control.
Discussion
==========
Using the considered methods, we observed that different markers were highlighted in unrelated individuals versus families. Given the extent of monomorphic and nearly monomorphic causal variants with Q1 on chromosome 4, it is not surprising that none of the adopted methods perform satisfactorily in identifying genetic effects in the presence of rare variants. In particular, marker C4S4935 (Additional file [1](#S1){ref-type="supplementary-material"}) has only one heterozygous individual in the unrelated individuals data, and hence no method will be powerful enough to highlight this marker. However, this heterozygous individual was selected as a founder and propagated in one of the eight families, leading to an increased number of copies of the variant allele and consequently increased power to identify C4S4935 in the family data.
As a side remark, we also investigated whether the MB-MDR approach was able to identify the gene-smoking interaction effect present in the data. It is not surprising that detecting it was virtually powerless. Six out of 10 SNPs showing gene-environment interaction with smoking have such extremely low MAFs that no homozygous individuals for the rare allele and only one heterozygous individual were observed. Hence, for these SNPs, information about their potential to change the effects of smoking on Q1 is basically nonexistent because the one heterozygous individual is either a smoker or a nonsmoker. For unrelated individuals, none of the 944 markers are monomorphic, whereas 403 of the markers are monomorphic in the family data, leaving only 541 markers of interest in 77 genes. This can be explained by existing founder effects.
The beauty of the permutation-based corrective method for multiple testing used in the MB-MDR approach is that it tackles the issue of testing a large number of marker sets for evidence of gene-gene interactions with the trait, by controlling FWER at 5% \[[@B3]\]. We argue that the uncontrolled FWER levels might be a direct consequence of the distributional properties of association test statistics involving rare variants and their effect on the validity of both the adopted testing procedure and the applied multiple testing corrective methods. For instance, max *T* and min *P* adjusted *p*-values are known to be similar when the test statistics are identically distributed. When this is not the case, max *T* adjustments may be unbalanced such that not all tests equally contribute to the adjustment, leading to suboptimal power. The drawback of the min *P* implementation is that it is less computationally tractable than the max *T* approach and that a large number of permutations are needed to detect possible improved effects over max *T* implementations. A promising alternative approach may be the max *T* scaled method of Nacu et al. \[[@B14]\]. This method adjusts each test statistic by subtracting its null mean and dividing by its null standard deviation, leading to comparable null distributions. The max *T* scaled method can be considered a parametric and fast version of the min *P* method and requires a comparable number of permutations as the max *T* approach.
The total contribution to FWER of markers in linkage disequilibrium with functional markers (*r*^2^ \> 0.9) is only 0.01; hence linkage disequilibrium can be ruled out as an explanation of the increased FWER. In contrast, rare effects seem to be the major cause of the observed elevated FWER estimates. This is further supported by the observation that 1 out of 200 simulated replicates gives an erroneous result among the markers with MAF \> 0.1 (Figure [1a](#F1){ref-type="fig"}). Under the assumption that the markers with MAF \< 0.1 (90% of the data) and the markers with MAF \> 0.1 (10% of the data) behave similarly, we expect that 1 + 9 = 10 out of 200 replicates will give rise to an erroneous result (all markers considered). Hence the FWER would indeed be controlled at 5%. The same reasoning can be adopted to explain the conservativeness of the PBAT approach in the presence of rare variants, especially when the empirical variance option (test of no association in the presence of linkage) is used. In effect, the apparent liberal results observed in Pedigree based association testing with default screening parameters seem to be caused by a limited number of problematic markers (Figure [1b](#F1){ref-type="fig"}). Omitting marker C4S4694 (with MAF = 0.08) from the analysis indeed decreases the FWER from 0.895 to 0.445. When we remove three additional markers with moderate MAFs showing errors in multiple replicates, FWER tends to 0.04.
Joint application of the MB-MDR approach and gene collapsing leads to increased power, which can be explained by both the reduced multiple testing burden (note the increase in power for the common variants) and the creation of variables that exhibit larger amounts of information. For unrelated individuals, of the 944 markers, 199 have MAF ≥ 0.01 and 745 have MAF \< 0.01, and they are collapsed into 72 gene-specific variables. For the families, of the 541 nonmonomorphic markers, 227 have MAF ≥ 0.01 and 314 have MAF \< 0.01, and they are collapsed into 60 gene-specific variables. Surprisingly, FWER increased when the MB-MDR approach was applied to unrelated individuals. Notably, one of the drawbacks of adopting collapsing methods is that singular effects for rare variants cannot be distinguished from global gene effects.
Conclusions
===========
We compared several genetic association strategies to detect main effects, including the MB-MDR approach, PBAT screening, and penalized regression. Although none of the methods exhibited sufficient power to detect rare variants, remarkable differences were observed between these methods within and between study designs. At this point it is not clear whether these differences are due to the particular way the genetic effects were simulated in the family-based or population-based data or whether they are actually due to the methods themselves. However, most important, we postulate that the rarity of certain marker alleles hampers the validity of model assumptions and distributional properties of test statistics as well as assumptions underlying some commonly used measures to correct for multiple testing or to control false-positive rates.
Competing interests
===================
The authors declare that there are no competing interests.
Authors' contributions
======================
JMMJ, TC and KVS participated in the statistical analyses related to the MB-MDR technique. LDL and KVS participated in the analyses related to PBAT and penalized regression. FVL participated in optimizing the MB-MDR software for this project. AE participated in data handling and manipulation. All authors read and approved the final manuscript.
Supplementary Material
======================
###### Additional file 1
**Table 1 - Power to detect functional markers and FWER** Power and FWER results are shown for the MB-MDR approach and penalized regression on unrelated individuals, and FAM-MDR and FBAT results are shown for family data, both on original and collapsed chromosome 4 data. Power values greater than 0.1 are indicated in bold, and FWER values greater than 0.1 are indicated in italic. ^a^ At least 10 markers are selected using penalized regression, with Sex, Age, and Smoke as the fixed covariates. ^b^*P*-values are Bonferroni-corrected according to the total number of markers. Sex, Age, and Smoke are fixed covariates in the final model. ^c^ PBAT screening uses FBAT statistic to test the null hypothesis of no association in the presence of linkage.
######
Click here for file
Acknowledgments
===============
JMMJ, TC, FVL, and KVS acknowledge research opportunities offered by the Belgian Network BioMAGNet (Bioinformatics and Modeling: From Genomes to Networks), funded by the Interuniversity Attraction Poles Program (Phase VI/4), initiated by the Belgian State Science Policy Office. Their work was also supported in part by the Information Society Technologies (IST) Program of the European Community, under the PASCAL2 Network of Excellence (Pattern Analysis, Statistical Modeling, and Computational Learning) grant IST-2007-216886. In addition, TC is a postdoctoral researcher at the Fonds de la Recherche Scientifique (FNRS), and FVL acknowledges support from Alma in Silico, which is funded by the European Commission and Walloon Region through the Interreg IV Program.
This article has been published as part of *BMC Proceedings* Volume 5 Supplement 9, 2011: Genetic Analysis Workshop 17. The full contents of the supplement are available online at <http://www.biomedcentral.com/1753-6561/5?issue=S9>.
|
Objection 2. Further, the virtuousgood consists in accord with reason, as was clearly shown above (55, 4, ad 2). But that which accords with reason is natural to man; since reason is part of man'snature. Therefore virtue is in man by nature.
Objection 3. Further, that which is in us from birth is said to be natural to us. Now virtues are in some from birth: for it is written (Job 31:18): "From my infancy mercy grew up with me; and it came out with me from my mother's womb." Therefore virtue is in man by nature.
I answer that, With regard to corporeal forms, it has been maintained by some that they are wholly from within, by those, for instance, who upheld the theory of "latent forms" [Anaxagoras; Cf. I, 45, 8; 65, 4]. Others held that forms are entirely from without, those, for instance, who thought that corporeal forms originated from some separate cause. Others, however, esteemed that they are partly from within, in so far as they pre-existpotentially in matter; and partly from without, in so far as they are brought into act by the agent.
In like manner with regard to sciences and virtues, some held that they are wholly from within, so that all virtues and sciences would pre-exist in the soulnaturally, but that the hindrances to science and virtue, which are due to the soul being weighed down by the body, are removed by study and practice, even as iron is made bright by being polished. This was the opinion of the Platonists. Others said that they are wholly from without, being due to the inflow of the active intellect, as Avicenna maintained. Others said that sciences and virtues are within us by nature, so far as we are adapted to them, but not in their perfection: this is the teaching of the Philosopher (Ethic. ii, 1), and is nearer the truth.
To make this clear, it must be observed that there are two ways in which something is said to be natural to a man; one is according to his specific nature, the other according to his individualnature. And, since each thing derives its species from its form, and its individuation from matter, and, again, since man's form is his rational soul, while his matter is his body, whatever belongs to him in respect of his rational soul, is natural to him in respect of his specific nature; while whatever belongs to him in respect of the particular temperament of his body, is natural to him in respect of his individualnature. For whatever is natural to man in respect of his body, considered as part of his species, is to be referred, in a way, to the soul, in so far as this particular body is adapted to this particular soul.
In both these ways virtue is natural to man inchoatively. This is so in respect of the specific nature, in so far as in man's reason are to be found instilled by nature certain naturallyknown principles of both knowledge and action, which are the nurseries of intellectual and moral virtues, and in so far as there is in the will a naturalappetite for good in accordance with reason. Again, this is so in respect of the individualnature, in so far as by reason of a disposition in the body, some are disposed either well or ill to certain virtues: because, to wit, certain sensitive powers are acts of certain parts of the body, according to the disposition of which these powers are helped or hindered in the exercise of their acts, and, in consequence, the rational powers also, which the aforesaid sensitive powers assist. In this way one man has a natural aptitude for science, another for fortitude, another for temperance: and in these ways, both intellectual and moral virtues are in us by way of a natural aptitude, inchoatively, but not perfectly, since nature is determined to one, while the perfection of these virtues does not depend on one particular mode of action, but on various modes, in respect of the various matters, which constitute the sphere of virtue's action, and according to various circumstances.
It is therefore evident that all virtues are in us by nature, according to aptitude and inchoation, but not according to perfection, except the theological virtues, which are entirely from without.
This suffices for the Replies to the Objections. For the first two argue about the nurseries of virtue which are in us by nature, inasmuch as we are rational beings. The third objection must be taken in the sense that, owing to the natural disposition which the body has from birth, one has an aptitude for pity, another for living temperately, another for some other virtue.
Objection 2. Further, sin and virtue are contraries, so that they are incompatible. Now man cannot avoid sin except by the grace of God, according to Wisdom 8:21: "I knew that I could not otherwise be continent, except God gave it." Therefore neither can any virtues be caused in us by habituation, but only by the gift of God.
Objection 3. Further, actions which lead toward virtue, lack the perfection of virtue. But an effect cannot be more perfect than its cause. Therefore a virtue cannot be caused by actions that precede it.
I answer that, We have spoken above (51, A2,3) in a general way about the production of habits from acts; and speaking now in a special way of this matter in relation to virtue, we must take note that, as stated above (55, A3,4), man'svirtue perfects him in relation to good. Now since the notion of good consists in "mode, species, and order," as Augustine states (De Nat. Boni. iii) or in "number, weight, and measure," as expressed in Wisdom 11:21, man'sgood must needs be appraised with respect to some rule. Now this rule is twofold, as stated above (19, A3,4), viz. humanreason and Divine Law. And since Divine Law is the higher rule, it extends to more things, so that whatever is ruled by humanreason, is ruled by the Divine Law too; but the converse does not hold.
It follows that humanvirtue directed to the good which is defined according to the rule of humanreason can be caused by human acts: inasmuch as such acts proceed from reason, by whose power and rule the aforesaid good is established. On the other hand, virtue which directs man to good as defined by the Divine Law, and not by humanreason, cannot be caused by human acts, the principle of which is reason, but is produced in us by the Divine operation alone. Hence Augustine in giving the definition of the latter virtue inserts the words, "which God works in us without us" (Super Ps. 118, Serm. xxvi). It is also of these virtues that the First Objection holds good.
Reply to Objection 2. Mortal sin is incompatible with divinely infused virtue, especially if this be considered in its perfect state. But actual sin, even mortal, is compatible with humanly acquired virtue; because the use of a habit in us is subject to our will, as stated above (Question 49, Article 3): and one sinful act does not destroy a habit of acquired virtue, since it is not an act but a habit, that is directly contrary to a habit. Wherefore, though man cannot avoid mortal sin without grace, so as never to sin mortally, yet he is not hindered from acquiring a habit of virtue, whereby he may abstain from evil in the majority of cases, and chiefly in matters most opposed to reason. There are also certain mortal sins which man can nowise avoid without grace, those, namely, which are directly opposed to the theological virtues, which are in us through the gift of grace. This, however, will be more fully explained later (109, 4).
Reply to Objection 3. As stated above (1; 51, 1), certain seeds or principles of acquired virtue pre-exist in us by nature. These principles are more excellent than the virtues acquired through them: thus the understanding of speculative principles is more excellent than the science of conclusions, and the natural rectitude of the reason is more excellent than the rectification of the appetite which results through the appetite partaking of reason, which rectification belongs to moral virtue. Accordingly human acts, in so far as they proceed from higher principles, can cause acquired humanvirtues.
Article 3. Whether any moral virtues are in us by infusion?
Objection 1. It would seem that no virtues besides the theological virtues are infused in us by God. Because God does not do by Himself, save perhaps sometimes miraculously, those things that can be done by second causes; for, as Dionysius says (Coel. Hier. iv), "it is God's rule to bring about extremes through the mean." Now intellectual and moral virtues can be caused in us by our acts, as stated above (Article 2). Therefore it is not reasonable that they should be caused in us by infusion.
Reply to Objection 1. Some moral and intellectualvirtues can indeed be caused in us by our actions: but such are not proportionate to the theological virtues. Therefore it was necessary for us to receive, from God immediately, others that are proportionate to these virtues.
Reply to Objection 2. The theological virtues direct us sufficiently to our supernatural end, inchoatively: i.e. to God Himself immediately. But the soul needs further to be perfected by infused virtues in regard to other things, yet in relation to God.
Reply to Objection 3. The power of those naturally instilled principles does not extend beyond the capacity of nature. Consequently man needs in addition to be perfected by other principles in relation to his supernatural end.
Article 4. Whether virtue by habituation belongs to the same species as infused virtue?
Objection 1. It would seem that infused virtue does not differ in species from acquired virtue. Because acquired and infused virtues, according to what has been said (3), do not differ seemingly, save in relation to the last end. Now humanhabits and acts are specified, not by their last, but by their proximate end. Therefore the infused moral or intellectualvirtue does not differ from the acquired virtue.
Objection 2. Further, habits are known by their acts. But the act of infused and acquired temperance is the same, viz. to moderate desires of touch. Therefore they do not differ in species.
Objection 3. Further, acquired and infused virtue differ as that which is wrought by God immediately, from that which is wrought by a creature. But the man whom God made, is of the same species as a man begotten naturally; and the eye which He gave to the man born blind, as one produced by the power of generation. Therefore it seems that acquired and infused virtue belong to the same species.
On the contrary, Any change introduced into the difference expressed in a definition involves a difference of species. But the definition of infused virtue contains the words, "which God works in us without us," as stated above (Question 55, Article 4). Therefore acquired virtue, to which these words cannot apply, is not of the same species as infused virtue.
I answer that, There is a twofold specific difference among habits. The first, as stated above (54, 2; 56, 2; 60, 1), is taken from the specific and formal aspects of their objects. Now the object of every virtue is a good considered as in that virtue's proper matter: thus the object of temperance is a good in respect of the pleasures connected with the concupiscence of touch. The formal aspect of this object is from reason which fixes the mean in these concupiscences: while the material element is something on the part of the concupiscences. Now it is evident that the mean that is appointed in such like concupiscences according to the rule of humanreason, is seen under a different aspect from the mean which is fixed according to Divine rule. For instance, in the consumption of food, the mean fixed by humanreason, is that food should not harm the health of the body, nor hinder the use of reason: whereas, according to the Divine rule, it behooves man to "chastise his body, and bring it into subjection" (1 Corinthians 9:27), by abstinence in food, drink and the like. It is therefore evident that infused and acquired temperance differ in species; and the same applies to the other virtues.
The other specific differences among habits is taken from the things to which they are directed: for a man's health and a horse's are not of the same species, on account of the difference between the natures to which their respective healths are directed. In the same sense, the Philosopher says (Polit. iii, 3) that citizens have diverse virtues according as they are well directed to diverse forms of government. In the same way, too, those infused moral virtues, whereby men behave well in respect of their being "fellow-citizens with the saints, and of the household [Douay: 'domestics'] of God" (Ephesians 2:19), differ from the acquired virtues, whereby man behaves well in respect of human affairs.
Reply to Objection 1. Infused and acquired virtue differ not only in relation to the ultimate end, but also in relation to their proper objects, as stated.
Reply to Objection 2. Both acquired and infused temperance moderate desires for pleasures of touch, but for different reasons, as stated: wherefore their respective acts are not identical.
Reply to Objection 3.God gave the man born blind an eye for the same act as the act for which other eyes are formed naturally: consequently it was of the same species. It would be the same if God wished to give a man miraculouslyvirtues, such as those that are acquired by acts. But the case is not so in the question before us, as stated. |
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Ten days into the uprising in Benghazi, Libya, the United Nations’ Human Rights Council established the International Commission of Inquiry on Libya. The purpose of the Commission was to “investigate all alleged violations of international human rights law in Libya.” The broad agenda was to establish the facts of the violations and crimes and to take such actions as to hold the identified perpetrators accountable. On June 15, the Commission presented its first report to the Council. This report was provisional, since the conflict was still ongoing and access to the country was minimal. The June report was no more conclusive than the work of the human rights non-governmental organizations (such as Amnesty International and Human Rights Watch). In some instances, the work of investigators for these NGOs (such as Donatella Rovera of Amnesty) was of higher quality than that of the Commission.
Due to the uncompleted war and then the unsettled security state in the country in its aftermath, the Commission did not return to the field till October 2011, and did not begin any real investigation before December 2011. On March 2, 2012, the Commission finally produced a two hundred-page document that was presented to the Human Rights Council in Geneva. Little fanfare greeted this report’s publication, and the HRC’s deliberation on it was equally restrained.
Nonetheless, the report is fairly revelatory, making two important points: first, that all sides on the ground committed war crimes with no mention at all of a potential genocide conducted by the Qaddafi forces; second, that there remains a distinct lack of clarity regarding potential NATO war crimes. Not enough can be made of these two points. They strongly inferthat the rush to a NATO “humanitarian intervention” might have been made on exaggerated evidence, and that NATO’s own military intervention might have been less than “humanitarian” in its effects.
It is precisely because of a lack of accountability by NATO that there is hesitancy in the United Nations Security Council for a strong resolution on Syria. “Because of the Libyan experience,” the Indian Ambassador to the UN Hardeep Singh Puri told me in February, “other members of the Security Council, such as China and Russia, will not hesitate in exercising a veto if a resolution – and this is a big if – contains actions under Chapter 7 of the UN Charter, which permits the use of force and punitive and coercive measures.”
Crimes Against Humanity.
The Libyan uprising began on February 15, 2011. By February 22, the UN Human Rights Chief Navi Pillay claimed that two hundred and fifty people had been killed in Libya, “although the actual numbers are difficult to verify.” Nonetheless, Pillay pointed to “widespread and systematic attacks against the civilian population” which “may amount to crimes against humanity.” Pillay channeled the Deputy Permanent Representative to the UN from Libya, Ibrahim Dabbashi, who had defected to the rebellion and claimed, “Qaddafi had started the genocide against the Libyan people.” Very soon world leaders used the two concepts interchangeably, “genocide” and “crimes against humanity.” These concepts created a mood that Qaddafi’s forces were either already indiscriminately killing vast numbers of people, or that they were poised for a massacre of Rwanda proportions.
Courageous work by Amnesty International and Human Rights Watch last year, then much later the 2012 report from the UN belies this judgment, (as does my forthcoming book Arab Spring, Libyan Winter, AK Press), which goes through the day-by-day record and show two things: that both sides used excessive violence and that the rebels seemed to have the upper hand for much of the conflict, with Qaddafi’s forces able to recapture cities, but unable to hold them.
The UN report is much more focused on the question of crimes committed on the ground. This is the kind of forensic evidence in the report:
(1) In the military base and detention camp of Al Qalaa. “Witnesses, together with the local prosecutor, uncovered the bodies of 43 men and boys, blindfolded and with their hands tied behind their backs.” Qaddafi forces had shot them. Going over many of these kinds of incidents, and of indiscriminate firing of heavy artillery into cities, the UN Report notes that these amount to a war crime or a crime against humanity.
(2) “Over a dozen Qadhafi soldiers were reportedly shot in the back of the head by thuwar [rebel fighters] around 22-23 February 2011 in a village between Al Bayda and Darnah. This is corroborated by mobile phone footage.” After an exhaustive listing of the many such incidents, and of the use of heavy artillery against cities notably Sirte, the UN report suggests the preponderance of evidence of the war crime of murder or crimes against humanity.
There is no mention of genocide in the Report, and none of any organized civilian massacre. This is significant because UN Resolution 1973, which authorized the NATO war, was premised on the “the widespread and systematic attacks currently taking place in the Libyan Arab Jamahiriya against the civilian population” which “may amount to crimes against humanity.” There was no mention in Resolution 1973 of the disproportionate violence of the thuwar against the pro-Qaddafi population (already reported by al-jazeera by February 19), a fact that might have given pause to the UN as it allowed NATO to enter the conflict on the rebels’ behalf. NATO’s partisan bombardment allowed the rebels to seize the country faster than they might have had in a more protracted war, but it also allowed them carte blanche to continue with their own crimes against humanity.
With NATO backing, it was clear that no one was going to either properly investigate the rebel behavior, and no-one was going to allow for a criminal prosecution of those crimes against humanity. Violence of this kind by one’s allies is never to be investigated as the Allies found out after World War 2 when there was no assessment of the criminal firebombing of, for example, Dresden. No wonder that the UN Report notes that the Commissioners are “deeply concerned that no independent investigation or prosecution appear to have been instigated into killings committed by thuwar.” None is likely. There are now over eight thousand pro-Qaddafi fighters in Libyan prisons. They have no charges framed against them. Many have been tortured, and several have died (including Halah al-Misrati, the Qaddafi era newscaster).
The section of the UN report on the town of Tawergha is most startling. The thirty thousand residents of the town were removed by the Misratan thuwar. The general sentiment among the Misratan thuwar was that the Tawerghans were given preferential treatment by the Qaddafi regime, a claim disputed by the Tawerghans. The road between Misrata and Tawergha was lined with slogans such as “the brigade for purging slaves, black skin,” indicating the racist cleansing of the town. The section on Tawergha takes up twenty pages of the report. It is chilling reading. Tawerghans told the Commission “that during ‘interrogations’ they were beaten, had hot wax poured in their ears and were told to confess to committing rape in Misrata. The Commission was told that one man had diesel poured on to his back which was then set alight; the same man was held in shackles for 12 days.” This goes on and on. The death count is unclear. The refugees are badly treated as they go to Benghazi and Tripoli.
To the Commission, the attacks against Tawerghans during the war “constitute a war crime” and those that have taken place since “violate international human rights law” and a “crime against humanity.” Because of the “current difficulties faced by the Libyan Government,” the Commission concludes, it is unlikely that the government will be able to bring justice for the Tawerghans and to undermine the “culture of impunity that characterizes the attacks.”
NATO’s Crimes.
For the past several months, the Russians have asked for a proper investigation through the UN Security Council of the NATO bombardment of Libya. “There is great reluctance to undertake it,” the Indian Ambassador to the UN told me. When the NATO states in the Security Council wanted to clamor for war in February-March 2011, they held discussions about Libya in an open session. After Resolution 1973 and since the war ended, the NATO states have only allowed discussion about Libya in a closed session. When Navi Pillay came to talk about the UN Report, her remarks were not for the public.
Indeed, when it became clear to NATO that the UN Commission wished to investigate NATO’s role in the Libyan war, Brussels balked. On February 15, 2012, NATO’s Legal Adviser Peter Olson wrote a strong letter to the Chair of the Commission. NATO accepted that the Qaddafi regime “committed serious violations of international law,” which led to the Security Council Resolution 1973. What was not acceptable was any mention of NATO’s “violations” during the conflict,
“We would be concerned, however, if ‘NATO incidents’ were included in the Commission’s report as on a par with those which the Commission may ultimately conclude did violate law or constitute crimes. We note in this regard that the Commission’s mandate is to discuss ‘the facts and circumstance of….violations [of law] and…crimes perpetrated.’ We would accordingly request that, in the event the Commission elects to include a discussion of NATO actions in Libya, its report clearly state that NATO did not deliberately target civilians and did not commit war crimes in Libya.”
To its credit, the Commission did discuss the NATO “incidents.” However, there were some factual problems. The Commission claimed that NATO flew 17,939 armed sorties in Libya. NATO says that it flew “24,200 sorties, including over 9,000 strike sorties.” What the gap between the two numbers might tell us is not explored in the report or in the press discussion subsequently. The Commission points out that NATO did strike several civilian areas (such as Majer, Bani Walid, Sirte, Surman, Souq al-Juma) as well as areas that NATO claims were “command and control nodes.” The Commission found no “evidence of such activity” in these “nodes.” NATO contested both the civilian deaths and the Commission’s doubts about these “nodes.” Because NATO would not fully cooperate with the Commission, the investigation was “unable to determine, for lack of sufficient information, whether these strikes were based on incorrect or outdated intelligence and, therefore, whether they were consistent with NATO’s objective to take all necessary precautions to avoid civilian casualties entirely.”
Three days after the report was released in the Human Rights Council, NATO’s chief Anders Fogh Rasmussen denied its anodyne conclusions regarding NATO. And then, for added effect, Rasmussen said that he was pleased with the report’s finding that NATO “had conducted a highly precise campaign with a demonstrable determination to avoid civilian casualties.” There is no such clear finding. The report is far more circumspect, worrying about the lack of information to make any clear statement about NATO’s bombing runs. NATO had conducted its own inquiry, but did not turn over its report or raw data to the UN Commission.
On March 12, UN Secretary General Ban Ki-moon went to the UN Security Council and stated that he was “deeply concerned” about human rights abuses in Libya, including the more than eight thousand prisoners held in jails with no judicial process (including Saif al-Islam Qaddafi, who should have been transferred to the Hague by NATO’s logic). Few dispute this part of the report. The tension in the Security Council is over the section on NATO. On March 9, Maria Khodynskaya-Golenishcheva of the Russian Mission to the UN in Geneva noted that the UN report omitted to explore the civilian deaths caused by NATO. “In our view,” she said, “during the NATO campaign many violations of the standard of international law and human rights were committed, including the most important right, the right to life.” On March 12, Russia’s Foreign Minister Sergei Lavrov accused NATO of “massive bombings” in Libya. It was in response to Lavrov’s comment that Ban’s spokesperson Martin Nesirky pointed out that Ban accepts “the report’s overall finding that NATO did not deliberately target civilians in Libya.”
NATO is loath to permit a full investigation. It believes that it has the upper hand, with Libya showing how the UN will now use NATO as its military arm (or else how the NATO states will be able to use the UN for its exercise of power). In the Security Council, NATO’s Rasmussen notes, “Brazil, China, India and Russia consciously stepped aside to allow the UN Security Council to act” and they “did not put their military might at the disposal of the coalition that emerged.” NATO has no challenger. This is why the Russians and the Chinese are unwilling to allow any UN resolution that hints at military intervention. They fear the Pandora’s box opened by Resolution 1973.
Vijay Prashad’s new book, Arab Spring, Libyan Winter (AK Press) will be out in late March. On March 25, he will be speaking at the plenary panel of the United National Anti-War Coalition National Conference in Stamford, CT, alongside Bill McKibben, Richard Wolff and Nada Khader on “Global Economic Meltdown, Warming and War.” |
Bitcoin’s Scalability: SegWit and Lightning Networks
The obvious need for Bitcoin to scale is just that: obvious. If you’ve been following the cryptocurrency scene, you have probably heard of Segregated Witness and Lightning Networks, but probably not what they are - both strengths and weaknesses.
A Bumpy Roadmap of Solutions
Bitcoin Core developers have long created a scaling roadmap and back at 2015, Segregated Witness was first introduced.
This protocol, developed by Pieter Wuille, first proposed that a soft-fork update with the SegWit protocol in mind would suffice in order to increase the block size limit and give Bitcoin a scalability solution. Unfortunately for most Bitcoin miners, an increase of block size does not sit very well.
Many decentralists like Bitcoin at the current setting. They fear that introducing an increase in transactions per second (tps) or block size would give rise to centralized mining, creating oligarchy-like pools that can dominate the little pools. Decentralists also assume that creating protocols could give decrease the anonymity of the cryptocurrency, going against the primary operating principle of Bitcoin.
On the other end of the spectrum, people who are proponents of the increase - let’s call them blockgressives - are sure that the increase in size will only lead to Bitcoin having less volatility, most likely leading to a lower price, but will become far more stable as a cryptocurrency.
Blockgressives and Decentralists, both, have their fair arguments, but the currency has to move into a direction or it will eventually fall behind - with Litecoin having already implemented SegWit into their core code, it just goes to show as to how willing cryptos are to experiment.
A complete different point-of-view from Bitcoin Core developer, Luke-jr, claimed that an increase in block size isn’t really even needed - the surprising third statement! In a reddit comment, he said that if we put aside all the inefficient and microtransaction usages, a block size of 500k would suffice.
So many opinions to weigh on, but SegWit and Lightning Networks still remain a mystery.Meanwhile, Bitcoin’s mempool reaches 110 MB, leaving us confused, thinking: So... is this an issue or not?
Barely Explain Like I’m Five: Segregated Witness
There are two Bitcoin transaction fields that interest us when it comes to understanding SegWit:
scriptPubKey - Public Key Script
scriptSig - Signature Script
Script is a language developed by Satoshi Nakamoto himself, a stack language that executes from left-to-right in a Last In, First Out (LIFO) manner. These signatures, although small in size, surprisingly take up a lot of space in a block. According to Dr. Peter Wuille, the developer of SegWit, digital signatures account for 65% of the space in transactions.
The entire idea of SegWit is to separate transaction signatures - taking the data from the signatures and only attaching it to the end of a transaction, after bundling them, while also increasing the size of a block from 1 MB to 4 MB.
Not only does SegWit claim to increase the throughput of the entire Bitcoin network, it also nullifies some risks that have to do with Bitcoin transactions, such as the recipient modifying the sender’s transaction ID and sending himself more coins.
Although SegWit is a very useful protocol, and as of 07/01/2017, 40% of the community signaled a willingness for SegWit support (The requirement is 95%), there are many issues that the community cannot simply agree with when it comes to its implementation. Many people believe that the trade-off is between the increase of transactions per second (tps) and decentralization.
The increase of block size could potentially increase the tps (I say could because if traffic increases, there will eventually be congestion, it’s only a matter of time) but could also lead to a centralization of block mining. This is because larger blocks take longer to transfer between nodes, this could give a head start to larger pools that could essentially outgrow all other competitors.
An increase in size from 1 MB to 4 MB will burden full nodes far more than currently (blockchain size is already past the 100 GB milestone). This is because to run a full node, the bitcoin blockchain uses your bandwidth, CPU power, and a sizeable amount of disk space. All of which increase in demand with the possible increase of block size.
The other issue is that SegWit is primarily worried about authenticating transactions, skipping many signature protocols “checkpoints”, which can lead to issues with tracing back all the transactions inside the Bitcoin blockchain - a key feature that allows us to find the genesis of every Bitcoin ever spent.
This protocol is complicated. The many users that vouch for it, agree that it is a great solution to stabilizing the Bitcoin value and making it more accessible, some disagree and say the
complete opposite. Both sides have their arguments, and Bitcoin development is at a “halt”, but the network is growing very fast and it requires a solution just as fast.
Lightning Networks: Bunching Signatures Up
Lightning Network is another great protocol that can open the door up for a new type of transaction inside the Bitcoin blockchain: Microtransactions.
Although the fee for a Bitcoin transaction is usually very low, these fees cripple microtransactions completely. Lightning Networks promises a solution through the use of payment channels.
Payment channels open when two or more parties want to transact. Transactions start process and end within a payment channel. These transactions follow standard procedures of signature confirmation and all data necessary needed to authenticate them. Though the process is normally done as if within the Bitcoin blockchain, the payment channels are much faster than the normal network.
The Lightning Network then groups all the transactions are done within the payment channel, creates a total sum from the back-and-forth trading and sends only the last summed transaction data to the blockchain. This saves space from the many little transactions that are advertised to a block, leaving room for bigger transactions.
This protocol also promises to monitor the blockchain for any potential double-spenders, making it virtually impossible to double-spend any amount of money, since any attempt is met with refunds. Lightning Network would also allow for different blockchains to communicate with one another, which can lead to many interesting projects being developed.
Although the features are very interesting, there are many uncertainties to them.
First, the promise of a potentially “unlimited” tps does not mean that the network will not face any issues anymore. If Bitcoin wants to take on the throughput of Visa, payment channels have to be opened and closed at incredibly fast rates. This could lead to large network congestions which the Bitcoin blockchain is not ready to handle (yet?).
Furthermore, Lightning Networks promise to solve some security flaws very easily. Almost too easy. The double-spending protection feature is one of them. Lightning Network promises that they will provide a way of monitoring the blockchain constantly, 24/7, and protect from any potential double-spenders, but such a feature doesn’t exist for now.
The problem with payment channels is that they could bring more issues than they could solve. For example, a user with malicious intent could resend an old payment channel, advertising that into a new payment channel and could possibly send more coins to himself from your personal wallet.
Finally, Lightning Network can lead to centralization. since people are required to send money to one-another in the channel. Which begs the question: How many people have to partake in a channel for it to be effective? Which leads to the main dilemma: Do third-parties have to partake in each payment channel, effectively making Lightning Network a bank?
Protocols: The Good, the Bad and the Conclusion
These protocols sound and are ingenious, but the loopholes behind them are a cause for a lot of predicaments within the Bitcoin community, and until the miners and nodes are satisfied, we won’t be seeing any implementations.
Promises of unlimited throughput, higher security, lower costs are met with the exact opposite when further analyzed, which is why Bitcoin doesn’t have one simple answer to everything. |
Category Archives: Fall 2014
In early 2013, the Board and subsequently the membership voted to change the Bylaws to combine the Nominations Committee and the Elections Committee into one committee. Thus the Nominations and Elections committee inaugural year was this year.
The first task of the Committee was to determine who should be nominated for the positions of Vice- President/President Elect, Treasurer, and Director. After requesting nominations from the membership and brainstorming ideas for potential candidates, the Committee presented the following slate of candidates to the Board for approval:
Vice-President/President Elect: Debbie Ginsberg and Julie Pabarja
Treasurer: Stephanie Crawford and Valerie Kropf
Director: Jesse Bowman and Robert Martin
The Board approved the slate and approved the election take place between Tuesday, February 18th and Friday, March 14th.
The Committee working with AALL got all of the voting credentials set for all of the eligible voters in time for the start of the election. There were no CALL members without e-mail addresses, so no paper ballots were produced. The election began as scheduled on February 18th and ended as scheduled on March 14th. There were a few members that did not receive their e-mail from AALL with their voting credentials, however those issues were resolved quickly and the members were able to vote.
Of the 266 members eligible to vote, 144 members elected the following candidates:
Julie Pabarja, Vice-President/President Elect
Stephanie Crawford, Treasurer
Robert Martin, Director
The Nominations and Elections Committee members included Denise Glynn, Ramsey Donnell, Joan Ogden, Kathleen Bruner, Lenore Glanz, Lyonette Louis-Jacques, and Susan Retzer. A very special thank you to Joan Ogden – she is a wealth of information and frankly the knowledge keeper of all things related to the CALL election. We would not have had such a successful election without her wonderful expertise.
This year we had a 54.1% voting rate. In years past the rates have been:
54.7% in 2012/2013
45.4% in 2011/2012
46.5% in 2010/2011
51.9% in 2009/2010
47.8% in 2008/2009
Hopefully next year we can have an unprecedented turn-out to choose our new Board members from a wonderful slate of dedicated CALL members!
The Placement & Recruitment Committee continued utilizing the job posting procedure which was updated during the 2012-2013 membership year. The procedure successfully serves members, employers, job seekers, and enables an efficient process for committee use.
Employers fill out a simple web form on the CALL website. The committee member who receives the form confirms the posting and uploads it on the website, usually within a day. The procedure also triggers an email to the listserv. When requested by an employer submitting a job opening, the committee member sends an announcement to nearby library schools. It helps connect CALL with library students and recent alumni from graduate library programs. Using this described procedure, the committee posted 30 jobs on the CALL website and listserv during the membership year.
One enhancement to the Jobs Form this year was the addition of a print button which allows each job position to be easily printed. The print feature was added through the efforts of Debbie Ginsberg of the Public Relations Committee.
The committee also collaborated with the Public Relations Committee in the updating of the CALL Brochure. Additionally, Ms. Kara Dunn, an attorney interested in law librarianship contacted the Committee who wanted a “Day in the Life: Law Librarian” experience as promoted on the CALL Jobs and Careers web page. A member of the committee met with her and was able to connect with a law librarian from Northwestern University. It was challenging to find somebody who was willing to meet with Ms. Dunn and by extension, arrange for a shadowing opportunity. It is suggested that the CALL board deliver some sort of message to the membership that part of their professional responsibilities is to try, as much as it is possible, to make themselves available to individuals who are considering entering the profession.
Projects for 2014-2015
Participate in local college and university career
Work with Continuing Education committee to develop a CALL program on the profession of law librarianship for library science and other interested
In collaboration with the Education Committee, develop and education program relating to placement or recruitment.
Meetings
In the 2013-2014 year, the Committee conducted two in-person status meetings, in addition to an online meeting. The in-person meetings were well received, as they better facilitated discussion and brainstorming among the members regarding Committee plans and objectives. Following the meetings, the Committee members were provided a meeting summary with action items.
Public Relations
The Committee continued to seek opportunities to promote CALL and its members to the public and through AALL.
CALL at AALL/AALL Marketing Award
Member Scott Vanderlin set up a unique and engaging table display at AALL’s 2013 Annual Meeting. The display, “Call CALL in the Exhibit Hall” featured a phone which attendees used to listen to pre-recorded information about CALL. The table was submitted for an AALL Excellence in Marketing Award, Best Use of Technology and was selected as the winner.
Scott will also design the table for the 2014 Annual Meeting.
Brochure
With the help of member Carolyn Hersch and Membership Committee Member Karl Pettit, the CALL Brochure was revised for the 2014 AALL Annual Meeting. The new brochure is informative yet visually engaging.
Law Day
Working with outgoing Director Pamela Cipkowski, CALL put an ad in the Chicago Daily Law Bulletin for Lay Day 2014 (May 1).
Pictures at Events
Member Emily Barney and other members took many pictures at CALL business meetings in 2013-14. The pictures have been useful for projects such as the new Brochure. CALL also now has a Flickr account to help share these pictures and promote their use.
CONELL/Give-Away
CALL will participate in the CONELL Marketplace at the 2014 Annual Meeting. Members will be on hand to answer questions as well as give away brochures and lip balm.
Plans for the Future
Over the 2014-15 year, the Committee plans to work more closely with AALL, providing the organization with more information about chapter events and members. The Committee will also reach out to the Meetings Committee to help promote events and speakers. The Committee will also work more to promote relevant events at individual libraries and member happenings.
Social Media
Facebook/Twitter
The Committee is currently engaging with the CALL membership through the social media platforms Facebook (79 Likes), Twitter (64 Followers) and LinkedIn (76 Members). This year, the social media efforts were focused on improving user engagement on Facebook. Through Facebook Insights, we were able to determine that the posts that users engaged with the most were announcements for the CALL business meetings. Our Facebook fans also responded well to articles on the law librarian profession. Other posts that had a large reach discussed current news and developments related to the Association, including CALL award winners, AALL election results and the AALL Annual Conference.
In the 2013-2014 year, the Committee unlinked the CALL Twitter account from the Facebook account. This allowed us to generate more Twitter friendly content, which entailed limiting our posts to 140 characters or less. The Committee aims to use Twitter as a platform to interact with CALL members, potential members and the law librarian community. To achieve this goal, the CALL twitter page has begun following the feeds of individual CALL members, law school libraries and professional library associations.
Website
Archives
The Board requested that the Committee research how other chapters archive their websites. From what the Committee was able to learn, other chapters do not have procedures to formally archive their sites.
Website Updates
The Committee added a Grants/Awards section to better promote these important activities. While no longer in the navigation menu, CALL website continues to promote “Finding IL Law” through a prominent side button.
The Committee upgraded the CALL WordPress installation to version 3.9 to ensure that the site remains secure and up to date.
Plans for the future
The Committee will solicit member feedback on the website’s usability. We will also work with the Bulletin Committee to help create a more web-friendly CALL Bulletin.
Listserv
Member Kara Young monitored CALL’s listserv and made changes as needed. Kara will serve as co-chair in 2014-15.
Often, whether in a law school or law firm setting, the challenge is finding enough time to get everything done. In particular, as summer’s leisurely stroll winds down and fall accelerates into full sprint mode, you may wish you had more time in your day. |
(b) g (c) 2/7
c
Let n = 11.4 + -11. Let q = -10 + 22. Let d = q - 12.4. What is the nearest to 2 in 6/5, d, n?
6/5
Suppose -3*t = 0, 2*n = n - 5*t - 4. Let z = 6 - 6. Let s be (1/10)/(12/24). Which is the closest to z? (a) -2 (b) s (c) n
b
Let n = -0.125 - 25.375. Let w = 25 + n. What is the nearest to -2/7 in 3, 4/3, w?
w
Let g = 961 + -908. Which is the closest to -2/3? (a) -3 (b) g (c) 0.1
c
Suppose -g - 7*n + 5*n = 2, 3*g + 2 = -4*n. What is the nearest to g in 0.5, -5, -2?
0.5
Let g = 1.51 + -1.56. Let i = 0.25 - g. What is the nearest to 8 in -0.3, i, -3?
i
Let w = -9.9 - -10. Let s = -149.1 + 149. Which is the nearest to s? (a) w (b) -0.1 (c) -5
b
Let s(w) = w**2 - 8*w - 6. Let x be s(9). Let d = -11.84 - -11.94. What is the closest to 0.3 in -4/5, x, d?
d
Let d be 0 - (-3)/12 - 0. Let h = -109 - -114. Let v = -6 - -5.6. What is the closest to d in h, -2, v?
v
Let q = 3/46 + -153/230. Let v = 6.1 + -6. Let i = -36.4 + 36. Which is the nearest to v? (a) 0.4 (b) i (c) q
a
Let w be 9/(-12)*42/63. Suppose 4*n + 10 = -2. Let u be ((-12)/(-10))/(n/10). What is the nearest to 2/5 in u, -0.1, w?
-0.1
Let l = 63.3 - 63.4. Which is the nearest to l? (a) -37 (b) 2 (c) -1
c
Let r = -719 + 719. Which is the nearest to r? (a) -7 (b) 1 (c) -3/4
c
Let p = 2 - 2.5. Let k = -7.1031 + 0.1031. Which is the nearest to 0? (a) p (b) k (c) 0.2
c
Let o = -195 + 194. Which is the closest to o? (a) 2/11 (b) 0.5 (c) 4
a
Let q = 507/2 + -253. Let j = 1/2 + -7/10. Which is the closest to j? (a) 0.4 (b) 2 (c) q
a
Let p be 72/18 - (-84)/(-22). Which is the nearest to p? (a) 7 (b) 3/7 (c) -2/5
b
Suppose -3*v = 1 + 2. Let w be (-85)/102 + v/(-3). What is the nearest to 3 in -4, w, 3?
3
Suppose x + 76 = -4*n, -2*n + 2*x - 21 = 7. Which is the closest to 1? (a) 1 (b) 3 (c) n
a
Let t = -5.2 + 0.2. Let x = 14/23 - 89/184. Let l = -37.9 + 38. Which is the closest to l? (a) t (b) 0.5 (c) x
c
Let g = -23.2 - -21.2. What is the closest to 0 in g, 3/4, -1/3?
-1/3
Let h(u) = 12*u - 57. Let w be h(5). Which is the nearest to 0? (a) 2 (b) 29 (c) w (d) 4
a
Let z = -309 - -308. What is the nearest to z in -5, 1, 5?
1
Let h = 1 - 2. Let a = -1.3 + -86.7. Let y = -85 - a. What is the closest to y in h, 2/13, -4?
2/13
Let k = 342 - 341.6. Which is the nearest to -2? (a) k (b) 5 (c) 0.3
c
Let d = 17 - 17. Let w = -3.7 + 0.7. Let f be 0 + -1 + 3 - -2. Which is the closest to d? (a) f (b) w (c) 2/7
c
Let z be ((-11)/(-55))/(-2*(-2)/8). What is the nearest to 1 in -12, z, 5/2, -4/5?
z
Let f = -14 + 14.9. Let a = 2.9 - f. What is the closest to -2/9 in 1, a, -3?
1
Let h be 3*(20/(-3))/(-4). Let x be 3 + (-1 - 13/h). What is the nearest to x in 1, 2/13, -2/5?
-2/5
Let f = -2 - -2. Let q = -45 - -45.3. Which is the nearest to f? (a) q (b) -8 (c) -2
a
Let x = 0 - -0.2. Let r = 0.14 - 0.238. Let j = -0.198 - r. Which is the closest to j? (a) x (b) 2/5 (c) 6
a
Let o = 45.33 + -46. Let d = 0.47 + o. Which is the nearest to 0? (a) -0.5 (b) -2 (c) d
c
Suppose 6*g = 3*g - 21. Let b(n) = n**3 + 5*n**2 - 15*n - 8. Let q be b(g). Let c = -0.46 - 0.04. What is the closest to 0.2 in 0, q, c?
0
Let v = 69 + -481/7. Let n = 3221/5 + -12879/20. Which is the closest to -5/2? (a) n (b) 3/2 (c) v
a
Let n = 128 - 88. Let r = -40.4 + n. Which is the nearest to 1/3? (a) 2 (b) 0.2 (c) r
b
Let t = -398.5 + 397. Which is the closest to -1? (a) -1/3 (b) t (c) 0.4
b
Let s(u) = -u**3 - 2*u**2 + 4*u + 3. Let l be s(-3). Let v = -2203/4 + 1657/3. Let o = -1/12 + v. Which is the closest to -1? (a) 5 (b) l (c) o
b
Let f = 20 + -20.7. Let j = 0.3 - f. What is the nearest to j in 1, -1/7, -8?
1
Let f = -639 - -638.73. What is the nearest to f in 3/2, 0.4, 3?
0.4
Let u = -30.5 + 34.5. Let c = -0.03 - 1.97. What is the nearest to -2/5 in c, u, 17?
c
Suppose 15 = 14*d + 1. Let x be 9/6*8/(-6). What is the nearest to x in -1, d, -0.5?
-1
Let z = -0.2 + 0.1. Let w = 0.5068 - 0.9068. Which is the closest to z? (a) w (b) -4/7 (c) -1
a
Let p = 757 - 648.1. Let v = p - 109. What is the closest to v in 2/7, -0.16, -3/8?
-0.16
Let p be 9/(-46)*(5 - 133/21). What is the nearest to -1 in p, -5, -1, -2/3?
-1
Let l = 364/3 + -122. Let d = -12 - -10. Which is the closest to l? (a) 3 (b) d (c) -0.3
c
Let z be -6 - -3 - (-1)/(-8)*-39. Let j = z - 2. Which is the nearest to j? (a) 1/5 (b) 1/7 (c) -2/3
b
Let h be (-1 - 0) + (-1)/(-1). Let m = 0.027 - 16.527. Let t = m + 17. What is the nearest to -1 in h, t, 5?
h
Suppose 8 + 7 = -5*w, -11 = -4*x - 3*w. Let s be (2/((-4)/(-2)))/x. Let h be -2 - ((-10)/3 + 1). What is the closest to 0.1 in s, 5, h?
s
Let i = -157 + 152. Which is the nearest to -0.02? (a) -2/5 (b) i (c) -1
a
Let z = -35092 + 350527/10. Let a = 235/6 + z. Let o = 7 - 7.1. What is the closest to o in -5, 0, a?
a
Suppose 2*m + 3 = -r + 2, 5*m + 2*r = 0. Suppose -4*s - 15 = 5*o, -6 = -3*s + 4*o - m*o. Which is the nearest to 2/5? (a) -1/4 (b) 3 (c) s
c
Let a = -0.02 + -1.98. Suppose -f + k - 4*k = 21, 4*f = k - 6. What is the closest to 0.1 in -0.4, a, f?
-0.4
Let r = 180 + -180. What is the closest to -1/5 in -2/23, r, 2/5?
-2/23
Let u(h) = h**3 + 8*h**2 + 5*h + 34. Let z be u(-8). What is the closest to 2/15 in -0.3, 0.1, z?
0.1
Suppose b = -4*t + 1, t - 4*b - 6 - 7 = 0. Let a = 20.91 + -18.9. Let i = a - 0.01. What is the nearest to t in i, -1/6, 5?
i
Let o be 1589/(-11) + 1 + 1. Suppose -5*d - f = -713, -284 = -2*d - f - 0*f. Let k = d + o. Which is the closest to 1? (a) k (b) -4 (c) 1/4
a
Let t be (48/(-120))/((-2)/5). Which is the nearest to t? (a) -2/7 (b) -0.5 (c) -3 (d) 0.3
d
Suppose 0 = 2*f + d - 3, 3*f + 4*d + 8 - 15 = 0. Let j = 0.5 + 1.5. Let k be 152/(-36) + (-4)/(-18). Which is the nearest to j? (a) k (b) -3 (c) f
c
Let l = -6/19 - 45/38. Let n = 79 - 81. What is the nearest to -0.2 in n, -3/5, l?
-3/5
Let h be ((-4)/3)/(30/(-45)). What is the nearest to 1 in 4, -5, h, 2/13?
2/13
Let u = 6.2 - 5.8. Which is the nearest to -1? (a) 0.5 (b) u (c) -1
c
Let d(f) = 13*f + 13. Let q be d(-6). Let n be (-10026)/154 + (-2)/(-7). Let x = q - n. Which is the nearest to -2/3? (a) -5 (b) x (c) -1
c
Let y = -15.3 - -18.3. What is the nearest to y in 2, 1, -0.2?
2
Let o = 3.585 - 3.885. Let g = 6 - 4. Let v = g + -2.1. What is the closest to v in -2, o, 6/11?
o
Let h = 933 + -931. Which is the nearest to 1/5? (a) -2 (b) -6 (c) h
c
Let n be (-56)/(-18) + (-19)/171. What is the closest to -1/10 in n, 3/7, 4, 0.4?
0.4
Let f = -2717 + 2716. Suppose 4*a - 12 = -3*d, 0*a + 6 = -5*d + 2*a. What is the nearest to f in 0.4, d, 0.06?
d
Let o = -5.4 - -5. Let h = -20.1 - -20. Which is the closest to h? (a) -4 (b) 5 (c) o
c
Let l(g) = g**3 - 25*g**2 + 2*g - 45. Let d be l(25). What is the nearest to 0.2 in -0.5, d, 2, 4?
-0.5
Let u be (2/2 + (-11)/4)*4. Let d be u/2*6/(-28). Which is the closest to 0? (a) -1 (b) d (c) 0
c
Let x = 1651 + -1649. What is the closest to 32 in x, 5, 0.4, -1/9?
5
Let p = -806 - -807.2. Let c = -30.7 - -29. Let y = c + p. What is the nearest to -2/5 in 2/9, y, 0.2?
y
Let d be ((-14)/49)/((8/2)/4). Let f = -0.5 - 0.3. Let l = f + 1. Which is the closest to 0? (a) d (b) -2 (c) l
c
Let r = -198/5 + 40. Let m be (-1)/26*(7 + -3). Let j be 50/(-8)*4/20 + 1. Which is the closest to -1? (a) m (b) r (c) j
c
Let c(v) = -v**2 - 9*v - 22. Let q be c(-8). Let w be 18/(-9) - ((-4)/q - 2). Let o(y) = y - 10. Let u be o(8). What is the nearest to w in 0.4, 5, u?
0.4
Suppose -u + 5*x + 2 = 3*x, -u = 3*x - 2. Let n be (-2)/(84/(-45)) - (-8)/(-16). Let p = 116 - 111. Which is the nearest to 1? (a) n (b) u (c) p
a
Let u = -73 - -72.29. Let q = u + 0.41. Let w = -3 - -4. Which is the closest to -1? (a) 5 (b) q (c) w
b
Let v = 1619 + -1618.84. Which is the nearest to -1/2? (a) v (b) 0.06 (c) 2
b
Suppose -v - 4*p - 2 = -10, v + 5*p - 9 = 0. Suppose q + 4*w = -3*q - 1316, -v*q - 1308 = 2*w. Let o = 4223/13 + q. What is the closest to 0.1 in o, -1/8, 5?
-1/8
Let c = 914/5 - 184. Let x be (-9)/(-8)*(-30)/135. Let y = -0.3 + 0.5. What is the closest to x in -4, c, y?
y
Let m = -576 + 577. Let l = -0.1 - -0.1. Let z = -4 + l. Which is the closest to 0? (a) z (b) -0.3 (c) m
b
Let p(x) = -x**3 - x**2 - 2*x - 19. Let k be |
Species must overcome multiple barriers to successfully establish in a novel range[@b1]. One such barrier is associated with mutualistic interactions, which are predicted to limit invasion success because the new range may not contain effective mutualist partners required for initial establishment[@b2]. Legumes (*Fabaceae*) are a globally distributed and highly diverse family of flowering plants, many of which are dependent on symbiotic nitrogen-fixing bacteria for growth and reproduction[@b3]. Anthropogenic activity has introduced legumes into new regions and continents at an unprecedented global scale[@b4]. However, it remains untested whether legume dependency on symbiotic nitrogen fixation has facilitated or hindered establishment into novel ranges.
Legume hosts acquire rhizobial symbionts horizontally via the environment. This could limit legume establishment following long distance dispersal by reducing access to compatible symbiont partners[@b5][@b6] or suitable environmental conditions for efficient nitrogen fixation[@b7]. On the other hand, symbiotic nitrogen fixation has been purported to facilitate legume colonization, especially in disturbed or degraded habitats[@b8][@b9], potentially favouring the establishment of symbiotic nitrogen-fixing legumes over non-symbiotic legumes. According to these contrasting hypotheses, symbiotic nitrogen fixation could either impede or promote plant establishment in new ranges. However, we currently lack a global macro-ecological analysis to support or refute the generality of either of these claims.
Morphological and molecular evidence show that legumes (*Fabaceae*) form one large monophyletic group and that rhizobial symbiosis evolved from a single origin over 59 million years ago[@b10][@b11]. This origin was followed by multiple gains and losses of the ability to symbiotically fix nitrogen across multiple clades[@b10][@b12], allowing us to directly compare the relative prevalence of symbiotic and non-symbiotic legume species in non-native areas. Using an expert-annotated global legume distribution database[@b13] and the most comprehensive list of nitrogen-fixing trait data available[@b10], we evaluated differences in recent establishment in introduced areas between symbiotic and non-symbiotic legumes (see Methods).
In total, our data set comprises 3,213 symbiotic species and 317 non-symbiotic species. Each species record consists of its symbiotic nitrogen-fixing status and a broad characterization of its global range distribution (as shown by a list of geographic polygons, referred to as 'regions\' hereafter, describing countries, islands or states in which the species is found), and the 'native\' or 'non-native\' designation for each geographic region (see Methods section). We found that non-symbiotic legumes have spread to a greater number of geographic areas compared to symbiotic species at a global scale, providing evidence that symbiosis with nitrogen-fixing bacteria has limited establishment of legumes into novel islands, regions and continents.
Results
=======
The role of symbiosis in introduction success
---------------------------------------------
Within our dataset, 21.6% of all legume species occur in at least one non-native region (that is, polygon) and 15.8% occur in two or more non-native regions, confirming that many symbiotic and non-symbiotic legume species have successfully invaded or been introduced into new regions, continents and islands ([Fig. 1](#f1){ref-type="fig"}). Our analysis of all species in the dataset at the regional level (see Methods section) show that symbiotic legumes have a significantly lower probability of occurring in non-native regions ([Table 1](#t1){ref-type="table"}), which translates into 49.7% fewer non-native regions per species ([Fig. 2a](#f2){ref-type="fig"}). Furthermore, for successfully introduced species with at least one non-native range, we found that symbiotic legumes retain a lower probability of occurring in multiple non-native regions ([Table 1](#t1){ref-type="table"}), translating into 37.1% fewer numbers of non-native regions compared to non-symbiotic legumes ([Fig. 2b](#f2){ref-type="fig"}). We excluded the possibility that non-native symbiotic legume species simply occurred in fewer yet much larger countries ([Supplementary Note 1](#S1){ref-type="supplementary-material"}) by confirming that each non-symbiotic species had, on average, a larger total non-native range area ([Supplementary Table 1](#S1){ref-type="supplementary-material"}) and no difference in the average size of individual regions that comprise the total introduced range area ([Supplementary Table 1](#S1){ref-type="supplementary-material"}).
For species occurring in more than one non-native region we also measured the degree of geographic dispersion between non-native regions and found no difference in the degree of geographic dispersion between either legume group ([Supplementary Table 1](#S1){ref-type="supplementary-material"}), showing that introduced symbiotic legumes do not have more or less geographically widespread non-native regions than non-symbiotic legumes. Together, our analyses show that the contrast in introduction success between symbiotic and non-symbiotic legumes was characterised by differences in the number of non-native regions. These results combined support the hypothesis that non-symbiotic legumes have a higher chance of establishing and subsequently spreading to a greater number of geographic areas ([Fig. 3](#f3){ref-type="fig"}).
Accounting for potentially confounding species traits
-----------------------------------------------------
We found that latitude of origin, size of a species\' native range, plant life form (woody or not woody), life-history (annual or perennial), number of human uses, and the interaction between symbiosis and number of human uses were all significant predictors of introduction success. Non-symbiotic legumes tended to occur more frequently at or near the equator in their native range ([Fig. 3](#f3){ref-type="fig"}; ref. [@b14]). However, our analysis show that latitudinal bias in introduction success favours legume species naturally occurring away from the equator ([Table 1](#t1){ref-type="table"}), indicating that biased dispersal related to latitudinal effects would favour symbiotic rather than non-symbiotic legumes. Total native area was a significant factor in predicting the prevalence of establishment in non-native regions, ([Table 1](#t1){ref-type="table"}), but we found no difference in total native range areas between symbiotic and non-symbiotic species ([Supplementary Fig. 4](#S1){ref-type="supplementary-material"}).
While woodiness was the dominant life form in non-symbiotic legumes ([Supplementary Fig. 4](#S1){ref-type="supplementary-material"}), being woody did not always predict introduction success. Specifically, while woody plants had a higher probability of occurring in non-native regions among all species in the dataset, when the analysis was restricted to introduced species, woody plants had a significantly lower probability of being introduced into multiple non-native regions ([Table 1](#t1){ref-type="table"}). Furthermore, annual species were more likely to establish in non-native regions ([Table 1](#t1){ref-type="table"}), but only 0.8% of non-symbiotic species are annual ([Supplementary Fig. 4](#S1){ref-type="supplementary-material"}). In total, our analysis show that while total native area, latitude, plant life form and life-history are important (as other studies have also shown[@b15]), their effects do not eliminate the symbiosis trait as a key determinant of establishment in novel ranges.
The geographic area of a region had no effect on the prevalence of non-native species within it ([Table 1](#t1){ref-type="table"}). This likely reflects limited variation in area between our regions ([Supplementary Fig. 6](#S1){ref-type="supplementary-material"}), combined with other factors being much more important for successful introduction such as the amount of trade a nation receives (this variation due to unknown factors would be reflected in the region-level random effect).
The role of human use in successful introductions
-------------------------------------------------
We found that ∼30% of species in our dataset had at least one human use, and that legume species with more uses are much more likely to establish in non-native regions ([Table 1](#t1){ref-type="table"}). Species with human uses may be more likely to establish due to more frequent intentional introduction attempts (i.e., higher human-mediated propagule pressure), which may mask or confound differential establishment patterns driven by the symbiosis trait itself. Our analysis accounts for this potential bias by including it as a covariate (along with its interaction with symbiosis), and then statistically evaluating the main effect of symbiosis at no (that is, zero) human uses (this is important because of the presence of the interaction[@b16]). The main effect of symbiosis ([Table 1](#t1){ref-type="table"}) thus evaluates any differences in non-native establishment patterns that are least likely to be impacted by human-mediated propagule pressure. After accounting for the number of human uses in this manner, we found that non-symbiotic legumes are still much more likely to establish in non-native regions ([Figs 2](#f2){ref-type="fig"} and [4](#f4){ref-type="fig"}; [Table 1](#t1){ref-type="table"}).
We also found a significant interaction between symbiosis and the number of human uses, suggesting that human use does have an influence on the successful introduction of symbiotic versus non-symbiotic legumes. We predicted that if human uses were exacerbating the spread of non-symbiotic legumes over symbiotic legumes (above the disparity observed at no human uses) that we should observe a negative interaction in our main model. However, we found a positive interaction, indicating that the disparity between symbiotic and non-symbiotic legumes decrease, rather than increase ([Fig. 4](#f4){ref-type="fig"}). These results combined provide evidence that human-mediated propagule pressure is not generating the pattern that non-symbiotic legumes are more prevalent in non-native regions.
Influence of phylogenetic history on introduction success
---------------------------------------------------------
The ability to symbiotically fix nitrogen has been gained and lost multiple times across the legume phylogeny, although the trait is more concentrated in certain clades ([Supplementary Fig. 1](#S1){ref-type="supplementary-material"}). If the pattern of successful introductions across species also shows strong phylogenetic structure, it is possible that our results could reflect a lack of independence among the species we used in this study due to their shared evolutionary history with respect to other predictive yet unmeasured traits. However, the probability of having a non-native range has no phylogenetic signal (phylogenetic parameter alpha=31.27; [Supplementary Note 2](#S1){ref-type="supplementary-material"}). When we incorporated phylogenetic structure into our analysis, which included all covariates from our main analysis ([Supplementary Note 2](#S1){ref-type="supplementary-material"}), non-symbiotic legume species still had a significantly higher probability of establishing in non-native regions ([Supplementary Table 2](#S1){ref-type="supplementary-material"}), consistent with results of our main analysis. Overall, these analyses indicate that the increased ability of non-symbiotic legume species to establish in a greater number of non-native ranges was not driven by phylogenetic dependence and makes it unlikely that our results can be explained by another trait that is evolutionarily correlated with symbiosis and also influences introduction success.
Discussion
==========
In summary, our findings clearly support the argument that nitrogen-fixing legumes are highly dependent on the symbiosis and that this dependency is sufficiently large to generate dispersal or establishment barriers at a global scale across multiple legume species, regions and continents ([Fig. 3](#f3){ref-type="fig"}). Inadequate population density of compatible rhizobia or appropriate environmental conditions for effective nitrogen fixation in introduced ranges are viable explanations for our results. This explanation would suggest that symbiotic legume hosts and their compatible symbionts would frequently need to be introduced simultaneously or that introductions would favour legumes that are able to form associations with a broad diversity of rhizobia[@b17][@b18], which is consistent with empirical findings from previous studies examining introduced *Acacia* species[@b18][@b19][@b20].
Our results are also consistent with the explanation that an evolutionary investment in the mutualistic interaction with rhizobia has resulted in reduced competitive ability of symbiotic nitrogen-fixing legumes[@b21], relative to non-symbiotic legumes. This explanation would require that the fitness cost of harbouring the symbiosis trait is higher in non-native ranges relative to the native range. Changes in soil resource availability have been proposed as a mechanism to alter the cost-benefit ratio of plant nitrogen-fixation[@b21] and human activity is often associated with increased nutrient deposition[@b22]. However, experimental evidence has shown that invasive nitrogen-fixing plants have greater growth in fertile soils compared to invasive co-occurring non-fixing plants[@b23], suggesting that symbiotic nitrogen-fixation is a net fitness benefit in non-native ranges, rather than a cost.
Our study also highlights the prominent effects of propagule pressure, mediated by increased intentional introductions associated with human use attributes of species. The number of human uses for a species was a powerful predictor of the prevalence of successful introduced ranges. This is consistent with a number of other studies which found human use to be important in predicting establishment of plant species outside their native range[@b24][@b25], including legumes[@b4][@b26][@b27]. Among highly useful species, we found that the difference in introduction success between symbiotic and non-symbiotic legumes lessens and eventually reverses ([Fig. 4](#f4){ref-type="fig"}). This suggests that if species are highly useful, any natural establishment barriers among symbiotic legumes (that is, lack of mutualist partners) may be overcome through increased human effort to intentionally introduce a species (for example, increased effort to inoculate new sites lacking rhizobia). It is possible that after human intervention has allowed a symbiotic legume species to overcome its establishment barriers, the benefits of nitrogen fixation then allow it to be more successful. However, the majority of species looked at in this study have no recorded human uses, so that the effect prevailing at low human uses is of particular importance for legume species as a whole.
Transplant trials have shown that many legumes rely on soils that are pre-inoculated with compatible microbial symbionts to establish[@b28][@b29] and that soils are highly variable in the abundance[@b30][@b31][@b32] and inter-continental genetic structure[@b33] of compatible rhizobia. However, symbiotic nitrogen-fixation has also been implicated in facilitating the invasion of some of the most widespread and problematic legume species of the world[@b30], giving the appearance that compatible rhizobia are cosmopolitan in their distribution. Based on these isolated observations and studies, it has been difficult to establish a general pattern with respect to the role of symbiosis in limiting or facilitating legume establishment[@b34]. Though the size of our analysis and its global extent is unprecedented, we acknowledge that only a fraction of the estimated ∼19,000 legume species have been characterized for their symbiosis ability (∼20% species and ∼60% of legume genera[@b35]). Nevertheless, based on an examination of ∼3,500 legume species, our study reveals that symbiotic mutualism traits are important in predicting the introduction success of legumes across multiple continents and islands. Our study further highlights likely ecological costs associated with being a nitrogen-fixing species, and the potential for plant species distributions to be influenced by soil microbial biogeography at a global scale.
Methods
=======
Experimental design
-------------------
The objective of our study was to investigate whether symbiosis with nitrogen-fixing legumes had any predictive power with respect to legume introductions globally. We compiled symbiotic nitrogen-fixation data and geographic distribution data matched to as many legume species as possible (see below). We measured introduction success by counting the number of non-native regions of occurrence for each available species. We then analysed the predictive power of the symbiosis trait on introduction success in the presence of other potentially confounding or correlated covariates that might be important in predicting legume introductions. Once we verified that the significance and direction of response for symbiosis remained after the inclusion of other covariates, we analysed the predictive power of symbiosis, incorporating phylogenetic structure into our analyses.
Symbiotic nitrogen-fixation data
--------------------------------
Nitrogen-fixation status was extracted for all available legume species (members of the family *Fabaceae*) from the publicly available database compiled by Werner *et al*[@b36]. This database scores each species as either 'symbiotic\' or not, and has been compiled from a number of experimental and observational studies examining the presence or absence of rhizobial infections on 5,427 legume species (see Werner *et al*.[@b36] for more details). For the species we used in this study, information on nitrogen-fixation status covers ∼20% of all known legume species (3,530 species out of ∼19,700) and ∼60% of all known legume genera (440 genera out of ∼750). Since we aimed to determine whether symbiosis is a potential barrier or facilitator of initial legume establishment, we evaluated the presence or absence of the ability to symbiotically fix nitrogen as specified in Werner *et al*.[@b36]; see the original source reference list on figshare[@b37] for all references related to every species used in this study.
Global introduced status data
-----------------------------
For each legume species found in the nitrogen fixation database, we searched the International Legume Database and Information Service (ILDIS)[@b13] and extracted geographic distribution information using a webscraper written in R[@b38]. The ILDIS geographic data was compiled by experts who synthesized regional floristic data from the primary literature. Because ILDIS data are a synthesis of recorded locations of living observations and herbarium records by flora experts, they likely encapsulate established species in a given region. In total, 3,973 legume species were found in ILDIS (species not found in ILDIS were discarded from the analyses) that matched the nitrogen-fixation trait database. Species distribution data in ILDIS is coded using the names of hierarchically structured geographic regions (i.e., continent, region, area, and country where available), and indicates whether each region is native, introduced, or unknown, thus capturing dispersal events at both regional and continental scales. We scraped geographic data at all available hierarchies and excluded areas where the introduced status was considered unknown. The geographic names in ILDIS were based on the World Geographical Scheme for Recording Plant Distributions developed by the Taxonomic Database Working Group (TDWG)[@b39]. We eliminated species records from our dataset just containing 'unknown\' regions, giving a total sample size of 3,530 species. The final dataset used in this study contained 317 non-fixing legumes out of 3,530 (9%), whereas the full Werner *et al*.[@b36] database contained 482 non-fixing legumes out of a total 5,427 total legumes (8.9%); therefore, our dataset showed no bias with respect to the proportion of non-fixers relative to all known data on legume nitrogen fixation.
To convert the geographic names in the ILDIS database into usable geographic coordinate data, we downloaded a shapefile containing the standardized TDWG geographic regions as polygons[@b40], then matched these polygons to ILDIS geographic names. Where TDWG polygons and ILDIS geographic names could not be matched, we used the next available polygon in the geographic hierarchy (for example, if we could not find a polygon corresponding to an area name, we used the region name instead). Moving up to the next geographic level was only necessary for less than 10% of recorded regions and did not exceed one level. Once all geographic areas were matched to polygons, we only retained those at the lowest available hierarchical scale.
Before analysis we merged any species range polygons that were touching each other and had the same introduction status, to prevent biases in the number of ranges due to finer subdivision within some areas. This way, all final polygons represent non-contiguous ranges.
We checked the accuracy of the polygon occurrences by comparing our polygon data to occurrence records in the Global Biological Information Facility (GBIF)[@b41]. GBIF gives higher resolution point occurrence records, but for far fewer species (1,830 species) and invasive or introduced status is not recorded for each GBIF record. We found that, on average, ILDIS polygons for each species captured 93% of GBIF points (see [Supplementary Fig. 2](#S1){ref-type="supplementary-material"} for some example species maps). For points that fell outside ILDIS polygons, we calculated the geographic distance to the nearest ILDIS polygon and found that most points were geographically very close to an ILDIS polygon, with no obvious bias in the distribution of geographic distances between symbiotic and non-symbiotic legumes ([Supplementary Fig. 3](#S1){ref-type="supplementary-material"}). There was no obvious differences in the presence or number of 'unknown\' introduction status polygons between symbiotic and non-symbiotic species ([Supplementary Fig. 4](#S1){ref-type="supplementary-material"}), indicating that any ambiguities in polygon status was not different between our legume comparison groups. Together, these indicate that ILDIS geographic range data was reliable.
Other species trait data
------------------------
We also scraped plant life-form (woody or not woody), life-history (annual or perennial), and information on human uses from ILDIS, as previous invasion studies have found these to be important factors in predicting legume invasion success[@b15]. We were able to obtain plant life form for 3,500 legume species and life-history for 3,462 legume species. We converted life form and history data into two binary traits by coding life form as a 1 for species that were woody (trees or shrubs), and as 0 for non-woody (herbs). Likewise, for life history, species that had an annual life history were assigned a value of 1, and perennial species assigned a 0.
Life history and life form data was unavailable for ∼500 species, which would lead to a fairly large reduction in our sample size when including this data as covariates. To maintain full power in our models (see next section for model details), while still accounting for the potentially confounding effects of life form and life history, we imputed the missing values in these traits. We did this using a simple taxonomic imputation. If there were other species in the same genus as a missing species, its value was assigned to be the mean of the life form or life history values for that genus (for example, a value of 0.9 for life form would be assigned to a species in a genus with 90% woody species). If the data were missing for an entire genus, we used the mean of all species found in the same tribe in the same manner. Therefore, the life form and life history variables can be interpreted as the probability that a species is woody or annual respectively, based on their taxonomic group. 83 and 84.6% of missing species were filled at the genus level, for life form and life history respectively, and the remaining missing species at the tribe level. Some genera contained a mixture of either trait value, but 87.5 and 91.2% of genera could be coded greater than 0.75 or less than 0.25 (for example, more than 75% of the genus was one trait or the other) for life-form and life-history respectively. Most genera that contained species with missing data were entirely of one life form (73%) or life history (77%) and could be coded unambiguously as 0 or 1 based on their genus grouping. We repeated our main analysis with two other trait imputation methods (see [Supplementary Note 3](#S1){ref-type="supplementary-material"}) and our results did not change qualitatively, with all model coefficients changing only superficially, and no change in levels of significance for any factor, indicating that our results are robust to several methods of imputation. Therefore, only the results using the first method described above (that is, taxonomic mean imputation) are reported.
Human use data was recorded in ILDIS by specifying whether a species was known to have a use in any of 11 different use categories (Chemical products, Domestic, Environmental, Fibre, Food and Drink, Forage, Medicine, Miscellaneous, Toxins, Weed or Wood). If none of these categories was specified in ILDIS, we assumed the species had no known uses. We calculated a human use covariate by counting the number of known human use categories for each species to create a value which could range from 0 to 9 (no species in our study had all 11 use categories), which we refer to here as 'number of human uses\'.
Statistical analysis
--------------------
We modelled the prevalence of successfully introduced species in regions across the world using a generalised linear mixed model (GLMM).
Under the TDWG scheme, there are four nested levels of geographic range specification, from smallest to largest: the country, area, region, and continent level (though the country level does not necessarily always correspond to political countries). In our data, after translating from ILDIS to TDWG, geographic range was determined to different degrees of resolution, depending on the species. Some but not all species were specified at the TDWG area level, for example. To make all species comparable, we analysed introduced ranges on a single level. All non-native ranges were specified to at least the TDWG region level or below, so we used this as our focal geographic unit for the range during our analysis. Henceforth, we will refer to what TDWG calls region level simply as 'regions\'. There were 51 regions in total (see [Supplementary Fig. 6](#S1){ref-type="supplementary-material"} for a map of the regions used in this part of the analysis).
Our response data therefore is made up of a vector of zeroes and ones *y*~*ij*~, which could be arranged into a matrix of *n*~species~ rows, and *n*~region~ columns *Y*~*ij*~ containing a one if species *i* is found non-natively in region *j* and a zero if it is not (e.g., the species is coded as one if at least one of its non-native polygons fell in the region). We were interested in testing whether symbiosis affects non-native prevalence across the globe, while controlling for several potentially biasing factors. Our model is the following:
The non-native presence of a species *i* in region *j* is modelled as a realization of a binomial process on the probability of species *i* in region *j*, *P*~*ij*~:
The probability of species *i* in region *j* is a function of the symbiosis status of species *i* (*SS*~*i*~; equals 1 if symbiotic, 0 if non-symbiotic), a number of potential covariates (*x*~*ik*~ and *x*~*jk*~), and random effects for species (SP\[*i*\]) and region (RE\[*j*\]):
Where *α* is an intercept term, *β*~SS~ is the fixed effect coefficient determining the effect of symbiosis, *β*~*k*~ is the fixed effect coefficient determining the effect of species-level covariate *k*, *β*~*z*~ is the fixed effect coefficient determining the effect of region-level covariate *z*, and *V*~species~ and *V*~region~ are the variance parameters for the species and region random effects, respectively.
We also initially included the TDWG continent level region as a higher level random effect (within which region was nested), however, we removed it in our final analysis as it explained almost no variation in the model (that is, variance parameter was very close to zero).
This mixed effects model with crossed random effects has a number of advantages over a simpler species-level analysis. First, it allows the inclusion of both region-level as well as species-level covariates. Second, the random effect for region accounts for spatial non-independence within regions of the world. In a species-level only analysis, we would not be able to say if our results were driven just by one or a few regions across the globe, whereas with the full mixed model, our inferences are applicable globally.
Species-level covariates (*x*~*k*~) included in the model were: the absolute latitude of the centroid of a species\' native range polygons, the total area of the species\' native range polygons, the species\' two binary life history traits (woody or not woody, and annual or perennial), and the number of human uses of the species according to ILDIS. We also included a symbiosis by number of human uses interaction, because we hypothesized that the number of human uses would reflect the probability of a species being deliberately introduced (as opposed to unintentionally), and this may affect the strength of any biological factors on introduction probability.
We included one region level covariate (*x*~*z*~): the area of the introduced regions. This was to control for the possibility that larger areas may be more likely to have more introduced species simply due to a sampling effect.
To fit the model, we used the lme4 package in R[@b42]. When fitting the model, all continuous covariates were mean centred (subtracted the mean such that zero corresponds to the mean) and scaled by the standard deviation, except for the number of human uses, for which zero is a biologically meaningful value, corresponding to the state at which deliberate introduction attempts should be lowest, and thus acting as the best reference point at which to evaluate other effects (see Frasier[@b16] for useful discussion).
We ran two versions of the above model. The first model included all data on all species. Given the excess number of zeroes present in our analysis (that is, ∼78% species only occur natively), we ran a second model only on the species occurring in at least one non-native region to confirm similar results when zeroes were removed from the dataset.
All response variables were analysed in R[@b38] and included the symbiosis trait, latitude of origin, total native area, plant life-form (woody or not woody), plant life-history (annual or perennial), number of human uses, the interaction between symbiosis and number of human uses, and the area of the introduced region as predictors. We calculated the correlation between all of our species-level model predictors ([Supplementary Fig. 5](#S1){ref-type="supplementary-material"}) and the highest correlation occurred between being woody and annual in our first (r=−0.49) and second (*r*=−0.59) model ([Supplementary Fig. 5](#S1){ref-type="supplementary-material"}).
Testing the model effects
-------------------------
We tested whether symbiosis and covariates were significant predictors of the prevalence of successful species introductions using parametric bootstrapping. We simulated 1,000 new response vectors (*y*~*ij*~) from the fitted model, using observed values of the fixed effect variables, and fixing species and region random effects at their estimated values. For each bootstrapped response vector we refit the same model to it and collected the fixed effect coefficients. We then calculated the 95% confidence intervals by determining the 0.025 and 0.975 quantiles of each coefficient\'s bootstrapped sample ([Table 1](#t1){ref-type="table"}). A fixed effect was classified as significant if its 95% confidence interval did not overlap zero. We also calculated 99 and 99.9% confidence intervals ([Table 1](#t1){ref-type="table"}).
Visualising the results
-----------------------
To translate the model results into a set of more intuitive measures for display, we again used parametric bootstrapping. To show the effect of symbiosis on the prevalence of successful introduced ranges, after controlling for all covariates, we simulated 1,000 response vectors from the fitted model, but this time setting all covariates to a value of zero (symbiosis remained at its observed values). This procedure removes the variation explained by the covariates in a way analogous to least square means in a standard statistical analysis.
We took these 1,000 sampled response vectors and calculated several summary statistics for plotting. For each bootstrap sample, we calculated the mean number of introduced ranges for symbiotic and non-symbiotic species. We then plotted the mean and 95% confidence intervals of these values based on the bootstrap samples ([Fig. 2](#f2){ref-type="fig"}).
Data availability
-----------------
The full data set, including cleaned up ILDIS data, nitrogen-fixation data, and all covariates, is available from the authors on request. All data in their original form are available from public repositories (see Methods).
Additional information
======================
**How to cite this article:** Simonsen, A. K. *et al*. Symbiosis limits establishment of legumes outside their native range at a global scale. *Nat. Commun.* **8,** 14790 doi: 10.1038/ncomms14790 (2017).
**Publisher\'s note:** Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Material {#S1}
======================
###### Supplementary Information
Supplementary Figures, Supplementary Tables, Supplementary Notes and Supplementary References
We kindly thank the curators of the data sources used for this study who are fully listed and acknowledged in the Methods section. We also want to thank Mathew Hill and Kylie Ireland for manuscript comments.
The authors declare no competing financial interests.
**Author contributions** A.K.S. conceived of the study design. R.D. contributed data. A.K.S. and R.D. analysed the data. A.K.S. wrote the manuscript. All authors discussed the analyses, results and commented on the manuscript.
{#f1}
![Non-native ranges between symbiotic and non-symbiotic legumes species.\
(**a**) Mean number of introduced ranges across all legume species studied (including those with no introduced ranges) \[(*n*~total~=180,030=(*n*~species~=3,530) × (n~regions~=51)\]. (**b**) Mean number of introduced ranges for legume species recorded from at least one non-native region \[(*n*~total~=41,412=(*n*~species~=812) × (*n*~regions~=51)\]. A species\' introduced range is defined by a list of geographic regions of non-native occurrence. Points and error bars represent the mean and 95% confidence intervals from parametric bootstraps, controlling for all covariates (absolute native latitude, total native area, life form, life history, area of non-native region and number of human uses).](ncomms14790-f2){#f2}
![Global proportional distribution of symbiotic legume species.\
Regions are coloured according to the proportion of symbiotic legume species in (**a**) native and (**b**) non-native ranges. Lighter colours indicate higher proportions of non-symbiotic legume species. Non-symbiotic legume species tend to primarily occur near the equator in their native range. Non-symbiotic legume species currently account for a higher proportion of species within introduced ranges compared to their proportion within native ranges. The figure shows that the increased spread of non-symbiotic legumes spans multiple continents and islands across the world. Grey areas indicate terrestrial ecoregions where legumes are not known to occur[@b43]. Regions are defined using the Taxonomic Distribution Working Group system[@b39].](ncomms14790-f3){#f3}
{#f4}
###### Introduction success as predicted by the symbiosis trait.
**Factor** **All species** **Non-native species Only**
------------------------------------- ----------------------------------- ----------------------------- -------- ----------------------------------- -------- --------
Intercept −8.055 --- --- −3.125 --- ---
Symbiosis? −0.523[†](#t1-fn3){ref-type="fn"} −0.960 −0.437 −0.587[†](#t1-fn3){ref-type="fn"} −0.832 −0.416
Latitude 0.142[†](#t1-fn3){ref-type="fn"} 0.094 0.210 0.026 −0.013 0.063
Total native area 0.194[†](#t1-fn3){ref-type="fn"} 0.119 0.211 −0.058[†](#t1-fn3){ref-type="fn"} −0.092 −0.038
Annual? 1.092[†](#t1-fn3){ref-type="fn"} 0.915 1.267 0.198[†](#t1-fn3){ref-type="fn"} 0.065 0.329
Woody? 0.353[‡](#t1-fn4){ref-type="fn"} 0.084 0.404 −0.476[†](#t1-fn3){ref-type="fn"} −0.634 −0.408
Number of human uses 0.964[†](#t1-fn3){ref-type="fn"} 0.865 0.981 0.323[†](#t1-fn3){ref-type="fn"} 0.282 0.370
Area of introduced region 0.010 −0.049 0.046 0.019 −0.046 0.051
Symbiosis by human uses interaction 0.152[†](#t1-fn3){ref-type="fn"} 0.104 0.223 0.080[†](#t1-fn3){ref-type="fn"} 0.042 0.129
CI, 95% confidence interval.
Symbiosis is incorporated into the model as the presence or absence of the trait, with the inclusion of other factors found to predict introductions in our legume dataset. A negative coefficient indicates lower introduction success for symbiotic legumes compared with non-symbiotic legumes. We excluded non-significant interaction terms. 95% confidence intervals were obtained from parametric bootstrapping. Each response variable is modelled at the species by region level, and the model included a species and a region random effect to account for non-independence of observations within species or regions. The estimated variance for the species and region random effects respectively were 4.83 and 0.85 for the all species model, and 0.9 and 1.43 for the non-native species only model.
^†^99.9% CI does not overlap zero.
^‡^99% CI does not overlap zero.
[^1]: These authors contributed equally to this work.
|
General Multicarrier System
A multicarrier system described herein indicates that one or more individual carriers are used as a group. FIGS. 1(A) and 1(B) show a signal transmission and reception method based upon a multiband radio frequency (RF).
For efficient use of multiband (or multicarrier), a technique has been proposed in which one medium access control (MAC) entity handles multiple carriers (e.g., several frequency allocation (FA)).
As shown in FIG. 1, one MAC layer in each of a transmitting end and a receiving end may manage several carriers for efficient multicarrier use. Here, for effective transmission and reception of the multicarrier, it is assumed that both the transmitting and receiving ends can transmit and receive multicarrier. Since frequency carriers (FCs) managed by one MAC layer do not have to be contiguous to one another, it may be flexible in view of resource management.
That is, a contiguous aggregation and a non-contiguous aggregation are all available.
Referring to FIGS. 1(a) and 1(b), PHY0, PHY1, . . . , PHY n−2, PHY n−1 denote multiband according to this technique, and each band may have a magnitude (bandwidth) of FA assigned for a specific service according to a predefined frequency policy.
For example, PHY0 (RF carrier 0) may have a bandwidth of FA assigned for a typical FM radio broadcast, and PHY1 (RF carrier 1) may have a bandwidth of FA assigned for cellular phone communications.
Each frequency band may have a different frequency bandwidth according to each frequency band characteristic. However, it may be assumed in the following description, for the sake of brief explanation, that each FA has A [MHz] magnitude.
Also, each FA may be represented as a carrier frequency for using a baseband signal at each frequency band. Hereinafter, each FA is referred to as “carrier frequency band”or, if not ambiguous, simply as “carrier” representing each carrier frequency band.
As shown in 3GPP LTE-A in recent time, to distinguish the carrier from a subcarrier used in a multicarrier technique, the carrier may be referred to as “component carrier.”
In this regard, the “multiband” technique may be referred to as “multicarrier” technique or “carrier aggregation” technique.
In order to send signals via multiband as shown in FIG. 1(a) and receive signals via the multiband as shown in FIG. 1(b), the transmitting and receiving ends are required to include RF modules, respectively, for transmission and reception of signals over the multiband. Also, in FIG. 1, the configuration of “MAC” may be decided by a base station regardless of downlink (DL) and uplink (UL).
Briefly explaining, this technique indicates that one MAC entity (hereinafter, simply referred to as “MAC” if not obscure) manages/runs a plurality of RF carriers (radio frequencies) for signal transmission and reception. Also, the RF carriers managed by the one MAC may not have to be continuous to each other. Hence, in accordance with this technique, it is more flexible in view of resource management.
In IEEE 802.16m system as one of wireless communication systems, the carriers may be divided into two carrier types from the perspective of a base station. For example, the carrier types may be divided into a fully configured carrier type (FCCT) and a partially configured carrier type (PCCT).
The FCCT indicates a carrier by which every control information and data can be sent or received, and the PCCT indicates a carrier by which only downlink (DL) data can be sent or received. Here, the PCCT may be used for services, such as an enhanced multicast broadcast service (E-MBS), which usually provides DL data.
From the perspective of a mobile terminal, assigned carriers may be divided into two types, for example, a primary carrier type and a secondary carrier type. Here, the mobile terminal may be allocated with one primary carrier and a plurality of sub-carriers from the base station.
The primary carrier may be selected from the fully configured carriers. Most of essential control information related to the mobile terminal may be sent on the primary carrier. The subcarriers may be selected from the fully configured carriers or the partially configured carriers, and also additionally allocated in response to request of the mobile terminal or instruction of the base station.
The mobile terminal may send and receive not only every control information but also control information related to the subcarriers over the primary carrier, and exchange (transceive) data with the base station over the subcarriers. Here, the subcarrier, as a fully configured carrier, allocated to a specific mobile terminal, may be set to a primary carrier of another mobile terminal.
Multicarrier Switching
Multicarrier switching indicates a multicarrier mode for a terminal to switch a physical layer connection from a primary carrier to a partially configured subcarrier or a fully configured subcarrier. Here, the carrier switching of the terminal may be performed based upon instruction (indication) from a base station in order to receive E-MBS service at a subcarrier.
After being connected to the subcarrier for a specific time, the terminal may come back to the primary carrier. While the terminal is connected to the subcarrier for the specific time, the terminal does not have to maintain transmission or reception via the primary carrier.
Basic Multicarrier (MC) Mode
A basic multicarrier (MC) mode indicates a mode that a terminal operates using only one carrier. However, the terminal may support not only optimized scanning for carriers related to a multicarrier operation but also a primary carrier switching procedure.
Carrier Switching Operation for E-MBS Service
E-MBS service may be performed by a specific carrier (e.g., subcarrier) other than a primary carrier. In a connected state with a base station, an E-MBS terminal having only one transceiver (i.e., a terminal operating in a carrier switching mode) may perform carrier switching from a primary carrier to another carrier to receive E-MBS data burst, E-MBS configuration message and E-MBS MAP, and carrier switching from the another carrier to the primary carrier to receive a unicast service from the base station.
The E-MBS terminal may perform a carrier switching operation based upon its E-MBS subscription information assigned from the base station to the terminal during a dynamic service addition (DSA) procedure. The E-MBS subscription information may be MSTIDs and FIDs, for example.
In an actual E-MBS environment, basic (default) E-MBS channels may be assigned (allocated) to every terminals subscribed in the E-MBS service, and the number of default E-MBS channels may be much more than the number of specific E-MBS channels (e.g., premium channels). all the E-MBS terminals subscribe in all the default contents via default free channels. Additionally, some premium users may subscribe in premium contents.
In other words, E-MBS terminals subscribed in the premium contents may stay longer in the E-MBS carrier than terminals merely subscribed in the default contents.
FIG. 2 is a flowchart showing a carrier switching operation performed based upon terminal subscription information.
As shown in FIG. 2, it is assumed that a terminal 1 merely subscribed in default contents and a terminal 2 subscribed in the default contents and a premium content 2.
It is also assumed that E-MBS data bursts 1 and 3 are data for the default contents, E-MBS data burst 2 is data for a premium content 1, and E-MBS data bursts 4 and 5 are data for the premium content 2.
Referring to FIG. 2, the terminal 1 may stay at a primary carrier while a base station sends E-MBS data bursts 2, 4 and 5 (S201), and the terminal 2 may stay at a primary carrier while the base station sends E-MBS data burst 2 (S202). That is, the base station may allocate unicast resources to terminals, which have subscribed in the premium contents having the lowest unicast scheduling efficiency.
During free E-MBS service, a terminal may not need to perform a joining/leaving process at an upper layer. That is, in this case, when E-MBS terminal starts or ends E-MBS service reception, DSA/dynamic service deletion (DSD) process may not be performed. However, in the carrier switching mode, the base station must be known of whether a terminal is receiving the E-MBS service for efficient unicast scheduling. If the terminal is not receiving the E-MBS service, the base station may provide the unicast service to the terminal at the primary carrier at any time. |
Introduction
============
The medical nursing represents a field characterized by strong emotions, dominated by the care for the patient and the total attention they should always receive from the medical team, but mostly from the team's main representative in relation with the patient, the medical nurse. Learning to practice medical nursing means, among many others, to deal with one's own states of mind and emotions, in order to reach the personal and professional maturity the job requires. This, in turn, involves a high psychological effort which, sooner or later, can lead to depression, anxiety or stress. This occurs especially because learning to practice this job means, among others, to accept death, beyond its significance as a clinical effort, but as a natural phenomenon, part of everyday life \[[@B1]\], and learning to face the stress which such a situation and all other daily interactions generate is a continuous challenge. \[[@B2]\]. This is why the individual or organizational interventions meant to diminish the stress and its effects have to be based on the knowledge and identification of the stress-inducing factors which affect the professional's wellbeing \[[@B3]\].
The Aim of the Study
====================
This study aims at investigating the stress in first year students of the Medical Nursing Department within the Medical Midwife and Nurse Faculty from Craiova, by collecting answers to the following questions:
Is stress higher in female subjects than in male ones?
Are there any differences regarding the level of stress as far as the graduated high school courses are concerned? Is yes, are the subjects who graduated humanistic courses more stressed than those who graduated science courses? And are the women who graduated humanistic courses more stressed than those who graduated science courses?
Are there any differences between those who are following courses of a second faculty than those who are students for the first time?
Matherial and Method
====================
The questionnaire used for this study consists in 15 items and it was elaborated based on the responses provided by a sample group of 20 subjects, first year students of the Medical Midwives and Nurse Faculty, who answered to the question: "What causes would you identify so as to consider the first year of faculty difficult?" Based on the results of the frequency analysis, the items were elaborated and then pre-tested on a sample group of another 20 subjects, students at the same faculty, with an equal distribution of the two genders. The subjects were provided with a scale from 1 to 6, where 1 is totally disagree, 2 partially disagree, 3, rather disagree, 4, rather agree, 5 partially agree, 6 totally agree. The value of the alpha-Cronbach coefficient calculated by considering all 155 items was 0.76. The t test for independent sample groups was used and an alpha below .05 was considered significant.
**The Sample Group**
For this research, 100 subjects were used, of which 28 male subjects and 72 female subjects. From these, 44 graduated a humanistic high school and 56 a science high school; for 76 of them this is the first faculty whose courses they are following, while for 24, the second.
Results
=======
The effect of the biological gender variable on the stress level variable
-------------------------------------------------------------------------
By applying the t test for independent sample groups, no statistically significant differences were recorded for the stress level (t = 1.863; p = 0.067; p \> 0.05), the average of male subjects is 5.11, while the average of female subjects is 4.86 (Table [1](#T1){ref-type="table"}).
######
The effect of the biological gender variable on the stress level variable
---------------------- ---------- ------------
**Male** **Female**
Average 5.11 4.86
Standard Deviation 0.55 0.72
C.V. (%) 10.76% 14.81%
t= 1.863
p - Student's t test 0.067 \- NS
---------------------- ---------- ------------
The effect of the graduated high school profile variable on the stress level variable
-------------------------------------------------------------------------------------
The t test for independent sample groups was applied in order to verify the effect of the graduated high school profile variable on the level of stress. No significant differences were recorded (t=1.045; p=0.299, p \> 0.05), meaning that the subjects who graduated humanistic high school courses experience the same level of stress like the subjects who graduated science high school courses (Table [2](#T2){ref-type="table"}).
######
The effect of the graduated high school profile variable on the stress level variable
---------------------- ---------------- -------------
**Humanistic** **Science**
Average 5.01 4.87
Standard Deviation 0.58 0.76
C.V. (%) 11.58% 15.61%
t= 1.045
p - Student's t test 0.299 \- NS
---------------------- ---------------- -------------
The effect of the prior university studies variable on the stress level variable
--------------------------------------------------------------------------------
The t test for independent sample groups was applied in order to verify the effect of the prior university studies variable on the level of stress. No significant differences were recorded (t=0.072; p=0.943, p \> 0.05), meaning that the subjects who are currently following courses of the first faculty experience the same level of stress like the students who are following the courses of a second faculty (Table [3](#T3){ref-type="table"}).
######
The effect of the prior university studies variable on the stress level variable
---------------------- ------------------- --------------------
**First faculty** **Second faculty**
Average 4.93 4.94
Standard Deviation 0.73 0.54
C.V. (%) 14.81% 10.93%
t= 0.072
p - Student's t test 0.943 \- NS
---------------------- ------------------- --------------------
There are no significant differences regarding the stress level of the female subjects who graduated a high school with a humanistic profile compared to the female subjects who graduated a high school with a science profile (t= 0.409; p = 0.685).
There are no significant differences regarding the stress level of the male subjects who graduated another faculty compared to the male subjects who currently following the courses of the first faculty (t = 1.11; p = 0.289).
Discussion
==========
The majority of the studies performed on students, including on those who study the medical field, reveals that the women have the tendency to be more stressed than men \[[@B4],[@B5]\], and the studies which recorded equal levels of stress explained this through the different ways the individuals interpret the same stressing factors. For men, showing you are stressed is a sign of weakness, while for women, the stressing situations have a higher negative impact. \[[@B6]\] Such is the explanation for the current case. Furthermore, in a field in which the number of women is significantly higher and the job requirements are more easily fulfilled by members of this gender, considering the women in the medical field tend to be perceived as more communicative, more easily to approach and better handling the social skills which involve maintaining relations through communication \[[@B7]\], men can face new challenges which would stretch them even more. Also, other studies have shown there are no differences regarding the stress level in the men and women who study in a medical profile faculty, as the identified causes are diverse, ranging from food habits to learning strategies. \[[@B8]\].
One of the myths the teaching in medical faculties from Romania is founded on is that students who graduated high school science classes perform better during the faculty than those who graduated a humanistic high school. The basis of this assumption rested on the conviction that the number of curriculum topics which are currently classified as within the science field and are part of the program is higher than the number of humanistic topics and, implicitly, those who are more accustomed with them and previously obtained positive results at them will also perform better during faculty. Until now, there is no such research as to study the correlation between the two variables. If we assume that this belief is based on the experience the student has with this type of requirements and work style of the named academic topics, then we can use, for analysis purposes, the idea that coping strategies which were successfully used in the past form a general stable style of adapting to that sort of issues. \[[@B9]\]
Moreover, such an optimistic and confident attitude ("I've been through this before and I know how to handle it" or "I know I'm good at this topic") diminishes the stress experienced during the current situation which seems familiar. \[[@B10]\]
The results from this study refuted the myth, as the students experienced the same level of stress, regardless of the high school they had graduated. This aspect can also be explained by the higher difficulty level of the studied topics, as well as by the different work rhythm in the first year, much more alert than the one during high school. One can notice a fracture between the almost parentlike style the high school students are treated by the teachers and the rather independent one of the university professors, where the learning responsibility falls largely on the students. Besides, being a student also involves having the capacity to memorize large amounts of information in a relatively short time, without being able to practice the mechanical learning from high school.
Starting from the same assumptions according to which prior experience in a certain field forms a valid and stable work strategy to be applied in similar situations, ne expected the students who graduated another faculty to have a lower level of stress in comparison with those who experience being students for the first time. The results showed there are no significant differences, as the prior experience had no influence whatsoever. If we are to take into consideration the economic and social factors, then we may be able to explain this phenomenon as result of the lack of concordances between educational offers, in general, and the requirements on the labor market in Romania, as there are still attempts to reconcile the two aspects. Thus, there are graduates in over-saturated filed, who, at a certain moment, decide to reorient themselves towards others where there are more job opportunities, in the country or abroad. This aspect can generate, along with the frustration of giving up the profession one initially desired, as frustration is one of the important causes of stress \[[@B10]\], the pressure of financial and social discomfort stemmed from the impossibility of finding a workplace or a better paid one. The new requirements, the high expectations from the more experienced students, coming from themselves or from those around, have been identified as a source for stress in other studies as well, which emphasize the idea that the level of stress will increase in the following years. \[[@B11]\]. Because the pressure is high and of a relatively new nature, it is mandatory to employ an additional preparation of the students, aimed at adapting them to both the current educational requirements and to the future professional ones, so that, besides the basic preparation, the nursing department students would benefit from strategies which will enable them to face challenges while preserving their health. In addition to this sort of pressure, previous research have shown that, for the nursing department students, learning is difficult due to the large amount of time spent in school, the large workload and the uncertainty regarding their own necessary competencies and abilities, but also due to the difficulty of coping with the patients' suffering or death. \[[@B11]\]
Similarly, no differences were recorded as far as the subjects' genders were concerned, neither within the same gender category in these two results, which determine us to favor the external factors, especially the social and economic ones \[[@B12]\], some of them driving the students towards choosing a certain faculty.
Conclusions
===========
The stress equally affects the nursing department students, regardless of their gender or prior studies. The pressure of specific economic and social factors seem to be the most important in this respect, along with the pressure of the new tasks and abilities or competencies which have to be learned in an environment which allows for very few mistakes.
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Background {#Sec1}
==========
Dementia has become a global challenge for public health. Currently, over 40 million people worldwide live with this condition and this number would double by 2030 and more than triple by 2050 \[[@CR1]\]. Alzheimer's disease (AD) is the most prevalent cause of dementia, characterized by progressive cognitive and functional impairments and as well as memory deterioration. Although much effort has been made in the past several decades to uncover the mechanism of AD pathogenesis and to further translate these findings into the clinic, there are still no mechanism-based treatments approved for this devastating disease and the current therapies only provide transient symptomatic release.
The two most well-known pathological hallmarks of AD are extracellular amyloid plaques comprised of aggregated Aβ, and intracellular neurofibrillary tangles (NFTs) generated by hyperphosphorylated microtubule-associated protein tau. Increasing evidence indicates that neuroinflammation can act as an independent factor at very early stage of AD, where the immune-related genes and cytokines are the key participants.
Cytokines are a heterogeneous group of proteins with molecular weights ranging from 8 to 40 kDa. These multifunctional molecules can be synthesized by nearly all nucleated cells and generally act locally in a paracrine or autocrine manner. Many of them are referred to as interleukins (ILs), indicating that they are secreted by and act on leukocytes. Other important types of cytokines, such as tumor necrosis factors (TNFs), interferons (IFNs) and transforming growth factors (TGFs) that can cause cell death, activate natural killer cells and macrophages, and induce phenotypic transformation and act as a negative autocrine growth factor, respectively. Another member of the big cytokine family is the chemokines, which can attract and activate leukocytes. In view of their relatively exclusive functions, chemokines are usually discussed separately.
As cytokines are rapidly changed in response to infections or trauma, they have been classified as either "pro-inflammatory" or "anti-inflammatory". The balance between the two types of cytokines guarantees immediate elimination of the invading pathogens and the timely withdraw of excessive reaction, which is the key to preventing many diseases including the neurodegenerative diseases. The expression of cytokine receptors is temporally and spatially regulated in the central nervous system (CNS) \[[@CR2]\], and they are closely involved in cell proliferation, gliogenesis, neurogenesis, cell migration, apoptosis, and synaptic release of neurotransmitters \[[@CR3], [@CR4]\].
Cytokines have attracted much attention towards their exact roles in different stages of AD and the possibility for therapeutics. However, cytokines levels detected in AD patients were inconsistent among different research groups, while regulating the expression of cytokines in AD animal models yielded unexpected results as well. Here, we will focus on the most extensively studied cytokines, including ILs, TNF-α, TGF-β and IFN-γ, looking for the commonness, reasoning the disagreement among recent studies and give suggestions about how to translate these precious findings from the laboratories to the clinic in AD.
Evidence from AD patients {#Sec2}
=========================
The postmortem analysis of the AD brains has provided pioneering evidence for involvement of inflammation in AD pathology. IL-1β \[[@CR5]\], IL-6 \[[@CR6]\] and TGF-β \[[@CR7]\] and many other cytokines have been found to accumulate around the amyloid plaques in the brain of AD patients, which led to numerous studies investigating the levels of pro-inflammatory and anti-inflammatory cytokines in the cerebral spinal fluid (CSF) or serum of patients with mild cognitive impairment (MCI) or AD. Although results are inconclusive, there appears a trend that pro-inflammatory (IL-1β, IL-6, TNF-α) and anti-inflammatory cytokines (IL-1 receptor antagonist (IL-1ra), IL-10) are both elevated in the CSF and plasma of AD patients \[[@CR8]\]. The alterations of cytokine levels reflect the disturbance of immune system in AD, however, the evidence from the body fluid is insufficient to decide whether these changes are a initiating or secondary event of the disease, thus more approaches should be adopted to illustrate a more reliable picture for the role of cytokines.
Although the established genetic causes such as gene mutations encoding amyloid precursor protein (*APP*), presenelin 1 (*PSEN1*) and *PSEN2* are only dominant to a minority of familial type of AD, these risk genes have deepened our understanding of AD mechanisms in many aspects. For instance, the heterozygous rare variants in gene coding triggering receptor expressed on myeloid cells 2 (TREM2) increases risk of AD with an unfavorable inflammatory condition for Aβ clearance \[[@CR9]\], thus shedding a light on the possible initiating role of inflammation in AD pathogenesis.
To date, at least 23 cytokine polymorphisms involving 13 types of cytokines have been identified to be associated with AD. Based on the following three conditions (1) having polymorphisms that are significantly associated with AD, (2) having corresponding genotype/phenotype data, and (3) having previous records of the changed levels in AD patients, these cytokines can be divided into five groups as follows: (i) Cytokines like IL-1β, IL-6, IL-18 and TNF-α have the above three conditions. (ii) Cytokines like IL-4, IL-12, IL-23 and IFN-γ have the first two conditions but have no level change or the related data in AD, demanding new strategies to measure the cytokine level in AD patients, especially in those with the polymorphisms. (iii) Cytokines like IL-10 have conditions 1 and 3, calling for future studies. (iv) Cytokines like IL-1ra and TGF-β only meet condition 3 but have numerous evidence from both in vivo and in vitro studies, indicating that the genetic factor may not be crucial for their actions in AD or need further studies. (v) Cytokines like IL-16, IL-15 and IL-17 that either only have condition 1 or lack all three conditions still needs more evidence to confirm their involvement in AD.
Although many studies have discussed the polymorphism-related cytokine level changes, the data are mostly referenced from other research fields than AD, such as cancer. The direct evidence for the cytokine levels in different populations is also not convincing enough to draw a definite conclusion.
In the subgroup meta-analysis of cytokine polymorphisms, many grouping factors could decrease heterogeneity and improve significance, such as races \[[@CR10]--[@CR14]\], apolipoprotein E (ApoE) *ε4* allele and time of AD onset. As for races, it is rare to find significance in Asian and Caucasian populations, and in more extreme cases, a polymorphism indicates higher risk of AD in a population while shows lower risk in the other \[[@CR12], [@CR13]\]. This may be a result of the different frequencies of the polymorphism between different races and interplay of the variant with other unknown race-specific genes, or even with the environment. Of course, the influence from limited sample size of certain population cannot be excluded \[[@CR15]\]. ApoE *ε4* allele, the widely recognized late-onset AD triggering factor, is associated with at least 5 cytokine polymorphisms \[[@CR16]--[@CR20]\], indicating a potential synergistic interaction between them. ApoE *ε4* can modify AD risk in patients with diabetes or cardiovascular disease, which could be attributable to related hyperlipidemia and hypercholesterolemia. ApoE4 could also independently cause neurovascular dysfunction through triggering inflammatory cascades \[[@CR21]\]. Thus, it would be necessary to know whether cytokines play the initiating or secondary role in the interaction with ApoE. In addition, although few studies clarified the time of AD onset in their samples, it seems from the present studies the alteration cytokine levels have more influence on the late-onset AD (LOAD). As many cytokines have a close interaction with ApoE, whether this potential synergistic effect is the sole reason to the onset-time association deserves further investigation.
When single polymorphism of a cytokine does not always guarantee significance, the haplotype of one or more different types of cytokines may show associations with AD \[[@CR20], [@CR22], [@CR23]\]. There is also a positive and linear relation between the numbers of the pro-inflammatory cytokine polymorphisms and AD risk \[[@CR24]\], which suggests that their corresponding proteins might interact with each other in a cumulative manner \[[@CR25]\].
Compared with the widely recognized genetic risk factors like TREM2 or CD33 \[[@CR26]\], the genetic evidence from cytokines may be insufficient to prove that cytokines levels imbalance alone is able to trigger AD. However, a polymorphism of IFN-γ is associated with fast progressing AD makes it certain that cytokines could play an active role in exacerbating the AD course \[[@CR27]\]. Together, the cytokine polymorphisms may not markedly assist in predicting AD risk, but they have irreplaceable value in identifying pathways involved in the disorder and potential drug targets. The relationship between cytokines with races and ApoE and some of the AD-related cytokine polymorphisms are summarized in Table [1](#Tab1){ref-type="table"}.Table 1Cytokine polymorphisms and levels in serum or CSFCytokines^a^Levels^b^Polymorphisms/haplotypesCorresponding cytokine expression^c^Results^d^MethodsRef.MCIADPlasma/serumCSFPlasma/serumCSFIL-1 family \[[@CR144]\]IL-1α=\\= or ↓\\-889 C/T (rs1800587)T: ↑\* ↑ in EOADMeta-analysis\[[@CR145]\]No \* in LOAD.\* ↑ in CaucasiansMeta-analysis\[[@CR14]\]No \* in Asians.IL-1β↑=↑or == or ↑-511 C/T (rs16944)?no\*Meta-analysis\[[@CR15]\]-31 T/C (rs1143627)C: ?\*↓ in ItaliansCase--control\[[@CR25]\]−511C/−31 T/IL1RN2?\*↓ in elderly group of BraziliansCase--control\[[@CR23]\]−511C/−31C/IL1RN1?\* ↑ in BraziliansCase--control+3953 C/T (rs1143634)T: ↑\* ↑ in non-AsiansMeta-analysis\[[@CR15]\], \[[@CR14]\]Exon 5 E1/E2\\No\* in Taiwan populationCase--control\[[@CR146]\]IL-1ra\\\\-↓ \[[@CR139]\]Intron 2 I/II/IV\\IL-18 \[[@CR71]\]=\\= or ↑↑-607 A/C (rs1946518)C: ↑\* ↑ in LOAD of Han Chinese.Case--control\[[@CR20]\]\*↑↑ in ApoE ε4 carrier.-137 C/G (rs187238)G: ↑-607 C or -137 G↑\* ↑ in LOAD of Han Chinese.IL-33 \[[@CR147]\]\\\\\\\\rs11792633 C/TT: ↑\*↓ in non-ApoE ε4 carrier in both Caucasians and Han Chinese.Case--control\[[@CR19]\],\[[@CR148]\]IL-4 \[[@CR149]\]\\\\\\\\-1098 T/G (rs2243248)G: Possibly ↓\*↑ in Han ChineseCase--control\[[@CR150]\]T: Possibly ↓\*↑ in Caucasians\[[@CR151]\]-590 C/T (rs2243250)C: ↓\*↑ in Han Chinese and Caucasians\[[@CR150]\], \[[@CR151]\]IL-6 familyIL-6 \[[@CR152], [@CR153]\]=\\↑or == or ↑-174 G/C (rs1800795)C: ↓\*↓ in Asians, No\* in Caucasians.Meta-analysis\[[@CR10]\].\*↓ in Italians.Case--control\[[@CR25]\]-572 C/G (rs1800796)C: ?\*↑ in ApoE ε4 carriers.Case--control\[[@CR16]\]IL-11 \[[@CR154]\]=\\= or ↑↑\\\\\\\\\\IL-10 \[[@CR155], [@CR156]\]=↑= or ↑=-1082 A/G (rs1800896)A: ?\*↑ in Caucasians, No\* in Asians.Meta- analysis\[[@CR11]\]G: ↑↓ in CaucasiansMeta- analysis\[[@CR22]\]-819 T/C (rs1800871)?no \*-592 A/C (rs1800872)-1082G/-819C/-592C?↓IL-12 family \[[@CR157]\]IL-12A=\\==rs2243115 T/GG: ↓\*↓ in LOAD in ApoE ε4 carrier of Northern Han ChineseCase--control\[[@CR17]\]rs568408 G/AA: ↓\*↓ in LOAD of Northern Han ChineseIL-12B=\\==rs3212227 A/CC: ↓\*↓ in LOAD of Northern Han ChineseIL-23\\\\\\\\rs10889677 A/C (L-23R)C: ↓\*↓ risk in Northern Han Chinese.Case--control\[[@CR18]\]rs1884444 T/G (IL-23R)G: ↓\*↑ in ApoE ε4 carrier of Northern Han Chinese.Case--controlIL-15 \[[@CR158]\]\\\\==\[[@CR159]\]\\\\\\\\\\IL-16 \[[@CR160]\]\\\\\\\\rs4072111 C/TT: ?\*↓ in LOAD of Iranians.Case--control\[[@CR161]\]IL-17 \[[@CR162]\]\\\\\\\\\\\\\\\\\\TNF-α \[[@CR163]\]= or ↑↓= or ↑ or ↓= or ↑ or ↓-308 G/A (rs1800629)A: ↑\*↑ in East AsianMeta-analysis\[[@CR12]\], \[[@CR13]\]\*↓ in Northern European population.No\* in ItaliansCase--control\[[@CR25]\]TGF-β \[[@CR164]\]\\↓↑ or ↓ or =↑ or ↓ or =\\\\\\\\\\IFN-γ \[[@CR165]\]\\\\==-874 T/A (rs62559044)A: ↓\*↑ in fast progressing ADCase--control\[[@CR27]\]*Abbreviation*: *IL-1 ra* IL-1 receptor antagonist, *EOAD* early-onset Alzheimer's disease, *LOAD* late-onset Alzheimer's disease^a^Each cytokine or cytokine family was supplemented with a latest review for detailed information of physiological parameters^b^↑: up-regulated, ↓: down-regulated, =: no change, \\: no data. Unless otherwise noted, all the data of cytokine levels is from Brosseron et al. 2014 \[[@CR8]\]^c^↑: enhance the cytokine expression, ↓: attenuate the cytokine expression, ?: unknown yet^d^\*: significant, ↑: higher risk of AD onset, ↓: lower risk of AD onset
Cytokines related to AD-like Aβ abnormalities {#Sec3}
=============================================
As one of the most well-known hallmarks of AD, Aβ is actively involved in the neuroinflammation. It is believed that Aβ has a predominant role in launching the detrimental self-exaggerated inflammation process that is responsible for the disease progression. The Aβ peptide is derived from amyloid precursor protein (APP) by sequential cleavages of two membrane-bound proteases. Aβ of different length, especially Aβ~1-42~ then form soluble oligomers and fibrils, the latter is the major component of extracellular amyloid plaques. Soluble Aβ can be degraded by various extracellular proteases, while fibrillary Aβ is phagocytosed by microglia, the resident phagocytes of CNS, then enter the endolysosomal pathway \[[@CR28]\]. Astrocytes are also capable of degrading Aβ, primarily the cerebrovascular Aβ \[[@CR29]\]. The dysregulation of Aβ clearance process resulted from the skewing of microglia or astrocytes to pro-inflammatory state, characterized by elevated levels of pro-inflammatory cytokines and compromised ability in Aβ clearance, will lead to Aβ accumulation and a sustained immune activation.
Several environmental factors, including diabetes, obesity, aging that are associated with immune disturbance could trigger the phenotype transformation of glial cells \[[@CR28]\] through either direct modulation of the relevant mediators \[[@CR30]\] or epigenetic modification \[[@CR31]\]. Then, elicited by a self-propagating circle through the interaction between Aβ and pro-inflammatory cytokines \[[@CR32]--[@CR34]\], the chronic inflammation state is ultimately independent of the primary stimulus, which is a possible explanation to the failure of anti-amyloid treatment strategies in late stage of AD \[[@CR35]\].
Several anti-TNF-α biologic medications have rescued Aβ deposition, behavioral impairments and inflammation in AD animal models \[[@CR36]--[@CR39]\], suggesting that TNF-α is a detrimental factor in AD course and can serve as a reliable AD target. However, hippocampal expression of TNF-α in APP transgenic mice at early stage induced robust glial activation that attenuate Aβ plaques without altering the APP levels \[[@CR40]\]. Although there was only a suspicious infiltration of peripheral immune cells, increased major histocompatibility complex class II (MHC-II) cells were detected in the TNF-α expressing mice, indicating an enhanced antigen-presenting efficiency and more frequent communication with infiltrating T cells, which may facilitate Aβ removal.
Several studies indicate that overexpression of IL-1β in APP/PS1 mice reduces Aβ plaque accompanied by an activated population of microglia with greater phagocytosis \[[@CR41], [@CR42]\]. It is proposed that this group of microglia might be endogenous Arg-1+ M2a phenotype induced by Th2 cytokines, such as IL-4, secreted by a group of cells recruited to the Aβ plaques during the sustained IL-1β neuroinflammation \[[@CR42]\]. The mice deficient in IL-1R had lower recruitment of microglia to amyloid plaques, implying that IL-1β can mediate microglial chemotaxis \[[@CR43]\]. Moreover, IL-4 can down-regulate TNF-α and up-regulate MHC-II, insulin-like growth factor (IGF)-1 and CD36 in microglia \[[@CR44]\], and thus not only decrease the neurotoxicity but also promote the ability of presenting antigen to T cells \[[@CR45]\]. Similar results were also seen in IL-6 \[[@CR46]\]. These studies indicate that overexpressing pro-inflmmatory cytokines in CNS may generate Aβ-clearance-promoting effect with a peripheral responses involved. However, it is noteworthy that none of these studies have relevant behavioral results (see Table [2](#Tab2){ref-type="table"}), thus we cannot assess the overall result of this type of cytokine modulation. It is reported that chronic neuronal TNF-α expression in 3xTg AD mice led to large amount of neuronal death \[[@CR47]\]. Whether the enhanced local inflammation and direct neurotoxicity or periphery-mediated Aβ reduction has larger impact on the cognitive performance needs further studies. Moreover, as the expressions of human APP or tau in AD animal models are driven by various unnatural transgene promoters, the possibility that some anti-cytokine molecules may act through interacting with these regulatory elements cannot be ruled out \[[@CR37]\]. Therefore, a critical verification with alternative AD models is needed.Table 2Methods and results from in vivo studies of cytokinesCytokines^a^AnimalsMain AD-like Pathology and initiating timeCytokines Expression SystemExpression DurationResults^b^Ref.Delivery MethodAdministration RoutesImmuno-histochemistryBehaviors**IL-1β**3xTg AD mice (9 months old)Aβ plaque: 6 mo. Tau: 12 -15 mo.anti-IL-1R blocking antibodyPeritoneal Injectionevery 8-9 days for 6 monthsAβ deposition ↓; Tau phosphorylation ↓Cognition ↑\[[@CR83]\]Rats adult-IL-1β injectionsCerebral ventricles1 dTNF-α, IL-10 ↑No significance\[[@CR34]\]8 dTNF-α, IL-1β ↑ IL-10 ↓; APP mRNA ↑Memory ↓3xTg AD mice (8 months old)Aβ plaque: 6 mo. Tau:12 -15 mo.IL-1β-XAT cassetteSubiculum1 and 3 mo.Aβ deposition ↓; Tau phosphorylation ↑\\\[[@CR41]\]APPswe/PSEN1dE9 mice (8 months old)Aβ plaque: 6 mo.rAAV2-IL-1βHippocampi1 mo.Aβ deposition ↓\\\[[@CR42]\]IL-6TgCRND8 mice (0 -12 h old (P0)/36 -48 h old (P2))Early Aβ plaque: 3mo. Dense-cored plaques: 5 mo.rAAV2/1-IL-6Cerebral ventricles5 mo.Aβ deposition ↓\\\[[@CR46]\]TgCRND8 mice (4 mo.)rAAV2/1-IL-6Hippocampi1-1.5 mo.Aβ deposition ↓\\Tg2576 mice (P0)Numerous Aβ plaques:11-13 mo.rAAV2/1-IL-6Hippocampi3 mo.Aβ deposition ↓\\**IL-4**Tg2576 + PS1 mice (3 months old)Aβ plaques: 6 mo.rAAV2/1-IL-4Hippocampi5 mo.Aβ↓; Gliosis ↓; Neurogenesis ↑Spatial learning ↑\[[@CR54]\]TgCRND8 mice (4 months old)Early Aβ plaque: 3 mo.rAAV2/1-IL-4Hippocampi1.5 mo.Aβ↑; Gliosis ↑\\\[[@CR55]\]APPswe/PSEN1dE9 mice (3 months old)Aβ plaque: 6 mo.rAAV2/1-IL-4Frontal cortex, Hippocampi43 d.Aβ↓ with no significance; Enhanced M2a phenotype of microglia\\\[[@CR56]\]**IL-10**APPswe/PSEN1dE9 mice (3 months old)Aβ plaques: 6 mo.rAAV2/1-IL-10Hippocampi5 mo.Aβ =; Gliosis ↓; Neurogenesis ↑.Spatial learning ↑\[[@CR52]\]TgCRND8 mice (P0/P2)Early Aβ plaque: 3mo.rAAV2/1-IL-10Cerebral ventricles6 mo.Aβ deposition ↑Cognition ↓\[[@CR51]\]Tg2576 mice (8 months old)Numerous Aβ plaques: 11-13 mo.rAAV2/1-IL-10Hippocampi5 mo.Aβ deposition ↑Cognition ↓APPswe/PSEN1dE9 miceAβ plaque: 6 mo.Bred with IL-10 KO miceThe whole body12-13 mo.Aβ deposition ↓Cognition ↑\[[@CR53]\]IL-12/IL-23APPswe/PSEN1dE9 miceAβ plaque: 6 mo.Bred with p40 (IL-12 and IL-23 shared) KO, p35 (IL-12) KO or p19 (IL-23) KO miceThe whole body4 mo.Aβ deposition ↓ (especially with p40 KO)Cognition ↑\[[@CR65]\]Senescence accelerated mouse (SAMP8) mice (6 months old)Accelerated aging.siRNA KO of p40Dorsal third ventricle1 mo.Aβ deposition ↓Cognition ↑\[[@CR66]\]**TNF-α**TgCRND8 mice (4 months old)Early Aβ plaque: 3 mo.rAAV2/1-TNF-αHippocampi1.5 mo.Aβ deposition ↓\\\[[@CR40]\]3xTg AD mice (10, 17 months old)Aβ plaque: 6 mo. Tau: 12 -15 mo.TNF-α-lowering agent (3,6\'-dithiothalidomide)Peritoneal Injection1.5 mo.APP, Aβ peptide and Aβ deposition ↓; Tau phosphorylation ↓Cognition ↑\[[@CR37]\]3xTg AD mice (6 months old)TNF-α-lowering agent (IDT)Oral administration10 mo.Fibrillar Aβ↓; PHF-tau ↓Cognition ↑\[[@CR39]\]TGF-βhAPP J9 line miceAβ plaques :5-7 mo.Bred with transgenic expressing astrocytes-induced TGF-β1 miceBrain12-15 mo.Aβ deposition ↓; Perivascular Aβ deposition ↑\\\[[@CR57]\]Transgenic mice with inducible neuron-specific expression of TGF-β1 (3 months old)-The heterologous tTA systemNeocortex, hippocampi, striatum54 dPerivascular Aβ deposition ↑\\\[[@CR62]\]24 dDeath of neurons induced by 3-nitropropionic acid ↓\\SD rats with Aβ1-42 injection in bilateral hippocampusAβTGF-β1 injection 7 d after Aβ injectionLeft cerebral ventricles3dAPP ↓Cognition ↑\[[@CR166]\]SD rats with Aβ1-42 injection in bilateral hippocampusAβTGF-β1 administration1h prior to Aβ injectionCerebral ventricles7 dAPP ↓; PP2A ↑; TNF-α, IL-1β, iNOS, IFN-γ, IL-2, IL-17 and IL-22 ↓.Cognition ↑\[[@CR58]\]TGF-β1 administration7 d after Aβ injectionNares7 dPP2A ↑; IL-1β, iNOS, IFN-γ, IL-2 and IL-17 ↓.Cognition ↑**IFN-γ**APP Tg J20 miceAβ plaques : 5-7 mo.Bred with Tg SJL mice expressing IFN-γThe whole body9 mo.Oligodendrogenesis ↓\\\[[@CR167]\]3xTg AD mice (2 months old)Aβ plaque: 6 mo. Tau:12 -15 mo.rAAV2/1- IFN-γHippocampi10 mo.Aβ deposition ↑; Tau phosphorylation ↓\\\[[@CR168]\]TgCRND8 mice P2Early Aβ plaque: 3mo. Dense-cored plaques: 5 mo.rAAV2/1- IFN-γCerebral ventricles5 mo.Aβ deposition ↓; Gliosis ↑; Complement expression ↑; Peripheral monocytes infiltration ↑\\\[[@CR63]\]TgCRND8 mice (4 months old)Hippocampi1.5 mo.JNPL3 mice (P2), rTg4510 mice (P2)Tau:4 mo.rAAV2/1- IFN-γCerebral ventricles3 mo.Soluble tau phosphorylation ↑\\\[[@CR87]\]*Abbreviation*: *PHF-tau* Paired helical filament tau, *KO* knockout^a^Cytokines with controversial results are in bold.^b^↑: increase or improve, ↓: decrease or exacerbate, =: no change, \\: no dataFor more detailed information for the model animals mentioned above, please refer to <http://www.alzforum.org/research-models> \[[@CR169]\]
On the other hand, the typical anti-inflammatory cytokines such as IL-4 and IL-10 suppress the inflammation through inhibiting the secretion of IL-1β, IL-6, TNF-α by microglia \[[@CR48]--[@CR50]\] in vitro. In contrast to IL-4 that triggers M2a activation state associated with development of an anti-inflammatory environment and enhanced phagocytosis, IL-10 drives M2c polarization that is associated with deactivation of microglia. Overexpressing IL-10 in several AD animal models weakened the phagocytosis of soluble Aβ by microglia and exacerbeted Aβ deposits with cognitive impairment \[[@CR51]--[@CR53]\]. Although inconsistent outcomes do exist, a recent study using IL-10 knockout mice supports the benefit of IL-10 removal. Considering that the IL-10 level increased in AD patients \[[@CR53]\], it appears that the imbalance of pro- and anti- inflammatory activity co-exist in AD. Whether there is a corresponding, sequential transfer of microglia from M1 to M2c or mixed phenotype is unclear. It is also interesting to know whether this kind of transformation indicate exacerbation of the disease and "a point of no return" of the disease. As the previous in vivo studies of IL-10 all gave intervention before the formation of typical AD pathology (see Table [2](#Tab2){ref-type="table"}), more data of the IL-10 impact on the late stage of AD is required.
The in vivo IL-4 studies generated more controversial results: One shows that overexpression of IL-4 in pre-deposition phase of AD animal models resulted in attenuation of Aβ pathology and improved behavior \[[@CR54]\], while another one with short-term IL-4 expression in mice exacerbated amyloid deposition \[[@CR55]\]. The acute suppression of glial clearance activity due to the relative short duration of IL-4 exposure is a possible explanation to the inconsistency. IL-4 expression initiating time is another major difference of the two studies that worth further investigation. It worth mentioning that a IL-4 study has to be terminated prematurely due to the increased animal death after the intervention \[[@CR56]\]. One possible interpretation for the death was the multiple cortex injection sites and resultant higher virus and cytokine load.
TGF-β, an immunosuppressive cytokine which protects neurons against damages, has a complex role in modulating Aβ pathology. Long-term overexpressing TGF-β by astrocytes in transgenic mice led to increased clearance of Aβ plaque by activated microglia \[[@CR57]\] and improvement of Aβ-induced behavior impairment \[[@CR58]\]. However, TGF-β can also promote astrocytes aggregating around brain microvessels and Aβ deposits on the vascular basement membranes \[[@CR59]--[@CR62]\]. Therefore, TGF-β can reduce Aβ pathology of brain parenchyma while at the same time cause the blood perfusion impairment in the associated regions.
IFN-γ is a pleiotropic cytokine which has a similar but weaker function to IL-4 in upregulating glial MHC class II \[[@CR44]\], implying an immunosuppressive feature of the cytokine. The level change of IFN-γ in AD patients has not been reported, however, overexpressing IFN-γ results in a significant decrease of Aβ deposits and infiltration of peripheral monocytes \[[@CR63]\], which is consistent to the observations that IFN-γ increases Aβ uptake by microglia and activates microglia to facilitate T cell motility and synapse formation in vitro \[[@CR64]\].
The microglia-derived IL-12 and IL-23 is up-regulated in APP/PS1 transgenic mice and blocking these cytokines reverses the Aβ burden and the cognitive impairment \[[@CR65]\]. Another study using accelerated senescence mice (SAMP8) reproduced the results \[[@CR66]\]. In addition, a linear correlation of cognitive performance and CSF levels of p40, the common unit of IL-12 and IL-23, in AD subjects further supports the role of IL-12 and IL-23 in AD pathogenesis. IL-18, a member of IL-1 family, was elevated in LPS-stimulated blood mononuclear cells and brains of AD patients, and a significant correlation between IL-18 production and cognitive decline was observed \[[@CR67], [@CR68]\]. IL-18 promotes APP processing \[[@CR69]\], tau phosphorylation \[[@CR70]\] and can modulate the production of other cytokines \[[@CR71]\]. Similarly, another IL-1 family member, IL-33 and its receptor ST2, showed strong expression in the AD brains, and incubation with Aβ increased astrocytic IL-33 expression \[[@CR72]\]. The in vivo evidence of IL-18 and IL-33 in AD pathogenesis is currently missing and further studies may also explore whether these cytokines are detectable in CSF or serum of AD.
Cytokines related to AD-like tau abnormalities {#Sec4}
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Abnormal post-translational modification of tau proteins plays a crucial role in AD neurodegeneration, and hyperphosphorylation is one of them that has been most extensively studied \[[@CR73], [@CR74]\]. Accumulating studies suggest that targeting the down-regulated protein phosphatase-2A (PP2A) \[[@CR75], [@CR76]\] or up-regulated glycogen synthase kinase-3β (GSK-3β) \[[@CR77]--[@CR80]\] or modulating the upstream membranous receptors may attenuate tau hyperphosphorylation \[[@CR81], [@CR82]\]. Currently, the role of tau in the neuroinflammation process of AD remains poorly understood and is far less studied compared to Aβ. However, the interplay between tau and cytokines has shed a light on the relevant mechanisms.
Pro-inflammatory cytokines have shown a consistent impact on tau pathology. Overexpression of IL-1β in 3xTg AD mice exacerbated tau hyperphosphorylation within one month \[[@CR41]\], while blocking IL-1β signaling via IL-1 receptor antagonist (IL-1ra) or anti-IL-1β antibody reversed the cognitive impairment with a diminished tau pathology \[[@CR83], [@CR84]\]. The decreased activity of IL-1β-dependent tau kinases, such as cyclin-dependent kinase-5 (CDK5)/p25, GSK-3β and p38-mitogen activated protein kinase (MAPK) contributed to the reduction of phosphorylated tau \[[@CR41], [@CR83]\]. Additionally, a recent study showed that microglia can drive tau pathology, pathological tau spreading and memory impairment in the human tau40 mice through a IL-1β-dependent pathway since the inclusion of IL-1ra significantly reduced microglia-induced tau pathology \[[@CR85]\]. 3, 6\'-dithiothalidomide, a TNF-α-lowering agent, had no effect on total tau levels, but reduced phosphorylated tau in 3xTg AD mice \[[@CR37]\]. Another study used a different TNF-α modulator, IDT in the same animal models also reduced paired helical filament tau (PHF-tau) and improved the cognition \[[@CR39]\]. Treating hippocampal neurons with physiologic dose of IL-6 exhibited an increase in the amount of hyperphosphorylated tau of AD type, which may be attributed to an increased activity of CDK5/p35 complex \[[@CR86]\].
In primary glial cultures, recombinant adeno-associated virus (rAAV)-mediated expression of IFN-γ did not alter endogenous tau production or phosphorylation. However, IFN-γ increased hyperphosphorylation and conformational changes of soluble tau in two animal models with tauopathy \[[@CR87]\]. In turn, overexpressing tau40 increased secretion of TNF-α, IL-1β, IL-6, IL-10 and NO in rat microglia, which show greater phagocytosis of microspheres \[[@CR88]\]. However, the phenotype of the microglia and how this phenotype would influence the Aβ pathology need further studies. Moreover, upregulating PP2A in astrocytes stimulates astrocytes migration via inhibiting p38-MAPK in Tg2576 mice \[[@CR89]\], indicating that the tau-associated pathology may be involved in the impaired Aβ clearance.
It seems that tau pathology can be consequence of the deregulated inflammation, or serve as an inflammation promoter like Aβ to exacerbate inflammation. Nevertheless, to what extent tau may influence the inflammation, and what will be the sum effects of tau, Aβ and inflammation are mostly unknown. Besides, no related studies so far have examined the influence of anti-inflammatory cytokines on tau pathology. Cytokines also have important influence on neuron survival \[[@CR90]--[@CR93]\], blood brain barrier (BBB) integrity \[[@CR94]\] and other normal physiological events in the CNS \[[@CR3], [@CR4]\], which cannot be reflected in animal models of single type of pathology. Thus, a more careful examination of the current animal models \[[@CR95]\] and developing novel models more close to the real pathology of AD are needed \[[@CR28]\].
The adaptive immune system in AD {#Sec5}
================================
The most recent evidence has shown presence of a classical lymphatic system in the CNS \[[@CR96]\], suggesting a frequent communication of the immune activities between periphery and the CNS on a regular basis. Over 80 % of the T cells in the CSF are CD4+ that can be classified into four subsets, including type 1 helper-inducer T (Th1) cells and Th17 cells defined as pro-inflammatory; and Th2 cells and regulatory T (Treg) cells defined as anti-inflammatory. The activating state and subtype of T cells in the circulation, CSF and parenchyma are modified in AD patients \[[@CR97], [@CR98]\]. In an immune-deficient AD mouse model, lack of T, B, and natural killer cells exhibits an increased Aβ with decreased phagocytic efficiency of microglia and significant elevation of several key pro-inflammatory cytokines including IL-1β, IL-6 and TNF-α \[[@CR99]\]. These findings strongly suggest the active involvement of the adaptive immune system in AD pathogenesis.
Previous studies have highlighted the importance of cytokines in mediating the activity of peripheral immune cells in AD. Cytokines can facilitate the peripheral immune cells infiltration into the brain, resulting in direct Aβ phagocytosis by recruiting immune cells or inducing phagocytic activity of other cell types, such as microglia. The choroid plexus (CP) stroma is enriched with CD4+ T cells that are able to produce IL-4 and IFN-γ \[[@CR98]\], and the IFN-γ plays an essential role in assisting leukocyte trafficking \[[@CR100]\]. Decreased IFN-γ level in both 5XFAD and APP/PS1 mice were reversed by transient depletion of Treg cells at intermediate stage of AD, which at the same time led to increased leukocyte infiltration and recruitment to Aβ plaques, and attenuation of the AD pathology \[[@CR101]\]. However, amplification of Treg cells at early disease stages through peripheral low-dose IL-2 treatment increased numbers of plaque-associated microglia, and restored cognitive functions in APP/PS1 mice \[[@CR102]\]. Therefore, a more careful examination of Treg cells in different stages of the disease may help determining the proper therapeutic strategies.
Furthermore, when co-cultured with Aβ-treated microglia, the secretion of Th1 and Th17 cells increases, which then up-regulates MHC II, co-stimulatory molecules and pro-inflammatory cytokines in microglia \[[@CR103], [@CR104]\], thus improving the efficiency of presenting antigens to the T cells of microglia and enhancing Aβ clearance by both. However, IL-17 and IL-22, which are exclusively produced by Th17 cells, can also cause BBB disruption and infiltration of Th17 cells, but led to a direct injury to the neurons by Th17 cells via Fas/FasL pathway in Aβ-induced AD model rats \[[@CR105]\]. In addition, respiratory infection of APP/PS1 mice increased infiltration of IFN-γ + and IL-17+ T cells into the brains of older mice and this was correlated with an increased Aβ level \[[@CR106]\]. Together, these studies indicate that future studies should consider the complex interplay among many participants as seen in the real situation of AD.
The basal level of anti-inflammatory cytokines in CSF may help skewing the infiltrating T cells to the Th2 or Treg phenotype in physiological condition \[[@CR98]\]. In AD patients, the pro-inflammatory cytokines in CSF increases, which induces more Th1 or Th17 cells that can be detrimental. Several in vivo studies via cerebral ventricles or systemic administration to examine the impact of cytokines or the relevant antibodies on AD pathology (see Table [2](#Tab2){ref-type="table"}), the concomitant influence on the transformation of T cells phenotypes and following effects should be taken into consideration for a more reasonable interpretation of the outcomes.
Cytokines as potential biomarkers for AD diagnosis {#Sec6}
==================================================
So far, a CSF signature of low Aβ~1-42~ and high tau concentrations and significant retention in PET imaging with amyloid tracers are suggested as the standard diagnostic criteria, with the highest specificity and accuracy \[[@CR107]\]. However, lumbar puncture required for CSF has limited its application. Thus, novel biomarkers based on more accessible materials, such as plasma, are attractive in improving AD diagnosis. Several cytokines have shown disease progression-dependent manner, which suggests that cytokines may serve as potential disease predictors. For instance, data collected from a 20-years cohort study demonstrate greater possibility of cognitive impairment in individuals with increased IL-6 \[[@CR108]\]. After reviewing 118 research articles and comparing 66 cytokines in plasma or CSF obtained from MCI and AD, it was found that the cytokines increased steadily or had peak level upon the transformation from MCI to AD. This may help predicting the risk of suffering from AD and recognizing AD subgroups, such as IL-1β, IL-6, TNF-α, IL-18, monocyte chemotactic protein (MCP)-1 and IL-10 \[[@CR8]\]. However, in the latest meta-analysis, no significant differences in cytokines such as IL-1β, IL-6, IL-8, IL-10 or TNF-α were found between subjects with MCI and healthy controls, while significant heterogeneity was observed in some comparisons \[[@CR109]\].
Considering the unstable outcome of single cytokine level, combinational use of multiple proteins is a more reasonable approach. However, since the first AD predicting model made up of 18 plasma biomarkers containing multiple cytokines has been proposed \[[@CR110]\], few biomarker sets have shown stable performance and good reproducibility \[[@CR111], [@CR112]\]. Nevertheless, by using multiplex assays, two research groups have independently set up a panel of plasma proteins recently. These two panels are of high reproducibility and diagnostic accuracy, which were strongly associated with severity and progression of AD \[[@CR113], [@CR114]\]. Although no cytokines were involved in neither of the panels, one of the studies found positive correlations between the biomarkers and some cytokines altered in AD \[[@CR114]\]. In addition, after screening 120 inflammatory molecules in CSF and serum of AD, MCI and healthy controls through protein-array analysis, a combination of soluble IL-6 receptor (sIL-6R), tissue inhibitor of metalloproteinases-1 (TIMP-1) and soluble TNF-α receptor I (sTNFR-I) in CSF was found to provide the best prediction to AD among other molecules \[[@CR115]\].
Certainly, these results still need further verification by other research groups, while the heterogeneity in BBB integrity, physical state and disease stage of patients should be taken into consideration at the same time \[[@CR8], [@CR116]\]. Besides, the lack of standardization of sample collections or detections remains the dominant cause of failure of developing serum-based AD biomarkers. To address this problem, many organizations raise guidelines for standardization of blood-based biomarker studies in AD, covering the pre-blood draw, blood collecting, processing and storage \[[@CR117]\]. Furthermore, longitudinal sampling over years \[[@CR8]\] is a better approach to eliminate heterogeneity but needs optimization of its feasibility.
Although no evidence supports a direct association of systemic infections with AD \[[@CR118]--[@CR120]\], some specific pathogens have been identified as potential risks for AD, such as Herpes simplex virus type 1, *Chlamydophila pneumoniae*, *Helicobacter pylori* and periodontal bacteria \[[@CR121]\]. A recent study shows that the infection burden (IB) consisting of common pathogens is associated with AD after adjusted for ApoE genotype and various comorbidities. AD patients or healthy controls with more seropositivities have significantly higher serum levels of IFN-γ, TNF-α and IL-6 \[[@CR122]\]. As IB is a relatively stable indicator of systemic inflammation burden, the practical value of combinational use of IB with other biomarkers worth further investigations. Overall, single type of biomarker is far from enough to classify all phenotypes and stages of AD, the combination of plasma cytokines and other factor is the most realistic and promising approach to develop convenient and practical plasma biomarkers for AD.
Cytokines as potential targets for AD therapy {#Sec7}
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The anti-inflammatory therapies using non-steroidal anti-inflammatory drugs (NSAIDs) were once considered promising. However, after the positive reports from the pioneering randomized trial of indomethacin \[[@CR123], [@CR124]\], the followed trials have not reached a definitive conclusion \[[@CR28]\]. Lately, two meta-analyses have been conducted to reevaluate the role of NSAIDs in AD. Although it supported the use of NSAIDs for prevention of AD, there were no positive results from the randomized control trials (RCTs) \[[@CR125], [@CR126]\]. Moreover, in a follow-up evaluation study of the randomized AD anti-inflammatory prevention trial (ADAPT) and its follow-up study (ADAPT-FS) that treatment for 1 to 3 years with naproxen, a nonselective cyclooxygenase (COX) inhibitor, or celecoxib (a selective COX-2 inhibitor), the results show no prevention for the onset of dementia or no attenuation for the cognitive functions in older adults with a family history of AD \[[@CR127]\]. Many reasons to the failure have been proposed, including duration of treatment \[[@CR127]\], ApoE *ε4* allele \[[@CR128], [@CR129]\], ages \[[@CR127]\], disease stages \[[@CR130]\] and disease progressing speeds \[[@CR131]\]. Therefore, long-term and large-scale RCTs based on more tolerable novel NSAIDs are needed for understanding the positive findings from molecular and epidemiologic studies. In the absence of such RCTs, indirect treatment comparisons or mixed treatment comparisons may also help to reach more robust conclusions \[[@CR125]\].
As the broad anti-inflammatory medications are not promising, more specific immune pathways or molecules that are not affected by NSAIDs may be targeted. Etanercept is a TNF-α inhibitor originally used in the treatment of rheumatoid arthritis (RA). A noticeable clinical improvement was observed in AD patients minutes after perispinal administration of etanercept \[[@CR132]\]. To explain the rapid effect of etanercept, the authors propose that the vertebral venous system may be an anatomical route to bypass the BBB and to deliver high molecular drugs to the CNS \[[@CR133]\]. However, a recent study has challenged this claim, as three radio iodinated drugs including etanercept, were perispinally injected but the drug was not visualized in all but one of the rats using PET \[[@CR134]\]. Recent studies indicate that intravenously-administered etanercept has no apparent clinical benefit to AD patients, although good tolerability of subcutaneous etanercept over a 24-week period was observed \[[@CR133], [@CR135]\], suggesting better effects by perispinal administrating compared to peripheral route. Together, these studies confirm the pathogenic role of TNF-α in AD and show great potential of anti-TNF-α therapies through various administration routes.
Although targeting cytokines is a relatively new approach compared to other anti-inflammatory therapies in AD, it is noteworthy that a great number of cytokine inhibitors have already been successfully used in the treatments of autoimmune diseases and cancers \[[@CR136], [@CR137]\], and more biologics are under development \[[@CR138]\]. Repurposing these drugs in AD treatments could be a reasonable approach. For instance, IL-1ra is decreased in CSF of AD patients \[[@CR139]\] and its protecting effect towards AD has been confirmed in animal models \[[@CR84], [@CR85]\]. Although there is still no clinical evidence supporting the use of IL-1ra in AD patients, the success in treating RA and cortical infarcts \[[@CR140]\] makes it a very promising target in AD treatments. Similarly, p40-neutralizing antibodies, which block the IL-12/IL-23 signaling pathway, have been approved by Food and Drug Administration (FDA) for the treatment of psoriasis, thus may be ideal for the initiation of clinical trials \[[@CR65]\].
Besides, indirect approaches such as targeting upstream regulators of the cytokine expression seem also attractive. For instance, the Aβ-dependent induction of IL-1β requires two sequential signals. The first signal is triggered by Aβ binding to the toll-like receptors (TLRs) and leads to the production of IL-1β precursor. The second signal occurs via NLRP3 (NACHT, LRR and PYD domains-containing protein 3) inflammasome activation, which requires cathepsin B leakage from phagolysosomes or mitochondrial damage, and the subsequent reactive oxygen species (ROS) production. Then the NLRP3 inflammasome can activate caspase-1, which processes the pro-IL-1β into its bioactive form \[[@CR141]\]. Although there are no FDA-approved drugs that exclusively and specifically target NLRP3, a small molecule inhibitor of NLRP3 has been identified \[[@CR142]\]. Therefore, more initiative attempts of repurposing anti-cytokine drugs in AD treatments and more careful assessments of the results may lead to unexpected cheerful outcomes.
Conclusions {#Sec8}
===========
The cytokines are involved in various physiological and pathological pathways, therefore, inconsistent results have been observed in AD pathologies and treatment. The present evidence strongly indicates that dysregulation of the cytokines drives pathogenic process primarily through influencing the phenotype of microglia, and co-existence of both pro-inflammatory cytokines and the suppressing state of microglia may represent an irreversible point of the disease. Future studies on AD should extend to more pathogens than Aβ, and investigate the interplay between cytokine and other participators. The genome-wide association studies and the online database analysis will provide continuously updated polymorphism information associated with AD, while development of brain banks is critical for identification of new genes and proteins \[[@CR143]\]. Given that increasing studies have proven the role of adaptive immune system in AD, the impact of peripheral T cells and relevant cytokines cannot be ignored in future studies. As the immune events may change during the disease course and the heterogeneity in AD, it is not necessarily that all individuals with AD exhibit neuroinflammation, or at all-time points in the course of the disease. To learn from the existing therapy strategies of other related inflammatory diseases or to develop novel cytokine inhibitors could be reasonable approaches to making progress in AD anti-inflammatory therapies.
AD
: Alzheimer's disease
ADAPT
: anti-inflammatory prevention trial
ADAPT-FS
: anti-inflammatory prevention trial-follow-up study
ApoE
: apolipoprotein E
APP
: amyloid precursor protein
Aβ
: beta amyloid
BBB
: blood brain barrier
CDK5
: cyclin-dependent kinase-5
CNS
: central nervous system
COX
: cyclooxygenase
CP
: choroid plexus
CSF
: cerebral spinal fluid
FDA
: food and drug administration
GSK
: glycogen synthase kinase
htau40
: human tau40 protein
IDE
: insulin-degrading enzyme
IFNs
: interferons
IGF-1
: insulin-like growth factor-1
IL-1ra
: IL-1 receptor antagonist
ILs
: interleukins
MAPK
: mitogen activated protein kinase
MCI
: mild cognitive impairment
MCP-1
: monocyte chemotactic protein -1
MHC-II
: major histocompatibility complex class II
NFTs
: neurofibrillary tangles
NSAIDs
: non-steroidal anti-inflammatory drugs
PHF-tau
: paired helical filament tau
PP2A
: protein phosphatase-2A
PSEN
: presenelin
RA
: rheumatoid arthritis
rAAV
: recombinant adeno associated virus
ROS
: reactive oxygen species
SAMP8
: senescence accelerated mouse
sIL-6R
: soluble IL-6 receptor
sTNFR-I
: soluble TNF-α receptor I
TGFs
: transforming growth factors
Th1 cells
: type 1 helper-inducer T cells
TIMP-1
: tissue inhibitor of metalloproteinases-1
TLRs
: toll-like receptors
TNFs
: tumor necrosis factors
Treg cells
: regulatory T cells
TREM2
: triggering receptor expressed on myeloid cells 2
α1-ACT
: α1-antichymotrypsin
**Competing interests**
The authors declare that they have no competing interests.
**Authors' contributions**
All authors read and approved the final manuscript.
This work was supported in parts by grants from Natural Science Foundation of China (91132305, 81261120570, 81528007 and 81171195) and The National Key Technology Research and Development Program of the Ministry of Science and Technology of China (2013DFG32670, 2012BAI10B03).
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Hydrogen is an important feedstock in the manufacture of ammonia, methanol, and a variety of other chemicals; but its largest market is the crude oil processing industry. In crude oil refineries, hydrogen is used in a number of processes including hydrodesulfurization where hydrogen is reacted with sulfur containing compounds over a catalyst to form hydrogen sulfide. Hydrogen sulfide itself is already produced in great quantities during the drilling and processing of natural gas and oil. A process that can economically extract hydrogen from low value feedstocks or wastes such as hydrogen sulfide would bring tremendous benefits to the petroleum sector as this sector consumes large amounts of hydrogen.
Many processes exist for the production of hydrogen. The production of hydrogen is currently dominated by the steam reforming process where a relatively light hydrocarbon is reacted with steam inside a bed of reforming catalyst, usually nickel. Since steam reforming of hydrocarbon is endothermic, the energy to drive the reactions must be provided from an external source. In the steam reforming process, the hydrocarbon-containing stream must be free of sulfur or other contaminants such as carbon particles that can poison and deactivate the catalyst.
Another hydrogen production method is partial oxidation. In a partial oxidation reaction, a hydrogen-containing feed is reacted with an oxidizer, such as oxygen or air, in substoichiometric proportion normally referred to as a rich mixture where the equivalence ratio spans from one 1 to the upper flammability limit of the fuel being utilized as the feedstock. The equivalence ratio, defined as the stoichiometric oxidizer to fuel ratio divided by the actual oxidizer to fuel ratio, is shown in equation R1.
EquivalenceRatio = ( fuel Oxidizer ) actual / ( fuel Oxidizer ) stoichimetry R1 An equivalence ratio less than unity is considered lean, also referred to as fuel-lean, since a portion of the oxidizer is leftover after all of the fuel is consumed by the oxidation reaction. Where the fuel content of the mixture lies below the lower flammability limit of the fuel used as the feedstock, the fuel and oxidizer mixture is considered ultra-lean. Conversely, fuel and oxidizer mixtures of equivalence ratio greater than unity are considered rich, also referred to as fuel-rich, since a portion of the fuel is leftover after the oxidation reaction is complete. Mixtures of equivalence ratios greater than rich mixtures, normally taken to be higher than the upper flammability limit of the fuel being utilized as the feedstock, are considered ultra-rich. Ultra-rich mixtures do not normally produce self-sustained flames without the aid of external energy sources or preheating the mixture.
Although the partial oxidation process does not need an external source of heat since it is exothermic, it is still less common than steam reforming since it is generally less efficient than steam reforming particularly at large scale. As a normally non-catalytic process, partial oxidation can utilize any hydrocarbon feeds. The steam reforming and partial oxidation processes can be combined into a single process normally referred to as an autothermal process. In the autothermal process, the energy for the reforming reactions is provided by oxidizing a small portion of the fuel inside the bed of a reforming catalyst. Due to its catalytic nature, the autothermal process falls under the same constraints as the steam reforming process in that the catalyst bed is susceptible to poisoning and deactivation by sulfur, carbon, and other poisons in the feed stream. The hydrocarbon stream must be desulfurized in a first step prior to entering the autothermal reactor. During reforming, whether by the steam reforming or autothermal process, water must be provided in excess of the stoichiometric quantity to prevent carbon formation. Additionally, excessive temperature must be prevented in the reactions to avoid sintering the reforming catalyst. Steam reforming, partial oxidation, and the autothermal process are well known methods in the industry that are practiced on industrial scales.
The invention disclosed herein can be an economical process for producing hydrogen from hydrocarbons and various other hydrogen containing fuels. U.S. Pat. No. 6,517,771 to Li, incorporated herein by reference, disclosed a reverse flow inert porous media reactor for the purpose of heat-treating metals. Li limited the reactant stream to methane and oxygen or air, and the preheater to initiate the process is located inside the porous bed. Drayton et. al 27th, International Symposium on Combustion, 27, pp. 1361-1367, 1998, incorporated herein by reference, disclosed an application of the reverse flow reactor for fuel reforming, producing synthetic gas from methane in a reactor similar to Li's. None of the disclosed references above include an external energy source for the reverse flow reactor or are applied to the reformation of hydrogen sulfide.
A number of studies in reverse flow inert porous media reactors are carried out in applications not intended for hydrogen production from hydrocarbons. Hoffman et al, Combustion and Flame, 111, pp. 32-46, 1997, incorporated herein by reference, operated a reverse flow reactor with ultra-lean air and methane mixtures for the purpose of heating fluids. Barcellos et. al. Clean Air 2003, Seventh International Conference on Energy for a Clean Environment; Lisbon, Portugal, Jul. 7-10, 2003, incorporated herein by reference, tested a reactor similar to Hoffman's for the production of saturated steam through heat exchangers protruding directly through the inert porous media and fitted at the extremities of the reactor.
Production of hydrogen from both light and heavy hydrocarbons as well as other hydrogen containing wastes such as hydrogen sulfide is not addressed in the prior art. Hydrogen is a much more valuable commodity then sulfur. A process that can economically recover the hydrogen as well as other compounds could have significant impact on the petroleum and other industries. The reformation of hydrogen sulfide (H2S) to hydrogen and sulfur presents certain challenges not encountered in hydrocarbon reformation. For example, the low heat content of H2S precludes obtaining very high temperature in the partial oxidation regime. More importantly, H2S reforming requires the reaction to reach near equilibrium conditions at high temperature to obtain high yield. In the current invention, the intrinsic heat recuperating mechanism of the inert porous media matrix and the reactor's ability to create an isothermal high temperature volume render it a cost effective option for the reformation of H2S and other hydrocarbons by providing the necessary residence time and temperature without the requirement of an external energy source to be used continuously throughout the reactions.
Specifically, all of the reforming reactions in these above-mentioned prior art references occur inside a hollow chamber. None of these references disclose an apparatus and process where the reaction zone may be located in any portion of a reactor chamber, where the reaction zone is allowed to freely propagate through the reactor chamber filled with a porous media matrix and where the reforming reactions occur directly in a heated inert porous media matrix, or packed bed. Therefore, there has developed a need for a reactor which can efficiently reform both hydrocarbon and hydrogen sulfide fuels to pure hydrogen while not requiring continuous external energy to produce a viable hydrogen yield. |
Research in contextEvidence before this studyThe incidence and mortality of cholangiocarcinoma, a primary hepatic malignancy, are rising in the world. The absence of accurate diagnostic marker restricts early detection and treatment choices. Elevated levels of serum carbohydrate antigen 19--9, a widely used biomarker for cholangiocarcinoma, are also known to occur with other forms of tumors and benign liver disease, which restricts the sensitivity and specificity of diagnosis. We found the expression of peptidase inhibitor 15 (PI15), a secretory trypsin inhibitor, was significantly upregulated in cholangiocarcinoma by analyzing the microarray and TCGA database. Previous study indicated that PI15 could not be detected in a range of healthy human tissues (heart, brain, placenta, lung, liver, skeletal muscle, kidney, and pancreas), suggesting it may be a potential diagnostic marker for cholangiocarcinoma with high specificity.Added value of this studyWe demonstrated the PI15 was highly expressed in cholangiocarcinoma tumor tissues, and could not be detected in normal liver tissues. We detected high levels of plasma PI15 in cholangiocarcinoma patients, but low levels in patients with hepatocellular carcinoma, benign liver disease, chronic hepatitis B patients, and healthy individuals. Moreover, plasma PI15 levels in cholangiocarcinoma patients were obviously reduced after surgery. Altogether, PI15 holds potential diagnostic and follow-up value for patients with cholangiocarcinoma.Implications of all the available evidenceThis study suggests plasma PI15 holds significant value for predicting diagnosis for cholangiocarcinoma patients, and the combination of PI15 and carbohydrate antigen 19--9 improves diagnostic performance for cholangiocarcinoma.Alt-text: Unlabelled Box
1. Introduction {#s0025}
===============
Cholangiocarcinoma (CCA) is the second most common liver cancer (10%--15%) and is associated with high levels of invasiveness and a poor prognosis \[[@bb0005]\]. In recent years, the incidence of CCA has been increasing worldwide \[[@bb0010],[@bb0015]\]. Unfortunately, CCA is frequently diagnosed at an advanced stage, which restricts the treatment options to only radical surgery or liver transplantation \[[@bb0020],[@bb0025]\]. Serum carbohydrate antigen 19--9 (CA19--9) is the most widely used biomarker for CCA \[[@bb0030]\]. However, 10% of the general population are negative for Lewis-antigen, meaning that CA19--9 levels are undetectable in the serum; furthermore, elevated levels of serum CA19--9 are also known to occur with other forms of tumors and benign liver disease \[[@bb0035],[@bb0040]\]. Therefore, a sensitive and specific biomarker is urgently required to facilitate the detection of CCA.
Secretory proteins may serve as diagnostic markers for a variety of tumors \[[@bb0045], [@bb0050], [@bb0055], [@bb0060], [@bb0065]\]. Peptidase inhibitor 15 (PI15), a secretory trypsin inhibitor, was originally identified and purified from the serum-free conditioned medium of human glioblastoma T98G cells as a novel 25-kDa trypsin-binding protein \[[@bb0070]\]. PI15 belongs to the cysteine-rich secretory proteins, antigen 5, and pathogenesis-related 1 proteins (CAP) superfamily. CAP superfamily proteins are frequently secreted with an extracellular endocrine or paracrine function \[[@bb0075]\]. Northern blotting analysis previously indicated that PI15 could not be detected in a range of healthy human tissues (heart, brain, placenta, lung, liver, skeletal muscle, kidney, and pancreas), and could only be found in glioblastoma and neuroblastoma cell lines among multiple cancer cell lines (5 glioblastoma lines, 7 neuroblastoma lines, 8 gastric carcinoma lines, 6 squamous cell carcinoma lines, 5 hepatocellular carcinoma lines, 2 bladder carcinoma lines, and 1 fibrosarcoma line) \[[@bb0080]\].
In the present study, we demonstrated that PI15, a secretory trypsin inhibitor, was highly expressed in CCA tumor tissue compared to matched normal tissue. In addition, plasma PI15 levels in CCA patients were higher than that in patients with hepatocellular carcinoma (HCC), benign liver disease, chronic hepatitis B (CHB), and healthy individuals, thus indicating its potential diagnostic value for CCA. Receiver operating characteristic (ROC) curve analysis suggested that PI15 had a high diagnostic value for CCA, especially for iCCA patients, an important subtype of CCA. Furthermore, the combination of plasma PI15 and serum CA19--9 improved diagnostic performance. Additionally, plasma PI15 level was significantly reduced after surgery in CCA patients, which further illustrated that the origin of the elevated plasma PI15 concentration was the CCA tumor. Collectively, these results suggest that PI15 is a potential diagnostic and follow-up biomarker for CCA patients.
2. Materials and methods {#s0030}
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2.1. Patient samples {#s0035}
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Fresh samples of CCA patients (n = 67), HCC patients (n = 83), benign liver disease patients (n = 33; 13 as hepatic hemangioma; 20 as intrahepatic stones), CHB patients (n = 45), and healthy individuals (n = 45) were collected from the First Affiliated Hospital of Anhui Medical University. The pre- and postoperative plasma and serum of CCA, HCC, and benign liver disease patients were included. In addition, fresh normal liver tissues, tumor tissues, and matched normal tissues were collected. Healthy controls were matched to the CCA patients by age. CCA and HCC patients were diagnosed as primary cases by histological and clinical examination. Plasma and tissue samples were stored at −80 °C until they were used. HCC and CCA patients did not receive radiotherapy, chemotherapy or targeted therapy prior to surgery. The clinical characteristics of CCA, HCC, benign liver disease, CHB, and healthy individuals are shown in Supplementary Tables S1--4, respectively.
This research was approved by the Ethics Committee of the First Affiliated Hospital of Anhui Medical University (Quick-PJ 2018-07-22), and all patients provided signed informed consent for the use of their samples for biomedical research.
2.2. Gene expression profile assay {#s0040}
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The gene expression profiles of tumor tissues and matched normal tissues were analyzed using a whole human genome oligo microarray (G4112F; Agilent). Agilent\'s Feature-Extraction software (version 9.1.3; Agilent Technologies) was used for microarray image analysis. The gene expression values were log2-transformed, and the following analysis was performed using online SAS statistical software (<http://sas.ebioservice.com/>). Cluster 3.0 (Complete Linkage Clustering) was used to accomplish hierarchical clustering. Heat maps and green-red scale schemes were constructed using MultiExperiment Viewer (MEV). The microarray data were deposited into the National Center for Biotechnology Information Gene Expression Omnibus (GEO) repository under accession number GSE117361.
2.3. Analysis of The Cancer Genome Atlas (TCGA) datasets {#s0045}
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RNA-seq data from multiple tumors was obtained from The Cancer Genome Atlas (TCGA, <http://cancergenome.nih.gov>/), including data for cholangiocarcinoma (CHOL/CCA, 36 cancer and 9 normal), liver hepatocellular carcinoma (LIHC/HCC, 374 cancer and 50 normal), pancreatic adenocarcinoma (PAAD, 178 cancer and 4 normal), stomach adenocarcinoma (STAD, 375 cancer and 32 normal), colon adenocarcinoma (COAD, 480 cancer and 41 normal), rectum adenocarcinoma (READ, 167 cancer and 10 normal), lung squamous cell carcinoma (LUSC, 502 cancer and 49 normal), lung adenocarcinoma (LUAD, 535 cancer and 59 normal), kidney renal papillary cell carcinoma (KIRP, 289 cancer and 32 normal), kidney renal clear cell carcinoma (KIRC, 539 cancer and 72 normal), kidney chromophobe (KICH, 65 cancer and 24 normal), breast invasive carcinoma (BRCA, 312 cancer and 36 normal), and prostate adenocarcinoma (PRAD, 499 cancer and 52 normal). The analysis of differentially expressed genes (DEGs) between tumor tissue and normal tissue was conducted using the Edger package in R \[[@bb0085]\]. The criteria for defining DEGs was as follows: false discovery rate (FDR) \< 0.05 and \|log2(FC)\| \> 1, where FC represents the fold change.
2.4. Quantitative polymerase chain reaction {#s0050}
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Total RNA was isolated from tissue specimens using TRIzol (Invitrogen), and reverse transcribed into cDNA with Moloney Murine Leukemia Virus (M-MLV; Invitrogen). Quantitative polymerase chain reaction (qPCR) analysis was then performed on a Roche LightCycler 96 using SYBR premix Ex Tap II (Takara). The data analysis involved the ΔΔ*C*t method. All primers were synthesized by Sangon (Shanghai, China). The tumor markers were AFP, CEA, CA125, PSA, and GH, and the corresponding genes were *AFP*, *CEACAM5*, *MUC16*, *KLK3*, and *GH1*, respectively. We designed two *PI15* primers for PCR, which were designated *PI15*--1 and *PI15*--2, respectively. Supplementary Table S5 shows detailed information relating to the PCR primers used for *PI15*, *AFP*, *CEACAM5* \[[@bb0090]\], *MUC16*, *KLK3* \[[@bb0095]\], and *GH1* \[[@bb0100]\].
2.5. Enzyme-linked immunosorbent assay {#s0055}
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Plasma PI15 level was measured using a Human-PI15 ELISA kit (QY-E01315; China) in accordance with the manufacturer\'s instructions. We first prepared the reagents, samples, and standards. We then incubated each prepared sample and standard with HRP-Conjugate Reagent for 60 min at 37 °C. Each plate was then washed five times, chromogen solution A and B were added, and the mixture was incubated for 5 min at room temperature away from light. Finally, the stop solution was added and the optical density (OD) at 450 nm was measured within 15 min. A standard curve linear regression equation was then estimated based on standard concentrations and the corresponding OD values. The OD value for each sample was then added into the regression equation to calculate the sample\'s concentration. Each sample was analyzed in duplicate.
2.6. Electrochemiluminescence {#s0060}
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The concentration of serum carbohydrate antigen 19--9 (CA19--9) was measured using Electrochemical luminescence kit (Roche; Switzerland) in accordance with the manufacturer\'s instructions. The Roche Cobas e601 was used to analyze the detection data.
2.7. Statistical analysis {#s0065}
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Data were summarized and represented as mean ± standard error of the mean (SEM). Statistical analysis was conducted using SPSS (version 22.0) and GraphPad Prism (version 6.0) software programs. The student\'s *t*-test and paired *t*-test were used to analyze the statistical significance between independent groups and paired data, respectively. ROC curve analysis was used to evaluate the diagnostic value of the different markers. The area under the ROC curve (AUC) was used to assess the accuracy of each marker. Univariate and multivariate logistic regression models were used to consider the diagnostic value of PI15 alone and PI15 combined with CA19--9 \[[@bb0105]\]. *P* \< .05 was considered statistically significant.
3. Results {#s0070}
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3.1. Identification of a potential marker for CCA {#s0075}
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In order to identify a potential diagnostic marker for CCA, we analyzed the gene expression profiles of CCA and HCC tissue samples by gene expression profile assays. The detection of secretory protein biomarkers in plasma is a non-invasive diagnostic method, which is imperative in the clinic due to the need for duplicate tests and low costs. Thus, we screened a range of secretory proteins and found that *PI15*, a secretory trypsin inhibitor, was overexpressed in CCA tumor tissues compared to matched normal tissues ([Fig. 1](#f0005){ref-type="fig"}a, Left). To further demonstrate our finding, we analyzed CCA (CHOL, n = 36) mRNA expression data accessed by RNA-seq from TCGA using Edger analysis to identify differentially expressed genes (DEGs). We found that *PI15* expression was elevated by 3.8-fold in CCA tumor tissues relative to normal tissues, which was consistent with our initial finding.Fig. 1Discovery of a candidate marker for CCA.(a) Gene expression profile assay of CCA tumor tissues and matched normal tissues for screening candidate diagnostic markers. Heat map shown differentially expressed secretory proteins and tumor markers in CCA. The left heat map was based on the gene expression profile of CCA tumor tissues and matched normal tissues. The right heat map was based on CCA (CHOL, n = 36) RNA-seq data from the TCGA database. (b) Gene expression profile assay of HCC tumor tissues and matched normal tissues. Heat map shown selected secretory proteins and tumor markers in HCC. The left heat map was based on microarray data of HCC tumor tissues and matched normal tissues. The right heat map was based on HCC (LIHC, n = 374) RNA-seq data from the TCGA database. Each column depicts an individual sample. Blue squares represent normal tissues, yellow squares represent tumor tissues. RNA-seq data were normalized with MultiExperiment Viewer. (c) The positive rate of PI15 expression in various tumors. (d) The fold change of PI15 expression in various tumors. CCA (CHOL), cholangiocarcinoma (n = 36); HCC (LIHC), hepatocellular carcinoma (n = 374); PAAD, pancreatic adenocarcinoma (n = 178); STAD, stomach adenocarcinoma (n = 375); COAD, colon adenocarcinoma (n = 480); READ, rectum adenocarcinoma (n = 167); LUSC, lung squamous cell carcinoma (n = 502); LUAD, lung adenocarcinoma (n = 535); KIRP, kidney renal papillary cell carcinoma (n = 289); KIRC, kidney renal clear cell carcinoma (n = 539); KICH, kidney chromophobe (n = 65); BRCA, breast invasive carcinoma (n = 312); and PRAD, prostate adenocarcinoma (n = 499). Tumor samples are from the TCGA database. Red columns indicate positive expression of PI15, blue columns indicate negative expression of PI15.Fig. 1
To further illustrate whether *PI15* possessed potential as a diagnostic marker for CCA, we analyzed the sensitivity and specificity of the expression of *PI15* and other tumor markers in CCA. We selected tumor markers used in the clinic, consisting of AFP, CEA, CA125, GH, and PSA \[[@bb0110], [@bb0115], [@bb0120], [@bb0125], [@bb0130]\]. The corresponding genes were *AFP*, *CEACAM5*, *MUC16*, *GH1*, and *KLK3*, respectively. We characterized the expression of *PI15*, other secretory proteins, and tumor markers in CCA ([Fig. 1](#f0005){ref-type="fig"}a). We found that the sensitivity and specificity of *PI15* expression was superior to those of other tumor markers. Furthermore, we performed the same analysis in HCC samples; we analyzed the expression of *PI15*, other secretory proteins, and 5 tumor markers in HCC samples ([Fig. 1](#f0005){ref-type="fig"}b), and found that *PI15* was upregulated in a fraction of HCC. Thus, PI15 might be used as a novel diagnostic marker for CCA, with better sensitivity and specificity than other markers.
After the analysis of PI15 expression in cases with CCA and HCC, we focused on the positive rate and fold change of PI15 expression in various human tumors ([Fig. 1](#f0005){ref-type="fig"}c and d). The highest expression of PI15 in normal tissue was regarded as the upper limit of normal expression. When PI15 expression exceeded this upper value in tumor tissue, we defined such cases as positive-expression. The positive rate and fold change analysis were performed in various human tumors, accessed by RNA-seq deposited in TCGA. Consequently, we observed that the positive rate of PI15 expression was the highest (83.3%) in CCA (CHOL, n = 36) among various tumors ([Fig. 1](#f0005){ref-type="fig"}c), and that the fold change of PI15 was 3.8 in CCA (CHOL, n = 36) and 4.1 in HCC (LIHC, n = 374), which were higher than that in other tumors ([Fig. 1](#f0005){ref-type="fig"}d). Therefore, PI15 expression had higher specificity in CCA, indicating utility as a diagnostic marker.
3.2. Increased expression of the secretory protein PI15 in CCA patients {#s0080}
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To further investigate the sensitivity and specificity of PI15 expression in CCA, we measured the expression of PI15 and tumor markers (AFP, CEA, CA125, PSA, and GH) in 10 pairs of CCA tumor tissues and matched tumor adjacent normal tissues, 11 pairs of HCC tumor tissues and matched tumor adjacent normal tissues, and 5 normal liver tissues. As shown in [Fig. 2](#f0010){ref-type="fig"}a and b, the positive rate of PI15 expression was higher in CCA cases (70%, 7/10) than in HCC cases (9.1%, 1/11), and PI15 could not be detected in tumor adjacent normal tissues and normal liver tissues. Additionally, the positive rates of tumor markers expression in CCA were lower than that of PI15, including for AFP (40%, 4/10), CEA (50%, 5/10), and CA125 (20%, 2/10), GH and PSA could not be detected in CCA. Therefore, the sensitivity and specificity of PI15 expression was higher than those of other tumor markers in CCA. Moreover, we evaluated the relative expression levels of PI15 and tumor markers by qPCR in CCA and HCC, and found that only PI15 expression was higher in CCA tumor tissues compared with normal tissues (*p* \< .05, paired *t*-test), but this was not the case in HCC, and no significant differences of other tumor markers expression were observed in CCA and HCC ([Supplementary Fig. 1](#ec0005){ref-type="supplementary-material"}a and b).
Next, we focused on the positive rate of PI15 and tumor marker expression in CCA (CHOL, n = 36) and HCC (LIHC, n = 374) ([Supplementary Fig. 1](#ec0005){ref-type="supplementary-material"}c), and observed that the positive rates of *PI15* and tumor markers in CCA (CHOL, n = 36) were 83.3% (*PI15*), 69.4% (*MUC16*), 69.4% (*CEACAM5*), 44.4% (*KLK3*), 11.1% (*GH1*), and 2.8% (*AFP*). In HCC (LIHC, n = 374), the positive rates were 41.7% (*PI15*), 36.4% (*AFP*), 5.4% (*MUC16*), 6.7% (*KLK3*), 1.3% (*GH1*), and 0.5% (*CEACAM5*). Thus, PI15 expression in CCA showed a higher positive rate than other tumor markers, and the positive rate of PI15 expression was much higher in CCA than in HCC.
ROC curve analysis was then conducted to determine the diagnostic value of PI15 and tumor markers at the mRNA level in CCA (CHOL, n = 36) and HCC (LIHC, n = 374). We found that *PI15* showed an AUC of 0.981 (95% confidence interval \[CI\], 0.943 to 1.000) for discriminating CCA tumor tissue from normal tissue, which was superior to the diagnostic performance of other tumor markers ([Fig. 2](#f0010){ref-type="fig"}c). In addition, *PI15* exhibited an AUC of 0.806 (95% CI, 0.760 to 0.853) for discriminating HCC tumor tissue from normal tissue, which was higher than *AFP* with an AUC of 0.705 (95% CI, 0.653 to 0.758) ([Fig. 2](#f0010){ref-type="fig"}d). Thus, PI15 expression was significantly upregulated in CCA, and the diagnostic sensitivity and specificity of PI15 at the mRNA level were superior to those for other tumor markers in CCA.Fig. 2Expression of secretory protein PI15 was significantly upregulated in CCA.(a) The expression of PI15 and tumor markers (AFP, CEA, CA125, PSA, and GH) were determined by reverse transcription PCR (RT-PCR) in CCA tumor tissues (n = 10) and matched normal tissues (n = 10). Each band represents a different patient sample. (b) The expression of PI15 and tumor markers (AFP, CEA, CA125, PSA, and GH) were determined by RT-PCR in normal liver tissues (n = 5), HCC tumor tissues (n = 11), and matched normal tissues (n = 11). Each band represents a different patient sample. (c-d) ROC curve analysis of the expression of PI15 and tumor markers (assessed by RNA-seq) for discriminating tumor tissue from normal tissue in CCA (CHOL, n = 36) and HCC (LIHC, n = 374). The genes that encode the tumor markers (AFP, CEA, CA125, PSA, and GH) were *AFP*, *CEACAM5*, *MUC16*, *KLK3*, and *GH1*, respectively. PI15--1 and PI15--2 were the two primers used to amplify *PI15*. CCA/CHOL, cholangiocarcinoma; HCC/LIHC, hepatocellular carcinoma; Tumor adjacent, matched normal tissue; Normal liver, normal liver tissue.Fig. 2
3.3. PI15 as a potential diagnostic blood marker for CCA patients {#s0085}
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To determine the potential diagnostic value of PI15 in CCA, we examined the plasma PI15 level in CCA patients (n = 61), HCC patients (n = 72), benign liver disease patients (n = 28), CHB patients (n = 45), and healthy individuals (n = 45) using a quantitative ELISA assay. Consequently, we found that the plasma PI15 concentration was upregulated in CCA patients ([Fig. 3](#f0015){ref-type="fig"}a). Specifically, the plasma PI15 concentration was significantly increased in HBV negative CCA patients (60.64 ± 20.78 ng/ml) but not in HBV positive CCA patients (2.34 ± 0.39 ng/ml) ([Fig. 3](#f0015){ref-type="fig"}a). In addition, the plasma PI15 mean concentration was only 4.91 ± 0.50 ng/ml in HCC patients, which was significantly lower than in CCA patients (*p* \< .0001, unpaired *t*-test), and the plasma PI15 mean concentration was 20.26 ± 9.13 ng/ml in benign liver disease patients, 10.81 ± 3.84 ng/ml in healthy individuals, and 1.83 ± 0.24 ng/ml in CHB patients ([Fig. 3](#f0015){ref-type="fig"}a).Fig. 3PI15 as a potential diagnostic marker for CCA.(a) Plasma PI15 levels were measured by quantitative ELISA in CCA (HBV-) patients (n = 51), CCA (HBV+) patients (n = 10), HCC patients (n = 72), benign liver disease patients (n = 28), CHB patients (n = 45), and healthy individuals (n = 45). (b) Plasma PI15 levels in iCCA (n = 26), pCCA (n = 12), and dCCA (n = 13) patients. (c) ROC curves for PI15 levels in plasma samples from patients with CCA (HBV-) patients (n = 51) *versus* HCC patients (n = 72), benign liver disease patients (n = 28), CHB patients (n = 45), and healthy individuals (n = 45). HBV-, HBV negative; HBV+, HBV positive; Benign, benign liver disease; CHB, chronic hepatitis B; Normal, healthy individuals; iCCA, intrahepatic cholangiocarcinoma; pCCA, perihilar cholangiocarcinoma; dCCA, distal cholangiocarcinoma. Unpaired *t*-test; Data are presented as mean ± SEM.Fig. 3
We further compared the plasma PI15 level in different CCA subtypes categorized by anatomical location as intrahepatic cholangiocarcinoma (iCCA), perihilar cholangiocarcinoma (pCCA), and distal cholangiocarcinoma (dCCA). The mean plasma PI15 concentration was 78.5 ng/ml, 53.48 ng/ml, and 31.51 ng/ml in the iCCA (n = 26), pCCA (n = 12), and dCCA (n = 13) patients, respectively ([Fig. 3](#f0015){ref-type="fig"}b). Thus, the plasma PI15 level in iCCA patients was higher than in pCCA (*p* = .6631, unpaired *t*-test) patients and dCCA patients (*p* = .4441, unpaired *t*-test) ([Fig. 3](#f0015){ref-type="fig"}b).
ROC curve analysis was performed to further illustrate the diagnostic value of plasma PI15 for CCA patients. PI15 exhibited an AUC of 0.735 (95% CI, 0.632 to 0.838) for CCA samples compared to HCC controls ([Fig. 3](#f0015){ref-type="fig"}c; [Table 1](#t0005){ref-type="table"}). Additionally, the AUC of PI15 was 0.678, 0.692, and 0.875 for discriminating CCA patients from benign liver disease patients, healthy individuals, and CHB patients, respectively ([Fig. 3](#f0015){ref-type="fig"}c; [Table 1](#t0005){ref-type="table"}). In conclusion, plasma PI15 was able to discriminate effectively between CCA cases and other controls, suggesting great potential as a diagnostic marker.Table 1AUC calculations of ROC analysis for patients with CCA and iCCA *versus* HCC, benign liver disease, CHB, and healthy individuals.Table 1PI15CA19--9PI15 + CA19--9nAUC95% CIAUC95% CIAUC95% CICCA *versus* Controls CCA *versus* HCC51/720.7350.6320.8380.8750.8050.9460.9080.8460.97 CCA *versus* Benign51/280.6780.5550.80.7370.6240.850.750.6420.858 CCA *versus* CHB51/450.8750.7930.9570.8880.8130.9640.9620.9151.000 CCA *versus* Normal51/450.6920.580.8040.8810.8030.960.8780.7990.958
iCCA *versus* Controls iCCA *versus* HCC26/720.750.6140.8860.8490.7350.9630.9210.8411.000 iCCA *versus* Benign26/280.6990.5580.840.7120.5730.850.7610.6340.888 iCCA *versus* CHB26/450.8990.80.9980.8550.7290.980.9630.8971.000 iCCA *versus* Normal26/450.7090.5640.8550.8540.7280.980.850.7240.977
3.4. 3.4 Use of the PI15/CA19--9 marker panel improved diagnostic performance for CCA {#s0090}
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To investigate whether a combination of plasma PI15 and serum CA19--9 could constitute a combined diagnostic panel with higher discriminatory ability than each alone, we performed logistic regression to evaluate the diagnostic capacity of the combination of PI15 and CA19--9. A combination of PI15 and CA19--9 for CCA cases *versus* HCC controls yielded an AUC of 0.908 (95% CI, 0.846 to 0.97), outperforming either of the markers alone ([Fig. 4](#f0020){ref-type="fig"}a; [Table 1](#t0005){ref-type="table"}). In addition, the AUC of the two-marker panel discriminating CCA from benign liver disease was 0.750 (95% CI, 0.642 to 0.858), which was higher than 0.678 (PI15 alone) and 0.737 (CA19--9 alone) ([Fig. 4](#f0020){ref-type="fig"}a; [Table 1](#t0005){ref-type="table"}). The PI15/CA19--9 panel was able to discriminate CCA cases *versus* CHB patients with an AUC of 0.962 ([Fig. 4](#f0020){ref-type="fig"}a; [Table 1](#t0005){ref-type="table"}). Moreover, the PI15/CA19--9 panel for CCA *versus* healthy individuals exhibited an AUC of 0.878, which was close to 0.881, the AUC of CA19--9 alone ([Fig. 4](#f0020){ref-type="fig"}a; [Table 1](#t0005){ref-type="table"}). Thus, the PI15/CA19--9 panel was able to distinguish CCA from CHB patients and helped to distinguish CCA from HCC and benign liver disease compared to CA19--9 alone.Fig. 4The combination of PI15 and CA19--9 improves diagnostic performance for CCA.(a) ROC curves for PI15, CA19--9, and PI15 + CA19--9 levels in patients with CCA (HBV-) patients (n = 51) *versus* HCC patients (n = 72), benign liver disease patients (n = 28), CHB patients (n = 45), and healthy individuals (n = 45). (b) ROC curves for PI15, CA19--9, and PI15 + CA19--9 levels in patients with iCCA (HBV-) patients (n = 26) *versus* HCC patients (n = 72), benign liver disease patients (n = 28), CHB patients (n = 45), and healthy individuals (n = 45). HBV-, HBV negative; CHB, chronic hepatitis B; Normal, healthy individuals; iCCA, intrahepatic cholangiocarcinoma.Fig. 4
In the clinic, iCCA is usually diagnosed as a hepatic mass, frequently similar to the imaging performance of HCC with cirrhosis; thus, the differential diagnosis of HCC and iCCA can be difficult. In our present study, the plasma PI15 level in iCCA patients was highest among the different CCA subtypes tested, suggesting better diagnostic value for iCCA. Therefore, we further investigated the diagnostic performance of PI15 alone and the PI15/CA19--9 panel for iCCA. PI15 exhibited an AUC of 0.750 (95% CI, 0.614 to 0.886) for iCCA samples compared to HCC controls ([Fig. 4](#f0020){ref-type="fig"}b; [Table 1](#t0005){ref-type="table"}). In the same sample set, CA19--9 had a comparable AUC of 0.849 for iCCA samples compared to HCC controls ([Fig. 4](#f0020){ref-type="fig"}b; [Table 1](#t0005){ref-type="table"}). Furthermore, the PI15/CA19--9 panel displayed an AUC of 0.921 (95% CI, 0.841 to 1.000), indicating the superiority of the two-marker panel ([Fig. 4](#f0020){ref-type="fig"}b; [Table 1](#t0005){ref-type="table"}). When considering iCCA samples *versus* benign liver disease, the AUC including CA19--9 increased from 0.712 (alone) to 0.761 (with PI15) ([Fig. 4](#f0020){ref-type="fig"}b; [Table 1](#t0005){ref-type="table"}). The PI15/CA19--9 panel yielded the AUC of 0.963 for discriminating iCCA samples *versus* CHB controls ([Fig. 4](#f0020){ref-type="fig"}b; [Table 1](#t0005){ref-type="table"}). For healthy individuals, the combination of PI15 and CA19--9 was not able to increase the ability to discriminate between iCCA samples and healthy individuals ([Fig. 4](#f0020){ref-type="fig"}b; [Table 1](#t0005){ref-type="table"}). In conclusion, our results indicated that the PI15/CA19--9 marker panel exhibited better performance in diagnosing iCCA patients.
3.5. Establishing a cutoff concentration for plasma PI15 in iCCA patients {#s0095}
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In order to determine a plasma PI15 concentration which could act as a diagnostic cut off value with which to distinguish between iCCA and HCC. We firstly analyzed the concentration distribution of plasma PI15 in HCC patients to obtain cut-off values corresponding to the false-positive rates (FPRs) of 0%, 3%, and 5%. Subsequently, these cut off values were further analyzed and evaluated for their sensitivity and specificity in diagnosing iCCA patients. As seen in [Table 2](#t0010){ref-type="table"}, plasma PI15 could detect approximately 57.7% of iCCA patients (sensitivity) with 94.4% specificity when the cut off value was set to 13 ng/ml. Furthermore, when we used CA19--9 \> 98.5 U/ml, and a cut off value of 13 ng/ml for plasma PI15, the two-marker panel yielded 84.62% sensitivity and 94.44% specificity ([Table 2](#t0010){ref-type="table"}).Table 2PI15 concentration cut off values for iCCA and CCA based on percentiles of distribution in HCC plasma controls.Table 2MarkerCutoffiCCA *versus* HCCCCA *versus* HCCSensitivitySpecificitySensitivitySpecificityCA19-9 (\>98.5)69.2098.6066.7098.60PI15 (ng/ml) 95%1157.7093.1054.9093.10 97%1357.7094.4054.9095.80 100%25.238.5098.6033.3098.60CA19-9 (\>98.5) and PI15 (ng/ml) 95%1184.6293.0680.3993.06 97%1384.6294.4480.3994.44 100%25.280.7798.6174.5198.61
3.6. Evaluation of the postoperative recovery of CCA patients using plasma PI15 level {#s0100}
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Due to our results suggested that plasma PI15 could be used as a diagnostic marker for CCA patients, we further investigated whether plasma PI15 level could evaluate the postoperative recovery of CCA patients. We measured the pre- and postoperative plasma PI15 levels in CCA patients (n = 27), HCC patients (n = 30), and benign liver disease patients (n = 20); Meanwhile, we also detected the pre- and postoperative serum CA19--9 levels in CCA patients (n = 12), all of patients underwent curative hepatectomy. We observed that PI15 and CA19--9 were significantly reduced after surgery in CCA patients ([Fig. 5](#f0025){ref-type="fig"}a). The pre-operative mean plasma PI15 concentration in CCA patients reached 80.42 ng/ml. However, on the 4th and 7th days after surgery, the plasma PI15 mean concentration decreased to 53.17 ng/ml and 59.75 ng/ml, respectively ([Fig. 5](#f0025){ref-type="fig"}a). In the pre-operative plasma of HCC patients, the mean PI15 concentration was only 3.98 ng/ml, and the mean concentration was 4.12 ng/ml and 4.05 ng/ml on the postoperative 4th and 7th days, respectively ([Fig. 5](#f0025){ref-type="fig"}b). For benign liver disease patients, the mean pre- and postoperative mean plasma PI15 concentrations were 27.02 ng/ml and 26.79 ng/ml, respectively ([Fig. 5](#f0025){ref-type="fig"}c). Thus, plasma PI15 level was obviously reduced after surgery in CCA patients ([Fig. 5](#f0025){ref-type="fig"}a), whereas there was no significant change in HCC and benign liver disease patients ([Fig. 5](#f0025){ref-type="fig"}b and c). The dynamic change of plasma PI15 level in CCA patients confirmed that the elevated plasma PI15 concentration originated from the CCA tumor, demonstrating outstanding potential diagnostic and follow-up value for CCA patients. Consequently, the detection of plasma PI15 was able to evaluate the outcomes of surgical treatment, and could be used as potential follow-up marker for CCA patients after surgery.Fig. 5Determination of plasma PI15 level for the prediction of postoperative recovery in CCA patients.(a) The levels of plasma PI15 and serum CA19--9 in preoperative (day "-1") and postoperative (days "4" and "7") CCA patients (n = 27) were measured by quantitative ELISA and electrochemiluminescence respectively. The PI15 and CA19--9 concentration of representative CCA cases were shown. (b) Plasma PI15 levels in preoperative (day "-1") and postoperative (days "4" and "7") HCC patients (n = 30) were measured by quantitative ELISA. The PI15 concentration of representative HCC cases were shown. (c) Plasma PI15 levels in preoperative (day "-1") and postoperative (days "4" and "7") benign liver disease patients (n = 20) were measured by quantitative ELISA. The PI15 concentration of representative benign liver disease cases were shown. The abscissa of the coordinate axis is the number of days after surgery (postoperative days), and "-1" refers to the preoperative day. Before, before surgery; After, after surgery. Paired *t*-test; Data are presented as mean ± SEM.Fig. 5
4. Discussion {#s0105}
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In this study, our present results indicated that PI15 was highly expressed in CCA tumor tissues, and could not be detected in normal liver tissues. PI15 was also increased in the plasma of CCA patients, demonstrating that PI15 represents a potential diagnostic marker for CCA. The differentially methylated CpG of *PI15* was previously found to be a potential novel prognostic marker capable of distinguishing prostate cancer patients with metastatic-lethal tumors from nonrecurrent tumors \[[@bb0135]\]. The *PI15* gene had also been identified as a candidate oncogene in colorectal cancer \[[@bb0140]\]. However, no previous study has investigated the expression of PI15 in CCA. Human PI15 is situated on chromosome 8q21.11, and is adjacent to Cysteine Rich Secretory Protein LCCL Domain Containing 1 (*CRISPLD1*), another mammalian CAP superfamily gene. Most of the CAP superfamily proteins are structurally conserved, which leads to members with a CAP domain exhibiting similar fundamental functions. CAP superfamily proteins are frequently secreted with an extracellular endocrine or paracrine function. N-terminal sequencing of PI15 derived from the serum-free conditioned medium of glioblastoma cells indicated that the predicted secretory signal peptide was active \[[@bb0075]\], suggesting that the secretory protein PI15 has the potential to be a marker for detection in the peripheral blood.
In our present study, plasma PI15 levels in CCA patients were significantly higher compared to patients with HCC, benign liver disease, CHB patients, or healthy individuals, indicating that PI15 could be regarded as a diagnostic marker for CCA patients. Importantly, the combination of PI15 and CA19--9 exhibited superior diagnostic performance.
Moreover, the PI15 concentration in postoperative plasma was significantly decreased compared with that in the preoperative plasma in CCA patients, thus confirming that the elevated plasma PI15 concentration was related to CCA tumor tissue, which may help us to judge whether tumor tissue has been completely removed. However, there was no significant change in the plasma PI15 levels of benign liver disease patients, ruling out surgery, health care interventions, and other factors as contributors to the change in plasma PI15 in CCA patients. Meanwhile, PI15 and CA19--9 showed same decreasing trendency after surgery in CCA patients, which further illustrated the potential diagnostic value of PI15. Thus, we propose that the plasma PI15 is able to evaluate the outcomes of surgical treatment. Further work needs to be performed to investigate how PI15 is released into the plasma of CCA patients.
Further research still needs to be performed in the future. Long-term follow-up data collection and multi-center study are necessary to further validate the diagnostic and follow-up value of PI15 for CCA. Moreover, we will determine plasma PI15 levels at different stages of CCA to further investigate the early diagnostic value, thereby potentially enhancing its value for clinical application. Additionally, the combination of plasma PI15 and serum CA19--9 improved the diagnostic performance for CCA. However, for serum CA19--9 positive patients with liver diseases including cholangitis and duct obstruction \[[@bb0145]\], or serum CA19--9 negative CCA patients, the diagnostic performance of plasma PI15 needs to be further explored.
In conclusion, PI15 has the potential to act as a novel blood diagnostic marker for CCA, and could also be used as an indicator to evaluate postoperative recovery in CCA patients. The combination of plasma PI15 and serum CA19--9 improves the diagnostic performance for CCA.
The following are the supplementary data related to this article.Supplementary Fig. 1Evaluation of PI15 and other tumor markers expression in CCA and HCC. (a-b) The relative expression level of PI15 and other tumor markers accessed by real-time qPCR in CCA and HCC; (c) The positive rate of PI15 and other tumor markers expression in CCA (CHOL, n = 36) and HCC (LIHC, n = 374). The genes that encode the tumor markers (AFP, CEA, CA125, PSA, and GH) were *AFP*, *CEACAM5*, *MUC16*, *KLK3*, and *GH1*, respectively. Red columns indicate positive expression of PI15, blue columns indicate negative expression of PI15. CCA/CHOL, cholangiocarcinoma; HCC/LIHC, hepatocellular carcinoma; Normal, normal tissue; Paired *t*-test; ns, nonsignificant; \*, *p* \< .05.Supplementary Fig. 1Supplementary Table 1-5Image 1
Funding sources {#s0110}
===============
This work was supported by the Natural Science Research Foundation of Anhui Province (1508085MH173, KJ2015A137), and this work was also supported by the Natural Science Foundation of China (81602491).
Declaration of interests {#s0115}
========================
The authors declare no potential conflict of interest.
Authors\' contributions {#s0120}
=======================
Conception and design: Yong Jiang, Xiaohu Zheng, Yeben Qian, Haiming Wei.
Acquisition of data: Yong Jiang, Xiaohu Zheng, Defeng Jiao, Peng Chen.
Data analysis and interpretation: Yong Jiang, Xiaohu Zheng, Defeng Jiao, Yechuan Xu.
Manuscript writing: Yong Jiang, Xiaohu Zheng, Yeben Qian, Haiming Wei.
Final approval of manuscript: All authors.
We thank Mr. Wang Dongyao, Mr. Chen He and Ms. Ren Chunxia for their assistance in collecting the specimens involved in this study.
[^1]: These authors contributed equally to this work.
|
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/*******************************************************************************
* * Copyright 2012 Impetus Infotech.
* *
* * Licensed under the Apache License, Version 2.0 (the "License");
* * you may not use this file except in compliance with the License.
* * You may obtain a copy of the License at
* *
* * http://www.apache.org/licenses/LICENSE-2.0
* *
* * Unless required by applicable law or agreed to in writing, software
* * distributed under the License is distributed on an "AS IS" BASIS,
* * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* * See the License for the specific language governing permissions and
* * limitations under the License.
******************************************************************************/
package com.impetus.kundera.metadata.model.attributes;
import java.lang.reflect.Field;
import java.lang.reflect.Member;
import java.util.Date;
import javax.persistence.CollectionTable;
import javax.persistence.Column;
import javax.persistence.JoinColumn;
import javax.persistence.Temporal;
import javax.persistence.metamodel.Attribute.PersistentAttributeType;
import javax.persistence.metamodel.ManagedType;
import javax.persistence.metamodel.Type;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import com.impetus.kundera.metadata.model.annotation.DefaultFieldAnnotationProcessor;
import com.impetus.kundera.metadata.model.annotation.FieldAnnotationProcessor;
import com.impetus.kundera.metadata.model.type.AbstractManagedType;
/**
* Abstract class for to provide generalisation, abstraction to
* <code>Type</code> hierarchy.
*
* @param <X>
* the generic mananged entitytype
* @param <T>
* the generic attribute type
* @author vivek.mishra
*/
public abstract class AbstractAttribute<X, T>
{
/** The Constant log. */
private static final Logger log = LoggerFactory.getLogger(AbstractAttribute.class);
/** The attrib type. */
protected Type<T> attribType;
/** The attrib name. */
private String attribName;
/** The persistence attrib type. */
private PersistentAttributeType persistenceAttribType;
/** The managed type. */
private ManagedType<X> managedType;
/** The member. */
protected Field member;
/** Column name */
private String columnName;
/** Name of Table, to which this attribute belongs to */
private String tableName;
private FieldAnnotationProcessor fieldAnnotationProcessor;
/**
* Instantiates a new abstract attribute.
*
* @param attribType
* the attrib type
* @param attribName
* the attrib name
* @param persistenceAttribType
* the persistence attrib type
* @param managedType
* the managed type
* @param member
* the member
*/
AbstractAttribute(Type<T> attribType, String attribName,
javax.persistence.metamodel.Attribute.PersistentAttributeType persistenceAttribType,
ManagedType<X> managedType, Field member)
{
this.attribType = attribType;
this.attribName = attribName;
this.persistenceAttribType = persistenceAttribType;
this.managedType = managedType;
this.member = member;
this.columnName = getValidJPAColumnName();
this.fieldAnnotationProcessor = new DefaultFieldAnnotationProcessor(member);
this.fieldAnnotationProcessor.validateFieldAnnotation(
fieldAnnotationProcessor.getAnnotation(Column.class.getName()), (Field) member, this.managedType);
this.tableName = getTableName();
}
/*
* (non-Javadoc)
*
* @see javax.persistence.metamodel.Bindable#getBindableType()
*/
public abstract javax.persistence.metamodel.Bindable.BindableType getBindableType();
/*
* (non-Javadoc)
*
* @see javax.persistence.metamodel.Attribute#isCollection()
*/
public abstract boolean isCollection();
/*
* (non-Javadoc)
*
* @see javax.persistence.metamodel.Bindable#getBindableJavaType()
*/
public Class<T> getBindableJavaType()
{
return attribType.getJavaType();
}
/*
* (non-Javadoc)
*
* @see javax.persistence.metamodel.Attribute#getName()
*/
public String getName()
{
return attribName;
}
/*
* (non-Javadoc)
*
* @see javax.persistence.metamodel.Attribute#getPersistentAttributeType()
*/
public javax.persistence.metamodel.Attribute.PersistentAttributeType getPersistentAttributeType()
{
return persistenceAttribType;
}
/*
* (non-Javadoc)
*
* @see javax.persistence.metamodel.Attribute#getDeclaringType()
*/
public ManagedType<X> getDeclaringType()
{
return managedType;
}
/*
* (non-Javadoc)
*
* @see javax.persistence.metamodel.Attribute#getJavaMember()
*/
public Member getJavaMember()
{
return member;
}
/*
* (non-Javadoc)
*
* @see javax.persistence.metamodel.Attribute#isAssociation()
*/
public boolean isAssociation()
{
return persistenceAttribType.equals(PersistentAttributeType.MANY_TO_MANY)
|| persistenceAttribType.equals(PersistentAttributeType.MANY_TO_ONE)
|| persistenceAttribType.equals(PersistentAttributeType.ONE_TO_MANY)
|| persistenceAttribType.equals(PersistentAttributeType.ONE_TO_ONE);
}
/**
* Returns assigned jpa column name.
*
* @return column name jpa column name.
*/
public String getJPAColumnName()
{
// In case of Attribute override.
Column column = ((AbstractManagedType) this.managedType).getAttributeBinding(member);
if (column != null)
{
columnName = column.name();
}
return columnName;
}
/**
* Returns assigned table name.
*
* @return table name.
*/
public String getTableName()
{
return ((DefaultFieldAnnotationProcessor) fieldAnnotationProcessor).getTableNameOfColumn();
}
/**
* Gets the valid jpa column name.
*
* @param entity
* the entity
* @param f
* the f
* @return the valid jpa column name
*/
private final String getValidJPAColumnName()
{
String name = null;
if (member.isAnnotationPresent(Column.class))
{
Column c = member.getAnnotation(Column.class);
if (!c.name().isEmpty())
{
name = c.name();
}
}
if (member.isAnnotationPresent(Temporal.class))
{
if (!member.getType().equals(Date.class))
{
log.error("@Temporal must map to java.util.Date for @Entity(" + managedType.getJavaType() + "."
+ member.getName() + ")");
return name;
}
}
else if (member.isAnnotationPresent(JoinColumn.class))
{
JoinColumn c = member.getAnnotation(JoinColumn.class);
if (!c.name().isEmpty())
{
name = c.name();
}
}
else if (member.isAnnotationPresent(CollectionTable.class))
{
CollectionTable c = member.getAnnotation(CollectionTable.class);
if (!c.name().isEmpty())
{
name = c.name();
}
}
return name == null ? getName() : name;
}
public FieldAnnotationProcessor getFieldAnnotation()
{
return fieldAnnotationProcessor;
}
public void setColumnName(final String columnName)
{
this.columnName = columnName;
}
}
|
Gary Bettman has aged badly since he signed his first CBABy New York World-Telegram and the Sun Newspaper Photograph Collection staff photographer
Yesterday there was a flurry of CBA proposals made by the NHLPA. Today, one came from another source: Twitter user @67sound. It's an interesting proposal -- unlike the overwhelming majority of the fan/media proposals, it actually works to deliver what the players and owners say they need. So I want to break down how it works.
The basic stances of the two sides have been made clear. The owners want a 50/50 split of hockey-related revenue (HRR). The players are open to a 50/50 split but do not want a rollback (or the equivalent increase in escrow withholdings) of their existing contracts, which add up to more than 50%. The owners say the drop to 50/50 needs to be effective immediately to save certain struggling franchises.
What the new proposal suggests is that the cap, floor, and escrow calculations be based on a 50/50 split, but that teams be permitted to spend more than that if they choose. Teams could spend up to the current $70.2M, but the excess over the 50/50 split would come out of their own share of the revenues rather than affecting what other owners and players get.
Let's go through some numbers to illustrate how that works.
The soft cap system
The NHL's proposal of a 50/50 split estimated that the cap would be $59M. That means that they estimate that having player salary and bonuses total $1.53B would mean that their share (including benefits) was 50% of HRR. So if the player salaries add up to more than $1.53B (it's currently $1.76-1.82B depending how many bonuses get hit), under the league's proposal each player would give back ~13-15% of their salary via escrow to reduce their total to $1.53B.
This proposal suggests setting a soft cap at $59M and a hard cap at $70.2M, and if a team decides it wants to spend over the soft cap, the excess will come out of their share instead of the players's share, which would mean that it is removed from the escrow withholding calculation. So using the current salaries, it would look something like this (assuming half of performance bonuses end up getting paid):
So escrow would withold from each salary the amount required to reduce the total amount below the red line from $56.3M per team to $51M per team. Here is how the calculation of escrow witholdings under this proposal compares to the NHL's flat 50/50 proposal:
This is how we calculate how much money each team receives, to achieve the desired goal of having expenditures over $59M come from the individual owner's pocket instead of the collective owners' pool. Obviously, it can't be how we calculate the withholdings from each individual -- if Buffalo ($75M payroll) and Toronto ($59M) stripped the same $5.6M from their players, the percentage in Toronto would be much larger and a player with a $3M contract there would find himself taking home less money than his $3M counterpart on the Sabres. Instead, we add the total money withheld ($160M) and work out that each player's salary would be reduced by 9% (or less if there is appreciable revenue growth).
So the players don't reach their goal of exactly preserving current the contracted salary, but doing so would actually mean giving them an effective raise, since escrow has always reduced their contracts by a bit. We don't have the 2011-12 figures yet, but in the three previous years escrow withholding reduced their take-home pay by an average of 8.2%. So giving back 9% this year is consistent with what they should have expected when they signed the contracts.
The unequal payout to teams of the withheld money results in a bit of a redistribution. Under this scheme, the Islanders' player costs are being reduced by about 10% (they get back $4M on about $42M payroll), while the Sabres' player costs are being reduced by only 7% ($5.6M back on $75M payroll). This is in keeping with the players' goal of shared sacrifice, having the wealthy teams pitch in a little more in revenue sharing rather than demand that the players bear all the burden of supporting the poorer teams.
Does this deal work?
Here's how it looks from each party's perspective:
The large-market teams are accepting increased costs over the NHL proposal, but in return they gain a competitive advantage that they have shown (through their decision to take on those high-salary players) they value more than the cost reduction.
The small-market teams are also getting slightly increased costs over the NHL proposal, but not by much. This might be acceptable, but it was actually not what @67sound had intended; he was thinking that their costs would match the NHL proposal. In private conversation he suggested a more sloped distribution of the withholdings distribution akin to the NBA luxury tax, with the teams that spend above the $59M limit receiving none of the withholdings and their share being used to increase payments to teams in smaller markets. This is a detail that could be negotiated within the framework of this approach.
The players are taking a bit of a reduction in salary, but nothing beyond what they should have expected when they signed their contracts. Since their current salaries total quite a bit more than 50% (thanks in part to the trend in recent years toward front-loaded contracts), maintaining their current pay without escrow seems unlikely; it is hard to see them getting much more money than this.
Each party gets most of their primary desires. That's not an easy thing to achieve, no matter how many people say they have a simple solution. The thresholds might be adjusted a bit during the negotiation process, but this generally seems like a decent framework for negotiation.
Bettman stormed out of the board room yesterday and was clearly angered at the players proposal. I think his head might explode if the players ever came back proposing a soft cap system.
The problem is, this goes against everything the owners have argued for in the last CBA negotiation. The owners want a fixed cost system because their competitive egos won't let them control their own spending. They want to fix costs at the lowest possible number. Furthermore, this is a horrible deal for small market franchises because they will have a harder time being competitive as salaries for the top players will be driven up.
Also, how long does this "soft cap" system remain in place? Is it permanent? Does the hard cap ($70.2M) rise with revenues?
Ah, yeah, I failed to make that last part clear: this is basically a short-term fix, since they're both agreed on a 50/50 split in the long run. The $70.2M figure is fixed, and goes away once HRR is high enough that the 50/50 split puts a cap above $70M.
I don't agree that it goes against everything the owners have argued for. They still have cost certainty, every bit as much as they do today. Costs won't exceed the greater of $70.2M or 50% of HRR. That's lower than what was negotiated in the previous CBA (which would have it at 57%, $70.2M this year and rising), so it seems like this is a clear gain, not the step backwards you are painting it as.
We know that some small-market franchises want to reduce their spending considerably from its current levels. You are suggesting that giving them that option is a horrible deal for them unless we also rule that the large-market franchises have to reduce their spending as well -- which obviously means a substantial reduction in player salaries. If giving them lower costs and more revenue sharing (as this proposal does) is a horrible deal for them because it doesn't also reduce the costs for the large market teams, then you're basically just anti-player. Since the league is already making a healthy profit as a whole and the players are giving back still more money in this proposal, I find your stance extreme.
I still assume Bettman stormed out of the room in anger because the PR guys told him to never let on that the NHLPA had made any concessions, to paint the players as the obstinate ones refusing to meet in the middle. For all we know, he was on the phone with Fehr 20 minutes later talking about the minor concessions he needed to see to reach a deal.
So I spent this whole article explaining the differences between this system and the NHL's offer, but it also bears striking similarities to the players' offer number three (50/50 split but honor current contracts).
The changes to that offer are:
1) "Honor current contracts" doesn't mean pay them in full; it means pay them at roughly the level they would've ended up getting paid under the old CBA.
2) Since that increases the players share to a level that the NHL says small markets can't afford, increase revenue sharing to make up most of the difference (or all, if desired).
3) Since that takes money from the high-spending teams, give them a bit more competitive advantage as a carrot (and a good chance at revenue increases that more than offset what they are giving away).
If the players really won't accept any reduction of their salary by any mechanism, then we probably really are at an impasse, because that would mean they're asking for a significant _raise_ in year 1 when the owners are saying they need cuts. This offer, which keeps things roughly level for them, is probably all they can reasonably ask for. The small markets are getting everything they've asked for (unless you subscribe to the theory that the Islanders expect a structure that allows them to remain competitive while spending $35M).
It really boils down to whether the large market teams can live with the trade-off of money for competitive advantage -- so far, everything in the free agency era says they'll make that trade every day of the week, but perhaps how they see things at CBA negotiation time is different from how they see things on July 1. |
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The express journey of Warren Mundine from shining new hope of indigenous etc etc to vague embarrassment continued apace this week, with his recent speech in Queensland arguing for — well, for a whole pile of stuff that contradicts a lot of what he’s been going on about for years, and would be disastrous to boot.
Mundine would like the defining of Aboriginal identity as a special characteristic to become even more complex and entailed than it already is, to create an overarching native title eligibility that appears to me to be legally incoherent.
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Best of all, he wants to abandon the drive for a single treaty between indigenous and non-indigenous Australians, and have one with each of the hundreds of Aboriginal nations that existed pre-1788, of which more in a sec.
Indeed, Mundine wants to dissolve collective Aboriginal identity altogether and have Aboriginal people claim their second citizenship as that of a specific nation. He wants that process to be “transparent”, based on being able to trace your ancestry to that nation.
At which point, I can’t even.
OK, let’s start with the basics. A people is not constituted as a people by its mythopoetic origins, retrojected into the past, but by its relation to other peoples, of reciprocity, power, oppression or what have you.
The treaty Mundine wants would be a treaty arising from the “event” of January 26, 1788. On that day, Great Britain brought the Aboriginal people into being, as a unified notion, by invading them. The British didn’t invade the Eora nation, and then get a little inland and say “oh, we’ve hit the Dharag, shall we stop here or invade them too?” They occupied, and the expansion of their occupation was solely dependent on their own priorities.
So those are the people any treaty would be between — between the invaders and the invaded. It doesn’t make sense as a treaty in any other conception. There may well be an argument for separate treaties between non-indigenous Australians and Aborigines, and non-indigenous and Torres Strait Islanders owing to their clear, separate material history, but that’s about it.
To say that invasion constitutes a people in their collectivity shouldn’t be taken as a slur or a diminishment, obviously. Collectivity born in struggle is a step towards self-determination. What Mundine is proposing is to decompose it back to the social form of smaller geographical groups defined against each other, rather than being defined against whites.
Secondly, let’s look at these “nations” that Mundine wants to trace back to. Are they real? Are they a fiction? They are both. The term “nation” was adopted in recent decades to get away from inaccurate talk of “tribes”, and to recognise that, over geographic and language areas, tribes and smaller groups saw themselves as part of a larger whole.
“Mundine clearly means well, has a long history of struggle, but his ideas come like bubbles, tested with no one, and are in a speech the next day.”
But the term is also misleading. Firstly, it was adopted from the Native American usage. But Native Americans were a semi-agricultural people with vestigial class structures, aristocratic hierarchies, and super-chiefs who were not unlike kings. Power extended across wide areas, which is why they were able to mount a more explicit resistance to white settlers, something they could know as a war. Even so, the nationness of a lot of these nations only fully emerged as a product of the struggle with whites.
In Aboriginal Australia, hunter-gatherer/kinship societies, no such hierarchies emerged — or could, given the absence of agriculture. Aboriginal groups were knit together by the most head-spinningly complex system of kinship relations, totem animals, taboos, obligations, gift-giving circles and rules of marriage (one of the most damaging things of the destructive ignorance of people like Gary Johns is their simple disdain for this history. They construct Aboriginality as simple absence, waiting for whites).
So what were these larger ensembles? Well, there is no word for them, because they were no one thing. They could break apart and recombine, internally divide, and suffer, it would seem, sudden derecognition. They interleaved territorially sometimes and became tightly bounded in others. Nation has been used as a catch-all term, in part to remove the primitivist associations of “tribe”. But some of those who have pushed its use, from the Left, are guilty of a current confection for simplistic political purposes.
Thus what Mundine is proposing is a series of treaties between a real and powerful entity, the Australian state, and a series of historically retrojected ones whose current form — by people who claim allegiance to them — is very different to the sort of thing they once described. The one powerful “other” that indigenous people have in relation to the settler state — their collective being — would be taken out of the equation. Sheer genius.
Oh, and there’s also the transparent establishment of identity. Jaysus. Getting the voting rolls for the Aboriginal and Torres Strait Islander Commission established was hard enough; this would be … well, never-ending and never settled. Mundine’s argument is really sinister here — he wants to remove the notion of communal association as defining indigenous identity and substitute some sort of bloodline, like an aristocratic descent. There’s a lot of old junk bound up in this: a rebiologisation of race, a touch of noble savagery, a political attempt to exclude urban mixed-heritage Aboriginal people — and a dangerous tilt towards pedigree, to rendering race as a category of physicality, rather than as a historical and material identity.
But it gets weirder, because Mundine would like to abolish the continuous connection provision in native title. So you have to have a pedigree to have nationhood identity, but no continuous connection with the land. The continuous connection provision is too restrictive in many ways, but unless I’m mistaken, Mundine’s arrangement would result in people with uncheckable claims to pedigree in an oral culture being able to make claims on territory remote from them, whose “nation” provenance has been established through scholarship that often involves a bit of guesswork. Is that the transparency Mundine is after? That Aboriginal people would want to continue and strengthen the particularity of such nations is necessary and good. But Mundine’s approach would deaden, bureaucratise and hierarchise the process.
Good god, what a mess. What an utter confused farrago — from a government adviser who was hired for his alleged no-nonsense approach to material conditions, jobs, health, the Protestant ethic, etc, etc. This is another screw-up by the Abbott government it would seem because … Mundine clearly means well, has a long history of struggle, but his ideas come like bubbles, tested with no one, and are in a speech the next day.
Most likely, this will be another opportunity for Tony Abbott to say, “No. we won’t be doing that”. How long before Mundine is quietly asked to announce that he is resigning to “pursue other opportunities”?
This crisis will cut hard and deep but one day it will be over.
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Kyle Webb
Norman Hanscombe
One has to concede the whole indigenous issue has long been a farrago, but it seems that it’s only when the dreamers encounter someone saying something which doesn’t help their various noble causes that it’s noticed.
Kyle Webb
Hi 20/20, that’s a great point. There’s a problem with that, in that certain individuals who have a set of ideological leanings (although, not an inherently bad thing) are given more platform and voice over Indigenous policy. This has effectively created a bit of a stranglehold on dialogue between Indigenous and non-Indigenous people, and limited the debate in a way the preferences aforementioned ideological viewpoints. |
756 N.W.2d 320 (2008)
2008 ND 178
Jody DRAYTON, Claimant and Appellee
v.
WORKFORCE SAFETY AND INSURANCE, Appellant and
WW Wallwork, Inc., Respondent.
No. 20070281.
Supreme Court of North Dakota.
September 25, 2008.
*322 David A. Garaas, Garaas Law Firm, Fargo, N.D., for claimant and appellee.
Jacqueline Sue Anderson, Special Assistant Attorney General, Fargo, N.D., for appellant.
SANDSTROM, Justice.
[¶ 1] Workforce Safety and Insurance ("WSI") appeals from a district court judgment reversing a WSI order reinstating Jody Drayton's disability benefits to the date of their termination and awarding her attorney's fees. We conclude that WSI appropriately exercised its continuing jurisdiction to assess Drayton's vocational rehabilitation; that Drayton was properly found in noncompliance with vocational rehabilitation; and that a reasoning mind could reasonably find Drayton intentionally manipulated the results of a functional capacity assessment and engaged in "a first instance of noncompliance" with vocational rehabilitation without good cause. We also conclude the district court erred in awarding Drayton attorney's fees under N.D.C.C. § 28-32-50. We therefore reverse the district court judgment and reinstate WSI's order discontinuing Drayton's temporary disability benefits.
I
[¶ 2] In August 1993, Drayton was injured in a motor vehicle accident while employed by W.W. Wallwork, Inc. Drayton filed a claim for workers compensation benefits, which was accepted. Drayton was subsequently unable to continue in her employment. In August 1997, Drayton was offered a modified job at Wallwork as a delivery coordinator based upon 1997 work restrictions from her chiropractor. Drayton refused this position. In November 1997, WSI suspended her partial disability benefits after she failed to return to work and did not accept a modified position. In November 1997, Drayton obtained employment with Jim Drayton Insurance, her husband's insurance agency, and WSI then began paying her temporary partial disability benefits based upon her earning capacity at that time.
[¶ 3] In December 2005, WSI began an internal review of her claim, gathering information on her current diagnosis and work release status. In January 2006, WSI received a letter from her chiropractor, Dr. Vincent Rokke, providing her present diagnosis included continuing neck and back pain, and specifically stating "cervical, thoracic and lumbar segmental dysfunctions resulting in myofascial pain in each region, left cervicobrachial syndrome and intermittent sciatica." Dr. Rokke said her treatment was unlikely to change from a palliative nature, or just easing her pain symptoms, requiring periodic chiropractic adjustments for pain management. Dr. Rokke stated that he did not believe a work-conditioning program would be effective in increasing Drayton's workday tolerance.
[¶ 4] In April 2006, WSI told Drayton to attend a functional capacity assessment ("FCA") at MeritCare Occupational Health. In May 2006, occupational therapist Bryce Nelson conducted an FCA and concluded in part that the result was invalid as a manipulated effort. On June 23, 2006, WSI issued an order suspending disability benefits and establishing a "first instance of noncompliance" with vocational rehabilitation, under N.D.C.C. § 65-05.1-04, permitting WSI to discontinue benefits if noncompliance continues. Drayton requested a hearing from that order. In July 2006, another FCA was scheduled at *323 MeritCare Occupational Health. Occupational therapist Dianne Nechiporenko conducted this FCA, concluding that the FCA was invalid on portions that Drayton had completed and that Drayton did not complete all of the FCA's portions.
[¶ 5] An evidentiary hearing was held in February 2007. After the hearing, the administrative law judge ("ALJ") recommended affirming WSI's June 2006 order suspending Drayton's disability benefits, which had found Drayton had engaged in a first instance of noncompliance without good cause:
11. ... On April 14, 2006, Dr. Rokke approved of Ms. Drayton's participation in the FCA.
12. WSI directed Ms. Drayton to attend an FCA at MeritCare in Fargo on May 12, 2006. The FCA was conducted by Bryce Nelson. Mr. Nelson determined Ms. Drayton had a spinal injury based upon his review of her medical records and because he asked her and she reported her injury involved her low back, neck, tailbone, and left arm as well as a closed head injury. He concluded the FCA Ms. Drayton participated in on May 12, 2006, was invalid and represented a manipulated effort based upon the protocols for determining validity of the test.
13. Mr. Nelson is a licensed occupational therapist with a bachelor of science degree from the University of North Dakota. He has been working at MeritCare for 16 years. He received initial training and has attended annual conferences in administering the Key Functional Assessment protocol (KFA). Mr. Nelson receives referrals to perform the KFA from WSI as well as from attorneys, chiropractors, physicians, and self-referrals for SSDI applications. He has done approximately 2500 FCAs using the KFA protocol. When he receives a referral he looks at the medical records to determine the area of injury, the diagnosis and medications being taken. Medications are considered in part because some medications affect heart rate and the KFA uses increase in heart rate as one of the indicators to determine consistency. He instructs each participant to pay attention to what they are doing and stop before they hurt themselves. He also tells them that he does not want them to overwork or under work themselves. He tells each of the assessment participants to let him know "what is going on," "when it is going on" and "when they need to stop." Testimony of Bryce Nelson.
. . . .
16. The May 12, 2006, FCA results in Ms. Drayton's case revealed many inconsistencies. She demonstrated an ability to stand for only one minute, but was able to walk for several minutes during a break immediately before the standing test. Her grip dynometer measurements were inconsistent with expected measurements, specifically the mid-grip measurement not being the largest. Ms. Drayton's heart rate never increased the expected 20 beats when lifting or 40 beats when climbing stairs. She only performed 2 repetitions of the foot pedal, but was able to walk up and down seven steps, which was more physically demanding. She could only do a half squat when asked to squat, but was able to do a full squat when lifting something from the floor with a container. When asked to walk she could only walk ten feet before she had to stop, yet on her breaks she walked more than a 100 feet. Moreover walking from station to station during the evaluation involved more than ten feet of walking. Mr. Nelson noted that during the squat Ms. Drayton said she might need to quit, so *324 he gave her the first break at which point she walked out the door and walked down the street to a point where he could no longer see her. With regard to pain reports, Mr. Nelson noted that she was able to spontaneously rotate her neck and flip her hair back. She reported pain when lifting 30 inches to 18 inches, but did not report pain lifting above her shoulders, a task that requires greater effort. Mr. Nelson also noted inconsistency when comparing how she moved as though limited during the test but walked freely during the breaks. He observed her sitting for 21 minutes while answering questions during the assessment. (Footnotes omitted.)
17. Bryce Nelson approved Ms. Drayton for receptionist and information clerk, customer service representative, and telemarketers positions if her sitting tolerances and workday tolerances were followed. The basis for Mr. Nelson's approval of these positions was the May 12, 2006, FCA results. Mr. Nelson felt she could do these jobs based upon the May 12, 2006, FCA even though it did not represent a true measure of her capabilities, because she demonstrated the ability to sit for 20 minutes, and she demonstrated that she could stand, walk, and sit during the three hours it took for the FCA. Mr. Nelson did not approve office clerk because this was in the light level of work. Mr. Nelson did not believe that Ms. Drayton could do an office clerk's job based upon the FCA because it requires her to lift more than she demonstrated. He acknowledged that Dr. Rokke says she could lift 30 pounds, but disputes the validity of this claim because it was not based upon any testing.
. . . .
19. On May 12, 2006, after the FCA, Ms. Drayton went to Dr. Rokke because she was having pain in her low back, mid-back and lower cervical spine. Dr. Rokke's notes reflect that she told him she had been having increasing symptoms since May 7, 2006, but that she attended an FCA that day and "pushed herself slightly." Pg. 519. Ms. Drayton reported to WSI that she could not drive home for a couple of hours after the FCA, but that May 12, 2006, was otherwise not different from any other day.
20. On May 23, 2006, WSI issued an order terminating Ms. Drayton's benefits for failure to comply with vocational rehabilitation without good cause. When Ms. Drayton requested a reconsideration, she stated she had been having pain before the FCA and she was not feeling well on the day of the FCA. She asked to repeat the FCA but requested a different evaluator.
21. Dianne Nechiporenko performed the second FCA on July 18, 2006, because she is the back up and a different therapist was requested. Additionally, Ms. Nechiporenko performed the FCA because when there is an invalid result, MeritCare has a policy to have the second assessment performed by another therapist who can bring a fresh view to the assessment. Ms. Nechiporenko instructed Ms. Drayton to tell her what was going on, when it was going on, when she thought she needed to stop and why she needed to stop.
22. Ms. Nechiporenko is an occupational therapist. She has been practicing in this field for 25 years. She has a certification in the Key Functional Assessment process and has completed between 50 and 100 KFAs. Currently she is a supervisor working mostly with hand therapy. She performs therapy only 5% of the time.
*325 23. The July 18, 2006, FCA was not completed because Ms. Drayton terminated early. During the second FCA, Ms. Drayton took her first break after only 10 minutes, her second after 30 minutes and she terminated after that break. She completed only 13 of the test components. While Ms. Drayton did not complete enough of the FCA to determine an appropriate job, she did complete enough to determine that her efforts were inconsistent and that the FCA result was an invalid FCA. Ms. Drayton's test on the grip dynometer was the only valid test, but she only performed that one time because she terminated the test early. Ms. Drayton also demonstrated the ability to sit for 30 minutes. The other results of the second FCA were, like the results of the first, inconsistent. Ms. Drayton's heart rate did not become sufficiently elevated, her weights lifted did not follow the expected pattern, and the difference between the weights on the resistance dynometer were too great. Ms. Drayton's reports of pain were also inconsistent. She reported needing to lay down, but continued to walk around when given a break. Her "pain complaints were all over the map." Testimony of Ms. Nechiporenko. Ms. Nechiporenko acknowledged that the term "manipulated effort" was a term used by Key to define an invalid test result, but that there was no way to tell if the manipulation was conscious. (Footnotes omitted.)
24. Because the July 18, 2006, FCA results could not be used to establish work guidelines, Ms. Nechiporenko, disapproved all of the four positions identified... for Ms. Drayton.
The ALJ also recommended, in part, the following conclusions of law:
7. The Key Functional Assessment system makes a record of circumstantial evidence that can be considered in determining if an individual's actions were intentional or not. The KFA system uses inconsistencies to determine invalidity of test results. It also uses objective measurements of heartbeat and weights to determine if an individual is making an effort and performing the test to the best of their ability. In this case, Ms. Drayton's conduct at the May 18[sic], 2006, FCA was inconsistent when she was asked to walk for the test she refused due to pain, but her pain did not stop her from walking around the building during her break just prior to this request. Her heart rates were not near the expected rate that would show either that she was putting forth an effort or was having increased pain. Her behavior at the second FCA was not any more cooperative. She did not deny or even explain any of the findings of the FCA or any of the activities attributed to her when she testified other than to say she was having pain. But that assertion is not borne out by anything objective. Despite her claims of increased pain her pulse remained low, and her actions and pain complaints were not consistent. Both Ms. Drayton's FCA results were determined to be invalid based upon objective measurements. Neither Mr. Nelson nor Ms. Nechiporenko would determine that the manipulation was intentional. But that determination is not, as contended by Ms. Drayton, a medical determination that requires a doctor's opinion. Whether Ms. Drayton intentionally manipulated her test results must be determined by looking at the circumstances and her conduct. [Dean v. North Dakota Workers Comp. Bur., 1997 ND 165, ¶ 20, 567 N.W.2d 626.] Considering all of the evidence in the record and especially the many inconsistencies and obvious failures to perform (e.g. refusing to *326 walk more than 10 feet when she had just walked more than 100 is a particularly troubling result) at either of the FCA's that is it is not difficult to conclude that the greater weight of the evidence in this case shows that Ms. Drayton willfully failed to participate to her fullest capacity in the FCAs.
8. With regard to whether there is sufficient evidence to support WSI's June 23, 2006, order, I conclude that considering all of the evidence in the record, the greater weight of the evidence shows that Ms. Drayton did not comply with the order to participate in the May 18[sic], 2006, FCA because she did not give a maximum consistent effort.
9. Ms. Drayton has also not demonstrated that she had good cause to fail the FCA. In part, this is a reflection of her argument that WSI is only in the "investigative" stages of the vocational rehabilitation process and therefore cannot impose the first instance of noncompliance penalty and her position that she did not fail to cooperate. But even if she had argued that she had good cause, I find that, when compared to her behaviors during the testing and on her breaks, the inconsistencies in her test results, do not support her claims that it was her pain that caused her to have inconsistent assessment results. (Footnote omitted.)
[¶ 6] WSI adopted the ALJ's recommended decision, concluding WSI had jurisdiction to issue its June 2006 order, the 2005 version of the relevant statutes applied, the greater weight of the evidence showed Drayton willfully failed to participate to her fullest in the FCAs, and Drayton did not demonstrate "good cause" for her failure to apply maximum consistent effort in the FCAs.
[¶ 7] Drayton appealed WSI's final order to the district court. The district court reversed WSI's final order. The court held that WSI's continuing jurisdiction is limited, administrative res judicata precluded WSI from changing Drayton's benefits, WSI's actions violated due process, and WSI failed to properly analyze and explain the evidence. The court also awarded Drayton attorney's fees under N.D.C.C. § 28-32-50. WSI appealed to this Court.
[¶ 8] Drayton's appeal to the district court was timely, and the district court had jurisdiction under N.D. Const. art. VI, § 8, and N.D.C.C. §§ 27-05-06, 65-10-01, and 28-32-42. WSI's appeal was timely under N.D.R.App.P. 4(a) and N.D.C.C. § 28-32-49. This Court has jurisdiction under N.D. Const. art. VI, §§ 2 and 6, and N.D.C.C. § 28-32-49.
II
[¶ 9] Under the Administrative Agencies Practice Act, N.D.C.C. ch. 28-32, courts exercise only a limited review in appeals from administrative agency decisions. Tverberg v. Workforce Safety and Ins., 2006 ND 229, ¶ 7, 723 N.W.2d 676. Under N.D.C.C. §§ 28-32-46 and 28-32-49, the district court, and this Court on further appeal, must affirm an administrative agency decision unless:
1. The order is not in accordance with the law.
2. The order is in violation of the constitutional rights of the appellant.
3. The provisions of this chapter have not been complied with in the proceedings before the agency.
4. The rules or procedure of the agency have not afforded the appellant a fair hearing.
5. The findings of fact made by the agency are not supported by a preponderance of the evidence.
*327 6. The conclusions of law and order of the agency are not supported by its findings of fact.
7. The findings of fact made by the agency do not sufficiently address the evidence presented to the agency by the appellant.
8. The conclusions of law and order of the agency do not sufficiently explain the agency's rationale for not adopting any contrary recommendations by a hearing officer or an administrative law judge.
[¶ 10] "WSI is responsible for weighing the credibility of witnesses and resolving conflicts in the evidence, and we do not `make independent findings of fact or substitute our judgment for that of the agency.'" Tverberg, 2006 ND 229, ¶ 8, 723 N.W.2d 676 (citation omitted). This Court determines only "whether a reasoning mind reasonably could have determined that the factual conclusions reached were proved by the weight of the evidence from the entire record." Power Fuels, Inc. v. Elkin, 283 N.W.2d 214, 220 (N.D.1979). However, "[t]he interpretation of a statute is a question of law." Reopelle v. Workforce Safety and Ins., 2008 ND 98, ¶ 9, 748 N.W.2d 722. Questions of law are fully reviewable on appeal from an administrative decision. Id.
[¶ 11] To determine a statute's meaning, we look to the statute's language, giving the statute's words their plain, ordinary, and commonly understood meaning. N.D.C.C. § 1-02-02. Statutes are construed as a whole and, if possible, are harmonized to give meaning to each word and phrase. N.D.C.C. § 1-02-07. If the statute's language is clear and unambiguous, "the letter of [the statute] is not to be disregarded under the pretext of pursuing its spirit." N.D.C.C. § 1-02-05.
III
[¶ 12] WSI initially contends it properly exercised its continuing jurisdiction to review and investigate Drayton's current work status and utilize vocational rehabilitation services. Drayton argues that WSI did not properly initiate vocational rehabilitation services on her claim because WSI did not file a "formal" motion under N.D.C.C. § 65-05-04 and did not provide her notice and an opportunity to respond before proceeding.
[¶ 13] Section 65-05-04, N.D.C.C., provides in part that WSI "at any time, on its own motion or on application, may review the award, and in accordance with the facts found on such review, may end, diminish, or increase the compensation previously awarded...." (Emphasis added). Additionally, N.D.C.C. § 65-05.1-01(8)(a) provides that WSI may initiate vocational rehabilitation services "on its own motion." See also N.D.C.C. § 65-05.1-01(7)(a) (1993).
[¶ 14] We have explained that "WSI has continuing jurisdiction when an original claim has been timely filed, and WSI, on its own motion or on application, may review a previous decision and may end, diminish, or increase compensation previously awarded or, if compensation has been refused or discontinued, may award compensation." Houn v. Workforce Safety & Ins., 2005 ND 115, ¶ 12, 698 N.W.2d 271 (citing N.D.C.C. § 65-05-04). Under N.D.C.C. § 65-05-04, WSI's decision whether or not to reopen a matter falls totally within its discretion. Furthermore, under this statute, "an unappealed WSI decision is res judicata unless WSI reopens the claim, but the res judicata effect extends only to matters adjudicated at the time of that decision and does not extend to future changes in the claimant's medical condition." Houn, at ¶ 12 (citing Lass v. *328 North Dakota Workmen's Comp. Bur., 415 N.W.2d 796, 800-01 (N.D.1987)).
A
[¶ 15] WSI contends no "formal" motion is necessary to assert its continuing jurisdiction or initiate vocational rehabilitation services. Drayton argues, however, that WSI did not invoke its continuing jurisdiction under N.D.C.C. § 65-05-04 by bringing "its own motion" and, further, did not institute rehabilitation services by bringing "its own motion" under N.D.C.C. § 65-05.1-01. Drayton asserts that since a "formal" motion was not brought by WSI, she was not permitted to respond to any purported reopening of her claim or award of vocational rehabilitation. Drayton also asserts that WSI's failure to bring a formal motion means that WSI only conducted an investigation as to whether the claim should be reopened or as to the appropriateness of providing rehabilitation services. In essence, Drayton suggests that while WSI is permitted to investigate her condition under these statutes, WSI did not actually reopen her claim or award rehabilitation benefits under these statutes so as to permit the consequences of noncompliance.
[¶ 16] This Court, however, has not previously interpreted the statutes to require WSI to make a formal motion to itself, with a corresponding opportunity to respond and presumably a hearing, to either investigate or reopen a claim. The phrase "on its own motion" has been interpreted as having identical meaning as the expression "sua sponte." See State v. Ham, 45 Ohio St.2d 112, 341 N.E.2d 594, 596 (1976). "Sua sponte" is defined as "`of one's own accord; voluntarily'" and "[w]ithout prompting or suggestion; on its own motion." Black's Law Dictionary 1464 (8th ed. 2004). In interpreting a court rule's use of the phrase "upon its own motion" as relating to change of venue, the court held a trial court was authorized in its discretion to voluntarily order a change of venue "without consultation with counsel and without conducting a hearing." Ham, 341 N.E.2d at 596; see also United States v. Seltzer, 127 F.Supp.2d 172, 174 (E.D.N.Y.2000) (discussing Ham, supra). Under the plain language of these statutes, the phrase "on its own motion" portends that WSI may act voluntarily, sua sponte, or on its own accord, rather than by formal motion practice. We thus conclude no formal motion is necessary for WSI to act "on its own motion" for vocational rehabilitation services under either N.D.C.C. § 65-05-04 or N.D.C.C. § 65-05.1-01.
[¶ 17] Furthermore, although Drayton suggests due process requires a formal motion, we have previously discussed due process requirements for termination of benefits. See, e.g., Rojas v. Workforce Safety & Ins., 2005 ND 147, ¶ 11, 703 N.W.2d 299; Sjostrand v. North Dakota Workers Comp. Bur., 2002 ND 125, ¶¶ 9-10, 649 N.W.2d 537; Stewart v. North Dakota Workers Comp. Bur., 1999 ND 174, ¶¶ 12-13, 599 N.W.2d 280; Tooley v. Alm, 515 N.W.2d 137, 142 (N.D.1994). In this case, however, Drayton was provided with pre-termination notice and an opportunity to respond, in addition to a full evidentiary hearing. See Beckler v. North Dakota Workers Comp. Bur., 418 N.W.2d 770, 775 (N.D.1988) (holding claimant entitled to pretermination notice that benefits would be terminated, summary of evidence supporting termination, and opportunity to respond, but not requiring pretermination evidentiary hearing). We conclude Drayton was not denied due process when WSI initiated vocational rehabilitation services without a formal motion.
B
[¶ 18] Drayton asserts that her workday limitation and other medical restrictions *329 are subject to administrative res judicata, barring WSI from exercising continuing jurisdiction and terminating her disability benefits for failure to comply with vocational rehabilitation services. In reversing WSI's order, the district court concluded administrative res judicata precluded termination of Drayton's disability benefits for noncompliance with rehabilitation services. Relying on WSI's 1997 order that determined Drayton's eligibility for disability benefits, the district court held "WSI could not require Drayton to undergo rehabilitation services as a condition precedent to receiving further disability benefits." The court held that "WSI must first determine if there is new evidence or a change in Drayton's medical condition before it can exercise continuing jurisdiction under N.D.C.C. § 65-05-04 and change Drayton's benefits." The court's decision, however, misstates our precedent on the application of administrative res judicata to WSI decisions. See Houn, 2005 ND 115, ¶ 12, 698 N.W.2d 271 ("an unappealed WSI decision is res judicata unless WSI reopens the claim, but the res judicata effect extends only to matters adjudicated at the time of that decision and does not extend to future changes in the claimant's medical condition").
[¶ 19] Generally, res judicata prohibits the relitigation of claims that were raised or could have been raised in a prior proceeding between the same parties or their privies and that were resolved by final judgment in a court of competent jurisdiction. See Ungar v. North Dakota State Univ., 2006 ND 185, ¶ 11, 721 N.W.2d 16. "Administrative res judicata is the judicial doctrine of res judicata applied to an administrative proceeding." Cridland v. North Dakota Workers Comp. Bur., 1997 ND 223, ¶ 18, 571 N.W.2d 351. This Court is more circumspect about applying administrative res judicata than judicial res judicata, "taking into account (1) the subject matter decided by the administrative agency, (2) the purpose of the administrative action, and (3) the reasons for the later proceeding." Id. In Cridland, at ¶ 29, in which a formal "trial-type" hearing led to a WSI order deciding the claimant's continued entitlement to medical and disability benefits, we stated:
The plain language of N.D.C.C. § 65-05-04, authorizes the Bureau to review an award "at any time" and "in accordance with the facts found on such review" to "end, diminish, or increase the compensation previously awarded." That language, however, does not preclude application of the doctrine of administrative res judicata to Bureau decisions entered after a formal adjudicative hearing. Although the Bureau has some discretionary authority to review previous awards under N.D.C.C. § 65-05-04, that statutory authority does not mean the Bureau can relitigate issues that were or should have been decided in a prior formal adjudicative proceeding. We are not persuaded the Legislature intended to give the Bureau unlimited authority to relitigate issues that should have been raised in a prior formal adjudicative hearing. Rather, Johnson [v. North Dakota Workers' Comp. Bur., 484 N.W.2d 292 (N.D.1992)] and N.D.C.C. §§ 65-05-04 and 65-05-29(3) must be considered in light of the doctrine of administrative res judicata, the importance of finality of agency decisions, and the purpose of the workers compensation law to provide injured workers with "sure and certain relief" to preclude the Bureau, in the absence of new evidence or a change in medical condition, from relitigating claims which were, or should *330 have been decided, in a prior formal adjudicative hearing.
(Footnote omitted.)
[¶ 20] As a part of its ongoing monitoring, WSI may initiate vocational rehabilitation services, including evaluation, if it believes it is beneficial. See N.D.C.C. § 65-05.1-01(8)(a) [N.D.C.C. § 65-05.1-01(7)(a) (1993)] (WSI is permitted to initiate rehabilitation services "on its own motion" or sua sponte). In this case, the issue is not whether Drayton continues with her disability, but rather whether she was noncompliant with vocational rehabilitation services. WSI is not attempting to relitigate the fact that Drayton is disabled. WSI has not sought to adjust or terminate Drayton's benefits on the basis of a change in her medical condition or evidence that she is no longer disabled. Rather, the issue is Drayton's noncompliance with vocational rehabilitation services and the consequences of her actions under N.D.C.C. §§ 65-05-28 or 65-05.1-04.
[¶ 21] Here, with regard to the proper application of administrative res judicata, the record does not reflect that any formal "trial-type" hearing led to WSI's November 1997 order. Further, whether additional rehabilitation services would be beneficial almost 13 years after Drayton's injury could not have been contemplated by the November 1997 order. While it does appear that some rehabilitation services were previously attempted before or about the time of the 1997 order, those attempts do not preclude initiating vocational rehabilitation services now. Cf. Fischer v. North Dakota Workers Comp. Bur., 530 N.W.2d 344, 347 (N.D.1995) (for res judicata purposes, an agency's final order corresponds with a court's final judgment, but the bureau's vocational assessment does not meet this description).
[¶ 22] We conclude administrative res judicata does not preclude WSI from either initiating vocational rehabilitation services or imposing consequences for noncompliance with those services under N.D.C.C. §§ 65-05-28 or 65-05.1-04.
C
[¶ 23] WSI argues Drayton could be properly found in noncompliance with vocational rehabilitation under N.D.C.C. § 65-05.1-04 after initiating the functional capacity assessment. Drayton contends, however, that the provisions relating to noncompliance under N.D.C.C. § 65-05.1-04(6) apply only after a vocational rehabilitation "program" has begun.
[¶ 24] We disagree with Drayton's narrow interpretation of what constitutes initiating "vocational rehabilitation services," thus invoking the application of N.D.C.C. ch. 65-05.1. Under N.D.C.C. § 65-01-02(26), "[r]ehabilitation services" are defined as "nonmedical services reasonably necessary to restore a disabled employee to substantial gainful employment" and may include "vocational evaluation, counseling, education, workplace modification, and vocational retraining...." See also N.D.C.C. § 65-01-02(27) (1993). Under N.D.C.C. § 65-05.1-01(2), "comprehensive rehabilitation services" are further defined to include "medical, psychological, economic, and social rehabilitation." Additionally, as will be discussed further, N.D.C.C. § 65-05.1-04, which defines an injured worker's responsibilities for vocational rehabilitation services, specifically contemplates a claimant's testing and medical and vocational assessment in connection with those services.
[¶ 25] When WSI initiated vocational rehabilitation services under N.D.C.C. ch. 65-05.1 for Drayton, and initiated the functional capacity assessment in April 2006, Drayton's corresponding responsibilities under N.D.C.C. § 65-05.1-04 were implicated. *331 We reject Drayton's distinction that N.D.C.C. § 65-05.1-04(6) does not apply until a rehabilitation program or plan has actually been awarded and that the FCAs in this case were mere investigation as to whether to initiate services under N.D.C.C. ch. 65-05.1. We conclude that Drayton could be properly found in noncompliance with vocational rehabilitation under N.D.C.C. § 65-05.1-04.
IV
[¶ 26] WSI argues, and the ALJ concluded, that the 2005 version of N.D.C.C. § 65-05.1-04, which was in effect on the date of Drayton's functional capacity assessment, governs the issues in this case. WSI also argues, however, that even under the 1993 version of the statutes, WSI could discontinue Drayton's disability benefits for noncompliance with vocational rehabilitation on the basis of Drayton's failure to give maximum consistent effort on her two FCAs.
[¶ 27] This Court has consistently held that "[u]nless otherwise provided, statutes in effect on the date of injury govern a claimant's right to collect workers compensation benefits." Reopelle, 2008 ND 98, ¶ 11, 748 N.W.2d 722; see also Rodenbiker v. Workforce Safety & Ins., 2007 ND 169, ¶ 16, 740 N.W.2d 831; Sjostrand, 2002 ND 125, ¶ 14, 649 N.W.2d 537; Wanstrom v. North Dakota Workers Comp. Bur., 2000 ND 17, ¶ 7, 604 N.W.2d 860; Saari v. North Dakota Workers Comp. Bur., 1999 ND 144, ¶ 10, 598 N.W.2d 174; Thompson v. North Dakota Workers' Comp. Bur., 490 N.W.2d 248, 251 (N.D.1992). In Reopelle, at ¶ 11, we explained:
That rule is an outgrowth of the requirement that statutory provisions are not retroactive unless "expressly declared to be so." N.D.C.C. § 1-02-10; White v. Altru Health Sys., 2008 ND 48, ¶ 20, 746 N.W.2d 173 (applying N.D.C.C. § 1-02-10 and Reiling v. Bhattacharyya, 276 N.W.2d 237 (N.D.1979) and stating statutory directive is clear that "[i]f a statute is to be retroactive, the Legislature must expressly declare it to be so"). However, a statutory provision may not operate retroactively to abrogate a vested right or a valid obligation. N.D.C.C. § 1-02-30; Tedford [v. Workforce Safety & Ins.], 2007 ND 142, ¶ 17, 738 N.W.2d 29; Sjostrand, at ¶ 14; Saari, at ¶ 10; Gregory v. North Dakota Workers Comp. Bureau, 1998 ND 94, ¶¶ 32-33, 578 N.W.2d 101. A vested right is an immediate or fixed right to present or future enjoyment that does not depend upon an event that is uncertain. Sjostrand, at ¶ 14; Saari, at ¶ 10; Jensen v. North Dakota Workers Comp. Bureau, 1997 ND 107, ¶ 11, 563 N.W.2d 112. A common thread connecting our cases about retroactive application of statutes and vested rights is that statutes may not be retroactively applied to discontinue or reduce benefits that a claimant had been receiving, or already had a vested right in receiving. Saari, at ¶ 17.
[¶ 28] At issue here is whether the vocational rehabilitation statutes in effect on the date of Drayton's injury govern her vocational rehabilitation, or whether the statutes in effect when the vocational rehabilitation determination is made govern her case. Some of our cases support the application of the statutes in effect when the vocational rehabilitation determination is made. See Thompson, 490 N.W.2d at 251 n. 4 (stating rehabilitation claims are made after a claimant has reached maximum medical recovery, and claimant had not demonstrated a vested right to rehabilitation under law effective at time of his injury because there was no immediate or fixed right to present or future enjoyment and which did not depend upon an event that was uncertain). See also Sjostrand, 2002 ND 125, ¶ 15, 649 N.W.2d 537 (holding *332 a determination of whether a recipient remains disabled and entitled to benefits may be made any time and a determination of continuing disability should be based on the law when the determination is made, not that in effect at the time of injury); Tangen v. North Dakota Workers Comp. Bur., 2000 ND 135, ¶¶ 15-16, 613 N.W.2d 490 (holding 1995 amendment to statute applied to claimant's reapplication for aggravation benefits, while date of original injury was 1992); Snyder v. North Dakota Workers Comp. Bur., 2001 ND 38, ¶ 9, 622 N.W.2d 712 (applying subsequent amendments of N.D.C.C. § 65-05-08(3) requiring monthly reports despite not having been in effect on date of injury). In Rodenbiker, 2007 ND 169, ¶ 16, 740 N.W.2d 831 (applying law in effect in March 2000, despite functional capacity assessments in 2002 and 2003), this Court recently said the statute in effect on the date of the claimant's injury applied to vocational rehabilitation services. In Rodenbiker, this Court stated:
Two statutes are central to this case: N.D.C.C. § 65-05.1-01 and N.D.C.C. § 65-05-10. The parties mistakenly agreed that the 2003 version of the statutes was the appropriate version to apply to Rodenbiker's claim. However, the applicable statutes are those effective on March 2000, the date Rodenbiker suffered her work-related injury.... Thus, the 1999 versions of N.D.C.C. § 65-05.1-01 and N.D.C.C. § 65-05-10 apply to this case. Although those statutory provisions were amended between 1999 and 2003, the amendments did not relate to eligibility for partial disability benefits and do not affect the outcome of this case.
Rodenbiker, at ¶ 16 (citing Robertson v. North Dakota Workers Comp. Bur., 2000 ND 167, ¶ 21, 616 N.W.2d 844 and N.D.C.C. § 1-02-10).
[¶ 29] In this case, however, as in Rodenbiker, even if we agreed with Drayton's assertion that the 1993 version of the statutes apply, we conclude that WSI properly discontinued Drayton's benefits on the basis of WSI's findings of Drayton's willful noncompliance with vocational rehabilitation services.
[¶ 30] WSI asserts a reasoning mind could reasonably determine that Drayton intentionally manipulated the results of the functional capacity assessment and, therefore, engaged in a first instance of noncompliance without good cause. In reversing WSI's order, the district court concluded that WSI failed to properly analyze and explain the evidence. Here, the ALJ concluded that on the basis of the evidence, WSI properly terminated Drayton's benefits under N.D.C.C. §§ 65-05.1-04 and 65-05-28(4). Although the ALJ applied the 2005 version of the statutes, and WSI adopted the ALJ's decision as its final order, the ALJ made sufficient findings to sustain WSI's termination under either the 1993 or 2005 statutes.
[¶ 31] Specifically, N.D.C.C. § 65-05.1-04(6) (1993) provides, in part:
If, without good cause, the injured employee fails to attend a scheduled medical or vocational assessment, or fails to attend a specific qualified rehabilitation program within ten days from the date the rehabilitation program commences, the employee must be deemed to be in noncompliance with vocational rehabilitation.... If the employee establishes a pattern of noncooperation as heretofore described, involving two or more incidents of noncooperation, subsequent efforts by the employee to come into compliance with vocational rehabilitation may not be deemed successful compliance until the employee has successfully returned to the job or training program for a period of sixty days. In all cases *333 of noncompliance by the employee, the bureau, by administrative order, shall discontinue lost-time benefits. If, upon the bureau order becoming final, the period of noncompliance continues for sixty days, the bureau has no further jurisdiction in awarding any further temporary total, temporary partial, permanent total, or vocational rehabilitation benefits.
(Emphasis added.) See also N.D.C.C. § 65-05.1-04(3) (1993) ("The injured employee shall be available for testing under subsection 6 or 7 of section 65-05.1-02, and for any further examinations and testing as may be prescribed by the bureau to determine whether or not a program of rehabilitation is necessary."); N.D.C.C. § 65-05-28(4) (1993) (providing, in part: "If an employee ... refuses to submit to, or in any way intentionally obstructs, any examination, or refuses reasonably to participate in medical or other treatments, the employee's right to claim compensation under this title is suspended until the refusal or obstruction ceases."); Zueger v. North Dakota Workers Comp. Bur., 1998 ND 175, ¶ 13, 584 N.W.2d 530 ("We have held that a claimant who attempts to manipulate an FCE by willfully failing to perform to the full extent of his or her abilities can be found to have intentionally obstructed the test, and benefits may be suspended under N.D.C.C. § 65-05-28(4).").
[¶ 32] We have held that a willful failure to give a maximum consistent effort in a functional capacity assessment can constitute noncompliance with vocational rehabilitation under N.D.C.C. § 65-05.1-04(6). See Thomas v. Workforce Safety & Ins., 2005 ND 52, ¶ 6, 692 N.W.2d 901; see also Hoffman v. North Dakota Workers Comp. Bur., 2002 ND 138, ¶ 21, 651 N.W.2d 601 ("the word `attend' in the statute clearly contemplates not only a mere physical presence, but also participation in the medical or vocational assessment"). We reject Drayton's contention that under the 1993 version of N.D.C.C. § 65-05.1-04(6), WSI must prove a pattern of noncooperation. Under the statute's plain language, it is when the employee has established a pattern of noncooperation that additional conditions are imposed before the employee may be again considered successfully in compliance with vocational rehabilitation. WSI, on the other hand, is authorized to discontinue benefits in all cases of the employee's noncompliance. In Hoffman, at ¶¶ 14-15, this Court also explained:
[A] "claimant has good cause for failing to attend a rehabilitation program if the claimant has a reason that would cause a reasonably prudent person to refuse to attend the rehabilitation program under the same or similar circumstances." Whether a claimant has "good cause" under the statute is determined under an objective, reasonable person standard.... [T]he Bureau also has the burden of showing noncompliance with a rehabilitation plan. Once the Bureau establishes noncompliance, it becomes the claimant's burden to establish good cause for noncompliance.
(Citation omitted.)
[¶ 33] Here, WSI found that relying on the evidence in the record, including testimony of the occupational therapists who performed the FCAs, and considering "the many inconsistencies and obvious failures to perform [on the FCAs] (e.g. refusing to walk more than 10 feet when she had just walked more than 100 is a particularly troubling result)," the greater weight of the evidence in this case showed Drayton "willfully failed to participate to her fullest capacity in the FCAs." WSI also found "the greater weight of the evidence shows that Ms. Drayton did not comply with the order to participate in *334 the [May 2006], FCA because she did not give a maximum consistent effort." Further, WSI concluded that Drayton had not demonstrated good cause to fail the FCA and that even if Drayton had argued that she had good cause, "when compared to her behaviors during the testing and on her breaks, the inconsistencies in her test results, do not support her claims that it was her pain that caused her to have inconsistent assessment results." From our examination of the record, we conclude a reasoning mind could reasonably find, as WSI did, that its finding of noncompliance was proven by the weight of the evidence on the entire record.
[¶ 34] Drayton contends that WSI disregarded medical evidence favorable to her, including Dr. Rokke's determination that she was still disabled and unlikely to improve. The findings of fact must "sufficiently address the evidence presented to the agency by the appellant." N.D.C.C. § 28-32-46(7). In its findings, however, WSI addresses Dr. Rokke's opinion:
25. Dr. Rokke wrote a letter on Ms. Drayton's behalf stating that the "results of the Functional Capacity Evaluations performed in June and July [had] not changed" his opinion that Ms. Drayton's work limitations were as set forth in his January 10, 2006, letter to WSI. His letter goes on to describe Ms. Drayton's statements to him about the second FCA, but does not address any specifics of the first FCA. Moreover his letter does not address if he thinks the results of the FCA were inaccurate or whether they did or did not represent an intentional manipulation of the FCA.
[¶ 35] Here, WSI considered the evidence in the record, including the testimony of occupational therapists Nelson and Nechiporenko that the invalid test results indicated a manipulated effort, and Drayton's testimony regarding her own explanations for her performance on the FCAs and that she did not intentionally manipulate the FCAs. WSI also explained its reasons for disregarding Dr. Rokke's opinion, who, while maintaining that Drayton remained disabled, did not address the results or intentional manipulation on the first FCA. WSI weighs the credibility of witnesses and resolves conflicts in the evidence, and we do not make independent findings of fact or substitute our judgment for that of the agency. WSI sufficiently addressed the medical evidence favorable to Drayton and we conclude a reasoning mind could reasonably find Drayton's noncompliance was proven by the weight of the evidence on the entire record.
[¶ 36] We therefore conclude WSI properly discontinued Drayton's benefits under N.D.C.C. §§ 65-05.1-04 and 65-05-28(4).
V
[¶ 37] WSI argues the district court erred in awarding Drayton attorney's fees under N.D.C.C. § 28-32-50, because the court erred in concluding WSI had acted without substantial justification.
[¶ 38] Section 28-32-50(1), N.D.C.C., requires a court to award reasonable attorney's fees and costs to a prevailing claimant when an administrative agency has acted without substantial justification. That statute requires a claimant to not only prevail, but also to prove the agency acted without substantial justification. Rojas v. Workforce Safety & Ins., 2006 ND 221, ¶ 14, 723 N.W.2d 403. We have held that statute applies to WSI, but only in "rare cases" if WSI denies or reduces an employee's benefits without substantial justification. Id. at ¶¶ 16-17. "Substantial justification means, justified in substance or in the main that is, justified to a degree that could satisfy a reasonable *335 person." Rojas, at ¶ 17 (internal quotation omitted).
[¶ 39] We review a district court's decision whether an agency acted with substantial justification for an abuse of discretion. Tedford v. Workforce Safety & Ins., 2007 ND 142, ¶ 26, 738 N.W.2d 29. In this case, because we have reversed the district court's judgment and determined WSI properly terminated Drayton's benefits, we also conclude the court abused its discretion in finding WSI acted without substantial justification. We reverse the district court's award of attorney's fees.
[¶ 40] Drayton nevertheless argues an award of attorney's fees is authorized under the 1993 version of N.D.C.C. § 65-10-03, which permitted broader awards of attorney's fees. WSI, however, contends this Court should decline to consider this issue because it is not ripe for determination. WSI asserts Drayton is entitled to an administrative hearing under N.D.C.C. § 65-02-08 on any denial or dispute concerning payment of attorney's fees, from which an appeal then could be pursued.
[¶ 41] Currently, N.D.C.C. § 65-10-03 requires WSI to pay attorney's fees only to an injured employee who prevails on appeal:
The organization shall pay the cost of the judicial appeal and the attorney's fee for an injured employee's attorney when the employee prevails. The employee has prevailed when any part of the decision of the organization is reversed and the employee receives an additional benefit as a result. An injured employee does not prevail on a remand for further action or proceedings unless the injured employee ultimately receives an additional benefit....
Section 65-10-03 (1993), N.D.C.C., while similar, provided in part:
The cost of the judicial appeal and an attorney's fee for the claimant's attorney must be borne by the bureau when the claimant prevails. The claimant is deemed to have prevailed when any part of the decision of the bureau is reversed or the claim is remanded to the bureau for further administrative proceedings. In an appeal by the bureau to the North Dakota supreme court, the claimant shall recover costs and attorneys' fees incurred in responding to the appeal....
(Emphasis added.) In 1995, the Legislature deleted the language authorizing the claimant to recover costs and attorney's fees in responding to an appeal to this Court by the bureau, now WSI. 1995 N.D. Sess. Laws, ch. 614, § 5. The Legislature further expressly declared the effective date, "This Act applies to any request for arbitration, hearing, or appeal taken from an administrative order issued after August 1, 1995." 1995 N.D. Sess. Laws, ch. 614, § 7.
[¶ 42] Drayton asserts the date of her work-related injury should control her statutory right under N.D.C.C. § 65-10-03 to receive attorney's fees and costs when WSI appeals to this Court. Drayton argues that her rights under this statute involve substantive rights, a vested right to the services of an attorney, and that subsequent amendments cannot therefore be applied to her claim retroactively.
[¶ 43] As we have explained, although a statutory provision may not operate retroactively to abrogate a vested right or valid obligation, a vested right is one which is immediate or fixed to present or future enjoyment and does not depend upon an event that is uncertain. See Reopelle, 2008 ND 98, ¶ 11, 748 N.W.2d 722. Here, however, the claimant's right under the 1993 statute to attorney's fees in a subsequent appeal is contingent upon a *336 number of future events occurring. As such, Drayton's claim to attorney's fees under these circumstances cannot be said to have vested at her injury date because her fees claim largely depends on uncertain future events, i.e., the need to respond when WSI has appealed an adverse decision to this Court. Moreover, the Legislature specifically provided that the act applied to "any appeal taken from an administrative order after August 1, 1995."
[¶ 44] We also reject Drayton's claim that the "effective date" language does not apply here because Drayton is appealing from a district court judgment rather than an "administrative order." Drayton's argument ignores that this proceeding is a further appeal from a WSI administrative order, and this Court reviews that order rather than the district court's decision. See N.D.C.C. § 28-32-49; Genter v. Workforce Safety & Ins. Fund, 2006 ND 237, ¶ 12, 724 N.W.2d 132. We therefore reject Drayton's contention that the 1993 version of the statute applies to her request for attorney's fees for this appeal.
[¶ 45] Because Drayton has not ultimately prevailed on appeal, we conclude Drayton is not entitled to attorney's fees under N.D.C.C. § 65-10-03.
VI
[¶ 46] We have considered Drayton's remaining arguments and find them without merit. We reverse the district court judgment and reinstate WSI's final order discontinuing Drayton's temporary disability benefits.
[¶ 47] GERALD W. VANDE WALLE, C.J., RONALD E. GOODMAN, S.J., CAROL RONNING KAPSNER, and MARY MUEHLEN MARING, JJ., concur.
[¶ 48] The Honorable RONALD E. GOODMAN, S.J., sitting in place of CROTHERS, J., disqualified.
|
/*++
Copyright (c) 1999 - 2014, Intel Corporation. All rights reserved
This program and the accompanying materials are licensed and made available under
the terms and conditions of the BSD License that accompanies this distribution.
The full text of the license may be found at
http://opensource.org/licenses/bsd-license.php.
THE PROGRAM IS DISTRIBUTED UNDER THE BSD LICENSE ON AN "AS IS" BASIS,
WITHOUT WARRANTIES OR REPRESENTATIONS OF ANY KIND, EITHER EXPRESS OR IMPLIED.
Module Name:
IgdOSBCB.ASL
Abstract:
IGD OpRegion/Software SCI Reference Code for the Baytrail Family.
This file contains the system BIOS call back functionality for the
OpRegion/Software SCI mechanism.
--*/
Method (SBCB, 0, Serialized)
{
// Supported Callbacks: Sub-function 0
If (LEqual(GESF, 0x0))
{
//<TODO> An OEM may support the driver->SBIOS status callbacks, but
// the supported callbacks value must be modified. The code that is
// executed upon reception of the callbacks must be also be updated
// to perform the desired functionality.
Store(0x00000000, PARM) // No callbacks supported
If(LEqual(PFLV,FMBL))
{
Store(0x000F87FD, PARM) // Mobile
}
If(LEqual(PFLV,FDTP))
{
Store(0x000F87BD, PARM) // Desktop
}
Store(Zero, GESF) // Clear the exit parameter
Return(SUCC) // "Success"
}
// BIOS POST Completion: Sub-function 1
If (LEqual(GESF, 1))
{
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Not supported, but no failure
}
// Pre-Hires Set Mode: Sub-function 3
If (LEqual(GESF, 3))
{
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Not supported, but no failure
}
// Post-Hires Set Mode: Sub-function 4
If (LEqual(GESF, 4))
{
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Not supported, but no failure
}
// Display Switch: Sub-function 5
If (LEqual(GESF, 5))
{
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Not supported, but no failure
}
// Set TV format: Sub-function 6
If (LEqual(GESF, 6))
{
//<TODO> If implemented, the input values must be saved into
// non-volatile storage for parsing during the next boot. The
// following Sample code is Intel validated implementation.
Store(And(PARM, 0x0F), ITVF)
Store(ShiftRight(And(PARM, 0xF0), 4), ITVM)
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC)
}
// Adapter Power State: Sub-function 7
If (LEqual(GESF, 7))
{
// Upon notification from driver that the Adapter Power State = D0,
// check if previous lid event failed. If it did, retry the lid
// event here.
If(LEqual(PARM, 0))
{
Store(CLID, Local0)
If(And(0x80000000,Local0))
{
And(CLID, 0x0000000F, CLID)
GLID(CLID)
}
}
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Not supported, but no failure
}
// Display Power State: Sub-function 8
If (LEqual(GESF, 8))
{
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Not supported, but no failure
}
// Set Boot Display: Sub-function 9
If (LEqual(GESF, 9))
{
//<TODO> An OEM may elect to implement this method. In that case,
// the input values must be saved into non-volatile storage for
// parsing during the next boot. The following Sample code is Intel
// validated implementation.
And(PARM, 0xFF, IBTT) // Save the boot display to NVS
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Reserved, "Critical failure"
}
// Set Panel Details: Sub-function 10 (0Ah)
If (LEqual(GESF, 10))
{
//<TODO> An OEM may elect to implement this method. In that case,
// the input values must be saved into non-volatile storage for
// parsing during the next boot. The following Sample code is Intel
// validated implementation.
// Set the panel-related NVRAM variables based the input from the driver.
And(PARM, 0xFF, IPSC)
// Change panel type if a change is requested by the driver (Change if
// panel type input is non-zero). Zero=No change requested.
If(And(ShiftRight(PARM, 8), 0xFF))
{
And(ShiftRight(PARM, 8), 0xFF, IPAT)
Decrement(IPAT) // 0 = no change, so fit to CMOS map
}
And(ShiftRight(PARM, 18), 0x3, IBLC)
And(ShiftRight(PARM, 20), 0x7, IBIA)
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Success
}
// Set Internal Graphics: Sub-function 11 (0Bh)
If (LEqual(GESF, 11))
{
//<TODO> An OEM may elect to implement this method. In that case,
// the input values must be saved into non-volatile storage for
// parsing during the next boot. The following Sample code is Intel
// validated implementation.
And(ShiftRight(PARM, 1), 1, IF1E) // Program the function 1 option
// Fixed memory/DVMT memory
And(ShiftRight(PARM, 17), 0xF, IDMS) // Program DVMT/fixed memory size
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Success
}
// Post-Hires to DOS FS: Sub-function 16 (10h)
If (LEqual(GESF, 16))
{
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Not supported, but no failure
}
// APM Complete: Sub-function 17 (11h)
If (LEqual(GESF, 17))
{
Store(ShiftLeft(LIDS, 8), PARM) // Report the lid state
Add(PARM, 0x100, PARM) // Adjust the lid state, 0 = Unknown
Store(Zero, GESF) // Clear the exit parameter
Return(SUCC) // Not supported, but no failure
}
// Set Spread Spectrum Clocks: Sub-function 18 (12h)
If (LEqual(GESF, 18))
{
//<TODO> An OEM may elect to implement this method. In that case,
// the input values must be saved into non-volatile storage for
// parsing during the next boot. The following Sample code is Intel
// validated implementation.
If(And(PARM, 1))
{
If(LEqual(ShiftRight(PARM, 1), 1))
{
Store(1, ISSC) // Enable HW SSC, only for clock 1
}
Else
{
Store(Zero, GESF)
Return(CRIT) // Failure, as the SSC clock must be 1
}
}
Else
{
Store(0, ISSC) // Disable SSC
}
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Success
}
// Post VBE/PM Callback: Sub-function 19 (13h)
If (LEqual(GESF, 19))
{
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Not supported, but no failure
}
// Set PAVP Data: Sub-function 20 (14h)
If (LEqual(GESF, 20))
{
And(PARM, 0xF, PAVP) // Store PAVP info
Store(Zero, GESF) // Clear the exit parameter
Store(Zero, PARM)
Return(SUCC) // Success
}
// A call to a reserved "System BIOS callbacks" function was received
Store(Zero, GESF) // Clear the exit parameter
Return(SUCC) // Reserved, "Critical failure"
}
|
'The Big Bang Theory': After floundering last season, top sitcom is wise to wrap up
"The Big Bang Theory" will end its run in May 2019 at the conclusion of the twelfth and final season.
USA TODAY
Fans will have only have a little while longer to see "The Big Bang Theory" gang together after CBS, Warner Bros. Television and Chuck Lorre Productions announced the hit comedy will end at the conclusion of Season 12 in May.(Photo: Monty Brinton, CBS)
Whatever the reason, it's the right move. After more than 250 episodes, "Bang" is still TV’s top-rated comedy – "Roseanne" briefly took that honor, but look where that is now – and likely will remain so. There was plenty of money to be made for everyone involved, and the departure will leave CBS, which successfully launched "Bang" prequel spinoff "Young Sheldon," with a huge scheduling hole. (Don't shed any tears. Although fans will soon be Penny-less, nobody connected to this money machine will leave penniless.)
Creatively, however, "Bang" is showing its age. Although long defying the decline that eventually afflicts long-running comedies, it started to flounder last season.
"The Big Bang Theory" premiered in 2007 with an intriguing triangle, socially awkward geniuses Sheldon (Jim Parsons), left, and Leonard (Johnny Galecki), right, navigating life in an apartment across the hall from actress/waitress Penny (Kaley Cuoco), who had a much higher emotional intelligence.(Photo: ROBERT VOETS, CBS)
For almost its entire run, “Big Bang,” created by sitcom master Chuck Lorre and Bill Prady, has been a well-oiled laugh factory. The initial story of two awkward scientific geniuses and their apartment neighbor, a Cheesecake Factory waitress with much sharper social skills, began with promise and took off from there, growing into a larger, talented ensemble that wove in character depth and emotion, without getting maudlin, while still delivering the jokes.
The initial cast – neighbor Penny (Kaley Cuoco) was on her own dealing with across-the-hall roommates Sheldon (Jim Parsons) and Leonard (Johnny Galecki) and their scientist pals Howard (Simon Helberg) and Raj (Kunal Nayyar) – was male-centric, but the show brought more balance introducing two brilliant women as female scientists: microbiologist Bernadette (Melissa Rauch) and neuroscientist Amy (Mayim Bialik).
They weren’t just grafted on for appearances. The writers and actors brought depth to Bernadette and Amy, integrating them smartly into the cast and creating new opportunities as the eternally immature guys took baby steps to grow up. Leonard eventually married Penny; Bernadette and Howard got hitched and became parents; and Amy and man-child Sheldon took their marital vows in last season’s finale.
Over the years, as Steven Molaro took a more prominent role as an executive producer, the show added a layer of emotion that gave the humor more depth. Fans strongly bonded with the characters, a great sign, with laughs coming from their idiosyncratic personalities as well as the jokes.
I remember being on set for a Season 6 episode where the band of friends tried to soften the blow of Howard's feelings of abandonment by his father. There was a sweetness to their support, punctuated by a hilarious and ridiculous effort from emotionally dense Sheldon.
“Big Bang” maintained that balance over the years as its longevity surpassed most other sitcoms, especially those shot in front of a studio audience. By the time it closes shop in May, the series will have racked up a record 279 episodes for the studio-audience format, more than classics “Frasier” (11 seasons, 263 episodes), “Friends” (10 seasons, 236 episodes) and “Seinfeld” (nine seasons, 173 episodes).
Past hits have ended for various reasons; stars and producers are eager to pursue other opportunities or the financial factors no longer make sense.
But there’s an underlying, unavoidable reason why all these shows end. Over time, they all lose some creativity, often simply resulting from repetition. What was once fresh can seem stale.
"The Big Bang Theory" featured many well-known guest stars from the fields of science, business and entertainment, including theoretical physicist Stephen Hawking, left, who is seen here with "Bang" physicist Sheldon (Jim Parsons).(Photo: SONJA FLEMMING/CBS)
“Bang” upheld its quality for many episodes past a sitcom's expected sell-by date, but it hit a wall last year. The season-long lead-up to the "Shamy" wedding, a truly joyous union of two great characters, started seeming more like a meandering walk than a wedding march. It just felt like "Bang" was spinning its wheels. Repetition and sameness may please obsessive Sheldon, but they don't do much for comedy.
With one and especially two more seasons beyond the upcoming one (Sept. 24, 8 EDT/PDT), “Bang” was in danger of veering toward comedic entropy (a term Sheldon and Leonard would understand), degrading and losing energy and moving toward flatness.
With just one season to go, however, I have faith the talented producers, writers and actors can generate a funny sprint, with pratfalls, to the finish line. “Big Bang” writers are famous for not plotting too far ahead, so there’s time to plan a satisfying conclusion, and there’s no longer any danger of the dreaded penultimate season, a deadening period for many otherwise stellar series as everyone anticipates the grand finale.
"Big Bang” hasn’t received its awards due over the years; Jim Parsons has been an Emmy magnet, winning four trophies as lead actor in a comedy, but the series has never won for best comedy. It was worthy of that honor.
But awards don’t determine a show’s quality and “Big Bang” stands with the best in its genre. Now, without being weighed down with two extra seasons (and, yes, the accompanying stacks of money), it has a chance to go out with … a sharp, funny flourish. (Did you think I’d say bang? Bazinga!)
Adam Rippon attends the Disney ABC press event at TCA. ABC recently announced that the season 26 winner of "Dancing With the Stars" will be a judge on "Dancing With the Stars: Juniors" beginning in October. Jon Kopaloff, FilmMagic
Ben Stiller, Patricia Arquette and Benicio del Toro respond to questions about "Escape at Dannemora," a miniseries about a New York State prison break, which will air on Showtime in November. Willy Sanjuan, Willy Sanjuan/Invision/AP
Tom Rob Smith, second from left, executive producer of the television miniseries "The Assassination of Gianni Versace: American Crime Story," accepts the award for Outstanding Achievement in Movies or Miniseries as cast members, from left, Ricky Martin, Edgar Ramirez, Finn Wittrock and Judith Light look on at the 34th annual TCA Awards. Chris Pizzello, Chris Pizzello/Invision/AP
Henry Louis Gates Jr., host and executive producer of "Finding Your Roots with Henry Louis Gates Jr.," discusses the new season of his show on PBS, which begins in January. Chris Pizzello, Chris Pizzello/Invision/AP
It's time for the Television Critics Association's summer press tour in Pasadena, Calif., where networks present their shows to TV journalists. Christiane Amanpour discusses her news program, "Christiane and Company," which will debut on PBS in September. Richard Shotwell, Richard Shotwell/Invision/AP
HGTV brough out its big stars with Drew Scott and Jonathan Scott of "Property Brothers" and Leanne Ford and Steve Ford of "Restored by the Fords" at TCA. Amanda Edwards, Getty Images for Discovery, Inc.
Heather Graham discusses "Bliss," in which she is married to a man who lives two different lives. The show, created by David Cross ("Arrested Development"), is on the streaming service Britbox. Richard Shotwell, Richard Shotwell/Invision/AP
The hosts of "Pod Save America" (from left, Jon Favreau, Jon Lovett, Dan Pfeiffer and Tommy Vietor) will bring their popular podcast to HBO for four hour-long specials this fall. FilmMagic, FilmMagic for HBO
Jeff Goldblum discusses "The Curiosity of Jeff Goldblum," his new show on National Geographic. The 12-part series examines unique scientific connections among ordinary things. Richard Shotwell, Richard Shotwell/Invision/AP |
---
abstract: 'For an amenable minimal topologically free dynamical system $\alpha$ of a group on a compact metrizable space $Z$ and for a compact metrizable space $Y$ satisfying a mild condition, we construct a minimal skew product extension of $\alpha$ on $Z\times Y$. This generalizes a result of Glasner and Weiss. We also study the pure infiniteness of the crossed products of minimal dynamical systems arising from this result. In particular, we give a generalization of a result of Rørdam and Sierakowski.'
address: 'Department of Mathematical Sciences, University of Tokyo, Komaba, Tokyo, 153-8914, Japan'
author:
- Yuhei Suzuki
title: Construction of minimal skew products of amenable minimal dynamical systems
---
Introduction {#Sec:intro}
============
Recall that a topological dynamical system $\Gamma \curvearrowright X$ is said to be minimal if every $\Gamma$-orbit is dense in $X$. It is an interesting question to ask that for a given group $\Gamma$ which space admits a minimal (topologically) free dynamical system of $\Gamma$. Certainly a space admitting a minimal $\Gamma$-dynamical system must have a nice homogeneity. However, this is not sufficient even for the simplest case, that is, the case $\Gamma=\mathbb{Z}$. For example, an obstruction from homological algebra shows that there is no minimal homeomorphism on even dimensional spheres $S^{2n}$ (see Chapter I.6 of [@Br] for instance).
In [@GW], Glasner and Weiss have shown the existence of minimal skew product extensions of a minimal homeomorphism under mild conditions. Their result in particular shows that many spaces admit a minimal homeomorphism. For example, it follows that there exists a minimal homeomorphism on the product of the Hilbert cube and $S^1$. This solved a question asked by T. Chapman [@Ch]. For certain amenable groups, their result is generalized in [@Ne]. (It also deals generalizations of other results in [@GW]; e.g., the existence of strictly ergodic skew products.) In this paper, following the argument of Glasner and Weiss in [@GW], we construct minimal skew products of amenable minimal topologically free dynamical systems (Theorem \[Thm:min\]). This provides many new examples of (amenable) minimal topologically free dynamical systems of exact groups.
We also study the reduced crossed product of these minimal skew products. Recall that a unital -algebra $A$ is purely infinite and simple if for any nonzero positive element $a\in A$, there is $b\in A$ with $b^{\ast} ab=1$. Pure infiniteness plays an important role in the study of -algebras. See [@Cun], [@Kir], [@KP], [@Phi], and [@Rord] for example. A -algebra is said to be a Kirchberg algebra if it is simple, separable, nuclear, and purely infinite. A deep theorem of Kirchberg [@Kir] and Phillips [@Phi] states that the Kirchberg algebras are classified in terms of the KK-theory. In particular, the Kirchberg algebras in the UCT class are classified by their K-theoretic data, and consequently each of which is isomorphic to the one constructed in [@Rord]. For these reasons, it is important to know whether a given -algebra is purely infinite. Obviously pure infiniteness implies other infiniteness properties; e.g., tracelessness, properly infiniteness. The latter conditions are easy to check in many situations. However, even in the nuclear case, Rørdam has constructed a counterexample for the converse implications [@Rord2]. See [@Ror] and the references therein for more information on pure infiniteness and Kirchberg algebras. In Section \[Sec:pi\], under certain assumptions on $Y$ and $\alpha\colon \Gamma \curvearrowright Z$, we show that the crossed products of many of dynamical systems obtained in our result are Kirchberg algebras in the UCT class (Proposition \[Prop:filling\]). For this purpose, we generalize the notion of the finite filling property, which is introduced in [@JR] for dynamical systems, to étale groupoids. It turns out that the generalized version is useful to construct minimal skew products with the purely infinite crossed products. This result is applied particularly to the case that $Y$ is a connected closed topological manifold and that $\alpha$ is a dynamical system on the Cantor set constructed in [@RS]. As a consequence, we generalize a result of Rørdam and Sierakowski [@RS], which is a result for the Cantor set, to the products of connected closed topological manifolds and the Cantor set (Theorem \[Thm:RS\]). This is the first generalization of their result, and shows that for topological dynamical systems, not only the structure of groups but also the structure of spaces is not an obstruction to form a Kirchberg algebra.
In Section \[Sec:free\], we study the K-theory of the crossed products of these minimal skew products in the free group case. Using the Pimsner–Voiculescu six-term exact sequence, we prove a K$\ddot{{\rm u}}$nneth-type formula for them. As an application, for any connected closed topological manifold $M$ and for any (non-amenable, countable) virtually free group $\Gamma$, we show that there exist continuously many amenable minimal free dynamical systems of $\Gamma$ on the product of $M$ and the Cantor set whose crossed products are mutually non-isomorphic Kirchberg algebras. This generalizes a result in [@Suz].
Spaces of dynamical systems {#spaces-of-dynamical-systems .unnumbered}
---------------------------
For a compact metrizable space $X$, let $\mathcal{H}(X)$ denote the group of homeomorphisms on $X$. We equip the metric $d$ on $\mathcal{H}(X)$ as follows. First let us fix a metric $d_X$ on $X$. Then define $$d(\varphi, \psi):=\max_{x\in X} (d_X(\varphi(x), \psi(x)))+\max_{x\in X}(d_X(\varphi^{-1}(x), \psi^{-1}(x)))$$ for $\varphi, \psi \in \mathcal{H}(X)$. It is not hard to check that the metric $d$ is complete and $\mathcal{H}(X)$ becomes a topological group with respect to $d$. Note that the sequence $(\varphi_n)_n$ in $\mathcal{H}(X)$ converges to $\varphi$ in this topology if and only if $\varphi_n$ uniformly converges to $\varphi$. For a countable group $\Gamma$, let $\mathcal{H}(\Gamma, X)$ denote the set of dynamical systems of $\Gamma$ on $X$, i.e., $\mathcal{H}(\Gamma, X)={\rm Hom}(\Gamma, \mathcal{H}(X))$. This set is naturally regarded as a closed subset of $\prod_{\Gamma}\mathcal{H}(X)$. Since $\Gamma$ is countable, this makes $\mathcal{H}(\Gamma, X)$ to be a complete metric space.
Next let $Y$ be a compact metrizable space and let $\mathcal{G} \curvearrowright Y$ be a continuous action of a topological group $\mathcal{G}$ on $Y$. Let $\alpha\colon \Gamma \curvearrowright Z$ be a topological dynamical system of a group $\Gamma$ on a compact metrizable space $Z$. Put $X=Z\times Y$. Recall that a continuous map $c\colon \Gamma \times Z \rightarrow \mathcal{G}$ is said to be a cocycle if it satisfies the equation $c(s, t.z)c(t, z)=c(st, z)$ for all $s, t\in \Gamma$ and $z\in Z$. When there is a continuous map $h\colon Z \rightarrow \mathcal{G}$ satisfying $c(s, z)=h(s.z)^{-1}h(z)$ for all $s\in \Gamma$ and $z\in Z$, the cocycle $c$ is said to be a coboundary. Each cocycle $c\colon \Gamma\times Z \rightarrow \mathcal{G}$ defines an extension of $\alpha$ on $X$ by the following equation. $$s.(z, y)=(s.z, c(s, z)y) {\rm \ for\ } s\in \Gamma {\rm\ and\ } (z, y)\in X.$$ Such an extension is called a skew product extension. Note that when $c$ is a coboundary, the associated skew product extension is conjugate to $\bar{\alpha}$. Here and throughout the paper, for a dynamical system $\alpha \colon \Gamma \curvearrowright Z$ and a compact space $Y$, we denote by $\bar{\alpha}$ the diagonal action of $\alpha$ and the trivial action on $Y$. Since the space $Y$ is always clear from the context, we omit $Y$ in our notation.
For a continuous map $h$ from $Z$ into $\mathcal{G}$, we have an associated homeomorphism $H$ on $X$ defined by the formula $H(z, y):=(z, h_z(y))$ for $(z, y)\in X$. We denote by $\mathcal{G}_s$ the set of homeomorphisms given in the above way. Obviously, $\mathcal{G}_s$ is a subgroup of $\mathcal{H}(X)$. For a topological dynamical system $\alpha\colon \Gamma \curvearrowright Z$, we define a subset $\mathcal{S}_{\mathcal{G}}(\alpha)$ of $\mathcal{H}(\Gamma, X)$ to be $$\mathcal{S}_{\mathcal{G}}(\alpha):=\{ H^{-1}\circ \bar{\alpha}\circ H: H\in \mathcal{G}_s\}.$$ We note that the set $\mathcal{S}_{\mathcal{G}}(\alpha)$ consists of skew product extensions of $\alpha$ by coboundaries. We denote by $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$ the closure of $\mathcal{S}_{\mathcal{G}}(\alpha)$ in $\mathcal{H}(\Gamma, X)$. Note that any $\beta \in \overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$ is a skew product extension of $\alpha$ on $X$ whose associated cocycle takes the value in $\overline{\mathcal{G}}$. Here $\overline{\mathcal{G}}$ denotes the closure of the image of $\mathcal{G}$ in $\mathcal{H}(X)$. In particular, when $\alpha$ is amenable, every dynamical system contained in $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$ is amenable. Throughout the paper, we always fix metrics $d_Y$ and $d_Z$ on $Y$ and $Z$ respectively and consider the metric on $X=Z\times Y$ defined by $d_X((z_1, y_1), (z_2, y_2))= d_Y(y_1, y_2) + d_Z(z_1, z_2)$, and use these metrics to define metrics on the homeomorphism groups.
In Section \[Sec:pi\], we discuss étale groupoids. Throughout the paper, we always assume that étale groupoids are locally compact Hausdorff and their unit spaces are compact and infinite (as a set). For an étale groupoid $G$, we denote by $r$ and $s$ the range and source map unless they are specified. As usual, for a dynamical system $\alpha$ of a discrete group $\Gamma$ on a compact space $X$, we usually regard the transformation groupoid $X\rtimes _\alpha \Gamma$ as the following subspace of $X \times \Gamma \times X$. $$X\rtimes _\alpha \Gamma = \{ (\alpha_g(x), g, x)\in X \times \Gamma \times X: x\in X, g\in \Gamma\}.$$ Note that the range and source map correspond to the projections onto the first and third coordinate respectively. For detailed explanations and basic knowledges of étale groupoids, we refer the reader to Section 5.6 of [@BO].
Notation {#notation .unnumbered}
--------
- For a subset $U$ of a topological space, its closure and interior are denoted by ${\rm cl}(U)$ and ${\rm int}(U)$ respectively.
- For a $\ast$-homomorphism $\alpha$ between -algebras, denote by $\alpha_{\ast, i}$ the homomorphism induced on the $K_i$-groups.
- Denote by $\mathbb{K}$ the -algebra of all compact operators on $\ell^2(\mathbb{N})$.
- Let $A$ be a -algebra. For a projection $p$ in $A$ or $A\otimes \mathbb{K}$, denote by $[p]_0$ the element of $K_0(A)$ represented by $p$.
- For a compact space $X$, we denote $K_i(C(X))$ by $K^i(X)$ for short. (Note that this coincides with the usual definition of $K^i$-group.)
Construction of minimal skew product {#Sec:min}
====================================
The goal of this section is to prove the following theorem. The proof is done by following the same line as that of Theorem 1 in [@GW].
Before the proof, recall that a dynamical system $\alpha\colon \Gamma \curvearrowright Z$ of a group $\Gamma$ on a compact metrizable space $Z$ is said to be amenable if there is a sequence of continuous maps $$\mu_n\colon Z \rightarrow {\rm Prob}(\Gamma)$$ satisfying $$\lim_{n\rightarrow \infty} \sup_{z\in Z}\| s.\mu_n^z- \mu_n^{s.z}\|_1 =0 {\rm\ for\ all\ }s\in \Gamma.$$ Here ${\rm Prob}(\Gamma)$ denotes the space of probability measures on $\Gamma$ with the pointwise convergence topology, and $\Gamma$ acts on ${\rm Prob}(\Gamma)$ by the left translation. It is shown by Ozawa [@Oz] that for discrete groups, the existence of an amenable action is equivalent to exactness. See [@Ana0] and [@BO] for more information on amenable actions. In the proof of the following theorem, we use amenability of dynamical systems to construct suitable continuous functions. In other word, amenability of dynamical systems plays the role of the Følner sets in the proof of Theorem 1 of [@GW].
\[Thm:min\] Let $\mathcal{G}\curvearrowright Y$ be a minimal action of a path connected group $\mathcal{G}$ on a compact metrizable space $Y$. Let $\alpha\colon \Gamma \curvearrowright Z$ be an amenable minimal topologically free dynamical system of a countable group $\Gamma$ on a compact metrizable space $Z$. Then the set $$\{\beta \in \overline{\mathcal{S}}_{\mathcal{G}}(\alpha): \beta{\rm\ is\ minimal}\}$$ is a $G_\delta$-dense subset of $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$.
Let $\mathcal{G}\curvearrowright Y$ and $\alpha\colon \Gamma\curvearrowright Z$ be as in the statement. For an open set $U$ of $X=Z\times Y$, we define the subset $\mathcal{E}_U$ of $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$ to be $$\mathcal{E}_U:=\{\beta\in \overline{\mathcal{S}}_{\mathcal{G}}(\alpha):\bigcup_{g\in \Gamma}\beta_g(U)=X \}.$$ Since $X$ is compact, it is not hard to check that the set $\mathcal{E}_U$ is open in $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$.
Let $(U_n)_n$ be a countable basis of $X$. We observe that an element in $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$ is minimal if and only if it is contained in $\bigcap_n \mathcal{E}_{U_n}$. Therefore, thanks to the Baire category theorem, our claim follows once we show the density of $\mathcal{E}_U$ in $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$ for each non-empty open set $U$ in $X$. To see this, it is enough to show the following claim. For any $H\in \mathcal{G}_s$ and any non-empty open set $U\subset X$, $H^{-1}\circ\bar{\alpha}\circ H \in {\rm cl}(\mathcal{E}_U).$ This is equivalent to the condition $\bar{\alpha}\in {\rm cl}(H\mathcal{E}_UH^{-1})$. A direct computation shows that $H\mathcal{E}_UH^{-1}=\mathcal{E}_{H(U)}$. Since $H(U)$ is again a non-empty open set, now it is enough to show the following statement. For any non-empty open set $U\subset X$, we have $\bar{\alpha}\in {\rm cl}(\mathcal{E}_U)$. Now let $U$ be a non-empty open set in $X$. Let $S$ be a finite subset of $\Gamma$ and let $\epsilon>0$. Take non-empty open sets $V\subset Y$ and $W\subset Z$ with $W\times V\subset U$. By assumption, there are $\tilde{h}_0, \ldots, \tilde{h}_n\in \mathcal{G}$ satisfying $\bigcup_{0\leq i\leq n} \tilde{h}_i(V)=Y$. Since $\mathcal{G}$ is path-connected, there is a continuous map $h \colon [0, 1]\rightarrow \mathcal{G}$ satisfying $h_{i/n}=\tilde{h}_i$ for $0\leq i\leq n$. By the continuity of $h$, there is $\delta>0$ such that the condition $|t_1-t_2|<\delta$ implies $d(h_{t_1}^{-1}h_{t_2}, {\mbox{\rm id}}_Y)<\epsilon$. Now we use the amenability of $\alpha$ to choose a continuous map $\mu\colon Z\rightarrow {\rm Prob}(\Gamma)$ satisfying $\sup_{z\in Z}\|s.\mu^z-\mu^{s.z}\| _1<\delta$ for all $s\in S$. By perturbing $\mu$ within a small error and replacing $W$ by a smaller one, we may assume that there is a finite set $F\subset \Gamma$ such that ${\rm supp}(\mu^w)\subset F$ for all $w\in W$. (Cf. Lemma 4.3.8 of [@BO].) Since $\alpha$ is topologically free, by replacing $W$ by a smaller one further, we may assume that the open sets $(g.W)_{g\in F^{-1}}$ are mutually disjoint. Since $W$ is a locally compact metrizable space without isolated points, we can choose a compact subset $K$ of $W$ homeomorphic to the Cantor set. (To see this, take a sequence of families $((K_{i_1, \ldots, i_n})_{0\leq i_1, \ldots, i_n \leq 1})_{n\in \mathbb{N}}$ satisfying the following conditions. Each family $(K_{i_1, \ldots, i_n})_{i_1, \ldots, i_n}$ consists of pairwise disjoint closed subsets of $W$ with non-empty interior, $K_{i_1, \ldots, i_n}\subset K_{i_1, \ldots, i_{n-1}}$ for any $i_1, \ldots, i_n$, and $\max_{i_1, \ldots, i_n}\{ {\rm diam}(K_{i_1, \ldots, i_n})\}$ converges to $0$ as $n$ tends to infinity. Then the set $\bigcap_n \bigcup _{i_1, \ldots, i_n} K_{i_1, \ldots, i_n}$ gives the desired subset.)
Next take a continuous surjection $\theta_0\colon K\rightarrow [0, 1]$. Extend $\theta_0$ to a map $\bigsqcup_{g\in F^{-1}} g K\rightarrow [0, 1]$ by the formula $\theta_0(g.z):=\theta_0(z)$ for $g\in F^{-1}$ and $z\in K$. Then take a continuous extension $\tilde{\theta}\colon Z\rightarrow [0, 1]$ of $\theta_0$. Using $\tilde{\theta}$ and $\mu$, we define $\theta\colon Z\rightarrow [0, 1]$ by $$\theta(z):=\sum_{g\in \Gamma}\mu^z(g^{-1})\tilde{\theta}(g.z).$$ Note that the continuity of $\tilde{\theta}$ and $\mu$ implies that of $\theta$. For $z\in K$, since ${\rm supp}(\mu^z)\subset F$, we have $\theta(z)=\theta_0(z)$. In particular, $\theta(K)=[0, 1]$. Moreover, for $z\in Z$ and $s\in S$, we have $$\begin{aligned}
|\theta(s.z)-\theta(z)|&=& |\sum_{g\in \Gamma}(\mu^{s.z}(g^{-1})\tilde{\theta}(gs.z)-\mu^{z}(g^{-1})\tilde{\theta}(g.z))|\\
&=&|\sum_{g\in \Gamma}(\mu^{s.z}(g^{-1})\tilde{\theta}(gs.z)-\mu^{z}(s^{-1}g^{-1})\tilde{\theta}(gs.z))|\\
&\leq&\|\mu^{s.z}-s.\mu^z\|_1\\
&<&\delta.\end{aligned}$$
Now define the map $g\colon Z\rightarrow \mathcal{G}$ by $g_z:=h_{\theta(z)}$ for $z\in Z$. We will show that the corresponding homeomorphism $G\in \mathcal{G}_s$ satisfies the following conditions.
1. $d(\bar{\alpha}_s, G^{-1}\circ \bar{\alpha}_s \circ G)<\epsilon$ for $s\in S$.
2. $G^{-1}\circ \bar{\alpha} \circ G\in \mathcal{E}_U$.
Since $U$, $\epsilon$, and $S$ are arbitrarily, this ends the proof. Let $s\in S$ and $(z, y)\in X$. Then a direct computation shows that $$(G^{-1}\circ \bar{\alpha}_s \circ G)(z, y)
=(\alpha_s(z), g_{s.z}^{-1} g_z(y)).$$ Since $d(g_{s.z}^{-1} g_z, {\mbox{\rm id}}_Y)< \epsilon$ for all $z \in Z$, we obtain the first condition.
For the second condition, note that $G^{-1}\circ \bar{\alpha} \circ G\in \mathcal{E}_U$ if and only if $\bigcup_{g\in \Gamma} \bar{\alpha}_g (G(U))=X$ holds. By the choice of $G$, for any $0\leq i \leq n$, there is $w\in W$ satisfying $g_w= \tilde{h}_{i}$. It follows that for any $0\leq i \leq n$, there is $w\in W$ with $\{w \}\times \tilde{h}_i(V)\subset G(U)$. Since $\bigcup_i \tilde{h}_i(V)=Y$, this shows that for any $y\in Y$, the intersection $(Z\times \{y\}) \cap G(U)$ is non-empty (which is open in $Z\times \{y \}$). This with the minimality of $\alpha$ shows that $\bigcup_{g\in \Gamma}\bar{\alpha}_g(G(U))=X$.
Theorem \[Thm:min\] does not hold when $Z$ is not metrizable. To see this, consider a minimal subsystem $\alpha\colon \Gamma \curvearrowright Z$ of $\Gamma \curvearrowright \beta \Gamma$. (Note that $\alpha$ is amenable when $\Gamma$ is exact.) Then $\alpha$ is the universal minimal $\Gamma$-system (see Theorem 1.24 of [@Gla]). Thus it does not have a nontrivial minimal extension.
Let $\alpha\colon \Gamma \curvearrowright Z$ be a minimal topologically free dynamical system of an amenable group $\Gamma$ whose crossed product is quasi-diagonal. Then for any $\beta \in \overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$, its crossed product is quasi-diagonal. Indeed, since $\beta$ is a limit of conjugations of $\bar{\alpha}$, there is a continuous field of -algebras over $\mathbb{N}\cup \{\infty \}$, the one-point compactification of $\mathbb{N}$, whose fiber at $n\in \mathbb{N}$ is isomorphic to $C(Y)\otimes (C(Z)\rtimes_\alpha \Gamma)$ and the one at $\infty$ is isomorphic to $C(X)\rtimes _\beta \Gamma$. (See Corollary 3.6 of [@Rie].) Now Lemma 3.10 of [@CDE] proves the quasi-diagonality of $C(X)\rtimes _\beta \Gamma$.
Pure infiniteness of crossed products of minimal skew products {#Sec:pi}
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Finite filling property for étale groupoids
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To study the pure infiniteness of crossed products of dynamical systems arising from Theorem \[Thm:min\], we introduce a notion of the finite filling property for étale groupoids. First recall from [@JR] the finite filling property for dynamical systems. Although their definition and result also cover noncommutative -dynamical systems, in this paper, we concentrate on the commutative case. See [@JR] for the general case. We remark that, although the following formulation is slightly different from the original one, it is easily checked that they are equivalent. (Cf. Definition 0.1, Proposition 0.3, and Remark 0.4 of [@JR].)
A dynamical system $\Gamma\curvearrowright X$ is said to have the $n$-filling property if for any non-empty open set $U$ of $X$, there are $n$ elements $g_1, \ldots, g_n \in \Gamma$ with $\bigcup_{i=1}^n g_i(U)=X$. We say that a dynamical system has the finite filling property if it has the $n$-filling property for some $n\in \mathbb{N}$.
Note that the finite filling property implies minimality. In [@JR], it is shown that the finite filling property of a topological dynamical system implies the pure infiniteness of the reduced crossed product by a similar way to the one in [@LaS]. However, as shown in [@JR], the $n$-filling property is inherited to factors. This makes the usage of the $n$-filling property restrictive in our application. To avoid this difficulty, we introduce a notion of the finite filling property for étale groupoids, which can be regarded as a localized version of [@JR]. This helps to construct minimal skew products with the purely infinite reduced crossed product.
Next we recall that a subset $U$ of an étale groupoid $G$ is said to be a $G$-set if both the range and source map are injective on $U$. For two $G$-sets $U$ and $V$, we set $UV:=\{uv\in G: u\in U, v\in V, s(u)= r(v)\}$. Obviously it is again a $G$-set. Furthermore, if both $U$ and $V$ are open, then $UV$ is again open. Recall also that an étale groupoid is said to be minimal if for any $x\in G^{(0)}$, the set $\{r(u):u\in G, s(u)=x\}$ is dense in $G^{(0)}$. Note that the unit space $G^{(0)}$ has no isolated points whenever $G$ is minimal. (Recall that $G^{(0)}$ is always assumed to be infinite.)
Let $G$ be an étale groupoid. For a natural number $n$, we say that $G$ has the $n$-filling property if every non-empty open set $W$ of $G^{(0)}$ satisfies the following conditon. There are $n$ open $G$-sets $U_1, \ldots, U_n$ satisfying $$\bigcup_{i=1}^n r(U_i W)=G^{(0)}.$$ For short, we say that a dynamical system has the weak $n$-filling (resp. weak finite filling) property if its transformation groupoid has the $n$-filling (resp. finite filling) property.
Obviously, for dynamical systems, the $n$-filling (resp. finite filling) property implies the weak $n$-filling (resp. weak finite filling) property. However, the converses are not true.
We also remark that it is possible to define the weak finite filling property without going through the transformation groupoid. However, this specialization does not make the arguments below easier and this generality makes notation simpler. Considering applications elsewhere also, we study the property under this generality.
When the unit space $G^{(0)}$ has finite covering dimension, we have a useful criteria for the finite filling property. The following definition is inspired from [@Mat] and [@RS].
We say that an étale groupoid $G$ is purely infinite if for any non-empty open set $U$ of $G^{(0)}$, there is a non-empty open subset $V$ of $U$ with the following condition. There are open $G$-sets $U_1$ and $U_2$ such that $r(U_i) \subset V\subset s(U_i)$ for $i= 1, 2$ and $r(U_1)$ and $r(U_2)$ are disjoint. We say that a dynamical system is purely infinite if its transformation groupoid is purely infinite.
We remark that Matui [@Mat] has introduced pure infiniteness for totally disconnected étale groupoids for the study of the topological full groups. Clearly, our definition is weaker than Matui’s one. We will see later that our definition of pure infiniteness coincides with Matui’s one for minimal totally disconnected étale groupoids.
\[Prop:pifill\] Let $G$ be a minimal purely infinite étale groupoid and assume that $\dim(G^{(0)})=n<\infty$. Then $G$ has the $(n+1)$-filling property.
Let $U$ be a non-empty open subset of $G^{(0)}$. Replacing $U$ by a smaller one, we may assume that there are open $G$-sets $U_1$ and $U_2$ such that $r(U_i)\subset U\subset s(U_i)$ for $i=1, 2$ and $r(U_1)$ and $r(U_2)$ are disjoint. We first show that for any $N\in \mathbb{N}$, there are $N$ open $G$-sets $V_1, \ldots, V_N$ satisfying $r(V_i)\subset U\subset s(V_i)$ for $i=1, \ldots, N$ and the ranges $r(V_1), \ldots, r(V_N)$ are mutually disjoint. To see this, first take $M\in \mathbb{N}$ with $2^M\geq N$ and then take $N$ mutually distinct elements from the set $$\{U_{i_1} U_{i_2} \cdots U_{i_M}: i_k=1 {\rm\ or\ }2 {\rm\ for\ each\ }k\}.$$ Then it gives the desired sequence.
By the compactness of $G^{(0)}$ and the minimality of $G$, for some natural number $N$, there are $N$ open $G$-sets $W_1, \ldots, W_N$ with $\bigcup_{i=1}^N r(W_i U)=G^{(0)}.$ Take $N$ open $G$-sets $V_1, \ldots, V_N$ as in the previous paragraph and put $Z_i:=W_i V_i^{-1}$ for each $i$. Then we have $$\bigcup_{i=1}^N r(Z_i U)\supset \bigcup_{i=1}^N r(W_i U)=G^{(0)}.$$ Note that since $s(Z_i)\subset r(V_i)$, the sources of $Z_i$’s are mutually disjoint. Since $\dim (G^{(0)})=n$, we can choose a refinement $(Y_j)_{j\in J}$ of $(r(Z_i U))_{i=1} ^N$ with the decomposition $J=J_0\sqcup J_1 \sqcup \cdots \sqcup J_n$ such that the members of the family $(Y_j)_{j\in J_k}$ are mutually disjoint for each $k$. Choose a map $\varphi\colon J \rightarrow \{1, \ldots, N \}$ satisfying $Y_j \subset r(Z_{\varphi(j)} U)$ for each $j\in J$. Set $X_k:= \bigcup_{j\in J_k} Y_j Z_{\varphi(j)}$ for each $k$. Then it is not hard to check that each $X_k$ is an open $G$-set and that $r(X_k U)=\bigcup_{j\in J_k}Y_j$. This shows $\bigcup_{k=0}^{n}r(X_k U)=G^{(0)}$.
\[Rem:pi\] The argument in Remark 4.12 of [@Mat] shows that for totally disconnected étale groupoids, the finite filling property implies pure infiniteness in Matui’s sense. Thus for a minimal totally disconnected étale groupoid $G$, pure infiniteness in Matui’s sense [@Mat], that in our sense, the finite filling property, and the $1$-filling property are equivalent. (Here total disconnectedness is used to replace open $G$-sets by clopen ones.)
Next we see a few examples of dynamical systems with the weak finite filling property. The following three examples are particularly important for us. See [@JR] for more examples of dynamical systems with the finite filling property.
\[Exm:1fill\] It follows from the proof of Theorem 6.11 of [@RS] that every countable non-amenable exact group admits an amenable minimal free purely infinite dynamical system on the Cantor set. (To see this, use the equivalence of conditions (i) and (iii) in Proposition 5.5 in the proof of Proposition 6.8.) By Proposition \[Prop:pifill\], it has the weak $1$-filling property. We remark that these dynamical systems almost never have the finite filling property.
Recall that a manifold is said to be closed if it is compact and has no boundaries.
\[Lem:man\] Let $M$ be a connected closed topological manifold. Let $\mathcal{H}_0(M)$ denote the path connected component of $\mathcal{H}(M)$ containing the identity. Then the action $\mathcal{H}_0(M)\curvearrowright M$ has the finite filling property.
It is not hard to show that the above action is transitive by using the connectedness of $M$ with the fact that $M$ is locally homeomorphic to $\mathbb{R}^n$.
Take an open cover $U_1, \ldots, U_N$ of $M$ each of which is homeomorphic to $\mathbb{R}^n$. We show that for any non-empty open set $V$ in $M$, for any $i$, and for any compact subset $K$ of $U_i$, there is an element $g\in \mathcal{H}_0(M)$ with $g(V)\supset K$. Since $M$ is compact, the claim with a standard argument for compactness shows the $N$-filling property of the action in the question. Since the action is transitive, replacing $V$ by $g(V)$ for a suitable $g\in \mathcal{H}_0(X)$ and replacing it by a smaller one further, we may assume that $V$ is contained in $U_i$. Take a homeomorphism $\varphi\colon U_i\rightarrow \mathbb{R}^n$ satisfying $0 \in \varphi(V)$. Take a sufficiently large positive number $\lambda >0$ with $\varphi(K)\subset \lambda\varphi(V)$. Then choose a continuous function $f\colon \mathbb{R}_{\geq 0} \rightarrow \mathbb{R}_{\geq 0}$ satisfying the following conditions.
1. For $t \leq {\rm diam}(\varphi(V))$, we have $f(t)=\lambda$.
2. For all sufficiently large $t$, we have $f(t)= 1$.
3. The function $t\mapsto tf(t)$ is strictly monotone increasing.
Now set $\varphi_f(x):=\varphi^{-1}(f(\| \varphi(x)\|) \varphi(x))$ for $x\in U_i$. Here $\|\cdot \|$ denotes the Euclidean norm on $\mathbb{R}^n$. From the assumptions on $f$, the map $\varphi_f$ is a homeomorphism on $U_i$ satisfying $K \subset \varphi_f(V)$. We extend $\varphi_f$ to a homeomorphism $\psi_f$ on $M$ as follows. $$\psi_f(x):=\left\{ \begin{array}{ll}
\varphi_f(x) & {\rm if\ } x\in U_i \\
x &{\rm if\ } x\in M\setminus U_i\\
\end{array}.\right.$$ It is clear from the properties of $f$ that $\psi_f$ is indeed a homeomorphism on $M$. Clearly we have $K \subset \psi_f(V)$. Moreover, the map $t\in [0, 1] \mapsto \psi_{(1-t)f+ tk}$ defines a continuous path in $\mathcal{H}(M)$ from $\psi_f$ to the identity. Here $k$ denotes the constant function of value $1$ defined on $\mathbb{R}_{\geq 0}$. Thus we have $\psi_f \in \mathcal{H}_0(M)$.
Next we see examples of finite filling actions of path-connected groups on infinite dimensional spaces. Let $Q:=\prod_{\mathbb{N}} [0, 1]$ be the Hilbert cube. Recall that a topological space is said to be a Hilbert cube manifold if there is an open cover each of the member is homeomorphic to an open subset of $Q$. It is not hard to show that open subsets of $Q$ in the definition can be taken to be $[0, 1)\times Q$. (See Theorem 12.1 of [@Ch] for instance.) Obvious examples are $Q$ itself and the product of $Q$ and a topological manifold (possible with boundary). We refer the reader to [@Ch] for more information of Hilbert cube manifolds.
\[Lem:Qman\] Let $M$ be a connected compact Hilbert cube manifold. Then the action $\mathcal{H}_0(M)\curvearrowright M$ has the finite filling property.
We first show the following claim. For any open subset $U$ of $[0, 1)\times [0, 1]^n$ of the form $(a, b)^n\times [0, 1]$ ($0<a<b < 1$) and for any compact subset $K$ of $[0, 1)\times [0, 1]^n$, there is a homeomorphism $h\in \mathcal{H}_{c, 0}([0, 1) \times [0, 1]^n)$ satisfying $K \subset h(U)$. Here, for a locally compact metrizable space $Y$, $\mathcal{H}_{c, 0}(Y)$ denotes the subgroup of homeomorphisms on $Y$ defined as follows. First we define $\mathcal{H}_{c}(Y)$ to be the group of homeomorphisms on $Y$ which coincide with the identity off a compact subset. Then we identify $\mathcal{H}_{c}(Y)$ with the inductive limit of subgroups of homeomorphism groups of compact subsets of $Y$ in the natural way. Then we topologize $\mathcal{H}_{c}(Y)$ with the inductive topology. Now we define $\mathcal{H}_{c, 0}(Y)$ to be the path-connected component of $\mathcal{H}_{c}(Y)$ containing the identity with respect to this topology. To show the claim, we first construct a homeomorphism $h_1 \in \mathcal{H}_{c, 0}([0, 1)\times [0, 1]^n)$ satisfying $h_1(\{0 \}\times [0, 1]^n) \subset (a, b)^n\times [0, 1]$ in a similar way to the proof of Lemma \[Lem:man\]. Then, since $h_1$ is a homeomorphism, there is a positive number $\delta>0$ satisfying $h_1([0, \delta)\times [0, 1]^n )\subset (a, b)^n\times [0, 1].$ On the one hand, it is easy to find $h_2 \in \mathcal{H}_{c, 0}([0, 1)\times [0, 1]^n)$ satisfying $K \subset h_2([0, \delta)\times [0, 1]^n).$ Now the homeomorphism $h:=h_2\circ h_1^{-1}$ satisfies the required condition.
Next we observe that for any compact metrizable space $X$ and its open subset $U$, any $h\in \mathcal{H}_{c, 0}(U)$ extends to a homeomorphism $\tilde{h}$ in $\mathcal{H}_0(X)$ by defining $\tilde{h}(x)=x$ off $U$. Now thanks to the claim in the previous paragraph with this observation, the rest of the proof can be completed by a similar way to that of Lemma \[Lem:man\].
We next show that the finite filling property gives a sufficient condition for the pure infiniteness of the reduced groupoid -algebra. Recall from [@Mat] that an étale groupoid $G$ is said to be essentially principal if the interior of the set $\{g\in G: r(g)=s(g)\}$ coincides with $G^{(0)}$. Note that for transformation groupoids, this condition is equivalent to the topological freeness of the original dynamical system.
\[Prop:pi\] Let $G$ be an étale groupoid with the finite filling property. Assume further that $G$ is essentially principal. Then the reduced groupoid -algebra ${\rm C}^\ast_{\rm r}(G)$ is purely infinite and simple. In particular, if $G$ is additionally assumed to be second countable and amenable, then ${\rm C}^\ast_{\rm r}(G)$ is a Kirchberg algebra in the UCT class.
We note that the last statement immediately follows from the first one since the reduced groupoid -algebra of an amenable étale groupoid is nuclear (see Theorem 5.6.18 of [@BO]) and is in the UCT class [@Tu]. To show the main statement, we need the following lemma, which is the analogue of Lemma 1.5 of [@JR].
\[Lem:pi\] Let $G$ be an étale groupoid with the $n$-filling property. Let $b$ be a positive element in $C(G^{(0)})$ with norm one. Then for any $\epsilon>0$, there is $c\in {\rm C}^\ast_{\rm r}(G)$ such that $\|c \|\leq \sqrt{n}$ and $c^\ast b c\geq 1-\epsilon$.
Set $U:=\{x\in G^{(0)}: b(x)>1-\epsilon\}$. Take $n$ mutually disjoint non-empty open subsets $U_1, \ldots, U_n$ of $U$. Since $G$ is minimal, there are $n$ open $G$-sets $V_1, \ldots, V_n$ with the property that the intersection $\bigcap_i r(V_i U_i)$ is non-empty. Using the $n$-filling property of $G$ with this observation, we can find $n$ open $G$-sets $W_1, \ldots, W_n$ satisfying $$\bigcup_{i=1}^n r(W_i U_i)=G^{(0)}.$$ By replacing $W_i$ by $W_i U_i$, we may assume $s(W_i)\subset U_i$. Since $G$ is locally compact and $G^{(0)}$ is compact, replacing each $W_i$ by a smaller one if necessary, we may assume further that each $W_i$ is relatively compact in $G$. Since $G$ is locally compact, for each $i$, it is not hard to find an increasing net $(W_{i, \lambda})_{\lambda \in \Lambda}$ of open subsets of $W_i$ that satisfies the following conditions. The closure of $W_{i, \lambda}$ in $G$ is contained in $W_i$ for each $\lambda$, and the union $\bigcup_\lambda W_{i, \lambda}$ is equal to $W_i$. Since the unit space $G^{(0)}$ is compact, there is $\lambda \in \Lambda$ satisfying $\bigcup_{i=1}^n r(W_{i, \lambda})= G^{(0)}$. Now fix such $\lambda$ and put $Z_i:= {\rm cl}(W_{i, \lambda})$ for each $i$. Then, by the choice of $W_{i, \lambda}$, the $Z_i$ is a compact $G$-set. Moreover we have $$G^{(0)} = \bigcup_{i=1}^n r(W_{i, \lambda})\subset \bigcup_{i=1}^n r(Z_i).$$ Now for each $i$, take a continuous function $f_i \in C_c(G)$ satisfying the following conditions.
1. $0 \leq f_i \leq 1.$
2. ${\rm supp}(f_i)\subset W_i$.
3. $f_i\equiv 1$ on $Z_i$.
(Since $Z_i$ and the closure of $W_i$ in $G$ are compact, such function exists.) Since $W_i$ is a $G$-set, these conditions imply that $f_i \ast f_i^\ast \in C(G^{(0)})$ and that $f_i \ast f_i^\ast \leq 1$. Since the sets $s(W_1), \ldots, s(W_n)$ are mutually disjoint, we have $f_i \ast f_j^\ast =0$ for two distinct $i$ and $j$. Now put $c:=\sum_{i=1}^n f_i^\ast$. The above observations show that $c^\ast \ast c\in C(G^{(0)})$ and that $c^\ast \ast c \leq n$. Thus $\|c\| \leq \sqrt{n}$. Since the $G$-sets $W_1, \ldots, W_n$ have mutually disjoint sources, we also get $c^\ast \ast b \ast c\in C(G^{(0)})$. Since $s(W_i)\subset U$ for each $i$ and $\bigcup_{i=1}^n r(Z_i)=G^{(0)}$, we further obtain $c^\ast \ast b \ast c\geq 1-\epsilon.$
The rest of the proof is basically the same as that in [@JR]. We first observe that since $G$ is essentially principal, it is not hard to show that for any $b\in C_c(G)$ and $\epsilon>0$, there is a positive element $y\in C(G^{(0)})$ with norm one satisfying $yby=yE(b)y$ and $\|yby \|> \|E(b)\|-\epsilon$, where $E$ denotes the restriction map $C_c(G)\rightarrow C(G^{(0)})$. Note that the map $E$ extends to a faithful conditional expectation on ${\rm C}^\ast_{\rm r}(G)$. From this with Lemma \[Lem:pi\], for any positive element $b\in C_c(G)$ with $\| E(b)\|=1$, there is an element $c\in C_c(G^{(0)})$ satisfying $\|c\|\leq \sqrt{n}$ and $c^{\ast} b c\geq 1/2.$ Since the norm of $c$ is bounded by the fixed constant $\sqrt{n}$, now a standard argument completes the proof.
Minimal skew products with purely infinite crossed products
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Now using the finite and weak finite filling property, we construct minimal skew products whose crossed products are purely infinite.
\[Prop:filling\] Let $\alpha\colon \Gamma \curvearrowright Z$ be an amenable topologically free dynamical system with the weak $n$-filling property. Let $\mathcal{G}\curvearrowright Y$ be a minimal dynamical system of a path connected group $\mathcal{G}$ with the $m$-filling property. Then the set $$\left\{ \beta\in \overline{\mathcal{S}}_{\mathcal{G}}(\alpha): \beta {\rm \ has\ the\ weak\ }(nm){\rm \mathchar`-filling\ property}\right\}$$ is a $G_\delta$-dense subset of $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha).$
For an open set $U$ of $X=Z\times Y$, let $\mathcal{F}_U$ denote the set of elements $\beta$ of $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$ satisfying the following condition. There are $nm$ open $G_ \beta$-sets $V_1, \ldots, V_{nm}$ with $\bigcup_i r(V_iU)= X$. Here $G_\beta$ denotes the transformation groupoid $X\rtimes_\beta \Gamma$ of $\beta$. Then for a countable basis $(U_n)_n$ of $X$, the set in the question coincides with the intersection $\bigcap_n \mathcal{F}_{U_n}$. Hence it suffices to show that each $\mathcal{F}_U$ is open and dense in $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$.
We first show the openness of $\mathcal{F}_U$. Let $\beta \in \mathcal{F}_U$. Let $V_1, \ldots, V_{nm}$ be open $G_\beta$-sets as above. Replacing $V_i$’s by smaller ones, we may assume that they are relatively compact in $G_\beta$ and that the sources $s(V_i)$ are contained in $U$. Set $F:=\pi(\bigcup_i V_i)$, where $\pi\colon X\rtimes_\beta \Gamma \rightarrow \Gamma$ denotes the projection onto the second coordinate. Since each $V_i$ is relatively compact in $G_\beta$, the set $F$ is a finite subset of $\Gamma$. Now we apply the argument in the proof of Lemma \[Lem:pi\] to $(V_i)_i$ to choose compact $G_\beta$-sets $W_1, \ldots, W_{nm}$ with the following properties. The $W_i$ is contained in $V_i$ for each $i$ and the union $\bigcup_i r({\rm int}(W_i))$ is equal to $X$. Now for a $G_\beta$-set $W$ and $g\in \Gamma$, define the subset $W_g\subset X$ to be $r(W\cap \pi^{-1}(\{g\})).$ Then, for each $i$, the sets $(W_{i, g})_{g\in F}$ are mutually disjoint compact sets in $X$. Moreover, the union $\bigcup_{i, g}{\rm int}(W_{i, g})$ is equal to $X$.
For $W \subset X$ and $\delta >0$, we define the (open) subsets $\mathcal{N}_\delta(W)$ and $\mathcal{I}_\delta(W)$ of $X$ as follows. $$\mathcal{N}_\delta(W) := \bigcup_{x\in W} B(x, \delta),$$ $$\mathcal{I}_\delta(W):=\{x\in X: {\rm there\ is\ }\eta>\delta {\rm \ with\ }B(x, \eta)\subset W\}.$$ Here for $x \in X$ and $\eta >0$, $B(x, \eta)$ denotes the open ball of center $x$ and radius $\eta$. Then, from the properties of $W_i$’s and the compactness of $X$, for a sufficiently small positive number $\delta >0$, the following conditions hold. The sets $(\mathcal{N}_\delta(W_{i, g}))_g$ are mutually disjoint for each $i$ and the sets $(\mathcal{I}_\delta(W_{i, g}))_{i, g}$ cover $X$. We fix such positive number $\delta$. From the first condition, for any $\gamma \in \overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$ satisfying $d(\gamma_s, \beta_s)< \delta$ for all $s\in F$, each $W_i$ is a $G_\gamma$-set. Here $W_i$ is regarded as a subset of $G_\gamma$ by identifying the transformation groupoids with the set $\Gamma \times X$ by ignoring the first coordinates. Let $r_\beta$ and $r_\gamma$ denote the range map of $G_\beta$ and $G_\gamma$ respectively. Then we have $$\bigcup_i r_\gamma ({\rm int} (W_i))\supset \bigcup_i \mathcal{I}_\delta ( r_\beta ({\rm int} (W_i)))
= \bigcup_{i, g} \mathcal{I}_\delta(W_{i, g}) =X.$$ Therefore we have $\gamma \in \mathcal{F}_U$, which proves the openness of $\mathcal{F}_U$.
To show the density of $\mathcal{F}_U$, by the similar reason to that in the proof of Theorem \[Thm:min\], it suffices to show the following statement. For any $\epsilon >0$ and any finite subset $S\subset \Gamma$, there is a homeomorphism $H \in \mathcal{G}_s$ satisfying the following conditions.
1. $d(\bar{\alpha}_s, H^{-1}\circ \bar{\alpha}_s \circ H)<\epsilon$ for $s\in S$.
2. $H^{-1}\circ \bar{\alpha}\circ H\in \mathcal{F}_U$.
Replacing $U$ by a smaller open set, we may assume $U=W\times V$ for some $W\subset Z$ and $V\subset Y$. By the $m$-filling property of $\mathcal{G}\curvearrowright Y$, we can choose $m$ elements $\tilde{h}_1, \ldots, \tilde{h}_m$ of $\mathcal{G}$ with $\bigcup_i \tilde{h}_i(V)= Y$. Now proceeding the same argument as in the proof of Theorem \[Thm:min\], we get a continuous map $g\colon Z\rightarrow \mathcal{G}$ with the following conditions.
1. $d(g_{s.z}^{-1}g_z, {\mbox{\rm id}}_Y)<\epsilon$ for all $z\in Z$ and $s\in S$.
2. There are $m$ elements $w_1, \ldots, w_m$ in $W$ with the condition $\bigcup_i {g_{w_i}}(V)=Y$.
Let $H \in \mathcal{G}_s$ be the element corresponding to $g$. Then from the first condition, we conclude $d(\bar{\alpha}_s, H^{-1}\circ \bar{\alpha}_s \circ H)<\epsilon$ for $s\in S$. To show $\beta := H^{-1}\circ \bar{\alpha} \circ H\in \mathcal{F}_U$, it suffices to show the following claim. There are $nm$ open $G_{\bar{\alpha}}$-sets $W_1, \ldots, W_{nm}$ with $\bigcup_i r(W_i H(U))=X.$ Indeed the sets $$\{(H^{-1}(z), s, H^{-1}(w))\in X \times \Gamma \times X: (z, s, w)\in W_i\}\ (i=1, \ldots, nm)$$ then define the desired open $G_\beta$-sets. To show the claim, first note that since $g$ is continuous, there are an open subset $U_i$ of $U$ containing $w_i$ for $i=1, \ldots, m$ and an open covering $(V_i)_{i=1}^m$ of $Y$ satisfying the following condition. For any $z\in U_i$, we have $V_i \subset g_z(V)$. From these conditions, we have $H(U)\supset \bigcup_{i=1}^m(U_i \times V_i)$. Now for each $1\leq i \leq m$, take $n$ open $G_\alpha$-sets $W_{i, 1}, \ldots, W_{i, n}$ with $\bigcup_{j=1}^n r(W_{i, j} U_i)=Z$. For each $1\leq i \leq m$ and $1\leq j \leq n$, set $Z_{i, j}:=\varphi^{-1}(W_{i, j})$, where $\varphi\colon G_{\bar{\alpha}}\rightarrow G_\alpha$ denotes the canonical quotient map. Then each $Z_{i, j}$ is an open $G_{\bar{\alpha}}$-set and we further get $$\bigcup_{i, j} r_{\bar{\alpha}} (Z_{i, j} H(U))\supset \bigcup_{i, j} r_{\bar{\alpha}} (Z_{i, j} (U_i \times V_i))=\bigcup_{i, j} (r_\alpha(W_{i, j}U_i)\times V_i) =X.$$
In [@RS], Rørdam and Sierakowski have shown that every countable non-amenable exact group admits an amenable minimal free dynamical system on the Cantor set whose crossed product is a Kirchberg algebra in the UCT class. Proposition \[Prop:filling\] particularly gives an extension of their result to more general spaces.
\[Thm:RS\] Let $M$ be a connected closed topological manifold, a connected compact Hilbert cube manifold, or a countable direct product of these manifolds. Let $X$ be the Cantor set. Then every countable non-amenable exact group admits an amenable minimal free dynamical system on $M\times X$ whose crossed product is a Kirchberg algebra in the UCT class.
For the first two cases, the statement immediately follows from Example \[Exm:1fill\], Lemmas \[Lem:man\] and \[Lem:Qman\], and Propositions \[Prop:pi\] and \[Prop:filling\].
For the last case, let $M_1, M_2, \ldots$ be a sequence of spaces each of which is either connected closed topological manifold or connected compact Hilbert cube manifold. Set $N_n:= M_1 \times \cdots \times M_n \times X$ for each $n$. We put $\alpha_0:=\alpha$ and $N_0:=X$ for convenience. We inductively apply Proposition \[Prop:filling\] to $\alpha_n\colon \Gamma\curvearrowright N_n$ and $M_{n+1}$ to get a minimal skew product extension $\alpha_{n+1}\colon \Gamma\curvearrowright N_{n+1}$ of $\alpha_n$ with the weak finite filling property. Then we get the projective system $(\alpha_n)_{n=1}^\infty$ of dynamical systems of $\Gamma$. Since pure infiniteness of -algebras is preserved under taking increasing union (Prop 4.1.8 of [@Ror]), the projective limit $\alpha_\infty:=\varprojlim \alpha_n$ possesses the desired properties.
Minimal dynamical systems of free groups on products of Cantor set and closed manifolds {#Sec:free}
=======================================================================================
In this section, we investigate the K-groups of the crossed products of minimal dynamical systems obtained in Theorem \[Thm:min\] for the free group case. By using the Pimsner–Voiculescu six term exact sequence [@PV], we give a K$\ddot{{\rm u}}$nneth-type formula for K-groups of their crossed products. As an application, we give the following generalization of Theorems 4.10 and 4.22 of [@Suz].
\[Thm:man\] Let $\Gamma$ be a countable non-amenable virtually free group. Let $M$ be either connected closed topological manifold or connected compact Hilbert cube manifold. Then there exist continuously many amenable minimal free dynamical systems of $\Gamma$ on the product of $M$ and the Cantor set whose crossed products are mutually non-isomorphic Kirchberg algebras.
In the below, we regard abelian groups as $\mathbb{Z}$-modules. We simply denote the tensor product ‘$\otimes_{\mathbb{Z}}$’ by ‘$\otimes$’ for short. Recall that for two abelian groups $G, H$, the group ${\rm Tor}_1^{\mathbb{Z}}(G, H)$ is defined as follows. First take a projective resolution of $G$. $$\cdots \rightarrow P_2\rightarrow P_1 \rightarrow P_0\rightarrow G \rightarrow 0.$$ Then by tensoring $H$ with the above resolution, we obtain a complex $$\cdots \rightarrow P_2\otimes H \rightarrow P_1\otimes H \rightarrow P_0 \otimes H \rightarrow 0.$$ The group ${\rm Tor}_1^{\mathbb{Z}}(G, H)$ is then defined as the first homology of the above complex. Note that the definition does not depend on the choice of the projective resolution. We remark that when we have a projective resolution of length one $$0\rightarrow P_1 \rightarrow P_0\rightarrow G \rightarrow 0,$$ then ${\rm Tor}_1^{\mathbb{Z}}(G, H)$ is computed as the kernel of the homomorphism $P_1\otimes H\rightarrow P_0\otimes H$. See [@Br] for the detail.
\[Prop:free\] Let $\alpha\colon \mathbb{F}_d \curvearrowright X$ be an amenable minimal topologically free dynamical system of the free group $\mathbb{F}_d$ on the Cantor set $X$. Let $\mathcal{G}\curvearrowright Y$ be a minimal action of a path-connected group $\mathcal{G}$ on a compact metrizable space $Y$. Let $\beta\in \overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$. Let $A$ and $B$ denote the crossed product of $\alpha$ and $\beta$ respectively. Then for $i=0, 1$, we have the following short exact sequence. $$0\rightarrow K_0(A)\otimes K^i(Y) \rightarrow K_i(B)\rightarrow
(K_1(A)\otimes K^{1-i}(Y))\oplus {\rm Tor}_1^\mathbb{Z}(K_0(A), K^{1-i}(Y))\rightarrow 0.$$ Moreover, the first map maps $[1_A]_0\otimes [1_Y]_0$ to $[1_B]_0$ when $i=0$.
Since $C(X)$ is an AF-algebra, we have a canonical isomorphism $$K^i(X \times Y)\rightarrow C(X, K^i(Y)) (\cong K^0(X)\otimes K^i(Y))$$ for $i=0, 1$. Here $C(X, K^i(Y))$ denotes the group of continuous maps from $X$ into $K^i(Y)$ and $K^i(Y)$ is regarded as a discrete group. For $i=0$, the isomorphism is given by mapping the element $[p]_0$ where $p$ is a projection in $\mathbb{K}\otimes C(X)\otimes C(Y)$ to the map $x\in X\mapsto [p(x, \cdot)]_0\in K^0(Y)$ and similarly for the case $i=1$.
From this isomorphism and the fact that $\mathcal{G}$ is path-connected, for any $\gamma \in \mathcal{S}_{\mathcal{G}}(\alpha)$ and $g\in \mathbb{F}_d$, we have $(\gamma_g)_{\ast, i}=(\alpha_g)_{\ast, 0} \otimes {\mbox{\rm id}}_{K^i(Y)}$ for $i=0, 1$. Here we identify $K^i(X\times Y)$ with $K^0(X)\otimes K^i(Y)$ under the above isomorphism. By continuity of the K-theory, the above equality holds for all $\gamma\in \overline{\mathcal{S}}_{\mathcal{G}}(\alpha)$. Now let $S$ be a free basis of $\mathbb{F}_d$. Then by the Pimsner–Voiculescu six term exact sequence [@PV], we have the following short exact sequence. $$0\rightarrow {\mbox{\rm coker}}(\varphi\otimes {\mbox{\rm id}}_{K^i(Y)})\rightarrow K_i(B)\rightarrow \ker(\varphi\otimes {\mbox{\rm id}}_{K^{1-i}(Y)})\rightarrow 0.$$ Here $\varphi$ denotes the homomorphism $$\varphi\colon K^0(X)^{\oplus S}\rightarrow K^0(X)$$ which maps $(f_s)_{s\in S}$ to $\sum_{s\in S}(f_s- (\alpha_s)_{\ast, 0}(f_s))$. Since $K^0(X)$ is a free abelian group, the exact sequence $$0\rightarrow K_1(A)\rightarrow K^0(X)^{\oplus S}\rightarrow K^0(X)\rightarrow K_0(A)\rightarrow 0$$ obtained by the Pimsner–Voiculescu six-term exact sequence is a free resolution of $K_0(A)$. This also gives the free resolution $$0\rightarrow {\rm im}(\varphi)\rightarrow K^0(X)\rightarrow K_0(A)\rightarrow 0$$ of $K_0(A)$. Here the first map is given by the inclusion map, say $\iota$.
Let $\psi\colon K^0(X)^{\oplus S}\rightarrow {\rm im}(\varphi)$ be the surjective homomorphism obtained by restricting the range of $\varphi$. By tensoring $K^i(Y)$ with the second free resolution, we obtain the following exact sequence. $$0\rightarrow {\rm Tor}_1^\mathbb{Z}(K_0(A), K^i(Y))\rightarrow {\rm im}(\varphi) \otimes K^i(Y) \rightarrow K^0(X)\otimes K^i(Y)\rightarrow K_0(A)\otimes K^i(Y)\rightarrow 0.$$ This shows that $$\ker(\iota\otimes {\mbox{\rm id}}_{K^i(Y)})\cong {\rm Tor}_1^\mathbb{Z}(K_0(A), K^i(Y)).$$ Since the second map surjects onto ${\rm im}(\varphi\otimes {\mbox{\rm id}}_{K^i(Y)})$, we also obtain the isomorphism $${\mbox{\rm coker}}(\varphi\otimes {\mbox{\rm id}}_{K^i(Y)})\cong K_0(A)\otimes K^i(Y).$$ Since $\varphi=\iota\circ \psi$ and $\psi$ is surjective, we have the following exact sequence. $$\label{eq:1}
0\rightarrow \ker(\psi \otimes {\mbox{\rm id}}_{K^i(Y)}) \rightarrow \ker(\varphi\otimes {\mbox{\rm id}}_{K^i(Y)}) \rightarrow \ker(\iota\otimes {\mbox{\rm id}}_{K^i(Y)}) \rightarrow 0.$$ Here the first map is the canonical inclusion and the second map is the restriction of $\psi\otimes {\mbox{\rm id}}_{K^i(Y)}$. Since ${\rm im}(\varphi)$ is free abelian, there is a direct complement $K$ of $\ker(\varphi)$ in $K^0(X)^{\oplus S}$. Note that the restriction of $\psi$ on $K$ is an isomorphism. Hence we have the isomorphism $$\ker(\psi\otimes {\mbox{\rm id}}_{K^i(Y)})=\ker(\psi)\otimes K^i(Y)\cong K_1(A)\otimes K^i(Y).$$ Again by the freeness of ${\rm im}(\varphi)$, we have a right inverse $\sigma$ of $\psi$. Then the homomorphism $\sigma\otimes {\mbox{\rm id}}_{K^i(Y)}$ gives a splitting of the short exact sequence (\[eq:1\]). Combining these observations, we obtain the isomorphism $$\ker(\varphi\otimes {\mbox{\rm id}}_{K^i(Y)})\cong (K_1(A)\otimes K^i(Y))\oplus {\rm Tor}_1^\mathbb{Z}(K_0(A), K^i(Y)).$$ Now the first exact sequence completes the proof.
Certainly, when $K^\ast(Y)$ has a good property, the short exact sequence in Proposition \[Prop:free\] is spilitting. For example, it holds true when $K^{1-i}(Y)$ is projective or one of $K_0(A)$ or $K^i(Y)$ is injective. (Recall that $K_1(A)$ is always free abelian and that the tensor product of an injective $\mathbb{Z}$-module with an arbitrary $\mathbb{Z}$-module is again injective by Corollary 4.2 of Ch.III of [@Br].) However, we do not know whether it is splitting in general. Recall that a splitting of the K$\ddot{{\rm u}}$nneth tensor product theorem is obtained by replacing considered -algebras by easier ones by using suitable elements of the KK-groups (see Remark 7.11 of [@RSc]). However, in our setting, this argument does not work. Such replacement does not respect the relation among $C(X), C(Y), A, B,$ and $\mathbb{F}_d$.
We first prove the claim for free groups. Theorem 5.3 of [@Suz2] shows that for any finite $d$, there is an amenable minimal topologically free dynamical system $\gamma$ of $\mathbb{F}_d$ on the Cantor set whose crossed product $A$ satisfies the following condition. The unit $[1]_0\in K_0(A)$ generates a direct summand of $K_0(A)$ isomorphic to $\mathbb{Z}$. Note that this property passes to unital -subalgebras of $A$. Moreover, since $\gamma$ is found as a factor of the ideal boundary action, its restriction to any finite index subgroup of $\mathbb{F}_d$ is minimal. It is also not hard to show that the restriction of $\gamma$ to any finite index subgroup of $\mathbb{F}_d$ is purely infinite (cf. the proof of Lemma 4.8 of [@Suz2]). Applying the argument in the proof of Theorem 4.22 in [@Suz] using $\gamma$ instead of the action used there, we obtain the following consequence. (By finite generatedness, in this case the proof becomes easier than the one there.) For any non-empty set $\mathcal{Q}$ of prime numbers, there is an amenable minimal free purely infinite dynamical system $\alpha_\mathcal{Q}$ of $\mathbb{F}_d$ on the Cantor set whose $K_0$-group $G$ satisfies the following condition. $$\{p\in \mathcal{P}: [1]_0\in pG\}= \mathcal{Q}.$$ Here $\mathcal{P}$ denotes the set of all prime numbers. The similar statement for $\mathbb{F}_\infty$ is shown in the proof of Theorem 4.22 of [@Suz]. We also denote by $\alpha_\mathcal{Q}$ a dynamical system of $\mathbb{F}_\infty$ satisfying the above conditions.
Now let $M$ be as in the statement. Put $$\mathcal{R}:=\{p\in \mathcal{P}: K^1(M){\rm \ contains\ an\ element \ of\ order\ }p\}.$$ Then by [@Ch0], $\mathcal{R}$ is finite. (Indeed, in either case, $M\times [0, 1]^\mathbb{N}$ is a compact Hilbert cube manifold. Now the main theorem of [@Ch0] shows that $K^1(M)$ is in fact finitely generated.)
Let $\mathcal{G}$ denote the path-connected component of $\mathcal{H}(M)$ containing the identity. For each non-empty subset $\mathcal{Q}$ of $\mathcal{P}\setminus \mathcal{R}$, we apply Proposition \[Prop:filling\] to $\alpha_\mathcal{Q}$ to choose $\beta$ from $\overline{\mathcal{S}}_{\mathcal{G}}(\alpha_\mathcal{Q})$ whose crossed product is a Kirchberg algebra. For $i=0, 1$, denote by $G_i$ and $H_i$ the $K_i$-group of the crossed products of $\alpha_\mathcal{Q}$ and $\beta$ respectively. We claim that $$\tilde{\mathcal{Q}}:=\{p\in \mathcal{P}\setminus \mathcal{R}: [1]_0\in pH_0\}= \mathcal{Q}.$$ Since the cardinal of the power set of $\mathcal{P}\setminus \mathcal{R}$ is continuum, this ends the proof. The inclusion $\mathcal{Q}\subset \tilde{\mathcal{Q}}$ is obvious. To see the converse, let $p\in \tilde{\mathcal{Q}}$ and take $h\in H_0$ with $ph=[1]_0$. Denote by $\partial_i$ the third map of the short exact sequence in Proposition \[Prop:free\]. Then since $\partial_0([1]_0)=0$, we have $p\partial_0(h)=0$. On the other hand, by the definition of $\mathcal{R}$ and the fact that $G_1$ is torsion free, there is no element of order $p$ in the third term of the short exact sequence. Thus $p\partial_0(h)=0$ implies $\partial_0(h)=0$. Hence there is an element $y$ in the first term of the short exact sequence with $\sigma_0(y)=h$. Here $\sigma_i$ denotes the second map in the short exact sequence. Then from the injectivity of $\sigma_0$ and the equality $ph=[1]_0$, we must have $py=[1]_0\otimes [1_M]_0$. Now let $\tau\colon K^0(M) \rightarrow \mathbb{Z}$ be the homomorphism induced from a character on $C(M)$. Put $w:=({\mbox{\rm id}}\otimes \tau)(y)\in G_0$. (We identify $G_0$ with $G_0\otimes \mathbb{Z}$ in the obvious way.) Then we have $pw=({\mbox{\rm id}}\otimes\tau)([1]_0\otimes [1_M]_0)=[1]_0$. Thus we get $p\in \mathcal{Q}$ as desired.
The proof for general case is done by taking the induced dynamical systems of the actions obtained in above. For the detail, see the proof of Theorem 4.7 in [@Suz] for instance.
Acknowledgement {#acknowledgement .unnumbered}
---------------
The author was supported by Research Fellow of the JSPS (No.25-7810) and the Program of Leading Graduate Schools, MEXT, Japan.
[99]{} C. Anantharaman-Delaroche, [*Systèmes dynamiques non commutatifs et moyennabilité.*]{} Math. Ann. [**279**]{} (1987), 297–315. C. Anantharaman-Delaroche, [*Purely infinite -algebras arising from dynamical systems.*]{} Bull. Soc. Math. France [**125**]{} (1997), 199–225. K. S. Brown, [*Cohomology of Groups.*]{} Graduate Texts in Mathematics 87 (1982), Springer-Verlag, New York-Berlin. N. P. Brown, N. Ozawa, [*-algebras and finite-dimensional approximations.*]{} Graduate Studies in Mathematics 88. American Mathematical Society, Providence, RI, 2008. xvi+509 pp. J. Carrion, M. Dadarlat, C. Eckhardt, [*On groups with quasidiagonal -algebras.*]{} J. Funct. Anal. [**265**]{} (2013), no. 1, 135–152. T. A. Chapman, [*Compact Hilbert cube manifolds and the invariance of Whitehead torsion.*]{} Bull. Amer. Math. Soc. [**79**]{} (1973), 52–56. T. A. Chapman, [*Lectures on Hilbert cube manifolds.*]{} Vol. 28 (1975), Amer. Math. Soc. J. Cuntz, [*K-theory for certain -algebras.*]{} Ann. of Math. [**113**]{} (1981), no. 1, 181–197. E. Glasner, [*Ergodic theory via joinings.*]{} Mathematical Surveys and Monographs 101, American Mathematical Society, Providence, RI, 2003. E. Glasner, B. Weiss, [*On the construction of minimal skew products.*]{} Israel J. Math. [**34**]{} (1979), 321–336. P. Jolissaint and G. Robertson, [*Simple purely infinite -algebras and $n$-filling actions.*]{} J. Funct. Anal. [**175**]{} (2000), no. 1, 197–-213. E. Kirchberg, [*The classification of purely infinite -algebras using Kasparov’s theory.*]{} Preprint. E. Kirchberg, N. C. Phillips, [*Embedding of exact -algebras in the Cuntz algebra $\mathcal{O}_2$.*]{} J. reine angew. Math. [**525**]{} (2000), 17–-53. M. Laca, J. Spielberg, [*Purely infinite -algebras from boundary actions of discrete groups.*]{} J. reine angew. Math. [**480**]{} (1996), 125–139. H. Matui, [*Topological full groups of one-sided shifts of finite type.*]{} J. reine angew. Math. [**705**]{} (2015), 35–84. M. Nerurkar, [*Ergodic continuous skew product actions of amenable groups.*]{} Pacific J. Math. [**119**]{} (1985), 343–363. N. Ozawa, [*Amenable actions and exactness for discrete groups.*]{} C. R. Acad. Sci. Paris Ser. I Math. [**330**]{} (2000), 691–695. N. C. Phillips. [*A classification theorem for nuclear purely infinite simple -algebras.*]{} Doc. Math [**5**]{} (2000), 49–114. M. Pimsner, D. Voiculescu, [*K-groups of reduced crossed products by free groups.*]{} J. Operator Theory [**8**]{} (1982), 131–156. M. A. Rieffel, [*Continuous fields of -algebras coming from group cocycles and actions.*]{} Math. Ann. [**283**]{} (1989). no. 4 631–643. M. Rørdam, [*Classification of certain infinite simple -algebras.*]{} J. Funct. Anal. [**131**]{} (1995), 415–458. M. Rørdam, [*Classification of nuclear -algebras.*]{} Encyclopaedia of Mathematical Sciences 126 (2002), 1–145. M. Rørdam, [*A simple C\*-algebra with a finite and an infinite projection.*]{} Acta Math. [**191**]{} (2003), 109–142. M. Rørdam, A. Sierakowski, [*Purely infinite -algebras arising from crossed products.*]{} Ergodic Theory Dynam. Systems [**32**]{} (2012), 273–293. J. Rosenberg, C. Schochet, [*The K$\ddot{u}$nneth theorem and the universal coefficient theorem for Kasparov’s generalized K-functor.*]{} Duke Math. J. [**55**]{} (1987), no. 2, 431–474. Y. Suzuki, [*Amenable minimal Cantor systems of free groups arising from diagonal actions.*]{} To appear in J. reine angew. Math., arXiv:1312.7098. Y. Suzuki, [*Group -algebras as decreasing intersection of nuclear C\*-algebras.*]{} To appear in Amer. J. Math., arXiv:1410.8347. J.-L. Tu, [*La conjecture de Baum–Connes pour les feuilletages moyennables.*]{} K-theory [**17**]{} (1999), 215–264.
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// Code generated by protoc-gen-gogo. DO NOT EDIT.
// source: k8s.io/api/imagepolicy/v1alpha1/generated.proto
/*
Package v1alpha1 is a generated protocol buffer package.
It is generated from these files:
k8s.io/api/imagepolicy/v1alpha1/generated.proto
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package v1alpha1
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return dAtA[:n], nil
}
func (m *ImageReviewContainerSpec) MarshalTo(dAtA []byte) (int, error) {
var i int
_ = i
var l int
_ = l
if m.Image != nil {
dAtA[i] = 0xa
i++
i = encodeVarintGenerated(dAtA, i, uint64(len(*m.Image)))
i += copy(dAtA[i:], *m.Image)
}
if m.XXX_unrecognized != nil {
i += copy(dAtA[i:], m.XXX_unrecognized)
}
return i, nil
}
func (m *ImageReviewSpec) Marshal() (dAtA []byte, err error) {
size := m.Size()
dAtA = make([]byte, size)
n, err := m.MarshalTo(dAtA)
if err != nil {
return nil, err
}
return dAtA[:n], nil
}
func (m *ImageReviewSpec) MarshalTo(dAtA []byte) (int, error) {
var i int
_ = i
var l int
_ = l
if len(m.Containers) > 0 {
for _, msg := range m.Containers {
dAtA[i] = 0xa
i++
i = encodeVarintGenerated(dAtA, i, uint64(msg.Size()))
n, err := msg.MarshalTo(dAtA[i:])
if err != nil {
return 0, err
}
i += n
}
}
if len(m.Annotations) > 0 {
for k, _ := range m.Annotations {
dAtA[i] = 0x12
i++
v := m.Annotations[k]
mapSize := 1 + len(k) + sovGenerated(uint64(len(k))) + 1 + len(v) + sovGenerated(uint64(len(v)))
i = encodeVarintGenerated(dAtA, i, uint64(mapSize))
dAtA[i] = 0xa
i++
i = encodeVarintGenerated(dAtA, i, uint64(len(k)))
i += copy(dAtA[i:], k)
dAtA[i] = 0x12
i++
i = encodeVarintGenerated(dAtA, i, uint64(len(v)))
i += copy(dAtA[i:], v)
}
}
if m.Namespace != nil {
dAtA[i] = 0x1a
i++
i = encodeVarintGenerated(dAtA, i, uint64(len(*m.Namespace)))
i += copy(dAtA[i:], *m.Namespace)
}
if m.XXX_unrecognized != nil {
i += copy(dAtA[i:], m.XXX_unrecognized)
}
return i, nil
}
func (m *ImageReviewStatus) Marshal() (dAtA []byte, err error) {
size := m.Size()
dAtA = make([]byte, size)
n, err := m.MarshalTo(dAtA)
if err != nil {
return nil, err
}
return dAtA[:n], nil
}
func (m *ImageReviewStatus) MarshalTo(dAtA []byte) (int, error) {
var i int
_ = i
var l int
_ = l
if m.Allowed != nil {
dAtA[i] = 0x8
i++
if *m.Allowed {
dAtA[i] = 1
} else {
dAtA[i] = 0
}
i++
}
if m.Reason != nil {
dAtA[i] = 0x12
i++
i = encodeVarintGenerated(dAtA, i, uint64(len(*m.Reason)))
i += copy(dAtA[i:], *m.Reason)
}
if len(m.AuditAnnotations) > 0 {
for k, _ := range m.AuditAnnotations {
dAtA[i] = 0x1a
i++
v := m.AuditAnnotations[k]
mapSize := 1 + len(k) + sovGenerated(uint64(len(k))) + 1 + len(v) + sovGenerated(uint64(len(v)))
i = encodeVarintGenerated(dAtA, i, uint64(mapSize))
dAtA[i] = 0xa
i++
i = encodeVarintGenerated(dAtA, i, uint64(len(k)))
i += copy(dAtA[i:], k)
dAtA[i] = 0x12
i++
i = encodeVarintGenerated(dAtA, i, uint64(len(v)))
i += copy(dAtA[i:], v)
}
}
if m.XXX_unrecognized != nil {
i += copy(dAtA[i:], m.XXX_unrecognized)
}
return i, nil
}
func encodeVarintGenerated(dAtA []byte, offset int, v uint64) int {
for v >= 1<<7 {
dAtA[offset] = uint8(v&0x7f | 0x80)
v >>= 7
offset++
}
dAtA[offset] = uint8(v)
return offset + 1
}
func (m *ImageReview) Size() (n int) {
var l int
_ = l
if m.Metadata != nil {
l = m.Metadata.Size()
n += 1 + l + sovGenerated(uint64(l))
}
if m.Spec != nil {
l = m.Spec.Size()
n += 1 + l + sovGenerated(uint64(l))
}
if m.Status != nil {
l = m.Status.Size()
n += 1 + l + sovGenerated(uint64(l))
}
if m.XXX_unrecognized != nil {
n += len(m.XXX_unrecognized)
}
return n
}
func (m *ImageReviewContainerSpec) Size() (n int) {
var l int
_ = l
if m.Image != nil {
l = len(*m.Image)
n += 1 + l + sovGenerated(uint64(l))
}
if m.XXX_unrecognized != nil {
n += len(m.XXX_unrecognized)
}
return n
}
func (m *ImageReviewSpec) Size() (n int) {
var l int
_ = l
if len(m.Containers) > 0 {
for _, e := range m.Containers {
l = e.Size()
n += 1 + l + sovGenerated(uint64(l))
}
}
if len(m.Annotations) > 0 {
for k, v := range m.Annotations {
_ = k
_ = v
mapEntrySize := 1 + len(k) + sovGenerated(uint64(len(k))) + 1 + len(v) + sovGenerated(uint64(len(v)))
n += mapEntrySize + 1 + sovGenerated(uint64(mapEntrySize))
}
}
if m.Namespace != nil {
l = len(*m.Namespace)
n += 1 + l + sovGenerated(uint64(l))
}
if m.XXX_unrecognized != nil {
n += len(m.XXX_unrecognized)
}
return n
}
func (m *ImageReviewStatus) Size() (n int) {
var l int
_ = l
if m.Allowed != nil {
n += 2
}
if m.Reason != nil {
l = len(*m.Reason)
n += 1 + l + sovGenerated(uint64(l))
}
if len(m.AuditAnnotations) > 0 {
for k, v := range m.AuditAnnotations {
_ = k
_ = v
mapEntrySize := 1 + len(k) + sovGenerated(uint64(len(k))) + 1 + len(v) + sovGenerated(uint64(len(v)))
n += mapEntrySize + 1 + sovGenerated(uint64(mapEntrySize))
}
}
if m.XXX_unrecognized != nil {
n += len(m.XXX_unrecognized)
}
return n
}
func sovGenerated(x uint64) (n int) {
for {
n++
x >>= 7
if x == 0 {
break
}
}
return n
}
func sozGenerated(x uint64) (n int) {
return sovGenerated(uint64((x << 1) ^ uint64((int64(x) >> 63))))
}
func (m *ImageReview) Unmarshal(dAtA []byte) error {
l := len(dAtA)
iNdEx := 0
for iNdEx < l {
preIndex := iNdEx
var wire uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
wire |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
fieldNum := int32(wire >> 3)
wireType := int(wire & 0x7)
if wireType == 4 {
return fmt.Errorf("proto: ImageReview: wiretype end group for non-group")
}
if fieldNum <= 0 {
return fmt.Errorf("proto: ImageReview: illegal tag %d (wire type %d)", fieldNum, wire)
}
switch fieldNum {
case 1:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field Metadata", wireType)
}
var msglen int
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
msglen |= (int(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
if msglen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + msglen
if postIndex > l {
return io.ErrUnexpectedEOF
}
if m.Metadata == nil {
m.Metadata = &k8s_io_apimachinery_pkg_apis_meta_v1.ObjectMeta{}
}
if err := m.Metadata.Unmarshal(dAtA[iNdEx:postIndex]); err != nil {
return err
}
iNdEx = postIndex
case 2:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field Spec", wireType)
}
var msglen int
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
msglen |= (int(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
if msglen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + msglen
if postIndex > l {
return io.ErrUnexpectedEOF
}
if m.Spec == nil {
m.Spec = &ImageReviewSpec{}
}
if err := m.Spec.Unmarshal(dAtA[iNdEx:postIndex]); err != nil {
return err
}
iNdEx = postIndex
case 3:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field Status", wireType)
}
var msglen int
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
msglen |= (int(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
if msglen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + msglen
if postIndex > l {
return io.ErrUnexpectedEOF
}
if m.Status == nil {
m.Status = &ImageReviewStatus{}
}
if err := m.Status.Unmarshal(dAtA[iNdEx:postIndex]); err != nil {
return err
}
iNdEx = postIndex
default:
iNdEx = preIndex
skippy, err := skipGenerated(dAtA[iNdEx:])
if err != nil {
return err
}
if skippy < 0 {
return ErrInvalidLengthGenerated
}
if (iNdEx + skippy) > l {
return io.ErrUnexpectedEOF
}
m.XXX_unrecognized = append(m.XXX_unrecognized, dAtA[iNdEx:iNdEx+skippy]...)
iNdEx += skippy
}
}
if iNdEx > l {
return io.ErrUnexpectedEOF
}
return nil
}
func (m *ImageReviewContainerSpec) Unmarshal(dAtA []byte) error {
l := len(dAtA)
iNdEx := 0
for iNdEx < l {
preIndex := iNdEx
var wire uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
wire |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
fieldNum := int32(wire >> 3)
wireType := int(wire & 0x7)
if wireType == 4 {
return fmt.Errorf("proto: ImageReviewContainerSpec: wiretype end group for non-group")
}
if fieldNum <= 0 {
return fmt.Errorf("proto: ImageReviewContainerSpec: illegal tag %d (wire type %d)", fieldNum, wire)
}
switch fieldNum {
case 1:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field Image", wireType)
}
var stringLen uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
stringLen |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
intStringLen := int(stringLen)
if intStringLen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + intStringLen
if postIndex > l {
return io.ErrUnexpectedEOF
}
s := string(dAtA[iNdEx:postIndex])
m.Image = &s
iNdEx = postIndex
default:
iNdEx = preIndex
skippy, err := skipGenerated(dAtA[iNdEx:])
if err != nil {
return err
}
if skippy < 0 {
return ErrInvalidLengthGenerated
}
if (iNdEx + skippy) > l {
return io.ErrUnexpectedEOF
}
m.XXX_unrecognized = append(m.XXX_unrecognized, dAtA[iNdEx:iNdEx+skippy]...)
iNdEx += skippy
}
}
if iNdEx > l {
return io.ErrUnexpectedEOF
}
return nil
}
func (m *ImageReviewSpec) Unmarshal(dAtA []byte) error {
l := len(dAtA)
iNdEx := 0
for iNdEx < l {
preIndex := iNdEx
var wire uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
wire |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
fieldNum := int32(wire >> 3)
wireType := int(wire & 0x7)
if wireType == 4 {
return fmt.Errorf("proto: ImageReviewSpec: wiretype end group for non-group")
}
if fieldNum <= 0 {
return fmt.Errorf("proto: ImageReviewSpec: illegal tag %d (wire type %d)", fieldNum, wire)
}
switch fieldNum {
case 1:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field Containers", wireType)
}
var msglen int
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
msglen |= (int(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
if msglen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + msglen
if postIndex > l {
return io.ErrUnexpectedEOF
}
m.Containers = append(m.Containers, &ImageReviewContainerSpec{})
if err := m.Containers[len(m.Containers)-1].Unmarshal(dAtA[iNdEx:postIndex]); err != nil {
return err
}
iNdEx = postIndex
case 2:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field Annotations", wireType)
}
var msglen int
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
msglen |= (int(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
if msglen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + msglen
if postIndex > l {
return io.ErrUnexpectedEOF
}
if m.Annotations == nil {
m.Annotations = make(map[string]string)
}
var mapkey string
var mapvalue string
for iNdEx < postIndex {
entryPreIndex := iNdEx
var wire uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
wire |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
fieldNum := int32(wire >> 3)
if fieldNum == 1 {
var stringLenmapkey uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
stringLenmapkey |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
intStringLenmapkey := int(stringLenmapkey)
if intStringLenmapkey < 0 {
return ErrInvalidLengthGenerated
}
postStringIndexmapkey := iNdEx + intStringLenmapkey
if postStringIndexmapkey > l {
return io.ErrUnexpectedEOF
}
mapkey = string(dAtA[iNdEx:postStringIndexmapkey])
iNdEx = postStringIndexmapkey
} else if fieldNum == 2 {
var stringLenmapvalue uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
stringLenmapvalue |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
intStringLenmapvalue := int(stringLenmapvalue)
if intStringLenmapvalue < 0 {
return ErrInvalidLengthGenerated
}
postStringIndexmapvalue := iNdEx + intStringLenmapvalue
if postStringIndexmapvalue > l {
return io.ErrUnexpectedEOF
}
mapvalue = string(dAtA[iNdEx:postStringIndexmapvalue])
iNdEx = postStringIndexmapvalue
} else {
iNdEx = entryPreIndex
skippy, err := skipGenerated(dAtA[iNdEx:])
if err != nil {
return err
}
if skippy < 0 {
return ErrInvalidLengthGenerated
}
if (iNdEx + skippy) > postIndex {
return io.ErrUnexpectedEOF
}
iNdEx += skippy
}
}
m.Annotations[mapkey] = mapvalue
iNdEx = postIndex
case 3:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field Namespace", wireType)
}
var stringLen uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
stringLen |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
intStringLen := int(stringLen)
if intStringLen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + intStringLen
if postIndex > l {
return io.ErrUnexpectedEOF
}
s := string(dAtA[iNdEx:postIndex])
m.Namespace = &s
iNdEx = postIndex
default:
iNdEx = preIndex
skippy, err := skipGenerated(dAtA[iNdEx:])
if err != nil {
return err
}
if skippy < 0 {
return ErrInvalidLengthGenerated
}
if (iNdEx + skippy) > l {
return io.ErrUnexpectedEOF
}
m.XXX_unrecognized = append(m.XXX_unrecognized, dAtA[iNdEx:iNdEx+skippy]...)
iNdEx += skippy
}
}
if iNdEx > l {
return io.ErrUnexpectedEOF
}
return nil
}
func (m *ImageReviewStatus) Unmarshal(dAtA []byte) error {
l := len(dAtA)
iNdEx := 0
for iNdEx < l {
preIndex := iNdEx
var wire uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
wire |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
fieldNum := int32(wire >> 3)
wireType := int(wire & 0x7)
if wireType == 4 {
return fmt.Errorf("proto: ImageReviewStatus: wiretype end group for non-group")
}
if fieldNum <= 0 {
return fmt.Errorf("proto: ImageReviewStatus: illegal tag %d (wire type %d)", fieldNum, wire)
}
switch fieldNum {
case 1:
if wireType != 0 {
return fmt.Errorf("proto: wrong wireType = %d for field Allowed", wireType)
}
var v int
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
v |= (int(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
b := bool(v != 0)
m.Allowed = &b
case 2:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field Reason", wireType)
}
var stringLen uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
stringLen |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
intStringLen := int(stringLen)
if intStringLen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + intStringLen
if postIndex > l {
return io.ErrUnexpectedEOF
}
s := string(dAtA[iNdEx:postIndex])
m.Reason = &s
iNdEx = postIndex
case 3:
if wireType != 2 {
return fmt.Errorf("proto: wrong wireType = %d for field AuditAnnotations", wireType)
}
var msglen int
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
msglen |= (int(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
if msglen < 0 {
return ErrInvalidLengthGenerated
}
postIndex := iNdEx + msglen
if postIndex > l {
return io.ErrUnexpectedEOF
}
if m.AuditAnnotations == nil {
m.AuditAnnotations = make(map[string]string)
}
var mapkey string
var mapvalue string
for iNdEx < postIndex {
entryPreIndex := iNdEx
var wire uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
wire |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
fieldNum := int32(wire >> 3)
if fieldNum == 1 {
var stringLenmapkey uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
stringLenmapkey |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
intStringLenmapkey := int(stringLenmapkey)
if intStringLenmapkey < 0 {
return ErrInvalidLengthGenerated
}
postStringIndexmapkey := iNdEx + intStringLenmapkey
if postStringIndexmapkey > l {
return io.ErrUnexpectedEOF
}
mapkey = string(dAtA[iNdEx:postStringIndexmapkey])
iNdEx = postStringIndexmapkey
} else if fieldNum == 2 {
var stringLenmapvalue uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return ErrIntOverflowGenerated
}
if iNdEx >= l {
return io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
stringLenmapvalue |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
intStringLenmapvalue := int(stringLenmapvalue)
if intStringLenmapvalue < 0 {
return ErrInvalidLengthGenerated
}
postStringIndexmapvalue := iNdEx + intStringLenmapvalue
if postStringIndexmapvalue > l {
return io.ErrUnexpectedEOF
}
mapvalue = string(dAtA[iNdEx:postStringIndexmapvalue])
iNdEx = postStringIndexmapvalue
} else {
iNdEx = entryPreIndex
skippy, err := skipGenerated(dAtA[iNdEx:])
if err != nil {
return err
}
if skippy < 0 {
return ErrInvalidLengthGenerated
}
if (iNdEx + skippy) > postIndex {
return io.ErrUnexpectedEOF
}
iNdEx += skippy
}
}
m.AuditAnnotations[mapkey] = mapvalue
iNdEx = postIndex
default:
iNdEx = preIndex
skippy, err := skipGenerated(dAtA[iNdEx:])
if err != nil {
return err
}
if skippy < 0 {
return ErrInvalidLengthGenerated
}
if (iNdEx + skippy) > l {
return io.ErrUnexpectedEOF
}
m.XXX_unrecognized = append(m.XXX_unrecognized, dAtA[iNdEx:iNdEx+skippy]...)
iNdEx += skippy
}
}
if iNdEx > l {
return io.ErrUnexpectedEOF
}
return nil
}
func skipGenerated(dAtA []byte) (n int, err error) {
l := len(dAtA)
iNdEx := 0
for iNdEx < l {
var wire uint64
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return 0, ErrIntOverflowGenerated
}
if iNdEx >= l {
return 0, io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
wire |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
wireType := int(wire & 0x7)
switch wireType {
case 0:
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return 0, ErrIntOverflowGenerated
}
if iNdEx >= l {
return 0, io.ErrUnexpectedEOF
}
iNdEx++
if dAtA[iNdEx-1] < 0x80 {
break
}
}
return iNdEx, nil
case 1:
iNdEx += 8
return iNdEx, nil
case 2:
var length int
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return 0, ErrIntOverflowGenerated
}
if iNdEx >= l {
return 0, io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
length |= (int(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
iNdEx += length
if length < 0 {
return 0, ErrInvalidLengthGenerated
}
return iNdEx, nil
case 3:
for {
var innerWire uint64
var start int = iNdEx
for shift := uint(0); ; shift += 7 {
if shift >= 64 {
return 0, ErrIntOverflowGenerated
}
if iNdEx >= l {
return 0, io.ErrUnexpectedEOF
}
b := dAtA[iNdEx]
iNdEx++
innerWire |= (uint64(b) & 0x7F) << shift
if b < 0x80 {
break
}
}
innerWireType := int(innerWire & 0x7)
if innerWireType == 4 {
break
}
next, err := skipGenerated(dAtA[start:])
if err != nil {
return 0, err
}
iNdEx = start + next
}
return iNdEx, nil
case 4:
return iNdEx, nil
case 5:
iNdEx += 4
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Are you looking for the best car seat cushion for long drives or for pain free life? Whether it is for long trip or for pain free happy life, worry no more. You’ve come to the RIGHT place. To ensure your satisfaction in purchasing a car seat cushion, we’ve compiled a very few seat cushions here which are highly recommended by the fitness experts and orthopedics. Moreover, you may need to buy a cushion suitable for long drive, but your elder brother or grand father may need one for back pain or sciatica pain. So, we’ve represented cushions here that’ll be amazingly helpful to let you enjoy pain free easy driving.
Did you notice that almost all the manufacturers claim that their cushions are the best to let you enjoy happy and pain free driving. That’s why it becomes so difficult to pick up a really good one. It’s also not impossible that all the cushions are of high quality. But, who knows which one is the best fit to fix your issue. So, it is better to carefully consider the features of a cushion for your car seat before buying it.
Table of Contents
List of the best car seat cushion for long drives
Must Have Features in the best car seat cushions
Things To Consider Before Buying a Seat Cushion for Your Car
A Few Tips For The Older Drivers
Final Verdict
List of the best car seat cushion for long drives
Before knowing the must have features of a car seat cushion, it’ll be wise to have a look at some high quality seat cushion for car which have a lots of positive customer reviews. A customer may leave a positive review for the money. A few people may write positive reviews on a particular cushion if they get this product for free. But, it’s impossible to have dozens of five star reviews to a product which is actually not so good. No more time wasting. Let’s see which are the most suitable car seat cushions for long drives.
Aylio Coccyx Seat Cushion With Washable Cover
The Aylio Coccyx Seat Cushion comes with a unique design that features a cut out where your tailbone sits to mitigate pressure off your lower spine, tailbone and hips. Particularly designed to give relief from all types of back pain. Moreover, this cushion ameliorates even weight distribution and can also promote your posture. It usually works by allowing your tailbone to levitate above the car seat rather than static sitting directly on it and so takes the weight off of this body parts which normally become the victim of the direct impact of car vibrations and bumps.
An over pressured foam makes up the inward of the cushion and its ergonomically fit structure to match the shape of your buttocks, ensuring better support on all sides. The other win win feature of this cushion is that it soft velour cushion cover can be manually removed which is easily machine washable. It is fully portable that even can easily be moved from your car seat to your indoor office chair. Hope this will save you from buying another one for your office chair.
To bring a light air of peace to your mind, hundreds of customers who drive for a living are using this cushion for hours at a time while driving and alluding that it amazingly compress down into nothing, which make it one of the best fits for long drive. It promises to hold its shape and remains supportive, all the day. Whether you are experiencing tailbone pain in pregnancy, an injury or just because of your old age, this cushion has an incredible number of positive reviews on Amazon.
To say something about its proud manufacturer, Aylio was started by a happy couple in the US. The best point to consider buying this cushion is that wife Larisa is a certified occupational therapist. Her background helped her in designing that so many wellness products their company offers. Moreover, they offer a lifetime warranty on their products which makes buying this cushion a pretty right decision.
Everlasting Comfort 100% Pure Orthopedic Design Luxury Seat Cushion
Everlasting Comfort is such a name you can trust to assuage your pain and uneasiness from long driving, and to bring the everlasting comfort and ultimate softness to your life. They have a strict product policy that if any of their products fail to outperform the most idolized and highest rated competitors in the cushion industry, they will then not bring that product to market. This is the reason we can’t but suggesting you to consider checking customer reviews and its price on Amazon.
Similarly designed as the Aylio Coccyx Seat Cushion With Washable Cover, this Everlasting Comfort 100% Pure Orthopedic Design Cushion has the same topcellent cut out. But this one is made from memory foam which allows this cushion molds to the shape of the body as it warms up. But unlike any normal memory foam cushions, heavier customers point out that this one doesn’t flatten down even after sitting for long time.
It is burly enough to hold its original shape and thus it stays supportive It’s also wide enough to accommodate all shapes and all sizes. You know, this cushion comes with a pliable and flexible cover that permits you to remove it for washing, which is really great for the customers who have to spend long hours in their car and forced to eat while driving. This one is the right choice for the customers who suffers from disc issues or the problems with leg numbness. Another cool feature of this seat cushion is just what some shorter customers appreciate, the little height boost which this cushion provides.
Clever Yellow Auto Drivers Wedge Car Seat Cushion with Strap
Do long drives hurt you?
Does sitting on your car seat for long periods of time lead you to suffer back pain?
Worry no more! To make all of your next rides more enjoyable, Clever brings auto drivers wedge car seat cushion with memory foam and ultra slim wedge to ensure comfort and lumbar support. Though the Clever Yellow Car Seat Cushion has the same tailbone cut out feature, the overall design and style is completely different than the above two amazing models. It also has a peculiarly designed wedge shape to provide comfort to the fullest.
The unique idea behind the 3 inch high wedge is to bevel the buttocks slightly, which in turn is meant to improve posture while remissiving the pressure on your lower back and hips. Designed mainly for driving, this amazing seat cushion has an adjustable strap that goes around the back of your car seat to keep it in place which also can easily be attached to an office chair and even can be used at home.
Three layer technology inside the cushion ascertains that it won’t flatten down over long time and it includes molded foam core with a dense memory foam to enhance comfort level. To make the cushion easily breathable and heat wicking during the long drives in the hot summer days, the foam is covered with a mesh material on the outside, and of course, the cover is removable and hand or machine washable. And about customer reviews, it’s of course better to check out customer review section on Amazon, though we also noticed that quite a very few customers experience back pain due to the structure of this bucket shape seat, specifically those who are a bit shorter than the average people. It’s also true that a few people have found this cushion to give a nice boost to the seat height and a decent amount of relief from car seats that don’t agree with their backs. A considerable fact is that being a family business based in the UK, Clever Yellow cushions are sold almost all over the world. So, it completely depends on you whether choose it or not.
Conformax Combo Set “Cocoon of Comfort” Gel Car Cushion
Are you looking for something completely different? Are you searching for extended all day driving comfort and relief from any annoying discomfort caused from long driving? Yes, bringing yet another completely different but, nice looking style to our list of favorites, the Conformax Combo Set “Cocoon of Comfort” Gel Car Cushion gives an arresting option for those looking for whole day long full support throughout the seat and back.
In fact, two separate cushions, this one offers a seat cushion with matching facility for the back which is easily adjustable in accordance with the height of the user and the shape of their car seat. The seat back cushion attaches to the head rest support pillars of the car seat which has also a lower strap that attaches to the bottom of the car seat to ensure maximum stability of your cushion.
Both the cushions are covered with the Conformax Airmax cushion cover which is a 2-way stretch, breathable mesh that continuously provides good air circulation and wicks sweat. Moreover, to keep the cushion cool and comfortable during the long periods of driving in hot days, this seat cushion comes with an installed gel layer inside. As this cushion is latex free as well as environmentally sound, so there’s no problem in sitting on this cushion set for hours after hours even if you have allergies. But, you know, it’ll be better for you to visit your doctor before buying this cushion if you’re suffering from allergies.
Lovehome Cool Gel Lower Back Pain Relief Seat Cushion
A rich people isn’t generally supposed to sit on the car seat for whole day long. But, if it’s true to you that you’re always hot in your car, or if you live in a hot climate area, then, the LoveHome Cool Gel Seat Cushion might be the most suitable choice for you. A simple pad shaped seat cushion with no angles or cut outs, this one is great for those who want to intersperse their body weight while sitting for long periods of time but need some extra air circulation.
The dimples in the cushion work as cooling vents which are paired with the comfortable cool gel top layers along with a water resistant Lycra Neoprene and an antimicrobial cover. And a high density polyurethane foam pad makes up the lower layer of the cushion which help keeping the cushion shape unaffected even after long periods of constant use. Also the bottom of the cushion has a rubberized anti slipping coating so it stays in right place on your car seat while you drive.
This renowned cushion company is based in China and makes a wide range of cushions for lumbar support. The optimal part is that all the seat cushions of this company come with a no hassle, money back guarantee along with a twelve-month service warranty. So, I think there will be no issue in having a try to this cushion at least for a week. Then, you’ll firmly be able to decide whether to keep it on your car seat or packing it up for return.
Aylio Comfort Foam Wedge Coccyx Car Seat Cushion
Another cushion from Aylio. The Aylio ergonomically designed high quality comfort wedge cushion will decrease the pressure on your lower tailbone (coccyx) while driving trucks, cars, or any vehicles for long time. This cushion is also usable in the airplane seat. From a top seller in automotive on Amazon.com, it is also a very good choice for using in office chairs or any other common chair at home. (this is not suitable for rocking chair).
As it comes from Aylio, from using this cushion on your car or any other seat, pressure will be lessened on your hip bones which may become sore while driving or sitting for long time. It fits tight and close to your back bottom and prevent slipping. It also increases your blood circulation when sitting for hours without any break.
This super soft cushion lets you to enjoy driving with its maximum support. The cutout section on the rear edge of this car seat cushion ensures weight distribution and thus improves your posture while keeping your spine safely aligned. It does not have a belt, which may appear to be a fact of issue to you. But, from practical use, it has been proven to us that your body weight will hold it in its right place. There is a Lifetime Warranty for this cushion and you can easily clean it as it has removable zippered velour cover. So, what do you think now?
WonderGel Roll-n-Go Car Seat Cushion
The gel materials may grip your back while leaving the car seat, this cushion looks not so attractive and whenever you get out of the car, this odd looking seat cushion moves and kind of bunches up. If these are not a problem to you, then you can check it’s customer reviews on Amazon.
Being manufactured in the United States, the WonderGel Roll-n-Go Car Seat Cushion will give you a therapeutic support to keep you pain free while driving and relieve pressure with its column buckling gel technology. The cushion is right choice for the drivers who drive for a living. It also can be a good choice for any type of car seats and even for your chairs to provide a reliable support for your butt and thighs.
This exceptional cushion is designed with the ultra soft but strong rubber-like elastic material which helps your bottom to be held perfectly to reduce pressure on your bones. Though it is manufactured to use in various types of seats, professional truck drivers love this very much. For your better consideration, the WonderGel is made from Gelastic which is originated from a very special type of gel in a form of hollow columns. These columns come together to form one of the nature’s strongest and most effective patterns which resembles most like a honeycomb.
To relieve your pressure in a very effective way, each of this cushion column walls are shared by other adjoining columns that work together. This cushion has breathable feature which lets it return to its original shape when you get off it after enjoying your driving. Like any other high quality cushion, it has 2 sides. The softer side gives you comfort and the other side provides strong support for your physical shape and weight.
You can easily take it with you to put on the bleachers at sports events(if you’re also a big fan of sports). The cushion is featured with a black zippered washable nylon cover with a carrying handle to take the cushion with you wherever you need or wish to carry it. You may think that its gel will be a issue. But, its gel is not liquid, and is waterproof and you can wash it with lukewarm water and detergent or mild soap. Using any heat to make it dry after washing is not allowed. Now, if a 12 month Limited Warranty seems to be enough, feel then free to check its price on Amazon.
I-pure items Comfortable Car Seat Cushion with Memory Foam
The I-pure items Comfortable Car Seat Cushion with Memory Foam is very comfortable for truckers and car drivers, though anybody can use it at their office or anywhere else to help with pain from their lower back,coccyx and sciatica. It comes with a black mesh cover and zipper to be washable in your washing machine. Use gentle cycle with cold water and mild soap or detergent and let it dried by air.
To get relief from lower tailbone pain and have better posture when sitting straight finally without any pain, it can be a wise selection. The hollow center section of this cushion provides more airflow while the mesh cover keeps you cool in hot weather. You know, the private area of your body should never become sweaty and sticky. So, the inside of this seat cushion is made of 100% memory foam to keep it solid and flat over time and perfectly fits the shape of your body. Moreover, the rear of the cushion is slightly higher to lift your spine and to keep your cushion stay in place it comes with a no slip rubber bottom. This cushion is ideal for even wheelchairs, airplane pilots, airplane passengers. So, you can check its other features, dimension and price on Amazon.
PharMeDoc Foam Seat Cushion for Trucks and Cars
The PharMeDoc foam seat cushion is designed in California, but made with love in China. This budget cushion is designed specially for your coccyx, sciatica, and butt pain which is so fitting to use in trucks, cars, at home and even in the office — anywhere you expect supporting comfort. You’ll get this cushion available in black, blue, brown, gray, or pink color. Breathable mesh cover is actually a common feature for most of the quality cushions and this one also has this feature with a zipper which can be easily removed for washing and fast drying. It is hypoallergenic, but it has no phthalates or latex and its rear cut out shape is suitable for your tailbone to relieve pressure on it and to help with stiffness in your hips after sitting and comfortably staying for long time on the seat without sweating.
The cushion will keep its shape unaffected after continual using and never go flat. Being bearable and lightweight, you can effortlessly take it everywhere with you. The cushion will raise you up for better position and align your spine by keeping it upright, while driving or writing. It also is very effective to reduce pressure sores, pain, and aches. You will receive a User’s Manual and a Lifetime Manufacturer’s Warranty with this cushion. So, here your satisfaction is 100% guaranteed. Now, how about to check its price on Amazon!
SOFTaCARE Memory Foam Car Seat Cushion
The Soft & Care brand memory foam cushion is 2 pieces; one for your bottom, and the other one is for your back. This is a nice combination for OTR semi drivers, truck drivers, and all other vehicle drivers. To enjoy sitting for extended time without pain and have comfort at the same time, the performance of this cushion is really so impressive. As this seat cushion has two parts, the top part has a pocket for your cell phone and both have carrying handles for easy transporting to the places you need to go.
About the features of this cushion –
The cutout in the rear of the bottom cushion reduces pain It’s ergonomically designed to support your tailbone It’s also very effective for sciatica, herniated discs, pregnancy back pain, and more The lumbar lower back top cushion supports this area well to ensure extra comfort. The back part of the top cushion comes with a rubberized bottom for not slipping off The bottom cushion also has this same anti slipping feature The adjustable strap keeps your cushion in right place The 3D breathable mesh will never have you feeling too hot or too cold The zippered velour cushion is removable for easy washing It’s made of 100% pure high-density memory foam that holds its shape unchanged Usable in airplane, boats, tractors, and buses
Do you expect something more? If not, then this one can satisfy you with its 30 day 100% money back guarantee. A poor quality cushion can never provide this type of confirmation and we are here not to waste your time, but to assist you in finding out a quality cushion which will keep you pain free. If you can count on our clues, you can check its price on Amazon.
Must Have Features in the best car seat cushions
As I promised earlier, so, now I’m gonna show you a few must have features of a quality car seat cushion. Have a look at these features and then try to find out them in to above cushions. If you get those features into a cushion, then this one undoubtedly will be of high quality. In this way, you yourself can be able to identify a car seat cushion whether it is a best fit for you or not.
Quality
The first and foremost feature of a product is quality. No one wants to buy a poor quality product. So, you should come to know about this before taking a buying decision. To know the quality of a cushion, read its user manual, know its function and then go the customer review section on Amazon to justify its credibility.
Support
The next important thing is manufacturer’s support. When purchasing for a quality seat cushion, look for one that offers a satisfactory level of support as well as their products give a good support for your back and don’t collapse under the pressure of your body weight. Whatever the material the cushion is made of, it should stand up for long hours of use without being unaffected and be just as comfortable after a few hours as when you first sit down on it.
Durability
As you know, a car seat cushion can get a lot of use without any break. So, don’t forget to look for a good one that is made of durable and sturdy materials that will last and stand up months after months. A purchasable cushion should be covered with a strong fabric that won’t cleave or rip and the quality of the filling materials should be soft, comfortable and good.
Breathability
As it’s amazing to have a comfy and cozy cushion, you might need to drive your car for long hours even in the hot summer and you know, nobody likes that their cushion will make their back sweat and also make them feel hotter. So, a reliable car seat cushion for long drives should be breathable and wick away moisture from a sweaty back and should be mesh covered.
Comfort
Without a car seat cushion, driving, especially for the long trips, becomes very uncomfortable and painful. And if you drive for your living or have to drive long for your business, then it is not negotiable in any way. You need a docile, soft, comfortable and well-designed cushion for your car seat. You can easily buy one that is tailor made to distribute your weight and ensure breathing to make it much more comfortable.
Protect Your Leather Seat
Most of the car has built in leather seat and if yours is not different, then you will notice that it has been poked or rip somewhere because of rough cover. This also may happen if you drive with your car keys, other keys ring, wallets or even coins in your pocket. The function of a good car seat cushion should provide a smooth bottom that will not damage the leather seats of your car.
Health
A well-designed top quality cushions are made to improve your blood circulation, remove exhaustion of driving and damp extra stress. There are different seat cushions for different functions below the fold. Bes sure that you are going to buy the seat cushion that will solve your specific problem. Speaking of health, here is an amazing post I found about how to modify your car seat for a pain-free ride.
Appearance
A beautiful car seat cushion may boost the outlook and aesthetic appearance of your car. You can choose tailor made and custom design cushions for your car seat. You can also buy separate covers of perfect color for your seat cushions to match your mood or occasion and to enhance the aesthetic appearance of your car.
Ergonomic Shape
It’s a must that a comfortable cushion should be ergonomic in shape and fit the structure of your body properly. Whether you choose a cushion for your car seat that only covers your lower seat, or if you are looking for a cushion that covers the whole seat including your back, If the cushion shape is not ergonomic, you won’t get any chance to stay pain free while sitting on that rubbish seat. Memory foam or any other man-made materials that follow the shape of the small of your back and provide extended support to the lumbar region of your back will definitely prevent your back from getting sore over long periods of sitting and/or driving.
Driving for long periods of time can cause back pain, sciatica and hip pain even to the wholesome person. So, driving can easily become uncomfortable and full of pain to the person who suffer from any back issues. Specially truckers and delivery workers are just two of many professions those have to do lengthy hours of sitting and driving.
In one of the most visited Men’s Health article, Sir Alan Hedge, professor of ergonomics at Cornell University, Ithaca, NY 14850, USA, talks about the tangible types of strain on the human back that can occur from the concentrated situation of sitting while driving. He explains that –
the vibration of the spine pushes on the discs between your vertebrae–the cushions that act as shock absorbers and allow spinal movement–which can cause mechanical damage to the disks.
If the car seats were designed following ergonomic structure, nobody would then feel pain because of driving. So, a lots of famous chiropractors and senior orthopedic doctors suggest to use a soft cushion on the car seat to have an extra support for your back that the car seats lack. There are hundreds of car seat cushions available out there in the market, with each type serving a different need and issue. So, the hope for enjoying a pain free happy driving is not end here.
You can choose any of the above cushions for long driving if you’re now completely free from any back issue. These cushions will keep you pain free in future. But, if you have already fall into prey of coccyx, sciatica or any other back issues, here you’ll get specific cushions for your particular problem. This post is specially designed for you. Just read the given details with care.
Things To Consider Before Buying a Seat Cushion for Your Car
Before purchasing a car seat cushion, it is a matter of great important to consider the product features which we’ve already provided. But, professional drivers, for instance, may have different requirements than commuters with chronic lower back pain. By reflecting on your personal expectations and criterions, you can better determine which type of cushion is the most suitable to make your driving comfortable. Here’s some clues:
Source of Pain:
Most of the car cushions aim at either the posterior with a seat cushion or the lower back with a lumbar cushion. Some of the exclusive cushions cover both areas, with a few cushions supporting the cervical spine too. So, the cushion you’re going to buy should ideally address the type of pain you are experiencing.
A normal car seat cushion will usually suit those who have sciatica or experience numbness and pain in the legs, tailbone, hips or buttocks. The ergonomic design of these cushions will generally improve your sitting posture, but they will not offer any reliable support to the lumbar or cervical spine.
On the other hand, lumbar cushions actively and mainly work on the lower back. Though these cushions are the best fit for lumbar pain, they will not reduce your discomfort in the buttocks and legs which at times can be crucial. So, you’ll get some other cushions like Soft&Care Memory Foam Car Seat Cushion which cover both parts of the car seat. Some even offer a neck pillow for additional cervical support.
So, those who experience ache and pain in their hips, legs, and lower back may need to consider buying more than a single piece car seat cushion. A seat cushion for the legs and hips can easily be paired with a separate lumbar cushion to support the entire lower part of your body. So, why not letting your pain guide you to the cushion that’s most suitable for you.
Typical Car Temperature:
Based on the weather you live in, you may wish for a seat cushion that either remains cool on hot summer days or stays a little warm when it’s cold outside. Seat cushions with gel like the WonderGel Roll-n-Go Car Seat Cushion are generally best for those living in a warmer area. But, peoples living in comparatively cooler places will have no problem in using foam and fabric seat cushions which, those are living in warmer climates, may get a bit warm on hot season.
Material:
A lots of car cushions are being manufactured from materials like canvas, fabric, memory foam, and gel. So, don’t forget to consider the support, comfort level and heat retention offered by the material you choose. You know, foam seats provide lots of support and cushioning, making them about to perfect for your buttocks, cradling the spine and thighs. But, this cushion material, however, tends to get quite warm, which is better in the winter. The fabric usually gives less support but also tends to retain cool even after long use. And the gel memory foam cushions are generally more comfortable even in the high temperatures than any normal memory foam cushion.
Price:
May be this is the most important fact for the budget customers. Most of the budget car seat cushions tend to cost between $15 and $50. Though some cheap cushions are available for lower prices. But, be wary of extreme bargains, as these may come with inferior qualify. And there are also some luxury cushions. From my experience, those expensive luxury cushions are not always superior to cushions with more affordable prices, though some may be worth considering. So, now it’s up to you whether to break the bank or go for the budget one.
Customer Reviews:
When in doubt, even after having so handful resources at hand, it’s the only option to reference customer reviews to determine whether to go for a particular cushion or not. Inspect different cushions from different stores and see which benefits other customers mention. Also, take the time to read negative review (if any) to see what flaws and issues the cushion might have. Though we recommend all of the above products, customer reviews can help you better to pick up the best one.
A Few Tips For The Older Drivers
Driving and particularly driving for a living can be a daunting job as we get older and have less confidence behind the wheel. But a few simple cautions can help you in maintaining your confidence and command over the wheel and also can ensure a safe and comfortable driving.
Even if you have never experienced any issues with your vision or hearing, it’s important to visit your doctor and test your vision and hearing regularly.
Cushions will undoubtedly improve your level of comfort in driving. But, it’s so significant to stay active and do some fitness exercise in order to maintain flexibility and mobility of your body.
To enjoy safe driving, leave plenty of space between you and the other car before you and always start braking early.
Final Verdict
You’ll be amazed at how a car seat cushion can completely change your driving experience. The right seat cushion for your car will relieve your pain and will allow you to sit in comfort even on your long drives. Which means, you can get back to visiting new places as well as your loved ones. Happy driving. |
The present invention is directed to telecommunication networks, and especially to telecommunication networks involving calls from mobile calling instruments to special number service stations. An example of such a call from a mobile calling instrument to a special number service station is a call from a cellular phone, from a Voice over Internet Protocol (VoIP) calling instrument or from another wireless or otherwise mobile device to an emergency service station such as a Public Safety Answering Point (PSAP) in an emergency service call system.
An emergency service call system, commonly known in the United States as an E9-1-1 System, will be employed herein as an exemplary preferred embodiment of the present invention. Other special number systems are deployed and would benefit from the present invention. Examples of such other special number systems include (by way of example and not by way of limitation) non-emergency police or fire call systems, telephone network maintenance call systems and commercially established special numbers (e.g., “dial ‘GOTIX’ on your AT&T Wireless phone for tickets”).
A basic 9-1-1 (Emergency Services) System provides for programming with special 9-1-1 software a telephone company end office (also known as a “central office” or a “Class 5 office”) to route all 9-1-1 calls to a single destination. The single destination is termed a Public Safety Answering Point (PSAP). In such an arrangement, all telephones served by the central office would have their 9-1-1 calls completed to the PSAP. However, the areas served by respective telephone company central offices do not line up with the political jurisdictions that determine the boundaries for which PSAP may be responsible. That is, a municipal fire department or police department may geographically include an area outside the area served by the central office, a condition known as underlap. Likewise, the municipal fire or police department may encompass an area of responsibility that is less expansive than the area served by the central office, a situation known as overlap. Further, the original basic 9-1-1 systems did not provide any identification of the caller; the PSAP human operator had to obtain such information verbally over the line after the call was connected. The major shortcoming of the basic 9-1-1 systems was that they could not support interconnection to other telecommunication providers such as independent telephone service companies, Alternate Local Exchange Carriers (ALECs), or wireless carriers. The “basic” nature of the basic 9-1-1 system also indicates that the system does not have Automatic Location Information (ALI) capability or Automatic Number Identification (ANI) capability with a call back capability.
Similar abbreviated number systems are in place for handling emergency service calls in countries other than the United States. The abbreviated number system established in Canada is the foreign system most similar to the system established in the United States. There are other abbreviated number calling systems in place in the United States and abroad for such purposes as handling municipal information and services calls (3-1-1) and for other purposes. All of these special or abbreviated number call systems that have geographic-based content suffer from similar shortcomings in their abilities to automatically place incoming calls to an action-response facility geographically proximate to the locus of the caller. It is for this reason that the 9-1-1 emergency call system of the United States is employed for purposes of this application as a preferred embodiment of the system and method of the present invention.
Automatic Number Identification (ANI) is a feature for 9-1-1 services that allows the caller's telephone number to be delivered with the call and displayed at the PSAP. This ANI feature is sometimes referred to as Calling Party Number (CPN). The feature is useful for identifying the caller and, if the caller cannot communicate, for callback. A signaling scheme known as Centralized Automatic Message Accounting (CAMA), originally used to identify the originator of a long distance call for billing purposes, was adapted to facilitate ANI delivery to the PSAP.
The availability of the caller's telephone number to the PSAP (the ANI feature) led quickly to providing the caller's name and address as well. This was straightforwardly accomplished using the subscriber information stored by telephone companies based upon telephone number since the 1980's. New equipment at the PSAP enabled queries of an Automatic Location Information (ALI) database using the caller's number provided by the ANI feature to ascertain name and address information. The ALI databases are typically maintained by the respective telephone company serving the PSAP. This was an improvement, but a problem still remained where several telephone company central offices served a town or county. Other problems also developed with the growing volume of mobile callers using wireless phones, satellite phones and communications over the Internet. Information regarding the locus of the origin of the call merely identified the locus where the call entered the wireline network; even such limited location information is not always provided. No indication was presented to identify the geographic location of such mobile callers.
As the situation of multiple central offices serving a PSAP occurred more frequently, it was clear that it was inefficient to build communication trunks from several central offices to a PSAP. As a result the 9-1-1 Tandem was developed. With that equipment, trunks from central offices are concentrated at a tandem office (a 9-1-1 Tandem) from which a single trunk group serves a given PSAP. Often a 9-1-1 tandem comprises an otherwise common Class 5 telephone system end office (EO), with added software to configure it for 9-1-1 operations. Such concentration of trunks reduces size and cost of PSAP equipment. The tandem is a telephone company switch that provides an intermediate concentration and switching point. Tandems are used for many purposes, including intra-LATA (Local Access and Transport Area) toll calls, access to other local exchange carriers (LECs), and access to long distance carriers and telephone operators.
A significant development in 9-1-1 services has been the introduction of Enhanced 9-1-1 (E9-1-1). Some of the features of E9-1-1 include Selective Routing, ANI, ALI, Selective Transfer and Fixed Transfer. Selective Transfer enables one-button transfer capability to Police, Fire and EMS (Emergency Medical Service) agencies appropriate for the caller's location listed on the ALI display. Fixed Transfer is analogous to speed dialing. Enhanced 9-1-1 services also permit provisioning supplemental data or information regarding calling parties, such as allergies to medications, presence of pets, infants or handicapped persons at the premises or similar information useful to responding to emergency service personnel.
Selective Routing is a process by which 9-1-1 calls are delivered to a specific PSAP based upon the street address of the caller. Selective Routing Tandems do not directly use address information from the ALI database to execute decisions regarding which PSAP to connect. Recall that emergency services (Police, Fire and EMS) are typically delivered on a municipality basis. Often there will be one Police Department (e.g., municipal, county or state), but there may be several Fire Departments and EMS Agencies. The town will be divided into response areas served by each respective agency. The response areas are overlaid and may be defined as geographic zones served by one particular combination of Police, Fire and EMS agencies. Such zones are referred to as Emergency Service Zones (ESZ). Each ESZ contains the street addresses served by each type of responder. The ESZs are each assigned an identification number (usually 3–5 digits), known as Emergency Service Numbers (ESN).
The Assignment of ESZs and corresponding ESNs enables the compilation of selective routing tables. The street addresses are derived from a Master Street Address Guide (MSAG), a database of street names and house number ranges within associated communities defining Emergency Service Zones (ESZs) and their associated Emergency Service Numbers (ESNs). This MSAG enables proper routing of 9-1-1 calls by the 9-1-1 Tandem; this is Selective Routing as implemented in an E9-1-1 system. Thus, the telephone company must have an MSAG valid address to be assigned the appropriate ESN for selective routing purposes and that information must be added to the E9-1-1 ALI database. It is by using such information that the selective routing capability of the Selective Routing Tandem can properly route an E9-1-1 call to the correct PSAP. If the information is not available in the ALI database, the record is placed into an error file for further manual handling.
A portion of the ALI database may be loaded into a Selective Routing Data Base (SRDB) for use by the 9-1-1 Tandem. The SRDB may be located in the Tandem, in an adjunct processor, or in the ALI database.
Reliability is a very important factor considered in designing 9-1-1 systems. One approach to providing reliability is to provide diversely routed trunk groups from each central office to its respective 9-1-1 Tandem. Preferably, each trunk group is large enough to carry the entire 9-1-1 traffic load for the respective central office. However, some systems are designed with less than full traffic capacity on trunk groups to “choke” or “congestion manage” incoming calls to a tandem in order to avoid overloading a PSAP. In some arrangements, parallel 9-1-1 Tandems are provided so that a central office has capable 9-1-1 Tandem ready for use (albeit with 50% call handling capacity) without interruption if one of the 9-1-1 Tandems fails. Switched bypass to an alternate 9-1-1 Tandem, commonly using digital crossover switches, is another approach to providing reliability in 9-1-1 systems.
Another approach to providing redundancy and robustness for a 9-1-1 system is the employment of Instant Network Backup (INB). Using INB, if a call does not complete to the 9-1-1 network for any reason (e.g., trunk failure, facility problem, 9-1-1 Tandem failure or port failure), the INB takes over and completes the call to a predesignated 7- or 10-digit number. Using this INB alternate path, ANI and ALI information are not delivered, but the call is completed to a local public safety agency, usually the local PSAP.
The interface between Operator handled calls and a 9-1-1 system is addressed in several ways. One system provides a direct connection between an Operator Tandem and the 9-1-1 Tandem. The operator forwards the call with the caller's ANI to the 9-1-1 Tandem. The 9-1-1 Tandem treats the call as though the caller had dialed the call. A second way to effect the desired interface is by using pseudo numbers. A pseudo number is a number that, when dialed, will reach a specific PSAP as a 9-1-1 call. Pseudo numbers have some special ALI information associated with them; for example, there may be a pseudo number associated with each municipality in a state. Dialing the pseudo number, usually from outside the LATA (Local Access and Transport Area), will generate a 9-1-1 to the PSAP for that municipality. The ALI display will indicate that it is a third party conference call from an unknown address in that town. The caller is not identified, but the call goes to the PSAP where the caller is believed, or claims, to be. Pseudo numbers are useful for Alternate Local Exchange Carrier (ALEC) or Competitive Local Exchange Carrier (CLEC) operators who may be located anywhere in the country.
A third method for effecting an interface for operator handled calls with a 9-1-1 system is through the Public Switched Telephone Network (PSTN), dialing the directory number for the PSAP. This is often referred to as the “back door” number by ALEC and CLEC operators.
The advent of wireless communications and other mobile phone capabilities (e.g., VoIP phones) has further exacerbated the difficulty of ascertaining caller location in telecommunication systems. The “patchwork” solutions described above regarding 9-1-1 systems have been mirrored in other special or abbreviated number systems to a significant extent. The “patchwork” solutions have created a capability-limited telecommunication system that cannot ascertain geographic information as fully or as easily as it should for all types of callers. This capability limitation has been especially felt in connection with calls made from mobile telephone instruments. The system is overly dependent upon human intervention to properly route calls to appropriate receivers, such as a proper PSAP. New modes of communication, such as Voice Over Internet Protocol (VoIP) and wireless communication instruments including wireless phones, wireless Personal Computers (PCs), wireless Personal Digital Assistant (PDA) devices and other mobile instruments, further contribute to telecommunication traffic not identifiable regarding geographic origin using present telecommunication routing systems.
Similar limitations will likely occur in other abbreviated number, or other special number, telephone systems handling location-based calls with resulting adverse limitations. Other such abbreviated number systems include emergency call systems in countries other than the United States, abbreviated number calling systems for reaching telephone maintenance services, abbreviated number calling systems for municipal information and services, and similar systems.
Provisioning of supplemental information to a special number service station (e.g., a PSAP in an emergency service call system) regarding a call originating from a mobile calling instrument is particularly difficult. Even with precise location information regarding locus of the origin of the call, such as would be available, for example, when the calling instrument has a Global Positioning System (GPS) capability, does not fulfill the need for availability of supplemental information regarding the calling party. Such supplemental information may include (by way of example and not by way of limitation) medical needs of the caller like allergies to medicines, or a request to notify specified personnel in the case of an emergency, or other information unique to the calling party that may be useful to responding emergency personnel. Other wireless systems, such as Automatic Collision Notification systems (ACN; one such system is referred to as ONSTAR™) may find it useful to alert responding emergency personnel that an infant or an invalid may be in an automobile involved in an accident. No systems are presently available to effect provisioning such supplemental information to a responding service station (e.g., a PSAP) for mobile instrument-originated calls. Mobile instrument-originated calls may include mobile telephone devices, wireless Personal Computers (PCs), wireless Personal Digital Assistant devices (PDAs), pager devices and other wireless-communication capable devices, whether capable of one-way or two-way communication. The present invention is also beneficial for other calling equipment having no particular fixed position, such as Voice over Internet Protocol phone devices (VoIP phones).
There is a need for a system and method for providing particular information relating to a caller placing a call from a mobile calling instrument to a special number service station in a telecommunication network. |
649 N.E.2d 571 (1995)
271 Ill.App.3d 1016
208 Ill.Dec. 515
PEOPLE of the State of Illinois, Plaintiff-Appellee,
v.
David A. HOLT, Jr., Defendant-Appellant.
No. 3-94-0566.
Appellate Court of Illinois, Third District.
April 21, 1995.
*574 John P. Vespa, Peoria, for David A Holt, Jr.
John X. Breslin, Deputy Director, State's Attys. Appellate Prosecutor, Ottawa, Kevin W. Lyons, State's Atty., Peoria, Gary F. Gnidovec, State's Attys. Appellate Prosecutor, Ottawa, for the People.
Justice LYTTON delivered the opinion of the court:
Defendant, David A Holt, Jr., appeals his conviction for stalking under paragraph 12-7.3(a)(2) of the Illinois Criminal Code (720 ILCS 5/12-7.3(a)(2) (West Supp.1993)) following a bench trial. We affirm.
*575 FACTS
Defendant and the victim, M.S., dated from January 1993 until mid-August 1993, when M.S. ended the relationship. M.S. testified that defendant became angry and verbally abusive at that time, threatening to "make it so that [she] couldn't live in Peoria any more, and * * * that [she] would have to deal with him the rest of [her] life, whether [she] married him or not." Defendant also stated that although he "might not do anything, * * * you never know what [his] friends might do."
M.S. testified that defendant called her the next day and argued that they should not end the relationship. When M.S. disagreed, defendant renewed his prior threats, reminding M.S. of the unpredictable nature of his friends and his intention to do all he could to force her to move away from Peoria because chance meetings would be too painful for him. Two weeks later, defendant proposed marriage to M.S., but she refused his offer.
Defendant also made a series of telephone calls to Tammy Ford, a mutual acquaintance, seeking advice on how to win M.S. back. Over the course of these conversations, Ford became increasingly concerned about defendant's deteriorating and depressed mental state. When defendant told Ford that "[i]f he could not have [M.S.] then no one would have her", Ford reported the conversation to M.S. out of concern for her safety. M.S. immediately told defendant that she wanted no further contact with him.
The trial court found that between August and early December 1993, defendant "became obsessed with prank calls to M.S., making perhaps as many as 200, as well as becoming bent on a course of conduct whereby he sent her cards, put in her mail box small picture posters of M.S. alleging she had genital herpes, pasted on her car bumper stickers with her name emblazoned upon them, associating her with genital herpes. Defendant even went so far as to place a sign in the yard of M.S.'s parents in Barrington, Illinois, stating `get your genital herpes here.'" In response to these acts, M.S. obtained an order of protection against defendant on December 10, 1993.
Defendant and M.S. had two inadvertent meetings in public after December 10, 1993, but these incidents were inconsequential. On Friday, February 25, the first of the incidents that formed the basis for the present stalking charge occurred when M.S. saw defendant at the Owens Recreation Center, the only ice skating facility in Peoria. On that date, M.S. was leaving the ice rink at the end of her private skating time and saw defendant lacing up his skates. She testified that she became frightened because defendant had never shown any interest in skating during their relationship and she feared that he would try to harm her or restrict her movement.
On the following Monday, M.S. noticed defendant watching her from outside the rink for 40 minutes of her 45-minute private skating session. Similar incidents began to occur on other Fridays and Mondays. M.S. noted that defendant arrived at the ice rink up to 30 minutes before the start of the scheduled public skating time on March 4th, March 7th, and March 28. In each instance, defendant stared at M.S. through the window of the observation area adjoining the ice rink for the remainder of her private skating session. M.S. testified that she was frightened each time she saw defendant at the ice rink.
Defendant was initially charged with two counts of stalking under section 12-7.3(a) of the Illinois Criminal Code (720 ILCS 5/12-7.3(a)(1), (2) (West Supp.1993)). He was arraigned on these charges on January 27, 1994, approximately one month before the incidents at the skating rink began. The two original counts were later dismissed with leave to reinstate, and two new stalking counts were added, based on the events at the Owens Recreation Center. At the close of the state's case in the bench trial, the trial court acquitted defendant of count III of the indictment, which required transmission of a threat (720 ILCS 5/12-7.3(a)(1) (West Supp. 1993)). The trial continued on count IV, which required placing the victim under surveillance and "in reasonable apprehension of immediate or future bodily harm, sexual assault, confinement or restraint" (720 ILCS 5/12-7.3(a)(2) (West Supp.1993)). After closing arguments were completed, the trial *576 court found defendant guilty on count IV of the stalking charge.
Defendant filed a motion to reconsider; the trial court denied the motion and sentenced him to four months in prison and 30 months probation, with the first six months being intensive and the first three months including electronic monitoring. Defendant was also sentenced to perform 150 hours of public service work and to pay $1,145.00 in restitution. Defendant appeals.
I. STATUTORY INTERPRETATION
Defendant was convicted under section 5/12-7.3(a)(2) of the Illinois Criminal Code of 1961, which states:
"A person commits stalking when he or she, knowingly and without lawful justification, on at least 2 separate occasions follows another person or places the person under surveillance or any combination thereof and * * * places that person in reasonable apprehension of immediate or future bodily harm, sexual assault, confinement or restraint." (720 ILCS 5/12-7.3(a)(2) (West Supp.1993).)
The stalking statute specifies that a defendant "`places a person under surveillance' by remaining present outside the person's school, place of employment, vehicle, other place occupied by the person, or residence other than the residence of the defendant." (Emphasis added.) 720 ILCS 5/12-7.3(d) (West Supp.1993).
Defendant argues that this language is clear and the trial court improperly construed the statute's "remaining present outside" requirement to include instances in which the defendant and the victim are inside the same primary structure, in this case, the Owens Recreation Center. Defendant claims that this interpretation impermissibly expands the prohibited conduct beyond that specified by the statute.
In construing a criminal statute, we seek to ascertain the legislature's intent; the statutory language itself provides the best guide to legislative intent. (People v. Krawiec (1994), 262 Ill.App.3d 152, 160, 199 Ill. Dec. 819, 825, 634 N.E.2d 1173, 1179; People v. Boykin (1983), 94 Ill.2d 138, 141, 68 Ill. Dec. 321, 322, 445 N.E.2d 1174, 1175.) If the language is clear, we must apply its plain and ordinary meaning; if it is unclear, we must also consider the purpose of the law and the "evils the statute seeks to remedy." (Krawiec, 262 Ill.App.3d at 160, 199 Ill.Dec. at 825, 634 N.E.2d at 1179; see People v. Frieberg (1992), 147 Ill.2d 326, 349, 168 Ill.Dec. 108, 119, 589 N.E.2d 508, 519.) The statute's legislative history may be useful in this determination. (Krawiec, 262 Ill.App.3d at 160, 199 Ill.Dec. at 825, 634 N.E.2d at 1179.) We believe that the "remaining present outside" language in the stalking statute requires judicial construction because its application is not clear and unambiguous.
The legislative intent in enacting the stalking statute was to prevent violent attacks by prohibiting conduct that may precede them. The statute was also intended to avert the terror, intimidation, and justifiable apprehension caused by the harassing conduct itself. (Krawiec, 262 Ill.App.3d at 160, 199 Ill.Dec. at 825, 634 N.E.2d at 1179; Gregory W. O'Reilly, Illinois' Stalking Statute: Taking Unsteady Aim at Preventing Attacks, 26 J. Marshall L.Rev. 821, 835 (1993) (hereinafter O'Reilly, Illinois'Stalking Statute).) Too often the obsession underlying the stalking behavior is a forewarning of future violence against the victims and their families. O'Reilly, Illinois' Stalking Statute, 26 J. Marshall L.Rev. at 836 & n. 109 (listing highly publicized stalking incidents); Brenda K. Harmon, Comment, Illinois' Newly Amended Stalking Law: Are All the Problems Solved?, 19 S.Ill.U.L.J. 165, 168 & n. 23 (1994) (hereinafter Harmon, Amended Stalking Law) (also listing highly publicized stalking incidents).
During legislative debate on the statute, Representative Lee Daniels summarized its significance by stating that it would send the message that "Illinois will not tolerate the stalking crime ever, ever again." (87th Ill.Gen.Assem., House Proceedings, May 20, 1992, at 80.) Representative Thomas Homer, House sponsor of the stalking bill, believed that the Illinois statute would be the toughest and most effective in the country and would serve as a model for the rest of the nation. 87th Ill.Gen.Assem., House Proceedings, *577 May 20, 1992, at 72; 87th Ill.Gen.Assem., House Proceedings, June 23, 1992, at 7.
Legislators in both houses described recent instances in which young girls and women were repeatedly terrorized by stalkers because law enforcement officials could not act under existing Illinois laws until the victims were actually injured. (87th Ill.Gen.Assem., Senate Proceedings, May 21, 1992, at 61 (statements of Senator Adeline Geo-Karis); 87th Ill.Gen.Assem., Senate Proceedings, June 22, 1992, at 66 (statements of Senator Carl Hawkinson); 87th Ill.Gen.Assem., House Proceedings, May 20, 1992, at 69, 71-72 (statements of Representative Thomas Homer).) Representative Homer argued that the stalking statute was necessary because existing laws did not allow the police to "arrest someone who is merelyI say merelythreatening, following, harassing someone." (87th Ill.Gen.Assem., House Proceedings, June 26, 1992, at 156.) The stalking statute was designed in part to alleviate these problems.
During debate in the House, Representative Homer noted that the stalking statute would "provide a tool to law enforcement agencies that will allow them to [sic] the opportunity to save and protect some of these victims before it is too late." (87th Ill.Gen.Assem., House Proceedings, May 20, 1992, at 73.) Senator Hawkinson reiterated this purpose during the Senate debate when he stated that the statute would allow the criminal justice system to intervene and prevent attacks. 87th Ill.Gen.Assem., Senate Proceedings, June 22, 1992, at 66.
With this purpose in mind, we construe the statutory requirement that the defendant place his victim under surveillance "by remaining present outside the * * * other place occupied by the person" (720 ILCS 5/12-7.3(d)). This language does not require that defendant remain physically outside the building occupied by the victim, and the insertion of such a requirement would unduly restrict the scope of the statute, contrary to the legislative intent. Common sense dictates that a victim may be subjected to as much, or more, harassment by being placed under surveillance from within a separate portion of a large structure, such as a shopping mall or ice skating facility, as from outside such a structure.
The statute encompasses the surveillance of a person from a place within the same primary structure but distinct from the "other place occupied by the" person. The trial court properly determined that the scope of the stalking statute included defendant's surveillance of M.S. from a separate lobby and observation area adjoining the ice rink on which she skated.
II. SUFFICIENCY OF THE EVIDENCE
Defendant next argues that the evidence in this case was insufficient to prove his guilt beyond a reasonable doubt. We examine this contention by considering "whether, after viewing the evidence in the light most favorable to the prosecution, any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt." (Emphasis in original.) People v. Collins (1985), 106 Ill.2d 237, 261, 87 Ill.Dec. 910, 920, 478 N.E.2d 267, 277, cert. denied (1985), 474 U.S. 1027, 106 S.Ct. 585, 88 L.Ed.2d 567.
A.
The defendant first contends that the evidence was insufficient to prove by a subjective standard that his conduct placed M.S. "in reasonable apprehension of immediate or future bodily harm, sexual assault, confinement or restraint." To refute M.S.'s claim of subjective fear, defendant relies on the fact that she voluntarily returned to the ice rink after being frightened by seeing defendant there. We disagree.
M.S. testified at trial that she was frightened each time defendant appeared and stared at her from the area adjoining the ice rink. Evaluating the credibility of witnesses and resolving conflicting testimony is a function of the fact finder, and a reviewing court may not override this determination unless these findings are unreasonable and not based on the evidence. People v. Sanchez (1986), 115 Ill.2d 238, 261-62, 104 Ill.Dec. 720, 727, 503 N.E.2d 277, 284, cert. denied (1987), 483 U.S. 1010, 107 S.Ct. 3240, 97 *578 L.Ed.2d 745; Collins, 106 Ill.2d at 261-62, 87 Ill.Dec. at 920, 478 N.E.2d at 277. The trial court concluded that M.S.'s fear was genuine, and we will not reverse this finding on appeal.
Furthermore, the undisputed evidence shows that M.S. did not confront defendant at the ice rink. On each occasion M.S. was already skating during her reserved skating time when defendant arrived at the ice rink. It would be unreasonable and unfair to compel a stalking victim to demonstrate subjective fear by anticipating and actively avoiding places where the stalker might later appear.
B.
The defendant also alleges that it was objectively illogical for M.S. to have continued to confront defendant at the ice rink if she feared him. After carefully reviewing the record, we cannot agree that M.S.'s apprehension was objectively unreasonable. Between August and December 1993, defendant had repeatedly stated to M.S. and others that he intended to "make it so that [M.S.] couldn't live in Peoria any more, and he threatened that [she] would have to deal with him the rest of [her] life, whether [she] married him or not."
M.S. testified that after breaking up with defendant she received 5 to 10 anonymous calls per day in which the caller either hung up when she answered or played recorded messages about sexually transmitted diseases. A tap on M.S.'s phone line showed that these calls were made from pay phones and fax machines throughout Peoria. The calls ended shortly after defendant discovered that a warrant had been issued for his arrest, but the calls gradually returned in January 1994. The trial court found that defendant had made as many as 200 prank telephone calls to M.S.
Defendant also sent M.S. several harassing postcards. In a postcard dated September 23, defendant wrote, "I'm doing what I got to do [sic] for myself and you. * * * Ignoring me won't make me go away. It's just gonna [sic] make me try harder. * * * I'm entitled to one more chance with you, and you get one more chance to rectify a mistake. You're gonna [sic] have to deal with me one way or another." In October, M.S. received a postcard with a horoscope clipping attached; the clipping read, "a relocation is possible. Apply for a passport. * * * Romance seems sweeter the second time around." In November, M.S. received another postcard that stated, "The week of December 18 are finals at Bradley [University]. I'll help you move back up to Barrington if you need the help. I'll talk to you soon." M.S. testified that she had no plans to move to Barrington Hills, Illinois, where her parents' lived.
Defendant admitted preparing and delivering several small posters and bumper stickers containing M.S.'s name or photograph along with various references to venereal diseases. He stated that he intended these activities to force M.S. into leaving Peoria. During the week of Halloween 1993, defendant carved a jack-o'-lantern, smashed it, and left it on M.S.'s porch with a note declaring that M.S. had herpes. During this same time period, he left two notes in or taped to her mailbox; one was written in red and said, "Welcome back to hell", and the other was a moving notice from the post office. In early November, he also placed a sign reading, "Get your genital herpes here" on the yard of M.S.' parents' home in Barrington Hills.
Defendant's surveillance of M.S. at the skating rink occurred after this protracted harassment. An order of protection had been entered against defendant in December 1993, and he had been arraigned on two other stalking counts on January 27, 1994.
Based on this evidence, the trial court, as a rational finder of fact, could have determined that defendant's actions at the skating rink in February and March 1994 would have caused apprehension in a reasonable person. The evidence was sufficient to support the trial court's finding the statutory element of reasonable fear had been established.
C.
Defendant next argues that the evidence was insufficient to prove beyond a reasonable doubt that his presence at the skating rink was "without lawful justification" (720 ILCS *579 5/12-7.3(a)). Although defendant previously had not shown any interest in ice skating, he claims that watching ice hockey with a friend during the winter Olympics had inspired him to begin skating in February 1994. Defendant contends that his presence at the Owens Recreation Center was lawful because it was not a "manner of expression [that] is basically incompatible with the normal activity of a particular place at a particular time." Grayned v. City of Rockford (1972), 408 U.S. 104, 116, 92 S.Ct. 2294, 2303, 33 L.Ed.2d 222, 232.
Defendant's argument overlooks the fact that he did not simply mind his own business and skate during the public skating session. Defendant could have arrived at the skating rink later or waited in another part of the facility for the start of the public skating period. Instead, he arrived well before the open skating period and stared at M.S. for up to 40 minutes during her private skating time on at least four occasions. These events occurred after M.S. had obtained an order of protection against him and he had been arraigned on two other stalking counts. A rational fact finder could have inferred that defendant's presence at the ice rink was "without lawful justification" because he was there to stalk M.S. by placing her under surveillance.
D.
Defendant next argues that the evidence was insufficient to prove beyond a reasonable doubt that he "knowingly" placed M.S. "in reasonable apprehension of immediate or future bodily harm, sexual assault, confinement or restraint." Because M.S. allegedly did not appear frightened of him and continued to return to the skating rink, defendant contends that a reasonable person could not have known that he had placed M.S. in apprehension of harm.
Defendant misapprehends the statute's knowledge requirement. Knowledge may be inferred from the facts and circumstances of the case. (People v. Pinta (1991), 210 Ill.App.3d 1071, 1078, 155 Ill.Dec. 644, 649, 569 N.E.2d 1255, 1260.) Knowledge of a material fact can include an awareness of the substantial probability that the fact exists
or that specific conduct is practically certain to produce a given result (720 ILCS 5/4-5 (West 1992); Illinois Pattern Jury Instructions, Criminal, No. 5.01B(1), (2) (3d ed. 1992).) Contrary to defendant's argument, the victim's behavior is not the determining factor in this analysis.
The victim's behavior in this case did, however, demonstrate her apprehension of defendant. Defendant knew that M.S. had previously obtained an order of protection against him and that he had been charged with two other counts of stalking based on his earlier threatening statements and harassing conduct. Even so, defendant chose to arrive at the skating rink well before the time set aside for public skating and stare at M.S. from the observation area. He did not talk to other people while waiting or attempt to wait in another part of the facility. Combined with defendant's prior conduct and his goal of forcing M.S. to leave Peoria, this evidence is sufficient to find a "substantial probability" that defendant knew his behavior placed M.S. in reasonable apprehension of harm.
III. CONSTITUTIONALITY OF THE STATUTE
Defendant offers several grounds to support his claim that the stalking statute is unconstitutional. First, he argues that the statute is vague, both facially and in its application to him. He contends that the statute does not "give the person of ordinary intelligence a reasonable opportunity to know what is prohibited, so that he may act accordingly" (Grayned, 408 U.S. at 108, 92 S.Ct. at 2298-99, 33 L.Ed.2d at 227) because the common understanding of the term "remaining present outside" does not include "remaining present inside." He also argues that the statute improperly grants law enforcement officials excessive discretion and allows for uneven application of the law.
A.
Statutes carry a strong presumption of constitutionality (People v. La Pointe (1981), 88 Ill.2d 482, 499, 59 Ill.Dec. 59, 67, 431 N.E.2d 344, 352) and will be construed to *580 avoid absurdity or invalidity (People v. Wireman (1989), 181 Ill.App.3d 385, 388, 130 Ill. Dec. 135, 137, 536 N.E.2d 1346, 1348). Vagueness claims against statutes that do not involve first amendment rights must be reviewed in the context of the specific case facts. (People v. Haywood (1987), 118 Ill.2d 263, 270, 113 Ill.Dec. 236, 239, 515 N.E.2d 45, 48, citing United States v. Mazurie (1975), 419 U.S. 544, 550, 95 S.Ct. 710, 714, 42 L.Ed.2d 706, 713.) The stalking statute prohibits placing a person in reasonable apprehension of harm by "knowingly and without lawful justification" following or placing the person under surveillance on at least two occasions. (720 ILCS 5/12-7.3(a)(2).) Defendant fails to cite any authority stating that these activities are entitled to first amendment protection. Because the stalking statute does not involve first amendment rights, defendant cannot argue that it is facially vague.
A statute is unconstitutionally vague on its face only if it is "incapable of any valid application." (Steffel v. Thompson (1974), 415 U.S. 452, 474, 94 S.Ct. 1209, 1223, 39 L.Ed.2d 505, 523.) A statute need not define the proscribed conduct with mathematical precision to avoid invalidation on vagueness grounds. (Grayned v. City of Rockford (1972), 408 U.S. 104, 110, 92 S.Ct. 2294, 2300, 33 L.Ed.2d 222, 228-29.) Where a statute prohibits conduct "knowingly done with the purpose of doing that which" is prohibited, "the accused cannot be said to suffer from lack of warning or knowledge that the act which he does is in violation of the law." (Screws v. United States (1945), 325 U.S. 91, 102, 65 S.Ct. 1031, 1036, 89 L.Ed. 1495, 1503; see also People v. Tolliver (1992), 147 Ill.2d 397, 403, 168 Ill.Dec. 127, 130, 589 N.E.2d 527, 530 (modifying statute making knowing possession of an incomplete car title a felony to require knowledge plus criminal purpose).) The stalking statute contains sufficiently objective standards of conduct and knowledge to allow its valid application: the victim's apprehension must be reasonable, and the specified conduct must have been performed "knowingly and without lawful justification" on at least two occasions.
B.
The stalking statute is also constitutional as applied to this defendant. A statute is not unconstitutionally vague simply because it allows some room for judicial interpretation. (Grayned, 408 U.S. at 110, 92 S.Ct. at 2300, 33 L.Ed.2d at 228; Easter Enterprises, Inc. v. Illinois Liquor Control Commission (1983), 114 Ill.App.3d 855, 859, 70 Ill.Dec. 666, 670, 449 N.E.2d 1013, 1017.) The stalking statute adequately warns innocent persons of the conduct to be avoided: making threats, following, or placing someone under surveillance, and thereby reasonably producing intimidation, apprehension, and fear. Thus, the statute contains sufficiently clear standards to avoid arbitrary or discriminatory enforcement because it sets explicit, objective standards for defendant's actions, knowledge, and the effect of his conduct on his victim. (See Grayned, 408 U.S. at 108, 92 S.Ct. at 2298-99, 33 L.Ed.2d at 227.) Unlike provisions invalidated on vagueness grounds in other cases, the stalking statute does not rely on strictly subjective standards and beliefs. (See Coates v. City of Cincinnati (1971), 402 U.S. 611, 614, 91 S.Ct. 1686, 1688, 29 L.Ed.2d 214, 217 (invalidating an Ohio ordinance that made it illegal for "three or more persons to assemble * * * on any of the sidewalks * * * and there conduct themselves in a manner annoying to persons passing by").) The statute is not unconstitutionally vague either on its face or as it applies to defendant.
C.
Defendant next contends that the statute is overbroad because it prohibits constitutionally protected activity, such as ice skating. According to defendant, the question to be answered is "whether the manner of expression is basically incompatible with the normal activity of a particular place at a particular time." (Grayned, 408 U.S. at 116, 92 S.Ct. at 2303, 33 L.Ed.2d at 232.) Because he was skating at a public ice rink during open skating times, defendant claims that his conduct was constitutionally protected and that his actions were not "without lawful justification."
*581 Defendant again misapprehends the basis of his conviction. He was not convicted because of his ice skating, but rather because on at least two occasions he placed M.S. under surveillance during her reserved skating times. Defendant admitted at trial that his goal was to embarrass and annoy M.S.; these activities are not protected by the first amendment. (See Harmon, Amended Stalking Law, 19 S.Ill.U.L.J. at 181 & n. 108, citing Colten v. Kentucky (1972), 407 U.S. 104, 109, 92 S.Ct. 1953, 1956, 32 L.Ed.2d 584, 589 (actions taken solely to annoy and inconvenience are not given constitutional protection).) The statute is not overbroad as it applies to defendant.
The statute is also not facially overbroad. According to general principles of constitutional analysis,
"a person to whom a statute may constitutionally be applied will not be heard to challenge that statute on the ground that it may conceivably be applied unconstitutionally to others, in other situations not before the Court. [Citations.] A closely related principle is that constitutional rights are personal and may not be asserted vicariously" because "courts are not roving commissions assigned to pass judgment on the validity of the Nation's laws." Broadrick v. Oklahoma, 413 U.S. 601, 610-11, 93 S.Ct. 2908, 2915, 37 L.Ed.2d 830, 839.
However, parties may challenge a statute as overbroad "not because their own rights of free expression are violated, but because of a judicial prediction or assumption that the statute's very existence may cause others not before the court to refrain from constitutionally protected speech or expression." Broadrick, 413 U.S. at 612, 93 S.Ct. at 2915, 37 L.Ed.2d at 840; see People v. Holder (1982), 103 Ill.App.3d 353, 356, 59 Ill.Dec. 142, 145, 431 N.E.2d 427, 430 ("[T]he mere fact that other applications of the statute in question, to other facts, can have impact on First Amendment rights is sufficient to invalidate the statute regardless of whether the defendant has engaged in privileged conduct").
The courts have applied the overbreadth doctrine "sparingly and only as a last resort. Facial overbreadth has not been invoked when a limiting construction has been or could have been placed on the challenged statute." (Broadrick, 413 U.S. at 613, 93 S.Ct. at 2916, 37 L.Ed.2d at 841.) A statute will not be deemed overbroad unless it has a significant effect on constitutionally protected activities. See Village of Hoffman Estates v. Flipside, Hoffman Estates, Inc. (1982), 455 U.S. 489, 494, 102 S.Ct. 1186, 1191, 71 L.Ed.2d 362, 369.
The stalking statute specifically exempts conduct protected by the first amendment, such as lawful picketing "or any exercise of the right of free speech or assembly that is otherwise lawful." (720 ILCS 5/12-7.3(c) (West Supp.1993).) Although the statute is relatively broad, it does not substantially infringe upon constitutionally protected behavior or expression either generally or as applied to defendant.
D.
Defendant also argues that the statute improperly shifted the burden of proof to him because it forced him to defend his presence at the skating rink even though the State did not offer evidence that he was there with criminal intent and "without lawful justification."
After the State has presented a prima facie case of stalking, defendant may assert an "affirmative defense" by offering "evidence sufficient to raise a reasonable doubt as to [his] guilt." (People v. Larry (1986), 144 Ill.App.3d 669, 676, 98 Ill.Dec. 885, 890, 494 N.E.2d 1212, 1217, appeal denied (1986), 112 Ill.2d 587; People ex rel. Illinois State Dental Society v. Norris (1979), 79 Ill.App.3d 890, 897, 35 Ill.Dec. 213, 220, 398 N.E.2d 1163, 1170, appeal denied.) The State, however, always retains the ultimate burden of proving defendant guilty beyond a reasonable doubt. The stalking statute does not alter this fundamental principle by impermissibly shifting the burden of proof to defendant.
Defendant's contention that the State failed to offer evidence that he was at the ice rink with criminal intent and without lawful justification is also incorrect. Intent *582 may be inferred from the surrounding facts and circumstances, including defendant's acts and words. (People v. Steffens (1985), 131 Ill.App.3d 141, 148-49, 86 Ill.Dec. 392, 399, 475 N.E.2d 606, 613, appeal denied (1985), 106 Ill.2d 559.) The State offered evidence at trial of defendant's persistent harassment of M.S., his statements to third parties, his prior lack of interest in ice skating, and the filing of an order of protection and two previous stalking charges against him prior to the events at the Owens Recreation Center. When viewed in the light most favorable to the State, this evidence was sufficient to support a finding that defendant had the requisite criminal intent under the statute. See People v. Collins (1985), 106 Ill.2d 237, 261, 87 Ill.Dec. 910, 920, 478 N.E.2d 267, 277, cert. denied (1985), 474 U.S. 1027, 106 S.Ct. 585, 88 L.Ed.2d 567.
CONCLUSION
For the reasons stated, the judgment of the circuit court of Peoria County is affirmed.
Affirmed.
HOLDRIDGE and SLATER, JJ., concur.
|
761 F.2d 1411
6 Employee Benefits Ca 1614
Raymond J. DONOVAN, Secretary of U.S. Department of Labor,Plaintiff-Appellee,v.Joseph P. MAZZOLA, Robert E. Buckley, Robert J. Costello,etc., et al., Defendants-Appellants.
No. 83-2456.
United States Court of Appeals,Ninth Circuit.
Argued and Submitted Oct. 5, 1984.Decided May 28, 1985.
Lawrence Alioto, San Francisco, Cal., for defendants-appellants.
Thomas L. Holzman, Dept. of Labor, Washington, D.C., for plaintiff-appellee.
Appeal from the United States District Court for the Northern District of California.
Before FERGUSON and NELSON, Circuit Judges, and JAMESON,* District Judge.
NELSON, Circuit Judge:
1
The trustees of a labor pension fund were ordered in July 1982 to post an indemnity bond and make restitution of lost assets to the fund. Civil contempt orders issued in September 1982 on the indemnity bond, in January 1983 on the restitution bond, and in May 1983 on both bonds. After compliance, fines were assessed, based upon the September and January orders, at a hearing in August 1983.
2
This court previously affirmed both the July 1982 judgment on the merits and the September 1982 contempt sanction. Donovan v. Mazzola, 716 F.2d 1226 (9th Cir.1983) (Donovan I ), cert. denied, --- U.S. ----, 104 S.Ct. 704, 79 L.Ed.2d 169 (1984). The facts concerning the judgment on the merits are set forth in detail in that decision, id. at 1228-1231, and will not be repeated here. We now consider the validity of the September 1983 order which assessed contempt fines based upon orders issued in September 1982 and January 1983. We reverse and remand.
FACTS AND PROCEDURAL BACKGROUND
3
This proceeding involves civil contempt orders following a judgment entered for the Secretary of Labor against fourteen present and former members of the Board of Trustees of the Pension Fund of Local 38 of the United Association of Journeymen and Apprentices of the Plumbing and Pipefitting Industry ("the trustees"). The trustees were held to have violated their fiduciary obligations under the Employees Retirement Security Act of 1974 ("ERISA"), 29 U.S.C. Sec. 1001 et seq. The judgment ordered the trustees to post an indemnity bond of $1 million and to make restitution to the pension fund of some $400,000 in lost assets. The judgment also provided for the appointment of an investment manager for the pension fund.
4
Under the judgment, the indemnity bond had to be posted by September 7, 1982 while the restitution money was due by October 7, 1982. On September 30, 1982, the district court held a hearing on the Government's motion to show cause why the trustees should not be held in contempt for their failure to post the indemnity bond. The court found the trustees in contempt and allowed them until November 1, 1982 to purge themselves; if the indemnity bond was not posted by that date, fines of $100 per day per trustee would begin to accrue on November 2. This contempt order was appealed on October 22, 1982, and was affirmed together with the final judgment. Donovan I, 716 F.2d at 1231, 1239-40.
5
Three hearings followed the September 30 order. After another motion to show cause, a contempt hearing was held in January concerning both the indemnity bond and the trustees' failure to make restitution, an obligation which had taken the form of a $600,000 supersedeas bond for restitution (the "restitution bond"). On January 13, 1983, the court found the trustees in contempt on the restitution bond, allowed them until February 13, 1983 to purge themselves, and ordered that otherwise fines would accrue at $100 per day per trustee starting on February 14, 1983. The court made clear that the restitution bond fines were to be in addition to the indemnity bond fines. The restitution bond was not filed by February 13. Unlike the September 30 order, this order was not appealed.
6
In May 1983 the court held a hearing on a motion to show cause why the trustees should not be imprisoned as a further coercive measure towards the posting of both the indemnity bond and the restitution bond. On May 9 the trustees were held to be continuing in civil contempt and were ordered jailed if both bonds were not filed by May 23. This order was not appealed.
7
The indemnity bond was posted on May 20, 1983 and on June 24, 1983 a bond securing the restitution requirement was filed. None of the trustees had been jailed, and the fines had not been assessed.
8
On August 25, 1983, the district court held a fine assessment hearing. From the bench, the judge stated a number of conclusions, later reflected in a judgment entered September 12, 1983. Because of the trustees' good faith efforts after May 10, any fines due on and after that date were remitted. Fines were assessed at $100 per trustee per day for contempt on the indemnity bond, however, and at the same rate for contempt on the restitution bond. On the indemnity bond, fines were ordered for 188 days, from November 2 through May 9, amounting to $18,800 for each of the thirteen trustees liable on that bond (one was not liable). In addition, the contempt fines on the restitution bond were assessed for 84 days, from February 14 through May 9, amounting to $8,400 for each of the fourteen trustees. The trustees have appealed the order.
9
The Donovan I decision, affirming the judgment on the merits and the September 30, 1982 contempt order, was first issued on August 23, 1983 and again, as amended (for typographical errors), on October 22, 1983. The mandate in Donovan I did not issue until January 17, 1984, having been stayed until the Supreme Court's disposition of the petition for writ of certiorari. The trustees' lawyer referred to Donovan I at the August 25 hearing, and the district judge mentioned the opinion in his September 12, 1983 order following the fine assessment hearing.
10
The fine assessment order which is here appealed, therefore, was issued before the appellate court had handed down the mandate in Donovan I, though the parties and the judge were aware of the appellate decision. The trustees' motion to stay the September 30, 1982 contempt order pending disposition of the Donovan I appeal had been denied, and the district judge apparently felt that he retained jurisdiction over the contempt order on the indemnity bond while an appeal of this order was pending before the appellate court.
ISSUES PRESENTED:
11
I. Indemnity Bond. Whether the district court had jurisdiction to quantify contempt sanctions assessed under its September 30, 1982 order while the appeal of that order was pending before this court in Donovan I.
12
II. Restitution Bond. A. Whether the January 1983 and May 1983 contempt orders concerning the restitution bond should be given res judicata effect.
13
B. Whether the district court abused its discretion in refusing to hear evidence, at the August hearing, of collective compliance efforts.
14
III. Whether the district court abused its discretion in refusing to hear evidence of individual impossibility defenses before imposing individual fines upon each of fourteen defendants for their failure to post the bonds under a joint and several obligation.
DISCUSSION
15
I. Indemnity Bond. District court's jurisdiction to quantify contempt sanctions assessed under its September 30, 1982 order while the appeal of that order was pending before this court in Donovan I.
16
The Ninth Circuit follows the general rule, with some exceptions, that the filing of a notice of appeal divests the district court of jurisdiction over the matters appealed. See, e.g., Miranda v. Southern Pacific Transportation Company, 710 F.2d 516, 519 (9th Cir.1983); Davis v. United States, 667 F.2d 822, 824 (9th Cir.1982). This rule has been recently applied to contempt orders. Shuffler v. Heritage Bank, 720 F.2d 1141, 1145 n. 1 (9th Cir.1983) (order quantifying sanction is void for lack of jurisdiction during pendency of appeal); Matter of Thorp, 655 F.2d 997, 999 (9th Cir.1981) (criminal contempt finding void because mandate from appellate decision on civil contempt on same issue had not yet issued). A 1976 case, however, stresses the exceptions to this rule in coercive civil contempt orders enforcing a labor injunction. Hoffman v. Beer Drivers and Salesmens' Local No. 888, 536 F.2d 1268, 1276-77 (9th Cir.1976). The Hoffman court held that:
17
in the kinds of cases where the court supervises a continuing course of conduct and where as new facts develop additional supervisory action by the court is required, an appeal from the supervisory order does not divest the district court of jurisdiction to continue its supervision, even though in the course of that supervision the court acts upon or modifies the order from which the appeal is taken.
18
Id. [emphasis added].
19
We must determine whether to follow Hoffman or Shuffler and Thorp in this case. In Thorp the court imposed fines and imprisonment to coerce a witness to respond, 655 F.2d at 999, and in Shuffler the court used fines to compel compliance with a money judgment and to compensate the prevailing party for delay. 720 F.2d at 1144. In Hoffman fines were imposed to compel compliance with an injunction against picketing. 536 F.2d at 1271-73. Shuffler and Hoffman differ on the extent to which the district court's continued enforcement of the order being appealed is permitted. Since Shuffler 's use of contempt to enforce a money judgment is most similar to the fact pattern before this panel, the Shuffler rule of complete transfer of jurisdiction to the appeals court should properly be applied to this case.
20
We conclude, therefore, that the district court lacked jurisdiction over the contempt order quantifying sanctions on the indemnity bond. Cf. Ruby v. Secretary of the Navy, 365 F.2d 385, 388-89 (9th Cir.1966) (when "a notice of appeal does not transfer jurisdiction to the court of appeals, then such jurisdiction must remain in the district court: it cannot float in the air"). The district court held hearings in January, May and August during the pendency of Donovan I, when the appellate court had jurisdiction over the indemnity contempt sanction and thereby deprived the district court of jurisdiction over that issue. Under Shuffler, the assessment of fines at the August 1983 hearing is therefore void to the extent it was based upon the September 30, 1982 order. See Shuffler, 720 F.2d at 1145 n. 1. The district court also lacked jurisdiction over the imprisonment sanction issued in May to the extent that it was based upon continuing violation of the September 30, 1982 order. The district court must therefore consider evidence on the indemnity bond sanctions for the whole period in question, September 30 through May 9.
21
II. Restitution bond.
22
It remains for us to consider the validity of the fine assessment at the August 1983 hearing as far as it quantified the fines imposed in the January 1983 contempt order on the restitution bond. The district court had jurisdiction over the restitution bond contempt order and the fines assessed pursuant to it. We therefore consider the trustees' next claim: that they should have been permitted to present evidence at the August hearing of compliance efforts. Appeal of one order does not necessarily deprive the district court of jurisdiction over issues not raised in that order. See, e.g., Oliver v. Kalamazoo Board of Education, 640 F.2d 782, 788 (6th Cir.1980). Hoffman supports this conclusion. Id., 536 F.2d at 1267. Compare Shuffler, 720 F.2d at 1145 (involved only one issue of contempt).
23
A. Res judicata effect of the January 1983 and May 1983 contempt orders concerning the restitution bond.
24
The trustees argue that the district judge improperly refused to consider evidence at the August fine assessment hearing because this opportunity had been presented at the January and May hearings, and sanctions were not imposed for dates subsequent to the May hearing. The Government responds that this court's affirmance of the September 30, 1982 order and the finality of the January and May orders precludes the trustees' claim that their efforts to present evidence, of their attempts to comply from September 30 to May 10,1 were improperly denied at the August fine assessment hearing.
25
Only the January and May orders insofar as they concerned the restitution bond are relevant here. To recapitulate the facts, the January order found the trustees in continuing contempt of court for their failure to post the restitution bond from its due date, October 7, 1982, through the hearing date of January 13, 1983. The order allowed the trustees until February 13, 1983 to purge themselves, and ordered that otherwise fines of $100 per trustee per day would begin on February 14, 1983. The May order found that the trustees were continuing in civil contempt from the previous hearing date, January 13, 1983, through the hearing date of May 9, 1983. The trustees were ordered jailed if both bonds were not filed by May 23, 1983.
26
The Government argues that the January and May orders were final judgments, and that the matters adjudicated by these orders--that the trustees continued in contempt from October 7, 1982 through May 9, 1983--are therefore res judicata. In consequence, the trustees could not challenge the judgment of contempt at the August hearing. This argument rests upon the assertion that the January and May orders were final judgments, for it is "familiar law that only a final judgment is res judicata. " G. & C. Merriam Co. v. Saalfield, 241 U.S. 22, 28, 36 S.Ct. 477, 480, 60 L.Ed. 868 (1916). See Russell v. C.I.R., 678 F.2d 782, 786 (9th Cir.1982). See also Horner v. Ferron, 362 F.2d 224, 230 (9th Cir.), cert. denied, 385 U.S. 958, 87 S.Ct. 397, 17 L.Ed.2d 305 (1966). To determine the finality of the order, we consider the criteria used to determine finality for the purposes of 28 U.S.C. Sec. 1291, on finality as a prerequisite for appealability.
27
The January restitution fine order and the May imprisonment order were conditionally phrased. Each ordered the trustees to comply by a certain date some weeks hence, after which fines would begin to accrue if non-compliance continued. We may examine the September 30, 1982 order, which was appealed to this court, and supplies a model for the January and May orders.2 The September 30 order imposed sanctions beginning November 1 but was appealed October 22, while the trustees still retained the opportunity to avoid sanctions entirely through prompt compliance.3
28
The contempt order satisfied several of the well-established criteria for finality of a civil contempt order, but lacked one essential factor. Two requirements were present: the order against the trustees followed the final judgment on the merits, and the appeal was taken together with the appeal from the final judgment. See Shuffler v. United States, 720 F.2d 1141, 1145 (9th Cir.1983). Compare Hughes v. Sharp, 476 F.2d 975 (9th Cir.1973) (civil contempt order remains interlocutory if against party during proceedings). Sanctions had not yet been imposed, however.
29
The requirement of a sanction to render a contempt order final under section 1291 is expressed in Alexander v. United States, 201 U.S. 117, 121-22, 26 S.Ct. 356, 357-58, 50 L.Ed. 686 (1906):... [A]n order may coerce a witness, leaving to him no alternative but to obey or be punished ... but from such a ruling it will not be contended there is an appeal. Let the court go further and punish the witness for contempt of its order, then arrives a right of review.... This power to punish being exercised the matter becomes personal to the witness and a judgment as to him. Prior to that the proceedings are interlocutory....
30
Id. See also Cohen v. Beneficial Loan Corp., 337 U.S. 541, 546, 69 S.Ct. 1221, 1225, 93 L.Ed. 1528 (1949); Flanagan v. United States, 465 U.S. 259, 104 S.Ct. 1051, 1054, 79 L.Ed.2d 288 (1984). Our circuit has frequently held that an adjudication of civil contempt is not appealable until sanctions have been imposed. Weyerhaeuser Company v. International Longshoremen's and Warehousemen's Union Local 21, 733 F.2d 645 (9th Cir.1984); Hoffman v. Beer Drivers & Salesmen's Local No. 888, 536 F.2d 1268, 1272-73 (9th Cir.1976). See also Steinert v. United States, 571 F.2d 1105, 1107 (9th Cir.1978) (dicta ). Compare Shuffler, 720 F.2d at 1145 (since contempt order required immediate payment of $1,000/week into court, sanction had been imposed and was appealable though final quantification of fine not yet determined); Falstaff Brewing Corp. v. Miller Brewing Co., 702 F.2d 770, 777 (9th Cir.1983) (penalty ordered paid to court but motion for refund would be entertained if compliance obtained within ninety days of order). Until the imposition of sanctions, therefore, the September 1982, January, and May orders were interlocutory.
31
Interlocutory orders do not have res judicata effect. See, e.g., Russell, 678 F.2d at 786. The January and May orders cannot be viewed as final for the res judicata purposes of treating the orders as barring all arguments on the duration of the trustee's contempt as untimely. In this case, the orders do not preclude presentation of evidence at the fine assessment hearing based upon res judicata alone.
32
B. Whether the district court abused its discretion in refusing to hear evidence on collective compliance efforts concerning the joint obligation.
33
The doctrine of res judicata does not preclude the trustees from presenting evidence of their compliance efforts on the restitution bond from January through May, but this does not end the inquiry. We must determine whether the district judge committed an abuse of discretion in refusing to hear evidence in August. We therefore address the trustees' argument that they should have been allowed to present evidence at the fine assessment hearing concerning compliance efforts.
34
The district court stated at the August hearing that the trustees' opportunity to present evidence for the period preceding May 10 had passed, since such an opportunity had been available at the May hearing. The district court apparently understood its obligation to consider evidence at a fine assessment hearing, and considered that this opportunity had already been supplied. See Pennwalt Corp. v. Durand-Wayland, 708 F.2d 492, 493, 495 (9th Cir.1983) (evidence must be considered on reasonableness of fee assessed even if award quantifies a previously issued sanction order). The judge's consideration of evidence at each hearing will be discussed seriatim.
35
1. September 30, 1982 order and Donovan I.
36
Donovan I affirmed the September 30, 1982 order for contempt on the indemnity bond at $100 per day per trustee starting November 2, 1983. 716 F.2d at 1240. The appellate court found that evidence had been considered. Id. The res judicata effect of this order, which was affirmed in Donovan I, does not eliminate the district court's obligation to hear evidence at subsequent contempt hearings, since present inability to comply is a complete defense and past ability to comply is not res judicata as to continuing ability to comply. United States v. Rylander, 460 U.S. 752, 103 S.Ct. 1548, 1552, 75 L.Ed.2d 521 (1983) ("Rylander I "); Maggio v. Zeitz, 333 U.S. 56, 75-76, 68 S.Ct. 401, 411-412, 92 L.Ed. 476 (1948). Cf. United States v. Rylander, 714 F.2d 996, 1002 (9th Cir.1983), cert. denied, --- U.S. ----, 104 S.Ct. 2398, 81 L.Ed.2d 355 (1984) (" Rylander II "). Ability to comply is a crucial inquiry for the court's decision concerning coercive civil contempt orders, and "a court should weigh all the evidence properly before it determines whether or not there is actually a present ability to obey and whether failure to do so constitutes deliberate defiance or willful disobedience which a coercive sanction will break." Falstaff, 702 F.2d at 781 n. 6 (citing Maggio, 333 U.S. at 76, 68 S.Ct. at 411).
37
2. January hearing on both bonds.
38
The district court was thus obliged to consider evidence at the January hearing on the trustees' ability to post the restitution bond. The record indicates that most of the discussion at that hearing concerned the indemnity bond, and the court's refusal to approve an agreement by the parties to supply letters of credit rather than a bond to satisfy that obligation. On the restitution bond, the record shows that the court twice told the trustees' attorney that he would hear nothing further, after beginning the hearing with the statement that "I don't think I need very much argument on this matter." The court agreed with the Government that "once again, nothing has been offered by the defendants to show inability to comply with the judgment."
39
The district judge apparently determined that the two reasons given by the trustees for non-compliance--first, their agreement with the Government to supply letters of credit instead of a bond on indemnity and second, the Government's unsubordinated judgment lien on the trustees' property--did not constitute inability to comply. He did not abuse his discretion in limiting the trustees' attorney's comments and ruling that the excuses offered did not constitute collective inability to comply with the restitution bond. Evidence on inability to post the restitution bond from October 7 through the hearing date, January 10, was heard at the January hearing.4
40
3. May hearing on both bonds.
41
The imprisonment contempt order was a sanction for both the indemnity and restitution bonds. The hearing concerned both the restitution bond and indemnity bond. The imprisonment sanction explicitly concerned the trustees' failure to post both bonds, and we cannot determine from the record the role played in the court's decision by the trustees' failure to post both bonds. See Gompers v. Bucks Stove & Range Co., 221 U.S. 418, 449-50, 31 S.Ct. 492, 501-02, 55 L.Ed. 797 (1911) (where contempt sentence does not indicate amount of punishment for each act, entire sentence must be reversed if one violation was improperly found). Compare Hoffman, 536 F.2d at 1275. Thus, the indemnity sanction cannot be distinguished from the restitution issue, and the May hearing should not have precluded later presentation of evidence on the restitution bond. Since jurisdiction was lacking over the indemnity bond, evidence on efforts to post both bonds should be allowed on remand: from January 10 through May 9 on the restitution bond, and from September 30 through May 20 on the indemnity bond.
42
III. Evidence concerning individual compliance efforts.
43
It remains to clarify for remand purposes whether, as the trustees argue, the trial judge should hear individual impossibility defenses as well as the evidence of collective impossibility discussed above. When individual defenses were offered by the trustees' attorney at the May hearing, the court responded that since the obligation was joint and several, individual impossibility defenses would "waste time." At the August hearing, the court again refused to hear offers of proof on impossibility defenses for individuals, though he indicated that he thought that individual ability to pay was an important factor.5
44
The trustees contend on appeal that the district court did not make individual assessments of ability to comply with the judgment. This argument has merit. While the court repeatedly found that the collective assets of the trustees could satisfy a joint obligation, see, e.g., Donovan I, 716 F.2d at 1240, it never found that a single individual was capable of satisfying the whole obligation. Thus before assessing contempt fines on individuals, because each trustee had failed in his "individual" obligation to post both bonds, the court should have considered the evidence presented concerning whether certain individual trustees had impossibility defenses on their ability to singlehandedly supply the total funds for both bonds. The district court did not do so. It imposed uniform fines on each defendant amounting to $27,200 for each of thirteen trustees and $8,400 for the fourteenth trustee (who was liable only on the restitution bond).
45
Donovan I 's affirmance of the September 30 order noted the "collective" ability to comply and did not reach the issue of the court's obligation to hear evidence before assessing fines individually. 716 F.2d at 1240. The district court's alternative was to impose a collective fine upon the trustees, whom it concluded had a collective ability to comply. See, e.g., Landman v. Royster, 354 F.Supp. 1292, 1301 (E.D.Va.1973) (joint and several fine of $25,000 upon all defendants). Before assessing individual fines even upon those trustees who had supplied their share of the funds and upon those who claimed poverty, the court should have considered evidence of individual impossibility defenses. Upon remand, it should do so.
CONCLUSION
46
The fine assessment based upon the indemnity bond contempt order is void for lack of jurisdiction and is remanded. The fine assessment based upon the restitution bond contempt order does not have jurisdictional defects but is reversed and remanded because it is inextricably intertwined with the indemnity bond issue and because the district judge abused his discretion in refusing to consider evidence of individual impossibility defenses in imposing individual fines for violation of a joint and several obligation. Upon remand, the district judge should consider evidence from September 30, 1982 through May 20, 1983 as to indemnity bond sanctions, and from January 13, 1983 through May 9, 1983 on the restitution bond sanctions.
*
The Honorable William J. Jameson, United States District Judge for the District of Montana, sitting by designation
1
Neither party on appeal nor the court at the hearing below discussed the presentation of evidence after May 10. The district court determined that it would not impose fines as to restitution bond sanctions after May 10, even though the bond was not filed until June 10, due to the good faith efforts of the trustees. Since the district court had jurisdiction over the restitution bond, this court will not disturb that finding. The district court also remitted indemnity bond fines from May 10 until May 20, the date the bond was filed. Since this action was void for lack of jurisdiction, on remand the district court is not bound by this limitation
2
The Donovan I opinion did not discuss the source of appellate jurisdiction over this order, which was considered together with the appeal from the final judgment. The issue was apparently not presented by the parties to that court. The Donovan I panel's decision is res judicata as to its subject-matter jurisdiction over the September 30, 1982 order. Underwriters National Assurance Co. v. North Carolina Life & Accident & Health Insurance Guaranty Ass'n., 455 U.S. 691, 706-07, 102 S.Ct. 1357, 1366-67, 71 L.Ed.2d 558 (1982); Insurance Corp. of Ireland, Ltd. v. Compagnie des Bauxites de Guinea, 456 U.S. 694, 702 n. 9, 102 S.Ct. 2099, 2104 n. 9, 72 L.Ed.2d 492 (1982). Even if the issue of jurisdiction was not argued to the Donovan I panel, if the parties had the opportunity to litigate the question of jurisdiction, it may not be reopened in a collateral attack upon the previous judgment. Sherrer v. Sherrer, 334 U.S. 343, 350, 68 S.Ct. 1087, 1090, 92 L.Ed. 1429 (1948); Underwriters National, 455 U.S. at 710, 102 S.Ct. at 1369
3
Practical considerations buttress the conclusion that the September 30 interlocutory order was not final and appealable on October 22. The trustees had 60 days to appeal a final order, FRAP 4(a)(1) (U.S. as party), a period which should not have begun until they had violated the order after November 1. Otherwise, the coercive purpose of the civil contempt order with a grace period between September 30 and November 1 is thwarted. Rather than devoting all of their efforts to complying before November 1, the trustees apparently chose to safeguard attempts to comply with simultaneous preparations for appeal, should compliance fail. The time for appeal should not run until it is clear that the contempt sanction has been incurred, in this case after November 1, for otherwise there is nothing to appeal
4
Since fines were not imposed until February 14, however, evidence on the trustees' efforts during this earlier period is not directly at issue
5
The court asked the trustees' attorney, "Have any of your clients signed an affidavit that they are impoverished and have no means of making any payment?" When one trustee said to the judge, "I signed my house away. What else can I do? I have no other money. What else can I do?", the judge responded that "the court will not punish for contempt where a person has complied to the very best of his ability."
|
IN THE SUPREME COURT, STATE OF WYOMING
2016 WY 87
APRIL TERM, A.D. 2016
August 30, 2016
IN THE MATTER OF THE WORKER’S
COMPENSATION CLAIM OF TODD JENSEN,
AN EMPLOYEE OF R.S. BENNETT
CONSTRUCTION:
TODD JENSEN,
Appellant
(Petitioner),
No. S-16-0017
v.
STATE OF WYOMING, ex rel., DEPARTMENT
OF WORKFORCE SERVICES, WORKERS’
COMPENSATION DIVISION,
Appellee
(Respondent).
Appeal from the District Court of Sublette County
The Honorable Marvin L. Tyler, Judge
Representing Appellant:
Jack D. Edwards of Edwards Law Office, P.C., Etna, Wyoming.
Representing Appellee:
Peter K. Michael, Wyoming Attorney General; John D. Rossetti, Deputy Attorney
General; Michael J. Finn, Senior Assistant Attorney General; Kellsie J. Singleton,
Assistant Attorney General.
Before BURKE, C.J., and HILL, DAVIS, FOX, and KAUTZ, JJ.
NOTICE: This opinion is subject to formal revision before publication in Pacific Reporter Third.
Readers are requested to notify the Clerk of the Supreme Court, Supreme Court Building,
Cheyenne, Wyoming 82002, of any typographical or other formal errors so that correction may be
made before final publication in the permanent volume.
FOX, Justice.
[¶1] The Office of Administrative Hearings (OAH) denied Mr. Jensen’s worker’s
compensation claim on the grounds that he failed to prove a causal relationship between
his automobile accident and his prior work-related accident. The district court upheld
that decision. We affirm.
ISSUES
[¶2] 1. Did the OAH properly apply the second compensable injury rule?
2. Was the OAH’s conclusion that Mr. Jensen did not prove by a preponderance
of the evidence that his automobile accident was causally connected to his work-related
injury supported by substantial evidence?
FACTS
[¶3] On October 13, 2011, Mr. Jensen suffered a work-related injury when he climbed
from the bed of a dump truck and fell onto a rock, fracturing his right hip. Dr. Brian
Tallerico performed surgery on the hip, inserting a nail into the femur to repair the
fracture. The Department of Workforce Services, Workers’ Compensation Division (the
Division) approved benefits for the injury to Mr. Jensen’s right hip.
[¶4] After surgery, Mr. Jensen’s legs were different lengths, causing a limp and
constant pain in both hips. The pain eventually became unbearable, and on July 12,
2012, Dr. Tallerico and Dr. Aaron Altenburg performed a total hip replacement in
Pocatello, Idaho. After his hip replacement, Mr. Jensen remained in pain, had bursitis,
and was pigeon-toed. This caused him to trip and fall down when he walked.
[¶5] Mr. Jensen sought treatment for the symptoms he was experiencing. He began
seeing pain specialist Dr. Holly Zoe in Idaho Falls, Idaho. He also revisited Dr.
Tallerico, with whom he discussed the possibility of returning to work and the
performance of a functional capacity evaluation and an impairment rating examination,
which were subsequently scheduled. Dr. Tallerico noted: “Musculoskeletal: gait and
station–[c]onventional walking: abnormal toe off.” He performed an impairment rating
examination in April of 2013. During that examination, Dr. Tallerico noted:
Gait Observation: He ambulates with an antalgic gait
favoring the right lower extremity with a shortened swing
phase and stance phase. It is not a true Trendelenburg
appearance however. Overall it does not appear that he has
excessive external or internal rotation of the right lower
extremity.
1
....
Manual motor testing however does reveal some give way
weakness in basically all major motor groups in the right
lower extremity.
....
It is my opinion that the claimant is now at maximal medical
improvement related to this industrial injury and he should be
considered fixed and stable at this time.
I am also of the opinion that Mr. Jensen does have permanent
work restrictions related to the industrial injury. I believe that
this individual has a sincere desire to return to work but given
his prior heavy requirements I doubt he can return to the job
of injury . . . .
[¶6] On June 3, 2013, Mr. Jensen notified the Division that he was having difficulty
walking because his pigeon-toed foot was causing him to fall and that he was going to see
Dr. Tallerico about it. On June 5, he followed up with Dr. Tallerico. During that visit,
according to Dr. Tallerico’s notes, Mr. Jensen “state[d] that he has a hard time walking as
right foot [wants] to roll [] underneath him and [is] pigeon toe[d] to where he trips over
and [falls].” Regarding Mr. Jensen’s physical examination, Dr. Tallerico’s notes state:
The patient[‘s] examination is quite interesting. As he sits in
the examination chair [it] appears that he does have inversion
and internal rotation of his right foot. However with
distraction this is not the case[.] [W]hen I inspected his shoes
there is no evidence of a [un]even wear pattern on the right
shoe sole. He ambulates with a slight limp as he always [is]
favoring the right lower extremity[.] [H]is supine exam
shows basically even limb length and with distraction and
log-rolling of his legs there is essentially no evidence of any
malrotation of his right lower extremity due to malposition of
his total hip implant. In fact in the supine position. [sic]
This is confirmed whereas [h]is foot progression angle is
actually symmetric. His hip range of motion is actually quite
impressive and symmetric with no abnormal findings on the
right side [and] no evidence of impingement[.]
2
Dr. Tallerico’s notes go on to state:
[Mr. Jensen’s] clinical symptoms are somewhat perplexing to
me. He seems to feel that he has significant internal rotation
and intoeing of the right lower extremity but I cannot find any
objective evidence to support that on exam . . . . However I
certainly have to take [Mr. Jensen’s] subjective complaints
into consideration so therefore we are going to have him see
the Ortho [tech] in Pocatello on the same day to give him a
lateral heel wedge for his right shoe orthotics to see if that
will help neutralize his foot[.]
[¶7] On June 10, Mr. Jensen saw Dr. Altenburg and his assistant, Matthew McKinlay,
PA-C. Mr. McKinlay’s notes state that Mr. Jensen “complains of soreness in his lateral
hip that has caused him to walk with pinching toe gait and he is also starting to go over
the lateral aspect of his foot.” The physical examination revealed the following:
Certainly, he does walk with his foot internally rotated and
seems to thrust his weight laterally. He has marked
tenderness at the greater trochanter. When his leg is relaxed
in extension, he externally rotates to a neutral position and the
pain resolves.
The note concluded that Mr. Jensen “has developed greater trochanteric bursitis and
intoeing.” Going forward, their plan was to “get [Mr. Jensen] set up for some gait
training and physical therapy focusing on externally rotating the foot and leg to get into
more of a neutral alignment.”
[¶8] The day after Mr. Jensen saw Dr. Altenburg, he was scheduled for appointments
with Idaho Prosthetics & Orthotics to be fitted with orthotics, and with East Idaho
Interventional Pain Center. En route to those appointments, Mr. Jensen was in an
automobile accident which resulted in a shattered right ankle, broken left arm, and a
broken pelvis.
[¶9] Immediately before the accident, Mr. Jensen was traveling north on Highway 89.
As he approached the bridge over the Salt River, the vehicle in front of him began to turn
right onto Lincoln County Road 128, and Mr. Jensen slowed down to allow room for the
vehicle to turn. At the hearing, Mr. Jensen testified regarding what happened next:
A. [Mr. Jensen:] Okay. There’s a vehicle in front of me a
quarter mile ahead of me. I’m -- I’m going well under the
speed limit. I put my left foot up on the clutch, pushed it in
and shifted down. I needed to slow the pickup down. I put
my right foot up on the brake pedal.
3
Q. [Counsel for Mr. Jensen:] Why are you slowing your
vehicle down?
A. Just to make sure I give him enough room to make his
turn.
....
So, I put my right foot up, my pigeon toed foot up on the
pedal, and it did what it does when I walked, it rolled off the
pedal and down between the gas pedal and the brake pedal.
And instead of being straight it’s, like I say, pigeon toed.
And I reached down with my leg tried to pull it out. Couldn’t
get it to come.
I glanced down to see what I needed to do to get it out,
and when I glanced back up, there was a bridge abutment
right in front of me.
I made a hard left. I heard a bunch of crunching sound,
thought I had made it out of it, and thought that maybe I just
crunched in the side of my pickup was going through my
head, and thinking, Oh, boy. Because it was a nice little
pickup, and it was in very good shape for how old it was.
And I was thinking, Oh boy. And right at the moment
I’m thinking this, boom, I’m upside down twirling on my
roof, and I twirled across the road, hit the curb on the other
side of the bridge, and it bounced me back to the northbound
lane. That’s where it spun to a stop.
Q. So during this time when this -- when your vehicle
crashed, where was your right foot?
A. It was in between the gas pedal and the clutch or the
brake pedal, I’m sorry.
[¶10] Immediately after the accident, UPS driver John Pittman arrived on the scene and
helped Mr. Jensen out of his truck. Mr. Jensen laid his head on Mr. Pittman’s lap until
the ambulance arrived. At that time, he also called his wife from his cell phone. Mrs.
Jensen testified that he spoke to her on the phone and told her that the accident happened
when his foot got lodged between the brake and gas pedals and he could not get it out.
4
[¶11] An ambulance transferred Mr. Jensen to the Star Valley Medical Center, and he
was ultimately life-flighted to the University of Utah Hospital in Salt Lake City, Utah,
where he received treatment for his injuries. The Division denied Mr. Jensen’s request
for worker’s compensation benefits for the injuries sustained in the automobile accident.
After a contested case hearing, the OAH again denied his request. Mr. Jensen appealed
that decision to the Sublette County District Court, which affirmed the OAH’s decision.
Mr. Jensen timely filed this appeal.
STANDARD OF REVIEW
[¶12] Our standard of review of a district court’s review of an administrative agency’s
decision in worker’s compensation cases is:
When an appeal is taken from a district court’s review
of an administrative agency’s decision, we examine the case
as if it had come directly from the agency without giving any
deference to the district court’s decision. Dutcher v. State
ex rel. Wyo. Workers’ Safety & Comp. Div., 2010 WY 10, ¶ 9,
223 P.3d 559, 561 (Wyo. 2010); Dale v. S & S Builders, LLC,
2008 WY 84, ¶ 8, 188 P.3d 554, 557 (Wyo. 2008). Our
review is governed by Wyo. Stat. Ann. § 16-3-114(c)
(LexisNexis 2013) . . . .
Guerrero v. State ex rel. Dep’t of Workforce Servs., Workers’ Comp. Div., 2015 WY 88,
¶ 11, 352 P.3d 262, 265 (Wyo. 2015).
[¶13] We review the agency’s findings of fact by applying the substantial evidence
standard. Wyo. Stat. Ann. § 16-3-114(c)(ii)(E) (LexisNexis 2015); see also Dale v. S & S
Builders, LLC, 2008 WY 84, ¶ 22, 188 P.3d 554, 561 (Wyo. 2008).
Substantial evidence means “such relevant evidence as a
reasonable mind might accept as adequate to support a
conclusion.” Bush v. State ex rel. Wyo. Workers’ Comp. Div.,
2005 WY 120, ¶ 5, 120 P.3d 176, 179 (Wyo. 2005) (citation
omitted). See also Kenyon v. State ex rel. Wyo. Workers’
Safety & Comp. Div., 2011 WY 14, ¶ 11, 247 P.3d 845, 849
(Wyo. 2011). “Findings of fact are supported by substantial
evidence if, from the evidence preserved in the record, we can
discern a rational premise for those findings.” Id., ¶ 11, 247
P.3d at 849 (citation omitted).
5
When an agency rules that the claimant did not satisfy
his burden of proof, we apply the following standard:
If the hearing examiner determines that the burdened
party failed to meet his burden of proof, we will decide
whether there is substantial evidence to support the
agency’s decision to reject the evidence offered by the
burdened party by considering whether that conclusion
was contrary to the overwhelming weight of the
evidence in the record as a whole. If, in the course of
its decision making process, the agency disregards
certain evidence and explains its reasons for doing so
based upon determinations of credibility or other
factors contained in the record, its decision will be
sustainable under the substantial evidence test.
Importantly, our review of any particular decision
turns not on whether we agree with the outcome, but
on whether the agency could reasonably conclude as it
did, based on all the evidence before it.
Dale, ¶ 22, 188 P.3d at 561 (citations omitted).
Guerrero, 2015 WY 88, ¶¶ 12-13, 352 P.3d at 266.
[¶14] We review an agency’s conclusions of law de novo, and will affirm those
conclusions only when they are in accordance with the law. Id., 2015 WY 88, ¶ 14, 352
P.3d at 266 (citing Middlemass v. State ex rel. Wyo. Workers’ Safety & Comp. Div., 2011
WY 118, ¶ 13, 259 P.3d 1161, 1164 (Wyo. 2011)).
DISCUSSION
I. Did the OAH properly apply the second compensable injury rule?
[¶15] Mr. Jensen argues that the Hearing Examiner failed to properly apply the second
compensable injury rule. Mr. Jensen takes issue with the Hearing Examiner’s comments
that he had failed to pursue the “but for” theory of analysis. The Hearing Examiner
stated: “Jensen has alleged only that the residual injuries caused the automobile accident.
He has not alleged a theory, similar to that of In re Fisher [Fisher v. State ex rel. Wyo.
Workers’ Safety & Comp. Div., 2008 WY 89, 189 P.3d 866 (Wyo. 2008)] that ‘but for’
the work related accident he would not have suffered the degree of injuries he did in the
automobile accident.” She also stated that “[t]he court in Fisher and Alvarez [v. State ex
rel. Wyo. Workers’ Safety & Comp. Div., 2007 WY 126, 164 P.3d 548 (Wyo. 2007)]
found in both cases that ‘but for’ the work related injuries the subsequent injuries would
6
not have occurred,” and that “Jensen has not alleged or attempted to prove that ‘but for’
his prior work related injury he would not have suffered the same or as severe of injuries
in the car accident.” Although Mr. Jensen is correct that the “but for” analysis does not
govern the determination of a second compensable injury, the evidence shows that the
Hearing Examiner applied the correct standard in reaching her conclusion.
[¶16] To qualify for worker’s compensation, an employee must show that he suffered a
compensable injury. Guerrero, 2015 WY 88, ¶ 15, 352 P.3d at 266. An “injury is not
compensable if it cannot fairly be traced to the employment as a contributing cause and if
it comes from a hazard that the employee would have been equally exposed to outside of
the employment.” Ball v. State ex rel. Wyo. Workers’ Safety & Comp. Div., 2010 WY
128, ¶ 23, 239 P.3d 621, 628 (Wyo. 2010) (citing Finley v. State ex rel. Wyo. Workers’
Safety & Comp. Div., 2006 WY 46, ¶ 8, 132 P.3d 185, 188 (Wyo. 2006) (quoting State
ex rel. Wyo. Workers’ Safety & Comp. Div. v. Bruhn, 951 P.2d 373, 377 (Wyo. 1997)).
[¶17] The second compensable injury rule applies when “an initial compensable injury
has resulted in an injury or condition that requires additional medical intervention.” Ball,
2010 WY 128, ¶ 24, 239 P.3d at 628. See also Alvarez, 2007 WY 126, ¶ 18, 164 P.3d at
552; Yenne-Tully v. Workers’ Safety & Comp. Div., 12 P.3d 170, 172 (Wyo. 2000).
“Under the rule, a subsequent injury is compensable if it is causally related to the initial
compensable work injury.” Alvarez, 2007 WY 126, ¶ 18, 164 P.3d at 552 (citing Yenne-
Tully, 12 P.3d at 172); see also Ball, 2010 WY 128, ¶ 24, 239 P.3d at 628. In order to
prove a second compensable injury, the employee must prove, “by a preponderance of
the evidence, that it is more probable than not that there exists a causal connection
between the first and second injuries.” Guerrero, 2015 WY 88, ¶ 29, 352 P.2d at 271
(citing State ex rel. Wyo. Workers’ Safety & Comp. Div. v. Kaczmarek (In re Kaczmarek),
2009 WY 110, ¶ 11, 215 P.3d 277, 282-83 (Wyo. 2009)). In order to establish that causal
connection, the employee “must present evidence demonstrating that the initial work
injury contributed to the second injury.” Id. at ¶ 31, 352 P.3d at 271. In Ball, we
explained the language we have used to describe the rule’s causation requirement:
We have used a number of terms to describe the required
causal connection between the first and second injuries
including: “direct cause” (Pino v. State ex rel. Wyo. Workers’
Safety & Comp. Div., 996 P.2d 679, 684 (Wyo. 2000); Taylor
v. State ex rel. Wyo. Workers’ Safety & Comp. Div., 2003 WY
83, ¶ 12, 72 P.3d 799, 803 (Wyo. 2003)); “caused by”
(Casper Oil Co. v. Evenson, 888 P.2d 221, 226 (Wyo. 1995));
“causally related to” (Chavez v. State ex rel. Wyo. Workers’
Safety & Comp. Div., 2009 WY 46, ¶¶ 26-27, 204 P.3d 967,
973-74 (Wyo. 2009); Walsh v. Holly Sugar Corp., 931 P.2d
241, 243 (Wyo. 1997)); “direct causal connection” (Alvarez v.
State ex rel. Wyo. Workers’ Safety & Comp. Div., 2007 WY
7
126, ¶ 17, 164 P.3d 548, 552 (Wyo. 2007)); “direct and
natural result” (Stewart v. State ex rel. Wyo. Workers’ Safety
& Comp. Div., 2007 WY 58, ¶ 12, 155 P.3d 198, 203 (Wyo.
2007) (quoting 1 Arthur Larson & Lex K. Larson, Larson’s
Workers’ Compensation Law § 10.10, at 10-2 (2006)));
“significant causal connection” and “predominant cause”
(Yenne-Tully v. State ex rel. Wyo. Workers’ Safety & Comp.
Div., 2002 WY 90, ¶ 11, 48 P.3d 1057, 1062 (Wyo. 2002));
“fairly be traced to” and “a contributing cause” (State ex rel.
Wyo. Workers’ Safety & Comp. Div. v. Bruhn, 951 P.2d 373,
377 (Wyo. 1997)). Regardless of the terminology used to
describe the causal connection, the burden remains the same:
the claimant must show, by a preponderance of the evidence,
that it is more probable than not that the second injury was
caused by the first.
Ball, 2010 WY 128, ¶ 24, 239 P.3d at 628 (quoting Kaczmarek, 2009 WY 110, ¶ 11 n.3,
215 P.3d at 282 n.3).
[¶18] Here, the Hearing Examiner recognized that the second compensable injury rule
applies in this instance. She stated: “This case concerns the second compensable injury
rule.” She went on to properly identify the relevant issue as “whether [Mr. Jensen’s]
work related injury caused the accident as he suggests in that due to his work related hip
injury his foot was not functioning properly and slipped off the brake pedal and got
stuck.” She also stated that “[t]he causal connection . . . is dependent upon whether or
not the work related injuries were the cause of the accident.”
[¶19] The Hearing Examiner then applied the second compensable injury rule, finding
that “[w]hile the Office finds and concludes that Jensen did have residual problems from
the work related injury, i.e., the in toeing and even rolling of the foot, the Office does not
find that the preponderance of the evidence shows that those residual problems were the
cause of the automobile accident.”
[¶20] The second compensable injury rule was applicable in this case and the Hearing
Examiner applied that rule. Therefore, Mr. Jensen’s claim that “[t]he wrong rule of law
was applied” cannot be sustained.
II. Was the OAH’s conclusion that Mr. Jensen did not prove by a preponderance of
the evidence that his automobile accident was causally connected to his work-
related injury supported by substantial evidence?
[¶21] Mr. Jensen argues that the OAH’s findings were not supported by substantial
evidence. As we explained in the preceding section, in order to receive worker’s
8
compensation benefits, Mr. Jensen had to prove by a preponderance of the evidence that
the injuries he suffered in the automobile accident on June 11, 2013, were causally
connected to his 2010 work-related injury. Guerrero, 2015 WY 88, ¶ 29, 352 P.2d at
271; Hoffman v. State ex rel. Wyo. Workers’ Safety & Comp. Div., 2012 WY 164, ¶ 9,
291 P.3d 297, 301-02 (Wyo. 2012).
[¶22] In his endeavor to make that showing, Mr. Jensen relied on his medical records
prior to the accident, testimony of his treating physicians, statements he made
immediately after the accident in the presence of Mr. Pittman and to his wife, and his
testimony at the hearing before the OAH, as well as his affidavit. That evidence consists
of the following:
• February 14, 2013: Dr. Zoe noted a “decreased [range of motion] with right hip
flexion, extension, adduction, abduction, internal rotation, and external rotation.”
• March 26, 2013: Dr. Tallerico’s record shows Mr. Jensen’s musculoskeletal
evaluation as “gait and station–[c]onventional walking: abnormal toe off.” At
that appointment Mr. Jensen complained of intoeing.
• April 11, 2013: Dr. Tallerico notes “weakness in basically all major motor
groups in the right lower extremity.”
• June 3, 2013: Mr. Jensen notified the Division regarding his pigeon-toed foot
causing him to fall.
• June 5, 2013: Dr. Tallerico noted Mr. Jensen’s right foot wants “to roll []
underneath him and pigeon toe to where he trips over and [falls].” He also
described Mr. Jensen’s condition in a seated position: “As he sits in the
examination chair [it] appears that he does have inversion and internal rotation
of his right foot.” At this deposition Dr. Tallerico again described his
observation: “Well, when he was sitting down, he appeared to invert and
internally rotate his right foot, which is basically turning his foot inward.” Dr.
Tallerico also noted that this rotation was not due to malposition of his total hip
implant, recognized his symptoms as “somewhat perplexing” in that he could
find no “objective evidence” that would cause the internal rotation and intoeing.
• June 10, 2013: Dr. Altenburg and his assistant note that upon physical
examination, Mr. Jensen “does walk with his foot internally rotated” but when
his leg is “relaxed in extension, he externally rotates to a neutral position . . . .”
They conclude that Mr. Jensen “has developed greater trochanteric bursitis and
intoeing.”
[¶23] In his deposition, Dr. Altenburg testified regarding hip weakness:
Q. [State’s counsel:] [W]ould an individual have any
difficulties in performing any tasks or any movement from a
sitting position?
9
A. [Dr. Altenburg:] A sitting position? You know,
generally these abduct -- these muscles work in an abductor
function. And just to explain that, if you consider your leg in
a midline position, if you bring your leg in towards the
opposite leg, that’s an a-d-duction, adduction movement. If
you take your leg away from midline, or out extended away
from the body, that’s an abduction . . . motion. . . . [C]ertain
seated positions that require you to bring your leg up and take
it away from midline may create some difficulty for [Mr.
Jensen]. Again, I’m only surmising that that could cause
some weakness in trying to do some of those things.
....
[If lifting the leg directly off the ground is combined
with] moving the leg, per se, out or in an adduction manner, I
could surmise that there may be some weakness or some
difficulty with that.
(Emphasis added.)
[¶24] In his affidavit, Mr. Jensen stated that when he saw the vehicle in front of him, he
attempted to slow his truck down:
When I downshifted, I also applied the brake. Then I felt my
foot slip off the brake pedal. I tried to use my right hand to
free my foot and was unsuccessful. Then I looked down and
saw that my foot was trapped between the brake pedal and the
accelerator. I again used my right hand to try to free my right
foot and was unsuccessful.
Similarly, at the hearing, Mr. Jensen testified:
So, I put my right foot up, my pigeon toed foot up on the
pedal, and it did what it does when I walked, it rolled off the
pedal and down between the gas pedal and the brake pedal.
And instead of being straight it’s, like I say, pigeon toed.
And I reached down with my leg tried to pull it out. Couldn’t
get it to come.
[¶25] Statements made by Mr. Jensen immediately after the accident corroborate his
testimony. Mr. Pittman testified that at the scene Mr. Jensen stated that “he reached
down, pulled his foot out from underneath the brake pedal and lost control . . . .” Mrs.
10
Jensen also testified that when Mr. Jensen called her on his cell phone from the scene, he
told her that the accident happened when his right foot “got stuck” and “he couldn’t get it
out.”
[¶26] In rejecting this evidence, the Hearing Examiner ruled:
66. . . . While the Office finds and concludes that Jensen did
have residual problems from the work related injury, i.e., the
in toeing and even rolling of the foot, the Office does not find
that the preponderance of the evidence shows that those
residual problems were the cause of the automobile accident.
67. As noted above, the weight of the evidence showed that
Jensen’s residual problems occurred when he was standing,
walking and/or weight bearing. Neither Jensen nor his wife
ever described the problems occurring when he was seated or
driving. There is only one mention in all of the records of
Jensen’s foot pointing inward while in a seated position. That
is in Dr. Tallerico’s June 5, 2013 record. While Dr.
Altenburg’s deposition testimony suggests that there could be
problems when someone with Jensen’s condition would be
lifting a knee and moving it outward, the testimony did not in
the Office’s opinion rise to the level of proof necessary.
68. Pittman’s testimony that at the scene Jensen made the
comment his foot became stuck and he was trying to remove
it was compelling, however, it still did not go far enough to
make the connection to the work related injury. Further, and
more compelling to the Office was the lack of any statements
from Ms. Jensen or Jensen himself to the case worker in the
days and even the months following the accident. It would
certainly seem to the Office that Jensen would have made
those comments to the case worker in his conversation with
[her] in July. In that regard, it simply appeared to the Office
that the rolling of the foot off the pedal became an after the
fact theory in this case, not one advanced until the case was
referred to the Office.
69. While the Office found the majority of Jensen’s and
Mrs. Jensen’s testimony credible and the accident was
unfortunate indeed, the Office simply did not accept the
testimony that Jensen’s foot rolled off the pedal causing the
accident given the lack of prior or subsequent complaints or
11
evidence that Jensen had problems with his foot while
seated or told anyone at the time of or within the month
after the accident that his foot had slipped off the pedal.
(Emphasis added.)
[¶27] We have held that “[i]n a second compensable injury case, the causal connection
between the work injury and the second injury is satisfied if the medical expert testifies
that the work injury contributed to the second injury.” Hoffman, 2012 WY 164, ¶ 17, 291
P.3d at 303. “Our precedent establishes that medical testimony stating the claimant’s
work ‘contributed to’ the injury or the injury was ‘most likely’ or ‘probably’ the product
of the workplace is sufficient to satisfy the requirements.” Middlemass, 2011 WY 118,
¶ 28, 259 P.3d at 1168 (citing Boyce v. State ex rel. Wyo. Workers’ Safety & Comp. Div.,
2005 WY 9, ¶ 21, 105 P.3d 451, 458 (Wyo. 2005); Jim’s Water Serv. v. Eayrs, 590 P.2d
1346, 1349 (Wyo. 1979); Claim of Vondra, 448 P.2d 313 (Wyo. 1968)).
[¶28] Here, Dr. Altenburg “surmised” that Mr. Jensen “could” have difficulty in lifting
his knee and moving it outward. “[S]peculative medical testimony is insufficient to
satisfy a claimant’s burden of proof.” Jacobs v. State ex rel. Wyo. Workers’ Safety &
Comp. Div., 2013 WY 62, ¶ 24, 301 P.3d 137, 147 (Wyo. 2013) (citing Anastos v.
General Chemical Soda Ash, 2005 WY 122, 120 P.3d 658, 666-67 (Wyo. 2005)). The
OAH found that Dr. Altenburg’s testimony was speculative and did not satisfy Mr.
Jensen’s burden of proof. We have held that “opinions expressed by medical experts in
terms of ‘can,’ ‘could,’ or ‘possibly’ are not sufficient to meet an employee’s burden of
proof.” Middlemass, 2011 WY 118, ¶ 28, 259 P.3d at 1168 (quoting Boyce, 2005 WY 9,
¶ 22, 105 P.3d at 458); see also Guerrero, 2015 WY 88, ¶ 19, 352 P.3d at 268
(physician’s statement that it was “possible” claimant’s back problems were related to his
work injury was not sufficient proof of causation). Thus, Dr. Altenburg’s testimony that
Mr. Jensen “could” have weakness supports the OAH’s determination that Mr. Jensen did
not meet his burden of proof.
[¶29] Dr. Altenburg’s testimony was not the only medical testimony presented to the
OAH. As early as February of 2013, Dr. Zoe noticed that Mr. Jensen had a “decreased
[range of motion] with right hip flexion, extension, adduction, abduction, internal
rotation, and external rotation.” And, Dr. Tallerico’s records indicate that Mr. Jensen’s
walk was “abnormal” with his “toe off” and that he had “weakness in basically all major
motor groups in the right lower extremity.” He also noted that the tendency of Mr.
Jensen’s foot to rotate inward occurred in a seated position: “As he sits in the
examination chair [it] appears that he does have inversion and internal rotation of his
right foot.” This evidence, however, does not even reach the point of speculation
regarding whether Mr. Jensen’s work-related injury caused the accident.
12
[¶30] We have held that “the causal connection between the work injury and the second
injury is satisfied if the medical expert testifies that the work injury contributed to the
second injury.” Hoffman, 2012 WY 164, ¶ 17, 291 P.3d at 303. In Hoffman, the
claimant’s treating physician testified that his second injury was “clearly related to” and
“more probably resulted from” his original work injury and the treatment of that injury.
We held that this testimony satisfied the causal connection requirement under the second
compensable injury rule. Id. Here, however, none of this medical evidence relied upon
by Mr. Jensen establishes a causal connection between Mr. Jensen’s work-related injury
and his subsequent accident.
[¶31] In addition, Mr. Jensen points to the testimony of other witnesses regarding the
cause of the accident. He correctly states that both Mrs. Jensen and Mr. Pittman testified
that shortly after the accident he told them his foot had become lodged between the brake
and gas pedals, and he was unable to get it out. He also highlights his own testimony
where he described his foot falling from the brake pedal, getting stuck, and his
unsuccessful attempts at removing it as the cause of the accident.
[¶32] We have recognized that
[t]he testimony of an injured worker alone is sufficient to
prove an accident if there is nothing to impeach or discredit
the worker’s testimony and the worker’s statements are
corroborated by surrounding circumstances. Duncan v.
Hardware Mutual Casualty Company, 275 So.2d 462, 463
(La.App. 1973). Moreover, the occurrence of injuries
resulting from accidents to which there are no eye-witnesses
does not prevent fair inferences from being drawn and
findings of facts from being made. Bohan v. Lord & Keenan,
Inc., 98 N.H. 144, 95 A.2d 786, 788 (1953).
Ikenberry v. State ex rel. Wyo. Workers’ Comp. Div. (In re Ikenberry), 5 P.3d 799, 803
(Wyo. 2000); see also Seherr-Thoss v. Teton Cty. Bd. of Cty. Comm’rs, 2014 WY 82,
¶ 15, 329 P.3d 936, 944 (Wyo. 2014) (“An individual’s testimony alone is sufficient to
carry the individual’s burden if there is nothing to impeach or discredit the individual’s
testimony and the individual’s statements are corroborated by surrounding
circumstances.”).
[¶33] The Hearing Examiner found Mr. Pittman’s testimony to be “compelling,”
however she noted that the theory advanced by Mr. Jensen was not supported by the
circumstances and his testimony did not establish causation. She observed that Mr.
Pittman “did not mention any statements Jensen made . . . that his foot had rolled off the
pedal.” It was this lack of evidence of Mr. Jensen’s foot rolling off the pedal that led the
OAH to conclude that the foot rolling was a theory developed later in the case. The OAH
13
rejected Mr. Jensen’s testimony that his foot rolled off the pedal due to a lack of prior
complaints about his foot while seated and because there was no evidence that he “told
anyone at the time or within the month after the accident that his foot had slipped off the
pedal.” While the record is replete with uncontested evidence that Mr. Jensen
complained of weakness, intoeing, and foot rolling in the months prior to the accident,
and his doctor also noted his foot’s tendency to rotate inward while he was in a seated
position, we cannot say that the hearing examiner’s conclusion that Mr. Jensen did not
meet his burden of proving a causal connection between the automobile accident and his
prior work-related accident was unreasonable and not supported by substantial evidence.1
[¶34] Evidentiary findings are not supported by substantial evidence when they are
“contrary to the overwhelming weight of the evidence in the record as a whole.” Dale,
2008 WY 84, ¶ 22, 188 P.3d at 561 (citations omitted). “If, in the course of its decision
making process, the agency disregards certain evidence and explains its reasons for doing
so based upon determinations of credibility or other factors contained in the record, its
decision will be sustainable under the substantial evidence test.” Id. at ¶ 22, 188 P.3d at
561. Here, the OAH provided its reasons for rejecting the testimony of Mr. Jensen that
his foot had slipped off the pedal. We find that the OAH could reasonably have
concluded that Mr. Jensen did not meet his burden of proving by a preponderance of the
evidence that his accident was causally connected to his original work-related hip injury.
CONCLUSION
[¶35] The OAH properly applied the second compensable injury rule in this case. The
OAH also reasonably concluded, based upon all of the evidence in the record, that Mr.
Jensen had not established by a preponderance of the evidence that his automobile
accident was causally connected to his original work-related injury. Affirmed.
1
In addition, Dr. Carter, the emergency room physician who treated Mr. Jensen, testified that Mr. Jensen
did not tell him that his foot rolled off the gas pedal. Dr. Carter’s emergency room report indicates that
“[Mr. Jensen] reports that he thinks his truck blew a tire . . . .” Dr. Carter also noted in his report that Mr.
Jensen had a GLASCOW score of 15, suggesting that he was alert, talking, and fairly coherent at the time
he spoke with Dr. Carter. Dr. Tallerico also treated Mr. Jensen in the emergency room, and in his chart
noted that “[u]nfortunately [Mr. Jensen] was involved in a severe motor vehicle accident earlier today
when he lost control of his car supposedly while he dozed off . . . .” This evidence contradicts the
testimony of Mr. Jensen and other witnesses as to the cause of the accident.
14
|
1. Field of the Invention
The present invention relates to a receiver for receiving navigation messages such as satellite time data, satellite orbit data, etc. from artificial satellites in a global positioning system to determine the position of a user of the global positioning system.
2. Description of the Prior Art
There are known global positioning systems (GPS) for determining the position of a user based on navigation messages from a plurality of artificial satellites orbiting around the earth.
Each of the artificial satellites transmits a signal which is produced by spectrally spreading a navigation message with pseudo random noise (having a chip frequency of 1.023 MHz) and modulating a carrier (having a frequency of 1,575.42 MHz or 1227.6 MHz) with the spectrally spread signal by way of phase-shift keying (PSK).
Since the artificial satellites employ pseudo random noise of different code patterns, a GPS receiver can separately receive the navigation messages from the respective artificial satellites by using pseudo random noise of corresponding code patterns.
A process of determining the position (xu, yu, zu) of a user based on navigation messages from four artificial satellites will be described below.
As well known in the art, the navigation message from each artificial satellite contains satellite time data, satellite orbit data, etc. Each artificial satellite keeps a GPS time scale which is atomic time. The GPS time scale is started from 0 o'clock, coordinated universal time (UTC), Jan. 6, 1980 as 0 o'clock, GPS time, Jan. 6, 1980.
As shown in FIG. 1 of the accompanying drawings, the time bases according to the time data contained in the navigation messages from the respective artificial satellites are indicated by SV1, SV2, SV3, SV4, respectively, and the time base according to the time data of the user is indicated by SVu. When the data from the artificial satellites are received by the user at a time tu, these data have been transmitted from the respective artificial satellites at times t1, t2, t3, t4, respectively.
Therefore, distances r1, r2, r3, r4 from the user position (xu, yu, zu) to the respective positions (xi, yi, zi) (i=1, 2, 3, 4) of the artificial satellites are represented by: EQU r1=C.times.(tu-t1), EQU r2=C.times.(tu-t2), EQU r3=C.times.(tu-t3), EQU r4=C.times.(tu-t4) (1)
where C is the speed of light.
From the above equations (1), there are derived four equations (2) given below. The positions (xi, yi, zi) (i=1, 2, 3, 4) of the artificial satellites are calculated based on the orbit data contained in the navigation messages from the respective artificial satellites. ##EQU1##
By solving the simultaneous linear equations (2), the user position (xu, yu, zu) can be determined. Since the equations (2) can be calculated with the time tu being unknown, the receiver of the user is not required to have an expensive atomic clock.
The format of the navigation messages from the artificial satellites will be described below with reference to FIGS. 2A, 2B, 2C and 3A, 3B, 3C of the accompanying drawings.
The navigation messages have a bit rate of 50 bps, and have main frames each composed of 1,500 bits. Therefore, it takes 30 seconds to transmit one main frame. Each main frame is divided into five subframes each composed of 300 bits. Therefore, one subframe can be transmitted in 6 seconds.
Each of the subframes includes an 8-bit preamble (synchronizing signal) at its starting end that is followed by a 17-bit subframe number TOWC (Time Of Week Count) which indicates the number of subframes counted from the start of the week. In the subframe 1, the TOWC is followed by a 10-bit WN (Week Number). FIG. 2A shows the first main frame of the first week starting from 0 o'clock, Jan. 6, 1980. FIG. 2B shows first four main frames of the nth week.
As show in FIG. 2C, each subframe is principally composed of 10 words each of 30 bits. It takes 600 msec. to transmit one word. 8 bits at the starting end of the word 1 serve as a preamble, and 17 bits at the starting end of the word 2 serve as TOWC. Each of the words 1 through 10 contains 6 error-correcting parity bits at its terminal end. The parity bits in each word are added for the error correction of the remaining 24 bits of the word and also the last 2 bits of the preceding word.
Since a navigation message has a bit rate of 50 bps, as described above, its bit period is 20 msec. as shown in FIG. 3B. FIG. 3A shows a subframe. The navigation messages of the above format are spectrally spread with pseudo random noise (see FIG. 3C) whose chip frequency is 1.023 MHz. The pseudo random noise has a code length (repetition period) of 1 msec., and the code lengths corresponding to 20 periods are equal to one bit of the navigation message. The period of one chip is approximately 1 .mu.sec.
The GPS receiver which receives the above navigation messages from the artificial satellites calculates the times t1, t2, t3, t4 on the respective time bases SV1, SV2, SV3, SV4 according to the following equation (3): ##EQU2## where i=1.about.4.
In the equation (3), the number of words counted is used as a word number WORDi, which is reset to 0 at the starting end of each subframe.
The number of bits counted is used as a bit number BITi, which is reset to 0 at the starting end of each word.
The number of repetition periods counted of the pseudo random noise used in reverse spreading is used as SEQi, which is reset to 0 at the starting end of each bit.
The number of chips counted is used as CHIPi, which is reset to 0 at the starting end of the repetition period of the pseudo random noise.
In the case where the GPS receiver is installed on an automobile, it tends to be brought out of synchronism with the pseudo random noise from the satellites when signals from the satellites are blocked by buildings, standing trees, or other obstacles. When the GPS receiver is out of synchronism with the pseudo random noise from the satellites, since the parameters TOWi, WORDi, BITi, etc. in the equation (3) cannot be determined, the user position (xu, yu, zu) cannot be calculated.
When the GPS receiver is brought out of synchronism with the pseudo random noise from the satellites, therefore, it is necessary to effect a synchronization process to determine the parameters TOWi, WORDi, BITi, etc. in the equation (3).
Whether the GPS receiver is brought out of synchronism or not can be determined by the magnitude of the level of a correlation output signal that is produced by spectrally reverse-spreading the received signals.
The conventional synchronization process is carried out as follows:
It is known that when the magnitude of the level of a correlation output signal that is produced by spectrally reverse-spreading the received signals exceeds a predetermined value, it is determined that the GPS receiver is in synchronism with the pseudo random noise from the satellites, and a bit synchronization process is effected on the basis of a bit stream that is produced by demodulating the output by way of PSK.
However, if it is determined that the receiver is not in synchronization with the pseudo random noise, it must be brought into synchronization. In order to synchronize the GPS receiver with the pseudo random noise, the phase of the pseudo random noise which is multiplied by the signals from the satellites by the spectral reverse spreading is adjusted. The time consumed after the GPS receiver is synchronized with the pseudo random noise until the bit synchronization process is completed is about 20 msec. because the bit period is 20 msec.
Once the bit synchronization is completed, CHIPi is determined from the count of chips of the pseudo random noise, and SEQi is determined from the count of repetition periods of the pseudo random noise with bit edges as a reference.
Then, a preamble is detected from a navigation message (bit stream). Since an 8-bit preamble is positioned at the starting end of each subframe, when a preamble is detected, WORDi and BITi are determined.
The time spent after the bit synchronization is determined until a preamble is detected is at least 6 seconds because the subframe period is 6 seconds.
Thereafter, TOWC is detected from a navigation message, determining TOWi. While the preamble is positioned at the starting end of the word 1, TOWC is positioned at the starting end of the word 2 with the word period being 600 msec. The time spent after the preamble is detected until TOWC is detected is about 600 msec.
Then, WN is detected from a navigation message. Inasmuch as WN is included in every 5 subframes, the time spent after TOWC is detected until WN is detected is at most 30 seconds. WN remains unchanged within the week, and hence the detection of WN is not required for the determination of WNi within the week.
Therefore, when the GPS receiver is brought out of synchronism with the pseudo random noise from the satellites, the parameters TOWi, WORDi, BITi, etc. can be determined by the above synchronization process, and the times ti (i=1.about.4) can be calculated, so that the user position (xu, yu, zu) can be determined.
The disadvantages with the above synchronization process, however, are that as long as 6 seconds may be required until a preamble is detected after the synchronization is detected, and about 600 msec. are additionally required until TOWC is detected.
In other words, in order to determine the parameters TOWi, WORDi, BITi, etc., as much as a little over 6 seconds are required after the synchronization is achieved. It is thus impossible to determine the user position, i.e., the position of the GPS receiver, before the elapse of those 6 seconds. |
---
abstract: 'A general method of the Foldy-Wouthyusen (FW) transformation for relativistic particles of arbitrary spin in strong external fields has been developed. The use of the found transformation operator is not restricted by any definite commutation relations between even and odd operators. The final FW Hamiltonian can be expanded into a power series in the Planck constant which characterizes the order of magnitude of quantum corrections. Exact expressions for low-order terms in the Planck constant can be derived. Finding these expressions allows to perform a simple transition to the semiclassical approximation which defines a classical limit of the relativistic quantum mechanics. As an example, interactions of spin-1/2 and scalar particles with a strong electromagnetic field have been considered. Quantum and semiclassical equations of motion of particles and their spins have been deduced. Full agreement between quantum and classical theories has been established.'
author:
-
title: 'Foldy-Wouthyusen Transformation and Semiclassical Limit for Relativistic Particles in Strong External Fields'
---
Introduction
============
The Foldy-Wouthuysen (FW) representation [@FW] occupies a special place in the quantum theory. Properties of this representation are unique. The Hamiltonian and all operators are block-diagonal (diagonal in two spinors). Relations between the operators in the FW representation are similar to those between the respective classical quantities. For relativistic particles in external fields, operators have the same form as in the nonrelativistic quantum theory. For example, the position operator is $\bm r$ and the momentum one is $\bm p=-i\hbar\nabla$. These properties considerably simplify the transition to the semiclassical description. As a result, the FW representation provides the best possibility of obtaining a meaningful classical limit of the relativistic quantum mechanics. The basic advantages of the FW representation are described in Refs. [@FW; @CMcK; @JMP].
Interactions of relativistic particles with strong external fields can be considered on three levels: (i) classical physics, (ii) relativistic quantum mechanics, and (iii) quantum field theory. The investigation of such interactions on every level is necessary. The use of the FW representation allows to describe strong-field effects on level (ii) and to find a unambiguous connection between classical physics and relativistic quantum mechanics. To solve the problem, one should carry out an appropriate FW transformation (transformation to the FW representation). The deduced Hamiltonian should be exact up to first-order terms in the Planck constant $\hbar$. This precision is necessary for establishment of exact connection between the classical physics and the relativistic quantum mechanics. However, known methods of exact FW transformation either can be used only for some definite classes of initial Hamiltonians in the Dirac representation [@Nikitin; @JMP] or need too cumbersome derivations [@E].
In the present work, new general method of the FW transformation for relativistic particles in strong external fields is proposed. This method gives exact expressions for low-order terms in $\hbar$. The proposed method is based on the developments performed in Ref. [@JMP] and can be utilized for particles of arbitrary spin. Any definite commutation relations between even and odd operators in the initial Hamiltonian are not needed. An expansion of the FW Hamiltonian into a power series in the Planck constant is used. Since just this constant defines the order of magnitude of quantum corrections, the transition to the semiclassical approximation becomes trivial. As an example, interaction of scalar and spin-1/2 particles with a strong electromagnetic field is considered. We use the designations $[\dots,\dots]$ and $\{\dots,\dots\}$ for commutators and anticommutators, respectively.
Foldy-Wouthyusen transformation for particles in external fields
================================================================
In this section, we review previously developed methods of the FW transformation for particles in external fields.
The relativistic quantum mechanics is based on the Klein-Gordon equation for scalar particles, the Dirac equation for spin-1/2 particles, and corresponding relativistic wave equations for particles with higher spins (see, e.g., Ref. [@FN]). The quantum field theory is not based on these fundamental equations of the relativistic quantum mechanics (see Ref. [@W]). Relativistic wave equations for particles with any spin can be presented in the Hamilton form. In this case, the Hamilton operator acts on the bispinor wave function $\Psi=\left(\begin{array}{c} \phi \\ \chi \end{array}\right)$: $$i\hbar\frac{\partial\Psi}{\partial t}={\cal
H}\Psi. \label{eqi}$$ A particular case of Eq. (\[eqi\]) is the Dirac equation. We can introduce the unit matrix $I$ and the Pauli matrices those components act on the spinors: $$I=\left(\begin{array}{cc}1&0\\0&1\end{array}\right),
~~~\rho_1=\left(\begin{array}{cc}0&1\\1&0\end{array}\right),
~~~ \rho_2=\left(\begin{array}{cc}0&-i\\i&0\end{array}\right),
~~~ \rho_3\equiv\beta=\left(\begin{array}{cc}1&0\\0&-1\end{array}\right).$$ The Hamiltonian can be split into operators commuting and noncommuting with the operator $\beta$: $${\cal H}=\beta {\cal M}+{\cal E}+{\cal O},~~~\beta{\cal M}={\cal M}\beta,
~~~\beta{\cal E}={\cal E}\beta, ~~~\beta{\cal O}=-{\cal O}\beta,
\label{eq3}$$ where the operators ${\cal M}$ and ${\cal E}$ are even and the operator ${\cal O}$ is odd. We suppose that the operator ${\cal E}$ is multiplied by the unit matrix $I$ which is everywhere omitted.
Explicit form of the Hamilton operators for particles with arbitrary half-integer spin has been obtained in Ref. [@NGNN]. Similar equations have been derived for spin-0 [@FV] and spin-1 [@CS; @YB] particles. To study semiclassical limits of these equations, one should perform appropriate FW transformations.
The wave function of a spin-1/2 particle can be transformed to a new representation with the unitary operator $U$: $$\Psi'=U\Psi.$$ The Hamilton operator in the new representation takes the form [@FW; @JMP; @Gol] $${\cal H}'=U{\cal H}U^{-1}-i\hbar U\frac{ \partial U^{-1}}{\partial
t}, \label{eq2}$$ or $${\cal H}'=U\left({\cal
H}-i\hbar\frac{\partial}{\partial t}\right)U^{-1}+
i\hbar\frac{\partial}{\partial t}.$$
The FW transformation has been justified in the best way. In the classical work by Foldy and Wouthuysen [@FW], the exact transformation for free relativistic particles and the approximate transformation for nonrelativistic particles in electromagnetic fields have been carried out. There exist several other nonrelativistic transformation methods which give the same results (see Ref. [@JMP] and references therein). A few methods can be applied for relativistic particles in external fields. However, the transformation methods explained in Refs. [@B; @GS] require cumbersome calculations. The block-diagonalization of two-body Hamiltonians for a system of two spin-1/2 particles and a system of spin-0 and spin-1/2 particles can be performed by the methods found by Chraplyvy [@Chraplyvy] and Tanaka *et al* [@Tanaka], respectively.
Some methods allow to reach the FW representation without the use of unitary transformations. The so-called elimination method [@Pa] makes it possible to exclude the lower spinor from relativistic wave equations. Variants of this method useful for relativistic particles have been elaborated in Refs. [@Neznamov; @STMP]. Another method which essentially differs from the FW and elimination methods has been presented in Ref. [@Gos]. This method defines a diagonalization procedure based on a formal expansion in powers of the Planck constant $\hbar$ and can be used for a large class of Hamiltonians directly inducing Berry phase corrections [@Gos]. An important feature of this method is a possibility to take into account strong-field effects.
Any method different from the FW one should also be justified. The validity of the elimination method is proved only by the coincidence of results obtained by this method and the FW one [@VJ]. Impressive agreement between results presented in Ref. [@Gos] and corresponding results obtained by the FW method is reached for first-order terms in $\hbar$. These terms define momentum and spin dynamics that can be well described in the framework of classical physics. To prove the validity of the method, one should show such an agreement for terms derived from second-order commutators (e.g., for the Darwin term [@FW]). Therefore, we desist from a definitive estimate of the method developed in Ref. [@Gos].
We suppose the consistence with the genuine FW transformation to be necessary for any diagonalization method. For example, the Eriksen-Korlsrud method [@EK] does not transform the wave function to the FW representation even for free particles [@PRD]. The use of this method in Refs. [@Obukhov; @Heidenreich] instead of the FW one could cause a misunderstanding of the nature of spin-gravity coupling (see the discussion in Refs. [@PRD; @Mashhoon2]).
In the general case, the exact FW transformation has been found by Eriksen [@E]. The validity of the Eriksen transformation has also been argued by de Vries and Jonker [@VJ]. The Eriksen transformation operator has the form [@E] $$U=\frac12(1+\beta\lambda)\left[1+\frac14(\beta\lambda+\lambda\beta-2)\right]^{-1/2},
~~~ \lambda=\frac{{\cal H}}{({\cal H}^2)^{1/2}}, \label{E}$$ where ${\cal H}$ is the Hamiltonian in the Dirac representation. This operator brings the Dirac wave function and the Dirac Hamiltonian to the FW representation in one step. However, it is difficult to use the Eriksen method for obtaining an explicit form of the relativistic FW Hamiltonian because the general final formula is very cumbersome and contains roots of Dirac matrix operators. Therefore, the Eriksen method was not used for relativistic particles in external fields.
To perform the FW transformation in the strong external fields, we develop the much simpler method elaborated in Ref. [@JMP] for relativistic spin-1/2 particles. In this work, the initial Dirac Hamiltonian is given by $${\cal H}=\beta m+{\cal E}+{\cal O}, \label{eq3N}$$ where $m$ is the particle mass. In Eqs. (\[eq3N\])–(\[eq31\]), the system of units $\hbar=c=1$ is used.
When $[{\cal E},{\cal O}]=0$, the FW transformation is exact [@JMP]. This transformation is fulfilled with the operator $$U=\frac{\epsilon+m+\beta{\cal
O}}{\sqrt{2\epsilon(\epsilon+m)}}, ~~~\epsilon=\sqrt{m^2+{\cal
O}^2} \label{eq18}$$ and the transformed Hamiltonian takes the form $${\cal H}_{FW}=\beta \epsilon+{\cal
E}. \label{eq17}$$
The same transformation is valid for Hamiltonian (\[eq3\]) when not only does the operator ${\cal E}$ commutates with ${\cal O}$ but also the operator ${\cal M}$: $$[{\cal M},{\cal O}]=0. \label{comm}$$ In this case, Eq. (\[eq17\]) remains valid but the operator $\epsilon$ takes the form $$\epsilon=\sqrt{{\cal M}^2+{\cal O}^2}.$$
In the general case, the FW Hamiltonian has been obtained as a power series in external field potentials and their derivatives [@JMP]. As a result of the first stage of transformation performed with operator (\[eq18\]), the following Hamiltonian can be found: $${\cal H}'=\beta\epsilon+{\cal
E}'+{\cal O}',~~~\beta{\cal E}'={\cal E}'\beta, ~~~\beta{\cal
O}'=-{\cal O}'\beta. \label{eq7}$$ The odd operator ${\cal O}'$ is now comparatively small: $$\begin{array}{c} \epsilon=\sqrt{m^2+{\cal O}^2}, \\ {\cal
E}'=i\frac{\partial}{\partial t}+\frac{\epsilon+m}
{\sqrt{2\epsilon(\epsilon+m)}}\left({\cal
E}-i\frac{\partial}{\partial t}
\right)\frac{\epsilon+m}{\sqrt{2\epsilon(\epsilon+m)}}\\-\frac{\beta{\cal
O}} {\sqrt{2\epsilon(\epsilon+m)}}\left({\cal
E}-i\frac{\partial}{\partial t} \right)\frac{\beta{\cal
O}}{\sqrt{2\epsilon(\epsilon+m)}}, \\ {\cal O}'=\frac{\beta{\cal
O}}{\sqrt{2\epsilon(\epsilon+m)}} \left({\cal
E}-i\frac{\partial}{\partial t}
\right)\frac{\epsilon+m}{\sqrt{2\epsilon(\epsilon+m)}}\\-
\frac{\epsilon+m}{\sqrt{2\epsilon(\epsilon+m)}}\left({\cal
E}-i\frac{\partial} {\partial t}\right)\frac{\beta{\cal
O}}{\sqrt{2\epsilon(\epsilon+m)}}. \end{array} \label{eq28}$$
The second stage of transformation leads to the approximate equation for the FW Hamiltonian: $${\cal
H}_{FW}=\beta\epsilon+{\cal E}'+\frac14\beta\left\{{\cal
O}'^2,\frac{1}{\epsilon}\right\}. \label{eq31}$$
To reach a better precision, additional transformations can be used [@JMP].
This method has been applied for deriving the Hamiltonian and the quantum mechanical equations of momentum and spin motion for Dirac particles interacting with electroweak [@JMP] and gravitational [@PRD; @PRD2] fields. The semiclassical limit of these equations has been obtained [@JMP; @PRD; @PRD2]. To determine the exact classical limit of the relativistic quantum mechanics of arbitrary-spin particles in *strong* external fields, we need to generalize the method.
General properties of the Hamiltonian depend on the particle spin. The Hamiltonian is hermitian (${\cal H}={\cal H}^\dagger$) for spin-1/2 particles and pseudo-hermitian for spin-0 and spin-1 ones (more precisely, $\beta$-pseudo-hermitian, see Ref. [@Mostafazadeh] and references therein). In the latter case, it possesses the property ($\beta^{-1}=\beta$) $${\cal
H}^\dagger=\beta{\cal H}\beta$$ that is equivalent to $${\cal
H}^\ddagger\equiv\beta{\cal H}^\dagger\beta={\cal H}.$$
The normalization of wave functions is given by $$\int{\Psi^\dagger\Psi dV}=\int{(\phi\phi^\ast+\chi\chi^\ast)
dV}=1$$ for spin-1/2 particles and $$\int{\Psi^\ddagger\Psi
dV}\equiv\int{\Psi^\dagger\beta\Psi
dV}=\int{(\phi\phi^\ast-\chi\chi^\ast) dV}=1$$ for spin-0 and spin-1 particles.
We suppose ${\cal M}={\cal M}^\dagger,~{\cal E}={\cal
E}^\dagger,~{\cal O}={\cal O}^\dagger$ when ${\cal H}={\cal
H}^\dagger$ and ${\cal M}={\cal M}^\ddagger,~{\cal E}={\cal
E}^\ddagger,~{\cal O}={\cal O}^\ddagger$ when ${\cal H}={\cal
H}^\ddagger$. These conditions can be satisfied in any case.
Since the FW Hamiltonian is block-diagonal and a lower spinor describes negative-energy states, this spinor should be equal to zero. The FW transformation should be performed with the unitary operator $U^\dagger =U^{-1}$ for spin-1/2 particles and with the pseudo-unitary operator $U^\ddagger\equiv\beta U^\dagger\beta
=U^{-1}$ for spin-0 and spin-1 particles.
FOLDY-WOUTHYUSEN TRANSFORMATION IN STRONG EXTERNAL FIELDS
=========================================================
We propose the method of the FW transformation for relativistic particles in strong external fields which can be used for particles of arbitrary spin. The FW Hamiltonian can be expanded into a power series in the Planck constant which defines the order of magnitude of quantum corrections. The obtained expressions for low-order terms in $\hbar$ are exact. The proposed FW transformation makes the transition to the semiclassical approximation to be trivial. The power expansion can be available only if $$pl\gg\hbar, \label{rel1}$$ where $p$ is the momentum of the particle and $l$ is the characteristic size of the nonuniformity region of the external field. This relation is equivalent to $$\lambda\ll l, \label{rel2}$$ where $\lambda$ is the de Broglie wavelength. Eqs. (\[rel1\]),(\[rel2\]) result from the fact that the Planck constant appears in the final Hamiltonian due to commutators between the operators ${\cal M},{\cal E}$, and ${\cal O}$.
The expansion of the FW Hamiltonian into the power series in the Planck constant is formally similar to the previously obtained expansion [@JMP] into a power series in the external field potentials and their derivatives. However, the equations derived in Ref. [@JMP] do not define the semiclassical limit of the Dirac equation for particles in strong external fields, while these equations exhaustively describe the weak-field expansion. The proposed method can also be used in the weak-field expansion even when relations (\[rel1\]),(\[rel2\]) are not valid.
When the power series in the Planck constant is deduced, zero power terms define the quantum analogue of the classical Hamiltonian. On this level, classical and quantum expressions should be very similar because the classical theory gives the right limit of the quantum theory. Terms proportional to powers of $\hbar$ may describe quantum corrections. As a rule, interactions described by these terms also exist in the classical theory. However, classical expressions may differ from the corresponding quantum ones because the quantum corrections to the classical theory may appear. We generalize the method developed in Ref. [@JMP] in order to take into account a possible non-commutativity of the operators ${\cal M}$ and ${\cal O}$. The natural generalization of transformation operator (\[eq18\]) used in Ref. [@JMP] is $$U=\frac{\beta\epsilon+\beta {\cal M}-{\cal
O}}{\sqrt{(\beta\epsilon+\beta {\cal M}-{\cal O})^2}}\,\beta,~~~
U^{-1}=\beta\,\frac{\beta\epsilon+\beta{\cal M}-{\cal
O}}{\sqrt{(\beta\epsilon+\beta{\cal M}-{\cal O})^2}},
\label{eq18N}$$ where $U^\dagger=U^{-1}$ when ${\cal
H}={\cal H}^\dagger$ and $U^\ddagger=U^{-1}$ when ${\cal H}={\cal
H}^\ddagger$. This form of the transformation operator allows to perform the FW transformation in the general case. The special case ${\cal M}=mc^2$ has been considered in Ref. [@JMP] and commutation relation (\[comm\]) has been used in Refs. [@PRD; @JETP].
We consider the general case when external fields are nonstationary. The exact formula for the transformed Hamiltonian has the form $$\begin{array}{c} {\cal H}'=\beta\epsilon+{\cal
E}+ \frac{1}{2T}\Biggl(\left[T,\left[T,(\beta\epsilon+{\cal
F})\right]\right] +\beta\left[{\cal O},[{\cal O},{\cal
M}]\right]\\- \left[{\cal O},\left[{\cal O},{\cal F}\right]\right]
- \left[(\epsilon+{\cal M}),\left[(\epsilon+{\cal M}),{\cal
F}\right]\right] - \left[(\epsilon+{\cal M}),\left[{\cal M},{\cal
O}\right]\right]\\-\beta \left\{{\cal O},\left[(\epsilon+{\cal
M}),{\cal F}\right]\right\}+\beta \left\{(\epsilon+{\cal
M}),\left[{\cal O},{\cal F}\right]\right\} \Biggr)\frac{1}{T},
\end{array} \label{eq28N}$$ where ${\cal F}={\cal E}-i\hbar\frac{\partial}{\partial t}$ and $T=\sqrt{(\beta\epsilon+\beta{\cal M}-{\cal O})^2}$.
Hamiltonian (\[eq28N\]) still contains odd terms proportional to the first and higher powers of the Planck constant. This Hamiltonian can be presented in the form $${\cal
H}'=\beta\epsilon+{\cal E}'+{\cal O}',~~~\beta{\cal E}'={\cal
E}'\beta, ~~~\beta{\cal O}'=-{\cal O}'\beta,
\label{eq27}$$ where $\epsilon=\sqrt{{\cal M}^2+{\cal
O}^2}.$ The even and odd parts of Hamiltonian (\[eq27\]) are defined by the well-known relations: $${\cal
E}'=\frac12\left({\cal H}'+\beta{\cal
H}'\beta\right)-\beta\epsilon,~~~ {\cal O}'=\frac12\left({\cal
H}'-\beta{\cal H}'\beta\right).$$
Additional transformations performed according to Ref. [@JMP] bring ${\cal H}'$ to the block-diagonal form. The approximate formula for the final FW Hamiltonian is $${\cal
H}_{FW}=\beta\epsilon+{\cal E}'+\frac14\beta\left\{{\cal
O}'^2,\frac{1}{\epsilon}\right\}. \label{eqf}$$ This formula is similar to the corresponding one obtained in Ref. [@JMP]. The additional transformations allow to obtain more precise expression for the FW Hamiltonian.
Eqs. (\[eq28N\])–(\[eqf\]) solve the problem of the FW transformation for relativistic particles of arbitrary spin in strong external fields.
Eq. (\[eq28N\]) can be significantly simplified in some special cases. When $[{\cal M},{\cal O}]=0$ and the external fields are stationary, it is reduced to $$\begin{array}{c} {\cal H}'=\beta\epsilon+{\cal
E}+ \frac{1}{2T}\Biggl(\left[T,\left[T,{\cal E}\right]\right] \\-
\left[{\cal O},\left[{\cal O},{\cal E}\right]\right] -
\left[(\epsilon+{\cal M}),\left[(\epsilon+{\cal M}),{\cal
E}\right]\right] \\-\beta \left\{{\cal O},\left[(\epsilon+{\cal
M}),{\cal E}\right]\right\}+\beta \left\{(\epsilon+{\cal
M}),\left[{\cal O},{\cal E}\right]\right\} \Biggr)\frac{1}{T}.
\end{array} \label{eqrd}$$ In this case, $[\epsilon,{\cal M}]=[\epsilon,{\cal O}]=0$ and the operator $T=\sqrt{2\epsilon(\epsilon+{\cal M})}$ is even.
SPIN-1/2 AND SCALAR PARTICLES IN STRONG ELECTROMAGNETIC FIELD
=============================================================
As an example, the FW transformation for spin-1/2 and scalar particles interacting with a strong electromagnetic field can be considered. The initial Dirac-Pauli Hamiltonian for a particle possessing an anomalous magnetic moment (AMM) has the form [@P] $$\begin{array}{c} {\cal
H}_{DP}=c\bm{\alpha}\cdot\bm{\pi}+\beta mc^2+e\Phi+\mu'(-\bm
{\Pi}\cdot \bm{H}+i\bm{\gamma}\cdot\bm{ E}),\\
\bm{\pi}=\bm{p}-\frac{e}{c}\bm{ A}, ~~~
\mu'=\frac{g-2}{2}\cdot\frac{e\hbar}{2mc}, \end{array}
\label{eqDP}$$ where $\mu'$ is the AMM, $\Phi,\bm{
A}$ and $\bm{ E},\bm{H}$ are the potentials and strengths of the electromagnetic field.
Here and below the following designations for the matrices are used: $$\begin{array}{c}\bm{\gamma}=\left(\begin{array}{cc} 0 & \bm{\sigma} \\ -\bm{\sigma} & 0
\end{array}\right), ~~~ {\beta}\equiv\gamma^0=\left(\begin{array}{cc} 1 & 0
\\ 0 & -1 \end{array}\right), ~~~\bm{\alpha}=\beta\bm\gamma=
\left(\begin{array}{cc} 0 & \bm{\sigma} \\ \bm{\sigma} & 0
\end{array}\right), \\ \bm{\Sigma}
=\left(\begin{array}{cc} \bm{\sigma} & 0 \\ 0 &
\bm{\sigma}\end{array}\right), ~~~\bm{\Pi}=\beta\bm\Sigma
=\left(\begin{array}{cc} \bm{\sigma} & 0 \\ 0 &
-\bm{\sigma}\end{array}\right), \end{array}$$ where $0,1,-1$ mean the corresponding 2$\times$2 matrices and $\bm{\sigma}$ is the Pauli matrix.
Terms describing the electric dipole moment (EDM) $d$ have been added in Ref. [@RPJ]. The resulting Hamiltonian is given by $$\begin{array}{c} {\cal
H}=c\bm{\alpha}\cdot\bm{\pi}+\beta mc^2+e\Phi+\mu'(-\bm {\Pi}\cdot
\bm{H}+i\bm{\gamma}\cdot\bm{ E}) %\\
-d(\bm {\Pi}\cdot
\bm{E}+i\bm{\gamma}\cdot\bm{ H}), ~~~
d=\frac{\eta}{2}\cdot\frac{e\hbar}{2mc}, \end{array} \label{eqEDM}$$ where $\eta$ factor for the EDM is an analogue of $g$ factor for the magnetic moment. It is important that $\mu'$ and $d$ are proportional to $\hbar$.
In the considered case $$\begin{array}{c} {\cal M}=mc^2,~~~ {\cal
E}=e\Phi-\mu'\bm {\Pi}\cdot \bm{H}-d\bm {\Pi}\cdot \bm{E}, ~~~%\\
{\cal O}=c\bm{\alpha}\cdot\bm{\pi}+i\mu'\bm{\gamma}\cdot\bm{
E}-id\bm{\gamma}\cdot\bm{ H}. \end{array}$$
Since only terms of zero and first powers in the Planck constant define the semiclassical equations of motion of particles and their spins, we retain only such terms in the FW Hamiltonian. The terms of order of $\hbar$ are proportional either to field gradients or to products of field strengths ($H^2,~E^2$ and $EH$). We do not calculate the terms proportional to products of field strengths because they are usually small in comparison with the terms proportional to field gradients.
The calculated Hamiltonian is given by $$\begin{array}{c} {\cal
H}_{FW}=\beta\epsilon'+e\Phi- \mu'\bm\Pi\cdot\bm
H-\frac{\mu_0}{2}\left\{\frac{mc^2}{\epsilon'}, \bm\Pi\cdot\bm
H\right\}\\+\frac{\mu'c}{4}\left\{\frac{1}{\epsilon'},
\left[\bm\Sigma\cdot(\bm \pi\times \bm E)-\bm\Sigma\cdot(\bm
E\times \bm\pi) \right]\right\}\\+
\frac{\mu_0mc^3}{\sqrt{2\epsilon'(\epsilon'+mc^2)}}\left[\bm\Sigma\cdot(\bm
\pi\times \bm E)-\bm\Sigma\cdot(\bm E\times \bm\pi)
\right]\frac{1}{\sqrt{2\epsilon'(\epsilon'+mc^2)}}\\+
\frac{\mu'c^2}{2\sqrt{2\epsilon'(\epsilon'+mc^2)}}\left\{(\bm{\Pi}\cdot\bm\pi),
(\bm{H}\cdot\bm\pi+\bm{\pi}\cdot\bm
H)\right\}\frac{1}{\sqrt{2\epsilon'(\epsilon'+mc^2)}}\\
-d\bm\Pi\cdot\bm E %\\
+\frac{dc^2}{2\sqrt{2\epsilon'(\epsilon'+mc^2)}}\left\{(\bm{\Pi}\cdot\bm\pi),
(\bm{E}\cdot\bm\pi+\bm{\pi}\cdot\bm
E)\right\}\frac{1}{\sqrt{2\epsilon'(\epsilon'+mc^2)}}\\
-\frac{dc}{4}\left\{\frac{1}{\epsilon'}, \left[\bm\Sigma\cdot(\bm
\pi\times \bm H)-\bm\Sigma\cdot(\bm H\times \bm\pi)
\right]\right\}, \end{array} \label{eq33}$$ where $$\epsilon'=\sqrt{m^2c^4+c^2\bm{\pi}^2} \label{eq34}$$ and $\mu_0=\frac{e\hbar}{2mc}$ is the Dirac magnetic moment.
The quantum evolution of the kinetic momentum operator, $\bm\pi$, is defined by the operator equation of particle motion: $$\frac{d\bm\pi}{dt}=\frac{i}{\hbar}[{\cal
H}_{FW},\bm\pi] -\frac{e}{c}\cdot\frac{\partial\bm A}{\partial t}.
\label{eqme}$$
The equation of spin motion describes the evolution of the polarization operator $\bm\Pi$: $$\frac{d\bm\Pi}{dt}=\frac{i}{\hbar}[{\cal
H}_{FW},\bm\Pi]. \label{eqpoe}$$
Because the operator $\bm\pi$ does not contain the Dirac spin matrices, the commutator of this operator with the Hamiltonian is proportional to $\hbar$. The equation of spin-1/2 particle motion in the strong electromagnetic field to within first-order terms in the Planck constant has the form $$\begin{array}{c} \frac{d\bm
\pi}{dt}=e\bm E+\beta\frac{ec}{4}\left\{\frac{1}{\epsilon'},
\left([\bm\pi\times\bm H]-[\bm H\times\bm\pi]\right)\right\}
%\\
+\mu' \nabla(\bm\Pi\cdot\bm H)+
\frac{\mu_0}{2}\left\{\frac{mc^2}{\epsilon'},
\nabla(\bm\Pi\cdot\bm
H)\right\}\\-\frac{\mu'c}{4}\left\{\frac{1}{\epsilon'},
\left[\nabla(\bm\Sigma\cdot[\bm\pi\times\bm E])-
\nabla(\bm\Sigma\cdot[\bm E\times\bm\pi]) \right]\right\}\\-
\frac{\mu_0mc^3}{\sqrt{2\epsilon'(\epsilon'+mc^2)}}\left[\nabla(\bm\Sigma\cdot[\bm\pi\times\bm
E])- \nabla(\bm\Sigma\cdot[\bm
E\times\bm\pi])\right]\frac{1}{\sqrt{2\epsilon'(\epsilon'+mc^2)}}\\
-\frac{\mu'c^2}{2\sqrt{2\epsilon'(\epsilon'+mc^2)}}\left\{(\bm{\Pi}\cdot\bm\pi),\left[\nabla
(\bm{H}\cdot\bm\pi)+\nabla(\bm{\pi}\cdot\bm H)\right]\right\}
\frac{1}{\sqrt{2\epsilon'(\epsilon'+mc^2)}}. \end{array}
\label{eq35}$$
This equation can be divided into two parts. The first part does not contain the Planck constant and describes the quantum equivalent of the Lorentz force. The second part is of order of $\hbar$. This part defines the relativistic expression for the Stern-Gerlach force. Since terms proportional to $d$ are small, they are omitted.
The equation of spin motion is given by $$\begin{array}{c} \frac{d\bm{\Pi}}{dt}=2\mu'\bm\Sigma\times\bm H+\mu_0 \left\{\frac{mc^2}{\epsilon'},
\bm\Sigma\times\bm H\right\} %\\
-\frac{\mu'c}{2}\left\{\frac{1}{\epsilon'},
\left[\bm\Pi\times(\bm \pi\times \bm E)-\bm\Pi\times(\bm E\times \bm\pi) \right]\right\}\\
- \frac{\mu_0mc^3}{\sqrt{\epsilon'(\epsilon'+mc^2)}}\left[\bm\Pi\times(\bm \pi\times \bm E)
-\bm\Pi\times(\bm E\times \bm\pi) \right]\frac{1}{\sqrt{\epsilon'(\epsilon'+mc^2)}}\\
- \frac{\mu'c^2}{\sqrt{2\epsilon'(\epsilon'+mc^2)}} \left\{(\bm\Sigma\times\bm \pi), (\bm{H}\cdot\bm\pi+\bm{\pi}\cdot\bm H)\right\}
\frac{1}{\sqrt{2\epsilon'(\epsilon'+mc^2)}} \\
+2d\bm\Sigma\times\bm E %\\
-\frac{dc^2}{\sqrt{2\epsilon'(\epsilon'+mc^2)}} \left\{(\bm\Sigma\times\bm \pi),
(\bm{E}\cdot\bm\pi+\bm{\pi}\cdot\bm E)\right\} \frac{1}{\sqrt{2\epsilon'(\epsilon'+mc^2)}} \\+\frac{dc}{2}\left\{\frac{1}{\epsilon'},
\left[\bm\Pi\times(\bm \pi\times \bm H)-\bm\Pi\times(\bm H\times \bm\pi) \right]\right\}.
\end{array} \label{eq36}$$
Eqs. (\[eq33\]),(\[eq35\]),(\[eq36\]) agree with the corresponding equations derived in Refs. [@JMP; @RPJ]. However, unlike the latter equations, Eqs. (\[eq33\]),(\[eq35\]),(\[eq36\]) describe strong-field effects.
We can also consider the interaction of spinless particles with the strong electromagnetic field. The initial Klein-Gordon equation describing this interaction has been transformed to the Hamilton form in Ref. [@FV].
In this case, the Hamiltonian acts on the two-component wave function which is the analogue of the spinor. The explicit form of this Hamiltonian is [@FV] $${\cal
H}=\rho_3mc^2+(\rho_3+i\rho_2)\frac{\bm\pi^2}{2m}+e\Phi.
\label{FV}$$ Therefore, $${\cal
M}=mc^2+\frac{\bm\pi^2}{2m}, ~~~{\cal E}=e\Phi, ~~~{\cal
O}=i\rho_2\frac{\bm\pi^2}{2m}, ~~~[{\cal M},{\cal O}]=0.
\label{MEO}$$ For spinless particles, $$\epsilon=\sqrt{m^2c^4+c^2\bm\pi^2}, ~~~
T=\sqrt{\frac{\epsilon}{mc^2}}\left(\epsilon+mc^2\right).
\label{eqep}$$
The Hamiltonian transformed to the FW representation is given by $${\cal H}_{FW}=\beta\epsilon+{\cal
E}=\beta\sqrt{m^2c^4+c^2\bm\pi^2}+e\Phi. \label{eqfz}$$ There are not any terms of order of $\hbar$ in this Hamiltonian, while it contains terms of second and higher orders in the Planck constant. We do not calculate the latter terms because their contribution into equations of particle motion is usually negligible.
The operator equation of particle motion takes the form $$\begin{array}{c} \frac{d\bm \pi}{dt}=e\bm
E+\beta\frac{ec}{4}\left\{\frac{1}{\epsilon},
\left([\bm\pi\times\bm H]-[\bm H\times\bm\pi]\right)\right\}.
\end{array} \label{eqpz}$$
The right hand side of this equation coincides with the spin-independent part of the corresponding equation for spin-1/2 particles. Eq. (\[eqfz\]) for the FW Hamiltonian agrees with Eq. (12) in Ref. [@PAN]. In this reference, the weak-field approximation has been used and the operator equation of particle motion in the strong electromagnetic field has not been obtained.
SEMICLASSICAL LIMIT OF RELATIVISTIC QUANTUM MECHANICS FOR PARTICLES IN STRONG EXTERNAL FIELDS
==============================================================================================
To obtain the semiclassical limit of the relativistic quantum mechanics, one needs to average the operators in the quantum mechanical equations. When the FW representation is used and relations (\[rel1\]),(\[rel2\]) are valid, the semiclassical transition consists in trivial replacing operators by corresponding classical quantities. In this representation, the problem of extracting even parts of the operators does not appear. Therefore, the derivation of equations for particles of arbitrary spin in strong external fields made in the precedent section solves the problem of obtaining the semiclassical limit of the relativistic quantum mechanics. If the momentum and position operators are chosen to be the dynamical variables, relations (\[rel1\]),(\[rel2\]) are equivalent to the condition $$|<p_i>|\cdot|<x_i>|\gg|<[p_i,x_i]>|=\hbar,~~~
i=1,2,3. \label{rel3}$$ The angular brackets which designate averaging in time will be hereinafter omitted.
Obtained semiclassical equations may differ from corresponding classical ones.
As a result of replacing operators by corresponding classical quantities, the semiclassical equations of motion of particles and their spins take the form $$\begin{array}{c}
\frac{d\bm \pi}{dt}=e\bm E+\frac{ec}{\epsilon'}
\left(\bm\pi\times\bm H\right)
%\\
+\mu'\nabla(\bm P\cdot\bm H)+ \frac{\mu_0}{mc^2\epsilon'} \nabla(\bm P\cdot\bm H)\\
-\frac{\mu'c}{\epsilon'} \nabla(\bm P\cdot[\bm\pi\times\bm E])%\\
-\frac{\mu_0mc^3}{\epsilon'(\epsilon'+mc^2)}\nabla(\bm
P\cdot[\bm\pi\times\bm E])\\
-\frac{\mu'c^2}{\epsilon'(\epsilon'+mc^2)}(\bm{P}\cdot\bm\pi)\nabla
(\bm{H}\cdot\bm\pi), ~~~~~~~ \bm P=\frac{\bm S}{S}, \end{array}
\label{eqw}$$ $$\begin{array}{c} \frac{d\bm P}{dt}=2\mu'\bm P\times\bm H+ \frac{2\mu_0mc^2}{\epsilon'}( \bm P\times\bm H)%\\
-\frac{2\mu'c}{\epsilon'} \left(\bm P\times[\bm \pi\times \bm
E]\right)\\ -\frac{2\mu_0mc^3}{\epsilon'(\epsilon'+mc^2)}\left(\bm
P\times[\bm \pi\times \bm E] \right)
%\\
-\frac{2\mu'c^2}{\epsilon'(\epsilon'+mc^2)} (\bm P\times\bm \pi)(\bm{\pi}\cdot\bm H)\\ %
+2d\bm P\times\bm E-\frac{2dc^2}{\epsilon'(\epsilon'+mc^2)} (\bm
P\times\bm \pi)(\bm{\pi}\cdot\bm E) %\\
+\frac{2dc}{\epsilon'} \left(\bm P\times[\bm \pi\times \bm
H]\right). \end{array} \label{eqt}$$ In Eqs. (\[eqw\]),(\[eqt\]), $\epsilon'$ is defined by Eq. (\[eq34\]), $\bm P$ is the polarization vector, and $\bm S$ is the spin vector (i.e., the average spin).
For scalar particles $$\begin{array}{c}
\frac{d\bm \pi}{dt}=e\bm E+\frac{ec}{\sqrt{m^2c^4+c^2\bm\pi^2}}
\left(\bm\pi\times\bm H\right). \end{array} \label{eqwl}$$
Two first terms in right hand sides of Eqs. (\[eqw\]),(\[eqwl\]) are the same as in the classical expression for the Lorentz force. This is a manifestation of the correspondence principle. The part of Eq. (\[eqt\]) dependent on the magnetic moment coincides with the well-known Thomas-Bargmann-Michel-Telegdi (T-BMT) equation. It is natural because the T-BMT equation has been derived without the assumption that the external fields are weak. The relativistic formula for the Stern-Gerlach force can be obtained from the Lagrangian consistent with the T-BMT equation (see Ref. [@PK]). The semiclassical and classical formulae describing this force also coincide. High-order corrections to the quantum equations of motion of particles and their spins should bring a difference between quantum and classical approaches.
DISCUSSION AND SUMMARY
======================
The new method of the FW transformation for relativistic particles of arbitrary spin in strong external fields described in the present work is based on the previous developments [@JMP]. However, the use of transformation operator (\[eq18N\]) is not restricted by any definite commutation relations \[see Eq. (\[comm\])\] between even and odd operators. The proposed method utilizes the expansion of the FW Hamiltonian into a power series in the Planck constant which defines the order of magnitude of quantum corrections. In the FW Hamiltonian, exact expressions for low-order terms in $\hbar$ can be obtained. If the de Broglie wavelength is much less than the characteristic size of the nonuniformity region of the external field \[see Eqs. (\[rel1\]),(\[rel2\])\], the transition to the semiclassical approximation becomes trivial. In this case, it consists in replacing operators by corresponding classical quantities. The simplest semiclassical transition is one of main preferences of the FW representation.
If Eqs. (\[rel1\]),(\[rel2\]) are not valid, the proposed method can be used in the weak-field expansion. This expansion previously used in Ref. [@JMP] presents the FW Hamiltonian as a power series in the external field potentials and their derivatives. In this case, the operator equations characterizing dynamics of the particle momentum and spin can also be derived. Solutions of these equations define the quantum evolution of main operators. Semiclassical evolution of classical quantities corresponding to these operators can be obtained by averaging the operators in the solutions. An example of such an evolution is time dependence of average energy and momentum in a two-level system.
When the FW Hamiltonian can be expanded into a power series in the Planck constant, we obtain the semiclassical limit of the relativistic quantum mechanics. Since the correspondence principle must be satisfied, classical and semiclassical Hamiltonians and equations of motion must agree. As an example, we consider the interaction of scalar and spin-1/2 particles with the strong electromagnetic field. We have carried out the FW transformation and have derived the quantum equations of particle motion. We have also deduced the quantum equations of spin motion for spin-1/2 particles. Averaging operators in the quantum equations consists in substitution of classical quantities for these operators and allows to obtain the semiclassical equations which are in full agreement with the corresponding classical equations. The proved agreement confirms the validity of both the correspondence principle and the aforesaid method. All calculations have been carried out for relativistic particles in strong external fields.
Acknowledgements {#acknowledgements .unnumbered}
================
The author is grateful to O.V. Teryaev for interest in the work and helpful discussions and to T. Tanaka for bringing to his attention Ref. [@Tanaka]. This work was supported by the Belarusian Republican Foundation for Fundamental Research.
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|
---
author:
- Max Hallgren
title: 'The Nonexistence of Noncompact Type-I Ancient 3-d $\kappa$-Solutions of Ricci Flow with Positive Curvature'
---
**Abstract**. In this short paper, we show there do not exist three-dimensional noncompact $\kappa$-solutions of Ricci flow that have positive curvature and satisfy a Type-I bound. This represents progress towards the proof of Perelman’s conjecture that the only complete noncompact three-dimensional $\kappa$-solution with positive curvature is the Bryant soliton.
Introduction
============
This paper addresses a class of noncompact solutions to Ricci flow essential to the classification of singularities in three-dimensions. Namely, we classify three-dimensional complete noncompact $\kappa$-solutions $(M^3, g(t))$, $t \in (-\infty, 0)$, that satisfy the Type-I condition $$|Rm(g(t))|_{g(t)} \leq \dfrac{C}{|t|} \hspace{6 mm} \mbox{ for all } t \in (-\infty, 0) .$$ Here, a $\kappa$ solution means a complete ancient solution of Ricci flow that is $\kappa$-noncollapsed on all scales and has bounded nonnegative curvature.
Let $(M^3, g(t)), \: t \in (-\infty, 0]$ be a complete noncompact 3-dimensional ancient Type-I $\kappa$-solution. Then $(M^3, g(t))$ is a quotient of the shrinking round cylinder.
This result was communicated to Lei Ni by Perelman, though Perelman did write down the proof. The proposition was recently proved independently in [@yongjia], but the proof differs from ours in that it uses crucially a result about backwards stability of necks proven in [@klott2].
Roughly speaking, the idea of the proof is as follows. We use Perelman’s results on the global structure of 3d $\kappa$-solutions to show that, at every time, the $\kappa$-solution looks neck-like outside of a compact subset. We take backwards limits based in this set to establish a contradiction. If this subset does not move too quickly as $t \to -\infty$, then Perelman’s asymptotic shrinker theorem gives convergence to a cylinder. If the subset moves quickly, we show its curvature must still be comparable to the maximum curvature of the time slice. Then we are able to show the set cannot move too quickly, making use of the Type-I distortion estimates and the global structure of the solution.\
The following is an easy consequence of the proof of Proposition 1, and does not depend on the Type-I assumption.
The scalar curvature at any soul of $(M, g(t))$ is comparable to that of the maximum curvature of the time slice.
For a moment, consider a 3d noncompact $\kappa$-solution $(M^3, g(t))_{t \in (-\infty, 0]}$ with PCO. Ding [@ding] showed that no such solution can have a Type-I forwards singularity. Cao-Chow-Zhang [@caoben] proved independently that the solution cannot be both Type-I forwards and Type-I ancient. It is conjectured that the only complete noncompact $\kappa$-solution with positive curvature is the Bryant Soliton, but for now combining the above results gives the following.
Suppose $(M^3, g(t))$, $t \in (-\infty, 0]$ is a noncompact 3d $\kappa$-solution with positive curvature. Then $(M, g(t))$ is Type-II ancient, and has either a forward Type-II singularity, or is eternal. In particular, after rescaling, $(M, g(t))$ has forward and backward limits equal to the Bryant soliton.
Note that, by Hamilton’s Type-II rescaling, any noncompact 3d $\kappa$-solution with PCO must have both forward and backwards limits equal to the Bryant soliton, though the point-picking method to achieve the forward limit depends on whether the solution is eternal or suffers a Type-II forward singularity.
The author is thankful to Yongjia Zhang for providing a simplification of Case 3 of the main result.
Preliminaries
=============
Throughout, we write $d_t(x, y) := d_{g(t)}(x, y)$ for $x, y \in M$.
Given an ancient solution $(M, g(t))$, $t \in (-\infty, 0]$ of Ricci flow, an evolving $\epsilon$-neck is a subset of the form $$N := \{ (x, t) \in M \times (-\infty, 0] \: ; \: d_0(x, x_0) < \epsilon^{-\frac{1}{2}} R(x_0, t_0)^{-\frac{1}{2}}, \: t \in (t_0 -\epsilon^{-1}R(x_0, t_0)^{-1}, t_0] \}$$ that is, after rescaling by $R(x_0, t_0)$, $\epsilon$-close in the $C^{|1/\epsilon|}$-topology to the shrinking cylinder ${\mathbb{S}}^2 \times (-\epsilon^{-1}, \epsilon^{-1}).$ The point $(x_0, t_0)$ is then called the center of $N$. We denote by $K(\epsilon)$ the set of points which are not the centers of evolving $\epsilon$-necks.
It is essential to our arguments to use the following version of Perelman’s result proved by Kleiner and Lott [@klott]:
(Global Structure of noncompact 3d $\kappa$-solutions [@klott]) For any $\epsilon >0$, there exists $D = D(\epsilon, \kappa) > 0$ such that if $(M^3, g(t))$, $t \in (-\infty, 0]$ is an noncompact $\kappa$-solution with PCO, then:\
i. $K(\epsilon)$ is a compact set with $$\mbox{diam}_{g(0)}K(\epsilon) < D R(x_0, 0),$$ ii. $D^{-1}R(x, 0) \leq R(x_0, 0) \leq D R(x, 0)$ for any $x \in K(\epsilon)$,\
where $x_0$ is any soul of $(M, g(0))$.
Next, we note that the scalar curvature at a fixed point in space cannot decay too quickly as $t \to -\infty$
For any Type-I ancient $\kappa$-solution $(M^3, g(t))$, $t \in (-\infty, 0]$, and any fixed $p \in M$, there exists $c = c(p) >0$ such that $|t|R(p, t) >c$ for all $t \in (-\infty, -1]$.
Suppose by way of contradiction that there is a sequence $t_k \to -\infty$ such that $|t_k|R(p, t_k) \to 0$. We know from [@cao] that the sequence $(M, g_k(t), (p, 0))$, where $g_k(t) = |t_k|^{-1}g(|t_k|t)$, converges in the $C^{\infty}$ Cheeger-Gromov sense to a nonflat shrinking soliton $(M_{\infty}^3, g_{\infty}(t), (p_{\infty}, 0))$, $t \in (-\infty, 0]$. Thus $$R_k(p, 0) = |t_k|R(p, t_k) \to R(p_{\infty}, 0) = 0,$$ a contradiction.
Finally, we need distortion estimates to control how fast the cap region can move as $t \to -\infty$.
For any Type-I ancient $\kappa$-solution $(M^3, g(t))$, $t \in (-\infty, 0]$ satisfying $|t|R(x, t) \leq C$ for all $(x, t) \in M \times (-\infty, 0]$, there exists $C' = C'(C)$ such that for any $x, y \in M$ and $t_1 < t_2 <0$ we have $$d_{g(t_1)}(x, y) \leq d_{g(t_2)}(x, y) + C'(\sqrt{|t_2|} - \sqrt{|t_1|}) .$$
Fix $x, y \in M$. Then the global curvature assumption gives $$\dfrac{\partial}{\partial t} d_{g(t)}(x, y) \geq -4(n-1)\sqrt{C|t|^{-1}} .$$ Integrating from $t_1$ to $t_2$, we get $$d_{g(t_2)}(x, y) - d_{g(t_1)}(x, y) \geq -8\sqrt{C}(\sqrt{|t_1|} - \sqrt{|t_2|}).$$ Moreover, the nonnegative curvature assumption ensures that distances are nonincreasing.
Proof of the Proposition
========================
*Proof of Proposition 1* Suppose by way of contradiction that $(M^3, g(t)), t \in (-\infty, 0]$ is not a quotient of the round cylinder. Then $(M^3, g(t))$ has positive sectional curvature everywhere, so is diffeomorphic to ${\mathbb{R}}^3$. Fix $\epsilon > 0$ sufficiently small. Then by Theorem 1, for each $t \in (-\infty, 0]$ there is a compact subset $K(t) \subseteq M$ such that $M \setminus K(t)$ is the set of points which are the center of evolving $\epsilon$-necks. Theorem 1 also states that $\mbox{diam}_{g(t)}K(t) \leq DR(y, t)^{-\frac{1}{2}}$ for all $t \in (-\infty, 0)$, $y \in K(t)$.
Fix $p \in M$. For large enough $|t|$, the spacetime point $(p, t)$ is the center of an evolving $\epsilon$-neck: otherwise there is a sequence $t_j \to -\infty$ where $(p, t_j)$ is not the center of an evolving $\epsilon$-neck. By the Type-I assumption, and applying the definition of reduced length to the path constant in space, we see that the spacetime sequence $(p, t_j)$ has uniformly bounded reduced length with respect to $(p, 0)$. Thus Perelman’s asymptotic shrinker theorem gives that $(M, |t_j|^{-1}g(|t_j|t), (p, -1)), t \in (-\infty, 0)$ converges in the $C^{\infty}$ Cheeger-Gromov sense to a noncompact, nonflat gradient Ricci soliton with bounded curvature. However, such a soliton is a shrinking cylinder by Perelman’s classification, leading to a contradiction.\
**Case 1:** There exists a sequence $(x_k, t_k)$ in $M \times (-\infty, 0]$ with $x_k \in K(t_k)$, $t_k \to -\infty$, and $$\liminf_{k \to \infty} \dfrac{d_{g(t_k)}(x_k, p)}{\sqrt{\tau_k}} < \infty .$$ In this case, we have the result of Naber [@naber] that $$l_{(p, 0)}(x_k, \tau_k) \leq A \left( 1 + \dfrac{d_{g(t_k)}(x_k, p)}{\sqrt{\tau_k}} \right)^2$$ for some $A< \infty$ universal. Thus we have a bound on $l_{(p, 0)}(x_k, \tau_k)$ independent of $k$, so we can apply Perelman’s asymptotic shrinker theorem [@poincare] to get subconvergence of $(M, |t_k|g(|t_k|t), (x_k, -1))_{t \in (-\infty, -1]}$ to a cylinder, a contradiction.\
**Case 2:** There exists a sequence $(x_k, t_k)$ in $M \times (-\infty, 0]$ such that $t_k \to -\infty$, $x_k \in K(t_k)$, and $$\lim_{k \to \infty} |t_k|R(x_k, t_k) = 0 .$$ In this case, using that $R(p, t_k) \geq c|t_k|$, we get $$\lim_{k \to \infty} \dfrac{R(x_k, t_k)}{R(p, t_k)} = 0 .$$ Also, note that any soul $y$ of $(M, g(t_k))$ must lie in $K(t_k)$ as long as $\epsilon$ was chosen smaller than some universal constant. In fact, we will show that $y$ must lie outside the middle two-thirds of any $\epsilon$-neck $N \subseteq (M, g(t))$.
Suppose by way of contradiction that $y$ is in the middle two-thirds of $N$. Then there is an open subset $N'$ that is a $10\epsilon$-neck that is disjoint from $y$, whose center sphere separates $M$, and is such that $y$ lies in the unbounded part of $M \setminus S$. However, by [@poincare Lem 2.20], this $10 \epsilon$-neck separates $y$ from the unique end of $M$, contradicting the fact that it is contained in the unbounded component of $M \setminus S$.
It is a fact from the theory [@poincare Cor 2.21] of noncompact manifolds of positive curvature that there exists $\bar{C} = \bar{C}(\epsilon) < \infty$ universal with the following property: for any $\epsilon$-neck centered at $z_1$ whose center sphere separates $y$ from another $\epsilon$-neck centered at $z_2$, we have $R(z_2, t_k) \leq \bar{C} R(z_1, t_k)$. Note that, in the statement of $\cite[Cor 2.21]{poincare}$, it is required that the $\epsilon$-necks are disjoint from $y$, but since $y$ lies outside of the middle two-thirds of any $\epsilon$-neck, $y$ is disjoint from the $2\epsilon$-necks centered at $z_1$ and $z_2$, so we may apply the theorem by replacing $\epsilon$ with $2\epsilon$. We apply this with $z_2 = p$, and with $z_1$ any point of $\partial K(t_k)$, so that $R(z_1, t_k) \leq C R(x_k, t_k)$. Combining this with Theorem 1 gives $$R(p, t_k) \leq \bar{C} C R(x_k, t_k)$$ for all $k$, contradicting the above inequality.\
**Case 3:** $$\liminf_{t \to -\infty} \dfrac{d_t(p, K(t))}{\sqrt{|t|}} = \infty , \hspace{6 mm} \liminf_{t \to -\infty}\inf_{x \in K(t)} |t|R(x, t) \geq b > 0 .$$ In this case we also have $$\liminf_{t \to -\infty} \inf_{x \in K(t)} R(x, t)d_t^2(x, p) = \infty.$$ Fix $t_0 < 0$ such that $p$ is the center of an evolving $\epsilon$-neck based at $(p, t)$ and such that $|t|R(x, t) \geq \frac{1}{2}b$ for all $t \leq t_0$, $x \in K(t)$. Then for $t \leq t_0$ we have $$\mbox{diam}_{g(t)}(K(t)) \leq D (2|t|/b)^{\frac{1}{2}}.$$ Recall the distortion constant $C' = C'(C)<\infty$ from Lemma 3, the constant $c = c(p) >0$ from Lemma 2, and the Elliptic-type constant $A< \infty$ from Lemma 1. By assumption, we may choose $t_1 \leq t_0$ such that $$C^* := \dfrac{d_{t_1}(p, K(t_1))}{\sqrt{|t_1|}} \geq 100,000((D+ A + 1)b^{-\frac{1}{2}} + C') \hspace{6 mm} \mbox{ and }$$ $$\dfrac{d_{25t_1}(p, K(25|t_1|))}{\sqrt{25|t_1|}} \geq C^* .$$ Set $t_2 := 25t_1$, and let $x_i \in K(t_i)$ be a soul of $(M, g(t_i))$. Then $$d_{t_2}(x_2, p) \geq 5C^* \sqrt{|t_1|},$$ $$d_{t_2}(x_2, x_1) \geq 5C^*\sqrt{|t_1|} - (C^* \sqrt{|t_1|} + 5C'\sqrt{|t_1|} + 2Db^{-\frac{1}{2}}|t_1|^{\frac{1}{2}}) \geq (3.99)C^*\sqrt{|t_1|} .$$
We claim that the center sphere $S(p)$ of the $\epsilon$-neck centered at $p$ separates $x_2$ from $x_1$. In fact, since $x_1$ lies outside the center two-thirds of the $\epsilon$-neck $N$ centered at $p$, [@poincare Lem A.9] implies that $S:= \partial B(x_1, R(p, t_1)^{-\frac{1}{2}} + d(x_1, p)) \cap N$ lies on the unbounded component of the complement of the center sphere $S(p)$ of $N$. Note that $R(p, t_1)^{-\frac{1}{2}} \leq c^{-\frac{1}{2}}|t_1|^{\frac{1}{2}}$. Since level sets for $d(x_1, \cdot)$ are connected [@poincare p.27], and $S$ is in the middle two-thirds of an $\epsilon$-neck, we must have $S = \partial B(x_1, R(p, t_1)^{-\frac{1}{2}} + d(x_1, p))$. Because $$d_{t_1}(x_1, x_2) \geq (4.99)C^* |t_1|^{\frac{1}{2}} \geq c^{-\frac{1}{2}}|t_1|^{\frac{1}{2}} + (C^* + Db^{-\frac{1}{2}})|t_1|^{\frac{1}{2}} + 3C^*|t_1|^{\frac{1}{2}} > R(p, t_1)^{-\frac{1}{2}} + d(x_1, p) + 3C^* |t_1|^{\frac{1}{2}},$$ so any minimal $g(t_1)$-geodesic from $x_1$ to $x_2$ must leave $B(x_1, d(x_1, p) + R(p, t_1)^{-\frac{1}{2}})$, hence it must leave the bounded component of $M \setminus S(p)$. In particular, $x_2$ is in the unbounded component of $M \setminus S(p)$.
We can take $\epsilon$ small enough so that $\epsilon^{-1} C^{-1} > 25$, so that $$\epsilon^{-1}R(y, t_1)^{-1} \geq \epsilon^{-1}C^{-1}|t_1| > 25|t_1| .$$ This means that $N \times \{t_2\}$ is a time slice of an evolving $\epsilon$-neck defined on a time interval containing $[t_2, t_1]$. In particular, $S(p)$ separates $x_2$ from the unique end of $M$ (again by [@poincare Lem 2.20]), so $x_2$ is in the bounded component of $M \setminus S(p)$, a contradiction.
$\qed$
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---
abstract: 'Noncentrosymmetric materials play a critical role in many important applications such as laser technology, communication systems,quantum computing, cybersecurity, and etc. However, the experimental discovery of new noncentrosymmetric materials is extremely difficult. Here we present a machine learning model that could predict whether the composition of a potential crystalline structure would be centrosymmetric or not. By evaluating a diverse set of composition features calculated using matminer featurizer package coupled with different machine learning algorithms, we find that Random Forest Classifiers give the best performance for noncentrosymmetric material prediction, reaching an accuracy of 84.8% when evaluated with 10 fold cross-validation on the dataset with 82,506 samples extracted from Materials Project. A random forest model trained with materials with only 3 elements gives even higher accuracy of 86.9%. We apply our ML model to screen potential noncentrosymmetric materials from 2,000,000 hypothetical materials generated by our inverse design engine and report the top 20 candidate noncentrosymmetric materials with 2 to 4 elements and top 20 borate candidates.'
author:
- |
Yuqi Song, Joseph Lindsay, Yong Zhao,Alireza Nasiri,Steph-Yves Loius\
Department of Computer Science and Engineering\
University of South Carolina\
Columbia, SC, 29201\
Jie Ling\
Department of Chemistry and Biochemistry\
Claflin University\
Orangeburg, SC, 29115\
Ming Hu\
Department of Mechanical Engineering\
University of South Carolina\
Columbia, SC, 29201\
Jianjun Hu \*\
Department of Computer Science and Engineering\
University of South Carolina\
Columbia, SC, 29201\
\* Correspondence author: `jianjunh@cse.sc.edu`
title: Machine Learning based prediction of noncentrosymmetric crystal materials
---
Introduction
============
Nonlinear optical materials (NLO), in which light waves interact with each other, are one of the key enablers for next generation of new lasers, fast telecommunication, quantum computing, quantum encryption, dynamic or optical storage data, and many other applications [@ok2006bulk; @halasyamani1998noncentrosymmetric; @kohn1999nobel; @abdeldayem07]. NLO materials are most broadly defined as those compounds capable of altering the frequency of light. Depending on the chemical and physical construct of the materials they can combine multiple photons to generate shorter wavelength photons or split one photon into several new photons of longer wavelengths. These new photons can be employed to perform all of the above applications as well as many others. The classes of NLO materials range broadly from inorganic oxides such as $KTiOPO_{4}$ and $LiNbO_{3}$ to semiconductors like to periodically poled GaAs, to organic polymers to metal organic framework (MOFs), and to simple small organic molecules like stilbene. This broad range of materials has many different properties and characteristics but all are united by one common factor, i.e. their lattice structure must not contain a center of symmetry and must be acentric [@ok2006bulk; @halasyamani1998noncentrosymmetric]. This is a rigorous requirement that can only be met in well-ordered lattice structures, meaning ordered crystals. It is generally difficult to design and grow acentric single crystals and less than 15% of all known structures are acentric. This demands exceptional determination on the part of the synthetic and crystal growth experimentalists. The process is made even more difficult by the fact that the NLO processes that enable frequency modification are inherently inefficient. Moreover, the ability to prepare new NLO materials and study their properties is not trivial and requires patient and detailed investigations. The payoff is enormous however, as the materials enable the development of devices used in next generation laser surgery, imaging, optical communication, advanced spectroscopy, optical data storage and a vast array of applications dependent on the interaction of light with matter. In Figure \[example\], We show the crystal structures of a centrosymmetric material and a noncentrosymmetric material, namely ScBO3 and SrB12O7.
[.45]{} ![Crystal Structures of centrosymmetric and noncentrosymmetric materials. (a) The crystal structures of ScBO3 of space group R$\overline{3}$c, where the purple nodes represent Sc atoms, the green nodes represent B atoms and red nodes are O atoms. (b) The crystal structure of SrB12O7 of space group R3, where the blue node represents Sr atom, the green nodes represent B atoms, and the red nodes are O atoms.[]{data-label="example"}](figures/fig1.png "fig:"){width="\textwidth"}
[.45]{} ![Crystal Structures of centrosymmetric and noncentrosymmetric materials. (a) The crystal structures of ScBO3 of space group R$\overline{3}$c, where the purple nodes represent Sc atoms, the green nodes represent B atoms and red nodes are O atoms. (b) The crystal structure of SrB12O7 of space group R3, where the blue node represents Sr atom, the green nodes represent B atoms, and the red nodes are O atoms.[]{data-label="example"}](figures/fig2.png "fig:"){width="\textwidth"}
Although the structure-property relation between NLO effects and microstructure can be used as a guide, new NLO crystals are still mainly explored using “trial and error” Edisonian approaches. A reliable determination of lattice symmetry is a crucial first step for materials characterization and analytics. Recently, a deep learning-based approach to automatically classify structures given a crystal structure (even with defects) has been recently proposed [@ziletti2018insightful]. Similarly, Kaufmann et. al. [@kaufmann2020crystal] proposed a crystal symmetry determination method from electron diffraction using machine learning. However, these methods cannot be applied for large-scale composition based screening as they both require experimental data. On the other hand, direct numerical calculation of the optical properties of a single crystalline material from its atomic structure by accurate first-principles without any other inputs has just been made available for a few years. Studies have focused on properties such as second harmonic generation (SHG) coefficients [@diatta2018density] and other important optical properties such as energy band gap, refractive indices [@dec2018dft], and birefringence. While first-principles calculations make it possible to predict some optical properties without any experimental data, such computation is usually tedious and very computationally demanding even for not too complicated primitive cells. Consider this: four-element compounds with different ratios can lead to a search space of 32.4 billion combinations. Currently, Density Functional Theory (DFT) based first-principles methods for optical properties calculation is out of the question for high-throughput screening of NLO materials. Especially, these methods cannot be used for discovery of new NLO materials as they all require the knowledge of the crystal structure information which is usually not available and computational prediction of crystal structures from composition is feasible only for a small subset of materials with simple compositions [@oganov2019structure]. In-depth understandings of the mechanism on how compositions form specific structures which further determines the NLO behavior would provide the guide for experimental explorations, and save enormous human and materials resources. On the other hand, data driven computational prediction models for noncentrosymmetric materials discovery can be used as the first step for nonlinear optical materials discovery.
In the past five years, machine learning (ML) has been increasingly applied to materials informatics problems from property prediction [@cao2019convolutional; @hamidieh18], to materials structure prediction, to computational screening [@choudhary2019accelerated], and inverse materials design [@sanchez2018inverse; @dan2019generative]. Among these ML algorithms and models, Random Forest (RF) models have shown great success for predicting a variety of materials properties such as the critical temperatures of superconducting materials [@stanev17; @matsu19] and for predicting the ability of a given composition to form an amorphous ribbon of metallic glass via melt spinning [@ward16; @ward2018machine]. In [@furmanchuk2016predictive], Furmanchuk et al. utilized a RF regression model to predict the bulk modulus. RF models have also been widely used in other research areas. For example, a RF based approach showed its superiority in automatically selecting molecular descriptors for ligands of kinases and nuclear hormone receptors [@cano2017automatic]. On the other hand, recent years have observed tremendous success of deep learning [@goodfellow2016deep] based neural network models in applications such as image recognition, automatic machine translation, robotics [@su2020dietary], and autonomous driving [@liu2017survey]. More importantly, their success in materials discovery problems such as the prediction of crystal stability [@ye2017crystal] and superconductor critical temperatures [@li2020critical], makes it promising for other applications in materials discovery. In our previous work, we have applied machine learning and deep learning for crystal space group and crystal system prediction from composition [@zhao2020machine] and for formation energy prediction [@cao2019convolutional].
Herein, we propose and evaluate two machine learning models including RF and multi-layer perceptron (MLP) neural network models for noncentrosymmetric classification given only material composition. The Magpie composition descriptors are used in our study. Cross-validation and hold-out experiments show that RF with Magpie features achieved the best results. A further application of our RF noncentrosymmetric prediction model to screening two million hypothetical materials generated by our generative ML model [@dan2019generative] allows us to identify and predict dozens of potential novel noncentrosymmetric materials with high confidence scores.
Our contributions can be summarized as follows:
\(1) We propose two machine learning algorithms (RF and MLP) for predicting noncentrosymmetric materials given only their composition.
\(2) We evaluate and compare the performances of different machine learning algorithms for noncentrosymmetric materials classification.
\(3) We apply our prediction models to screen the 2 million hypothetical materials generated by a generative adversarial network (GAN) based predictors and identify a list of top candidate materials with highly probable noncentrosymmetry structures.
Materials and Methods
=====================
Feature Calculation
-------------------
To accomplish the goal of noncentrosymmetry classification, one of the key steps is to identify the most relevant features of a chemical composition that correlates with symmetry tendency of its formed structure. To do this, we have tried the myriad of featurizers provided by the matminer library [@ward2018matminer], which is a Python-based software platform to facilitate data-driven methods of analyzing and predicting materials properties, such as composition, crystal structure, band structure, and more. The matminer featurizers package has a total of 5 different classes of featurizers present in the library’s current deployment, ranging from composition descriptors to structural ones.
We use the composition featurizer’s Element Property module to calculate the Magpie elemental descriptors for training our ML models. The Magpie feature set has 132 elemental descriptors [@ward2018machine], composed of 6 statistics of a set of elemental properties such as atomic number in the material, space group of the material, the Magnetic Moment calculated by Density Functional Theory (DFT). Magpie feature set was selected based on our evaluations of a couple of descriptors.
Machine learning models
-----------------------
We evaluate two machine learning models for noncentrosymmetry prediction, namely, a Random Forest (RF) classifier, and a Deep Neural Network (DNN) classifier.
Random Forest [@breiman2001random; @liaw2002classification] is a supervised learning method that can be applied to solve classification or regression problems. It is an ensemble algorithm that constructs a multitude of many decision trees at training time and outputs the class that is the mode of the classification of the individual trees. RF classifiers have shown strong prediction performance when combined with composition features in our previous studies [@cao19]. In our RF classifier model, we set the number of trees to be 200. This algorithm was implemented using the Scikit-Learn library in Python 3.6.
Deep learning excels at identifying patterns in unstructured data by building multiple layers to progressively extract higher-level features from the raw input to do the predictive task [@sze2017efficient]. For instance, Xie et al. [@xie2018crystal] proposed a graph convolutional neural network model for property predictions of materials and provided a universal and interpretable representation of crystalline materials. In this paper, we aimed to explore whether DNNs can achieve better predictive performance than RF models in noncentrosymmetry prediction. Therefore, we designed a MLP neural network classifier made of five fully connected layers, with four layers using LeakyReLU as their activation function and Sigmoid in the final layer for classifying. A dropout layer with a 0.05 drop rate was added to avoid overfitting. An Adam optimizer and binary cross entropy function are selected for training the DNN. In addition, the epoch, batch and learning rate are set to 50, 500, 0.001, respectively.
Hyper-parameter tuning
----------------------
Due to various hyperparameters and the impact of their combinations on the training process and the final performance of machine learning models, manual parameter tuning is time-consuming. Hence, automatic hyperparameter tuning method is needed for finding suitable parameters. To ensure fair comparison of the ML models, we use the Bayesian optimization [@snoek2012practical] algorithm to find optimal hyper-parameters for RF models, which has been proven to be an effective tool. This method requires that the objective be a scalar value depending on the hyperparamter configuration $x$, where the maximum is sought for an expensive function $ f: \mathcal{X} \rightarrow \mathbb{R}.$
$$\mathbf{x}_{o p t}=\underset{\mathbf{x} \in \mathcal{X}}{\arg \max } f(\mathbf{x})$$
We use the hyperopt package library [@bergstra2013hyperopt] to optimize n\_estimators, max\_depth and max\_features in RF models by supplying an optimization function which maximizes its precision.
Results and Discussion
======================
Herein, we describe the datasets, the evaluation criteria, and the experimental results. We analyze and compare the prediction performance of RF and DNN models. Besides, we discuss the application of our model to screening new hypothetical noncentrosymmetric materials. Our experiments on classifying noncentrosymmetry from composition include three parts: cross-validation experiments, holdout experiments on Borates, and screening a two million hypothetical materials.
Datasets
--------
Crystal structures with different space groups have different centrosymmetric tendencies. It is known that there are 138 noncentrosymmetric space groups and 92 centrosymmetric space groups, the detailed space group IDs and names and their centrosymmetric property are summarized in Table \[table:Space group\].
**** **group IDs** **group names**
----------------------- --------------------------------------------------------------------------------------- -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
centrosymmetric 2, 10-15, 47-74, 83-88, 123-142, 147-148, 162-167, 175-176, 191-194, 200-206, 221-230 P$\overline{1}$, P2/m, P2~1~/m, C2/m, P2/c, P2~1~/c, C2/c, Pmmm, Pnnn, Pccm, Pban, Pmma, Pnna, Pmna, Pcca, Pbam, Pccn, Pbcm, Pnnm, Pmmn, Pbcn, Pbca, Pnma, Cmcm, Cmca, Cmmm, Cccm, Cmma, Ccca, Fmmm, Fddd, Immm, Ibam, Ibca, Imma, P4/m, P4~2~/m, P4/n, P4~2~/n, I4/m, I4~1~/a, P4/mmm, P4/mcc, P4/nbm, P4/nnc, P4/mbm, P4/mnc, P4/nmm, P4/ncc, P4~2~/mmc, P4~2~/mcm, P4~2~/nbc, P4~2~/nnm, P4~2~/mbc, P4~2~/mnm, P4~2~/nmc, P4~2~/ncm, I4/mmm, I4/mcm, I4~1~/amd, I4~1~/acd, P$\overline{3}$, R$\overline{3}$, P$\overline{3}$1m, P$\overline{3}$1c, P$\overline{3}$m1, P$\overline{3}$c1, R$\overline{3}$m, R$\overline{3}$c, P6/m, P6~3~/m, P6/mmm, P6/mcc, P6~3~/mcm, P6~3~/mmc, Pm$\overline{3}$, Pn$\overline{3}$, Fm$\overline{3}$, Fd$\overline{3}$, Im$\overline{3}$, Pa$\overline{3}$, Ia$\overline{3}$, Pm$\overline{3}$m, Pn$\overline{3}$n, Pm$\overline{3}$n, Pn$\overline{3}$m, Fm$\overline{3}$m, Fm$\overline{3}$c, Fd$\overline{3}$m, Fd$\overline{3}$c, Im$\overline{3}$m, Ia$\overline{3}$d
noncentrosymmetric 1, 3-9, 16-46, 75-82, 89-122, 143-146, 149-161, 168-174, 177-190, 195-199, 207-220 P1, P2, P2~1~, C2, Pm, Pc, Cm, Cc, P222, P222~1~, P2~1~2~1~2, P2~1~2~1~2~1~, C222~1~, C222, F222, I222, I2~1~2~1~2~1~, Pmm2, Pmc2~1~, Pcc2, Pma2, Pca2~1~, Pnc2, Pmn2~1~, Pba2, Pna2~1~, Pnn2, Cmm2, Cmc2~1~, Ccc2, Amm2, Aem2, Ama2, Aea2, Fmm2, Fdd2, Imm2, Iba2, Ima2, P4, P4~1~, P4~2~, P4~3~, I4, I4~1~, P$\overline{4}$, I$\overline{4}$, P422, P42~1~2, P4~1~22, P4~1~2~1~2, P4~2~22, P4~2~2~1~2, P4~3~22, P4~3~2~1~2, I422, I4~1~22, P4mm, P4bm, P4~2~cm, P4~2~nm, P4cc, P4nc, P4~2~mc, P4~2~bc, I4mm, I4cm, I4~1~md, I4~1~cd, P$\overline{4}$2m, P$\overline{4}$2c, P$\overline{4}$2~1~m, P$\overline{4}$2~1~c, P$\overline{4}$m2, P$\overline{4}$c2, P$\overline{4}$b2, P$\overline{4}$n2, I$\overline{4}$m2, I$\overline{4}$c2, I$\overline{4}$2m, I$\overline{4}$2d, P3, P3~1~, P3~2~, R3, P312, P321, P3~1~12, P3~1~21, P3~2~12, P3~2~21, R32, P3m1, P31m, P3c1, P31c, R3m, R3c, P6, P6~1~, P6~5~, P6~2~, P6~4~, P6~3~, P$\overline{6}$, P622, P6~1~22, P6~5~22, P6~2~22, P6~4~22, P6~3~22, P6mm, P6cc, P6~3~cm, P6~3~mc, P$\overline{6}$m2, P$\overline{6}$c2, P$\overline{6}$2m, P$\overline{6}$2c, P23, F23, I23, P2~1~3, I2~1~3, P432, P4~2~32, F432, F4~1~32, I432, P4~3~32, P4~1~32, I4~1~32, P$\overline{4}$3m, F$\overline{4}$3m, I$\overline{4}$3m, P$\overline{4}$3n, F$\overline{4}$3c, I$\overline{4}$3d
\[table:Space group\]
: Space groups with noncentrosymmetric and centrosymmetric structures
[.45]{} ![Sample distribution of noncentrosymmetric and centrosymmetric space groups in MPF dataset[]{data-label="distribution of space group"}](figures/fig3.jpg "fig:"){width="\textwidth"}
[.45]{} ![Sample distribution of noncentrosymmetric and centrosymmetric space groups in MPF dataset[]{data-label="distribution of space group"}](figures/fig4.jpg "fig:"){width="\textwidth"}
We first downloaded the composition formulas of 97,217 crystal materials from the Materials Project database. We then remove those compositions belonging to multiple space groups with conflicting centrosymmetric tendencies. In total, we collecte 82,506 material compositions and assign the noncentrosymmetric property labels according to their corresponding space group. The dataset is called **MPF**, which have 60,587 positive (noncentrosymmetric) samples and 21,919 negative (centrosymmetric) samples, as shown in Table \[table:dataset\]. The distribution of noncentrosymmetric and centrosymmetric space groups in MPF dataset are shown in Figure \[distribution of space group\]. We find that the distribution of samples over different space groups are not well balanced.
In order to evaluate the extrapolation prediction performance of our machine learning prediction model of noncentrosymmetry, we select all the 315 borate compounds from MPF dataset and assign them as the hold-out test dataset Borates315. Borates contain boron (B) element and oxygen (O) element, which are a ubiquitous family of flame retardants found as boric acid and as a variety of salts. Previous research found that compared to other material family, borates tend to have higher percentage of nonlinear proprieties, which makes it a good hold-out test set. [@bubnova2017borates]. We further find that most borate materials include 3 elements. It is interesting to see if ML models trained with 3-element training samples can achieve better prediction performance. We select all 3-element materials from the MPF dataset and assigned them to the **MP3** dataset, which includes 30,762 centrosymmetric materials and 8,964 noncentrosymmetric materials as shown in Table \[table:dataset\]. The motivation is to check if our classification models trained with MP3 dataset can achieve better performance when testing on the hold-out borates dataset.
**** **\#symmetry** **\#non symmetry** **\#total**
------------------- ---------------- -------------------- -------------
MPF 63,376 19,130 82,506
MP3 30,762 8,964 39,726
Borates315 250 65 315
\[table:dataset\]
: Dataset
Evaluation criteria
-------------------
To evaluate the prediction performance of our model, precision, recall, accuracy, F1 score, and receiver operating characteristic area under the curve (ROC AUC) are used as performance metrics in this study.
The formula for these performance metrics are given as follows, where TP is number of true positives, FP is number of false positives, TN is number of true negatives, FN is number of false negatives, TPR is the true positive rate (also referred to as recall) of TP, and FPR refers to false positive rate of FP.
$$Precision = \frac{TP}{TP + FP}
\label{precison}$$
$$Recall = \frac{TP}{TP + FN}
\label{recall}$$
$$Accuracy = \frac{TP + TN}{TP + TN + FP + FN}
\label{accuracy}$$
$$F1-score = \frac{2TP}{2TP + FP + FN}
\label{f1}$$
$$AUC = \int_{x=0}^{1}TPR(FPR^{-1}(x))dx
\label{rocauc}$$
Prediction performance
------------------------
To evaluate how our machine learning models can predict whether a crystal material’s structure is noncentrosymmetry or not, we used two evaluation approaches: one is cross-validation over the MPF dataset and the other is the hold-out evaluation trained with non-borates datasets MPF and MP3 and tested on the Borates315 dataset. This hold-out test is especially important as the cross-validation performance can usually be over-estimated due to the redundancy of the training samples in most of the large-scale datasets such as the Materials Projects and the OQMD [@xiong2020evaluating].
### 10-fold cross-validation performance
We set the maximum tree depth to be 20 and the number of decision trees as 200. This was later expanded to include the minimum number of samples per leaf node, the minimum number of samples required to split a node, and the maximum number of leaf nodes. With these 5 settings tuned per featurizer iteration, we then train the final prediciton RF models and make prediction, and caculate the performance scores. To further verify the performance of our RF-based models, we compare it with those of the DNN-based models. Table \[table:performance\] shows the performances we achieved on two datasets using four evaluation criteria.
Model Dataset Precision Recall Accuracy F1 score
----------- --------- ----------- ----------- ----------- -----------
RF-based MPF 0.834 0.754 0.848 0.781
RF-based MP3 **0.845** 0.755 **0.869** **0.786**
DNN-based MPF 0.773 0.769 0.785 0.771
DNN-based MP3 0.784 **0.780** 0.792 0.782
: Ten-fold cross-validation performance of ML models for noncentrosymmetry prediction
\[table:performance\]
Firstly, we found that the precision and accuracy of the RF model are significantly better in comparison with DNN models: the 10 fold cross-validation accuracy of RF model on the MPF dataset is 0.848 compared to 0.785, which indicates 7.89% improvement. The F1 score of RF model is 0.781 compared to 0.771 of DNN. Although DNN achieves better Recall score, the F1-score of RF is higher than DNN’s. This validates the effectiveness of our RF-based model for predicting the noncentrosymmetric property for a given material. This is consistent with a recent evaluation of different ML methods for materials property prediction [@robinson2019validating].
Secondly, comparing the results of the same RF and DNN model on the MPF dataset and the MP3 dataset, we found that each model achieved better prediction performance for the MP3 dataset. Particularly, the precision, accuracy and F1 score of the RF classifier increase to 0.845, 0.869 and 0.786, respectively.
### Hold out experiment results
To explore the effectiveness of our model for extrapolative prediction of noncentrosymmetry where the test samples may not have the same distribution with the training set, we conducted a hold-out test over the Borates315 dataset.The training dataset is generated by filtering out all the samples of the Borates315 dataset from the MPF dataset and keeping the remaining ones, which includes 82,191 samples. Similarly, we also conduct a hold-out test for the MP3 dataset for which the training set is generated by removing all borates in the MP3 dataset. The number of samples of the no-borates 3-element training set is 39411. Their ROC curves and AUC scores are shown in Figure \[performance\].
[.45]{} ![ROC curves for cross-validation and hold-out experiments for the RF prediction models trained with the whole dataset and the 3-element dataset.[]{data-label="performance"}](figures/fig5.jpg "fig:"){width="\textwidth"}
[.45]{} ![ROC curves for cross-validation and hold-out experiments for the RF prediction models trained with the whole dataset and the 3-element dataset.[]{data-label="performance"}](figures/fig6.jpg "fig:"){width="\textwidth"}
[.45]{} ![ROC curves for cross-validation and hold-out experiments for the RF prediction models trained with the whole dataset and the 3-element dataset.[]{data-label="performance"}](figures/fig7.jpg "fig:"){width="\textwidth"}
[.45]{} ![ROC curves for cross-validation and hold-out experiments for the RF prediction models trained with the whole dataset and the 3-element dataset.[]{data-label="performance"}](figures/fig8.jpg "fig:"){width="\textwidth"}
In Figure \[performance\], each dotted yellow line corresponds to the ROC curve of a random predictor with AUC value of 0.5. Each blue curve represents the ROC curve of the classifier. As is well known the higher value of AUC, the better performance of the classifier. Among the four sub-figures, figure (c) shows the best result, with AUC reaching 0.91. Furthermore, comparing (a) (c) with (b) (d), we can find AUC scores of cross-validation experiments are higher than those of hold-out experiments over the same two datasets, which suggests the over-estimation of model performance due to dataset sample redundancy. Meanwhile, although the performance of hold out experiments is not as good as cross validation experiments, it only uses the non-borate materials as the training data for predicting the 315 borate materials, which interprets the 0.71 and 0.68 AUC are acceptable since this is extrapolation prediction performance. Based on this analysis, we use the RF model to predict and screen hypothetical materials from a large generated materials as discussed in detail in Section 3.4.
### The stability of our model
To evaluate the stability of our RF model performance, we made the following Box plot, which shows that the fluctuations of precision and F1 scores for the 10-fold cross-validation experiments are less than 0.01. However, we found that the precision scores of the hold out experiments over the MPF dataset range from 0.61 to 0.67, and the F1 scores are between 0.58 to 0.64. This shows that the prediction performance of our RF models with 10-fold cross-validation experiments are more stable than those of the hold out tests.
![The stability of RF models. (MPF and MP3 are datasets; CV and H are abbreviations of cross validation and hold out; P and F1 represent Precision and F1 score respectively.)[]{data-label="stability"}](figures/fig9.jpg){width="15cm"}
### Feature importance ranking in noncentrosymmetry prediction
There are 132 descriptors in the Magpie feature set. To gain further understanding of how different descriptors affect the ML model performance, we calculated the importance scores for all descriptors in the prediction of the RF model and sorted them by their scores. The top 15 descriptors are shown in Figure \[importance\] and the corresponding description of them are presented in Table \[table:importance\].
As can be seen from Figure \[importance\], the importance scores of top 15 features are above 0.014. The top six features have significantly higher scores than the remaining nine features, which shows they make more contributions to predicting the non-centrosymmetry. Combined with Table \[table:importance\], we find that range of atomic number, maximum melting temperature, mean number of valence, range of number of valence, mean number of Ns valence and minimum number of Nd valence are the six most important factors. We also find that the importance of valence number to noncentrosymmetry prediction is consistent with the physical knowledge: first the distribution of valence electrons have strong effect on chemical bond formation (strong covalent bonds or weaker ionic bonds), and thus the final crystal structure formation. Second, previous study [@maki1995surface] shows that the valence electrons of the atoms is involved in its nonlinear optical behavior: they construct the free electron gas, which can be polarized by the oscillating electric field and determine the harmonic excitation frequency by counting linear and nonlinear reflected waves.
![Ranking of top 15 features in terms of their importance scores[]{data-label="importance"}](figures/fig10.jpg){width="8cm"}
Feature ID Feature Name Feature Description
---------------------- --------------------------- ---------------------------------------------------
2 Range Number Range of Atomic Number
19 Maximum MeltingT Maximum Melting Temperature
75 Mean NValence Mean \# Valence
50 Range NsValence Range of \# Valence s-orbitals
63 Mean NdValence Mean \# Valence d-orbitals
48 Minimum NsValence Minimum \# Valence s-orbitals
43 Maximum Electronegativity Maximum Electro-negativity
49 Maximum NsValence Maximum \# Valence s-orbitals
20 Range MeltingT Range of Melting Temperature
76 Avg\_dev NValence Mean absolute deviation of \# Valence
88 Avg\_dev NpUnfilled Mean absolute deviation of \# Unfilled s Orbitals
4 Avg\_dev Number Mean absolute deviation of Atomic Number
52 Avg\_dev NsValence Mean absolute deviation of \# Valence s-orbitals
10 Avg\_dev MendeleevNumber Mean absolute deviation of Mendeleev Number
69 Mean NfValence Mean \# Valence f-orbitals
\[table:importance\]
: Top 15 features in noncentrosymmetry prediction
Predicting new noncentrosymmetric materials
-------------------------------------------
To identify interesting hypothetical new NLO noncentrosymmetric materials, we applied our RF-based noncentrosymmetric materials prediction model to screen the two million hypothetical materials generated by our Generative Adversarial Network (GAN) based new materials composition generator [@dan2019generative]. After predicting the probability of each candidate belonging to noncentrosymmetric materials, we sort them by the probability scores and report top 20 hypothetical noncentrosymmetric materials with 2, 3 and 4 elements here in Table \[table:Score\]. Furthermore, as we mentioned above that most borate materials are NLO materials. So we also reported top 20 borate materials with highest proability here. Please note that materials containing lanthanide and actinide elements have been filtered in these results because they are very rare.
2 element score 3 element score 4 element score Borate Score
----------------- ------- ----------- ------- ------------ ------- -------------- -------
Li4Ge 0.935 AlCuSe3 0.960 LaCeNdS4 0.975 CB2O6 0.840
Cu2S3 0.875 Cu2AsS3 0.955 LaCeNdSe4 0.965 N2B4O7 0.715
NO5 0.835 Cu3As2S4 0.945 CeNdEuS4 0.960 CB4O6 0.700
Li4Pb 0.830 Y2CeO5 0.945 CuZnInS3 0.955 S3B2O8 0.670
Li4Sn 0.800 CeTb2S4 0.935 AlCuZnTe4 0.925 CB2O4 0.665
Cl3S 0.745 DyErC3 0.930 MnNiAgSn 0.925 NCB4O6 0.665
SbC 0.740 MnDy2S4 0.925 AlCuInSe2 0.915 CoIB4O6 0.660
Pd2S 0.735 LaSm2S4 0.920 MnCoRuSn 0.915 EuB4O6 0.655
AsC 0.720 ZnGaSe2 0.920 LaNdUTe4 0.915 ZnSnO6B4 0.650
SeO6 0.715 AlCu2Te3 0.915 Cu2ZnInS6 0.900 As2B2O7 0.635
Ni3Ge2 0.715 AlCu2S4 0.910 NiCuSnSe3 0.895 PB2O6 0.630
Cl5S 0.710 CoCd2S3 0.905 MnCoAgSn 0.895 ZnB2O4 0.625
Zr2S3 0.695 NbSnIr 0.900 TiCoRhSn 0.880 SB2O6 0.620
S2O5 0.690 NbWTe4 0.900 MnFeSbO6 0.875 MnZnLaEuO6B2 0.610
LiOs 0.690 VSnAu 0.900 MnCu2AgS4 0.875 Zn3SB2O6 0.600
NH2 0.690 CrCu2S3 0.895 FeLaPbO6 0.875 Sr2TaB2O6 0.600
CrI 0.685 SnTaOs 0.890 V2Ni2RuSn2 0.875 PbB4O6 0.595
F3N 0.680 NdDySi3 0.885 MnFeBi2O6 0.875 AlB2O4 0.585
Cl6S 0.675 Dy2GeS4 0.885 TiCoBi2O6 0.870 NbRuCl2B4O6 0.585
S2O3 0.660 Mg6MnSn 0.885 SrLaNdS4 0.865 C3B4O6 0.580
\[table:Score\]
: Predicted hypothetical noncentrosymmetric materials with 2, 3, and 4 elements and predicted noncentrosymmetric borates (only top 20 are listed here)
As shown in Table \[table:Score\], the probability score range of top 20 2-element materials, 3-element materials, 4-element materials and borate materials are 0.935 to 0.660, 0.960 to 0.885, 0.975 to 0.865 and 0.885 to 0.670, respectively. It is clear that the predicted noncentrosymmetic probabilities of 3 element materials are higher than those of 2-element materials and 4-element materials. As those material are generated and hypothetical, we can only give the predicted noncentrosymmetry scores, which may guide experimental work to verify them in future research, which may further validate the effectiveness and the predictive capability of our models. More prediction results can be provided by the corresponding author upon reasonable request.
Conclusions
===========
Computational prediction of noncentrosymmetry of a given composition can be used for fast screening new nonlinear optical materials. Here we developed and evaluated two machine learning models including a Random Forest Classifier and a neural network model for computational prediction of materials noncentrosymmetry given only their composition information. By using the Magpie composition features, our best prediction model based on Random forest can achieve an accuracy of 84.8% when evaluated using 10-fold cross-validation over the Material Projects database. Further experiments showed that when the prediction model is trained only on 3-element samples, it can achieve even higher performance for the test set, which is made of mostly 3-element materials. A feature importance calculation shows the top six contribution factors for predicting noncentrosymmetry, many of which are related to the distribution of valence electrons. which is consistent with current physichochemical principles. Our developed model can be applied to discovering novel nonlinear materials as we conduct large-scale screening over two million hypothetical materials.
Author contributions
====================
conceptualization, J.H. and J.L.; methodology, J.H., S.Y., Y.Z., J.L.; software, Y.S., Y.Z., J.L.; validation, Y.S and J.L.; investigation, J.H., Y.S., J.L.; data curation, A.N. and J.L.; writing–original draft preparation, J.H., Y.S., and J.L.; writing–review and editing, J.H.,Y.S., J.L., M.H.; visualization, Y.S.; supervision, J.H. ; project administration, J.H.; funding acquisition, J.H., M.H. and J.L.
Acknowledgements
================
Research reported in this work was supported in part by the NSF and SC EPSCoR Program under award number (NSF Award \#OIA-1655740 and SC EPSCoR grant GEAR-CRP 2019-GC02). The views, perspective, and content do not necessarily represent the official views of the SC EPSCoR Program nor those of the NSF. This work was also partially supported by NSF under grant 1940099 and 1905775.
The authors declare no conflict of interest.
Data Availability:
The data required to reproduce these findings are downloaded from Materials Project database at https://materialsproject.org/.
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|
Update: Obama School Search Heats Up With Girls' Visit
The Obamaschool search is heating up: Malia, Sasha and their mom, Michelle, spent two hours yesterday morning with their mom touring Georgetown Day School, and are expected to visit the Sidwell Friends campus today. The family look-sees follow Michelle Obama's trips to the schools last week, which sparked intense debate about D.C.'s public and private education. Looks more and more like the first daughters will attend a private school; no word if the family will drop by Maret -- reportedly still in the running -- later in the week.
While it be wonderful to have the children attend public school, it may not be practical due to the security needs of the children and the impact on the school these extra measures would make. Then there is the issue of cost for all of this extra level of security.
It is likely a safer situation to be in a school very used to high profile children with high profile parents.
Too bad the media and terrorists will not give the girls the luxury to enjoy their new place on Pennsylvania Ave.
It was never a problem in the 50's and 60's growing up with children of famous parents (Sam Rayburn, etc.) No police, no photographers, just a normal high school in suburbia. Too bad that era has been replaced by a far too negative an audience.
There are now and always have been first class DC Public Elementary Schools. I went to one. There are many teachers who are dedicated, smart and caring. Security might be an issue on the secondary level but it is hard to justify security reasons to avoid public elementary school.
Amy Carter attended DC public shools and so did Obama's best bud Warren (Buffet doncha know). It is a slap in the face to the people of DC who are working so hard for the school system if Obama sends his kids to Maret or GDS or Cathedral or some other exclusive school, but it is not surprising given how what a phoney "man of the people" Obama is.
makes all the sense in the world to send the kids to private school. children of the first black president they can become a target. same with a private school but I'm inclined to believe security would be better.
still amusing to see that there are haters of OBAMA who will criticize everything he does. Your opinion is irrelevant as of now. OBAMA won and that's that.
It is a slap in the face to the people of DC who are working so hard for the school system if Obama sends his kids to Maret or GDS or Cathedral or some other exclusive school, but it is not surprising given how what a phoney "man of the people" Obama is.
This is an absurd comment. DC schools are not uniformly good and everyone knows it --most parents agonize over sending their children to public schools in the district, even at the grammar school level.
Security certainly is an issue and only someone predisposed to attack Obama would say it is a slap in the face of citizens for a President and First Lady to send their children to a private school.
Are you envious of their ability to make this choice or simply partisan?
If you are this pissy about the choice of school, you are in for a bumpy ride for at least 4 years!
Could someone, anyone, please explain this whole "security is better in a private school" trope? How is it easier to secure a multi-acre, multi-building private school campus with 500-1000 students? Most DCPS elementary schools are single buildings with at most 200-300 students.
Let's face it. The only thing that you all are afraid of is that the Obama girls will be exposed to inner city, lower class, black kids.
ophelia3 the Obama's should make their decision as to where their daughters will attend school as parents, not as two very public figures. They should not have to place their daughters in a public school just to please you or anyone else. If they were my children, the only question regarding public vs private, would be which private school they will attend!
Why would I be surprised to find partisan attacks even now that the election is over, considering the kind of commentary all the "patriotic" "Christians" flooded the internet with during the campaign cycle! Private schools that enroll children of high profile parents have sophisticated security systems, guards, personal security agents, and, in the case of the "First Children," Secret Service agents as well. The idea that a public school could afford to invest in that kind of security, or would want to subject their students, their families, and their staff and faculty to it, is kind of bizarre. Children of diplomats and other political parents are more used to security issues than most kids need to be, thankfully, so to subject them to it just to soothe partisans who will never have a kind word to say about our new President under any circumstance is pointless. If they sent the kids to public school, you would probably complain about the cost to the school district and the inconvenience to the employees, parents (security clearances to enter the building, etc.) and the kids. Some folks just want to trash talk and not think about what is safest for these children who will no doubt be subject to the same hostility and safety issues as their father.
No one is under any obligation to sacrifice their children to make a political statement, which is exactly what the pro-public shool folks here are demanding. Grow up, get over yourselves, and mind your own business.
The Obama's should choose the school they
feel is best for their two daughters.
Obviously security and privacy must be considerations but the overriding issue must be which school do they believe the girls get the best education. That school is almost certainly a private school. That is the reality of education in urban America. It would be wrong for the Obama's
to sacrifice the interests of their children to make a statement about the public education system in Washington, DC
The girls have been going to the University of Chicago Laboratory School already, if I recall correctly, and that's a private school operated by the U of C. It's not as if they were public schoolkids before. And I agree with those who say that it's better for them to attend a school that's accustomed to having the children of high-profile Washingtonians among their students. Though I suppose all the children at a public elementary or high school would benefit from heightened security.
Let me count the reasons the Obamas will not be sending their daughters to DC Public Schools.
The negatives are plentiful:
--The average school building is more than 65 years old. Fixing all the infrastructure problems is pegged at $2 billion over 20 years.
--Former Washington Teachers Union President Barbara Bullock and three others have pleaded guilty to stealing $4.6 million in union funds. Four others have been indicted. Bullock admitted embezzling more than $2.5 million during the six years she headed the union.
--D.C. students performed poorly on the latest National Assessment of Educational Progress reading and math tests for fourth- and eighth-graders.
--The city is looking at its seventh superintendent since 1995 with Michelle Rhee accepting the Chancellor position, replacing Superintendent Clifford B. Janey.
Please be serious people, and try to find fault with President-Elect Obama somewhere where you don't sound or even look so incredibly foolish.
OK. Now everybody who, if they were personally rich and had 2 beautiful daughters, would send their kids to DCPS instead of one of the best schools in this area, please, raise you hand.
You in the corner, put your hand down because you are lying. And you with your hand up, well, you're go ahead and do that. Buckling under public pressure instead of picking what is best for your kids must be a difficult decision.
The Obama's should send their children to whatever school they want - it' their choice and should not be construed as a political statement. With the number of threats already seen against Obama, I'm not sure I'd let them out of the house. There is just too many crazies that have already reared their ugly heads. I'm not sure how comfortable I would be if I was sending my children to a school already equipped with metal detectors.
Let's be honest about this. Security is not the issue. The Secret Service is perfectly capable of providing security for the girls wherever they go to school. If the Obamas choose to send them to private school, it's because they'll get a superior education there. And it's the decision most D.C. parents who have a choice would make.
The welfare of Malia and Sasha should be considerations 1, 2, ..., n. Satisfying politically-oriented critics should not be a consideration. Please, folks, try to think like PARENTS. I speak as the father of three successful grown daughters.
Okay, let me get this straight: the Republicans who demand vouchers (so they can choose their schools) and HOMESCHOOL in mass numbers (because they want to teach creationism or whatever) do NOT want the President to have a similar choice.
I think privacy is more of an issue than security. From what I've heard, Amy Carter repeatedly had the "paparazzi" tracking her every move as she went in and out of her public school. The media interest in the private lives of politicians and their families has only intensified in the last 30 years. These girls deserve to have as normal of a school life as possible and if that means sending them to private school where journalists can legitimately be banned from campus, then it's worth it. And yes, security is also an issue, especially given the number of threats, the president-elect has reportedly received.
The Obama's should follow their best judgment and send their girls to a PRIVATE school. Security will be much better and their parents will have a PEACE of mind. These politically correct folks who want the Obama's to send their girls to a public school do not have the girls' best interest at heart and only want to fulfill some fantasy in their own mind. I went to private school and I should know. DC public schools generally STINK. Improve the schools in DC first then people may feel more comfortable. Everyone else should mind their own business about the Obama's choice of school
There are now and always have been first class DC Public Elementary Schools. I went to one. There are many teachers who are dedicated, smart and caring. Security might be an issue on the secondary level but it is hard to justify security reasons to avoid public elementary school.
Amy Carter attended DC public shools and so did Obama's best bud Warren (Buffet doncha know). It is a slap in the face to the people of DC who are working so hard for the school system if Obama sends his kids to Maret or GDS or Cathedral or some other exclusive school, but it is not surprising given how what a phoney "man of the people" Obama is.
Posted by: ophelia3 | November 17, 2008 8:17 PM
-----------------------
You're so full of it. The Obamas can send their children to whatever school they feel is appropriate. Some people just have a need to be offended by everything.
basically... everyone always promotes something controversial by saying, "who cares!" until it affects them.. and all of a sudden, "NO FRIGGIN WAY!"
you can campaign on saying that the country is run down.. but we need to "INVEST" in it.. but then the bottom line comes around.. okay barack obama.. put your money where your mouth is.. and suddenly it's, "well..uh... we.. uh... we are sending our kids to private school... only because we like their school colors.. it has nothing to do with the quality of the public schools.. uhh.. yea.. that's it.. it's only because we like their team uniforms...."
yea right obama.
you realize of course.. moronic and presumptuous decisions you make in issues like this can make or break all the other POSITIVE assertions you are making to appease BOTH SIDES OF THE AISLE here and trying to win over people...
I could have sent my son to a private school but I chose my DC neighborhood public school because (1) I went to this school as a child and it still had a great reputation, good test scores and motivated principal & teachers; (2) my son could walk there (3) he had friends in the neighborhood who went there, all of whom also could have afforded private school; and (4) I wanted him to have a diverse class (this school has kids from every race, nation, economic background, creed etc.) and not be surrounded by privilege. DC has some good to great public schools. A little known secret is that high-performing graduates of DC high schools like Wilson and School Without Walls have a better chance of getting into great colleges than kids from private schools. Obama's daughters will get a great education no matter where they choose to go because no school would be allowed to let them down. And their safety will be as well protected in a public or private school. Choosing a public school would be a tremendous gesture of faith in DCPS that would do much to improve the quality of all the schools and give many DC kids a huge boost. I wonder if the Obamas realize how much good they could do for so many by making this choice.
First, the decision of which school to send Sasah and Malia to is a private decision. The Obamas have to consider the safety of Sasha and Malia. That is paramount. Should they decide to continue with private education, that is their right as parents. They should not choose public schools just for political gain or to appease America. No one should use their children in that manner. The same way that I should not be able to to tell YOU which schools your kids should go to, YOU should not be able to tell the Obamas which school their children should go to. We are living in different times than the Carter Administration not to mention the surge of threats against the Obamas, which stem largely because of the color of their skin. The Obamas are for the people, and what school they choose for their girls does not change that fact.
http://www.trailblazer-firstlady.blogspot.com
I believe in public education and would only remove my children from public school if it were not meeting their needs. The Obama girls are definitely "special needs" children. Perhaps Senator and Mrs. Obama should phone Amy Carter and ask her to share memories of attending public school during her years at the White House. I recall many photos of her trudging down the sidewalk looking resigned to the presence of the Secret Service agents, and reports that she could not go outside during recess. Many of the private schools have a large campus to provide a buffer zone and allow high-profile students more freedom.
If I were Michelle Obama, I would ask my daughters if they would prefer to stay in Chicago with their grandmother until the end of the school year. Probably they would say no, but they might like to feel they had the choice.
Oh, please, WHO CARES??? These girls are 10 and 7, why is there so much scrutiny placed on where they go to school? It's a decision between them and their parents, doesn't make them any better or worse than us regular folks. Why isn't the media more focused on other things, like how the economy totally sucks right now and we have 2 wars going on. Let these kids be!
Oh, please, really who cares? Leave these girls alone, it's a private matter. Aren't there more important things to scrutinize like the economy or the fact we have 2 wars and no money? Leave these kids be!
I am a product of DCPS and I now have a 8 and 6 year that do not attend DCPS. My family is middle class and I started out in private school, but after my parent separation I started going to public school. For those of you who believe that DCPS are the same as when Amy Cater attended them, you must have just come from out of a coma. When my son was 4 and attending a DCPS, he walked out of school during the middle of the day and came home. I had to call the school to find out how and why my son was able to just walk out and no one noticed (not even his teacher). None of my children will attend a DCPS until they have made some major changes.
My mom sent me to live with my God-mother so I can attend Wilson SHS. If DCPS are so great, why would my mom (a Black Woman) not want me to attend a school one block from my house (Cardozo).
I think that if a 4 year could walk out of school and others can walk in thru other doors, then what makes the schools so safe? Grant it, I have friends who are teachers in DCPS and they want a change in the system, but many of them graduated with me and they did not attend their nieghborhood school as well. Having only a handful of good schools is not enough and if President-Elect Obama sends his girls to a DCPS then everyone is going to want thier kids there as well because they are going to feel that is where their kids are going to get the best free education.
Oh yeah, can one of you thinks that Obama kids should go to DCPS tell me what DCPS did President Bush attend? I think I missed that and that don't seem to be an issue to you with all.
My husband and I are both products of public school systems. He was educated totally by DCPS through High School. I attended DCPS for elementary school and then on to Prince Georges County Public Schools. Our daughter attends GDS and it would be great if the Obama kids joined the GDS family. I chose not to place my child in public school because the shape they are in. We all know it. Why should the President of the United States have his kids attend DCPS to prove a point. Mayor Fentey I get putting him on the spot, but the President, come on people. Obama's kids don't attend public school now so why would they change. Face facts a lot of these "great DC elementary schools" like Murch, etc are like mini private schools because of parent involvment, etc. GDS or Sidwell would be a great choice.
"and ALSO, it SLAPS lower and middle america in the FACE because not only does barack obama have wonderful healthcare for himself and his family.. but he has his children in PRIVATE SCHOOLS...."
You're way off. My mom is middle class and I went to Sidwell Friends (and had excelled heath coverage). There are grants and financial aid available at the K-12 level for students. I'm all for the Obamas sending Malia and Sasha to a private school. Let's be honest, the quality of education is far superior to any DCPS. When I left Sidwell after 9th grade, my mom moved us to Maryland because she didn't want to send me to a DCPS and even in a MDPS, I could tell the difference between a private school education and a public school education. I was at least 2 years ahead of the rest of my class and didn't feel the lessons challenged me enough (and I took AP classes). Any parent with half a brain would want to give their kids the best possible education.
The people complaining are just fishing for something to bash Obama about and it's pathetic. Would we be having this conversation if it was Sarah Palin trying to determine where to send her kids to school?
Everyone is talking so negatively about choosing to send ones own children to private school. Isnt that what America is about?? I myself, am a product of private school, though not through privelege but by the sacrifices of my parents. Let us not forget that even if parents decide to send kids to private school they still pay the same taxes as a parent who chooses the public school system. So not only do you get the benefit of someone paying there portion of property taxes for a child that doesnt even attend that school, you have one less child in an already overcrowded environment. Its about choice and everyone even the president has the right to make the one they feel is best!!
No matter what school the Obama's choose for their kids, they will get criticized. If they have the means, and they do, then they should send them to a private school. The education and curriculum are better in private than public. Security wouldn't be an issue in either setting because of Secret Service protection. For those of you saying he is a hypocrite for sending the kids to a private school, get real. Even the mayor of DC sends his kids to a Private school. I went to Public school, not in DC thankfully, and I now send my kids to a private school for the superior education. Leave them alone.
PLEASE PEOPLE GET REAL. THE GIRLS ATTEND PRIVATE SCHOOL IN CHICAGO - SO WHY SHOULD THEY SWITCH TO PUBLIC SCHOOL. I WORK IN DC AND HAVE FRIENDS AND FAMILIES THAT ATTEND THE PUBLIC SCHOOLS - LET'S BE REAL -THEY SUCK. HOWEVER, THERE ARE A FEW THAT ARE OK.WHAT RESEARCH PROJECT ARE PEOPLE TRYING TO FULFILL AT THE COST OF THE BEST EDUCATION FOR TWO GIRLS. THE PARENTS CAN AFFORD THE BEST AND HAVE PROVIDED THE BEST BEFORE HE WAS ELECTED PRESIDENT. PEOPLE IN THIS COUNTRY ARE ALWAYS TRYING TO TELL AND INSTRUCT EVERY ONE HOW TO LIVE. IT IS EASY TO DO WHEN HIS/HER TRASH(LIFE) SUCKS/STINKS. TAKE CARE OF YOUR HOME/CHILDREN. THAT IS ALL YOU NEED TO BE CONCERNED ABOUT.
There are plenty of great DC public schools; I know because I have a daughter in one. But if the Obamas decide that a private school is best for their daughters, the issue is whether President Obama will support vouchers and charter school choices for DC parents who can't afford GDS or Sidwell. For him to choose a private school and oppose these options would suggest, at best, a blind allegiance to the NEA, and at worst, total hypocracy.
ophelia3................do you have kids ? doesn't sound like it. Amy Carter went to public school in the 70's 70's 70's 70's 70's
the climate was MUCH different then, no gangs, no crack being sold on the streets.
Malia and Sasha belong in a private school where the instructors understand their position. Not only are they the president's children but they are AFRICAN AMERICAN. don't you think the danger factor increased just a bit ? It is up to Barack and Michelle to decide where they go but i for one will not fault them for making the best decision for their children.
Well in the argument of security of the girls, private schools are leagues better. Just look at it, schools like Maret, Sidwell, and GDS all have fences and relatively CLOSED OFF CAMPUSES. this would make it alot harder for someone to just walk onto campus with a gun or something and just kill one of them. And seriously, why the hell would you want to sacrifice your daughters education just to make a point? I think all those people bashing the Obamas should take a tour of the DCPS before they say anything else. I GO TO DCPS (WIlson) and there is no way i would send my kids here. Yall must be smokin crack or something fo real. Yall are just ignorant people. leave them alone
If our new Commander in Chief was white I don't think anything would be said about the choice he made for HIS children's education. It would be expected that they would and should attend private school. Both of the Obama's are educated people and they want the same for their children and provided the same before winning this election. I wouldn't put my dog in a DC public school let alone my children. At the end of the day it is their decision and their decision alone.
My wife and I have two children in a MD public elementary school. Honestly, if we could afford to send them to private school, we would. That's not to say we're disappointed with the public school system; it's simply that the regional private schools offer a higher quality of education. If the Obamas are able to swing the costs, that's great. They should do what's best for their daughters within their means, no matter what the political circumstances. There is only one chance for doing the right thing for your children.
The girls already attended private school in Chicago. Why now that their dad is President should they have to attend Public School? That is crazy! Their life should continue the same way with Private school! |
/*
Copyright 2016 The Kubernetes Authors All rights reserved.
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
*/
package batch
import (
"k8s.io/kubernetes/pkg/api"
"k8s.io/kubernetes/pkg/api/unversioned"
)
// +genclient=true
// Job represents the configuration of a single job.
type Job struct {
unversioned.TypeMeta `json:",inline"`
// Standard object's metadata.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#metadata
api.ObjectMeta `json:"metadata,omitempty"`
// Spec is a structure defining the expected behavior of a job.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#spec-and-status
Spec JobSpec `json:"spec,omitempty"`
// Status is a structure describing current status of a job.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#spec-and-status
Status JobStatus `json:"status,omitempty"`
}
// JobList is a collection of jobs.
type JobList struct {
unversioned.TypeMeta `json:",inline"`
// Standard list metadata
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#metadata
unversioned.ListMeta `json:"metadata,omitempty"`
// Items is the list of Job.
Items []Job `json:"items"`
}
// JobTemplate describes a template for creating copies of a predefined pod.
type JobTemplate struct {
unversioned.TypeMeta `json:",inline"`
// Standard object's metadata.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#metadata
api.ObjectMeta `json:"metadata,omitempty"`
// Template defines jobs that will be created from this template
// http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#spec-and-status
Template JobTemplateSpec `json:"template,omitempty"`
}
// JobTemplateSpec describes the data a Job should have when created from a template
type JobTemplateSpec struct {
// Standard object's metadata of the jobs created from this template.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#metadata
api.ObjectMeta `json:"metadata,omitempty"`
// Specification of the desired behavior of the job.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#spec-and-status
Spec JobSpec `json:"spec,omitempty"`
}
// JobSpec describes how the job execution will look like.
type JobSpec struct {
// Parallelism specifies the maximum desired number of pods the job should
// run at any given time. The actual number of pods running in steady state will
// be less than this number when ((.spec.completions - .status.successful) < .spec.parallelism),
// i.e. when the work left to do is less than max parallelism.
Parallelism *int32 `json:"parallelism,omitempty"`
// Completions specifies the desired number of successfully finished pods the
// job should be run with. Setting to nil means that the success of any
// pod signals the success of all pods, and allows parallelism to have any positive
// value. Setting to 1 means that parallelism is limited to 1 and the success of that
// pod signals the success of the job.
Completions *int32 `json:"completions,omitempty"`
// Optional duration in seconds relative to the startTime that the job may be active
// before the system tries to terminate it; value must be positive integer
ActiveDeadlineSeconds *int64 `json:"activeDeadlineSeconds,omitempty"`
// Selector is a label query over pods that should match the pod count.
// Normally, the system sets this field for you.
Selector *unversioned.LabelSelector `json:"selector,omitempty"`
// ManualSelector controls generation of pod labels and pod selectors.
// Leave `manualSelector` unset unless you are certain what you are doing.
// When false or unset, the system pick labels unique to this job
// and appends those labels to the pod template. When true,
// the user is responsible for picking unique labels and specifying
// the selector. Failure to pick a unique label may cause this
// and other jobs to not function correctly. However, You may see
// `manualSelector=true` in jobs that were created with the old `extensions/v1beta1`
// API.
ManualSelector *bool `json:"manualSelector,omitempty"`
// Template is the object that describes the pod that will be created when
// executing a job.
Template api.PodTemplateSpec `json:"template"`
}
// JobStatus represents the current state of a Job.
type JobStatus struct {
// Conditions represent the latest available observations of an object's current state.
Conditions []JobCondition `json:"conditions,omitempty" patchStrategy:"merge" patchMergeKey:"type"`
// StartTime represents time when the job was acknowledged by the Job Manager.
// It is not guaranteed to be set in happens-before order across separate operations.
// It is represented in RFC3339 form and is in UTC.
StartTime *unversioned.Time `json:"startTime,omitempty"`
// CompletionTime represents time when the job was completed. It is not guaranteed to
// be set in happens-before order across separate operations.
// It is represented in RFC3339 form and is in UTC.
CompletionTime *unversioned.Time `json:"completionTime,omitempty"`
// Active is the number of actively running pods.
Active int32 `json:"active,omitempty"`
// Succeeded is the number of pods which reached Phase Succeeded.
Succeeded int32 `json:"succeeded,omitempty"`
// Failed is the number of pods which reached Phase Failed.
Failed int32 `json:"failed,omitempty"`
}
type JobConditionType string
// These are valid conditions of a job.
const (
// JobComplete means the job has completed its execution.
JobComplete JobConditionType = "Complete"
// JobFailed means the job has failed its execution.
JobFailed JobConditionType = "Failed"
)
// JobCondition describes current state of a job.
type JobCondition struct {
// Type of job condition, Complete or Failed.
Type JobConditionType `json:"type"`
// Status of the condition, one of True, False, Unknown.
Status api.ConditionStatus `json:"status"`
// Last time the condition was checked.
LastProbeTime unversioned.Time `json:"lastProbeTime,omitempty"`
// Last time the condition transit from one status to another.
LastTransitionTime unversioned.Time `json:"lastTransitionTime,omitempty"`
// (brief) reason for the condition's last transition.
Reason string `json:"reason,omitempty"`
// Human readable message indicating details about last transition.
Message string `json:"message,omitempty"`
}
// +genclient=true
// ScheduledJob represents the configuration of a single scheduled job.
type ScheduledJob struct {
unversioned.TypeMeta `json:",inline"`
// Standard object's metadata.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#metadata
api.ObjectMeta `json:"metadata,omitempty"`
// Spec is a structure defining the expected behavior of a job, including the schedule.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#spec-and-status
Spec ScheduledJobSpec `json:"spec,omitempty"`
// Status is a structure describing current status of a job.
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#spec-and-status
Status ScheduledJobStatus `json:"status,omitempty"`
}
// ScheduledJobList is a collection of scheduled jobs.
type ScheduledJobList struct {
unversioned.TypeMeta `json:",inline"`
// Standard list metadata
// More info: http://releases.k8s.io/release-1.3/docs/devel/api-conventions.md#metadata
unversioned.ListMeta `json:"metadata,omitempty"`
// Items is the list of ScheduledJob.
Items []ScheduledJob `json:"items"`
}
// ScheduledJobSpec describes how the job execution will look like and when it will actually run.
type ScheduledJobSpec struct {
// Schedule contains the schedule in Cron format, see https://en.wikipedia.org/wiki/Cron.
Schedule string `json:"schedule"`
// Optional deadline in seconds for starting the job if it misses scheduled
// time for any reason. Missed jobs executions will be counted as failed ones.
StartingDeadlineSeconds *int64 `json:"startingDeadlineSeconds,omitempty"`
// ConcurrencyPolicy specifies how to treat concurrent executions of a Job.
ConcurrencyPolicy ConcurrencyPolicy `json:"concurrencyPolicy,omitempty"`
// Suspend flag tells the controller to suspend subsequent executions, it does
// not apply to already started executions. Defaults to false.
Suspend *bool `json:"suspend"`
// JobTemplate is the object that describes the job that will be created when
// executing a ScheduledJob.
JobTemplate JobTemplateSpec `json:"jobTemplate"`
}
// ConcurrencyPolicy describes how the job will be handled.
// Only one of the following concurrent policies may be specified.
// If none of the following policies is specified, the default one
// is AllowConcurrent.
type ConcurrencyPolicy string
const (
// AllowConcurrent allows ScheduledJobs to run concurrently.
AllowConcurrent ConcurrencyPolicy = "Allow"
// ForbidConcurrent forbids concurrent runs, skipping next run if previous
// hasn't finished yet.
ForbidConcurrent ConcurrencyPolicy = "Forbid"
// ReplaceConcurrent cancels currently running job and replaces it with a new one.
ReplaceConcurrent ConcurrencyPolicy = "Replace"
)
// ScheduledJobStatus represents the current state of a Job.
type ScheduledJobStatus struct {
// Active holds pointers to currently running jobs.
Active []api.ObjectReference `json:"active,omitempty"`
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1. Introduction {#sec1-materials-13-01661}
===============
The fatigue behavior of disc springs can be described by models ranging widely in complexity. Simple models like the one described in \[[@B1-materials-13-01661],[@B2-materials-13-01661]\] can be implemented using spreadsheet applications, e.g., Microsoft Excel. As models become more sophisticated, the expense of building and evaluating the model rises. With the latest step in creating more complex models, the introduction of scanned geometries, superposed residual stresses, and the Walker damage parameter, the need for a novel algorithm for the determination of Walker damage in loaded disc springs has arisen.
The algorithm described in this paper is implemented in the Spring_stack Python module, which can also be used for other applications. For more information on the simulation of single disc springs without a 3D-scanned geometry or with multiple springs in one assembly, see \[[@B3-materials-13-01661],[@B4-materials-13-01661]\].
The algorithm is the first published algorithm to build and evaluate a finite element model from a 3D-scanned geometry without user interaction. It allows the user to obtain an understanding of the influence of geometric deviations that are present in a batch of disc springs on the lifetime of individual disc springs under cyclic loading. This would be impossible without the algorithm because manually conducting a finite element simulation for each disc spring is prohibitively expensive.
Introductions to the mathematical description of disc springs and to the Walker damage parameter are given in [Section 2](#sec2-materials-13-01661){ref-type="sec"}. In [Section 3](#sec3-materials-13-01661){ref-type="sec"}, an algorithm used to describe Walker damage at the surface of a 3D-scanned disc spring is presented. Its implementation is described in [Section 4](#sec4-materials-13-01661){ref-type="sec"}. An example application is presented in [Section 5](#sec5-materials-13-01661){ref-type="sec"}. We recommend that readers without programming experience read [Section 5](#sec5-materials-13-01661){ref-type="sec"} before [Section 4](#sec4-materials-13-01661){ref-type="sec"}.
2. Related Research {#sec2-materials-13-01661}
===================
2.1. Mechanical Behavior of Disc Springs {#sec2dot1-materials-13-01661}
----------------------------------------
The first mention of conical disc springs with a rectangular cross-section in the literature was Belleville's patent in 1861 \[[@B5-materials-13-01661],[@B6-materials-13-01661],[@B7-materials-13-01661]\]. The first formulas to compute the characteristic of disc springs, as well as the stresses present in disc springs under load were published by Almen and Laszlo in 1936. These formulas are still in use in today's standards \[[@B1-materials-13-01661],[@B2-materials-13-01661]\], supplemented by a friction formulation published by Curti and Montanini \[[@B8-materials-13-01661]\]. There is a variety of other approaches for the analytical assessment of disc springs, each bringing its own advantages, such as improved accuracy \[[@B9-materials-13-01661],[@B10-materials-13-01661],[@B11-materials-13-01661],[@B12-materials-13-01661],[@B13-materials-13-01661],[@B14-materials-13-01661],[@B15-materials-13-01661],[@B16-materials-13-01661],[@B17-materials-13-01661],[@B18-materials-13-01661],[@B19-materials-13-01661]\], improved simplicity \[[@B20-materials-13-01661]\], applicability for different geometries \[[@B21-materials-13-01661],[@B22-materials-13-01661],[@B23-materials-13-01661],[@B24-materials-13-01661],[@B25-materials-13-01661],[@B26-materials-13-01661],[@B27-materials-13-01661],[@B28-materials-13-01661]\], consideration of new material laws \[[@B29-materials-13-01661],[@B30-materials-13-01661],[@B31-materials-13-01661]\], offering a new concept for friction \[[@B32-materials-13-01661]\], or allowing the computation of resonance frequencies \[[@B33-materials-13-01661]\].
Analytical assessment of disc springs allows a direct understanding of the mechanical nature of disc springs and even the direct identification of links between geometric features and stresses. It also offers a sufficiently precise description of disc springs for applications like fatigue design according to EN 16983 and EN 16984 \[[@B1-materials-13-01661],[@B2-materials-13-01661]\] at low computational costs. They can also be automated easily, which makes these approaches attractive for optimization algorithms like \[[@B34-materials-13-01661],[@B35-materials-13-01661]\] and for analytical models of systems containing multiple components like \[[@B36-materials-13-01661],[@B37-materials-13-01661]\].
Since the 1980s \[[@B38-materials-13-01661]\], disc springs have also been assessed using finite element analysis (FEA). While FEA is expensive in licensing, computational cost, and training, it allows models to be adapted to new, similar problems quickly. The first FEA models were used to exceed the accuracy of the analytical approaches available at that time \[[@B39-materials-13-01661],[@B40-materials-13-01661]\]. FEA is still in use for the verification of new analytical models. FEA has extensively been used to describe residual stresses and changes in the characteristics created by plastic deformation and creep effects \[[@B41-materials-13-01661],[@B42-materials-13-01661],[@B43-materials-13-01661],[@B44-materials-13-01661],[@B45-materials-13-01661],[@B46-materials-13-01661]\]. It has also been used to describe disc springs with complex geometries \[[@B47-materials-13-01661],[@B48-materials-13-01661],[@B49-materials-13-01661],[@B50-materials-13-01661],[@B51-materials-13-01661]\] or complex load cases \[[@B52-materials-13-01661]\], as well as for disc springs made from new materials \[[@B48-materials-13-01661],[@B53-materials-13-01661],[@B54-materials-13-01661],[@B55-materials-13-01661],[@B56-materials-13-01661],[@B57-materials-13-01661]\] and to describe the behavior of assemblies containing disc springs \[[@B58-materials-13-01661],[@B59-materials-13-01661],[@B60-materials-13-01661]\].
Today, 2D models of disc springs solve quickly. An automated tool for the processing of 2D simulations of disc springs was implemented as early as 2000 \[[@B61-materials-13-01661]\]. FEA has been included in the curricula of most engineering programs. Therefore, graduates with basic FEA skills are available to companies. Disc springs have been numerically simulated by free finite element software \[[@B62-materials-13-01661]\]. These effects have led to the literature being split roughly in half between analytical formulas and FEA. The authors believe this distribution to roughly stay the same in the future because both approaches offer unique advantages and because of a legacy effect. The legacy effect is created by fatigue tests being evaluated using a certain method and the raw data like material laws and spring geometries not being documented. Furthermore, engineers are more experienced in the design of springs using analytical formulas, and this experience can only partially be used for the design of springs using FEA.
2.2. The Walker Damage Parameter {#sec2dot2-materials-13-01661}
--------------------------------
The Walker damage parameter \[[@B63-materials-13-01661]\] helps to compare the fatigue behavior of materials under different mean stresses. Compared with other approaches to the characterization of mean stress effects in steels \[[@B64-materials-13-01661],[@B65-materials-13-01661],[@B66-materials-13-01661]\], the Walker damage parameter shows a superior lifetime prediction \[[@B67-materials-13-01661]\]. In this paper, the stress-based approach is described. For the strain-based approach, see \[[@B68-materials-13-01661]\].
The Walker damage parameter $P_{Walker}$ is computed from the maximum stress $\sigma_{\max}$, the stress amplitude $\sigma_{amp}$, and the Walker exponent $\gamma$:$$P_{Walker} = \sigma_{\max}^{1 - \gamma}\sigma_{amp}^{\gamma}$$
The Walker exponent $\gamma$ is a material parameter that can be identified by fitting fatigue-curves with different mean stresses or R-ratios. A high Walker exponent implies a low sensitivity to mean stress effects, while a low Walker exponent implies a high sensitivity. If the Walker exponent $\gamma$ is fixed to 0.5, the stress Walker approach is equivalent to the stress Smith--Watson--Topper \[[@B66-materials-13-01661]\] approach.
The Walker equation requires $\sigma_{\max}$ and $\sigma_{amp}$ to be scalar values. At the surface of the disc spring, the stress state is two-dimensional; therefore, an equivalent stress must be computed. Here, the von Mises equivalent stress is used.
For proportional loads in Quadrant 1, the computation of the maximum stress $\sigma_{\max}$ and the stress amplitude $\sigma_{amp}$ from the minimum and maximum principal stresses $\sigma_{I,\max}$, $\sigma_{{II},\max}$, $\sigma_{I,\min}$, and $\sigma_{{II},\min}$ is obvious. $$\sigma_{\min} = \sqrt{\frac{\sigma_{I,\min}^{2} + \left( {\sigma_{I,\min} - \sigma_{{II},\min}} \right)^{2} + \sigma_{{II},\min}^{2}}{2}}$$ $$\sigma_{\max} = \sqrt{\frac{\sigma_{I,\max}^{2} + \left( {\sigma_{I,\max} - \sigma_{{II},\max}} \right)^{2} + \sigma_{{II},\max}^{2}}{2}}$$ $$\sigma_{amp} = 0.5 \cdot \left( {\sigma_{\max} - \sigma_{\min}} \right)$$
The stress state in disc springs however is non-proportional, especially in shot peened specimens. An example why the formulas given for the proportional case may give inconsistent results for the non-proportional case is depicted in [Figure 1](#materials-13-01661-f001){ref-type="fig"}. Given the stress states $\sigma_{a}$, $\sigma_{b}$, and $\sigma_{c}$ in Quadrant 1, the stress amplitude between $\sigma_{a}$ and $\sigma_{c}$ is equal to the stress amplitude between $\sigma_{b}$ and $\sigma_{c}$ if the von Mises equivalent stress in $\sigma_{a}$ is equal to the von Mises equivalent stress in $\sigma_{b}$. The same applies for mean stresses. In reality, the damage inflicted by cycling between $\sigma_{b}$ and $\sigma_{c}$ is smaller than the damage inflicted by cycling between $\sigma_{a}$ and $\sigma_{c}$.
To avoid the described misrepresentation of damage inflicted, the modified Manson--McKnight method \[[@B69-materials-13-01661]\] is used. Instead of computing two scalar stress states $\sigma_{\max}$ and $\sigma_{\min}$ and deducing a scalar amplitude and a scalar mean stress, a two-dimensional stress amplitude and a two-dimensional mean stress are deduced from a two-dimensional maximum and minimum stress state:$$\sigma_{I,{amp}} = 0.5 \cdot \left( {\sigma_{I,\max} - \sigma_{I,\min}} \right)$$ $$\sigma_{{II},{amp}} = 0.5 \cdot \left( {\sigma_{{II},\max} - \sigma_{{II},\min}} \right)$$ $$\sigma_{I,{mean}} = 0.5 \cdot \left( {\sigma_{I,\max} + \sigma_{I,\min}} \right)$$ $$\sigma_{{II},{mean}} = 0.5 \cdot \left( {\sigma_{{II},\max} + \sigma_{{II},\min}} \right)$$
These pairs of stress components are converted into von Mises equivalent stresses:$$\sigma_{amp} = \sqrt{\frac{\sigma_{I,{amp}}^{2} + \left( {\sigma_{I,{amp}} - \sigma_{{II},{amp}}} \right)^{2} + \sigma_{{II},{amp}}^{2}}{2}}$$ $$\sigma_{mean} = \frac{\sigma_{I,{mean}} - \sigma_{{III},{mean}}}{\sigma_{I,{mean}} + \sigma_{{III},{mean}}} \cdot \sqrt{\frac{\sigma_{I,{mean}}^{2} + \left( {\sigma_{I,{mean}} - \sigma_{{II},{mean}}} \right)^{2} + \sigma_{{II},{mean}}^{2}}{2}}$$
The maximum stress $\sigma_{\max}$ is defined with a lower bound to avoid complex numbers as Walker damage parameters. $$\sigma_{\max} = \max\left( {\sigma_{mean} + \sigma_{amp},0} \right)$$
3. The Algorithm {#sec3-materials-13-01661}
================
3.1. General Concept {#sec3dot1-materials-13-01661}
--------------------
The algorithm starts with a surface mesh (given as an .STL file) of a disc spring placed randomly in space. After aligning the disc spring approximately symmetrically around the y-axis, it imports the geometry information into a finite element application. In our implementation of the algorithm, the finite element application was used. Through the Abaqus Scripting interface \[[@B70-materials-13-01661],[@B71-materials-13-01661]\], it builds a model around the geometry data, using additional inputs like loads and friction coefficients provided by the user. It generates an output database file using the Abaqus/Standard Solver. Utilizing Abaqus/Viewer functionalities via the Scripting interface, a field of residual stresses is generated from input data. Aggregated minimum and maximum stress fields are computed by superposing the computed load stress field and the residual stress field. A Walker damage parameter field is computed from the minimum and maximum stress fields. The Walker damage parameter at the surface of the disc spring is computed and exported as tabular data.
3.2. Architecture {#sec3dot2-materials-13-01661}
-----------------
The software architecture used is called a pipeline in programming terms and resembles a production line: an instance of the class Spring_stack is passed through a series of different processing stations. The processing stations gradually transform the instance from input data to a solved finite element model with post-processed output fields and from there to easily readable tabular data and a graphical representation thereof. In programming terms, these processing stations are called methods. The flow of data is depicted in [Figure 2](#materials-13-01661-f002){ref-type="fig"}.
3.3. User-provided Inputs {#sec3dot3-materials-13-01661}
-------------------------
To conduct the inquiry described above, the algorithm requires several inputs. These inputs are provided by the user. They are comprised of an .STL file containing the triangle surface mesh of a scanned disc spring and one .JSON file for the description of the simulated physical situation and the numerical configuration of the simulation, respectively.
The .JSON file describing the simulated physical situation contains an array of parts defining the geometry, the Walker exponent $\gamma$, Young's modulus, the Poisson number, and a volumetric mass density (for numerical stability) for each. The geometry of scanned disc springs is given by means of a link to an .STL file. Plasticity may be defined for disc springs in the present implementation. However, this is not in the scope of this paper. Furthermore, the friction coefficients between springs stacked in parallel and springs stacked in series, as well as between springs and the plates and the pillar are committed. The axial load is committed as an array of paths, giving the displacements of one of the plates at the end of each time step. Measured residual stresses in the radial and tangential direction are committed for two points with different coordinates. These two points should be selected carefully by the user and ideally describe a linear model representing more measurements. Furthermore, a target value for the number of triangles of the coarsened triangle surface mesh is committed.
The .JSON file describing the numeric inputs contains several naming definitions, element types, solver options, contact and friction formulations, computing resource allowances, and flags determining whether stresses etc. are to be written to input files. Different modeling conventions for plates and pillars may be used in the current implementation. However, this is outside the scope of this paper.
4. Implementation {#sec4-materials-13-01661}
=================
4.1. Aligning the Disc Spring {#sec4dot1-materials-13-01661}
-----------------------------
In order to build a model around a part, the alignment of the part in space must be known. For example, to apply axial loads, the axial direction of the loaded part must be known. Because it makes the rest of the algorithm much easier, the input disc spring is preprocessed so it always has the same orientation. By convention, this position is in the point of origin, closely axially symmetric to the *y*-axis.
In the alignment process, the mesh $\mathcal{M}_{start}$ is processed as a set of vertices $\mathbf{V}_{start} = \left\{ \mathbf{v}_{1},\cdots,\mathbf{v}_{v} \right\}$ and a set of triangles $\mathbf{e} = \left\{ \mathbf{e}_{1},\cdots,\mathbf{e}_{e} \right\}$ connecting these vertices. The vertices $\mathbf{v}_{i,{start}} = \left( x_{i,{start}},y_{i,{start}},z_{i,{start}} \right)$ are defined in a Cartesian coordinate system $\left( x,y,z \right)$. The point set is aligned by a translation $\mathbf{t}\left( {t_{x},t_{y},t_{z},\mathbf{V}} \right)$ along and a rotation $\mathbf{A}\left( {\theta_{x},\theta_{y},\theta_{z}} \right)$ around the principal axes. $$\mathbf{V}_{aligned}\left( {\mathbf{A},\mathbf{t},\mathbf{V}_{start}} \right) = \mathbf{A}\left( {\theta_{x},\theta_{y},\theta_{z}} \right) \cdot \mathbf{t}\left( {t_{x},t_{y},t_{z},\mathbf{V}_{start}} \right)$$
The edges are defined as connectors between vertices; therefore, a geometric transformation of any mesh $\mathcal{M}$ is fully described by a geometric transformation of its vertices $\mathbf{V}$. The resulting mesh $\mathcal{M}_{aligned}$ is defined by the vertices $\mathbf{V}_{aligned}$ and the edges $\mathbf{e}$.
A feasible combination of translation $\mathbf{t}$ and rotation $\mathbf{A}$ is found by solving an optimization problem. $$\min\limits_{\mathbf{\theta}_{x,y,z},\mathbf{t}_{x,y,z}}f\left( {\mathbf{V}_{aligned}\left( {\mathbf{A},\mathbf{t},\mathbf{V}_{start}} \right)} \right)$$
To compute the objective function *f*, the transformed point cloud $\mathbf{V}_{aligned}$ is projected into the $xy$-plane, producing $\mathbf{V}_{xy} = \left\{ {\mathbf{v}_{xy,1},\cdots,\mathbf{v}_{xy,v}} \right\}$ by rotation around the *y*-axis. $\mathbf{V}_{xy}$ is computed using the coordinates of $\mathbf{V}_{aligned}$:$$\mathbf{v}_{xy,i} = \begin{pmatrix}
\sqrt{x_{i,{aligned}}^{2} + y_{i,{aligned}}^{2}} \\
z_{i,{aligned}} \\
\end{pmatrix}$$
The objective function *f* is defined as the area *A* of the convex hull of $\mathbf{V}_{xy}$. $$f = A\left( {Conv\left( \mathbf{V}_{xy} \right)} \right)$$
The convex hull is computed using the Quickhull algorithm \[[@B72-materials-13-01661],[@B73-materials-13-01661]\]. The objective function *f* is invariant to rotations around the *y*-axis. Therefore, $\theta_{y}$ is fixed to zero. To further simplify the optimization problem, it is assumed that the centroid of the aligned mesh $c\left( \mathcal{M}_{aligned} \right)$ lies in the point of origin. Although this assumption is applicable only for perfectly symmetric spring geometries, we assumed that for springs possessing minor deviations regarding their symmetry, the assumption holds true, too.
Based on this assumption, $\mathbf{t}$ is defined as translating the volumetric centroid *c* of the mesh $\mathcal{M}_{start}$ into the point of origin. $$c\left( \mathcal{M}_{translated} \right) = \left( {0,0,0} \right)$$
The computational cost for finding $\mathbf{t}$ is low because the volumetric centroid of any closed mesh $\mathcal{M}$ can be computed inexpensively.
In the following rotation $\mathbf{A}$, the mesh $\mathcal{M}_{translated}$ is only rotated around the principal axes. As the volumetric centroid lies on all three principal axes, it is invariant under said rotation $\mathbf{A}$. $$c\left( \mathcal{M}_{aligned} \right) = c\left( \mathcal{M}_{translated} \right) = \left( {0,0,0} \right)$$
By fixing the translation additionally to the rotation around the *y*-axis, the dimensionality of the optimization problem is reduced from six to two. $$\min\limits_{\mathbf{\theta}_{x,z}}f\left( {\mathbf{V}_{aligned}\left( {\mathbf{A},\mathbf{t},\mathbf{V}_{start}} \right)} \right)$$
The parameters $\theta_{x}$ and $\theta_{z}$ are calculated using the L-BFGS-B method \[[@B73-materials-13-01661],[@B74-materials-13-01661],[@B75-materials-13-01661]\].
The resulting mesh $\mathcal{M}_{aligned}$ may be aligned upside down. This being the case, it can simply be rotated by 180 degrees around the *x*-axis. To further ease the following steps, it is translated along the *y*-axis, so its lowest point is in the $xz$-plane. $$\min\left( y_{i,{postprocessed}} \right) = 0$$
The postprocessed, aligned mesh $\mathcal{M}_{postprocessed}$ is exported as an Abaqus input file (.inp).
4.2. Building the Finite Element Model {#sec4dot2-materials-13-01661}
--------------------------------------
The creation of the model is structured as a pipeline inside the pipeline depicted in [Figure 2](#materials-13-01661-f002){ref-type="fig"}. The sub-pipeline is depicted in [Figure 3](#materials-13-01661-f003){ref-type="fig"}. The allotment of tasks to processing stations (methods) along the pipeline is based on the allotment of functionalities to modules in the Abaqus/CAE environment. Each of the processing stations is customized according to input data. The following paragraphs describe the individual processing stations.
For the simulation of a single disc spring, four components are required: the disc spring itself, a guide pin, and two flat plates. The geometry of the disc spring is read from the input file generated from the 3D-scan data. The guide pin is defined as an idealized cylinder with the same height as the disc spring, and the plates are defined as idealized planes.
The plate and the guide pin part instances are defined as analytic rigid surfaces and therefore do not need to be meshed. The part instance representing the disc spring is imported as a triangle surface mesh and is converted into a volume tetrahedron mesh by the free mesher implemented in Abaqus/CAE. Mesh size cannot be controlled actively, but only by changing the mesh size of the imported surface mesh. The surface mesh size is adjusted by exporting very fine surface meshes from the 3D-scanning software GOM Scan and increasing the mesh size using the quadric edge collapse decimation algorithm \[[@B76-materials-13-01661]\]. In this application, quadric edge collapse is especially suitable because it reduces the mesh size at the flat surfaces, where the mesh may be more coarse, and keeps it nearly constant at the edges, where a fine mesh is needed.
In the approach described in this paper, the finite element analysis utilizes a purely elastic material law. Residual stresses are incorporated by superposition of the measured stresses committed by the user. This is implemented by building two axisymmetric field outputs, one for $\sigma_{{residual},\tan}$ and one for $\sigma_{{residual},{rad}}$, in Abaqus/CAE. These output fields will later be used for the computation of $\sigma_{I,\min}$, $\sigma_{I,\max}$, $\sigma_{{II},\min}$, and $\sigma_{{II},\max}$ according to Equations ([24](#FD24-materials-13-01661){ref-type="disp-formula"}) to ([27](#FD27-materials-13-01661){ref-type="disp-formula"}).
To introduce inertia and improve convergence, a volumetric mass density is defined for the disc spring. Because the spring was aligned beforehand, the assembly is straightforward. All four parts are joined in an assembly with a single coordinate system. The lower plate, the disc spring, and the guide pin are already in place. The upper plate is positioned in its place by a translation along the *y*-axis.
The lower plate and the guide pin are fixed in space, and loads are applied to the upper plate. To improve convergence, a small gravitational load is defined. No other loads are applied directly to the disc. Forces are transmitted via contacts. Surface to surface contacts are defined between the disc spring and each of the other part instances.
The Abaqus Scripting interface includes an option to customize output requests. This option is used in the algorithm to request stress and coordinate outputs. However, coordinates cannot be requested at integration points by means of the Scripting interface. Coordinate data in the integration points are necessary to compute residual stresses in the integration points.
A job instance is created to generate an input file. The input file is manipulated to create an output request for coordinate information in the integration points, and a second job instance pointing to the new input file is created. This way, a job is created that is identical to the first job except that it includes an output request for coordinate information in the integration points. The second job is converted into a system of partial differential equations and solved using Abaqus/Standard.
4.3. Computing Stresses and Walker Damage Parameters {#sec4dot3-materials-13-01661}
----------------------------------------------------
After solving the system of partial differential equations for the displacements of the nodes in the model, Abaqus/Standard computes stresses and coordinates in the integration points at different points in step-time, which refer to the minimum and the maximum load. In this section, the computation of Walker damage parameters at the surface of the disc spring between Edge II and Edge III (see [Figure 4](#materials-13-01661-f004){ref-type="fig"}) is described. Here, we may assume a plane stress state with a dominating tension component:$$\sigma_{{load},{II},\min} = 0 \vee \sigma_{{load},{III},\min} = 0$$ $$\sigma_{{load},{II},\max} = 0 \vee \sigma_{{load},{III},\max} = 0$$
For integration points close to the surface, this is approximately true. The assumption becomes more realistic with a finer mesh and is true with an infinitesimal mesh size. The minimal and maximal stress components $\sigma_{{load},{II},\min}^{\prime}$ and $\sigma_{{load},{II},\max}^{\prime}$ are redefined:$$\sigma_{{load},{II},\min}^{\prime} = \sigma_{{load},{II},\min} + \sigma_{{load},{III},\min}$$ $$\sigma_{{load},{II},\max}^{\prime} = \sigma_{{load},{II},\max} + \sigma_{{load},{III},\max}$$
In the surface of disc springs, $\sigma_{{load},I}$ points in the tangential direction and $\sigma_{{load},{II}}^{\prime}$ points in the radial direction. Residual stresses are measured in the tangential direction ($\sigma_{{residual},\tan}$) and in the radial direction ($\sigma_{{residual},{rad}}$). The input stresses for the computation of the Walker damage parameters are defined as:$$\sigma_{I,\max} = \sigma_{{load},I,\max} + \sigma_{{residual},\tan}$$ $$\sigma_{{II},\max} = \sigma_{{load},{II},\max}^{\prime} + \sigma_{{residual},{rad}}$$ $$\sigma_{I,\min} = \sigma_{{load},I,\min} + \sigma_{{residual},\tan}$$ $$\sigma_{{II},\min} = \sigma_{{load},{II},\min}^{\prime} + \sigma_{{residual},{rad}}$$
Walker damage parameters are computed according to Equations ([1](#FD1-materials-13-01661){ref-type="disp-formula"}) to ([11](#FD11-materials-13-01661){ref-type="disp-formula"}). For each surface triangle, a surface area $A_{i}$ and a Walker damage parameter $P_{{Walker},i}$ are computed. The surface Walker damage parameter is computed by averaging the Walker damage parameters of the neighboring nodes. These data pairs are saved as the set *S*.
4.4. Extracting Tabular Data {#sec4dot4-materials-13-01661}
----------------------------
The set *S* is too rich in information to be captured holistically without extraction and/or condensation. This is done by transforming the information into tabular data. Therefore, it is condensed into human readable tabular data. Each element of the set is defined as a Dirac delta function:$$f_{i}\left( P_{Walker} \right) = A_{i} \cdot \delta\left( {P_{Walker} - P_{{Walker},i}} \right)$$ The accumulated surface area $A_{acc}$ assigned to a given Walker damage parameter is computed as:$$A_{acc}\left( P_{Walker} \right) = \int_{P_{Walker}}^{\infty}\sum\limits_{i}f_{i}\left( P_{Walker} \right)dP_{Walker}$$
It describes the size of the surface area of the disc spring with a Walker damage equal to or greater than the given $P_{Walker}$. A graphical representation \[[@B77-materials-13-01661]\] of the accumulated surface area is created.
5. Example Application {#sec5-materials-13-01661}
======================
In this section, an example application of the algorithm presented in [Section 3](#sec3-materials-13-01661){ref-type="sec"} is given. A single disc spring was modelled. The surface mesh of the disc spring under investigation is presented in [Figure 5](#materials-13-01661-f005){ref-type="fig"}. The mesh was obtained using the commercially available 3D-scanning device GOM ATOS and the software GOM Scan. The number of surface triangles was already reduced for the displayed mesh, from 253,904 to 50,152. Convergence studies with different loads showed this mesh to be a good compromise between computational cost (about seven hours of CPU time on a i7-9800X and 16 GB of RAM vs. about 110 h of CPU time and 115 GB of RAM for the 253,904 surface triangle model) and accuracy (no significant bias of the Walker damage-surface area plot) \[[@B4-materials-13-01661]\].
Additionally, an idealized geometry derived from the scanned data is presented in [Figure 4](#materials-13-01661-f004){ref-type="fig"}. Edges I to IV are labelled for the reader's orientation. A major difference between both geometries is that the surfaces between Edges I and IV, as well as II and III of the idealized geometry are straight, while those of the 3D-scanned disc spring are curved. This is also visible in [Figure 6](#materials-13-01661-f006){ref-type="fig"}. Of course, the 3D-scanned geometry also was not perfectly symmetric.
In [Figure 7](#materials-13-01661-f007){ref-type="fig"}, the geometry according to the standard \[[@B1-materials-13-01661]\] is presented. It differs from the idealized geometry in having sharp edges and all angles between faces being 90°. This simplified geometry is usually utilized for the analysis of disc springs, regardless of whether analytical formulas or finite element models are used.
The triangle surface mesh was aligned and imported into Abaqus/CAE. Afterwards, it was converted into a tetrahedron volume mesh using the `generateMesh` method included in Abaqus Scripting \[[@B71-materials-13-01661]\]. The resulting linear tetrahedron C3D4 mesh was converted into a quadratic C3D10 mesh. Modified quadratic tetrahedrons C3D10M offer improved contact behaviour \[[@B78-materials-13-01661]\]; however, due to poor mesh quality, C3D10 tetrahedrons performed better in our experience. The elements were assigned a Young's modulus of 206,000 MPa, a Poisson ratio of 0.3, and a volumetric mass density of 8.05 g/mm${}^{3}$.
The volumetrically meshed disc spring was incorporated into an assembly. The load cycle was implemented in four steps. To obtain good convergence behavior, the steps were defined as dynamic steps. The implicit solver Abaqus/Standard was used. The purpose of Step 1 was to apply the lower load. Step 2 was to make sure there was no dynamic influence on the computed stresses. Step 3 was to apply the higher load. Step 4 was, again, implemented to eliminate dynamic influences. Step times for Steps 1 to 4 were 10 s, 1 s, 10 s. and 1 s. The boundary conditions were applied to the upper plate as displacements in the axial direction at a reference point; see [Figure 6](#materials-13-01661-f006){ref-type="fig"}. The prescribed displacements were 0.425 mm for Steps 1 and 2 and 1.19 mm for Steps 3 and 4. All other degrees of freedom of the reference points were fixed to zero. For the lower plate, all degrees of freedom were fixed to zero.
All contact formulations used in this model were defined as surface-to-surface contacts with a finite sliding penalty formulation and a friction coefficient of 0.01.
A job was created and committed to the solver Abaqus/Standard. The resulting output database was loaded. The resulting highest tensile load stresses in a cross-section are displayed in [Figure 8](#materials-13-01661-f008){ref-type="fig"}. The upper half of the disc spring was loaded compressively. This is why disc springs in general break between Edges II and III.
Two field outputs representing residual stresses in the tangential and radial direction were generated based on user input and the initial coordinates of the integration points (which were requested as outputs earlier). Since the measured residual stresses for the spring under investigation are confidential, the used inputs values were not the result of a measurement. They were however realistic for disc springs. The residual stresses between Edges II and III were approximated by a linear function, ignoring non-symmetric effects. The computed residual stresses were obviously wrong anywhere else. This does not matter here because the Walker damage parameter is a measure used to predict fracture. Fracture is initiated by cracks, which normally initiate from the surface between Edges II and III \[[@B79-materials-13-01661]\]. Cracks originating from between Edges I and IV are usually caused by too low preloading forces. The bias in the Walker damage parameter introduced outside the surface between Edges II and III is non-conservative. Therefore a false positive for fracture in this area can be ruled out. The computed output fields between Edges II and III are displayed in [Figure 9](#materials-13-01661-f009){ref-type="fig"}. The significantly higher residual stresses in the tangential direction compared to the radial direction are normal in disc springs because disc springs are overloaded in production to prevent plastic deformation in use, to increase lifetime, and to decrease creep effects \[[@B80-materials-13-01661],[@B81-materials-13-01661],[@B82-materials-13-01661],[@B83-materials-13-01661],[@B84-materials-13-01661],[@B85-materials-13-01661]\].
The output fields resulting from the finite element simulation describing stresses after Step 2 and the output fields describing the residual stresses were added up to compute output fields describing $\sigma_{I,\max}$ and $\sigma_{{II},\max}$. The calculation followed Equations ([24](#FD24-materials-13-01661){ref-type="disp-formula"}) and ([25](#FD25-materials-13-01661){ref-type="disp-formula"}). Field outputs describing $\sigma_{I,\min}$ and $\sigma_{{II},\min}$ were computed following Equations ([26](#FD26-materials-13-01661){ref-type="disp-formula"}) and ([27](#FD27-materials-13-01661){ref-type="disp-formula"}).
Based on these, field outputs describing the minimum and maximum equivalent stress, $\sigma_{\min}$ and $\sigma_{\max}$, were computed according to Equations ([2](#FD2-materials-13-01661){ref-type="disp-formula"}) and ([3](#FD3-materials-13-01661){ref-type="disp-formula"}); see [Figure 10](#materials-13-01661-f010){ref-type="fig"}. Especially in the minimum equivalent von Mises stress visualization, the contact line between the disc spring and the lower plate can be identified by a circle of locations with high compressive stresses.
These output fields were used to compute the output fields representing the stress amplitude $\sigma_{amp}$ according to Equation ([4](#FD4-materials-13-01661){ref-type="disp-formula"}) and finally the Walker damage parameter $P_{Walker}$ according to Equation ([1](#FD1-materials-13-01661){ref-type="disp-formula"}); see [Figure 11](#materials-13-01661-f011){ref-type="fig"}. The Walker exponent $\gamma = 0.5$ was used, which makes the Walker damage parameter equivalent to the Smith--Watson--Topper damage parameter. Compared to the other fields, the stress amplitude field was very smooth. The reason for this is that the elastic deformation of the spring partially compensated for the small asymmetries that were present. For higher load increments, the additional elastic stresses were therefore distributed more homogeneously.
The algorithm created a list of all surface triangles and computed an average Walker damage parameter $P_{{Walker},i}$, as well as a surface area $A_{i}$ for each triangle. The graph of the accumulated surface area over the Walker damage parameter was created; see [Figure 12](#materials-13-01661-f012){ref-type="fig"}. From this particular graph, the user can for example extract the surface area where the Walker damage parameter is over 750 MPa, which is 4.9 mm${}^{2}$. About half of the surface had a Walker damage parameter of zero because stresses there were purely compressive; see [Figure 12](#materials-13-01661-f012){ref-type="fig"}. This surface corresponds to the dark blue parts of the surface in [Figure 8](#materials-13-01661-f008){ref-type="fig"}. As can be seen on the graph on the right, the function starts to jump at high stresses. This is because Walker damage parameters were averaged over surface triangles. The part of the graph at very high stresses exists purely because of numerical singularities and therefore does not correspond to the fatigue behaviour of the disc spring.
The Walker damage parameter is not directly accessible through experiments. To evaluate the quality of the finite element model, a characteristic derived from a similar model (only boundary conditions were changed) was compared to a characteristic obtained in an experiment; see [Figure 13](#materials-13-01661-f013){ref-type="fig"}. As is customary for disc springs, the deflection was normalized over the deflection at which the disc spring lies flat on the ground. They agree well; especially, the correct representation of the progressive behaviour at the very start of the experiment has only been achieved by models directly implementing 3D-scanned geometry. To our knowledge, all published models directly implementing 3D-scanned geometry have been created using the algorithm presented in [Section 3](#sec3-materials-13-01661){ref-type="sec"}. The numerical characteristic is somewhat stiffer than the experimental one. This may be due to a misrepresentation of Young's modulus, which was set to the normative default of 206,000 MPa; however, tensile tests on specimens from the same batch of material and a similar heat treatment did not show a sufficient deviation in Young's modulus to use a lower value.
6. Summary {#sec6-materials-13-01661}
==========
A novel algorithm as implemented in the Spring_stack module was presented in this paper. The algorithm receives geometry data, residual stresses, material parameters, load cases, and further inputs and builds an FE model based on these. It evaluates the FE model after solving with respect to the Walker damage inflicted locally using a Manson--McKnight approach. In a post-processing step, the accumulated surface area as a function of the Walker damage parameter is computed. An example application of the algorithm was presented.
Conceptualization, M.B.G. and M.K.; methodology, M.B.G., M.K., and M.O.; software, M.B.G.; formal analysis, M.B.G., M.K., and M.O.; resources, M.O.; writing, original draft preparation, M.B.G.; writing, review and editing, M.K. and M.O.; visualization, M.B.G.; supervision, M.O.; project administration, M.K.; funding acquisition, M.O. All authors read and agreed to the published version of the manuscript.
This article was created as part of the research project AVIF A 309 'Bewertung des Einflusses realer Bauteilgeometrien auf die Beanspruchbarkeit von Tellerfedern anhand numerischer Simulation" (assessment of the influence of real geometries on the load capacity of disc springs by numerical simulation). This project is funded by Stiftung Stahlanwendungsforschung, which is part of Stifterverband für die Deutsche Wissenschaft e.V. (Donors' Association for the Promotion of Science and Humanities in Germany). The Association's mission is the promotion of research into the manufacturing and utilization of steel in Germany. The research proposal was audited by a panel of experts from the Research Association of the Working Group of the Iron- and Metal-processing Industries (AVIF), which is composed of specialists from the steelworking industry and academia. The project is accompanied by a working group from the Association of the German Spring Industry (VDFI).
The authors declare no conflict of interest.
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