text
stringlengths 0
6.48M
| meta
dict |
|---|---|
All gaskets are made from the finest rubber you can buy and are the correct duro rating. They are an EXACT replacement for the OEM SEIKO gaskets. They will pass a water resistance test assuming the case is in good condition (no corrosion, correct crown, correct crystal etc) and the gaskets are fitted correctly.
Related
Reviews (0)
Reviews
There are no reviews yet.
Only logged in customers who have purchased this product may leave a review.
By continuing to use the site, you agree to the use of cookies. more information
The cookie settings on this website are set to "allow cookies" to give you the best browsing experience possible. If you continue to use this website without changing your cookie settings or you click "Accept" below then you are consenting to this. | {
"pile_set_name": "Pile-CC"
} |
---
abstract: 'There are two formulations at non-zero chemical potential; one is the formulation that a Lagrangian includes a chemical potential, the other is the formulation that a Lagrangian does not include a chemical potential. The existence of two formulations makes a calculation complicated. The results from those formulations are not corresponding directly. This discrepancy exists in the imaginary time formalism and the real time formalism. However, since this is essentially caused by a difference of a frequency, the discrepancy vanishes by modifying the Fourier transform. We show a calculational procedure with a spectral function to understand this.'
author:
- |
S.Sasagawa and H.Tanaka\
\
Department of Physics, Rikkyo University, Tokyo 171-8501, Japan
title: Spectral Functions at finite temperature and chemical potential
---
Introduction
============
As shown in Ref. [@rf:weldon2], there is a cumbersome puzzle at finite temperature and chemical potential. The puzzle is caused by the existence of two formulations in the real time formalism at non-zero chemical potential[@rf:weldon2][@rf:kobe]. This raises a problem on a specific calculation. For example, a problem appears on a calculation of a summation at finite temperature and chemical potential. However, if the imaginary time formalism[@rf:fetter][@rf:kapsta] is consistently used, this problem does not emerge. It emerges when a method with real time is adopted. In particular, it emerges more directly in the real time formalism[@rf:weldon2][@rf:kobe]. For this reason, clarifying details of the puzzle is important to maintain the consistency between imaginary time and real time.
There are two formulations at non-zero chemical potential; one is the formulation (A) that a Lagrangian includes a chemical potential[@rf:weldon1], the other is the formulation (B) that a Lagrangian does not include a chemical potential[@rf:kobe]. A problem does not emerge as long as only either is used in the real time formalism. However, when one verifies whether a result agrees with a one from the imaginary time formalism, a problem emerges.
Since the formulation (A) is used in the imaginary time formalism, the formulation (A) with real time agrees with a result from the imaginary time formalism straightforwardly. On the other hand, the formulation (B) with real time does not agree with a result from the imaginary time formalism directly. Thus, most results in the formulation (A) and (B) are not corresponding.
We show topics that relate to a spectral function[@rf:bellac][@rf:lands]. Since it is useful to use a spectral function at finite temperature and density[@rf:mallik][@rf:wang][@rf:harada], an attention for the use might be important. We show formulations (A) and (B) in section \[sec:1\]. In section \[sec:2\], we explain the cause of the discrepancy intuitively. In section \[sec:3\], we perform a specific calculation using the formulation (A) and (B), and we show the difference on a calculational procedure.
Fermion propagator by a spectral function {#sec:1}
=========================================
Formulation (A)
---------------
The ensemble average of an operator at temperature $ T=1/\beta$ and chemical potential $\mu$ is defined as
$$\langle\hat{O}\rangle_{\beta}=Z^{-1}\mathrm{tr}[e^{-\beta(\hat{H}-\mu\hat{N})}\hat{O}], Z=\mathrm{tr}[e^{-\beta(\hat{H}-\mu\hat{N})}],$$
where $\hat{H}$ and $\hat{N}$ are a Hamiltonian and a number operator. Since we use a fermion field and the time contour $-\infty\sim+\infty$ (in our purpose it is sufficient to consider only this time contour), the time ordered propagator is defined as
$$\begin{aligned}
S(x,y)=&\theta(x_{0}-y_{0})\langle\hat{\psi}(x)\hat{\overline{\psi}}(y)\rangle_{\beta}-\theta(y_{0}-x_{0})\langle\hat{\overline{\psi}}(y)\hat{\psi}(x)\rangle_{\beta}\nonumber\\[0.21cm]
\vspace{1em}
=&\theta(x_{0}-y_{0})S^{>}(x,y)+\theta(y_{0}-x_{0})S^{<}(x,y),\label{eq:propa1}\end{aligned}$$
The advanced and the retarded green functions are defined as
$$\begin{aligned}
&S_{A}(x,y)=i\theta(x_{0}-y_{0})(S^{>}(x,y)-S^{<}(x,y)),\label{eq:adva1}\\[0.21cm]
\vspace{1em}
&S_{R}(x,y)=-i\theta(y_{0}-x_{0})(S^{>}(x,y)-S^{<}(x,y)).\label{eq:retad1}\end{aligned}$$
In addition, we define the thermal green function as
$$S_{\beta}(\tau,\bm{x},\tau^{\prime},\bm{y})=\theta(\tau-\tau^{\prime})\langle\hat{\psi}(\tau,\bm{x})\hat{\overline{\psi}}(\tau^{\prime},\bm{y})\rangle_{\beta}-\theta(\tau^{\prime}-\tau)\langle\hat{\overline{\psi}}(\tau^{\prime},\bm{y})\hat{\psi}(\tau,\bm{x})\rangle_{\beta}\label{eq:therm}$$
where $\tau$ is imaginary time $(\tau=it, 0\leq\tau\leq\beta)$.
We consider a case that the time evolution is given by
$$\hat{\psi}(t,\bm{x})=e^{i(\hat{H}-\mu\hat{N})t}\hat{\psi}(t=0,\bm{x})e^{-i(\hat{H}-\mu\hat{N})t}.$$
By this definition, the Kubo-Martin-Schwinger (KMS) condition for a c-number fermion field is
$$\psi(t)=-\psi(t-i\beta).\label{eq:KMS1}$$
The KMS condition for $S^{>}(t,\bm{x})$ is
$$S^{>}(t,\bm{x})=-S^{<}(t+i\beta,\bm{x}),$$
and $S^{>}(p)$ has the relation,
$$S^{>}(p)=\displaystyle \int_{-\infty}^{\infty}dt\int d^{3}xe^{ipx}S^{>}(t,\bm{x})=-e^{\beta p_{0}}S^{<}(p).\label{eq:1}$$
We define the spectral function in the momentum representation as[@rf:bellac][@rf:lands]
$$\rho(p)=S^{>}(p)-S^{<}(p).$$
Using this spectral function and (\[eq:1\]),
$$S^{>}(p)=(1-n_{F}(p_{0}))\rho(p),\ S^{<}(p_{0})=-n_{F}(p_{0})\rho(p),\label{eq:nf1}$$
with
$$n_{F}(p_{0})=\frac{1}{e^{\beta p_{0}}+1}.$$
The advanced, the retarded and the thermal green functions can be expressed by a spectral function. An explicit expression for spectral function is given by[@rf:fetter]
$$\displaystyle \rho(p_{0})=2\pi Z^{-1}\sum_{n,m}e^{-\beta K_{n}}(1+e^{\beta(K_{n}-K_{m})})\langle m|\overline{\psi}(0)|n\rangle\langle n|\psi(0)|m\rangle\delta(p_{0}+K_{n}-K_{m}),$$
where $K_{n}=E_{n}-\mu N_{n}.\ E_{n}$ and $N_{n}$ are eigenvalues of the operator $\hat{p}_{0}$ and $\hat{N}_{n}$ for eigenstates $|n\rangle$. We ignore spatial components for simplicity. Using this expression, the advanced, the retarded, and the thermal green functions with the spectral function are written by
$$\begin{aligned}
&S_{A}(p_{0},\displaystyle \bm{p})=-\frac{1}{2\pi}\int_{-\infty}^{\infty}dz\frac{\rho(z,\bm{p})}{p_{0}-z+i\eta},\label{eq:As1}\\[0.21cm]
\vspace{1em}
&S_{R}(p_{0},\displaystyle \bm{p})=-\frac{1}{2\pi}\int_{-\infty}^{\infty}dz\frac{\rho(z,\bm{p})}{p_{0}-z-i\eta},\label{eq:Rs1}\\[0.21cm]
\vspace{1em}
&S_{\beta}(i\displaystyle \omega_{n},\bm{p})=-\frac{1}{2\pi}\int_{-\infty}^{\infty}dz\frac{\rho(z,\bm{p})}{p_{0}-z}.\label{eq:Ts1}\end{aligned}$$
The free spectral function is deriven from the free Dirac equation. Since the Hamiltonian at a zero chemical potential is replaced by $H-\mu N$, the free Dirac equation at non-zero chemical potential is written by
$$(i\gamma_{0}\partial_{0}+\gamma_{0}\mu+i\bm{\gamma}\cdot\nabla-m)\psi(x)=0.\label{eq:dirac1}$$
Thus, (\[eq:propa1\]), (\[eq:adva1\]), and (\[eq:retad1\]) for the free theory are constructed by $\psi(x)$ satisfying (\[eq:KMS1\]) and (\[eq:dirac1\]). $S_{(0)}^{>}(t,\bm{x})$ obeys the equation,
$$(i\gamma_{0}\partial_{0}+\gamma_{0}\mu+i\bm{\gamma}\cdot\nabla-m)S_{(0)}^{>}(t,\bm{x})=0,\label{eq:S1}$$
Taking account of (\[eq:dirac1\]), we can obtain the spectral function for the free theory,
$$\rho^{(0)}(p)=2\pi((p_{0}+\mu)\gamma_{0}-\bm{\gamma}\cdot \bm{p}+m)\epsilon(p_{0}+\mu)\delta((p_{0}+\mu)^{2}-|\bm{p}|^{2}-m^{2}).\label{eq:spec1}$$
where $\epsilon(p_{0})=\theta(p_{0})-\theta(-p_{0})$.
Formulation (B)
---------------
The definitions of the green functions are the same as (\[eq:propa1\]), (\[eq:adva1\]), (\[eq:retad1\]), and (\[eq:therm\]). However, a fermion field is not same. We consider the case that the time evolution is given by
$$\hat{\psi}^{\prime}(t,\bm{x})=e^{i\hat{H}t}\hat{\psi}^{\prime}(t=0,\bm{x})e^{-i\hat{H}t}.$$
Then, the KMS condition is given by
$$\psi^{\prime}(t,\bm{x})=-e^{\beta\mu}\psi^{\prime}(t-i\beta,\bm{x}),\label{eq:KMS2}$$
and
$$S^{>\prime}(t,\bm{x})=-e^{\beta\mu}S^{<\prime}(t+i\beta,\bm{x}).$$
Then, $S^{>\prime}(p)$ has the relation,
$$S^{>\prime}(p)=\displaystyle \int_{-\infty}^{\infty}dt\int d^{3}xe^{ipx}S^{>\prime}(t,\bm{x})=-e^{\beta(p_{0}-\mu)}S^{<\prime}(p).\label{eq:2}$$
Since the definition for a spectral function is same, $S^{>\prime}(p)$ and $S^{<\prime}(p)$ can be expressed by
$$S^{>\prime}(p)=(1-n_{F}(p_{0}-\mu))\rho(p),\ S^{<\prime}(p)=-n_{F}(p_{0}-\mu)\rho(p),\label{eq:nf2}$$
with
$$n_{F}(p_{0}-\mu)=\frac{1}{e^{\beta(p_{0}-\mu)}+1}.$$
An explicit expression for the spectral function is given by[@rf:mallik]
$$\displaystyle \rho^{\prime}(p_{0})=2\pi Z^{-1}\sum_{n,m}e^{-\beta(E_{n}-\mu N_{n})}(1+e^{\beta(E_{n}-E_{m}+\mu)})\langle m|\overline{\psi}(0)|n\rangle\langle n|\psi(0)|m\rangle\delta(p_{0}+E_{n}-E_{m}).$$
If we perform the Fourier transform,
$$f(p_{0})=\displaystyle \int_{-\infty}^{\infty}dte^{ip_{0}t}f(t),\label{eq:four1}$$
the retarded green function is
$$S_{R}^{\prime}(p_{0},\displaystyle \bm{p})=-\frac{1}{2\pi}\int_{-\infty}^{\infty}dz\frac{\rho^{\prime}(z,\bm{p})}{p_{0}-z+i\eta}.\label{eq:Rs2}$$
As can be expected from (\[eq:nf2\]) and (\[eq:spec2\]), this does not agree with (\[eq:Rs1\]). On the other hand, using the different Fourier transform,
$$f(p_{0})=\displaystyle \int_{-\infty}^{\infty}dte^{ip_{0}t}e^{i\mu t}f(t),\label{eq:four2}$$
one obtains the result,
$$S_{R}(p_{0},\displaystyle \bm{p})=-\frac{1}{2\pi}\int_{-\infty}^{\infty}dz\frac{\rho^{\prime}(z,\bm{p})}{p_{0}+\mu-z+i\eta}.\label{eq:Rs3}$$
If $\rho(z,\bm{p})$ depends on $ z+\mu$, (\[eq:Rs3\]) relates to (\[eq:Rs1\]) by the change of variable (see also (\[eq:nf1\]) and (\[eq:nf2\])). Thus, using not (\[eq:four1\]) but (\[eq:four2\]), an equivalent result is derived. This replacement is equal to embedding (\[eq:rel\]) in the Fourier transform.
The free Dirac equation at non-zero chemical potential is
$$(i\gamma_{0}\partial_{0}+i\bm{\gamma}\cdot\nabla-m)\psi^{\prime}(x)=0.\label{eq:dirac2}$$
The Dirac equation in the formulation (B) is the same as the zero chemical potential form. From (\[eq:KMS1\]), (\[eq:dirac1\]), (\[eq:KMS2\]) and (\[eq:dirac2\]), $\psi(x)$ and $\psi^{\prime}(x)$ have the relation,
$$\psi(x)=e^{i\mu t}\psi^{\prime}(x).\label{eq:rel}$$
$S_{(0)}^{>\prime}(t,\bm{x})$ constructed by $\psi^{\prime}(x)$ must satisfy the equation,
$$(i\gamma_{0}\partial_{0}+\bm{\gamma}\cdot\nabla-m)S_{(0)}^{>\prime}(t,\bm{x})=0.\label{eq:S2}$$
Taking account of (\[eq:dirac2\]), we can obtain the spectral function for the free theory,
$$\rho^{(0)\prime}(p)=2\pi(p_{0}\gamma_{0}-\bm{\gamma}\cdot \bm{p}+m)\epsilon(p_{0})\delta(p_{0}^{2}-\bm{p}^{2}-m^{2}).\label{eq:spec2}$$
As pointed out above, this result is consistent with (\[eq:spec1\]).
Cause of the discrepancy {#sec:2}
========================
Obtaining a different result is understood from (\[eq:rel\]). More specifically, the different results from a plane wave solution. Plane wave solutions for (\[eq:dirac1\]) and (\[eq:dirac2\]) are
$$\psi(t)\sim e^{-i(p_{0}-\mu)t},\label{eq:plane1}$$
and
$$\psi^{\prime}(t)\sim e^{-ip_{0}t},\label{eq:plane2}$$
respectively. Thus, there is a difference of $\mu$ for a frequency (energy) between (\[eq:dirac1\]) and (\[eq:dirac2\]). Owing to this, after performing the same Fourier transform, the formulation (A) and (B) derive a different result.
Using (\[eq:plane1\]), $S^{>}(x)$ in (\[eq:S1\]) is written as
$$S^{>}(x)=\displaystyle \int\frac{d^{3}p}{(2\pi)^{3}}\frac{1}{2E_{\bm{p}}}(i\gamma_{0}(\partial_{0}-i\mu)+i\bm{\gamma}\cdot\nabla+m)e^{i\mu t}[(1-n_{F}(E_{\bm{p}}-\mu))e^{-ipx}-n_{F}(E_{\bm{p}}+\mu)e^{ipx}],\label{eq:plane11}$$
where $p_{0}=E_{\bm{p}}=\sqrt{\bm{p}^{2}+m^{2}}$. On the other hand, using Eq. (\[eq:plane2\]), $S^{>\prime}(x)$ in (\[eq:S2\]) is written as
$$S^{>\prime}(x)=\displaystyle \int\frac{d^{3}p}{(2\bm{\pi})^{3}}\frac{1}{2E_{\bm{p}}}(i\partial\hspace{-.50em}/+m)[(1-n_{F}(E_{\bm{p}}-\mu))e^{-ipx}-n_{F}(E_{\bm{p}}+\mu)e^{ipx}].\label{eq:plane21}$$
These satisfy each KMS condition. Since there is an extra factor $e^{i\mu t}$ in (\[eq:plane11\]), a different result is derived on a calculation of a Feynman diagram if one calculates straightforwardly. However, the difference is removed easily in the momentum representation using the Fourier transform (\[eq:four2\]).
Example {#sec:3}
=======
Calculation of the summation by (A)
-----------------------------------
We show a procedure of a sum over the Matsubara frequency by using a spectral function[@rf:bellac]. A sum over the Matsubara frequency can be done easily by this procedure. We calculate the summation,
$$I=T\displaystyle \sum_{m}\omega_{m}G_{\beta}(\omega_{m},E_{1})G_{\beta}(\omega_{n}-\omega_{m},E_{2}),\label{eq:sum1}$$
where $\omega_{n}$ and $\omega_{m}$ are the boson and the fermion Matsubara frequency, respectively. For simplicity, we use
$$G_{\beta}(\displaystyle \omega_{m},E_{1})=\frac{1}{-(i\omega_{m}+\mu)^{2}+E_{1}^{2}},\ G_{\beta}(\omega_{n}-\omega_{m},E_{2})=\frac{1}{-(i\omega_{n}-(i\omega_{m}+\mu))^{2}+E_{2}^{2}}.$$
$(p_{0}+\mu)\gamma_{0}-\bm{\gamma}\cdot \bm{p}+m\ \ $in (\[eq:spec1\]) is removed. The relation,
$$i\displaystyle \int_{0}^{\beta}d\tau\frac{dG(\tau,\bm{p})}{d\tau}e^{i\omega_{m}\tau}=\omega_{m}\int_{0}^{\beta}d\tau G(\tau,\bm{p})e^{i\omega_{m}\tau},\label{eq:sum2}$$
can be derived from
$$G_{\beta}(i\displaystyle \omega_{m},\bm{p})=\int_{0}^{\beta}d\tau G(\tau,\bm{p})e^{i\omega_{m}\tau},$$
and (\[eq:KMS1\]) changed by imaginary time $\tau$. Substituting (\[eq:sum2\]) into $I$, and using (\[eq:nf1\]),
$$\begin{aligned}
I=&\ iT\displaystyle \sum_{m}\int_{0}^{\beta}d\tau d\tau^{\prime}\frac{dG(\tau,E_{1})}{d\tau}G(\tau^{\prime},E_{2})e^{i\omega_{m}\tau}e^{i(\omega_{n}-\omega_{m})\tau^{\prime}}\nonumber\\[0.21cm]
\vspace{1em}
=&\ i\displaystyle \int_{-\infty}^{\infty}\frac{dp_{0}}{2\pi}\int_{-\infty}^{\infty}\frac{dk_{0}}{2\pi}k_{0}\frac{1-n_{F}(p_{0})-n_{F}(k_{0})}{i\omega_{n}-p_{0}-k_{0}}\sigma_{+}^{(0)}(k_{0},E_{1})\sigma_{-}^{(0)}(p_{0},E_{2})\label{eq:sum3}\end{aligned}$$
where
$$\sigma_{+}^{(0)}(k_{0},E_{1})=2\pi\epsilon(k_{0}+\mu)\delta((k_{0}+\mu)^{2}-E_{1}^{2}),$$
$$\sigma_{-}^{(0)}(p_{0},E_{2})=2\pi\epsilon(p_{0}-\mu)\delta((p_{0}-\mu)^{2}-E_{2}^{2})$$
Calculation of the summation by (B)
-----------------------------------
We consider the same summation (\[eq:sum1\]). However, the same Fourier transform and a spectral function are not available. Using the Fourier transform (\[eq:four2\]), (\[eq:sum2\]) turns into
$$\displaystyle \omega_{m}\int_{0}^{\beta}d\tau S(\tau,E_{1})e^{i(\omega_{m}-i\mu)\tau}=i\int_{0}^{\beta}d\tau\frac{dS(\tau,E_{1})}{d\tau}e^{i(\omega_{m}-i\mu)\tau}+i\mu\int_{0}^{\beta}d\tau S(\tau,E_{1})e^{i(\omega_{m}-i\mu)\tau}.$$
Substituting this into (\[eq:sum1\]),
$$\begin{aligned}
I=&\ iT\displaystyle \sum_{m}\int_{0}^{\beta}d\tau d\tau^{\prime}\frac{dS(\tau,E_{1})}{d\tau}S(\tau^{\prime},E_{2})e^{(i\omega_{m}+\mu)\tau}e^{(i\omega_{n}-i\omega_{m}-\mu)\tau^{\prime}}\nonumber\\[0.21cm]
\vspace{1em}
&+i\displaystyle \mu T\sum_{m}\int_{0}^{\beta}d\tau d\tau^{\prime}S(\tau,E_{1})S(\tau^{\prime},E_{2})e^{(i\omega_{m}+\mu)\tau}e^{(i\omega_{n}-i\omega_{m}-\mu)\tau^{\prime}}\nonumber\\[0.21cm]
\vspace{1em}
=&\ i\displaystyle \int_{-\infty}^{\infty}\frac{dk_{0}}{2\pi}\int_{-\infty}^{\infty}\frac{dp_{0}}{2\pi}(k_{0}-\mu)\frac{1-n_{F}(k_{0}-\mu)-n_{F}(p_{0}+\mu)}{i\omega_{n}-p_{0}-k_{0}}\sigma(k_{0},E_{1})\sigma(p_{0},E_{2}),\end{aligned}$$
where
$$\sigma(k_{0},E_{1})=2\pi\epsilon(k_{0})\delta(k_{0}^{2}-E_{1}^{2}).$$
This result agrees with (\[eq:sum3\]). Note that (\[eq:nf2\]) and (\[eq:spec2\]) are used. Simultaneous usage of the formulation (A) and the modified Fourier transform produces a incorrect result.
Spectral function in the 1-loop order
-------------------------------------
We consider the scalar boson-fermion interaction. We perform the summation without using the Fourier transform to reduce argument. Ignoring contributions of vertices, the 1-loop fermion self energy in the imaginary formalism is given by
$$\displaystyle \Sigma(i\omega_{n},\bm{p})=-T\sum_{l}\int\frac{d^{3}k}{(2\pi)^{3}}S_{\beta}(i\omega_{l},\bm{k})D_{\beta}(i\omega_{n}-i\omega_{l},\bm{p}-\bm{k}),$$
where $\omega_{n}$ and $\omega_{l}$ are the fermion Matsubara frequency. After replacing $S_{\beta}$ and $D_{\beta}$ with (\[eq:Ts1\]), performing the sum over the Matsubara frequency by a summation formula without using the Fourier transform,
$$\displaystyle \Sigma(i\omega_{n},\bm{p})=-\int\frac{d^{3}k}{(2\pi)^{3}}\int_{-\infty}^{\infty}\frac{dz_{1}}{2\pi}\frac{dz_{2}}{2\pi}\rho_{F}(z_{1},\bm{k})\rho_{B}(z_{2},\bm{p}-\bm{k})\frac{1}{i\omega_{n}-z_{1}-z_{2}}\big(n_{F}(z_{1})+n_{B}(-z_{2})\big),$$
where $n_{B}(z)=1/(e^{\beta z}-1),\ \rho_{F}$ and $\rho_{B}$ are the fermion and the boson spectral functions, respectively. After analytic continuation $ i\omega_{n}\rightarrow p_{0}+i\eta$ to an arbitrary continuous value $p_{0}$, the imaginary part is given by
$${\rm Im}\displaystyle \Sigma_{R}(p_{0},\bm{p})=\frac{1}{4\pi}\int\frac{d^{3}k}{(2\pi)^{3}}\int_{-\infty}^{\infty}dz_{1}dz_{2}\rho_{F}(z_{1},\bm{k})\rho_{B}(z_{2},\bm{p}-\bm{k})[n_{F}(z_{1})+n_{B}(-z_{2})]\delta(p_{0}-z_{1}-z_{2})$$
Using free spectral functions (\[eq:spec2\]) and $\rho_{B}^{(0)}(q)=2\pi\epsilon(q_{0})\delta(q^{2}-m_{B}^{2})$,
$$\begin{aligned}
{\rm Im}\displaystyle \Sigma_{R}(p_{0},\bm{p})=\frac{-\pi}{4E_{1}E_{2}}&\displaystyle \int\frac{d^{3}k}{(2\pi)^{3}}(E_{1}\gamma_{0}-\bm{\gamma}\cdot \bm{k}+m)\nonumber\\[0.21cm]
\vspace{1em}
&\times\big[(1-n_{F}(E_{1}-\mu)+n_{B}(E_{2}))\delta(p_{0}+\mu-E_{1}-E_{2})\nonumber\\[0.21cm]
\vspace{1em}
&\hspace{1.5em}+(n_{F}(E_{1}-\mu)+n_{B}(E_{2}))\delta(p_{0}+\mu-E_{1}+E_{2})\nonumber\\[0.21cm]
\vspace{1em}
&\hspace{1.5em}-(1-n_{F}(E_{1}+\mu)+n_{B}(E_{2}))\delta(p_{0}+\mu+E_{1}+E_{2})\nonumber\\[0.21cm]
\vspace{1em}
&\hspace{1.5em}-(n_{F}(E_{1}+\mu)+n_{B}(E_{2}))\delta(p_{0}+\mu+E_{1}-E_{2})\big]\end{aligned}$$
where $E_{1}=\sqrt{|\bm{k}|^{2}+m^{2}},\ E_{2}=\sqrt{|\bm{p}-\bm{k}|^{2}+m_{B}^{2}}$. The 1-loop fermion spectral function can be obtain by[@rf:bellac][@rf:lands]
$$\rho_{F}^{(1)}(p)=-i(\Sigma(p_{0}+i\eta)-\Sigma(p-i\eta))=2{\rm Im}\Sigma_{R}(p),$$
The delta functions in $\rho_{F}^{(1)}(p)$ obtained strictly by the imaginary time formalism are different from (50) in Ref [@rf:mallik], which used the formulation (B). Thus, the method in Ref [@rf:mallik] does not correspond to the imaginary time formalism. The source of mistake is the Fourier transform (23) in Ref [@rf:mallik]. If one wants to correspond to the imaginary time formalism, $p_{0}$ must be replaced by $ p_{0}+\mu$. However, when one does not consider corresponding to the imaginary time formalism, the method in Ref [@rf:mallik] is correct. (As above mentioned, it is nothing more than a shift of an energy.) In other words, the difference of $\mu$ is absorbed into an external line $p_{0}$ to regard $\Sigma_{R}(p_{0},\bm{p})$ as $\Sigma_{R}(p_{0}^{\prime}=p_{0}+\mu,\bm{p})$. In fact, using (\[eq:Rs3\]), the same retarded green function can be obtained.
Summary
=======
There are two formulations at non-zero chemical potential. One is the formulation (A) that a Lagrangian includes a chemical potential, the other is the formulation (B) that a Lagrangian does not include a chemical potential. The former corresponds to the imaginary time formalism more directly.
It is necessary to note that a calculational procedure in two formulations is different. For example, $S_{(0)}^{>}(x)$ in (A) has a factor $e^{i\mu t}$ as compared with $S_{(0)}^{>\prime}(x)$ in (B). This difference is important when performing a summation in imaginary time formalism and calculating a Feynman diagram in the real time formalism, etc. A wrong choice makes a mistake. Owing to this, it is necessary to understand the formulation used, combining (A) and (B) carelessly is unsafe. In particular, it is important to note that the advanced, the retarded, and the thermal green functions expressed by a spectral function are different.
\(B) does not correspond to the imaginary time formalism directly because a shift of an energy exists. This shift is removed by modifying the Fourier transform. The modified Fourier transform is equal to embedding (\[eq:rel\]) in the ordinary Fourier transform. Using the modified Fourier transform, a correspondence between (A) and (B) during a calculation becomes easier, (B) agrees with the imaginary time formalism.
Incidentally, it should be seen that (A) and (B) in the real time functional integral formulation are related by the canonical transform[@rf:weldon2]. Treating (B) as the canonical transform of (A), a source term has the factor $e^{i\mu t}$. Thus, the time ordered propagator obtained by a functional derivative in (B) corresponds to the one in (A).
[9]{}
H. A. Weldon, phys. rev. D[**76**]{} (2007), 125029.
R. L. Kobes, G. W. Semenoff and N. Weiss, Z. phys. C[**29**]{} (1985), 371.
A. L. Fetter and J. D. Walecka, [*Quantum Theory of Many-Particle Systems*]{} (McGraw-Hill, New York, 1971).
J. I. Kapsta, [*Finite Temperature Field Theory*]{} (Cambridge University Press, Cambridge, England, 1989).
H. A. Weldon, phys. rev. D[**26**]{} (1982), 1394.
M. Le Bellac, [*Thermal Field Theory*]{} (Cambridge University Press, Cambridge, England, 1996).
N. P. Landsman and Ch. G van Weert, Phys. Rep. [**145**]{} (1987) 141.
S. Mallik and S. Sarkar, Eur. Phys. J. C[**61**]{} (2009), 489.
S. Y. Wang, phys. rev. D[**70**]{} (2004), 065011.
M. Harada, Y. Nemoto and S. Yoshimoto, Prog. Theor. Phys. [**119**]{} (2008), 117.
| {
"pile_set_name": "ArXiv"
} |
Anthony Lazzaro (racing driver)
Anthony Lazzaro (born August 26, 1963) is a NASCAR and sports car racing driver. He is usually classified as a NASCAR road course ringer; however, he has made other starts in the Nextel Cup Series. He also has open-wheel oval racing experience.
Racing career
Lazzaro started in karting, winning numerous World Karting Association championships between 1987 and 1992.
Lazzaro came-up through the open-wheel ranks, first racing in the Olds Pro Series in 1993, winning at Road Atlanta, Watkins Glen, Dallas and again at Road Atlanta. He won the pole at Mid Ohio and a podium finish of third with other podium finishes at the Moroso National S2000 and at Trois Rivieres. He was also the Hooter Formula Cup Champion in 1995, winning 6 of the 14 races and 9 poles.
As a rookie in 1996, in the Toyota Atlantic Series, he won the race at the Milwaukee Mile. He won races in 1997 (Homestead-Miami Speedway) and 1998 (Road America, Laguna Seca Raceway, Houston). His rise culminated in a Toyota Atlantic championship in 1999. That year he won 4 races (Nazareth, Gateway International Raceway, Trois-Rivieres, Laguna Seca Raceway).
Lazzaro first began racing stock cars in the ARCA in 1999. At the ARCA event at the Talladega Superspeedway that year, Lazzaro was injured in a multi-car wreck late in the race after he made contact with Bil Baird and spun down to the grass, before his Thunderbird lifted off the ground and slammed the Turn 3 banking before being t-boned by Skip Smith. Lazzaro suffered a compression fracture of the thoracic T3 vertebra in the crash that eliminated half a dozen cars.
In 2000, Lazzaro raced ten Busch Series races for PPI Motorsports. He was planned to move up to Cup with the #96 McDonald's team. However, after a lack of results, he was released, and replaced by Andy Houston.
Besides the stint in the Busch Series, Lazzaro has raced mainly road course races, giving him the label of a road course ringer.
He also made 6 starts in the Indy Racing League in 2001 and 2002 for Sam Schmidt Motorsports with a best finish of 9th.
In addition, Lazzaro has had success in sports car racing. He won the GT3 class in the 24 Hours of Daytona in 1999, co-driving a Porsche 911. In 2002 he finished thrird in the SPII class after winning seven races. In 2003 he was fifth at the GT class of the American Le Mans Series, collecting six podiums with a Risi Ferrari 360. He took a GT win in the 2004 race at Lime Rock Park with Ralf Kelleners and ended seventh in the GT class. He made his debut in the 24 Hours of Le Mans in 2003, also racing a Ferrari.
In 2013, Lazzaro got three podiums in the LMP2 class of the ALMS with Extreme Speed Motorsports. He also competed in the Rolex Sports Car Series driving a GT class Ferrari 458. With four podiums, he ended fourth in the drivers championship. He switched to the SCCA World Challenge for 2014, where he races a Ferrari 458.
Motorsports career results
SCCA National Championship Runoffs
American Open Wheel
(key)1995 Hooters Formula Cup champion with 6 wins and 9 pole positions.
Indy Racing League
(key) (Races in bold indicate pole position)
Complete 24 Hours of Le Mans results
NASCAR
(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led.)
Nextel Cup Series
Busch Series
Craftsman Truck Series
ARCA Bondo/Mar-Hyde Series
(key) (Bold – Pole position awarded by qualifying time. Italics – Pole position earned by points standings or practice time. * – Most laps led.)
WeatherTech SportsCar Championship results
(key)(Races in bold indicate pole position, Results are overall/class)
References
External links
Anthony Lazzaro at Risi Competizione
Anthony Lazzaro at Driver Database
Anthony Lazzaro at Race Database
Anthony Lazzaro at Speedsport Magazine
Category:1963 births
Category:24 Hours of Daytona drivers
Category:24 Hours of Le Mans drivers
Category:American Le Mans Series drivers
Category:20th-century American racing drivers
Category:ARCA Menards Series drivers
Category:Atlantic Championship drivers
Category:IndyCar Series drivers
Category:Living people
Category:NASCAR drivers
Category:Sportspeople from Charleston, South Carolina
Category:Racing drivers from South Carolina
Category:Trans-Am Series drivers
Category:Rolex Sports Car Series drivers
Category:WeatherTech SportsCar Championship drivers
Category:SCCA National Championship Runoffs winners
Category:24 Hours of Spa drivers
Category:Blancpain Endurance Series drivers
Category:USF2000 drivers | {
"pile_set_name": "Wikipedia (en)"
} |
---
abstract: 'Motivated by a classical question of Mahler (1984), Levesley, Salp, and Velani (2007) showed that the Hausdorff measure of the set of points in the middle-third Cantor set which are $\psi$-well-approximable by triadic rationals satisfies a zero-full dichotomy. More precisely, the Hausdorff measure of this set is either zero or full according to, respectively, the convergence or divergence of a certain sum which is dependent on $\psi$. In this article, we prove an analogue of this result, obtaining a zero-full dichotomy for Hausdorff measure, in the setting of more general self-conformal sets with an appropriate adapted notion of approximation. Unlike in the work of Levesley, Salp, and Velani, we show that we are unable to apply the Mass Transference Principle due to Beresnevich and Velani (2006) in our setting. Instead, our proof relies on recasting the problem in the language of symbolic dynamics and appealing to several concepts from thermodynamic formalism, eventually enabling us to use an analogue of the mass distribution principle. In addition to demonstrating how our main result naturally extends the work of Levesley, Salp, and Velani, and complements some recent work of Baker (2018), we apply our main result to obtain a Jarník type statement for the Hausdorff measure of the set of badly approximable numbers which are “well-approximable” in some sense by fixed quadratic irrationals. This relies on the fact that the set of badly approximable numbers with partial quotients bounded above by a fixed $M \in {\mathbb{N}}$ forms a self-conformal, but not self-similar, set. Hence this is a novel application of our main result which does not follow directly from previous results in this direction.'
address:
- 'School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol, BS8 1UG, UK, and the Heilbronn Institute for Mathematical Research, Bristol, UK'
- 'Budapest University of Technology and Economics, Department of Stochastics, MTA-BME Stochastics Research Group, P.O.Box 91, 1521 Budapest, Hungary'
author:
- Demi Allen
- Balázs Bárány
title: 'Diophantine Approximation on Fractals: Hausdorff measures of shrinking targets on self-conformal sets'
---
[^1]
Introduction and Statement of Results
=====================================
The central theme of Diophantine Approximation is understanding how well real numbers can be approximated by rationals and various generalisations thereof. To this end, a classical set (and its variations and higher dimensional analogues) which has been studied extensively is the set of *$\psi$-well-approximable points*. Given an approximating function $\psi: {\mathbb{N}}\to {\mathbb{R}}^+:=[0,\infty)$, the classical set of *$\psi$-well-approximable points*, which we will denote by $W(\psi)$, is defined as follows: $$W(\psi):=\left\{x \in [0,1]: \left|x-\frac{p}{q}\right|<\psi(q) \text{ for infinitely many } (p,q) \in {{{\mathbb{Z}}}}\times {\mathbb{N}}\right\}.$$ In *metric* Diophantine Approximation, there is a particular emphasis on understanding the “size” of sets such as $W(\psi)$. For the set of $\psi$-well-approximable points, we have the following classical results due to Khintchine and Jarník regarding, respectively, Lebesgue measure and Hausdorff measure (see Section \[preliminaries\] for definitions of Hausdorff measure and dimension). Throughout we will denote the Lebesgue measure of a set $F \subset {\mathbb{R}}^d$ by $|F|$ and we will denote the Hausdorff $s$-measure of $F$ by ${{\mathcal H}}^s(F)$.
\[Khintchine’s Theorem\] Let $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$ be an approximating function. Then $$\lvert W(\psi)\rvert=\begin{cases}
0 &\text{if } \quad \sum_{q=1}^{\infty} {q\psi(q)}<\infty,\\&\\
1& \text{if } \quad \sum_{q=1}^{\infty} {q\psi(q)}=\infty\text{ and $\psi$ is monotonic.}
\end{cases}$$
\[Jarnik’s Theorem\] Let $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$ be an approximating function and let $s \in (0,1)$. Then $${{\mathcal H}}^{s}(W(\psi))=
\begin{cases}
0&\text{if}\quad\sum_{q=1}^{\infty}{q\psi(q)^s}<\infty,\\
&\\
\infty &\text{if}\quad\sum_{q=1}^{\infty}{q\psi(q)^s}=\infty\text{ and $\psi$ is monotonic.}
\end{cases}$$
The statements we give above are modern day improvements of Khintchine’s Theorem and Jarník’s Theorem. The original results published in, respectively, [@Khintchine24] and [@Jarnik31] were subject to additional technical constraints. For further details we refer the reader to, for example, [@BRVaspects] and references therein.
Taken together, Khintchine’s Theorem and Jarník’s Theorem provide a fairly comprehensive description of the “size” of the set $W(\psi)$ and so the metric description of $W(\psi)$ is essentially complete. However, the theory of how $W(\psi)$ interacts with other sets is currently somewhat less well understood and has become a highly popular topic in Diophantine Approximation. In recent years, there has been increasing interest in understanding how the set $W(\psi)$ interacts with certain fractal sets, especially Cantor-like sets, and establishing appropriate analogues of Khintchine’s Theorem and Jarník’s Theorem in these generalised settings.
Diophantine Approximation on the Cantor Set {#DA on the Cantor set}
-------------------------------------------
In his note “Some Suggestions for Further Research” [@Mahler84], Mahler posed the question:\
> *How close can irrational elements of Cantor’s set be approximated by rational numbers\
> (i) in Cantor’s set, and\
> (ii) by rational numbers not in Cantor’s set?*\
Subsequently, this question has attracted a great deal of attention and a number of papers have been published addressing Mahler’s question and natural analagous questions. One such paper which goes some way towards addressing part $(i)$ of Mahler’s question and which is, in a sense, the main motivation for the present article, is the work of Levesley, Salp and Velani [@LevSalpVel].
Before discussing the work of Levesley, Salp and Velani in more detail, for completeness, we briefly mention here several other works relating to Mahler’s question. In [@BroderickFishmanReich2011; @FishmanMerrillSimmons2018; @FishmanSimmons2014_intrinsic], Fishman and several coauthors have studied various aspects of part $(i)$ of Mahler’s question. Part $(ii)$ of Mahler’s question is considered in a complementary paper by Fishman and Simmons [@FishmanSimmons2015_extrinsic] and later by Simmons and Weiss [@SimmWeiss]. In [@Kristensen2006], Kristensen considered the problem of approximating points in *missing digit sets* by algebraic numbers (see Section \[LSV applications section\] for more information on missing digit sets). One can reformulate Mahler’s question as a question about *irrationality exponents* of points in the middle-third Cantor set, see [@Bugeaud2008]. From this point of view, the first step towards addressing Mahler’s question was the paper of Weiss [@Weiss2001] and further results of this nature have been obtained in [@Bugeaud2008; @BugeaudDurand2016; @LevSalpVel; @prohaska2019markov].
Returning to the motivating result of Levesley, Salp and Velani [@LevSalpVel], let $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$ be an approximating function and let ${{\mathcal A}}$ be any infinite subset of ${\mathbb{N}}$. We consider the following modified set of $\psi$-well-approximable points: $$W_{{{\mathcal A}}}(\psi):=\left\{x \in [0,1]: \left|x-\frac{p}{q}\right|<\psi(q) \text{ for infinitely many } (p,q) \in {{{\mathbb{Z}}}}\times {{\mathcal A}}\right\}.$$ Notice that if we were to take ${{\mathcal A}}= {\mathbb{N}}$ in the above definition then we would recover $W(\psi)$ precisely.
Throughout, let us denote by $K$ the middle-third Cantor set and let $\gamma := \operatorname{dim_H}{K} = \frac{\log{2}}{\log{3}}$. Note that $\operatorname{dim_H}{K}$ denotes the Hausdorff dimension of $K$ (see Section \[preliminaries\] for a definition). Next, consider the set ${{\mathcal B}}:=\{3^n: n=0,1,2,\dots\}$. The following is a specialised version[^2] of the main result of Levesley, Salp and Velani in [@LevSalpVel].
\[Levesley – Salp – Velani, [@LevSalpVel]\] \[LSV theorem\] Let $s \geq 0$. Then, $${{\mathcal H}}^{s}(W_{{{\mathcal B}}}(\psi) \cap K)=
\begin{cases}
0&\text{if}\quad\sum_{n=1}^{\infty}{\psi(3^n)^s \times (3^n)^{\gamma}}<\infty,\\
&\\
{{\mathcal H}}^s (K)&\text{if}\quad\sum_{n=1}^{\infty}{\psi(3^n)^s \times (3^n)^{\gamma}}=\infty.
\end{cases}$$
Recall that ${{\mathcal H}}^s(F)$ denotes the Hausdorff $s$-measure of a set $F \subset {\mathbb{R}}^d$ (see Section \[preliminaries\] for a definition).
The main motivating aim of the current paper was to provide a generalisation of Theorem \[LSV theorem\] for more general iterated function systems. The kinds of sets which this problem naturally leads us to consider bear a striking resemblance to so-called *shrinking target problems*.
Shrinking Target Problems
-------------------------
In so-called *shrinking target problems* the basic idea is that we have a point, say $y \in X$ where $X$ is a metric space, and a decreasing sequence $(r_n)_{n \in {\mathbb{N}}}$ of real numbers. The balls $B_n = B(y,r_n)$ are our *targets*. Given a map $T: X \to X$, we are interested in the set of points $x \in X$ for which $T^nx$ hits the target $B_n$ infinitely often; that is, we are interested in the set $$\begin{aligned}
{{\mathcal B}}(y):&=\{x \in X: T^nx \in B_n \text{ for infinitely many } n \in {\mathbb{N}}\} \\
&= \limsup_{n \to \infty}{T^{-n}B_n}.\end{aligned}$$
A related problem which is also of interest is when we have *moving targets*. Given a map $T: X \to X$, a point $y \in X$, and a (decreasing) sequence of real numbers $(r_n)_{n \in {\mathbb{N}}}$, in this case we consider the set of points which are hit infinitely often by the *targets* $B'_n = B(T^ny, r_n)$. That is, we are interested in the set $$\begin{aligned}
{{\mathcal B}}(T):&= \{x \in X: x \in B'_n \text{ for infinitely many } n \in {\mathbb{N}}\} \\
&=\limsup_{n \to \infty}{B'_n}.\end{aligned}$$ Another related problem is study of the *recurrence set*, when we consider the set $${{\mathcal B}}_r:= \{x \in X: T^nx \in B(x,r_n) \text{ for infinitely many } n \in {\mathbb{N}}\}$$ with a (decreasing) sequence of real numbers $(r_n)_{n \in {\mathbb{N}}}$.
The study of *shrinking target problems* was initiated by Hill and Velani [@HillVelanifirst] in 1995. Since then, many more authors have contributed to the study of *shrinking targets*, *moving targets*, and *recurrence sets*. To name but a few, see [@baker2019quantitative; @HillVelanifirst; @HillVelanitori; @Jarvenpaa_et_al_2017; @Jarvenpaa2017; @PerssonRams] and references within.
Recasting the set $W_{{{\mathcal A}}}(\psi)$ in the language of shrinking targets, Wang, Wu and Xu [@WWX2017] were able to prove an “inhomogeneous” counterpart to Theorem \[LSV theorem\]. For their purposes, fix $X=K$ to be the middle-third Cantor set and consider the map $T_3: K \to K$ defined by $$T_3x = 3x \mod 1.$$ For a map $\varphi: {\mathbb{N}}\to {\mathbb{R}}^+$ and a fixed $y \in K$, let $$\begin{aligned}
{{\mathcal S}}(y,\varphi):&= \{x \in K: |T_3^nx - y| < \varphi(n) \text{ for infinitely many } n \in {\mathbb{N}}\} \\
&= \limsup_{n \to \infty}{T_3^{-n}B(y,\varphi(n))}.\end{aligned}$$
Recall that $\gamma = \frac{\log{2}}{\log{3}}$. In [@WWX2017], Wang, Wu and Xu established the following statement[^3] regarding the Hausdorff measure of the set ${{\mathcal S}}(y,\varphi)$.
\[WWX theorem\] Let $s < \gamma$. Then, for any $y \in K$, $${{\mathcal H}}^{s}({{\mathcal S}}(y,\varphi))=
\begin{cases}
0&\text{if}\quad\sum_{n=1}^{\infty}{\left(\frac{\varphi(n)}{3^n}\right)^s \times (3^n)^{\gamma}}<\infty,\\
&\\
{{\mathcal H}}^s (K)&\text{if}\quad\sum_{n=1}^{\infty}{\left(\frac{\varphi(n)}{3^n}\right)^s \times (3^n)^{\gamma}}=\infty.
\end{cases}$$
When $\varphi(n)= 3^n\psi(3^n)$, we have that ${{\mathcal S}}(0,\varphi) = W_{{{\mathcal A}}}(\psi)$ and so, at least when $s < \gamma$, Theorem \[WWX theorem\] gives an inhomogeneous extension of Theorem \[LSV theorem\]. In recent years, several other authors have also studied the problem of shrinking targets on fractals. For example, Chernov and Kleinbock [@CherKlein] studied the measure of shrinking target sets with respect to ergodic measures, Chang, Wu and Wu [@ChangWuWu2019] very recently studied the problem of shrinking targets on linear iterated iterated function systems consisting of maps with equal contraction ratios, Koivusalo and Ramírez [@KoivusaloRamirez] considered shrinking targets on self-affine sets, the second author and Rams computed the Hausdorff dimension for certain shrinking targets on Bedford-McMullen carpets [@BaranyRams2018], and Seuret and Wang considered some related problems in the setting of conformal iterated function systems [@SeuretWang].
The main result (Theorem \[thm:main\]) of this paper constitutes an analogue of Theorem \[LSV theorem\] for self-conformal iterated function systems. As will become evident throughout the proof of Theorem \[thm:main\], it will often be most useful to view the sets under consideration as appropriate shrinking target sets. Before stating our main result in Section \[statement of results\], we will first establish a number of necessary preliminaries and notation which will be used throughout.
Some Preliminaries and Notation {#preliminaries}
-------------------------------
### Hausdorff measure and dimension
Here we briefly recall the definitions of *Hausdorff $s$-measure* and *Hausdorff dimension*. Suppose $F \subset {\mathbb{R}}^d$ and let $\rho > 0$ be a real number. A *$\rho$-cover for $F$* is a countable collection of balls $\{B_i\}_{i \in {\mathbb{N}}}$ such that $F \subset \bigcup_{i \in {\mathbb{N}}}{B_i}$ and $r(B_i) < \rho$ for all $i \in {\mathbb{N}}$. Here, $r(B)$ denotes the radius of a ball $B \subset {\mathbb{R}}^d$. Given a real number $s \geq 0$, we define the *$\rho$-approximate $s$-dimensional Hausdorff measure of $F$*, which we denote by ${{\mathcal H}}_{\rho}^s(F)$, as follows: $${{\mathcal H}}_{\rho}^s(F) = \inf\left\{\sum_{i\in{\mathbb{N}}}{r(B_i)^s} : \{B_i\}_{i \in {\mathbb{N}}} \text{ is a $\rho$-cover for $F$}\right\}.$$ The *Hausdorff $s$-measure of $F$*, denoted by ${{\mathcal H}}^s(F)$, is defined to be $${{\mathcal H}}^s(F) := \lim_{\rho \to 0}{{{\mathcal H}}_{\rho}^s(F)}.$$ The *Hausdorff dimension of $F$*, $\operatorname{dim_H}{F}$, is given by $$\operatorname{dim_H}{F} := \inf\{s \geq 0: {{\mathcal H}}^s(F)=0\}.$$ For further details regarding Hausdorff measure and dimension we refer the reader to [@falconerfractalgeom].
### Conformal iterated function systems
Here we collect together some concepts and notation relating to iterated function systems which will be used throughout. Fix $d \in {\mathbb{N}}$ and let $D\subset{\mathbb{R}}^d$ be a simply connected compact set such that $D=\overline{D^o}$. Here we denote the interior of a set $F \subset {\mathbb{R}}^d$ by $F^o$ and we denote its closure by $\overline{F}$. We say that a map $f\colon D\mapsto D$ is contracting if there exists a constant $0<c<1$ such that $$\|f(x)-f(y)\|\leq c\|x-y\|$$ for every $x,y\in D$. Throughout, $\|\cdot\|:{\mathbb{R}}^d \to {\mathbb{R}}^+$ will be any fixed norm on ${\mathbb{R}}^d$.
Let $\Lambda$ be a finite set of symbols and let $\Phi=\{f_i\colon D\mapsto D\}_{i\in\Lambda}$ be a finite set of contracting mappings. We call $\Phi$ an *iterated function system* (IFS). Hutchinson [@Hutchinson] showed that there exists a unique non-empty compact set $X$ such that $$X=\bigcup_{i\in\Lambda}f_i(X).$$ We call $X$ the *attractor* of $\Phi$.
We say that a mapping $f\colon D\mapsto D$ is $C^{1+\varepsilon}$-conformal if the derivative $f'(x)$ is Hölder continuous with exponent $\varepsilon>0$ and for every $x\in D$ and $y\in{\mathbb{R}}^d$, $$\|f'(x)y\|=\|f'(x)\|\|y\|.$$ Recall that a mapping $f: D \to {\mathbb{R}}$ is *Hölder continuous with exponent $\varepsilon$* if there exists a constant $C>0$ such that for all $x,y \in D$ we have $$\|f(x)-f(y)\| \leq C\|x-y\|^{\varepsilon}.$$
Using the conformality of $f$ and the simply connectedness of $D$, for every $x,y\in D$ there exist $\xi,\xi'\in D$ such that $$\label{MVT}
\|f'(\xi)\|\|x-y\|\leq\|f(x)-f(y)\|\leq\|f'(\xi')\|\|x-y\|.$$
Throughout the paper, we will always assume that the IFS $\Phi$ consists of $C^{1+\varepsilon}$-conformal mappings. In this case, we refer to $\Phi$ as a *conformal iterated function system* and we call the attractor of the conformal IFS $\Phi$ a *self-conformal set*. In the special case when the IFS consists of similarities, i.e. there exist constants $0<c_i<1$ for each $i \in \Lambda$ such that for all $x,y \in D$ we have $$\|f_i(x)-f_i(y)\|=c_i\|x-y\|,$$ we say that $\Phi$ is a *self-similar iterated function system* and that the attractor is a *self-similar set*. Clearly, self-similar sets are self-conformal.
Throughout this paper, we will also assume that $\Phi$ satisfies the *open set condition*. We say that $\Phi$ satisfies the open set condition (OSC) if there exists an open set $U\subset D$ such that $$f_i(U)\subset U \quad \text{for every } i \in \Lambda,$$ $$\text{and} \quad f_i(U) \cap f_j(U)=\emptyset \quad \text{for all }i\neq j \in \Lambda.$$ If the attractor $X$ of $\Phi$ satisfies the even stronger condition that $$f_i(X) \cap f_j(X) = \emptyset \quad \text{for all }i\neq j \in \Lambda,$$ we say that $X$ satisfies the *strong separation condition*. Moreover, by the compactness of $D$, there exist constants $0<a_{\min}\leq a_{\max}<1$ such that $$\begin{aligned}
\label{f' bounds}
a_{\min}\leq\min_{x\in D}\|f_i'(x)\|\leq\max_{x\in D}\|f_i'(x)\|\leq a_{\max}\end{aligned}$$ for every $i\in\Lambda$.
For more details on the basic theory of iterated function systems see, for example, [@falconerfractalgeom].
\[Cantor set example\] The middle-third Cantor set, $K$, is the attractor of the iterated function system $\Phi_{K}:=\{f_i:[0,1] \to [0,1]\}_{i\in\{1,2\}}$ consisting of the similarities $f_1(x)=\frac{1}{3}x$ and $f_2(x)=\frac{1}{3}x+\frac{2}{3}$. Thus, $K$ is a self-similar (and, therefore, also self-conformal) set. Also notice that $\Phi_K$ satisfies the open set condition.
Let us denote by $\Lambda^*$ the set of all finite sequences formed of the symbols in $\Lambda$, i.e. $$\Lambda^*=\bigcup_{n=0}^{\infty}\Lambda^n.$$ We will denote the length of ${\mathbf{i}}\in\Lambda^*$ by $|{\mathbf{i}}|$. We will also use the following shorthand notation: $$f_{\mathbf{i}}=f_{i_1}\circ f_{i_2}\circ\cdots\circ f_{i_{|{\mathbf{i}}|}}, \quad \text{and} \quad X_{{\mathbf{i}}}=f_{{\mathbf{i}}}(X).$$ We will adopt the convention that $f_\emptyset(x)=x$.
Combining with the chain rule, we have that for any ${\mathbf{i}}\in \Lambda^*$ that $$\begin{aligned}
\label{f' composition bounds}
a_{\min}^{|{\mathbf{i}}|}\leq\min_{x\in D}\|f_{{\mathbf{i}}}'(x)\|\leq\max_{x\in D}\|f_{{\mathbf{i}}}'(x)\|\leq a_{\max}^{|{\mathbf{i}}|}.\end{aligned}$$
The IFS $\Phi$ satisfies the so-called *bounded distortion property*. That is, there exists a constant $C \geq 1$ such that for every ${\mathbf{i}}\in\Lambda^*$ and for all $x,y\in X$ we have $$\label{eq:boundeddist}
C^{-1}\leq\dfrac{\|f_{{\mathbf{i}}}'(x)\|}{\|f_{\mathbf{i}}'(y)\|}\leq C.$$ For a proof of this fact we refer the reader to work of Simon, Solomyak and Urbański [@SSU1 Lemma 5.8].
Combining with the bounded distortion property we see that, for every $Y\subseteq D$, $\xi \in X$ and ${\mathbf{i}}\in \Lambda^*$, $$\begin{aligned}
\label{diameter comparisons}
C^{-1}{\mathrm{diam}}(f_{{\mathbf{i}}}(Y)) \leq \|f_{{\mathbf{i}}}'(\xi)\|{\mathrm{diam}}(Y) \leq C{\mathrm{diam}}(f_{{\mathbf{i}}}(Y)),\end{aligned}$$ where $C$ is the constant appearing in .
The *pressure function* $P\colon{\mathbb{R}}\mapsto{\mathbb{R}}$ corresponding to the IFS $\Phi$ is defined as follows, $$\label{eq:defP}
P(s)=\lim_{n\to\infty}\frac{1}{n}\log\sum_{{\mathbf{i}}\in\Lambda^n}\|f_{{\mathbf{i}}}'(x)\|^s,$$ where $x\in X$. Note that by the bounded distortion property , the function $P$ is independent of the choice of $x\in X$. It is easy to see that $P$ is strictly monotonically decreasing and continuous.
Peres, Rams, Simon and Solomyak [@PRSS Theorem 1.1] showed that $\Phi$ satisfies the open set condition if and only if $$\label{eq:finitemeas}
0<\mathcal{H}^d(X)<\infty,$$ where $d$ is the unique solution of the equation $P(d)=0$. In this case $d=\operatorname{dim_H}X$. This result was later generalized by Käenmäki and Rossi [@KaenRoss Proposition 3.5].
Statement of Results {#statement of results}
--------------------
Let $\Phi$ be a conformal iterated function system as described in the previous section. Suppose that $X$ is the attractor of $\Phi$. Given an approximating function $\Psi\colon\Lambda^*\mapsto{\mathbb{R}}^+$, for each $x\in X$ we will be interested in the Hausdorff measure of the set $$\label{eq:shrinking1}
W(x,\Psi):=\{y\in X:\|y-f_{\mathbf{i}}(x)\|<\Psi({\mathbf{i}})\text{ for infinitely many }{\mathbf{i}}\in\Lambda^*\}.$$
The Hausdorff dimension of $W(x,\Psi)$ was (implicitly) established by Hill and Velani in [@HillVelanifirst] for $\Psi: \Lambda^* \to {\mathbb{R}}^+$ of the form $$\begin{aligned}
\label{Psi special form}
\Psi({\mathbf{i}})={\mathrm{diam}}(X_{{\mathbf{i}}})\psi(|{\mathbf{i}}|)\end{aligned}$$ where $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$ is any monotonic decreasing approximating function. To state their result, let us define the the *shrinking rate* of a function $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ as $$\alpha=\alpha(\psi)=\liminf_{n\to\infty}-\frac{\log\psi(n)}{n}.$$ Note that $\alpha$ can be $+\infty$. The following theorem can be deduced from [@HillVelanifirst Theorem 7].
\[thm:hillvelani\] Let $\Phi$ be a conformal iterated function system with attractor $X$ satisfying the open set condition. Let $x\in X$ and let $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ be a monotonic decreasing function. Denote by $\alpha:=\alpha(\psi)$ the shrinking rate of $\psi$. Then, for the approximating function $\Psi({\mathbf{i}})=\mathrm{diam}(X_{\mathbf{i}})\psi(|{\mathbf{i}}|)$ and the set $W(x,\Psi)$ as defined in , we have $$\operatorname{dim_H}(W(x,\Psi))=\begin{cases}
0 & \text{if }\alpha=\infty, \\
s & \text{if }0\leq\alpha<\infty,
\end{cases}$$ where $s$ is the unique root of the equation $P(s)=s\alpha$.
More recently, Baker has made progress towards understanding the Hausdorff measure of the set $W(x,\Psi)$. More precisely, the next theorem can be deduced from Baker [@baker Theorem 1.4].
\[thm:baker\] Let $\Phi$ be a conformal iterated function system with attractor $X$ satisfying the open set condition. Let $x\in X$ and let $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ be a monotonic decreasing function. Let $\Psi({\mathbf{i}})=\mathrm{diam}(X_{\mathbf{i}})\psi(|{\mathbf{i}}|)$ and let $W(x,\Psi)$ be as defined in . Then $$\mathcal{H}^{d}(W(x,\Psi))=\begin{cases}
0 & \text{if }\sum_{{\mathbf{i}}\in\Lambda^*}\Psi({\mathbf{i}})^{d}<\infty,\\&\\
\mathcal{H}^{d}(X) & \text{if }\sum_{{\mathbf{i}}\in\Lambda^*}\Psi({\mathbf{i}})^{d}=\infty,
\end{cases}$$ where $d=\operatorname{dim_H}X$ is the unique solution of $P(d)=0$.
By combining the Mass Transference Principle (Theorem \[mtp\]) due to Beresnevich and Velani [@bervel] with Theorem \[thm:baker\], Baker also derives the following result in [@baker Theorem 5.1].
\[thm:baker mtp\] Let $\Phi$ be a conformal iterated function system with attractor $X$ satisfying the open set condition. Given $x \in X$ and $\Psi: \Lambda^* \to {\mathbb{R}}^+$, let $W(x,\Psi)$ be defined as in .
(i) [Let $s>0$ and suppose that $$\sum_{{\mathbf{i}}\in \Lambda^*}{\Psi({\mathbf{i}})^s} < \infty.$$ Then, ${{\mathcal H}}^s(W(x,\Psi))=0$ for all $x \in X$.]{}
(ii) [Let $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$ be a monotonic decreasing approximating function and suppose that $\Psi({\mathbf{i}})={\mathrm{diam}}(X_{{\mathbf{i}}})\psi(|{\mathbf{i}}|)$. Then, if $$\sum_{{\mathbf{i}}\in \Lambda^*}{\Psi({\mathbf{i}})^{\operatorname{dim_H}(X)}} = \infty$$ we have $${{\mathcal H}}^{s}(W(x,\Psi^{\frac{\operatorname{dim_H}{X}}{s}})) = {{\mathcal H}}^{s}(X)$$ for all $x \in X$ and $s \leq \operatorname{dim_H}{X}$. Here, $\Psi^t({\mathbf{i}})=\Psi({\mathbf{i}})^t=({\mathrm{diam}}(X_{{\mathbf{i}}})\psi(|{\mathbf{i}}|))^t$.]{}
We note that Theorem \[thm:baker mtp\] $(i)$ holds for any iterated function systems, not just those which are conformal and satisfy the open set condition. While we will only be concerned here with self-conformal sets satisfying the open set condition, for completeness we remark that Baker has also made progress in [@baker2019overlapping] more generally towards establishing analogues of Theorems \[thm:baker\] and \[thm:baker mtp\] when the iterated function systems under consideration do not satisfy the open set condition.
Complementary to the Hausdorff dimension result of Hill and Velani (Theorem \[thm:hillvelani\]) and the Hausdorff measure results of Baker (Theorems \[thm:baker\] and \[thm:baker mtp\]), the main result of the present paper is the following theorem which provides a more complete characterisation of the Hausdorff measure of the set $W(x,\Psi)$ when $\Psi$ takes the form given in .
\[thm:main\] Let $\Phi$ be a conformal iterated function system with attractor $X$ satisfying the open set condition. Let $x\in X$ and let $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ be a monotonic decreasing function. Let $\Psi({\mathbf{i}})=\mathrm{diam}(X_{\mathbf{i}})\psi(|{\mathbf{i}}|)$ and let $W(x,\Psi)$ be as in . Then, for any open ball $B\subset{\mathbb{R}}^d$, $$\mathcal{H}^s(W(x,\Psi)\cap B)=\begin{cases}
0 & \text{if }\sum_{{\mathbf{i}}\in\Lambda^*}\Psi({\mathbf{i}})^s<\infty,\\&\\
\mathcal{H}^s(X\cap B) & \text{if }\sum_{{\mathbf{i}}\in\Lambda^*}\Psi({\mathbf{i}})^s=\infty.
\end{cases}$$
In Theorem \[thm:baker mtp\] $(ii)$, Baker obtains the Hausdorff $s$-measure of the set $W(x,\Psi^{\frac{\operatorname{dim_H}{X}}{s}})$. That is, as $s$ varies so does the set for which the Hausdorff $s$-measure is obtained. By comparison, in Theorem \[thm:main\] we are able to vary $s$ and obtain the Hausdorff $s$-measure of $W(x,\Psi)$ without any modification to the function $\Psi$. The reason for this difference is that the strategy Baker uses in [@baker] to prove Theorem \[thm:baker mtp\] $(ii)$ involves an application of the Mass Transference Principle and this necessitates the slight modification that we see of the set under consideration. Actually, one might expect that the natural strategy for proving Theorem \[thm:main\] would also be to use the Mass Transference Principle. Indeed, the Mass Transference Principle plays a crucial role in [@LevSalpVel] in the proof of Theorem \[LSV theorem\]. However, interestingly, we show in Section \[sec:nomasstrans\] that the Mass Transference Principle cannot be applied in our setting to prove Theorem \[thm:main\]. That said, although we are unable to use the Mass Transference Principle directly, it is worth remarking that the overarching strategy we use for the proof of Theorem \[thm:main\] is still inspired by some of the underlying ideas in the proof of the Mass Transference Principle in [@bervel].
Some Applications/Consequences of Theorem \[thm:main\]
======================================================
In this section we discuss some applications and consequences of our main theorem (Theorem \[thm:main\]). Since the main aim of this paper was to provide a generalisation of Theorem \[LSV theorem\] to more general self-conformal iterated function systems, we first demonstrate in Section \[LSV applications section\] how Theorem \[LSV theorem\] can be deduced from Theorem \[thm:main\], albeit subject to an additional monotonicity condition which was not present in the original result of Levesley, Salp and Velani [@LevSalpVel]. Although we have to impose an additional monotonicity condition to deduce Theorem \[LSV theorem\], our result does provide some other advantages compared with Theorem \[LSV theorem\]. In Section \[LSV applications section\], we additionally discuss more general missing digit sets and record a higher dimensional analogue of the results of Levesley, Salp and Velani in [@LevSalpVel]. In Section \[Bad and QI application section\], we show how Theorem \[thm:main\] can be applied to study a problem related to approximating badly approximable numbers by quadratic irrationals. We obtain a Jarník type statement in our particular setting which, to the best of our knowledge, has not previously been considered.
The Cantor Set and Other Missing Digit Sets {#LSV applications section}
-------------------------------------------
We begin this section by showing how Theorem \[LSV theorem\] may be deduced from Theorem \[thm:main\], subject to an additional constraint on the monotonicity of the approximating function $\psi$. In particular, assume that $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$ is such that $3^n\psi(3^n)$ is monotonically decreasing.
Recall from Example \[Cantor set example\] that the middle-third Cantor set, $K$, is the attractor of the self-similar (and thus conformal) iterated function system $\Phi_{K}:=\{f_i:[0,1] \to [0,1]\}_{i\in\{1,2\}}$ consisting of the similarities $f_1(x)=\frac{1}{3}x$ and $f_2(x)=\frac{1}{3}x+\frac{2}{3}$.
Next, let $\varphi: {\mathbb{N}}\to {\mathbb{R}}^+$ be defined by $\varphi(n)=3^n\psi(3^n)$ and let $\Psi: \Lambda^* \to {\mathbb{R}}^+$ be defined by $$\Psi({\mathbf{i}}) = {\mathrm{diam}}(X_{{\mathbf{i}}})\varphi(|{\mathbf{i}}|),$$ as in . In this case $\Lambda = \{1,2\}$. Notice that if ${\mathbf{i}}\in \Lambda^*$ is such that $|{\mathbf{i}}|=n$, then $$\Psi({\mathbf{i}}) = {\mathrm{diam}}(X_{{\mathbf{i}}})\varphi(|{\mathbf{i}}|) = 3^{-n} \times 3^n \psi(3^n) = \psi(3^n)$$ and, hence, $$\begin{aligned}
\sum_{{\mathbf{i}}\in \Lambda^*}{\Psi({\mathbf{i}})^s} &= \sum_{n=1}^{\infty}{\#\{{\mathbf{i}}\in \Lambda^*: |{\mathbf{i}}| = n\} \times \psi(3^n)^s} \\
&= \sum_{n=1}^{\infty}{2^n \psi(3^n)^s} \\
&= \sum_{n=1}^{\infty}{(3^n)^{\gamma} \psi(3^n)^s}.\end{aligned}$$
Thus, it follows from Theorem \[thm:main\] that, for any $x \in K$, we have $$\mathcal{H}^s(W(x,\Psi)\cap [0,1])=\begin{cases}
0 & \text{if }\sum_{n=1}^{\infty}{(3^n)^{\gamma} \psi(3^n)^s}<\infty,\\&\\
\mathcal{H}^s(K) & \text{if }\sum_{n=1}^{\infty}{(3^n)^{\gamma} \psi(3^n)^s}=\infty.
\end{cases}$$
Theorem \[LSV theorem\] then follows (subject to the additional monotonicity) upon noting that $$W(0,\Psi) \cap [0,1] \subset W_{{{\mathcal B}}}(\psi) \cap K \subset (W(0,\Psi) \cap [0,1]) \cup (W(1,\Psi) \cap [0,1]).$$
In [@LevSalpVel], Levesley, Salp and Velani also extended Theorem \[LSV theorem\] to a statement about more general missing digit sets. Suppose $b \geq 3$ is an integer and $J(b)$ is any proper subset of the set $S(b):=\{0,1,\dots,b-1\}$. Denote by $K_{J(b)}$ the missing digit set consisting of the numbers $x \in [0,1]$ for which there exists a base-$b$ expansion consisting only of digits from $J(b)$. For example, the middle-third Cantor set is an example of a missing digit set corresponding to taking $b=3$ and $J(b)=\{0,2\}$. In general it can be seen that $K_{J(b)}$ can also be defined as the attractor of $\#J(b)$ similarities each with contraction ratio $\frac{1}{b}$. Furthermore, it can easily be verified that the Hausdorff dimension of $K_{J(b)}$ is $$\gamma^* := \operatorname{dim_H}{K_{J(b)}} = \frac{\log{\#J(b)}}{\log{b}}.$$
Now, let ${{\mathcal A}}(b) = \{b^n: n=0,1,2,\dots\}$ and let $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$ be an approximating function. Recall that, using our earlier notation, $$W_{{{\mathcal A}}(b)}(\psi):=\left\{x \in [0,1]: \left|x-\frac{p}{q}\right|<\psi(q) \text{ for infinitely many } (p,q) \in {{{\mathbb{Z}}}}\times {{\mathcal A}}(b) \right\}.$$ Note that in the present notation $W_{{{\mathcal B}}}(\psi)=W_{{{\mathcal A}}(3)}(\psi)$. In [@LevSalpVel], Levesley, Salp and Velani state the following generalisation[^4] of Theorem \[LSV theorem\].
\[Levesley – Salp – Velani, [@LevSalpVel]\] \[LSV missing digits theorem\] Let $s \geq 0$. Then, $${{\mathcal H}}^{s}(W_{{{\mathcal A}}(b)}(\psi) \cap K_{J(b)})=
\begin{cases}
0&\text{if}\quad\sum_{n=1}^{\infty}{\psi(b^n)^s \times (b^n)^{\gamma^*}}<\infty,\\
&\\
{{\mathcal H}}^s (K_{J(b)})&\text{if}\quad\sum_{n=1}^{\infty}{\psi(b^n)^s \times (b^n)^{\gamma^*}}=\infty.
\end{cases}$$
Using a similar argument to above, Theorem \[LSV missing digits theorem\] may also be deduced from Theorem \[thm:main\] subject to an appropriate monotonicity condition. Furthermore, we may also easily deduce a higher dimensional analogue of Theorem \[LSV missing digits theorem\] from Theorem \[thm:main\]. For this application of Theorem \[thm:main\], let us consider ${\mathbb{R}}^d$ equipped with the supremum norm. Again, let $b \geq 3$ be an integer and let $J_1(b),\dots,J_d(b)$ be proper subsets of $S(b)$. Let us consider the $d$-dimensional “missing digit” set $$K_{{\mathbf{J}}} = \prod_{i=1}^{d}{K_{J_{i}(b)}}$$ formed by taking the Cartesian product of the usual missing digit sets $K_{J_i(b)}$ ($1 \leq i \leq d)$. Notice that here we may have different “missing digits” in each coordinate direction.
Let $N_{{\mathbf{J}}} = \prod_{i=1}^{d}{\#J_i(b)}$ and notice that $K_{{\mathbf{J}}}$ is the attractor of an iterated function system consisting of $N_{{\mathbf{J}}}$ similarities which all have contraction ratio $\frac{1}{b}$. Additionally, $K_{{\mathbf{J}}}$ satisfies the open set condition and has Hausdorff dimension $$\gamma^{{\mathbf{J}}} := \operatorname{dim_H}{K_{{\mathbf{J}}}} = \frac{\log{N_{{\mathbf{J}}}}}{\log{b}}.$$
Theorem \[thm:main\] can be used to deduce the following corollary which constitutes a higher dimensional analogue of Theorems \[LSV theorem\] and \[LSV missing digits theorem\].
\[higher dimensional LSV\] Let $\Lambda:=\{1,2,\dots,N_{{\mathbf{J}}}\}$ and let $\Phi_{{\mathbf{J}}}:=\{f_i:[0,1]^d \to [0,1]^d\}_{i \in \Lambda}$ be the iterated function system as described above which has attractor $K_{{\mathbf{J}}}$. Let $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$ be an approximating function such that $b^n\psi(b^n)$ is monotonically decreasing. Let $\varphi: {\mathbb{N}}\to {\mathbb{R}}^+$ be defined by $\varphi(n) = b^n\psi(b^n)$ and let $\Psi({\mathbf{i}}) = {\mathrm{diam}}(X_{{\mathbf{i}}})\varphi({\mathbf{i}})$. For $x \in K_{{\mathbf{J}}}$, let $W(x,\Psi)$ be as defined in . Then, for any $x \in K_{{\mathbf{J}}}$ and $s \geq 0$, we have $${{\mathcal H}}^{s}(W(x,\Psi))=
\begin{cases}
0&\text{if}\quad\sum_{n=1}^{\infty}{\psi(b^n)^s \times (b^n)^{\gamma^{{\mathbf{J}}}}}<\infty,\\
&\\
{{\mathcal H}}^s (K_{{\mathbf{J}}})&\text{if}\quad\sum_{n=1}^{\infty}{\psi(b^n)^s \times (b^n)^{\gamma^{{\mathbf{J}}}}}=\infty.
\end{cases}$$
As far as we are aware, Corollary \[higher dimensional LSV\] has not been written down previously. While it follows easily as a corollary to Theorem \[thm:main\], we believe it is likely that Corollary \[higher dimensional LSV\] could also have been proved with more work using methods similar to those used in [@LevSalpVel] to prove Theorem \[LSV theorem\].
So far, we have only applied Theorem \[thm:main\] to iterated function systems formed of maps with equal contraction ratios. Although this nicely demonstrates that Theorem \[thm:main\] fits in with and is a natural generalisation of existing results, these examples do little to reflect the full generality of Theorem \[thm:main\]. Throughout the remainder of this section and Section \[Bad and QI application section\], we provide some examples which highlight some of the novel aspects of Theorem \[thm:main\]. For example, something quite simple which is novel about Theorem \[thm:main\] (and to some extent Theorems \[thm:baker\] and \[thm:baker mtp\]) is that it can also be applied to self-similar sets formed of maps with different contraction ratios. To illustrate this, let us consider again the middle-third Cantor set. Although arguably the most natural way to represent the middle-third Cantor set is as the attractor of the IFS described in Example \[Cantor set example\], this is by no means the only way. For example, let $\Phi_{K}'=\{f_1,f_2,f_3\}$ be the IFS consisting of the similarities $f_i:[0,1]\to[0,1]$ defined by $$f_1(x) = \frac{1}{9}x, \quad f_2(x)=\frac{1}{9}x+\frac{2}{9}, \quad \text{and} \quad f_3(x)=\frac{1}{3}x+\frac{2}{3}.$$ The attractor of $\Phi_{K}'$ is also the middle-third Cantor set. Notice though that here the similarities in the underlying IFS do not have the same contraction ratios. For this reason (see Section \[sec:nomasstrans\]), the methods from [@LevSalpVel] break down when using this representation of the middle-third Cantor set. However, in this respect, Theorem \[thm:main\] is more robust and still applies when we use $\Phi_{K}'$ (or any other sensible representation of the middle-third Cantor set).
Aside from this, the main advantage of Theorem \[thm:main\] over some of its predecessors is that it allows us to consider approximation in much more general iterated function systems. We give an example of this in the next section.
Badly Approximable Numbers and Quadratic Irrationals {#Bad and QI application section}
----------------------------------------------------
In this section, we apply Theorem \[thm:main\] to obtain a Jarník type statement for the set of badly approximable numbers which are “well-approximable” by a fixed quadratic irrational. We achieve this by utilising the correspondence between badly approximable numbers and partial quotients of continued fraction expansions, and by expressing the numbers with continued fraction expansions with partial quotients bounded by $M \in {\mathbb{N}}$ as the attractor of a conformal iterated function system.
Recall that a number $x\in[0,1]$ is said to be *badly approximable* if there exists a constant $c=c(x)>0$, dependent on $x$, such that for every $\frac{p}{q} \in {{{\mathbb{Q}}}}$ we have $$\left|x-\frac{p}{q}\right| > \frac{c}{q^2}.$$ It is well known that a number is badly approximable if and only if its continued fraction expansion has bounded partial quotients (see, for example, [@BRVaspects Theorem 1.15]).
For $x \in [0,1]$, let $[a_1,a_2,\dots]$ denote its continued fraction expansion. Note that this expansion will be finite if $x$ is rational. Recall that the $a_i$’s are called the *partial quotients* of $x$ and are the numbers which arise when we write $x$ in the form $$x=\frac{1}{a_1+\frac{1}{a_2+\frac{1}{a_3+\frac{1}{\phantom{=}\ddots}}}}$$ with $a_i \in {\mathbb{N}}$ for each $i \in {\mathbb{N}}$. The partial quotients, $a_i$, can also be defined via the Gauss map. The *Gauss map* is the map $T: [0,1] \to [0,1]$ defined by $$T(x)=
\begin{cases}
0 &\text{if } x=0,\\[2ex]
\frac{1}{x} - \left\lfloor \frac{1}{x}\right\rfloor&\text{for } x \in (0,1].
\end{cases}$$ For each $n \geq 1$, $\displaystyle{a_n=\left\lfloor\frac{1}{T^{n-1}x}\right\rfloor}$.
For our present purposes, another useful way for us to view the continued fraction expansion of $x \in [0,1]$ is the following. For every integer $a\geq1$, let $$f_a(y)=\frac{1}{a+y}.$$ We have $$x = [a_1,a_2,\ldots] = \lim_{n\to\infty}f_{a_1}\circ\cdots\circ f_{a_n}(1).$$
If $x\in(0,1]$ is badly approximable, then there exists $Q\geq1$ such that $a_n\leq Q$ for every $n\geq1$. Let us denote the set of badly approximable numbers in $(0,1]$ by $\mathbf{Bad}$, and denote by $\mathbf{Bad}_Q$ the numbers $x\in\mathbf{Bad}$ such that $a_n(x)\leq Q$ for every $n\geq1$ (where $a_n(x)$ is the $n$th partial quotient of $x$). By definition, $\mathbf{Bad}_Q$ is the attractor of the IFS $\{f_a\circ f_b\}_{a,b=1}^Q$. Moreover, it is easy to see that this IFS is conformal and satisfies the open set condition.
Recall that $x \in [0,1]$ is a *quadratic irrational* if it is irrational and is a root of a quadratic polynomial $ax^2+bx+c=0$, where $a\neq0$ and $a,b,c$ are integers. It is well known that $x \in [0,1]$ is a quadratic irrational if and only if $x$ has an *eventually periodic* continued fraction expansion; that is, there exist finite sequences ${\boldsymbol\omega}=(\omega_1,\ldots,\omega_{\ell})$ and ${\boldsymbol\tau}=(\tau_1,\ldots,\tau_m)$ such that $$x=[\omega_1,\ldots,\omega_{\ell},\overline{\tau_1,\ldots,\tau_m}],$$ where $\overline{{\boldsymbol\tau}}$ denotes the infinite periodic sequence formed by repeating ${\boldsymbol\tau}$. We will denote the set of quadratic irrationals in $[0,1]$ by $\mathbf{QI}$.
Given a monotonically decreasing approximating function $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$, let $$W(\psi;{\mathbf{Bad}};{\mathbf{QI}}):=\left\{x\in{\mathbf{Bad}}:\exists\alpha\in{\mathbf{QI}}:|T^n(x)-\alpha|<\psi(n)\text{ for infinitely many }n\in{\mathbb{N}}\right\}.$$ Thus, $W(\psi;{\mathbf{Bad}};{\mathbf{QI}})$ is the set of badly approximable numbers which are “well-approximable” by a fixed quadratic irrational. We will investigate the Hausdorff measure of $W(\psi;{\mathbf{Bad}};{\mathbf{QI}})$. Notice that it is sensible to fix the quadratic irrational in the definition of $W(\psi;{\mathbf{Bad}};{\mathbf{QI}})$ corresponding to a given $x \in {\mathbf{Bad}}$, otherwise we would necessarily have since quadratic irrationals are dense in the reals.
Let us now adapt some standard notation from the usual theory of continued fractions. For the proofs and more details, see [@LWWX Section 2] or [@Khint].
For a sequence of integers $\{a_n\}_{n=1}^{\infty}$, let $$\begin{aligned}
q_{n+1}(a_1,\ldots,a_{n+1})&:=q_{n+1}=a_{n+1}q_n+q_{n-1}, \text{ and} \\
\quad p_{n+1}(a_1,\ldots,a_{n+1})&:=p_{n+1}=a_{n+1}p_n+p_{n-1}\end{aligned}$$ for $n\geq1$, where we define $p_{-1}=q_0=1$ and $p_0=q_{-1}=0$. Then, $$f_{a_1}\circ\cdots\circ f_{a_n}(x)=\frac{p_{n-1}x+p_n}{q_{n-1}x+q_n}.$$ Moreover, for every $0<k<n$ and $a_1,\ldots,a_n\in{\mathbb{N}}$ we have $$\label{eq:compare}
1\leq\frac{q_n(a_1,\ldots,a_n)}{q_k(a_1,\ldots,a_k)q_{n-k}(a_{k+1},\ldots,a_n)}\leq 2,$$ and, for every $x\in[0,1]$, $$\frac{1}{4q_n^2}\leq|(f_{a_1}\circ\cdots\circ f_{a_n})'(x)|\leq\frac{1}{q_n^{2}}.$$ Thus, combining the above bounds with the bounded distortion property , there exists a constant $K\geq1$, depending on $Q$ but independent of the sequence $a_1,a_2,\dots,a_n$, such that $$\begin{aligned}
\label{example bounded distortion}
\frac{1}{K}\times\frac{1}{q_n(a_1,\ldots,a_n)^2} \leq{\mathrm{diam}}(f_{a_1}\circ\cdots\circ f_{a_n}(\mathbf{Bad}_Q))\leq \frac{K}{q_n(a_1,\ldots,a_n)^2}.\end{aligned}$$
Now, we are ready to state a corollary of our main result.
Let $W(\psi; {\mathbf{Bad}}; {\mathbf{QI}})$ be the set defined above. We have $$\mathcal{H}^s(W(\psi;{\mathbf{Bad}};{\mathbf{QI}}))=\begin{cases}
0 & \text{ if, $\forall \, Q\geq1$, }\sum\limits_{n=1}^\infty\sum\limits_{a_1,\ldots,a_n=1}^Q\dfrac{\psi(n)^s}{q_n(a_1,\ldots,a_n)^{2s}}<\infty, \\&\\
\infty & \text{ if $\exists \, Q \geq1$ such that }\sum\limits_{n=1}^\infty\sum\limits_{a_1,\ldots,a_n=1}^Q\dfrac{\psi(n)^s}{q_n(a_1,\ldots,a_n)^{2s}}=\infty.
\end{cases}$$
If $x\in W(\psi;{\mathbf{Bad}};{\mathbf{QI}})$ then there exists $\alpha=\alpha(x)\in\mathbf{QI}$ such that $|T^n(x)-\alpha|<\psi(n)$ for infinitely many $n\in{\mathbb{N}}$. On the other hand, there exists $Q_1\geq1$ such that $x\in\mathbf{Bad}_{Q_1}$ and since $\alpha$ is quasi-periodic there exists $Q_2\geq1$ such that $\alpha\in\mathbf{Bad}_{Q_2}$. Hence, $x\in\mathbf{Bad}_{Q}$ and $\alpha\in\mathbf{QI}\cap\mathbf{Bad}_Q$, where $Q=\max\{Q_1,Q_2\}$. Thus, $x\in W_Q(\psi;\alpha)$ where $$W_Q(\psi;\alpha)=\left\{x\in\mathbf{Bad}_Q:|T^{n}(x)-\alpha|<\psi(n)\text{ for infinitely many }n \in {\mathbb{N}}\right\}.$$ So, we have that $$\label{eq:decompbad}
W(\psi;{\mathbf{Bad}};{\mathbf{QI}})=\bigcup_{Q=1}^{\infty}\bigcup_{\alpha\in\mathbf{QI}\cap\mathbf{Bad}_Q}W_Q(\psi;\alpha).$$
It is easy to see that if $x\in W_Q(\psi;\alpha)$ then we must have $|T^{2n}(x)-\alpha|<\psi(2n)$ for infinitely many $n\in{\mathbb{N}}$ or $|T^{2n+1}(x)-\alpha|<\psi(2n+1)$ for infinitely many $n\in{\mathbb{N}}$. Hence, we can decompose $W_{Q}(\psi;\alpha)$ into $$W_Q(\psi;\alpha)=U_{Q}(\psi_0;\alpha)\cup T(U_{Q}(\psi_1;\alpha)),$$ where $\psi_0(n)=\psi(2n)$ and $\psi_1(n)=\psi(2n+1)$ and $$U_{Q}(\psi_i;\alpha)=\{x\in\mathbf{Bad}_Q:|T^{2n}(x)-\alpha|<\psi_i(n)\text{ for infinitely many } n \in {\mathbb{N}}\}.$$
Since the set $\mathbf{Bad}_Q$ is the attractor of the conformal IFS $\{f_a\circ f_b\}_{a,b=1}^Q$, it follows from Theorem \[thm:main\] taken together with that, for any $\alpha\in\mathbf{QI}\cap\mathbf{Bad}_Q$, we have $$\begin{aligned}
\label{eq:cor}
\mathcal{H}^s(U_{Q}(\psi_i, \alpha))=\begin{cases}
0 & \text{ if }\sum_{n=1}^\infty\sum_{a_1=1,\ldots,a_{2n}=1}^Q\frac{\psi_i(n)^s}{q_{2n}(a_1,\ldots,a_{2n})^{2s}}<\infty \\&\\
\infty & \text{ if }\sum_{n=1}^\infty\sum_{a_1=1,\ldots,a_{2n}=1}^Q\frac{\psi_i(n)^s}{q_{2n}(a_1,\ldots,a_{2n})^{2s}}=\infty.
\end{cases}\end{aligned}$$ On the other hand, $$\sum\limits_{n=1}^\infty\sum\limits_{a_1,\ldots,a_n=1}^Q\dfrac{\psi(n)^s}{q_n(a_1,\ldots,a_n)^{2s}}=\sum\limits_{n=1}^\infty\sum\limits_{a_1,\ldots,a_{2n}=1}^Q\dfrac{\psi(2n)^s}{q_{2n}(a_1,\ldots,a_{2n})^{2s}}+\sum\limits_{n=0}^\infty\sum\limits_{a_1,\ldots,a_{2n+1}=1}^Q\dfrac{\psi(2n+1)^s}{q_{2n+1}(a_1,\ldots,a_{2n+1})^{2s}}.$$ By , $$\begin{aligned}
\sum\limits_{n=0}^\infty\sum\limits_{a_1,\ldots,a_{2n+1}=1}^Q\dfrac{\psi(2n+1)^s}{q_{2n+1}(a_1,\ldots,a_{2n+1})^{2s}}&\leq2\sum\limits_{n=0}^\infty\sum\limits_{a_1,\ldots,a_{2n+1}=1}^Q\dfrac{\psi(2n+1)^s}{q_{1}(a_{2n+1})^{2s}q_{2n}(a_1,\ldots,a_{2n})^{2s}}\\
&=2\left(\sum\limits_{a=1}^Qq_{1}(a)^{-2s}\right)\sum\limits_{n=0}^\infty\sum\limits_{a_1,\ldots,a_{2n}=1}^Q\dfrac{\psi(2n+1)^s}{q_{2n}(a_1,\ldots,a_{2n})^{2s}},\\\end{aligned}$$ and the other inequality $$\sum\limits_{n=0}^\infty\sum\limits_{a_1,\ldots,a_{2n+1}=1}^Q\dfrac{\psi(2n+1)^s}{q_{2n+1}(a_1,\ldots,a_{2n+1})^{2s}}\geq\left(\sum\limits_{a=1}^Qq_{1}(a)^{-2s}\right)\sum\limits_{n=0}^\infty\sum\limits_{a_1,\ldots,a_{2n}=1}^Q\dfrac{\psi(2n+1)^s}{q_{2n}(a_1,\ldots,a_{2n})^{2s}}$$ follows by similar argument. Thus, $\sum\limits_{n=1}^\infty\sum\limits_{a_1,\ldots,a_n=1}^Q\dfrac{\psi(n)^s}{q_n(a_1,\ldots,a_n)^{2s}}$ is finite if and only if $$\sum_{n=1}^\infty\sum_{a_1=1,\ldots,a_{2n}=1}^Q\frac{\psi_i(n)^s}{q_{2n}(a_1,\ldots,a_{2n})^{2s}}<\infty$$ for $i=0,1$. Then the statement follows by and .
Proof of the Main Result (Theorem \[thm:main\])
===============================================
We first note that the convergence part of Theorem \[thm:main\] is contained in greater generality in Theorem \[thm:baker mtp\] $(i)$. When $\sum_{{\mathbf{i}}\in \Lambda^*}{\Psi({\mathbf{i}})^s}<\infty$, the proof that ${{\mathcal H}}^s(W(x,\Psi))=0$ follows from a standard covering argument combined with the definition of Hausdorff measure. For further details see the argument given in [@baker §3.2]. Thus, it remains to prove the divergence part of Theorem \[thm:main\].
An observation that is central to proving the convergence part of the result, and which we will also make use of for the divergence case, is that the set $W(x,\Psi)$ is the $\limsup$ set of the family of balls $\{B(f_{\mathbf{i}}(x),\Psi({\mathbf{i}}))\}_{{\mathbf{i}}\in\Lambda^*}$. That is, $$W(x,\Psi)= \{y \in {\mathbb{R}}^d: y \in B(f_{\mathbf{i}}(x),\Psi({\mathbf{i}})) \text{ for infinitely many } {\mathbf{i}}\in \Lambda^*\}.$$ Equivalently, we have $$W(x,\Psi)= \bigcap_{n=0}^\infty\bigcup_{\substack{ {\mathbf{i}}\in\Lambda^*\\|{\mathbf{i}}|\geq n}}B(f_{\mathbf{i}}(x),\Psi({\mathbf{i}})).$$ Throughout, $B(x,r)$ denotes a ball in ${\mathbb{R}}^d$, with respect to the fixed norm $\|\cdot\|$, centered at $x$ with radius $r$.
In proving Theorem \[thm:main\], we first show that it follows from Theorems \[thm:hillvelani\] and \[thm:baker\] that the problem can be reduced to the case when $P(s)=s\alpha$ where $\alpha:=\alpha(\psi)$ is the shrinking rate of $\psi$ and $P$ is the pressure function defined in . To tackle the proof in the remaining case, we use the following proposition.
\[prop:main\] Let $\Phi$ be a conformal iterated function system with attractor $X$ satisfying the open set condition. Let $x\in X$ and let $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ be a monotonic decreasing function with shrinking rate $0<\alpha(\psi)<\infty$. Let $\Psi({\mathbf{i}}) = {\mathrm{diam}}(X_{\mathbf{i}})\psi(|{\mathbf{i}}|)$ and let $s$ be the unique solution of the equation $P(s)=s\alpha(\psi)$. For the set $W(x,\Psi)$ defined in , if $$\sum_{n=1}^\infty\psi(n)^s\sum_{{\mathbf{i}}\in\Lambda^n}\|f_{{\mathbf{i}}}'(x)\|^s=\infty,$$ then $$\mathcal{H}^{s}(W(x,\Psi))=\infty.$$
In the remainder of this section, we will give the proof of Theorem \[thm:main\] assuming Proposition \[prop:main\]. The rest of the paper will then be devoted to establishing Proposition \[prop:main\] and a number of other required technical lemmas. The key to establishing Proposition \[prop:main\] is proving the existence of a suitable mass distribution as outlined in Proposition \[prop:massdist\]. We will give a more detailed outline of the structure of the rest of the paper in Section \[outline\].
Recall that we are given $$\begin{aligned}
\label{divergence sum}
\sum_{{\mathbf{i}}\in\Lambda^*}\Psi({\mathbf{i}})^s=\infty.\end{aligned}$$ It follows from together with the bounded distortion property that, for every $x\in X$, we have $$\begin{aligned}
\label{extra divergence}
\sum_{n=1}^\infty\psi(n)^s\sum_{{\mathbf{i}}\in\Lambda^n}\|f_{{\mathbf{i}}}'(x)\|^s=\infty.\end{aligned}$$
Next, let $\alpha$ denote the shrinking rate of $\psi$. First of all, let us consider the case when $\alpha=\infty$. It follows from that $$\infty=\sum_{n=1}^\infty\psi(n)^s\sum_{{\mathbf{i}}\in\Lambda^n}\|f_{{\mathbf{i}}}'(x)\|^s\leq\sum_{n=1}^\infty\psi(n)^s (\sharp\Lambda a_{\max}^s)^n,$$ which is possible if and only if $s=0$. Otherwise, it follows from the definition of $\alpha$ that the terms in the sum on the far right-hand side become too small, thus forcing the sum to converge. However, it can be seen that $W(x,\Psi)$ has continuum many elements. Indeed, it is a countable intersection of open and dense sets and, hence, it is a dense $G_\delta$ set by Baire’s category theorem, see [@HewStr Theorem 6.54]. Thus, $\mathcal{H}^0(W(x,\Psi)\cap B)=\infty$ for every open ball $B$ in $X$ and so we may assume that $\alpha<\infty$.
Next, observe that, by the root test, it follows from that $$\begin{aligned}
\label{root test}
1\leq\limsup_{n\to\infty}\sqrt[n]{\psi(n)^s\sum_{{\mathbf{i}}\in\Lambda^n}\|f_{{\mathbf{i}}}'(x)\|^s}=e^{-\alpha s}e^{P(s)}.\end{aligned}$$
If $\alpha=0$ then $P(s) \geq 0$. Furthermore, in this case, $\operatorname{dim_H}(W(x,\Psi))=d:=\operatorname{dim_H}X$ by Theorem \[thm:hillvelani\] and the result of Käenmäki and Rossi that $\operatorname{dim_H}X = d$ where $d$ is the unique solution of the equation $P(d)=0$. Since $P(s)$ is strictly monotonically decreasing, if $P(s)>0$ then $s<d$ and, hence, $\mathcal{H}^s(W(x,\Psi))=\infty$. If $P(s)=0$ then $s=d=\operatorname{dim_H}X$ and the statement follows from Theorem \[thm:baker\] since $W(x,\Psi)$ has full measure. Thus, we may assume that $0<\alpha<\infty$.
Note that it follows from that $P(s) \geq s\alpha$. If $P(s)>s\alpha$ then by Theorem \[thm:hillvelani\], $\operatorname{dim_H}(W(x,\Psi))>s$ and thus the statement follows again. So, for the remainder of the proof, suppose that $P(s)=s\alpha$.
Now, let $B$ be a ball such that $X\cap B\neq\emptyset$. Since the maps of $\Phi$ are uniformly contracting, there exists ${\mathbf{i}}\in\Lambda^*$ so that $f_{\mathbf{i}}(X)\subseteq B$. Let $\widetilde{\Psi}({\mathbf{j}})={\mathrm{diam}}(X_{\mathbf{j}})\widetilde{\psi}(|{\mathbf{j}}|)$, where $\widetilde{\psi}(n)=C^{-1}\psi(n+|{\mathbf{i}}|)$ and $C>1$ is the constant in . From and the bounds on $f'$ given in , we have $$\begin{split}
\sum_{n=0}^\infty\widetilde{\psi}(n)^s\sum_{{\mathbf{j}}\in\Lambda^n}\|f_{{\mathbf{j}}}'(x)\|^s&=C^{-s}\sum_{n=0}^\infty\psi(n+|{\mathbf{i}}|)^s\sum_{{\mathbf{j}}\in\Lambda^n}\|f_{{\mathbf{j}}}'(x)\|^s\\
&\geq C^{-s}(\sharp\Lambda)^{-|{\mathbf{i}}|}a_{\max}^{-s|{\mathbf{i}}|}\sum_{n=0}^\infty\psi(n+|{\mathbf{i}}|)^s\sum_{{\mathbf{j}}\in\Lambda^{n+|{\mathbf{i}}|}}\|f_{{\mathbf{j}}}'(x)\|^s=\infty.
\end{split}$$
Thus, by Proposition \[prop:main\], we have $\mathcal{H}^s(W(x,\widetilde{\Psi}))=\infty$.
Next, suppose that $\|y-f_{\mathbf{j}}(x)\|<\widetilde{\Psi}({\mathbf{j}})$. Employing the mean value theorem and , we see that $$\begin{aligned}
\|f_{{\mathbf{i}}}(y)-f_{{\mathbf{i}}{\mathbf{j}}}(x)\| &\leq \|f_{{\mathbf{i}}}'(\xi)\|\|y-f_{{\mathbf{j}}}(x)\| \\
&< \|f_{{\mathbf{i}}}'(\xi)\|\widetilde{\Psi}(|{\mathbf{j}}|) \\
&=C^{-1}\|f_{{\mathbf{i}}}'(\xi)\|{\mathrm{diam}}(X_{\mathbf{j}})\psi(|{\mathbf{i}}{\mathbf{j}}|) \\
&\leq {\mathrm{diam}}(f_{\mathbf{i}}(X_{\mathbf{j}}))\psi(|{\mathbf{i}}{\mathbf{j}}|)\\
&= {\mathrm{diam}}(X_{{\mathbf{i}}{\mathbf{j}}})\psi(|{\mathbf{i}}{\mathbf{j}}|).\end{aligned}$$ Hence, if $y\in W(x,\widetilde{\Psi})$ then $f_{{\mathbf{i}}}(y)\in W(x,\Psi)$ and thus $$\mathcal{H}^s(W(x,\Psi)\cap B)\geq\mathcal{H}^s(f_{{\mathbf{i}}}(W(x,\widetilde{\Psi}))\cap B)=\mathcal{H}^s(f_{{\mathbf{i}}}(W(x,\widetilde{\Psi}))).$$ The last inequality above follows since ${\mathbf{i}}\in \Lambda^*$ was chosen so that $f_{{\mathbf{i}}}(X) \subset B$ and so, consequently, we also have $f_{{\mathbf{i}}}(W(x,\widetilde{\Psi}) \subset B$.
Finally, it follows from and combined with the definition of Hausdorff $s$-measure that $$\mathcal{H}^s(f_{{\mathbf{i}}}(W(x,\widetilde{\Psi}))) \geq a_{\min}^{|{\mathbf{i}}|s}\mathcal{H}^s(W(x,\widetilde{\Psi})).$$ This completes the proof.
Structure of the paper {#outline}
----------------------
In the next three sections, we turn our attention to the proof of Proposition \[prop:main\], which will complete the proof of our main theorem (Theorem \[thm:main\]). As hinted at previously, although we cannot use the Mass Transference Principle directly for our purposes, the ideas underlying our argument do share some similarities with those present in the proof of the Mass Transference Principle [@bervel]. Namely, Proposition \[prop:main\] relies on the construction of a suitable Cantor-type set and a measure supported on this set satisfying certain conditions which enable us to use a version of the mass distribution principle. The existence of such a Cantor set together with an appropriate measure supported on this set is guaranteed by Proposition \[prop:massdist\]. In fact, establishing Proposition \[prop:massdist\] is arguably the most substantial part of the proof of Theorem \[thm:main\].
In Section \[symbolic section\], we describe the set $W(x,\Psi)$ in the language of symbolic dynamics and provide a proof of Proposition \[prop:main\] subject to Proposition \[prop:massdist\]. In Section \[mass distribution section\] we describe the required mass distribution, proving several technical lemmas along the way, before completing the proof of Proposition \[prop:massdist\] in Section \[end of proof section\] by showing that the mass distribution we have constructed satisfies the requirements of Proposition \[prop:massdist\]. This completes the proof of Theorem \[thm:main\].
In Section \[sec:nomasstrans\] we provide a more detailed discussion of why we are unable to use the Mass Transference Principle more directly in the present setting.
Proof of Proposition \[prop:main\]: A Symbolic Approach {#symbolic section}
=======================================================
In this section, we describe the shrinking target set symbolically and show how our main result follows from the existence of a symbolic mass distribution.
Throughout, let $\Sigma=\Lambda^{\mathbb{N}}$. Next, let $\sigma\colon\Sigma\mapsto\Sigma$ denote the usual left-shift operator on $\Sigma$; namely, for ${\mathbf{i}}= (i_1,i_2,i_3,i_4,\dots) \in \Sigma$, $$\sigma{\mathbf{i}}= \sigma(i_1,i_2,i_3,i_4,\dots) = (i_2,i_3,i_4,\dots).$$ For ${\mathbf{i}}=(i_1,\ldots,i_k)\in\Lambda^*$, the cylinder set $[{\mathbf{i}}]$ is defined as $$[{\mathbf{i}}]=[i_1,\ldots,i_k]:=\{{\mathbf{j}}\in\Sigma:i_1=j_1,\ldots,i_k=j_k\}.$$ By convention, $[\emptyset]=\Sigma$. For a sequence ${\mathbf{i}}\in\Sigma$ and $n, m \in {\mathbb{N}}$ with $n\leq m$, let $${\mathbf{i}}|_n^m:=(i_n,\ldots,i_m).$$ For $n>m$ we define ${\mathbf{i}}|_n^m=\emptyset$.
For any $\alpha\in(0,\infty)$, there exists a unique ergodic $\sigma$-invariant probability measure, $\mathbb{P}$, and a constant $C \geq 1$ such that for every ${\mathbf{i}}\in\Lambda^*$ and $x\in X$ $$\label{eq:measP}
C^{-1}\leq\dfrac{\mathbb{P}([{\mathbf{i}}])}{e^{-\alpha s|{\mathbf{i}}|}\|f_{{\mathbf{i}}}'(x)\|^s}\leq C,$$ see for example [@Bowen Theorem 1.2].
The elements of $\Sigma$ and $X$ can be associated in a natural way. More precisely, for every ${\mathbf{i}}\in\Sigma$ let $$\pi({\mathbf{i}})=\lim_{n\to\infty}f_{i_1}\circ\cdots\circ f_{i_n}(0).$$ We call the function $\pi\colon\Sigma\mapsto X$ the *natural projection*. It is easy to see that $\pi({\mathbf{i}})=f_{i_1}(\pi(\sigma{\mathbf{i}}))$. In particular, for any $n \in {\mathbb{N}}$, we have $$\begin{aligned}
\label{pi composition equality}
\pi({\mathbf{i}})=f_{{\mathbf{i}}|_1^n}(\pi(\sigma^n{\mathbf{i}})).\end{aligned}$$ For $x\in X$ and $\psi: {\mathbb{N}}\to {\mathbb{R}}^+$, let $$\widetilde{W}(x,\psi):=\{{\mathbf{i}}\in\Sigma:\|\pi(\sigma^n{\mathbf{i}})-x\|< C^{-2}\mathrm{diam}(X)\psi(n)\text{ for infinitely many }n \in {\mathbb{N}}\}.$$ Here, $C>0$ is the constant in . The next lemma shows that when $\Psi({\mathbf{i}}) = {\mathrm{diam}}(X_{{\mathbf{i}}})\psi(|{\mathbf{i}}|)$, the natural projection of $\widetilde{W}(x,\psi)$ is contained in the set $W(x,\Psi)$.
\[lem:incl1\] Let $x\in X$ and let $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ be a monotonically decreasing function. Let $\Psi({\mathbf{i}})=\mathrm{diam}(X_{\mathbf{i}})\psi(|{\mathbf{i}}|)$ and let $W(x,\Psi)$ be as in . Then $$\pi\widetilde{W}(x,\psi)\subseteq W(x,\Psi).$$
Let ${\mathbf{i}}\in\widetilde{W}(x,\psi)$. Then, using , , and , for infinitely many $n \in {\mathbb{N}}$ we have $$\begin{aligned}
\Psi({\mathbf{i}}|_1^{n})&=\mathrm{diam}(X_{{\mathbf{i}}|_1^{n}})\psi(n) \\
&\geq C^{-1}\|f_{{\mathbf{i}}|_1^{n}}'(\xi)\|{\mathrm{diam}}(X)\psi(n)\\
&\geq C\|f_{{\mathbf{i}}|_1^{n}}'(\xi)\|\|\pi(\sigma^n{\mathbf{i}})-x\| \\
&\geq\|\pi({\mathbf{i}})-f_{{\mathbf{i}}|_1^{n}}(x)\|.\end{aligned}$$ Thus, $\pi({\mathbf{i}})\in W(x,\Psi)$.
For the rest of the paper, we fix an $x\in X$ and a symbolic representation ${\mathbf{x}}\in \Sigma$ for which $\pi({\mathbf{x}})=x$. Next, let us define $\rho\colon{\mathbb{N}}\mapsto{\mathbb{N}}$ as follows; let $\rho(n)$ be the unique natural number such that $$\label{eq:defrho}
{\mathrm{diam}}(X_{{\mathbf{x}}|_1^{\rho(n)}})\leq C^{-2}{\mathrm{diam}}(X)\psi(n)<{\mathrm{diam}}(X_{{\mathbf{x}}|_1^{\rho(n)-1}}).$$ Note that $\rho$ is monotonically increasing. By combining with and the bounded distortion property , it can be seen that if $\alpha$ is the shrinking rate of $\psi$ defined earlier, $$\begin{aligned}
\label{alpha rho}
\alpha=\liminf_{n\to\infty}\dfrac{-\log\psi(n)}{n}=\liminf_{n\to\infty}\frac{-1}{n}\log{\mathrm{diam}}(X_{{\mathbf{x}}|_1^{\rho(n)}})=\liminf_{n\to\infty}\frac{-1}{n}\log\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(x)\|.\end{aligned}$$
For a monotonic increasing function $\xi\colon{\mathbb{N}}\mapsto{\mathbb{N}}$ let $$\label{eq:shrinking3}
\widehat{W}({\mathbf{x}},\xi)=\{{\mathbf{i}}\in\Sigma:\sigma^n{\mathbf{i}}\in[{\mathbf{x}}|_1^{\xi(n)}]\text{ for infinitely many }n\in{\mathbb{N}}\}.$$
\[lem:incl2\] Let ${\mathbf{x}}\in\Sigma$, let $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ be a monotonic decreasing function, and let $\rho$ be as defined in . Then, $$\widehat{W}({\mathbf{x}},\rho)\subseteq\widetilde{W}(\pi({\mathbf{x}}),\psi).$$
If ${\mathbf{i}}\in\widehat{W}({\mathbf{x}},\rho)$, then $\sigma^n{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(n)}]$ for infinitely many $n\in{\mathbb{N}}$. For each such $n \in {\mathbb{N}}$, we have $\pi(\sigma^n{\mathbf{i}})\in\pi([{\mathbf{x}}|_1^{\rho(n)}])=X_{{\mathbf{x}}|_1^{\rho(n)}}$. Hence, by the definition of $\rho$, for infinitely many $n\in{\mathbb{N}}$ we have $$\|\pi(\sigma^n{\mathbf{i}})-\pi({\mathbf{x}})\|\leq{\mathrm{diam}}(X_{{\mathbf{x}}|_1^{\rho(n)}})\leq C^{-2}\psi(n)\mathrm{diam}(X).\qedhere$$
Our goal now is to prove the following proposition, which implies Proposition \[prop:main\].
\[prop:mainsymb\] Let ${\mathbf{x}}\in\Sigma$ and let $\rho\colon{\mathbb{N}}\mapsto{\mathbb{N}}$ be any function such that $n \mapsto \rho(n)$ is monotonically increasing and for which $$\liminf_{n\to\infty}\frac{-1}{n}\log\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(\pi({\mathbf{x}}))\|=:\alpha\in(0,\infty).$$ Let $s$ be the unique solution of the equation $P(s)=s\alpha$. For the set $\widehat{W}({\mathbf{x}},\rho)$ defined in , if $$\sum_{n=0}^\infty e^{\alpha s n}\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(\pi({\mathbf{x}}))\|^{s}=\infty,$$ then $${{\mathcal H}}^{s}(\pi\widehat{W}({\mathbf{x}},\rho))=\infty.$$
Let ${\mathbf{x}}= (x_1,x_2,\dots)\in\Sigma$ be an arbitrary but fixed symbolic coding of $x\in X$ (i.e. $\pi({\mathbf{x}})=x$), and assume that $$\sum_{n=1}^\infty\psi(n)^s\sum_{{\mathbf{i}}\in\Lambda^n}\|f_{{\mathbf{i}}}'(x)\|^s=\infty.$$ Take $\mathbb{P}$ to be the measure described in and let $\rho: {\mathbb{N}}\to {\mathbb{N}}$ be as defined in . Then, from the definitions of ${\mathbb{P}}$ and $\rho$ it follows by and that $$\begin{split}
\infty=\sum_{n=0}^\infty\psi(n)^s\sum_{{\mathbf{i}}\in\Lambda^n}\|f_{{\mathbf{i}}}'(x)\|^s&\leq C^{2s+1}{\mathrm{diam}}(X)^{-s}\sum_{n=0}^\infty{\mathrm{diam}}(X_{{\mathbf{x}}|_1^{\rho(n)-1}})^s\sum_{{\mathbf{i}}\in\Lambda^n}e^{\alpha s n}{\mathbb{P}}([{\mathbf{i}}])\\
&\leq C^{3s+1}\sum_{n=0}^\infty\|f_{{\mathbf{x}}|_1^{\rho(n)-1}}'(f_{x_{\rho(n)}}(x))\|^{s}e^{\alpha s n}\\
&\leq C^{3s+1}\sum_{n=0}^\infty a_{\min}^{-s}\|f_{x_{\rho(n)}}'(x)\|^s\|f_{{\mathbf{x}}|_1^{\rho(n)-1}}'(f_{x_{\rho(n)}}(x))\|^{s}e^{\alpha s n}\\
&= C^{3s+1}a_{\min}^{-s}\sum_{n=0}^\infty\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(x)\|^{s}e^{\alpha s n}.
\end{split}$$ To obtain the penultimate line of the above we employ the bounded distortion property and to obtain the final inequality we use the chain rule.
Hence, by and Proposition \[prop:mainsymb\], $\mathcal{H}^{s}(\pi\widehat{W}({\mathbf{x}},\rho))=\infty.$ By Lemmas \[lem:incl1\] and \[lem:incl2\], $\mathcal{H}^{s}(\pi\widehat{W}({\mathbf{x}},\rho))\leq \mathcal{H}^{s}(W(x,\Psi))$, and thus the proof is complete.
The argument we use to prove Proposition \[prop:mainsymb\] is based on the classical mass distribution principle (see [@falconerfractalgeom Lemma 4.2]). In order to use such an argument, we need to prove the existence of a suitable measure. Proving the existence of such a measure is the content of the following lemma. In fact, proving this lemma is arguably the most substantial part of the argument required to allow us to establish the main result of this paper.
For simplicity, throughout the rest of the paper, we use the Vinogradov notation and write $A\ll B$ to denote that $A\leq dB$ for some constant $d > 0$. When we refer to explicit constants $C$, these may not always be the same constant but will typically be related to the bounded distortion property or the constant arising in .
\[prop:massdist\] Let ${\mathbf{x}}\in\Sigma$ and let $\rho\colon{\mathbb{N}}\mapsto{\mathbb{N}}$ be a monotonic increasing function with $$\liminf_{n\to\infty}\frac{-1}{n}\log\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(\pi({\mathbf{x}}))\|=:\alpha\in(0,\infty).$$ Let $s$ be the unique solution of the equation $P(s)=s\alpha$. Suppose that $$\sum_{n=0}^\infty e^{\alpha s n}\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(\pi({\mathbf{x}}))\|^{s}=\infty.$$ Then, there exists a probability measure $\eta$ such that $\eta(\widehat{W}({\mathbf{x}},\rho))=1$ and, for every $\delta>0$, there exists a $K\geq1$ such that for every ${\mathbf{i}}\in\Lambda^*$ with $|{\mathbf{i}}|\geq K$, $$\eta([{\mathbf{i}}])\ll\delta\cdot ({\mathrm{diam}}(X_{\mathbf{i}}))^s,$$ where the implicit constant is independent of ${\mathbf{i}}$ and $\delta$.
We proceed in this section by showing how Proposition \[prop:mainsymb\] follows from Proposition \[prop:massdist\]. In Section \[mass distribution section\] we describe how to construct a suitable mass distribution and in Section \[end of proof section\] we conclude the proof of Proposition \[prop:mainsymb\] by showing that the mass distribution we have constructed in Section \[mass distribution section\] satisfies all the necessary properties.
For $r>0$, denote by $\Theta_r$ the sequences ${\mathbf{i}}\in \Lambda^*$ for which the cylinders $f_{\mathbf{i}}(X)$ have diameter approximately equal to $r$. More precisely, $$\Theta_r=\{{\mathbf{i}}\in\Lambda^*:{\mathrm{diam}}(X_{\mathbf{i}})\leq r<{\mathrm{diam}}(X_{{\mathbf{i}}|_1^{|{\mathbf{i}}|-1}})\}.$$ Note that the collection of cylinders $\{[{\mathbf{i}}]:{\mathbf{i}}\in\Theta_r\}$ partitions $\Sigma$.
By [@KaenVil Corollary 5.8 and Theorem 3.9], there exists a constant $C\geq 0$ such that for any bounded Borel subset $I$ of ${\mathbb{R}}^d$ $$\sharp\{{\mathbf{i}}\in\Theta_{\mathrm{diam}(I)}:f_{\mathbf{i}}(X)\cap I\neq\emptyset\}\leq C.$$
Let $\eta$ be the probability measure described by Proposition \[prop:massdist\], let $\delta>0$ be arbitrary, and let $K$ be the corresponding index given in Proposition \[prop:massdist\]. Choose $R>0$ sufficiently small such that $\min\{|{\mathbf{i}}|:{\mathbf{i}}\in\Theta_r\}\geq K$ for every $0<r<R$.
Let $I$ be a bounded Borel subset of ${\mathbb{R}}^d$ such that ${\mathrm{diam}}(I)<R$. We will denote by $\pi_*\mu$ the *pushforward* of the measure $\mu$; that is, for a set $A \subseteq X$ we have $\pi_*\mu(A)=\mu(\pi^{-1}(A))$. Now, by Proposition \[prop:massdist\], we have $$\pi_*\eta(I)\leq\pi_*\eta\left(\bigcup_{\substack{{\mathbf{i}}\in\Theta_{\mathrm{diam}(I)}\\f_{\mathbf{i}}(X)\cap I\neq\emptyset}}f_{\mathbf{i}}(X)\right)\leq \sum_{\substack{{\mathbf{i}}\in\Theta_{\mathrm{diam}(I)}\\f_{\mathbf{i}}(X)\cap I\neq\emptyset}}\eta([{\mathbf{i}}])\ll \sum_{\substack{{\mathbf{i}}\in\Theta_{\mathrm{diam}(I)}\\f_{\mathbf{i}}(X)\cap I\neq\emptyset}} \delta {\mathrm{diam}}(X_{{\mathbf{i}}})^{s}\leq C\delta{\mathrm{diam}}(I)^{s}.$$ Let $\{I_i\}_i$ be such that $\pi\widehat{W}({\mathbf{x}},\rho)\subseteq\bigcup_iI_i$ and ${\mathrm{diam}}(I_i)<R$, i.e. let $\{I_i\}_i$ be an $R$-cover for $\pi\widehat{W}({\mathbf{x}},\rho)$. Also recall that, by Proposition \[prop:massdist\], we have $\eta(\widehat{W}({\mathbf{x}},\rho))=1$. Hence, using the above inequality, we have $$\sum_i{\mathrm{diam}}(I_i)^{s}\gg\sum_i\frac{1}{\delta}\pi_*\eta(I_i)\geq\frac{1}{\delta}\pi_*\eta\left(\bigcup_iI_i\right)\geq\frac{1}{\delta}\pi_*\eta(\pi\widehat{W}({\mathbf{x}},\rho))=\frac{1}{\delta}.$$ Therefore, by the definition of Hausdorff $s$-measure, $\mathcal{H}^{s}(\pi\widehat{W}({\mathbf{x}},\rho))\gg\frac{1}{\delta}$. Since $\delta>0$ was arbitrary, this completes the proof.
Before we turn to the proof of Proposition \[prop:massdist\], we prove a technical lemma. We say that ${\mathbf{i}}=(i_1,i_2,\ldots)\in\Sigma$ is *$m$-periodic* if $i_k=i_{k+m}$ for every $k\geq1$. We say that ${\mathbf{i}}\in \Sigma$ is *$m$-periodic on $(\ell,n)$*, where $n-\ell\geq m$, if $i_k=i_{k+m}$ for $\ell\leq k\leq n-m$.
\[lem:avoidcollision1\] Let ${\mathbf{x}}\in\Sigma$ and let $n\in{\mathbb{N}}$. Suppose that $$m({\mathbf{x}},n):=\min\{k:1\leq k\text{ and }{\mathbf{x}}|_1^{n-k}={\mathbf{x}}|_{k+1}^n\}<n/2.$$ Then, ${\mathbf{x}}$ is $m({\mathbf{x}},n)$-periodic on $(1,n)$. Moreover, for each $1\leq k\leq \left\lfloor\frac{n}{m({\mathbf{x}},n)}\right\rfloor m({\mathbf{x}},n)$, we have ${\mathbf{x}}|_1^{n-k}={\mathbf{x}}|_{k+1}^n$ if and only if there exists $p\in{\mathbb{N}}$ such that $k=p\cdot m({\mathbf{x}},n)$.
For convenience, let us write $m=m({\mathbf{x}},n)$. By the definition of $m$, we have $x_\ell=x_{m+\ell}$ for every $\ell=1,\ldots,n-m$ and, thus, the proof of the first part of the lemma is complete.
Next, let $q :=\left\lfloor\frac{n}{m}\right\rfloor$. Note that $q \geq 2$ since $m < \frac{n}{2}$. By using the $m$-periodicity of ${\mathbf{x}}$, we have that $x_\ell=x_{qm+\ell}$ for every . In other words, ${\mathbf{x}}|_1^{n-qm}={\mathbf{x}}|_{qm+1}^n$. Thus, again using the $m$-periodicity of ${\mathbf{x}}$, there are words ${\boldsymbol\tau}\in\Lambda^{n-qm}$ and ${\boldsymbol\omega}\in\Lambda^{(q+1)m-n}$ such that ${\mathbf{x}}={\boldsymbol\tau}{\boldsymbol\omega}{\boldsymbol\tau}\ldots{\boldsymbol\omega}{\boldsymbol\tau}$. Hence, for every $p=1,\ldots,q$, we have ${\mathbf{x}}|_1^{n-pm}={\mathbf{x}}|_{pm+1}^n$. In particular, this yields that ${\mathbf{x}}|_1^{n-k}={\mathbf{x}}|_{k+1}^n$ if $k=pm$ for some $p=1,\ldots,q$.
For the other direction, we argue by contradiction. Let us suppose that there exists some $k$ such that $m\nmid k$ and ${\mathbf{x}}|_1^{n-k}={\mathbf{x}}|_{k+1}^n$. By the definition of $m$, it follows that $m<k$. In order to obtain a contradiction, it is enough to show that $${\mathbf{x}}|_{k+1-m}^{n}={\mathbf{x}}|_{1}^{n-k+m}.$$ Then, by induction, one can find $\ell\in{\mathbb{N}}$ such that for $k'=k-\ell m<m$, we have , which is a contradiction.
Since ${\mathbf{x}}|_{n-m+1}^n={\boldsymbol\omega}{\boldsymbol\tau}$ and ${\mathbf{x}}|_1^{n-k}={\mathbf{x}}|_{k+1}^{n}$, by using the $m$-periodicity of ${\mathbf{x}}$ we have ${\boldsymbol\omega}{\boldsymbol\tau}={\mathbf{x}}|_{n-m+1}^n={\mathbf{x}}|_{n-k-m+1}^{n-k}={\mathbf{x}}|_{n-k+1}^{n-k+m}$. Similarly, ${\boldsymbol\tau}{\boldsymbol\omega}={\mathbf{x}}|_1^m={\mathbf{x}}|_{k+1}^{k+m}={\mathbf{x}}|_{k+1-m}^{k}$. Hence, using the $m$-periodicity of ${\mathbf{x}}$ and the fact that ${\mathbf{x}}|_{1}^{m}={\boldsymbol\tau}{\boldsymbol\omega}$, we have $$\begin{split}
{\mathbf{x}}|_1^{n-k+m}&={\mathbf{x}}|_1^{n-k}{\boldsymbol\omega}{\boldsymbol\tau}={\boldsymbol\tau}{\boldsymbol\omega}{\mathbf{x}}|_{m+1}^{n-k}{\boldsymbol\omega}{\boldsymbol\tau}={\boldsymbol\tau}{\boldsymbol\omega}{\mathbf{x}}|_1^{n-k-m}{\boldsymbol\omega}{\boldsymbol\tau}\\
&={\boldsymbol\tau}{\boldsymbol\omega}{\mathbf{x}}|_{k+1}^{n-m}{\boldsymbol\omega}{\boldsymbol\tau}={\boldsymbol\tau}{\boldsymbol\omega}{\mathbf{x}}|_{k+1}^n={\mathbf{x}}|_{k-m+1}^n,
\end{split}$$ as required.
Construction of the Mass Distribution {#mass distribution section}
=====================================
Let $\Phi=\{f_i\}_{i\in\Lambda}$ be a conformal iterated function system satisfying the open set condition. Throughout the next three sections, we fix an ${\mathbf{x}}\in\Sigma$ and a function $\rho\colon{\mathbb{N}}\mapsto{\mathbb{N}}$ such that $n \mapsto \rho(n)$ is monotonically increasing and for which $$\liminf_{n\to\infty}\frac{-1}{n}\log \|f_{{\mathbf{x}}|_1^{\rho(n)}}'(\xi)\|=:\alpha\in(0,\infty),$$ where $\xi \in X$. Note that by the bounded distortion property , we may take $\xi$ to be any element of $X$. Let $s$ be the unique solution of the equation $P(s)=s\alpha$ and suppose that $$\sum_{n=0}^\infty e^{\alpha s n}\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(\xi)\|^{s}=~\infty.$$
For a strictly monotonic increasing sequence ${{\underline{A}}}=(A_k)$ of natural numbers, let $$C_{{\underline{A}}}=\{{\mathbf{j}}\in\Sigma:\sigma^{\ell}{\mathbf{j}}\notin[{\mathbf{x}}|_1^{\rho(\ell)}]\text{ for every }A_k\neq\ell\geq0\text{ but }\sigma^{A_k}{\mathbf{j}}\in[{\mathbf{x}}|_1^{\rho(A_k)}]\text{ for every }k\geq1\}.$$
Observe that for every strictly monotonic increasing sequence ${{\underline{A}}}$, $C_{{\underline{A}}}$ is compact and for ${{\underline{A}}}\neq{{\underline{A}}}'$, $C_{{\underline{A}}}\cap C_{{{\underline{A}}}'}=\emptyset$.
In order to achieve the correct dimension (as given by Theorem \[thm:hillvelani\]), we restrict ourselves to the sequences ${{\underline{A}}}$, which are rapidly growing. By taking sequences ${{\underline{A}}}$ which are rapidly growing, we ensure that $C_{{{\underline{A}}}} \subset \widehat{W}({\mathbf{x}},\rho)$ but at the same time benefits from as much freedom as possible between consecutive “hits” of the shrinking target set. The next lemma guarantees for us an uncountable set of such sequences. To save on notation, let us write $$\varepsilon(n):=e^{\alpha s n}\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(\xi)\|^{s}.$$
\[lem:existseq\] There exist sequences $\{n_k\}$ and $\{m_k\}$ such that
(i) \[it:b1\] $n_1>\max\left\{4,\frac{4}{\alpha^2}\right\}$,
(ii) \[it:b2\] $n_1>\left(\dfrac{-4\log a_{\min}+\alpha}{\alpha}\right)^2$,
(iii) \[it:b3\] $\displaystyle{n_1>\frac{-8\log a_{\min}}{\alpha}\left(\frac{-2\log a_{\min}}{\alpha}+2\right)}$,
(iv) \[it:b4\] $\displaystyle{C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\min\{1,\frac{\alpha}{-2\log a_{\min}}\}\sqrt{1+\frac{\alpha}{-2\log a_{\min}}}\sqrt{n_1}}}\displaystyle{<1},$
and for every $n\geq n_1-\sqrt{n_1}$, we have $\rho(n)\geq\frac{\alpha}{-2\log a_{\min}}n$. Moreover, for every $k\geq1$,
Throughout this lemma, $C$ is the constant arising from .
First of all note that, by the definition of $\alpha$, there exists an $N \in {\mathbb{N}}$ such that for all natural numbers $n \geq N$, $$\frac{\alpha}{2} \leq \frac{-\log{\|f'_{{\mathbf{x}}|_1^{\rho(n)}}(\xi)\|}}{n}$$ for any $\xi \in X$. Combining this with the bounds in we see that $$\frac{\alpha}{2} \leq \frac{-\log{a_{\min}^{\rho(n)}}}{n} = \frac{-\rho(n)\log{a_{\min}}}{n}.$$ Thus, for all $n \geq N$, $$\rho(n) \geq \frac{\alpha}{-2\log{a_{\min}}}n.$$
We now construct sequences $\{n_k\}$ and $\{m_k\}$ inductively. Let us fix an arbitrary sequence converging to $0$, say $p_n=2^{-n}$. We begin by choosing $n_1$ sufficiently large so that - hold and $n_1-\sqrt{n_1}\geq N$. Then choose $m_1$ such that $n_1+\rho(n_1)<m_1$. We then proceed by induction. Suppose that $n_k$ and $m_k$ satisfying – have already been defined for $k=1,\ldots,\ell-1$. Next, find $m_\ell$ such that holds and $$\dfrac{C^{(1+s)\ell}a_{\min}^{-2s\ell}e^{s\alpha(\sum_{j=1}^{\ell-1}(m_j+\rho(m_j))+2\ell)}}{\prod_{j=1}^\ell\sum_{k=n_j}^{m_j}\varepsilon(k)}<p_\ell.$$
This is possible by the divergence of $\sum_{k=1}^{\infty}\varepsilon(k)$.
We then find $n_\ell$ so that holds and $$\dfrac{C^{(1+s)\ell}a_{\min}^{-2s\ell}e^{-s\alpha(n_{\ell}-\sum_{j=1}^{\ell-1}(m_j+\rho(m_j))-2\ell)}}{\prod_{j=1}^{\ell-1}\sum_{k=n_j}^{m_j}\varepsilon(k)}<p_\ell.$$ This is possible since $s,\alpha>0$. By construction, the sequences $\{n_k\}$ and $\{m_k\}$ satisfy all of the required conditions, thus completing the proof of the lemma.
Let $\Xi$ be the set of sequences such that $A_k\in[n_k,m_k]$ for every $k\geq1$. In the rest of the paper, we construct the mass distribution $\eta$ as follows. We define a family of probability measures $\{\mu_{{\underline{A}}}\}_{{{\underline{A}}}\in\Xi}$, where $\mu_{{\underline{A}}}$ is supported on $C_{{\underline{A}}}$, and an appropriate probability measure $\nu$ on $\Xi$. We will then set $\eta=\int\mu_{{\underline{A}}}d\nu({{\underline{A}}})$. Clearly, $\eta(\widehat{W}({\mathbf{x}},\rho))=1$ since, for every ${{\underline{A}}}\in \Xi$, $C_{{{\underline{A}}}} \subset \widehat{W}({\mathbf{x}},\rho)$.
Let us define $$R(n):=\max\{m\geq1:n\geq m+\rho(m)\}.$$ We adopt the convention that $R(n) = 1$ if $n < 1+\rho(1)$. Since $\rho(n)\geq\frac{\alpha}{-2\log a_{\min}}n$ for every $n\geq n_1-\sqrt{n_1}$, it follows from the definition of $R(n)$ that $$n \geq R(n)+\rho(R(n)) \geq \left(1+\frac{\alpha}{-2\log{a_{\min}}}\right)R(n) \quad$$ whenever $R(n) \geq n_1-\sqrt{n_1}$. In particular, for every $n \geq n_1-\sqrt{n_1} + \rho(n_1-\sqrt{n_1})$ we have $$\label{eq:ubR}
R(n)\leq\frac{-2\log a_{\min}}{\alpha-2\log a_{\min}}n.$$
Let $p+2<q$ be integers such that $p \geq 0$. Let $$\begin{split}
\Omega_{p,q}:=\left\{{\mathbf{i}}\in\Lambda^{q-p-2}:\right.&{\mathbf{i}}|_{1}^{\ell+\rho(\ell)-p-1}\neq{\mathbf{x}}|_{p-\ell+2}^{\rho(\ell)}\text{ for every }\ell=R(p+\sqrt{p}+1)+1,\ldots,p\\
&{\mathbf{i}}|_{\ell+1}^{\ell+\rho(\ell+p+1)}\neq{\mathbf{x}}|_1^{\rho(\ell+p+1)}\text{ for }\ell=0,\ldots,R(q-1)-p-1, \text{ and}\\
&\left.{\mathbf{i}}|_{\ell+1}^{q-p-2}\neq{\mathbf{x}}|_1^{q-p-\ell-2}\text{ for }\ell=R(q-1)-p,\ldots,q-\sqrt{q}\right\}
\end{split}$$
Let us recall that $$m({\mathbf{x}},n)=\min\{k:1\leq k\text{ and }{\mathbf{x}}|_1^{n-k}={\mathbf{x}}|_{k+1}^n\}.$$ Observe that if ${\mathbf{x}}|_1^{n-m({\mathbf{x}},n)}={\mathbf{x}}|_{m({\mathbf{x}},n)+1}^n$ then ${\mathbf{x}}|_1^{n-m({\mathbf{x}},n)-1}={\mathbf{x}}|_{m({\mathbf{x}},n)+1}^{n-1}$, and hence, $$\label{eq:mmon}
m({\mathbf{x}},n-1)\leq m({\mathbf{x}},n)\text{ for every }n\geq3.$$
Next, we define two functions ${\boldsymbol\omega},{\boldsymbol\tau}\colon\Xi\mapsto\Sigma$. For ${{\underline{A}}}\in \Xi$, since the $k$th coordinates of ${\boldsymbol\omega}$ and ${\boldsymbol\tau}$ will only depend on the $k$th coordinate $A_k$ of ${{\underline{A}}}$, we will use the notation $$\begin{aligned}
&{\boldsymbol\omega}({{\underline{A}}}) &= (\omega_1(A_1), \omega_2(A_2), \dots, \omega_k(A_k), \dots), \\
\text{and} \quad &{\boldsymbol\tau}({{\underline{A}}}) &= (\tau_1(A_1), \tau_2(A_2), \dots, \tau_k(A_k),\dots).\end{aligned}$$ For a sequence ${{\underline{A}}}\in\Xi$, we define the $k$th coordinate of ${\boldsymbol\omega}$ as follows:
- [if $m({\mathbf{x}},\rho(A_k-\sqrt{A_k}))<\rho(A_k-\sqrt{A_k})/2$, then choose $\omega_k(A_k)$ to be arbitrary but [*not*]{} equal to $x_{m({\mathbf{x}},\rho(A_k-\sqrt{A_k}))}$,]{}
- [otherwise let $\omega_k(A_k)$ be arbitrary.]{}
Similarly, for ${{\underline{A}}}\in\Xi$, define $\tau_k(A_k)$ as follows:
- [if $m({\mathbf{x}},\rho(A_k))<\rho(A_k)/2$ then choose $\tau_k(A_k)$ to be arbitrary but [*not*]{} equal to $x_{\rho(A_k)-\left\lfloor\frac{\rho(A_k)}{m({\mathbf{x}},\rho(A_k))}\right\rfloor\cdot m({\mathbf{x}},\rho(A_k))+1}$,]{}
- [otherwise let $\tau_k(A_k)$ be arbitrary.]{}
\[lem:gamset\] Let $y\in\Lambda$ be such that $y\neq x_1$ and let ${\underline{\mathbf{y}}}=(y,y,\ldots)$. For an ${{\underline{A}}}\in\Xi$, let $$\label{eq:gamma}
\Gamma_{{\underline{A}}}:=[{\underline{\mathbf{y}}}|_1^{A_1-1}]\times\prod_{k=1}^\infty\left(\{\omega_k(A_k){\mathbf{x}}|_{1}^{\rho(A_k)}\tau_k(A_k)\}\times\Omega_{A_k+\rho(A_k),A_{k+1}}\right).$$ Then $\Gamma_{{\underline{A}}}\subseteq C_{{\underline{A}}}$ for every ${{\underline{A}}}\in\Xi$.
Observe that if ${\mathbf{i}}=(i_1,i_2,\ldots)\in\Gamma_{{\underline{A}}}$, then ${\mathbf{i}}|_1^{A_1-1}={\underline{\mathbf{y}}}|_1^{A_1-1}$ and, for every $k\geq1$, we have:
- [$\displaystyle{i_{A_k}=\omega_k(A_k)}$,]{}
- [$\displaystyle{i_{A_k+\rho(A_k)+1}=\tau_{k}(A_k)}$,]{}
- [$\displaystyle{{\mathbf{i}}|_{A_k+1}^{A_k+\rho(A_k)}={\mathbf{x}}|_1^{\rho(A_k)}}$, and]{}
- [$\displaystyle{{\mathbf{i}}|_{A_k+\rho(A_k)+2}^{A_{k+1}-1}\in\Omega_{A_k+\rho(A_k),A_{k+1}}}$.]{}
In particular, $\sigma^{A_k}{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(A_k)}]$ for every $k\geq1$.
Now let $\ell\notin{{\underline{A}}}$. To show that ${\mathbf{i}}\in C_{{{\underline{A}}}}$, we need to show that $\sigma^\ell{\mathbf{i}}\notin[{\mathbf{x}}|_1^{\rho(\ell)}]$. We argue by contradiction, so suppose to the contrary that $\sigma^\ell{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(\ell)}]$. There are four possible cases to consider:
1. \[it:c0\] $A_k-\left\lfloor\sqrt{A_{k}}\right\rfloor\leq\ell\leq R\left(A_k+\rho(A_k)+\left\lfloor\sqrt{A_k+\rho(A_k)}\right\rfloor+1\right)$
2. \[it:c1\] $R\left(A_k+\rho(A_k)+\left\lfloor\sqrt{A_k+\rho(A_k)}\right\rfloor+1\right)+1\leq\ell\leq A_{k}+\rho(A_k)$
3. \[it:c2\] $A_{k}+\rho(A_k)+1\leq\ell\leq R(A_{k+1}-1)$,
4. \[it:c3\] $R(A_{k+1}-1)+1\leq\ell\leq A_{k+1}-1-\left\lfloor\sqrt{A_{k+1}}\right\rfloor$.
Suppose that holds. Since $\sigma^\ell{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(\ell)}]$, we have ${\mathbf{i}}|_{A_k+\rho(A_k)+2}^{\ell+\rho(\ell)}={\mathbf{x}}|_{A_k+\rho(A_k)-\ell+2}^{\rho(\ell)}$. However, ${\mathbf{i}}|_{A_k+\rho(A_k)+2}^{A_{k+1}-1}\in\Omega_{A_k+\rho(A_k),A_{k+1}}$ and so, by definition, we have ${\mathbf{i}}|_{A_k+\rho(A_k)+2}^{\ell+\rho(\ell)}\neq{\mathbf{x}}|_{A_k+\rho(A_k)-\ell+2}^{\rho(\ell)}$, which is a contradiction.
Similarly, if holds then again by definition ${\mathbf{i}}|_{\ell+1}^{\ell+\rho(\ell)}\neq{\mathbf{x}}|_1^{\rho(\ell)}$, and hence $\sigma^\ell{\mathbf{i}}\notin[{\mathbf{x}}|_1^{\rho(\ell)}]$, a contradiction.
If holds then, by $\sigma^\ell{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(\ell)}]$, we have ${\mathbf{i}}|_{\ell+1}^{A_{k+1}-1}={\mathbf{x}}|_1^{A_{k+1}-1-\ell}$. However, it follows from the fact that ${\mathbf{i}}|_{A_k+\rho(A_k)+2}^{A_{k+1}-1} \in \Omega_{A_k+\rho(A_k),A_{k+1}}$ that ${\mathbf{i}}|_{\ell+1}^{A_{k+1}-(A_k+\rho(A_k))-2} \neq {\mathbf{x}}|_{1}^{A_{k+1}-(A_k+\rho(A_k))-\ell-2}$. In particular, this implies that ${\mathbf{i}}|_{\ell+1}^{A_{k+1}-1} \neq {\mathbf{x}}_{1}^{A_{k+1}-1-\ell}$, which is again a contradiction.
Finally, we turn to the remaining case . First, let us consider the case when$A_k-\left\lfloor\sqrt{A_k}\right\rfloor\leq\ell<A_k$. Since $\sigma^\ell{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(\ell)}]$ and $\sigma^{A_k}{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(A_k)}]$, we have $${\mathbf{x}}|_{A_k+1-\ell}^{\rho(\ell)}={\mathbf{i}}|_{A_{k}+1}^{\rho(\ell)+\ell}={\mathbf{x}}|_1^{\rho(\ell)+\ell-A_k}.$$ Thus, $m({\mathbf{x}},\rho(\ell))\leq A_k-\ell\leq\sqrt{A_k}$. Observe that, by , we have $m({\mathbf{x}},\rho(\ell))\geq m({\mathbf{x}},\rho(A_k-\lfloor \sqrt{A_k} \rfloor))$ and also note that ${\mathbf{x}}|_{A_k+1-\ell}^{\rho(A_k-\lfloor \sqrt{A_k} \rfloor)}={\mathbf{x}}|_1^{\rho(A_k-\lfloor \sqrt{A_k} \rfloor)+\ell-A_k}$. By Lemma \[lem:existseq\], since ${{\underline{A}}}\in\Xi$, we have $$\rho(A_k-\lfloor\sqrt{A_k}\rfloor)\geq \frac{\alpha}{-2\log a_{\min}}\left(A_k-\sqrt{A_k}\right).$$ By Lemma \[lem:existseq\], we have $\sqrt{A_k}<\frac{\alpha}{-4\log a_{\min}}\left(A_k-\sqrt{A_k}\right)$ and, hence, $$m({\mathbf{x}},\rho(A_k-\lfloor \sqrt{A_k} \rfloor))<\frac{\rho(A_k-\lfloor \sqrt{A_k} \rfloor)}{2}.$$
Thus, it follows from Lemma \[lem:avoidcollision1\] that ${\mathbf{x}}$ is $m({\mathbf{x}},\rho(A_k-\lfloor \sqrt{A_k} \rfloor))$-periodic on . Furthermore, we also have that there exists $q\in{\mathbb{N}}$ such that Hence, by the definition of $\omega_k(A_k)$ and using that ${\mathbf{i}}|_{\ell+1}^{\rho(\ell)+\ell}={\mathbf{x}}|_1^{\rho(\ell)}$, we have $$\begin{aligned}
\omega_k(A_k)=i_{A_k}=i_{A_k-\ell+\ell}&=i_{q\cdot m({\mathbf{x}},\rho(A_k-\lfloor \sqrt{A_k} \rfloor))+\ell} \\
&=x_{q\cdot m({\mathbf{x}}, \rho(A_k-\lfloor \sqrt{A_k} \rfloor))}=x_{m({\mathbf{x}},\rho(A_k-\lfloor \sqrt{A_k} \rfloor))}\neq\omega_k(A_k),\end{aligned}$$ which is a contradiction.
The proof of the other case $A_k<\ell\leq R\left(A_k+\rho(A_k)+1+\left\lfloor\sqrt{A_k+\rho(A_k)}\right\rfloor\right)$ is similar. Recall that $\sigma^{A_k}{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(A_k)}]$ and we are assuming, in order to eventually reach a contradiction, that $\sigma^{\ell}{\mathbf{i}}\in[{\mathbf{x}}|_1^{\rho(\ell)}]$. Thus, $${\mathbf{x}}|_{\ell-A_k+1}^{\rho(A_k)}={\mathbf{i}}|_{\ell+1}^{\rho(A_k)+A_k}={\mathbf{x}}|_1^{\rho(A_k)-\ell+A_k}.$$
Thus, we have $$\begin{aligned}
m({\mathbf{x}},\rho(A_k))&\leq\ell-A_k \\
&\leq R\left(A_k+\rho(A_k)+1+\left\lfloor\sqrt{A_k+\rho(A_k)}\right\rfloor\right)-A_k\\
&\leq \rho(A_k) +1 +\sqrt{A_k+\rho(A_k)}-\rho\left(R\left(A_k+\rho(A_k)+1+\left\lfloor\sqrt{A_k+\rho(A_k)}\right\rfloor\right)\right)\\
&\leq\rho(A_k) +1 +\sqrt{A_k+\rho(A_k)}-\rho\left(R\left(A_k+\rho(A_k)\right)\right)\\
&=\rho(A_k) +1 +\sqrt{A_k+\rho(A_k)}-\rho\left(A_k\right)\\
&=\sqrt{A_k+\rho(A_k)}+1.\end{aligned}$$
By Lemma \[lem:existseq\] and the fact that $\rho(A_k)\geq\frac{\alpha A_k}{-2\log{a_{\min}}}$, we have $$A_k<\frac{\alpha}{-2\log a_{\min}}A_k\left(\frac{\alpha}{-8\log a_{\min}}A_k-2\right)<\rho(A_k)\left(\frac{\rho(A_k)}{4}-2\right)+1.$$ Hence, $m({\mathbf{x}},\rho(A_k))\leq\sqrt{A_k+\rho(A_k)}+1<\rho(A_k)/2$.
It follows from Lemma \[lem:avoidcollision1\] that there exists $p\in{\mathbb{N}}$ such that $\ell-A_k=p\cdot m({\mathbf{x}},\rho(A_k))$ and also that ${\mathbf{x}}$ is $m({\mathbf{x}},\rho(A_k))$-periodic on $(1,\rho(A_k))$. However, since ${\mathbf{i}}|_{\ell+1}^{\ell+\rho(\ell)}={\mathbf{x}}|_1^{\rho(\ell)}$, we have $$\begin{gathered}
\tau_k(A_k)=i_{A_k+\rho(A_k)+1}=i_{A_k-\ell+\ell+\rho(A_k)+1}=i_{\rho(A_k)-p\cdot m({\mathbf{x}},\rho(A_k))+\ell+1}\\
=x_{\rho(A_k)-p\cdot m({\mathbf{x}},\rho(A_k))+1}=x_{\rho(A_k)-\left\lfloor\frac{\rho(A_k)}{m({\mathbf{x}},\rho(A_k))}\right\rfloor\cdot m({\mathbf{x}},\rho(A_k))+1}\neq\tau_k(A_k),
\end{gathered}$$ which contradicts the definition of $\tau_k(A_k)$.
For ${\mathbf{i}}\in \Lambda^{q-p-2}$, let $${\mathbb{P}}_{p,q}({\mathbf{i}})={\mathbb{P}}([{\mathbf{i}}]),$$ where ${\mathbb{P}}$ is the measure defined by . Thus, ${\mathbb{P}}_{p,q}$ is the probability measure supported on $\Lambda^{q-p-2}$ corresponding to the equilibrium state ${\mathbb{P}}$.
Denote by $\widehat{\Omega}_{p,q}$ the subset of $\Sigma$ such that ${\mathbf{i}}\in\widehat{\Omega}_{p,q}$ if and only if ${\mathbf{i}}|_{p+2}^{q-1}\in\Omega_{p,q}$. Since ${\mathbb{P}}$ is $\sigma$-invariant by definition, ${\mathbb{P}}(\widehat{\Omega}_{p,q})={\mathbb{P}}_{p,q}(\Omega_{p,q})$.
\[lem:boundomega\] There exists a constant $C'>0$ such that for every $p>n_1$ (with $n_1$ as defined in Lemma \[lem:existseq\]) and for every $q>\max\{p+\rho(p)+2,(p+2)^2\}$, $${\mathbb{P}}_{p,q}(\Omega_{p,q})\geq1-C'\left(a_{\max}^{s}e^{-\alpha s}\right)^{\min\left\{\sqrt{p},\sqrt{q}-p,\frac{\alpha p}{-2\log a_{\min}}\right\}}.$$
First, note that $\min\{\rho(\ell+p+1),q-p-2-\ell\}=\rho(\ell+p+1)$ if and only if $\ell \leq R(q-1)-p-1$. Furthermore, note that $a_{\max}^s e^{-\alpha s} < 1$ since $\alpha > 0$ and $s>0$.
Denote the complement of $\widehat{\Omega}_{p,q}$ by $\widehat{\Omega}_{p,q}^c$. Observe that $$\label{complement inclusion}
\widehat{\Omega}_{p,q}^{c} \subseteq \left(\bigcup_{\ell=R(p+\sqrt{p}+1)+1}^{p}\sigma^{-(p+1)}\left[{\mathbf{x}}|_{p-\ell+2}^{\rho(\ell)}\right]\right)\bigcup\left(\bigcup_{\ell=0}^{q-\sqrt{q}}\sigma^{-(\ell +p+2)}\left[{\mathbf{x}}|_1^{\min\{\rho(\ell+p+1),q-p-2-\ell\}}\right]\right).$$
Then by the $\sigma$-invariance of ${\mathbb{P}}$, for every $q>p+\rho(p)+2$ we have $${\mathbb{P}}(\widehat{\Omega}_{p,q}^c) \leq \sum_{\ell=R(p+\sqrt{p}+1)+1}^{p}{\mathbb{P}}\left(\left[{\mathbf{x}}|_{p-\ell+2}^{\rho(\ell)}\right]\right)+\sum_{\ell=0}^{q-\sqrt{q}}{\mathbb{P}}\left(\left[{\mathbf{x}}|_1^{\min\{\rho(\ell+p+1),q-p-2-\ell\}}\right]\right).$$ Here, the assumption that $q > p+\rho(p)+2$ ensures that $\left[{\mathbf{x}}|_1^{\min\{\rho(\ell+p+1),q-p-2-\ell\}}\right] \neq \emptyset$ for $\ell \geq 0$. It then follows from and that $$\begin{aligned}
{\mathbb{P}}(\widehat{\Omega}_{p,q}^c)&\leq C\sum_{\ell=R(p+\sqrt{p}+1)+1}^{p}\|f_{{\mathbf{x}}|_{p-\ell+2}^{\rho(\ell)}}'(\xi)\|^se^{-(\rho(\ell)-p+\ell-1)\alpha s}\\
&+C\sum_{\ell=0}^{q-\sqrt{q}}\|f_{{\mathbf{x}}|_1^{\min\{\rho(\ell+p+1),q-p-2-\ell\}}}'(\xi)\|^se^{-\min\{\rho(\ell+p+1),q-p-2-\ell\}\alpha s} \\
&\leq C\sum_{\ell=R(p+\sqrt{p}+1)+1}^{p}\left(a_{\max}^{s}e^{-\alpha s}\right)^{\rho(\ell)+\ell-p-1}+C\sum_{\ell=0}^{q-\sqrt{q}}\left(a_{\max}^{s}e^{-\alpha s}\right)^{\min\{\rho(\ell+p+1),q-p-2-\ell\}}.\end{aligned}$$
Since $\ell\mapsto\rho(\ell)+\ell-p-1$ is a strictly monotonic increasing sequence of integers and $$\rho(R(p+\sqrt{p}+1)+1)+R(p+\sqrt{p}+1)+1-p-1>p+\sqrt{p}+1-p-1=\sqrt{p},$$ we have $$\begin{aligned}
\sum_{\ell=R(p+\sqrt{p}+1)+1}^{p}\left(a_{\max}^{s}e^{-\alpha s}\right)^{\rho(\ell)+\ell-p-1} &\leq\sum_{k=\sqrt{p}}^{\infty}a_{\max}^{k s}e^{-\alpha s k} \\
&=(a_{\max}^se^{-\alpha s})^{\sqrt{p}}\sum_{k=0}^{\infty}{a_{\max}^{ks}e^{-\alpha s k}} \\
&=\dfrac{\left(a_{\max}^{s}e^{-\alpha s}\right)^{\sqrt{p}}}{1-a_{\max}^se^{-\alpha s}}.\end{aligned}$$
Next, note that, by Lemma \[lem:existseq\], since $p > n_1$ by assumption, we have $$\rho(\ell+p+1) \geq \frac{\alpha(\ell+p+1)}{-2\log{a_{\min}}}$$ for any $\ell \geq 0$. Hence, we have $$\begin{aligned}
{\mathbb{P}}(\widehat{\Omega}_{p,q}^c)&\leq \dfrac{C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\sqrt{p}}}{1-a_{\max}^se^{-\alpha s}}+C\sum_{\ell=R(q-1)-p}^{q-\lfloor\sqrt{q}\rfloor}\left(a_{\max}^{s}e^{-\alpha s}\right)^{q-p-2-\ell}+C\sum_{\ell=0}^{R(q-1)-p-1}\left(a_{\max}^{s}e^{-\alpha s}\right)^{\rho(\ell+p+1)}\\
&\leq \dfrac{C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\sqrt{p}}}{1-a_{\max}^se^{-\alpha s}}+C\sum_{\ell=\sqrt{q}-p-2}^{q-R(q-1)-2}\left(a_{\max}^{s}e^{-\alpha s}\right)^{\ell}+C\sum_{\ell=0}^{R(q-1)-p-1}\left(a_{\max}^{s}e^{-\alpha s}\right)^{\frac{\alpha(\ell+p+1)}{-2\log a_{\min}}}\\
&\leq \dfrac{C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\sqrt{p}}}{1-a_{\max}^se^{-\alpha s}}+C\sum_{\ell=\sqrt{q}-p-2}^{\infty}\left(a_{\max}^{s}e^{-\alpha s}\right)^{\ell}+C\sum_{\ell=0}^{\infty}\left(a_{\max}^{s}e^{-\alpha s}\right)^{\frac{\alpha(\ell+p+1)}{-2\log a_{\min}}}\\
&\leq \dfrac{C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\sqrt{p}}}{1-a_{\max}^se^{-\alpha s}}+\dfrac{C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\sqrt{q}-p-2}}{1-a_{\max}^{s}e^{-\alpha s}}+\dfrac{C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\frac{\alpha(p+1)}{-2\log a_{\min}}}}{1-\left(a_{\max}^{s}e^{-\alpha s}\right)^{\frac{\alpha}{-2\log a_{\min}}}} \\
&\leq C' \left(a_{\max}^{s}e^{-\alpha s}\right)^{\min\left\{\sqrt{p},\sqrt{q}-p,\frac{\alpha p}{-2\log a_{\min}}\right\}}.\end{aligned}$$ Note that, since $\ell>0$, we require the condition $q > (p+2)^2$ to ensure the middle term above is valid.
Finally, since ${\mathbb{P}}_{p,q}(\Omega_{p,q})={\mathbb{P}}(\widehat{\Omega}_{p,q})=1-{\mathbb{P}}(\widehat{\Omega}_{p,q}^c)$, the statement follows.
\[lem:prod\] Let $0<p_n<1$ be a sequence such that $\sum_{n=1}^\infty p_n<\infty$ and $\max_n\{p_n\}<1$. Then $\prod_{n=1}^\infty(1-p_n)>0$.
Using the Taylor expansion of $\log(1-x)$, we see that $$\log(1-x)=-\sum_{k=1}^\infty\frac{x^k}{k}\geq-x-\sum_{k=2}^\infty \frac{x^k}{2}=-x-\frac{x^2}{2(1-x)}\geq-x\left(1+\frac{1}{2(1-x)}\right)$$ for every $0<x<1$. Therefore, $$\prod_{n=1}^\infty(1-p_n)=\prod_{n=1}^\infty e^{\log(1-p_n)}\geq\prod_{n=1}^\infty e^{-p_n\left(1+\frac{1}{2(1-\max_np_n)}\right)}= e^{-\left(1+\frac{1}{2(1-\max_np_n)}\right)\sum_{n=1}^\infty p_n}>0. \qedhere$$
\[lem:boundprodomega\] There exists a constant $Q>0$ such that for every ${{\underline{A}}}\in\Xi$, $${\mathbb{P}}([{\underline{\mathbf{y}}}|_1^{A_1-1}])\cdot\prod_{j=1}^{\infty}{\mathbb{P}}_{A_j+\rho(A_j),A_{j+1}}(\Omega_{A_j+\rho(A_j),A_{j+1}})\geq Q.$$
Observing that $a_{\min}^s e^{-\alpha s} < 1$, it follows from the definitions of ${\mathbb{P}}$ and $\Xi$ combined with that $$\label{eq:tob2}
{\mathbb{P}}([{\underline{\mathbf{y}}}|_1^{A_1-1}])\geq C^{-1}(a_{\min}^se^{-\alpha s})^{A_1-1}\geq C^{-1}(a_{\min}^se^{-\alpha s})^{m_1}>0.$$ By Lemma \[lem:existseq\] and Lemma \[lem:existseq\], $$\sqrt{n_{j+1}}-m_j-\rho(m_j)\geq m_j\geq n_j+\rho(n_j)\geq\sqrt{n_j+\rho(n_j)}\geq\sqrt{\left(1+\dfrac{\alpha}{-2\log a_{\min}}\right)n_j}.$$ Since $A_j\in[n_j,m_j]$, $$\begin{aligned}
\min&\left\{\sqrt{A_j+\rho(A_j)},\sqrt{A_{j+1}}-A_j-\rho(A_j),\frac{\alpha (A_j+\rho(A_j))}{-2\log a_{\min}}\right\}\\
&\geq\min\left\{\sqrt{n_j+\rho(n_j)},\sqrt{n_{j+1}}-m_j-\rho(m_j),\frac{\alpha (n_j+\rho(n_j))}{-2\log a_{\min}}\right\}\\
&\geq\min\left\{\sqrt{\left(1+\dfrac{\alpha}{-2\log a_{\min}}\right)n_j},\frac{\alpha}{-2\log a_{\min}}\left(1+\dfrac{\alpha}{-2\log a_{\min}}\right)n_j\right\} \\
&\geq\min\left\{1,\frac{\alpha}{-2\log a_{\min}}\right\}\sqrt{\left(1+\dfrac{\alpha}{-2\log a_{\min}}\right)n_j}.
\end{aligned}$$ Hence, by Lemma \[lem:boundomega\], $$\label{eq:tob1}
{\mathbb{P}}_{A_j+\rho(A_j),A_{j+1}}(\Omega_{A_j+\rho(A_j),A_{j+1}})\geq 1-C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\min\left\{1,\frac{\alpha}{-2\log a_{\min}}\right\}\sqrt{\left(1+\frac{\alpha}{-2\log a_{\min}}\right)n_j}}. \\[3ex]$$ Combining and , we have $$\begin{split}
{\mathbb{P}}([{\underline{\mathbf{y}}}|_1^{A_1-1}])\cdot&\prod_{j=1}^{\infty}{\mathbb{P}}_{A_j+\rho(A_j),A_{j+1}}(\Omega_{A_j+\rho(A_j),A_{j+1}})\\
&\geq C^{-1}(a_{\min}^se^{-\alpha s})^{m_1}\prod_{j=1}^\infty\left(1-C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\sqrt{n_j}\min\left\{1,\frac{\alpha}{-2\log a_{\min}}\right\}\sqrt{1+\frac{\alpha}{-2\log a_{\min}}}}\right)\\
&\geq C^{-1}(a_{\min}^se^{-\alpha s})^{m_1}\prod_{n=n_1}^\infty\left(1-C\left(a_{\max}^{s}e^{-\alpha s}\right)^{\sqrt{n}\min\{1,\frac{\alpha}{-2\log a_{\min}}\}\sqrt{1+\frac{\alpha}{-2\log a_{\min}}}}\right),
\end{split}$$ which is a positive constant by Lemma \[lem:existseq\] and Lemma \[lem:prod\].
Let $$\mathbb{S}_{p,q}:=\frac{\mathbb{P}_{p,q}|_{\Omega_{p,q}}}{{\mathbb{P}}_{p,q}(\Omega_{p,q})}.$$
For a sequence ${{\underline{A}}}\in\Xi$, let $\mathbb{Q}_{k}$ be the probability measure on $\Lambda^{\rho(A_k)+2}$ such that $$\mathbb{Q}_k({\mathbf{i}})=\begin{cases}
1 & \text{if }{\mathbf{i}}=\omega_k(A_k){\mathbf{x}}|_1^{\rho(A_k)}\tau_k(A_k),\\
0 & \text{otherwise.}
\end{cases}$$ For each ${{\underline{A}}}\in\Xi$, we define a probability measure $\mu_{{{\underline{A}}}}$ as follows: $$\label{eq:muA}
\mu_{{\underline{A}}}={\mathbb{S}}_{1,A_1+1}\times\prod_{k=1}^{\infty}\mathbb{Q}_k\times{\mathbb{S}}_{A_k+\rho(A_k),A_{k+1}}.$$
It follows from Lemma \[lem:boundprodomega\] that $\mu_{{\underline{A}}}$ is a well-defined probability measure on $\Sigma$ with respect to the $\sigma$-algebra generated by the cylinder sets, since Lemma \[lem:boundprodomega\] guarantees that the normalising factor in the definition of $\mu_{{\underline{A}}}$ is non-zero. Moreover, by construction, $\mu_{{\underline{A}}}(\Gamma_{{\underline{A}}})=1$, where $\Gamma_{{\underline{A}}}$ is the set defined in Lemma \[lem:gamset\].
Recall that we defined $\varepsilon(n):=e^{\alpha s n}\|f_{{\mathbf{x}}|_1^{\rho(n)}}'(\xi)\|^{s}$ and assumed that $\sum_{k=1}^\infty\varepsilon(n)$ is a divergent series. Finally, we define the probability measure $\nu$ on $\Xi$ as $$\label{eq:nu}
\nu([A_1,\ldots,A_\ell])=\prod_{j=1}^\ell\frac{\varepsilon(A_j)}{\sum_{k=n_j}^{m_j}\varepsilon(k)}.$$ To see that $\nu$ defines a probability measure observe that, for any $\ell \in {\mathbb{N}}$, we have $$\sum_{A_1=n_1}^{m_1}\sum_{A_2=n_2}^{m_2}\cdots\sum_{A_{\ell}=n_{\ell}}^{m_{\ell}}{\prod_{j=1}^{\ell}{\frac{\varepsilon(A_j)}{\sum_{k=n_j}^{m_j}{\varepsilon(k)}}}} = \sum_{A_1=n_1}^{m_1}\cdots\sum_{A_{\ell}=n_{\ell}}^{m_{\ell}}{\frac{\varepsilon(A_1)\varepsilon(A_2)\dots \varepsilon(A_{\ell})}{\sum_{k=n_1}^{m_1}{\varepsilon(k)}\sum_{k=n_2}^{m_2}{\varepsilon(k)}\dots\sum_{k=n_{\ell}}^{m_{\ell}}{\varepsilon(k)}}}.$$
By its construction, the measure $\eta:=\int\mu_{{\underline{A}}}d\nu({{\underline{A}}})$ is a well-defined probability measure on $\Sigma$ with respect to the $\sigma$-algebra generated by the cylinder sets. We conclude this section by observing that $\eta(\widehat{W}({\mathbf{x}},\rho))=1$. In fact, we actually have the stronger statement that $\eta\left(\bigcup_{{{\underline{A}}}\in\Xi}\Gamma_{{\underline{A}}}\right)=1$ since $$\int_{\Xi}\mu_{{\underline{A}}}(\bigcup_{{{\underline{A}}}\in\Xi}\Gamma_{{\underline{A}}}) d\nu({{\underline{A}}})=\int_{\Xi}\mu_{{\underline{A}}}(\Gamma_{{\underline{A}}}) d\nu({{\underline{A}}})=\int_{\Xi}1d\nu({{\underline{A}}})=1.$$ The conclusion that $\eta(\widehat{W}({\mathbf{x}},\rho))=1$ follows from the fact that $\eta\left(\bigcup_{{{\underline{A}}}\in\Xi}\Gamma_{{\underline{A}}}\right)=1$ upon recalling that $\Gamma_{{{\underline{A}}}} \subseteq C_{{{\underline{A}}}} \subseteq \widehat{W}({\mathbf{x}},\rho)$ for every ${{\underline{A}}}\in \Xi$.
Proof of Proposition \[prop:massdist\] {#end of proof section}
======================================
Before we turn to the proof, we give estimates for $\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])$.
\[lem:meas1\] For every ${{\underline{A}}}\in\Xi$ and every ${\mathbf{i}}\in\Gamma_{{\underline{A}}}$, $$\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])\ll\begin{cases}
\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(A_{\ell}-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}}{\|f_{{\mathbf{x}}|_1^{k-A_\ell}}'(x)\|^{s}\prod_{j=1}^{\ell-1}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}} & \text{ if }A_\ell\leq k<A_\ell+\rho(A_\ell), \\
\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(k-\sum_{j=1}^{\ell}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}} & \text{ if }A_\ell+\rho(A_\ell)\leq k<A_{\ell+1},
\end{cases}$$ where $C \geq 1$ is the constant taken here to be the maximum of the constants appearing in and .
First suppose that $A_\ell\leq k<A_\ell+\rho(A_\ell)$. Then ${\mathbf{i}}|_{A_{\ell}}^k=\omega_\ell(A_\ell){\mathbf{x}}|_1^{k-A_\ell}$ (see proof of Lemma \[lem:gamset\]) and thus, $$\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])={\mathbb{S}}_{1,A_1+1}([{\mathbf{i}}|_1^{A_1-2}])\prod_{j=1}^{\ell-1}{\mathbb{S}}_{A_j+\rho(A_j),A_{j+1}}([{\mathbf{i}}|_{A_j+\rho(A_j)+2}^{A_{j+1}-1}]).$$ By Lemma \[lem:boundprodomega\] we have ${\mathbb{P}}_{1,A_1+1}(\Omega_{1,A_1+1})\prod_{j=1}^{\ell-1}{\mathbb{P}}_{A_j+\rho(A_j),A_{j+1}}(\Omega_{A_j+\rho(A_j),A_{j+1}})\geq Q>0$, and hence $$\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])\leq Q^{-1}{\mathbb{P}}_{1,A_1+1}([{\mathbf{i}}|_1^{A_1-2}])\prod_{j=1}^{\ell-1}{\mathbb{P}}_{A_j+\rho(A_j),A_{j+1}}([{\mathbf{i}}|_{A_j+\rho(A_j)+2}^{A_{j+1}-1}]).$$ By , $$\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])\leq Q^{-1}C^{\ell}\|f_{{\mathbf{i}}|_1^{A_1-2}}'(\xi_0)\|^se^{-\alpha s (A_1-2)}\prod_{j=1}^{\ell-1}\|f_{{\mathbf{i}}|_{A_j+\rho(A_j)+2}^{A_{j+1}-1}}'(\xi_j)\|^s e^{-\alpha s(A_{j+1}-A_j-\rho(A_j)-2)},$$ where $\xi_0,\cdots,\xi_{\ell-1}\in X$ are arbitrary. So one can choose $\xi_{j}=f_{{\mathbf{i}}|^k_{A_j-1}}'(x)$, for $j=0\ldots,\ell-1$ and thus, by the chain rule and , we have $$\begin{aligned}
\|f_{{\mathbf{i}}|_1^{A_1-2}}'(\xi_0)\|&\prod_{j=1}^{\ell-1}\|f_{{\mathbf{i}}|_{A_j+\rho(A_j)+2}^{A_{j+1}-2}}'(\xi_j)\|\\
&=\|f_{{\mathbf{i}}|_1^k}'(x)\|\|f_{\omega_\ell(A_\ell){\mathbf{x}}|_1^{k-A_\ell}}'(x)\|^{-1}\prod_{j=1}^{\ell-1}\|f_{\omega_j(A_j){\mathbf{x}}|_1^{\rho(A_j)}\tau_j(A_j)}'(f_{{\mathbf{i}}|_{A_j+\rho(A_j)+2}^k}(x))\|^{-1}\\
&\leq \|f_{{\mathbf{i}}|_1^k}'(x)\|C^{\ell-1}a_{\min}^{-(2\ell-1)}\|f_{{\mathbf{x}}|_1^{k-A_\ell}}'(x)\|^{-1}\prod_{j=1}^{\ell-1}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{-1},\end{aligned}$$ where in the last inequality we used and . Thus,
$$\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])\ll \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\cdot C^{(1+s)\ell}a_{\min}^{-2\ell s} e^{-s\alpha(A_{\ell}-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}\|f_{{\mathbf{x}}|_1^{k-A_\ell}}'(x)\|^{-s}\prod_{j=1}^{\ell-1}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{-s}.$$ Now, consider the case when $A_\ell+\rho(A_\ell)\leq k<A_{\ell+1}$. Then, similarly to the previous argument, we have $$\begin{split}
\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])&={\mathbb{S}}_{1,A_1}([{\mathbf{i}}|_1^{A_1-2}])\left(\prod_{j=1}^{\ell-1}{\mathbb{S}}_{A_j+\rho(A_j),A_{j+1}}([{\mathbf{i}}|_{A_j+\rho(A_j)+2}^{A_{j+1}-1}])\right)\cdot{\mathbb{S}}_{A_\ell+\rho(A_\ell),A_{\ell+1}}([{\mathbf{i}}|_{A_\ell+\rho(A_\ell)+2}^k])\\
&\ll\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\cdot C^{(1+s)\ell}a_{\min}^{-2s\ell} e^{-s\alpha(k-\sum_{j=1}^{\ell}\rho(A_j)-2\ell)}\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{-s}.
\end{split}$$
\[lem:upperbound\] Let ${{\underline{A}}}\in\Xi$ and ${\mathbf{i}}\in\Gamma_{{\underline{A}}}$ be arbitrary. Then, for every $k\geq n_1$, $$\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])\ll\begin{cases}
\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(A_\ell-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}} & \text{ if }A_\ell\leq k<n_{\ell+1} \\
\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(n_{\ell+1}-\sum_{j=1}^{\ell}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}} & \text{ if }n_{\ell+1}\leq k<A_{\ell+1},
\end{cases}$$ where $C \geq 1$ is as in Lemma \[lem:meas1\].
Let $\ell\geq1$ be such that $A_\ell\leq k<A_{\ell+1}$. If $A_\ell\leq k<n_{\ell+1}$ then either $k< A_\ell+\rho(A_\ell)$ or $k\geq A_\ell+\rho(A_\ell)$. If $A_\ell\leq k<A_\ell+\rho(A_\ell)$ then, by Lemma \[lem:meas1\], $$\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])\ll \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(A_{\ell}-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}\cdot\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{-s}.$$ Note that it follows from Lemma \[lem:existseq\](1) and \[lem:existseq\](2) that $A_{\ell}-\sum_{j=1}^{\ell-1}{\rho(A_j)}-2\ell>0$.
If $A_\ell+\rho(A_\ell)\leq k<n_{\ell+1}$ then, by Lemma \[lem:meas1\] again, $$\begin{split}
\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])&\ll \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s) \ell}a_{\min}^{-2 \ell s}e^{-s\alpha(k-\sum_{j=1}^{\ell}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}\\
&\leq \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(A_\ell-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}.
\end{split}$$ On the other hand, if $n_{\ell+1}\leq k<A_{\ell+1}$ then $k\geq n_{\ell+1}>m_{\ell}+\rho(m_{\ell})\geq A_{\ell}+\rho(A_{\ell})$. Thus, in this case, by Lemma \[lem:meas1\], $$\begin{split}
\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])&\ll \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(k-\sum_{j=1}^{\ell}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}\\
&\leq \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(n_{\ell+1}-\sum_{j=1}^{\ell}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}.
\end{split}$$
Finally, we turn to the proof of our main proposition.
Let $\delta>0$ be arbitrary but fixed. One can find $L\geq1$ such that all the terms in Lemma \[lem:existseq\] and Lemma \[lem:existseq\] are smaller than $\delta$ for every $\ell\geq L$. Let us choose $K:=n_L+1$.
Let $k\geq K$ and ${\mathbf{j}}\in\Lambda^{k}$ be arbitrary. It can be seen that if $[{\mathbf{j}}]\cap\bigcup_{{{\underline{A}}}\in\Xi}\Gamma_{{\underline{A}}}=\emptyset$ then $\eta([{\mathbf{j}}])=0$ and thus, the bound holds trivially. So, without loss of generality, we may assume that $[{\mathbf{j}}]\cap\bigcup_{{{\underline{A}}}\in\Xi}\Gamma_{{\underline{A}}}\neq\emptyset$ and pick ${\mathbf{i}}\in\bigcup_{{{\underline{A}}}\in\Xi}\Gamma_{{\underline{A}}}$ such that ${\mathbf{i}}|_1^k={\mathbf{j}}$.
There are two possible cases to consider: either $m_\ell\leq k<n_{\ell+1}$ or $n_\ell\leq k<m_\ell$ for some $\ell\geq1$.
If $m_\ell\leq k<n_{\ell+1}$ then there exists a unique sequence $A_1,\ldots, A_\ell$ such that for $j=1,\dots,\ell$, and for every sequence ${{\underline{A}}}^*\in\Xi$ such that $A_{j}^{*}\neq A_j$ for some $j=1,\ldots,\ell$, we have $[{\mathbf{i}}|_1^k]\cap \Gamma_{{{\underline{A}}}^*}=\emptyset$. Moreover, $A_\ell\leq k<n_{\ell+1}$. So, by Lemma \[lem:upperbound\], $$\begin{split}
\eta([{\mathbf{i}}|_1^k])&=\int_\Xi \mu_{{{\underline{A}}}'}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}}')\\
& =\int_{[A_1,\ldots,A_\ell]}\mu_{{{\underline{A}}}'}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}}')\\
&\ll\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(A_\ell-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}\nu([A_1,\ldots,A_\ell])\\
&= \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(A_\ell-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}
\frac{\prod_{j=1}^{\ell}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}e^{\alpha s A_j}}{\prod_{j=1}^\ell\sum_{k=n_j}^{m_j}\varepsilon(k)}\\
&=\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{s\alpha(\sum_{j=1}^{\ell-1}(A_j+\rho(A_j))+2\ell)}}{\prod_{j=1}^\ell\sum_{k=n_j}^{m_j}\varepsilon(k)} \\
&\leq\delta\cdot\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s.
\end{split}$$ The final inequality above follows from Lemma \[lem:existseq\] and our choice of $\delta$.
If $n_\ell\leq k<m_{\ell}$ then there exists a unique sequence $A_1,\ldots, A_{\ell-1}$ such that for $j=1,\dots,\ell$, and for every sequence ${{\underline{A}}}^{*} \in \Xi$ such that $A_{j}^{*}\neq A_j$ for some $j=1,\ldots,\ell-1$, we have $[{\mathbf{i}}|_1^k]\cap \Gamma_{{{\underline{A}}}^{*}}=\emptyset$. Moreover, there is at most one $n_\ell\leq B\leq R(k)$ such that$[{\mathbf{i}}|_1^k]\cap\Gamma_{A_1,\ldots,A_{\ell-1},B,\ldots}\neq~\emptyset$ and in that case $[{\mathbf{i}}|_1^k]\cap\Gamma_{A_1,\ldots,A_{\ell-1},B',\ldots}=~\emptyset$ for any $B'\neq B$. To see this, note that if $B > R(k)$ then, by definition, $\rho(B)+B >k$ and so it is impossible for ${\mathbf{i}}|_{1}^{k}$ to contain (all of) ${\mathbf{x}}|_{1}^{\rho(B)}$. Motivated by this, we decompose $[n_\ell,m_\ell)$ into three parts with respect to $k$:
- [$[n_\ell,R(k)]$,]{}
- [$[R(k)+1,k)$, where ${\mathbf{i}}|_{1}^{k}$ may contain part, but not all, of ${\mathbf{x}}|_{1}^{\rho(B)}$, and]{}
- [$[k,m_\ell)$, in which case ${\mathbf{i}}|_{1}^{k}$ does not contain any of ${\mathbf{x}}|_{1}^{\rho(B)}$.]{}
First, suppose that there exists a $B\in[n_\ell,R(k)]$ such that $[{\mathbf{i}}|_1^k]\cap\Gamma_{A_1,\ldots,A_{\ell-1},B,\ldots}\neq~\emptyset$. Then, by Lemma \[lem:upperbound\], $$\begin{split}
\eta([{\mathbf{i}}|_1^k])&=\int_{\Xi}\mu_{{{\underline{A}}}'}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}}') \\
&=\int_{[A_1,\ldots,A_{\ell-1},B]}\mu_{{{\underline{A}}}'}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}}')\\
&\ll\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(B-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}}{\|f_{{\mathbf{x}}|_1^{\rho(B)}}'(x)\|^{s}\prod_{j=1}^{\ell-1}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}
\frac{\varepsilon(B)\prod_{j=1}^{\ell-1}\varepsilon(A_j)}{\prod_{j=1}^{\ell}\sum_{k=n_j}^{m_j}\varepsilon(k)}\\
&= \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2 \ell s}e^{s\alpha(\sum_{j=1}^{\ell-1}(A_j+\rho(A_j))+2\ell)}}{\prod_{j=1}^{\ell}\sum_{k=n_j}^{m_j}\varepsilon(k)} \\
&\leq \delta\cdot\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s,
\end{split}$$ where, again, the last inequality follows from Lemma \[lem:existseq\] and our choice of $\delta$.
If for every $B\in[n_\ell,R(k)]$ we have $[{\mathbf{i}}|_1^k]\cap\Gamma_{A_1,\ldots,A_{\ell-1},B,\ldots}=\emptyset$, then $$\eta([{\mathbf{i}}|_1^k])=\int_{\Xi}\mu_{{{\underline{A}}}'}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}}')=\sum_{B=R(k)+1}^{m_\ell}\int_{[A_1,\ldots,A_{\ell-1},B]}\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}}).$$ First, we give an estimate for the part $B=k,\ldots,m_\ell$. By Lemma \[lem:upperbound\] we have $$\begin{split}
\sum_{B=k}^{m_\ell}&\int_{[A_1,\ldots,A_{\ell-1},B]}\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}})\\
&\ll\sum_{B=k}^{m_\ell}\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(n_{\ell}-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}}{\prod_{j=1}^{\ell-1}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}
\frac{\varepsilon(B)\prod_{j=1}^{\ell-1}\varepsilon(A_j)}{\prod_{j=1}^{\ell}\sum_{k=n_j}^{m_j}\varepsilon(k)}\\
&= \sum_{B=k}^{m_\ell}\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(n_{\ell}-\sum_{j=1}^{\ell-1}(A_j+\rho(A_j))-2\ell)}\varepsilon(B)}{\prod_{j=1}^{\ell}\sum_{k=n_j}^{m_j}\varepsilon(k)}\\
&\leq\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(n_{\ell}-\sum_{j=1}^{\ell-1}(A_j+\rho(A_j))-2\ell)}}{\prod_{j=1}^{\ell-1}\sum_{k=n_j}^{m_j}\varepsilon(k)} \\
&\leq \delta \cdot\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s.
\end{split}$$ The last inequality above follows from Lemma \[lem:existseq\] and our choice of $\delta$.
Finally, to estimate the part corresponding to $B=R(k),\dots,k-1$, note that we have $B < k < B + \rho(B)$. Also note that it can be shown via the chain rule and the bounded distortion property that $\|f_{{\mathbf{x}}|_{1}^{k-B}}(x)\|^{-s} \|f_{{\mathbf{x}}|_{1}^{\rho(B)}}(x)\|^s = \|f_{{\mathbf{x}}|_{k-B+1}^{\rho(B)}}(x)\|^s$. Hence, using Lemma \[lem:meas1\] directly, we see that $$\begin{aligned}
\sum_{B=R(k)+1}^{k-1}&\int_{[A_1,\ldots,A_{\ell-1},B]}\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}})\\
&\ll\sum_{B=R(k)+1}^{k-1} \|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{-s\alpha(B-\sum_{j=1}^{\ell-1}\rho(A_j)-2\ell)}\cdot\|f_{{\mathbf{x}}|_1^{k-B}}'(x)\|^{-s}}{\prod_{j=1}^{\ell-1}\|f_{{\mathbf{x}}|_1^{\rho(A_j)}}'(x)\|^{s}}
\frac{\varepsilon(B)\prod_{j=1}^{\ell-1}\varepsilon(A_j)}{\prod_{j=1}^{\ell}\sum_{k=n_j}^{m_j}\varepsilon(k)}\\
&= \sum_{B=R(k)+1}^{k-1}\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\dfrac{C^{(1+s)\ell}a_{\min}^{-2\ell s}e^{s\alpha(\sum_{j=1}^{\ell-1}(A_j+\rho(A_j))+2\ell)}\cdot\|f_{{\mathbf{x}}|_{k-B+1}^{\rho(B)}}'(x)\|^{s}}{\prod_{j=1}^{\ell}\sum_{k=n_j}^{m_j}\varepsilon(k)}.\end{aligned}$$
Thus, it follows from Lemma \[lem:existseq\] and our choice of $\delta$, combined with , that $$\begin{aligned}
\sum_{B=R(k)+1}^{k-1}\int_{[A_1,\ldots,A_{\ell-1},B]}\mu_{{\underline{A}}}([{\mathbf{i}}|_1^k])d\nu({{\underline{A}}})
&\ll\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\cdot\delta\sum_{B=R(k)+1}^{k-1}(a_{\max})^{s(\rho(B)+B-k)}\\
&\leq\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\delta\sum_{B=0}^{\infty}(a_{\max})^{s(\rho(R(k)+B+1)+R(k)+1+B-k)}\\
&\leq\|f_{{\mathbf{i}}|_1^k}'(\xi)\|^s\delta \sum_{B=0}^\infty(a_{\max})^{Bs} \\
&\ll \delta\|f_{{\mathbf{i}}|_i^k}(\xi)\|^s.\end{aligned}$$
The proof of Proposition \[prop:massdist\] is complete upon noting that $\|f_{{\mathbf{i}}|_1^k}'(\xi)\|\leq C{\mathrm{diam}}(X)^{-1}{\mathrm{diam}}(X_{{\mathbf{i}}|_1^k})$ by .
Limitation of the Mass Transference Principle {#sec:nomasstrans}
==============================================
We conclude the paper by showing that the shrinking target sets considered here do not satisfy the conditions of the Mass Transference Principle if the underlying iterated function system consists of maps with different contraction ratios. More precisely, in this section, we consider iterated function systems of the form $$\label{eq:IFS}
\Phi=\{f_i\colon x\in{\mathbb{R}}^d\mapsto a_iO_ix+b_i\}_{i\in\Lambda},$$ where $a_i \in (0,1)$, $b_i \in {\mathbb{R}}^d$, and $O_i$ is a rotation. We will be particularly interested in the case when there exist $i, j \in \Lambda$ such that $a_i \neq a_j$.
First, we state a corresponding version of the Mass Transference Principle, introduced by Beresnevich and Velani in [@bervel], which is most applicable in our current setting. Theorem \[mtp\] below can be deduced from [@bervel Theorem 3], which was the result used by Levesley, Salp, and Velani in [@LevSalpVel] to study Diophantine Approximation on the middle-third Cantor set.
\[mtp\] Let $\Phi$ be a self-similar iterated function system of the form with attractor $X$ satisfying the open set condition. Let $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ be a monotonic decreasing function and denote by $\alpha(\psi)$ the shrinking rate of $\psi$. Let $s$ be the solution to $\sum_{i\in\Lambda}e^{-\alpha s}a_i^s=1$ and let us write $d=\operatorname{dim_H}X$. Let $x\in X$, let $\Psi({\mathbf{i}})=\mathrm{diam}(X_{\mathbf{i}})\psi(|{\mathbf{i}}|)$, and let $W(x,\Psi)$ be the set defined in . If, for any ball $B\subset{\mathbb{R}}^d$, $$\mathcal{H}^d(B\cap W(x,\Psi^{s/d}))=\mathcal{H}^d(B\cap X)$$ then, for any ball $B\subset{\mathbb{R}}^d$, $$\mathcal{H}^s(B\cap W(x,\Psi))=\mathcal{H}^s(B\cap X).$$
Recall from that $$W(x,\Psi)=\{y\in X:\|y-f_{\mathbf{i}}(x)\|<\Psi({\mathbf{i}})\text{ for infinitely many }{\mathbf{i}}\in\Lambda^*\}.$$
Recall that the shrinking rate $\alpha(\psi)$ of $\psi$ is defined to be $\alpha(\psi):=\liminf_{n \to \infty}{-\frac{\log{\psi(n)}}{n}}$. We show that if $0<\alpha(\psi)<\infty$ and there exist $i,j \in \Sigma$ such that $a_i \neq a_j$, then the Mass Transference Principle is not applicable in general.
Let $\Phi$ be a self-similar iterated function system of the form with attractor $X$ satisfying the strong separation condition. Suppose that there exist $i,j\in\Lambda$ such that $a_i\neq a_j$. Let $\psi\colon{\mathbb{N}}\mapsto{\mathbb{R}}^+$ be a monotonic decreasing function with shrinking rate $\alpha(\psi)\in(0,\infty)$. Let $s$ be the solution to $\sum_{i\in\Lambda}e^{-\alpha s}a_i^s=1$ and write $d=\operatorname{dim_H}X$. Let $x\in X$, let $\Psi({\mathbf{i}})=\mathrm{diam}(X_{\mathbf{i}})\psi(|{\mathbf{i}}|)$, and let $W(x,\Psi)$ and $W(x,\Psi^{s/d})$ be the sets as defined by . Then, $$\mathcal{H}^d(W(x,\Psi^{s/d}))=0.$$
Without loss of generality, we may assume that ${\mathrm{diam}}(X)=1$. Throughout the proof, let ${\mathbf{x}}$ be the unique coding of $x$, i.e. $\pi({\mathbf{x}})=x$. The uniqueness of this encoding is guaranteed by the strong separation condition.
Let us define $\lambda$ to be the natural $\sigma$-invariant ergodic probability measure on $\Sigma$, whose projection is equivalent to $\mathcal{H}^d|_X$. That is, $\pi_*\lambda=\lambda\circ\pi^{-1}=\frac{\mathcal{H}^d|_X}{\mathcal{H}^d(X)}$. Moreover, for each ${\mathbf{i}}=(i_1,\ldots,i_n)\in\Lambda^*$, $$\lambda([i_1,\ldots,i_n])=(a_{{\mathbf{i}}})^d.$$ Here we use the notation $a_{{\mathbf{i}}}=a_{i_1}a_{i_2}\dots a_{i_{|{\mathbf{i}}|}}$.
Let $\chi:=-\sum_{i\in\Lambda}a_i^d\log a_i=-\int\log a_{i_1}d\lambda({\mathbf{i}})$ and let $$F=\left\{{\mathbf{i}}\in\Sigma:\lim_{n\to\infty}\frac{-1}{n}\log a_{{\mathbf{i}}|_1^n}=\lim_{n\to\infty}\frac{-1}{n}\sum_{k=1}^n\log a_{i_k}=\chi\right\}.$$ By Birkhoff’s Ergodic Theorem (see, for example, [@EinsiedlerWard Theorem 2.30] or [@Walters Theorem 1.14]), $\lambda(F)=1$.
Now, let $$\widehat{W}(x,\Psi^{s/d}):=\left\{{\mathbf{j}}\in\Sigma:\|\pi({\mathbf{j}})-\pi({\mathbf{i}}{\mathbf{x}})\|< (a_{\mathbf{i}})^{s/d}\psi(|{\mathbf{i}}|)^{s/d}\text{ for infinitely many }{\mathbf{i}}\in\Lambda^*\right\}.$$ Since $\Phi$ satisfies the strong separation condition and so points in the symbolic space $\Sigma$ uniquely encode points in $X$, we have that $$\label{eq:proj}\pi \widehat{W}(x,\Psi^{s/d}) = W(x,\Psi^{s/d}).$$ Furthermore, recall that $\pi_*\lambda=\frac{{{\mathcal H}}^d|_{X}}{{{\mathcal H}}^d(X)}$. Thus, since $\lambda(F)=1$, it is sufficient to show that $\lambda(\widehat{W}(x,\Psi^{s/d})\cap F)=0$.
Next, let ${\mathbf{i}},{\mathbf{j}}\in\Sigma$ let $|{\mathbf{i}}\wedge{\mathbf{j}}|=\min\{k\geq1:i_k\neq j_k\}-1$ and let ${\mathbf{i}}\wedge{\mathbf{j}}=i_1,\ldots,i_{|{\mathbf{i}}\wedge{\mathbf{j}}|}$ be the common part of ${\mathbf{i}}$ and ${\mathbf{j}}$. If $|{\mathbf{i}}\wedge{\mathbf{j}}|=0$ then we define ${\mathbf{i}}\wedge{\mathbf{j}}$ as the empty word. We make the following claim.
\[c:1\] If ${\mathbf{j}}\in\widehat{W}(x,\Psi^{s/d})\cap F$ then $|{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}|\geq|{\mathbf{i}}|$ for infinitely many ${\mathbf{i}}\in\Lambda^*$ such that $\|\pi({\mathbf{j}})-\pi({\mathbf{i}}{\mathbf{x}})\|< (a_{\mathbf{i}})^{s/d}\psi(|{\mathbf{i}}|)^{s/d}$.
Suppose to the contrary that there exists $N=N({\mathbf{j}})\geq1$ such that if $|{\mathbf{i}}|>N$ and $\|\pi({\mathbf{j}})-\pi({\mathbf{i}}{\mathbf{x}})\|\leq (a_{\mathbf{i}})^{s/d}\psi(|{\mathbf{i}}|)^{s/d}$ then $|{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}|<|{\mathbf{i}}|$.
Let $\delta=\min_{i\neq j}d(f_i(X),f_j(X))>0$ where, for subsets $A,B\subset {\mathbb{R}}^n$, $d(A,B)=\min\{\|a-b\|:a \in A \text{ and } b \in B\}$. Then from the definitions of the common part ${\mathbf{i}}\wedge {\mathbf{j}}$ and $\delta>0$ and we have $$\begin{aligned}
\delta a_{{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}}&\leq a_{{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}}\|\pi(\sigma^{|{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}|}{\mathbf{j}})-\pi(\sigma^{|{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}|}{\mathbf{i}}{\mathbf{x}})\| \\
&=\|f_{{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}}(\pi(\sigma^{|{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}|}{\mathbf{j}}))-f_{{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}}(\pi(\sigma^{|{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}|}{\mathbf{i}}{\mathbf{x}}))\|\\
&=\|\pi({\mathbf{j}})-\pi({\mathbf{i}}{\mathbf{x}})\| \\
&\leq (a_{\mathbf{i}})^{s/d}\psi(|{\mathbf{i}}|)^{s/d}.\end{aligned}$$ The last equality above holds by assumption.
Since $s<d$ and we are assuming that $|{\mathbf{j}}\wedge {\mathbf{i}}{\mathbf{x}}| > |{\mathbf{i}}|$, it follows from the previous inequality that $$\delta\leq (a_{{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}})^{s/d-1}(a_{\sigma^{|{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}|}{\mathbf{i}}})^{s/d}\psi(|{\mathbf{i}}|)^{s/d}\leq(a_{{\mathbf{j}}\wedge{\mathbf{i}}{\mathbf{x}}})^{s/d-1}\psi(|{\mathbf{i}}|)^{s/d}\leq (a_{{\mathbf{j}}|_1^{|{\mathbf{i}}|}})^{s/d-1}\psi(|{\mathbf{i}}|)^{s/d}.$$ Thus, since ${\mathbf{j}}\in F$ $$\label{eq:contbaound}
0\geq\liminf_{n\to\infty}\frac{-1}{n}\log(a_{{\mathbf{j}}|_1^{n}})^{s/d-1}\psi(n)^{s/d}=\left(\frac{s}{d}-1\right)\chi+\frac{s}{d}\alpha.$$
Let $$D_{KL}(\lambda\|{\mathbb{P}}):=\sum_{i\in\Lambda}\lambda(i)\log\frac{\lambda(i)}{{\mathbb{P}}(i)}$$ denote the *Kullback-Leibler divergence* (or *relative entropy*) of the measure $\lambda$ with respect to ${\mathbb{P}}$, where ${\mathbb{P}}$ is the measure defined in . See [@MacKay Section 2.6] for a definition of Kullback-Leibler divergence. It is a property of the Kullback-Leibler divergence that $0\leq D_{KL}(\lambda\|{\mathbb{P}})$ and $0=D_{KL}(\lambda\|{\mathbb{P}})$ if and only if $\lambda={\mathbb{P}}$.
Since $\alpha>0$, we have that $s<d$. By the assumption that there exist contraction ratios $a_i\neq a_j$, it follows that there exists $i\in\Lambda$ such that $e^{\alpha s}a_i^s\neq a_i^d$. Indeed, otherwise we would have that $a_i^{d-s}=e^{\alpha s}=a_j^{d-s}$ for every $i,j\in\Lambda$, which is impossible. Thus, $\lambda\neq{\mathbb{P}}$ and it follows from the definitions of the measures ${\mathbb{P}}$ and $\lambda$ that $$\begin{aligned}
\label{KL equality}
0<D_{KL}(\lambda\|{\mathbb{P}})=\left(s-d\right)\chi+s\alpha,\end{aligned}$$ but this contradicts .
Claim \[c:1\] combined with implies that for every ${\mathbf{j}}\in \widehat{W}(x,\Psi^{s/d})\cap F$ there are infinitely many ${\mathbf{i}}\in\Lambda^*$ such that ${\mathbf{j}}|_1^{|{\mathbf{i}}|}={\mathbf{i}}$ and $$(a_{{\mathbf{i}}})^{s/d}\psi(|{\mathbf{i}}|)^{s/d}>\|\pi({\mathbf{j}})-\pi({\mathbf{i}}{\mathbf{x}})\|=\|f_{{\mathbf{i}}}(\pi(\sigma^{|{\mathbf{i}}|}{\mathbf{j}}))-f_{\mathbf{i}}(\pi({\mathbf{x}}))\|=a_{{\mathbf{i}}}\|\pi(\sigma^{|{\mathbf{i}}|}{\mathbf{j}})-\pi({\mathbf{x}})\|.$$ Hence, $$\widehat{W}(x,\Psi^{s/d})\cap F \subseteq \{{\mathbf{i}}\in\Sigma:\|\pi(\sigma^n{\mathbf{i}})-x\|<(a_{{\mathbf{i}}|_1^n})^{s/d-1}\psi(n)^{s/d}\text{ for infinitely many }n \in {\mathbb{N}}\}\cap F.$$
By the definition of $F$, it follows from Egorov’s Theorem (see, for example, [@Khar Theorem 12.1]) that, for every $\varepsilon>0$ there exists a set $E\subset F$ such that $\lambda(E)>1-\varepsilon$ and the sequence of functions ${\mathbf{i}}\mapsto\frac{-1}{n}\log a_{{\mathbf{i}}|_1^n}$ converges uniformly to $\chi$ on $E$.
In particular, there exists a natural number $N=N(E)$ such that for every ${\mathbf{i}}\in E$ and every $n\geq N$ $$a_{{\mathbf{i}}|_{1}^{n}}^{s/d-1}\psi(n)^{s/d} < e^{-\frac{n}{2d}D_{KL}(\lambda\|{\mathbb{P}})}.$$ To see this, recall the right-hand equalities of and . Thus, $$\begin{aligned}
\widehat{W}(x,\Psi^{s/d})\cap E&\subseteq W'':=\{{\mathbf{j}}\in \Sigma :\|\pi(\sigma^n{\mathbf{j}})-x\|< e^{-\frac{n}{2d}D_{KL}(\lambda\|{\mathbb{P}})}\text{ for infinitely many } n \in {\mathbb{N}}\}\\
&=\{{\mathbf{j}}\in \Sigma :\|\pi({\mathbf{j}})-f_{{\mathbf{i}}}(x)\|< a_{{\mathbf{i}}} e^{-\frac{|{\mathbf{i}}|}{2d}D_{KL}(\lambda\|{\mathbb{P}})}\text{ for infinitely many } {\mathbf{i}}\in \Lambda^*\}.
\end{aligned}$$ Since $$\sum_{{\mathbf{i}}\in\Lambda^*}(a_{{\mathbf{i}}} e^{-\frac{|{\mathbf{i}}|}{2d}D_{KL}(\lambda\|{\mathbb{P}})})^d=\sum_{n=1}^\infty e^{-nD_{KL}(\lambda\|{\mathbb{P}})/2}\left(\sum_{i\in\Lambda}a_i^d\right)^n<\infty,$$ we have that $\lambda(W'')=\mathcal{H}^d(\pi(W''))=0$ by Theorem \[thm:baker\]. Hence, by and the fact that $\lambda(F)=1$ we have $$\begin{aligned}
\mathcal{H}^d(W(x,\Psi^{s/d}))&=\mathcal{H}^d(X)\cdot\lambda(\widehat{W}(x,\Psi^{s/d}))\\
&=\mathcal{H}^d(X)\cdot\lambda(\widehat{W}(x,\Psi^{s/d})\cap F)\\
&\leq \mathcal{H}^d(X)\cdot\left(\lambda(W'')+\lambda(F\setminus E)\right) \\
&<\mathcal{H}^d(X)\cdot\varepsilon.\end{aligned}$$ Finally, since $\varepsilon>0$ was arbitrary and ${{\mathcal H}}^d(X)$ is finite by , the statement follows.
[**Acknowledgements.**]{} This project grew out of initial discussions had while both authors were in attendance at the program on *Fractal Geometry and Dynamics* at the Mittag–Leffler Institut in November 2017. We are indebted both to the organisers of the program and the staff at the Institut for a pleasant and productive stay at the Institut. The first author is grateful to the Budapest University of Technology and Economics for their hospitality during her visit there in October 2018, she would also like to thank Tom Kempton and Charles Walkden for patiently listening to her ramblings on this project. Both authors would like to thank Thomas Jordan for pointing out several useful references.
[44]{}
S. Baker. An analogue of khintchine’s theorem for self-conformal sets. , pages 1–31.
S. Baker. Overlapping iterated function systems from the perspective of metric number theory. , 2019.
S. Baker and M. Farmer. Quantitative recurrence properties for self-conformal sets. , 2019.
B. Bárány and M. Rams. Shrinking targets on [B]{}edford-[M]{}c[M]{}ullen carpets. , 117(5):951–995, 2018.
V. Beresnevich, F. Ramírez, and S. Velani. Metric [D]{}iophantine approximation: aspects of recent work. In [*Dynamics and analytic number theory*]{}, volume 437 of [ *London Math. Soc. Lecture Note Ser.*]{}, pages 1–95. Cambridge Univ. Press, Cambridge, 2016.
V. Beresnevich and S. Velani. A mass transference principle and the [D]{}uffin-[S]{}chaeffer conjecture for [H]{}ausdorff measures. , 164(3):971–992, 2006.
R. Bowen. , volume 470 of [*Lecture Notes in Mathematics*]{}. Springer-Verlag, Berlin, revised edition, 2008. With a preface by David Ruelle, Edited by Jean-René Chazottes.
R. Broderick, L. Fishman, and A. Reich. Intrinsic approximation on [C]{}antor-like sets, a problem of [M]{}ahler. , 1(4):3–12, 2011.
Y. Bugeaud. Diophantine approximation and [C]{}antor sets. , 341(3):677–684, 2008.
Y. Bugeaud and A. Durand. Metric [D]{}iophantine approximation on the middle-third [C]{}antor set. , 18(6):1233–1272, 2016.
Y. Chang, M. Wu, and W. Wu. Quantitative recurrence properties and homogeneous self-similar sets. , 147(4):1453–1465, 2019.
N. Chernov and D. Kleinbock. Dynamical [B]{}orel-[C]{}antelli lemmas for [G]{}ibbs measures. , 122:1–27, 2001.
M. Einsiedler and T. Ward. , volume 259 of [*Graduate Texts in Mathematics*]{}. Springer-Verlag London, Ltd., London, 2011.
K. Falconer. . John Wiley & Sons, Inc., Hoboken, NJ, second edition, 2003. Mathematical foundations and applications.
L. Fishman, K. Merrill, and D. Simmons. Uniformly de [B]{}ruijn sequences and symbolic [D]{}iophantine approximation on fractals. , 22(2):271–293, 2018.
L. Fishman and D. Simmons. Intrinsic approximation for fractals defined by rational iterated function systems: [M]{}ahler’s research suggestion. , 109(1):189–212, 2014.
L. Fishman and D. Simmons. Extrinsic [D]{}iophantine approximation on manifolds and fractals. , 104(1):83–101, 2015.
E. Hewitt and K. Stromberg. . Springer-Verlag, New York-Heidelberg, 1975. A modern treatment of the theory of functions of a real variable, Third printing, Graduate Texts in Mathematics, No. 25.
R. Hill and S. L. Velani. The ergodic theory of shrinking targets. , 119(1):175–198, 1995.
R. Hill and S. L. Velani. The shrinking target problem for matrix transformations of tori. , 60(2):381–398, 1999.
J. E. Hutchinson. Fractals and self-similarity. , 30(5):713–747, 1981.
V. Jarník. ber die simultanen diophantischen approximationen. , 33(1):505–543, 1931.
E. Järvenpää, M. Järvenpää, H. Koivusalo, B. Li, V. Suomala, and Y. Xiao. Hitting probabilities of random covering sets in tori and metric spaces. , 22:Paper No. 1, 18, 2017.
M. Järvenpää. Random covering sets, hitting probabilities and variants of the covering problem. In [*Recent developments in fractals and related fields*]{}, Trends Math., pages 175–187. Birkhäuser/Springer, Cham, 2017.
A. Käenmäki and E. Rossi. Weak separation condition, [A]{}ssouad dimension, and [F]{}urstenberg homogeneity. , 41(1):465–490, 2016.
A. Käenmäki and M. Vilppolainen. Separation conditions on controlled [M]{}oran constructions. , 200(1):69–100, 2008.
A. B. Kharazishvili. , volume 272 of [*Pure and Applied Mathematics (Boca Raton)*]{}. Chapman & Hall/CRC, Boca Raton, FL, second edition, 2006.
A. Khintchine. Einige sätze über kettenbrüche, mit anwendungen auf die theorie der diophantischen approximationen. , 92:115–125, 1924.
A. Y. Khintchine. . Translated by Peter Wynn. P. Noordhoff, Ltd., Groningen, 1963.
H. Koivusalo and F. A. Ramírez. Recurrence to shrinking targets on typical self-affine fractals. , 61(2):387–400, 2018.
S. Kristensen. Approximating numbers with missing digits by algebraic numbers. , 49(3):657–666, 2006.
J. Levesley, C. Salp, and S. L. Velani. On a problem of [K]{}. [M]{}ahler: [D]{}iophantine approximation and [C]{}antor sets. , 338(1):97–118, 2007.
B. Li, B.-W. Wang, J. Wu, and J. Xu. The shrinking target problem in the dynamical system of continued fractions. , 108(1):159–186, 2014.
D. J. C. MacKay. . Cambridge University Press, New York, 2003.
K. Mahler. Some suggestions for further research. , 29(1):101–108, 1984.
Y. Peres, M. Rams, K. Simon, and B. Solomyak. Equivalence of positive [H]{}ausdorff measure and the open set condition for self-conformal sets. , 129(9):2689–2699, 2001.
T. Persson and M. Rams. On shrinking targets for piecewise expanding interval maps. , 37(2):646–663, 2017.
R. Prohaska and C. Sert. Markov random walks on homogeneous spaces and diophantine approximation on fractals. , 2019.
S. Seuret and B.-W. Wang. Quantitative recurrence properties in conformal iterated function systems. , 280:472–505, 2015.
D. Simmons and B. Weiss. Random walks on homogeneous spaces and [D]{}iophantine approximation on fractals. , 216(2):337–394, 2019.
K. Simon, B. Solomyak, and M. Urbański. Hausdorff dimension of limit sets for parabolic [IFS]{} with overlaps. , 201(2):441–478, 2001.
P. Walters. , volume 79 of [*Graduate Texts in Mathematics*]{}. Springer-Verlag, New York-Berlin, 1982.
B.-W. Wang, J. Wu, and J. Xu. Dynamical covering problems on the triadic [C]{}antor set. , 355(7):738–743, 2017.
B. Weiss. Almost no points on a [C]{}antor set are very well approximable. , 457(2008):949–952, 2001.
[^1]: The first author was supported in part by EPSRC Doctoral Prize Fellowship grant EP/N509565/1 and the Heilbronn Institute for Mathematical Research. The second author acknowledges support from the grants OTKA K123782, NKFI PD123970, and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
[^2]: In [@LevSalpVel], Theorem \[LSV theorem\] is stated in terms of Hausdorff $f$-measure, ${{\mathcal H}}^f$, for a general gauge function $f$. Here, for simplicity, we state the result only in terms of Hausdorff $s$-measure.
[^3]: In [@WWX2017 Theorem 3.3], Wang, Wu and Xu state their result in terms of more general gauge functions $f$.
[^4]: In [@LevSalpVel Theorem 4] the result is stated for general gauge functions $f$ whereas here for simplicity, again, we opt to state the result only in terms of Hausdorff $s$-measure.
| {
"pile_set_name": "ArXiv"
} |
Machine components are often manufactured based on the physical and/or functional characteristics that define their desired operation. High quality, precise manufacturing is used to ensure that components will operate as expected and within acceptable tolerances. To verify that components are manufactured according to their specified criteria, manufacturers often perform quality control inspections during and/or following a manufacturing process.
For example, fuel injectors must be manufactured with predetermined dimensions in order to be compatible with a host machine. Further, fuel injectors must be manufactured so that they inject precise amounts of fuel in a manner required for efficient operation of the machine. Therefore, fuel injectors having high-tolerance, small-diameter fuel injector orifices are often manufactured in large quantities. In the manufacture of these fuel injectors, various metrology devices and methods have been used to confirm the geometry of orifices formed in the nozzles of the fuel injectors. Some of these devices include, for example, gage wires, optical measuring microscopes, coordinate measuring machines (CMMs), and Werth machines. Functional measurement has also been used, such as by spraying fuel through the nozzle orifices in a test environment to determine the accuracy and precision of the drilled orifices. Although many of these devices and methods may provide somewhat accurate results, they require human intensive operations, involve little or no automation, and cannot provide consistently repeatable precision.
Recently, attempts have been made to automate the quality-control inspection of various manufactured components by using computed tomography (CT) x-ray imaging. For example, U.S. Pat. No. 6,895,073 (the '073 patent), issued to Shih et al. on May 17, 2005, discloses a high-speed x-ray inspection apparatus and method. The system of the '073 patent includes three CT x-ray sources and an x-ray detector configured to obtain two-dimensional images of a manufactured component. The images are compared to one or more calibration images of the component, whereby components exceeding a certain threshold are designated as “defective.” Because the system only obtains a limited number of 2-D images, processing time is reduced and automated quality control of the component is expedited.
Although the '073 patent discloses the automated CT x-ray quality control of manufactured components, its usefulness may be limited. Specifically, the number of images provided by the system of the '073 patent may be insufficient to generate a high-resolution image that accurately represents the component. Further, the obtained 2-D images are only compared to the calibration images to determine if a threshold level of accuracy is obtained, without any feedback being provided to the manufacturing process. Therefore, the system may be unable to improve the quality of the manufacturing process itself and the resulting tolerances of the manufactured components.
The present disclosure is directed to overcoming one or more of the shortcomings set forth above. | {
"pile_set_name": "USPTO Backgrounds"
} |
First Steps in WHM - Initial Login and a Quick Tour
In order to access your WHM, you need to add /whm after your domain name (provided the domain is pointed to your VPS with us). So, for example, if your site is domain.com, you will be able to access your WHM interface by visiting http://domain.com/whm.
If your domain is not yet pointed to your VPS, don't worry, you will still be able to access your WHM by typing the server name and then again adding /whm after it. For example, if you are hosted on vps9999.sgvps.net, you will be able to access your WHM at any time by visiting http://vm9999.sgvps.net/whm.
Note that no matter which of the two ways for accessing WHM you use, you will receive a warning that the SSL certificate used for the secure connection cannot be trusted as it is not signed by a known Certificate Authority (CA).
You needn't worry about this warning - the connection is still secure and you can safely accept/trust the certificate. The reason for the warning is that cPanel uses a shared SSL which is self-signed. Once again, this is not a problem and you can safely accept the certificate and proceed to the login page.
When you accept the certificate, a login window will pop up asking you for a username and password. The username is your cPanel username and the password is your cPanel password. If you refuse to enter the login credentials now and click Cancel, you will see the default WHM login page:
Once you log in, you will see the WHM Home/Main page:
In the left column are all the options you have for managing your hosting service. They are divided into several sections and there is a Find option for quickly finding the option you need.
The names of the sections are pretty much self-explanatory and we will cover the most important ones in our tutorials. The sections you will probably visit the most are Packages and Account Functions. This is where you can create, edit and remove hosting packages and accounts. We will cover these in more details next, so read on. | {
"pile_set_name": "Pile-CC"
} |
With President Obama’s re-election, Al Gore’s “24 Hours of Climate Reality” coming up in a week, and the next UN Climate Change Conference starting two weeks later, we are going to be hearing a lot about the so-called consensus among climate experts that our greenhouse gases are causing a climate crisis. Consequently, it is important that climate realists have new, solid “talking points” to rebut this assertion.
Two pieces of evidence are most often cited to support the 97%/consensus argument:
1)A 2010 paper in the Proceedings of the National Academy of Sciences of the United States (PNAS) by Anderegg et al.
2)A poll conducted in April 2008 by Professor Peter Doran and then-graduate student Margaret R. K. Zimmerman at University of Illinois at Chicago . The survey results were summarized in a paper published in January 2009 in the science journal EOS.Contrary to popular belief, the Anderegg et al study did not poll any experts at all. Instead, the paper’s authors merely evaluated the publication record of scientists they chose to represent two sides in the global warming debate. Because I was personally involved in assembling some of the lists of experts cited by the researchers and so understand the limitations of those lists, I am preparing an article explaining why the Anderegg et al study is not a meaningful indicator of expert opinion about this topic.
The Doran/Zimmerman study, which did poll experts, has been thoroughly debunked by many writers and so there is little point in repeating their criticisms in my writings. However, there are two problems with the study that have received little or no coverage to date. Both of these problems destroy the poll’s credibility as a reliable measure of the stance of climate scientists on the supposed climate crisis and I think it is important that as many people as possible know about this. Consequently, the article I just wrote, which is now on the Web at the links below, about the Doran/Zimmerman study focuses on these two largely unknown points. | {
"pile_set_name": "Pile-CC"
} |
Micromandibularia rufa
Micromandibularia rufa is a species of beetle in the family Cerambycidae. It was described by Stephan von Breuning in 1954.
References
Category:Lamiinae
Category:Beetles described in 1954 | {
"pile_set_name": "Wikipedia (en)"
} |
Aahuti (1978 film)
Aahuti is a 1978 Hindi family drama film directed by Ashok V. Bhushan. The films stars Rajendra Kumar, Shashi Kapoor, Rakesh Roshan, Parveen Babi, Zaheera and Madan Puri.
Plot
The story unfolds with custom officer Ajit as Harnam Prasad apprehending a smuggling racket being run on the high seas by Madan Puri as Heeralal, wherein Hiralal is seen by two fisher women, one of whom he kills so that she is not able to testify against him, which is seen by Harnam Prasad. On Harnam Prasad's testimony in the courts as eyewitness to both the smuggling racket and murder of the fisher woman, Hiralal is jailed. Hiralal's gang now seeks revenge against the family of devout Harnam Prasad which comprises his wife; Kamini Kaushal as Kaushalya Prasad and three sons. They sabotage the picnic bus of his two sons, Ram and Laxman, leading it to being thrown off a cliff and burnt, wherein people assume both to be dead. Harnam Prasad is attacked on his boat in the sea, with his third son Bharat, by the same gang's assailant, which leads to the boat crashing on the rocks, and both being assumed, to be missing or dead. Kaushalya Prasad is attacked by this gang with kerosene fire which burns down their house, and she loses both her legs in the inferno. Having lost her family to her husband's duty she goes to commit suicide, but is saved by Dulari (actress) who takes her to her humble abode.
Ram Prasad grows up to be Rajendra Kumar as CID Inspector, and Laxman Prasad (L.P.) as worker in a factory which manufactures Lead Safety Containers for Uranium, for the Government of India also called Lead shielding; which he also protects from landing in the hands of terrorists who make bombs, and thus one of the chief workers, in the good books of the owner Raj Mehra. Rakesh Roshan as Bharat Prasad is however waylaid and is a criminal fisher man working for Heeralal now released from jail. His accomplice is Asha Sachdev as Poonam, who is none other than the daughter of the fisher woman who was killed by Heeralal for her testimony against him.
Heeralal is now into criminal smuggling of both gold and Uranium and wants to clandestinely acquire the Lead Safety Containers from Raj Mehra's factory. Ram Prasad posing as Rocky joins their gang as he wants to apprehend the uranium smugglers. Both Rocky and Bharat Prasad, who is named Badshah by the gang, are however chased by the police and they land in Laxman Prasad's house to whom they introduce themselves as factory workers, to cheat him into joining their nefarious plan of stealing the lead boxes.
The story then leads to how Laxman Prasad is wrongly framed for the theft of the boxes by Rocky and Badshah and the subsequent murder of Raj Mehra. Zaheera as Kusum who is the only daughter of Raj Mehra is pursued by Ram Prasad so that he can steal the lead boxes, but they fall in love. Laxman Prasad is saved from the police by Parveen Babi as Rekha, who is a fellow worker and his love interest. As the plot gets thicker Ram Prasad also reveals his true identity to Laxman Prasad, but not before a fight in which they discover they are brothers by the tattoos on their hands.
Ajit who has now become a CBI Officer, poses as a sea pirate and joins the gang of Heeralal to transport the uranium in the stolen lead boxes, in a ship. Kaushalya Prasad and Laxman Prasad, who had previously reunited when Laxman Prasad was escaping from the police on false charges, are however held hostage on the same ship. After a scuffle on the high seas in the ship, the family of Harnam Prasad is united by the tattoos of their names on their hands and symbol of Om. Pradeep Kumar, as Mac, is another gangster in league with international criminals and Heeralal, out to misuse uranium against India. The movie ends with the family of Harnam Prasad vanquishing the entire gang of smugglers, being true to their legacy of honesty towards their country, and matrimony of the three sons to their love interests.
Cast
Rajendra Kumar as CID Inspector Ram Prasad
Shashi Kapoor as Laxman Prasad (L.P.)
Rakesh Roshan as Bharat Prasad
Parveen Babi as Rekha
Zaheera as Kusum
Asha Sachdev as Poonam
Madan Puri as Heeralal
Ajit as Customs and CBI Officer Harnam Prasad
Kamini Kaushal as Kaushalya Prasad
Dulari (actress)
Raj Mehra as Kusam's Father
Birbal
Preeti Ganguli
Krishan Dhawan
The song "Sathie Mere Sathi Rut Aa Tee Jaate", by Mohd. Rafi, Mukesh and Lata Mangeshkar was the most popular among the songs. The playback singers for the movie were Mohd. Rafi, Kishore Kumar, Mukesh, Manhar, Mahendra Kapoor and Anuradha Paudwal, The music was by Laxmikant Pyarelal and Lyrics by Anand Bakshi.
Songs
"Bharat Ka Bhai Lachhman Lachhman Ka Bhai Raam" - Kishore Kumar, Mahendra Kapoor, Manhar Udhas
"Is Duniya Mein Kaun Sanwaare Sab Ke Bigade Kaam" - Mahendra Kapoor, Anuradha Paudwal
"Jugani Ek Ladki Ka Naam Hai" - Lata Mangeshkar
"Kaash Aisa Hota Kaash Aisa Hota" - Kishore Kumar, Lata Mangeshkar
"Naukari Sau Ki Hazaar Ki Kimat Nahin Hoti Pyaar Ki" - Kishore Kumar, Anuradha Paudwal
"Saathi Mere Saathi Rut Aati JaatiKahe Teri Meri Kahaani" - Mohammed Rafi, Mukesh, Lata Mangeshkar
References
External links
Aahuti YouTube
Category:1978 films
Category:Indian films
Category:1970s Hindi-language films
Category:Films scored by Laxmikant–Pyarelal | {
"pile_set_name": "Wikipedia (en)"
} |
Aging of sensorimotor processes: a systematic study in Fitts' task.
Though age-related decrease in information-processing capacities is hypothesized to be a prominent cause of behavioral slowing, it has been scarcely systematically studied in goal-directed motor tasks. The present study investigated how the decrease in information processing affects the sensorimotor processes underlying the control of a discrete Fitts' task. The index of difficulty (ID) of the task was manipulated using changes in either target distance (D) or target width (W). In each manipulation, movement (MTs), acceleration (ATs) and deceleration times (DTs) of young and older participants were compared across eight ID levels. They were analyzed with efficiency functions, state traces and Brinley plots. Our results showed that older participants were always slower. However, in both age groups, MTs were longer in D manipulation, which resulted from a slowing of both ATs and DTs, while W manipulation affected mainly DTs. In D manipulation, equivalent age-related slowing ratios were observed for AT and DT (1.3). In W manipulation, ATs of older participants were additively slower than those of young participants. Conversely, DTs presented a multiplicative slowing ratio of 1.3. These findings showed that ID manipulations differentially loaded information processing in the nervous system and that age-related slowing of multisensory control processes was independent of the manipulated dimension. Nevertheless, ID manipulations revealed different age-related adaptations to task constraints, suggesting that D and W manipulations are complementary means to assess age-related slowing of the processes involved in target-directed rapid-aiming tasks, with D scaling being more specific to capture the slowing of force-impulse control. | {
"pile_set_name": "PubMed Abstracts"
} |
Almost half of Personnel Today readers are still unsure about the implications of the Equality Act 2010, according to findings from Personnel Today's online quiz on the legislation, elements of which came into force today.
The quiz posed five key questions about issues covered by the Act, with multiple choice answers for each one. Only half (50.5%) of respondents answered all of the questions correctly.
The question that posed the hardest challenge for participants related to whether discrimination can occur when someone is perceived to be something that they are not. It asked whether or not the following statement is true: "If someone is discriminated against because others think they have a protected characteristic, for example, age, disability, gender reassignment, race, religion or belief, sex, or sexual orientation, but they do not, they will not be able to make a discrimination claim". | {
"pile_set_name": "Pile-CC"
} |
As recently reported by the Pneumonia Etiology Research for Child Health (PERCH) study group ([@B1]), the diseases responding to the WHO\'s definition of pneumonia, including pneumonia of bacterial or viral origin but also acute and classical bronchiolitis, are the leading killers of children worldwide (2 million children each year). These infections are usually transitory and can be treated symptomatically in adults. However, complications can result in superinfections originating in many cases by an acute viral or bacterial upper respiratory tract infection followed by invasion of the lower respiratory tract by bacteria, notably in children and in elderly or immunocompromised individuals. The PERCH study estimated that 61% of pneumonia requiring hospitalization in children had a primary viral cause. Respiratory syncytial virus (RSV) arrives on top of a list that also includes rhinovirus, human metapneumovirus (hMPV), parainfluenza virus, and influenza A virus (IAV). Bacterial pathogens such as *Streptococcus pneumoniae, Haemophilus Influenzae*, and *Mycobacterium tuberculosis* are also represented in that list. The development of new prophylactic and therapeutic approaches to reduce the morbidity and the mortality associated with these infections is thus critically needed.
In this Research Topic, a series of original articles and reviews provide some insights on new molecular and cellular therapeutic targets or innovative vaccine strategies against respiratory pathogens.
Current licensed vaccines against IAV are mainly inactivated or live-attenuated viruses that provide only an incomplete protection, most notably for groups at risk. Furthermore, the intranasal route appears to be a promising strategy of inoculation to fight against IAV directly at the primary portal of virus entry compared to classical parenteral administration. [Calzas and Chevalier](https://doi.org/10.3389/fimmu.2019.01605) review the development of innovative delivery/adjuvant systems used for intranasal instillation of inactivated influenza vaccines, including micro/nanosized particulate carriers such as lipid-based particles, virus-like particles (VLPs), and polymers associated or not with immunopotentiatory molecules including microorganism-derived toxins, TLR ligands, and cytokines. In their mini review, [Al-Halifa et al.](https://doi.org/10.3389/fimmu.2019.00022) present an overview of the advantages and limitations of the use of nanoparticle-based vaccines i.e., polymeric, inorganic, and self-assembling protein nanoparticles (VLPs) against respiratory viruses. The development of these new vaccines highlights the recent advances in chemical and biological engineering which allow the controlled design of safe nanoparticles (in size, shape, and functionality) to enhance antigen presentation and strong immunogenicity. The capacity of these vaccines to trigger specific mucosal and systemic humoral and cellular responses against respiratory pathogens and their (cross)-protective potential are also explored in those two reviews. The efficacy of vaccines is also correlated with the matching between the circulating and the vaccine strain, notably for IAV or RSV which are subject to a constant antigenic drift. In their original research article, [Bernasconi et al.](https://doi.org/10.3389/fimmu.2018.02060) describe the development of a broadly protective universal influenza vaccine based on porous nanoparticles of maltodextrin incorporating recombinant self-adjuvanted M2e (ectodomain of the matrix 2 protein of IAV which is highly conserved among IAV strains) and hemagglutinin. They demonstrate that the intranasal instillation of their vaccine enhances immune protection against live homologous or heterologous IAV infections and decreases the risk of virus transmission. The protection is mediated by specific mucosal and systemic humoral and cellular responses. The outcome of vaccination can also be impacted by the phenomenon known as the original antigenic sin mostly associated with pre-existing antibodies against close viral strains that might impair antibody formation against previously unseen strains. [Nienen et al.](https://doi.org/10.3389/fimmu.2019.00593) elucidate the role of IAV-specific helper T cells upon vaccination with unexperienced IAV strains in a healthy adult human cohort. In this original article, authors reveal that the pre-existing cross-reactive memory T cells provides sufficient help to naive B cells specific to previously unseen IAV strains and their baseline quantity directly correlated with vaccination efficacy.
Another alternative against respiratory pathogens is the development of anti-viral approaches. The dynamics of evolution, emergence and resistance of respiratory pathogens such as IAV highlights the critical need to enlarge the therapeutic arsenal available. [Pizzorno et al.](https://doi.org/10.3389/fimmu.2019.00531) summarize in their review the state-of-the-art of current antiviral options against IAV infection and focus on the recent advances of anti-IAV drug repurposing strategies. The development of new approaches based on the combined targeting of host cell and the viral components could constitute effective strategies to avoid the emergence of resistant IAV mutants as often observed with the use of conventional antivirals. Many strategies are exploited to achieve this goal and are well illustrated in the review with examples ranging from serendipitous observations to *in silico*-assisted repurposing. In the original article associated to this review, [Pizzorno et al.](https://doi.org/10.3389/fimmu.2019.00060) present the implementation of drug repurposing by exploiting *in vivo* global transcriptomic signatures of IAV-infected patients to determine the potential of already marketed drugs with newly identified inhibitory properties against IAV. Among a list of promising candidates, they demonstrate that diltiazem, a calcium channel blocker used to treat hypertension, in combination with oseltamivir increases antiviral efficacy. In their work, [Fusade-Boyer et al.](https://doi.org/10.3389/fimmu.2019.00134) identify Sephin1, an inhibitor of cellular phosphatase, as an antiviral molecule against RNA and DNA viruses, and notably RSV. [Nyanguile](https://doi.org/10.3389/fimmu.2019.01366) reviews peptide-based antiviral strategies against RSV and IAV. Long-acting macrocyclic peptides targeting large protein-protein interactions could be used to target critical regions such as the IAV hemagglutinin stalk domain or the RSV fusion protein to impede virus fusion. Finally, [Le Nouën et al.](https://doi.org/10.3389/fimmu.2019.01250) review synonymous recoding strategies used to attenuate RSV and IAV: deoptimization of codon or codon-pair usage, reduction of viral protein expression, increase of the content of immunomodulatory CpG and UpA RNA dinucleotides and substitution of codons limiting evolutionary potential of the virus by increasing the probability of insertion of non-sense codons. The accumulation of synonymous mutations inserted to obtain the deoptimized virus should reduce drastically the risk of reversion while preserving the integrity of viral antigens. Such deoptimized IAV and RSV viruses have been generated and their characterization as vaccine candidates is described in this review.
With the emergence and spread of drug-resistant strains of *M. tuberculosis*, there is an urgent need to develop alternative anti-tuberculosis strategies. The parenteral live attenuated Bacillus Calmette-Guérin (BCG) vaccine, widely used during the past decades, protects infants and children against severe extra pulmonary forms of tuberculosis. However, it is inconsistently efficient against the most common respiratory form of the disease (pulmonary tuberculosis), is known to cause adverse effects in immunocompromised individuals and does not prevent the establishment of latent persistent infection. In recent years, a better understanding of the immunopathogenesis of *M. tuberculosis* infection allowed the development of more efficient anti-tuberculosis strategies, including the generation of more refined subunit vaccines and host-directed therapies (HDTs).
A proposed effective vaccine strategy is to trigger mucosal and/or parenteral host immunity with selective recombinant *M. tuberculosis* antigens associated with suitable delivery/adjuvant systems. [Hu et al.](https://doi.org/10.3389/fimmu.2018.01796) demonstrate that a prime with BCG vaccine followed by a boost with a novel intranasal Sendai virus vectored vaccine encoding *M. tuberculosis* immunodominant antigens enhance the generation of specific systemic and lung poly-functional CD4^+^ and/or CD8^+^ T cell responses in mice. The authors suggest the improved protection against *M. tuberculosis* infection subsequent to the prime-boost immunization regimen is associated with higher levels of recall IL-2-mediated lung CD4^+^ and CD8^+^ T cell responses and a higher frequency of central memory CD4^+^ T cells in the lung. [Thakur et al.](https://doi.org/10.3389/fimmu.2018.02825) evaluate for the first time the immunogenicity of a multistage tuberculosis subunit vaccine combining early antigens and a latency-associated protein with liposome-based cationic adjuvant upon parenteral prime and intrapulmonary boost administration in mice. Stronger systemic and lung antigen-specific polyfunctional CD4^+^ T cells and IgA responses are elicited with this vaccination course in comparison with parenteral prime-boost vaccination. By using non-invasive tomography imaging, the authors gain information on the anatomical biodistribution and pharmacokinetics of the vaccine, which could help in the development of effective mucosal vaccines against pulmonary tuberculosis. Finally, based on structural and functional analyses of domains III and IV of *Staphylococcus aureus* immunomodulatory protein Sbi (Sbi-III-IV), [Yang et al.](https://doi.org/10.3389/fimmu.2018.03139) rationally design an auto-adjuvanted fusion protein vaccine against *M. tuberculosis*. By harnessing the alternative complement pathway dysregulating function of Sbi-III-IV, the authors improve immune responses against a *M. tuberculosis* vaccine antigen administered via the parenteral route in mice through its coating with C3 breakdown fragments.
[Soto et al.](https://doi.org/10.3389/fimmu.2018.02875) demonstrate that the use of the BCG vaccine as a vector for recombinant expression of heterologous antigens is an attractive vaccine approach against RSV and hMPV. Recombinant BCG vaccines expressing either the nucleoprotein of RSV or the phosphoprotein of hMPV induce a cellular immune response able to boost the humoral response against RSV or hMPV antigens beyond those encoded by the vaccines and prevent the disease caused by both pneumoviruses in mice. A pathological hallmark of tuberculosis is the formation of granulomas in the lung, which are organized immunological structures composed of various innate and adaptive immune cells containing the pathogen. However, granulomas can undergo complex structural changes resulting in tuberculosis progression and attractive HDTs against tuberculosis consist in targeting granulomas. [Remot et al.](https://doi.org/10.3389/fimmu.2019.00417) review and discuss the role of neutrophils within the tuberculosis granuloma and the impact of the hypoxic environment encountered in the tuberculosis granuloma on key neutrophil-released mediators. The authors highlight the modulation of hypoxia-induced factors as an attractive innovative HDT against tuberculosis. [Jones et al.](https://doi.org/10.3389/fimmu.2019.00644) also target neutrophils to fight against *Aspergillus fumigatus* by using bifunctional compounds combining moieties that bind to the surface of the pathogen and moieties that interact with chemoattractant receptors on human neutrophils. The authors show that these compounds enhance the activity of neutrophils against *Aspergillus fumigatus in vivo* and *in vitro*, using a zebrafish infection model and using neutrophils isolated from healthy humans and immunosuppressed patients, respectively.
[Voβ et al.](https://doi.org/10.3389/fimmu.2018.02405) validate that the intranasal vaccination with lipoproteins is a new protective strategy against nasopharyngeal colonization by *S. pneumoniae*. Lipoproteins (PnrA, DacB, and MetQ) from pneumococcal serotypes, known to act as adhesins, are abundant at the surface of the pathogen, conserved, and highly immunogenic in mice. The knowledge of host-pathogen interactions and of the mechanisms of immune responses allows proposing innovative immunomodulatory strategies by targeting innate receptors, such as Toll-like receptors (TLRs), to selectively boost innate immunity and therapeutic treatment outcome. In an original research article, [Matarazzo et al.](https://doi.org/10.3389/fimmu.2019.00723) demonstrate that the local delivery in the respiratory tract of flagellin, a natural agonist of TLR5, is able to provoke the production of various innate immunity-related components, including chemokines, inflammatory cytokines, and antimicrobial peptides. This treatment, in association with an antibiotic administration, induces synergistic antibacterial effects against infections caused by *S. pneumoniae* in mice. Innovative formulations targeting innate immune cells are also of great interest to improve vaccine efficacy. [Matthijs et al.](https://doi.org/10.3389/fimmu.2019.01087) compare the immunogenicity of novel *M. hyopneumoniae* bacterin formulations associated with a cocktail of TLR1/2, TLR7, and TLR9 ligands in pigs. In this original paper, authors adapt the human-based approach of "blood transcriptional modules" to identify early immune signatures in the blood related to adaptive responses in pigs ([@B2]).
Traditionally, anti-infectious vaccines aim at targeting specific microbes by generating potent and long-lasting antigen-specific adaptive B and T cell immune responses. However, a growing body of evidence demonstrates that some vaccines can exhibit non-specific beneficial effects against heterologous infections. [Cauchi et al.](https://doi.org/10.3389/fimmu.2018.02872) review the ability of a live attenuated pertussis vaccine to protect mice against heterologous airway infections, such as those caused by other *Bordetella* species, likely due the generation of cross-reactive B or (regulatory) T cells. The vaccine is also efficient against unrelated pathogens (IAV, RSV) and non-infectious inflammatory diseases (allergic asthma, contact dermatitis) and the authors discuss the presumed mechanisms involved in such protection, including trained innate immunity, as well as possible mechanisms underlying the anti-inflammatory effect of the pertussis vaccine.
In summary, the compilation of articles published within this Research Topic should give an overview of different innovative preventive and therapeutic approaches to fight against respiratory pathogens, including the rationale design of vaccine antigens and delivery/adjuvant systems in association with the understanding of immune mechanisms which contribute to vaccine efficacy, drug repurposing, and peptide therapeutics.
Author Contributions {#s1}
====================
CCa, DD, and CCh contributed to the preparation, review, and revision of the manuscript. MC participated in the preparation of the Research Topic.
Conflict of Interest
--------------------
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 all authors who participated in this Research Topic and reviewers for their insightful comments. We thank Jean Millet (VIM, INRAE, Jouy-en-Josas) for the critical reading of the manuscript. In memory of our collaborator, MC (1947--2019), Scientist Emeritus at INSERM, the French National Institute of Health and Medical Research and Associate Editor in this Research Topic.
**Funding.** This work was supported by a grant from the Livestock Vaccine Innovation Fund (LVIF) (Canada\'s International Development Research Centre, Bill & Melinda Gates Foundation, Global Affairs Canada).
[^1]: Edited and reviewed by: Denise Doolan, James Cook University, Australia
[^2]: This article was submitted to Vaccines and Molecular Therapeutics, a section of the journal Frontiers in Immunology
[^3]: †These authors share first authorship
| {
"pile_set_name": "PubMed Central"
} |
package com.enonic.xp.impl.server.rest.model;
import java.util.List;
import java.util.stream.Collectors;
import com.enonic.xp.dump.BranchDumpResult;
public class BranchDumpResultJson
{
private final String branch;
private final Long successful;
private final List<DumpErrorJson> errors;
private BranchDumpResultJson( final Builder builder )
{
this.branch = builder.branch;
this.successful = builder.successful;
this.errors = builder.errors;
}
public static BranchDumpResultJson from( final BranchDumpResult result )
{
return BranchDumpResultJson.create().
branch( result.getBranch().toString() ).
successful( result.getSuccessful() ).
errors( result.getErrors().stream().map( DumpErrorJson::from ).collect( Collectors.toList() ) ).
build();
}
@SuppressWarnings("unused")
public String getBranch()
{
return branch;
}
@SuppressWarnings("unused")
public Long getSuccessful()
{
return successful;
}
@SuppressWarnings("unused")
public List<DumpErrorJson> getErrors()
{
return errors;
}
private static Builder create()
{
return new Builder();
}
public static final class Builder
{
private String branch;
private Long successful;
private List<DumpErrorJson> errors;
private Builder()
{
}
public Builder branch( final String val )
{
branch = val;
return this;
}
public Builder successful( final Long val )
{
successful = val;
return this;
}
public Builder errors( final List<DumpErrorJson> errors )
{
this.errors = errors;
return this;
}
public BranchDumpResultJson build()
{
return new BranchDumpResultJson( this );
}
}
}
| {
"pile_set_name": "Github"
} |
1. BACKGROUND
=============
1.1. Prevalence of Croup
------------------------
Croup or acute laryngotracheobronchitis is a common illness, which is most prevalent in young children between the ages of 6 and 36 months, and has a large impact on health services. Croup is a common reason for accessing out-of-hours care \[[@r1]\] and is a frequent cause behind hospital admissions of children between 6 months and 3 years \[[@r2]\]. Admission rates of children assessed in outpatient settings range from 1.5% to 31% of the cases seen, depending on hospital admission policies, the severity of the disease, and the social and other characteristics of the population being assessed \[[@r3]\].
Usually appearing as a self-limiting illness, croup often causes parental anxiety, and imposes a large burden on healthcare systems \[[@r3]\]. However, most symptoms of mild croup usually resolve within 48 hours. In some cases, severe upper-airway obstruction can lead to respiratory failure and arrest, but such cases are rare \[[@r4]\]. Most children are managed through primary care, with less than 5% requiring hospitalisation, among which 1-3% require ventilator support in an intensive care setting \[[@r5]\].
The economic burden imposed by croup has been demonstrated in a study by Rosychuk *et al*, \[[@r6]\] which reported that there were 27,355 emergency admissions at accident and emergency settings in the province of Alberta, Canada, for episodes of croup over a six-year period. The incidence of croup among children is reported at three children per one hundred children in the United States in a typical year, with as many as 6% of those children requiring hospitalisation \[[@r6]\]. Figures are similar in Australia, with croup affecting 3% of children under 6 years of age in a typical year \[[@r7]\]. One retrospective Belgian study found that 16% of children aged 5-8 years had suffered from croup at least once and 5% of those children had experienced recurrent croup (at least 3 episodes) \[[@r8]\].
Respiratory tract infections such as croup in children are one of the most common reasons for parents consulting health professionals, with viral croup being the most common form of airway obstruction in children between six months to six years \[[@r9]\]. One long-term prospective cohort study suggested that croup occurred most commonly in children aged between 6 months and 3 years, but can also occur in children as young as 3 months and as old as 12-15 years \[[@r10]\].
1.2. Aetiology of Croup
-----------------------
Croup is more prevalent during autumn and early winter with major peaks coinciding with Para-influenza activity often observed in October \[[@r11]\]. The following are the most common viral causes for croup: Para influenza type 1 and 2, Influenza A, adenovirus, rhinovirus, respiratory syncytial virus and, mycoplasma pneumonia \[[@r12]\]. The Para influenza virus type 1 accounts for approximately half of all cases throughout the winter \[[@r13]\]. These common viruses can affect the narrowest part of the airway called the subglottic region, and even small amounts of swelling or oedema can significantly increase the difficulty involved in breathing in young children \[[@r14]\]. As oedema of the proximal airway epithelium progresses, inspiratory stridor and signs of breathing difficulties supervene \[[@r15]\]. This is due to the small children having a very narrow larynx such that even a small decrease in airway radius can cause a large decrease in airflow, leading to croup symptoms. Commonly between the ages of 1 and 3 because as children become older, their breathing tube becomes firmer and wider and so the incidence of croup reduces \[[@r1]\].
Several other factors may make a child more likely to suffer with croup. This may be due to the pre-existing narrowing of the upper airway, subglottic stenosis (congenital or secondary to prolonged neonatal ventilation) or Downs syndrome \[[@r16]\]. Furthermore, Alshehr **et al.**, \[[@r17]\] suggests that there is increasing evidence that an immunological component for acute croup coincides with high titres of both Para influenza virus and specific immunoglobulin E in the children's nasal secretions. This may explain why croup will often affect atopic children who may already suffer with asthma or eczema.
1.3. Corticosteroids in The Treatment of Croup
----------------------------------------------
Oral corticosteroids act on the subglottic oedema and obstruction by decreasing capillary permeability and suppressing localised inflammation \[[@r18]\]. The exact mechanism of the administration of steroids in croup is not fully understood \[[@r13]\] but it is known that glucocorticoids also have vaso-constrictive effects that may contribute to their clinical actions by resulting in reduced airway oedema, less micro-vascular leakage, and reduced airway mucus production \[[@r19]\]. When used as croup treatments, glucocorticoids reduce the inflammation in the airway obstruction as quickly as one hour after administration \[[@r20]\]. A reduction in these inflammatory properties leads to a decrease in the difficulty of breathing for the child.
Prednisolone or dexamethasone may be given orally or intramuscularly, both of which have superior efficacy to placebo but oral preparations of corticosteroids are the preferred mode of administration in most paediatric emergency departments because they are inexpensive, easy to administer, readily available, and result in measurable improvements \[[@r21]\]. Systemic corticosteroids (dexamethasone, prednisolone) are the treatment of choice because benefits can be seen in patients with all levels of croup severity \[[@r22]\].
The half-life of dexamethasone is approximately double of that of prednisolone, and estimates range from oral dexamethasone having an effective half-life of 48 hours, compared with the 24 hours' half-life of prednisolone to prednisolone's relatively short-acting half-life of 12-36 hours, thereby requiring daily dosages \[[@r23], [@r24]\]. In comparison, prednisolone is up to six times less potent than dexamethasone with hypothalamic-pituitary-adrenal axis suppression in prednisolone lasting 1.5 days against 2.5 days in case of dexamethasone \[[@r20]\]. Extensive evidence in the form of primary studies \[[@r14], [@r25]-[@r28],\] shows that the administration of steroids in a single dose of corticosteroid lessens the risk of a child needing hospital admission or re-presenting for further medical care. Meta-analysis of 24 randomised controlled trials \[[@r25]\] reviewed nine methodically satisfactory trials, five favourable and four unfavourable, involving steroids in the treatment of croup, which supported the use of steroids for children who were ill enough to be hospitalised. Among the included studies, dexamethasone, budesonide, and prednisolone were all included and the results were amalgamated, which made it not possible to identify each arm of the group, instead they were examined as a whole cohort. This meta-analysis concluded that glucocorticoids were effective at improving symptoms within six hours, for up to 12 hours \[[@r25]\]. A further meta-analysis \[[@r28]\] reports main outcomes, clinical improvement, and croup scores of the children at 12 and 24 hours post treatment and the incidence of endotracheal intubation, and provided a reliable estimate of the impact of steroid therapy on the morbidity associated with croup at that time. Reported data from the ten clinical trials involving children with severe croup showed that corticosteroid treatment decreased endotracheal intubation fivefold. Children with mild croup only require reassurance, suggesting that at that time there was no evidence that steroids have a place in management in this group, although a single dose of prednisolone is probably appropriate for children with 'stridor at rest', but no recession \[[@r29]\].
Evidence clearly supports the use of oral, parenteral, or nebulised corticosteroids for children admitted with croup \[[@r3], [@r14]\] and it has been demonstrated that the glucocorticoid treatment of croup has consistently led to improvements in symptoms so much so that they infer that studies involving just dexamethasone are unwarranted as there is so much evidence that it works, but there is a lack of direct comparison studies of dexamethasone *versus* prednisolone, with very little literature available \[[@r30]\]. However, concerns exist about using oral steroids to treat croup, as these types of drugs with their long serum half-lives could have sustained effects on multiple systems, and may reduce the immune function \[[@r17]\]. One study \[[@r31]\] reports that four or more courses of oral prednisolone during childhood may have adverse effects, including an increased fracture risk, although there are no relevant comparison studies. It appears that the risks of administering single-dose corticosteroids are very low, but should be considered in children with diabetes mellitus, children exposed to varicella virus, children at risk of bacterial super infection (*i.e.*, those who are immunocompromised), or have gastrointestinal bleeding \[[@r32]\]. The small benefits of steroids for mild croup have been discussed as not worth the risk of serious adverse effects which can be seen in as many as eight children per thousand who are treated with steroids \[[@r33]\]. A Cochrane review \[[@r34]\] disputed such safety concerns, providing comprehensive safety data on the use of steroids in 2,214 children with acute respiratory conditions, including croup and other respiratory problems such as asthma, concluding that the results showed no difference between children receiving steroids *versus* a placebo 1.5% V 1.8% (gastrointestinal bleeding and or abdominal pain in the steroid group *versus* the placebo group). Gastrointestinal bleeding would be unlikely in otherwise healthy children \[[@r12]\].
2. RATIONALE FOR THIS SYSTEMATIC REVIEW
=======================================
In the United Kingdom, there is currently a nationwide difficulty in obtaining dexamethasone syrup for the treatment of croup in children, which has led to the default prescription of the only other alternative, prednisolone. In some areas in the UK, clinicians have been unable to obtain dexamethasone syrup for some time, and dosing regimens vary between emergency, primary and secondary care settings. Many children with croup are being treated with a one-off dose of prednisolone, although a two or three-day treatment at varying doses has also been noted, with the prescribing of prednisolone appearing to be used in a similar way to treating exacerbations of asthma in children, with up to a three-day course; however, there is confusion in the available literature about what dose of prednisolone to give and for how long. It is not clear what the most therapeutically effective range is and this lack of clarity drives the need for this review. Commercially, at the time of writing, oral dexamethasone was only available locally as a tablet, which makes it unsuitable for young children \[[@r5]\]. Hospital pharmacists can make it up in the form of a dexamethasone elixir, but that is expensive and not available in general practice \[[@r35]\]. Prednisolone has pharmacokinetic properties similar to dexamethasone, and has the significant advantage in that it is commercially available in a liquid preparation. Prednisolone can be prescribed as a soluble tablet; which parents can crush into a little juice or water to give to their children.
In Australia, where a majority of the major croup studies have taken place, oral dexamethasone suspension is only available in hospitals and not at commercial pharmacies, thus necessitating the use of prednisolone in primary care settings \[[@r16]\]. Liquid dexamethasone preparations are also not available in many counties, including Germany and most other European countries \[[@r36]\].
3. MATERIALS AND METHODS
========================
The purpose of systematic reviews is to determine effectiveness and involve the comparison of two or more interventions \[[@r37]\]. Systematic reviews of other types of evidence can facilitate decision-making in areas where randomised controlled trials (RCTs) have not been performed or are not appropriate \[[@r38]\]. They are considered the best way to synthesise the findings of several studies, all investigated in the same way \[[@r39]\] noting that systematic reviews have become the gold standard for evidence-based decision-making, and provide building blocks for clinical practice guidelines \[[@r40]\]. Systematic reviews are essential to summarise evidence relating to efficacy and safety of healthcare interventions. With their synthesis of a large body of evidence they aid policy makers and professionals to keep up-to-date with advances \[[@r39]\].
Systemic reviews and meta-analysis provide the highest level of evidence. However, poor reporting may reduce their utility. The PRISMA statement was developed to help authors report their systematic reviews adequately \[[@r41]\] and has been incorporated into this systematic review. There are several approaches to this process but all follow similar steps, which are identifying the problem, finding the research, and determining the level of evidence \[[@r42]\]. The PRISMA statement aims to improve reporting focussing on systematic reviews of RCTs and systematic reviews that need to adhere to rigorous methodology to produce clear and unbiased results \[[@r43]\].
Centre for Reviews and Disseminations (CRD) \[[@r44]\] recommend that before undertaking a systematic review, researchers should check whether there are existent or on-going reviews on their area of interest, and whether a new review is justified, beginning the process by searching the Database of Abstracts of Reviews of Effects (DARE). To date, there are no other systematic reviews that specifically look at the issues of whether prednisolone is as effective as dexamethasone for this very common childhood complaint, which makes this work important. Yet it is acknowledged that there are several systematic reviews of all treatments for croup, which include prednisolones usage, and some of which compare prednisolone to dexamethasone \[[@r14], [@r20], [@r25]-[@r28]\]. However, no new systematic reviews have been conducted since 2011.
3.1. Review Aims
----------------
To investigate the comparative effectiveness at reducing croup in children under 12 years of oral dexamethasone and prednisolone, and to examine the optimum dose of prednisolone to prevent relapsing symptoms and re-admission.
3.2. PICO
---------
Using PICO helps structure a search, and should include the main terms relating to the research question \[[@r45]\]. PICO is one of the tools that can assist in formulating research questions \[[@r44]\], and a clear concise question will make it easier to generate the best available evidence \[[@r46]\]. The PICO developed for this systematic review is shown in (Table **[1](#T1){ref-type="table"}**).
3.3. Population
---------------
The population for this study is children who have croup. The area of interest is the treatment or therapy of children suffering with croup. The age range for this review is set at 3 months-12 years \[[@r1]\] as this is the most typical age bracket during which children are affected. Gender is not a variable in this study, although it is noted that croup typically affects more boys than girls.
3.4. Intervention
-----------------
The intervention will examine the use of prednisolone when used as a croup treatment in any severity of croup when used in either isolation or placebo or when used as alternative treatment to dexamethasone.
3.5. Comparative Intervention
-----------------------------
Only studies that examine prednisolone as a stand-alone treatment for croup, or compare prednisolone to dexamethasone will be used.
3.6. Outcomes
-------------
What is being measured is the reduction in symptoms in the children, based on the use of either drug, but only when compared to each other, *i.e.* primary outcomes are changed in clinical croup scoring from baseline to time in the future as defined by the researchers. Which drug they received, how much of it, and for how they long and which the key outcomes were measured. Also return visits and readmissions are secondary outcomes, which are measured.
3.7. Time Frame
---------------
2000-2016.
3.8. Review Questions
---------------------
The questions that this systematic review seeks to answer are:
1\. Is a single dose of oral prednisolone as effective as a single dose of dexamethasone at reducing croup severity score in children under 12 years?
2\. What is the optimum dose of prednisolone to prevent relapsing symptoms and re-admission?
3.9. Search Strategy
--------------------
A methodical approach based on PRISMA guidelines for undertaking reviews using electronic databases to search the literature, which was supplemented by hand searching and cross referencing. The search was based on a pre-determined series of keywords which are related as follows: Croup AND Prednisolone AND dexamethasone. Fig. (**[1](#F1){ref-type="fig"}**) shows the combined results of the searches in a PRISMA flow diagram.
The time period is selected on the basis that around 2000 onwards, the intervention of using steroids became more widespread with some of the biggest steroid trials in mild croup being conducted in the early part of that decade.
3.10. Databases
---------------
The following databases were searched:
CINAHL (Cumulative Index of Nursing and Allied Health Literature);
MEDLINE EBSCO;
MEDLINE OVID;
PubMed;
ProQuest;
EMBASE;
Joanna Briggs Institute;
SUM search;
OpenGrey;
Cochrane Database of Systematic Reviews (CDSR);
Cochrane Central Register of Controlled Trials (CCRCT);
BIOSIS and Health Services/Technology Assessment (HSTAT) and
The National Research Register.
In addition, AE wrote to trial authors of studies, and the two who replied both reported that no unpublished results were available at that time.
3.11. Inclusion and Exclusion Criteria
--------------------------------------
**Inclusion:**
- RCTs, Case controlled studies and cohort studies.
- Studies needed to be published in English and full text available.
- Content relates directly to croup and its treatments involving prednisolone alone or in comparison to dexamethasone.
- Publication of a research study within a peer-review journal.
- Research must be related to the treatment of croup in children.
- Research must include prednisolone alone or in comparison to dexamethasone, noting that oral or intra-muscular treatments were the preferred methods of treating croup for this systematic review.
**Exclusion:**
- Studies that did not examine prednisolone or dexamethasone in relation to croup.
- Studies that used other drug therapies such as nebulised adrenaline or budesonide.
- Studies that examined rectal dosing of prednisolone.
- Studies that just examined dexamethasone.
- Studies pertaining to cases when treatment was such that children were admitted to an Intensive Therapy setting.
- Studies involving children with illnesses other than croup, for example upper respiratory tract infections, asthma, or bronchiolitis.
- Studies examining severely ill children or children with a structural abnormality of the upper respiratory tract.
3.12. Screening
---------------
A two-stage process was used during screening. Stage one involved screening the article and the abstract against the inclusion criteria. If there was uncertainty over the suitability of the publication, the full text of the article was assessed. Potential usefulness was identified from the abstracts by the initial search for appropriateness to the study question. Relevance was based on the review of the title and the abstract. Two studies were excluded because they were systematic reviews. Stage two involved screening of the full text of articles against the inclusion criteria. Studies examining rectal doses or the ones that examined children who were intubated were also excluded because they did not appear relevant to study or its aims, and not did not seem applicable to primary care or general practice.
3.13. Quality Assessment
------------------------
Following the full-text selection, the studies were assessed for methodological quality. Systematic reviews rely substantially on the assessment of the methodological quality of the individual trials, and quality assessment allows means that papers can be excluded papers or weighted in the analysis phase of the review, and to determine whether research quality makes a difference to the nature of the findings \[[@r47], [@r48]\]. The quality of the randomised controlled studies and the chart reviews were assessed using the QualSyst tool for quantitative studies. The scoring system is peer-reviewed \[[@r38]\] and based upon established quality assessment tools for quantitative studies. To use the QualSyst assessment, each study is scored according to the degree to which they meet 14 criteria (yes = 2, partial = 1, No = 0). Items not applicable to a particular study design can be marked N/A and can be excluded from the total summary score \[[@r49]\].
In this systematic review, one reviewer (AE) and another author (GW) reviewed the studies independently, and both graded the quality of each paper to be included. Both authors agreed on the same quality scoring of all the papers included. All the studies selected met the minimum threshold of a summary score of 0.6. Four studies met all the criteria for inclusion.
4. RESULTS OF THE SYSTEMATIC REVIEW AND CRITICAL APPRAISAL
==========================================================
4.1. Heterogeneity
------------------
In the context of systematic reviews, statistical meta-analysis of findings is not always possible. Meta-analysis should only be considered when a group of studies is sufficiently homogeneous in terms of participants, interventions, and outcomes in order to provide a meaningful summary \[[@r50]\]. Since all of the studies included measured different outcomes, used different drug doses, and differing lengths of treatment time, it was not possible to pool the collective results and so a narrative approach was taken. This is outlined in Table **[2](#T2){ref-type="table"}**. Narrative synthesis aims to summarise and explain the findings of the synthesis primarily relying on the use of words and text to summarise (rather than statistics) and should encompass the analysis of the relationship within and between the studies, as well as provide an assessment of the evidence \[[@r51]\].
4.2. Randomisation and Blinding
-------------------------------
All of the randomised controlled trials in this review reported sufficient information for them to be assessed as adequately randomised with adequate concealment of allocation and blinding of the participants and researchers \[[@r56]\]. Allocation bias can occur when the measured treatment effect differs from the true treatment effect because of how participants were selected into the intervention or control groups \[[@r57]\]. To avoid this, patients should remain unaware of which treatment is being given until the study is completed \[[@r58]\], and this was achieved by double blinding the participants and the researchers in all the RCTs. It must be noted that allocation concealment is completely different when blinding the former, which seeks to eliminate selection bias during the process of recruitment and randomisation, whereas blinding the latter seeks to reduce performance and ascertainment bias after randomisation \[[@r59]\].
There was no selection bias in the RCTs, which is concerned with systematic differences arising between the sampling population and the sample drawn. Selection bias occurs when the subjects studied are not representative of the target population about whom the conclusions are to be drawn \[[@r60]\]. All the children were randomly selected upon entering the trial from either the emergency department or the selected primary care offices, although they needed to have similar baseline observations and follow-up ability as this was important. Selection bias as one of the major types of bias that can impair the results of a randomised control trial but due to the nature of the design of a trial it can, and should be, avoided \[[@r61]\]. Randomised control trials have the unique advantage of using randomisation as a method of determining patient allocation to treatment, which eliminates selection bias if correctly executed notes that bias can cause estimates of association to be either larger or smaller than a true association \[[@r62], [@r63]\]. Also randomised control trials rest on internal validity, which is based largely on the power of randomisation, to ensure that the only difference between two treatment arms is their exposure to the treatment of interest \[[@r63]\].
All of the studies clearly reported the number and the ages of the children who participated in the studies as well as the inclusion/exclusion criteria. In all of the RCTs, the studies reported co-interventions. For example, use of budesonide or adrenaline, or exclusion of children due to the severity of the illness. In fact, all of the studies reported dropouts, or children who needed intubation, or those whose parents withdrew consent.
4.3. Sample Sizes and Attrition
-------------------------------
New research studies should seek preliminary evidence that the intervention is likely to be beneficial (from other similar studies). Such information is needed to estimate sample sizes and justify the expense of a trial \[[@r58]\]. Since information is based on previous studies, a size calculation can be made based on whatever clinically meaningful difference is considered important to be detected \[[@r64]\].
The three trials used the intention to treat approach \[[@r52]-[@r54]\]. All of these studies appeared to report all the outcomes initially stated as their objectives. This means that patients were normally analysed within the group to which they were allocated, irrespective of whether they continue to experience the intended intervention or not (intention to treat analysis) \[[@r58]\].
The size varied in the trials but was generally small (under 200). However, to account for heterogeneity, RCTs need to be quite large to achieve statistical significance. Garbutt **et al.** \[[@r54]\] acknowledge recruiting issues in their trial with authors being unable to recruit their target sample of 200 patients, so much so that they remarked that there is a failure to demonstrate a significant difference between the two study drugs because of inadequate power associated with the small sample size \[[@r54]\]. Like Garbutt **et al.**'s trial \[[@r54]\], Fifoot and Ting \[[@r53]\] found that their trial was powered sufficiently to give primary outcome of reduction in the Westley croup score. However, they had insufficient numbers to prove that there would be no difference in representation between the groups' secondary outcomes. Also, inflation effect can be present in small low-powered studies, which can only detect effects that happen to be large \[[@r65]\]. Parker **et al.** \[[@r55]\], only analysed data from 188 children using descriptive statistics but did not include a power calculation for their trial. Every retrospective chart review requires a statistical power analysis to determine the appropriate sample size. Calculating this appropriate sample size is a necessary component in all research proposals and is dependent on the statistical tests used in the study \[[@r66]\].
Without detailed information regarding the sample size calculation used when publishing papers type II statistical errors cannot be discounted \[[@r67]\]. Relatively large samples obtained by probability or non-probability sampling are generally used for quantitative theory-testing research designs \[[@r42]\] as seen in the larger studies. Researchers have an ethical responsibility to recruit an adequate size for their trials \[[@r42]\], but it is unethical to include more research participants than are actually needed to obtain accurate data \[[@r68]\]. The minimum accepted level is considered to be 80%, which means there is an eight in ten chance of detecting a difference of the specified effect size \[[@r69]\]. Usually, most studies accept a power of 80%. This means that it is accepted that one in five times (that is 20%) real difference will be missed. Low statistical power (because of the low sample size of studies, small effects, or both) negatively affects the likelihood that a nominally statistically significant finding can actually reflect a true effect \[[@r65]\]. Power calculations tell us the number of patients that are required in order to avoid a type I or a type II error \[[@r70]\]. Nearly all quantitative studies can be subjected to a sample size calculation \[[@r70]\]. The statistical power describes the probability that the study will detect and affect where there is a genuine effect to be found \[[@r71]\]. Low power in the absence of other biases can contribute to producing unreliable findings even when all other research practices are ideal \[[@r65]\]. If statistical power is positively correlated with the sample size and the larger sample size, researchers will be enabled to find smaller differences, which are statistically significant \[[@r72]\]. Many null studies may be underpowered to detect the desired difference due to a smaller sample size \[[@r67]\], in which case they will be statistically inconclusive and may make the whole protocol a failure \[[@r72]\]. Some studies may be over-powered (too many participants) and so it is important to achieve the correct balance \[[@r69]\].
Garbutt **et al.** \[[@r54]\] did not recruit their target sample of 200 patients and failed to demonstrate a significant difference between the two study drugs, which was due to the inadequate power associated with the small sample size. Their target sample size was 100 patients per group, based on the goal of estimating the number of children needed in each arm of the trial to achieve a 95% confidence interval (CI). Fitfoot and Ting's (2007) sample size calculations were based on detecting a difference in the croup score baseline between the three intervention groups, and based on the sample size, the difference was calculated at 33 patients per group.
Many children suffering from croup were not approached owing to the pressure on emergency staff over a busy winter period \[[@r52]\]. Garbutt **et al.** \[[@r54]\] remarked that their results might not be generalizable to other communities as they recruited patients from just one geographic area. Additionally, they did not present or discuss how representative the patients were of all the patients with croup who were cared for at the study sites. Fifoot and Ting \[[@r53]\] suggest that 35.4% of eligible children were missed, again due to the high clinical activity in the emergency department. The researchers retrospectively analysed the data from these children to determine if they differed from those enrolled with baseline characteristics being similar to the enrolled group. Parents who were contacted during the 1-10 days of the trial may have been suggested to be subject to participant attrition. This can be seen in longitudinal studies, which can introduce systematic bias by favouring participants who return or take part in the follow-up, and thus increase the likelihood that those with complications will be underestimated because they did not take part \[[@r73]\].
Although randomised trials start as high-quality evidence, they can be down-rated if most of the relevant evidence comes from studies that suffer from a high risk of bias \[[@r74]\]. Acknowledging there are many types of bias, these RCTs all appeared to have inconsistencies in protocol adherence and participants dropping out. In some of the studies, researchers have accounted for this particular bias. Attrition is the loss of randomly assigned participants or participants' data \[[@r75]\]. This will ultimately bias an RCT\'s external validity by producing a final sample that is not representative of the population sampled \[[@r76]\]. It was noted that there appeared to be bias in Garbutt *et al* trial \[[@r54]\] with flaws in design conducting analysis and reporting which could have caused the effect their invention to be overestimated \[[@r77]\]. Garbutt **et al.**'s trial \[[@r54]\] was the only trial, which reported the duration of use and self-reported adherence, without differing between groups in their trial when measuring on-going symptoms. Such attrition means that the balance in baseline characteristics for those randomised may not be maintained in the subsample that has the outcome data \[[@r78]\]. However, the main evaluative strength of RCTs is that each group should be generally balanced in all characteristics, with any imbalance occurring by chance \[[@r79]\]. Conducting RCTs in paediatric research is challenging where recruiting more children than necessary risks unnecessary overexposure of children to inferior treatment, whereas underestimating the size will produce inconclusive results \[[@r64]\].
4.4. Heterogeneity of Outcome Measures
--------------------------------------
All these randomised studies specifically outlined their intent to report on whether prednisolone was as effective as dexamethasone or as in Parker **et al.**'s trial \[[@r55]\], how long stridor lasted for after the administration of prednisolone. The trials all measured different outcomes although the methodology was the same in the randomised double-blinded control trials and were all \[[@r52]-[@r55]\] explicit about their intention to study children of specific age groups and by specific methods of data collection. Although the studies were conducted in different areas, only Garbutt **et al.**'s \[[@r54]\] trial was based around primary care setting, whereas the others were based in Emergency Departments. All three \[[@r52]-[@r54]\] performed randomised double-blinded comparison trials of prednisolone *versus* dexamethasone, whereas Parker **et al.** \[[@r55]\] carried out a retrospective chart review questioning how long stridor at rest persists in croup after the administration of oral prednisolone.
There have been great improvements in patient's clinical indices due to introduction of croup scoring systems \[[@r80]\]. A variety of scoring systems were used in these studies: the Westley croup Score \[[@r52], [@r55]\], the Taussig Croup Score \[[@r53]\], the Geelhoed Score \[[@r55]\] and the Telephone Outpatient Score (TOP) \[[@r54]\]. Westley Croup score is the most widely used and its validity and reliability have been well demonstrated \[[@r27]\]. Such heterogeneity in outcomes measures makes analysing their results problematic and statistical meta-analysis impossible.
Only three of the scoring systems used in these studies have been shown to have reliability in independent studies. The Westley Croup Score \[[@r81]\] has been evaluated its use with respect to inter-rater reliability, construct validity, and responsiveness to change \[[@r5]\] and is the only method that has undergone validation and reliability testing and has shown to be sensitive to important changes in a patient's clinical status \[[@r14]\]. It performed well in all areas of assessment and inter-rater reliability between three research assistants was assessed prospectively. The weighted kappa was 0.90 for the total croup score, 0.47 for air entry, 0.93 for stridor and 0.87 for retractions \[[@r5]\]. Kappa was introduced as a measure of agreement in form of a test of inter-rater reliability, which adjusts the observed proportional agreement to take into account the amount of agreement which would be expected by chance, and represents the extent to which the data collected in the study are correct representations of the variables measured \[[@r82]\]. The Geelhoed score has demonstrated inter-rater reliability, with a weighted kappa of above 0.85 in two independent studies, indicating reasonable inter-observer agreement \[[@r83]\]. The Taussig score, which was used by Fifoot and Ting \[[@r53]\], does not appear to have been tested for validity and reliability with children experiencing croup \[[@r84]\] whilst the TOP score is a brief telephone outpatient scoring system that assess the presence of stridor and barky cough by asking parents about the child's symptoms in the last 24 hours and has undergone limited testing for validity and reliability \[[@r85]\]. Croup scores themselves at entry point to trials are subject to both inter- and intra-observer variation because not all the nurses scoring the children are the same or it may be unlikely that the same nurse scores the same child later, meaning that the formal establishment of inter-rater reliability is important, particularly if it has not been demonstrated.
4.5. Children's Ages
--------------------
The ages of the children in the studies varied. It is known that croup typically affects younger children, mostly under the age of six years \[[@r5]\], although NICE \[[@r1]\] suggest that children as young as three months of age, adolescents, and very rarely, even adults can be affected with croup. Croup diagnosed before the age of six months is uncommon and argues that a child of less than six months with acute stridor should not be considered to have croup since croup is rare in young babies \[[@r86]\]; even so two papers did enrol children from 3 months upwards \[[@r52], [@r55]\].
4.6. Medication Dosages, Lengths of Time of Administration and Responses to Treatment
-------------------------------------------------------------------------------------
Further analysis of the trials showed that they measured different ranges of drugs for different lengths of time. Sparrow & Geelhoed \[[@r52]\] examined a single dose of prednisolone *versus* a single dose of dexamethasone. Garbutt **et al.** \[[@r54]\] measured three days prednisolone *versus* one day of dexamethasone (and two days placebo) Fifoot and Ting \[[@r53]\] administered a single oral dose of either prednisolone at 1 mg/kg, and dexamethasone at 0.15 mg/kg as well as 0.6 mg/kg in this three arm trial. Parker **et al.** \[[@r55]\] calculated how long stridor persisted after a single dose of prednisolone.
Garbutt *et al*'s \[[@r54]\] trial is the only trial of its kind, which compared multiple doses of prednisolone with a single dose of dexamethasone, something that had not been evaluated before. Garbutt **et al.** \[[@r54]\] suggest that evidence to support the treatment of croup with a one-off dose of prednisolone is scant but it offers a convenient and familiar treatment for the primary care management of croup, as it is commonly used for in-office treatment of asthma exacerbations. Although prednisolone has not been widely studied there is no reason to suppose it would be less effective \[[@r3]\].
Further differences are noted in the information and outcomes that the researchers were interested in. Parker **et al.** \[[@r55]\] collected patient demographics, croup scores on presentation to the emergency department, and the duration of strider at rest (SAR), which was taken to be the time from administration of prednisolone to the first clear documentation that SAR has ceased approximated to the nearest half hour. This type of retrospective study relies entirely on the completeness and accuracy of the data from the children's medical records \[[@r87]\].
Sparrow and Geelhoed's study participants \[[@r52]\] were also observed at 30 minutes after administration and then hourly until the four-hour mark. In comparison, Garbutt **et al.**'s \[[@r54]\], main outcomes were unscheduled representations to medical care as determined by telephone follow-ups at 7-10 days. Other secondary outcome measures were adrenaline (epinephrine) use, croup score, and the time spent in the emergency department. Fifoot and Ting's \[[@r53]\] trial's primary outcomes were the severity and rate of reduction in the Westley croup score, rate of return for medical care with on-going croup, and further treatment with steroids in the week following the initial presentation. Their secondary outcome measures were the proportion of subjects requiring admission or salvage therapy, such as nebulised adrenaline, during the initial presentation. Sparrow and Geelhoed's \[[@r52]\] trial had similar follow-ups, although in this trial the primary outcomes were different in that the researchers wanted to know if the children who received prednisolone were more likely to represent for further medical care. Their secondary outcome measures were similar to that of Fifoot and Ting's \[[@r53]\] in that they included length of time spent in the emergency department, duration of croup symptoms (again reported by parents), and use of nebulised adrenaline.
In the studies that looked at longitudinal data to report 'on-going' symptoms and need for further treatment for example, as in Fifoot and Ting's study \[[@r53]\], it was suggest that the researchers' methods did not distinguish between unscheduled re-attendances and planned reviews \[[@r20]\] which made analysis difficult. Despite this, the two studies \[[@r52], [@r53]\] had good validity with appropriate randomisation, double blinding, and over 85% follow up with similar baseline characteristics \[[@r20]\]. Parker **et al.** \[[@r55]\] used a mixture of patient demographics, which included the Westley croup score and the Geelhoed scoring on presentation to the Emergency department. Fifoot and Ting \[[@r53]\] used modified Taussig score to assess croup severity. In the Garbutt **et al.** \[[@r54]\] trial, the researchers use the Westley croup scoring, which was assessed at the child's presentation. Sparrow and Geelhoed's \[[@r52]\] study participants had mild to moderate croup as defined by clinical symptoms and Taussig croup score.
Parker **et al.** \[[@r55]\] noted that they found it difficult to discriminate between mild, moderate, or severe retraction from the notes, thus leading to possible discrepancies in the croup scoring of these children. Inter-rater reliability in this case would be described as the extent to which two or more people would score or rate things \[[@r45]\]. Parker **et al.**'s \[[@r55]\] retrospective data on croup treatments is generally considered inferior to prospective designs, and which has been recorded for reasons other than research \[[@r87]\]. Another other advantages of conducting chart reviews is its relatively inexpensive ability to research readily accessible data \[[@r66]\].
A potential problem with data collection through chart reviews in case of Parker **et al.**'s study \[[@r55]\] was that the researchers collected data (from a busy children's ward) that may have had the potential for errors and inaccurate recording of symptoms. Intra-observer reliability of the croup scores by clinicians in the Parker **et al.** trial \[[@r55]\] was re-assessed by a blinded re-calculation of the scores from 10.6% of the original records selected at random from the initial data collection using two researchers. In each group, the extent to which intra-observation agreement was assessed using a weighted Cohen K score, which in this case was moderate. Intra-observation agreement in the busy practice setting of a paediatric emergency department showed the existence of substantial inter-observer variability among health care providers in the measurement of respiratory signs associated with croup in young children \[[@r88], [@r89]\].
Parker **et al.** \[[@r55]\] recorded measurements of prednisolone's effectiveness at a thirty-minute mark and thereafter used this retrospective data to analyse the duration of stridor after administration of steroids as determined by nursing observations. Data collected may have been inaccurate due to the busy state of the ward and subject to recall bias, with the timings rounded up to the nearest 30 minutes. This was a surprising weakness in this study given that the objective was to determine the specific duration of stridor. However, acknowledging that the trial was conducted in a busy emergency department, 10-15 minute observations may not have been feasible or possible. The time noted for the cessation of stridor at rest (SAR) relied heavily on researcher's finding the comment 'nil stridor at rest', usually found in the nursing records. The nursing notes may have been completed sometime after the actual disappearance of the SAR, and this may have under or overestimated the duration of the symptoms. Results showed that SAR at rest was well documented in the nursing notes. However, it is suggested that overall figures for calculating stridor are suggested to be too open to inter-rater variability to be able to accurately describe the severity in each group, *i.e.* the nurses graded the child's symptoms differently.
Other examples of possible inter-rater reliability and intra-observer reliability issues in the trials were found in all three of the randomised control trials due to which the studies had limitations because the subjective information from parents/guardians in the follow-up telephone reviews would have relied entirely on the parents accurately describing their child's symptoms. Although, Sparrow and Geelhoed's \[[@r52]\] main outcomes' measure was determined by unscheduled re-presentation to medical care, as determined by a telephonic follow-up at 7-10 days, which was less inclined to erroneous data from parents.
Fifoot and Ting \[[@r53]\] interviewed the parents of 86 patients (87%) in 1 week, asking them to recall symptoms and further needs for care. Garbutt **et al.** \[[@r54]\] also collected similar outcomes with telephone interviews on days 1, 2, 3, 4, and 11. Intra-observer reliability issues that were noted by this particular approach were the potential issues of recall bias as the information might have been extremely subjective. Information gathered depended entirely on memory, which can often be imperfect and thereby unreliable, as in the case of people who have difficulty remembering or accurately retrieving incidents that happened in the past, leading to poor versions of the original percept. Recall bias is a classic form of information bias and represents a major threat to the internal validity of studies that use self-reported data \[[@r90]\].
When considering the factors that might explain any differences in the direction and size of effect seen across the included studies, further analysis of the studies showed that a proportion of the children treated by Garbutt **et al.** \[[@r54]\] (which evaluated three days of treatment with prednisolone (2/mg/kg) *versus* one dose of dexamethasone for croup) needed treatment with further steroids at with the same frequency, regardless of the initial treatments assignment. This concluded that prednisolone at initial presentation and at one and four hours is as effective as dexamethasone. Garbutt **et al.** \[[@r54]\] remark that they did not demonstrate whether prednisolone prevents representation after the initial presentation, thus overall supporting the use of prednisolone for croup. This was disappointing as their three-day trial of prednisolone was the first of its kind. In contrast, the Sparrow and Geehoeld's \[[@r52]\] trial reported on unscheduled representation rates and found that 7% of the dexamethasone group returned for care, whereas 29% of the prednisolone group showed that a single dose of prednisolone does not work as well as a single dose of dexamethasone for children with mild or moderate croup. The absolute difference of 22% between the groups had 95% confidence intervals between 8% and 35%, which was well outside the authors' definition of equivalence \[[@r52]\]. Further analysis showed that dexamethasone worked significantly better than prednisolone (P \< 0.01) on this measure \[[@r52]\]. Based on this study, however, the authors recommend that if prednisolone is used, a two-day course of 1-2 mg/kg is probably justified.
In comparison, Fifoot and Ting \[[@r53]\] found no difference between the three groups of prednisolone when compared to 0.5 mg dexamethasone or 0.6mg dexamethasone, reporting that there were no significant differences in primary or secondary outcome measures. However, Johnson \[[@r27]\] while reporting on the Fifoot and Ting study \[[@r53]\] proposed different findings as 13% of the dexamethasone 0.15 mg group re-attended a week later, *versus* 11% of the dexamethasone 0.6% group *versus* prednisolone 1mg / kg, which equals to 17%. Furthermore, he criticises the trials for not reporting on the significance of each dexamethasone group alone *versus* prednisone alone. Fifoot & Ting \[[@r53]\] disagree, suggesting that both prednisolone at 1 mg/kg and a low dose of dexamethasone (0.15 mg/kg) were found not to differ in efficacy. Children randomised to dexamethasone were significantly less likely to have a return visit/re-admission than those randomised to prednisolone (RR 0.3, 95% CI 0.2 to 0.6; I^2^ statistic 0%) \[[@r14]\], which contradicts the author's own findings of no significant differences in primary or secondary outcome measures. Johnson (2008) was also critical of both trials \[[@r52], [@r53]\] as their GRADE analysis highlighted they had quality points being deducted for incomplete reporting of results, and not carrying out between-group assessments and their inconsistency in reporting of results.
Parker **et al.**'s \[[@r55]\] chart review found that symptoms of croup recovered quickly after administration of prednisolone but did not report on the need for on-going care after the initial treatments as the other trials did. Further analysis of the chart review data showed statistical analysis of the children's croup scores, demographics, and cessation of SAR, concluding that the median time for SAR was 6.5 hours in children who had been given prednisolone.
4.7. External Validity
----------------------
It is likely that the applicability evaluated in the included studies is representative of, or can be reproduced in, usual clinical care. This is important and can be seen as a consideration in all the trials presented with the extent to which external validity is representative of the study population and thus likely to be representative of the general population \[[@r91]\]. Appraising the applicability of the results of a study is intertwined with the quality of reporting, *i.e.* the extent to which an article provides information about the patients, the intervention, and the context of care which is good in all of the studies. Often there are concerns about generalizability of trials not in secondary or tertiary care when practiced in primary care. However, we believe that hospital studies would not be any less representative of the types of children seen or whether the outcomes would be any different from those observed in primary care settings \[[@r92]\], except that the children may be sicker. External validity in any of the studies presented is not a concern as the randomly selected results of the chart review are selected from one geographical area and it is suggested the RCTs are very likely to representative of the general population who use the treatment \[[@r93]\].
5. SUMMARY OF REVIEW FINDINGS
=============================
Four studies \[[@r52]-[@r55]\] met the inclusion criteria, but they were too heterogeneous to combine in statistical meta-analysis. Narrative synthesis was undertaken, which suggests that although prednisolone appears as effective when first given, it is less so for preventing re-presentation. However, because trial sample sizes were small, outcomes measures and croup scoring methods so different, firm conclusions are difficult, but it appears as a second dose of prednisolone the following day may be useful. We are unable to state the optimum dosages required.
6. DISCUSSION
=============
Unfortunately, the four studies included were too heterogeneous for statistical meta-analysis to take place. Combining studies that are not similar can cause significant inaccuracies in summary effects as well as associated conclusions, thus misleading decision makers and others \[[@r94]\] and so by not attempting to combine them we have avoided made this mistake. Variability in the intervention effects being evaluated in the different studies is known as statistical heterogeneity, which is a consequence of clinical or methodological diversity \[[@r50]\]. While exploring relationships within the data from this systematic review, there was some difficulty in organising the findings from the studies and describing patterns across the studies, in terms of the direction of effect and of the size of effects because the studies measured different outcomes and used differing methods. Measuring outcomes is suggested to be a key factor in analysis of the trials \[[@r25], [@r28]\], but there was too much inconsistency in outcomes assessment because of the different croup scoring scales or worse, no croup scoring, within the studies \[[@r52]-[@r55]\]. Where secondary outcomes such as on-going symptoms are vague, this may be due to poor inter-rater reliability \[[@r95]\].
6.1. Clinical Effectiveness
===========================
The relatively small sample sizes, heterogeneity of outcomes and effects, and other limitations noted above make this systemic review limited as a means of indicating clinical effectiveness' assessing optimum dosages and rates of re-presentation, which were our original aims. Although three of the studies are RCTs, which might indicate that this body of evidence sits towards the top of accepted hierarchies of evidence, this systematic review would be rated weak as a guide for clinical practice \[[@r45]\].
6.2. Grey Literature and Eliminating Bias
=========================================
A significant amount of time was devoted to identifying grey literature. Authors of the studies included in the literature review were written to. A review of the materials found in the reference lists of included studies was also conducted by looking through university theses as well as by hand searching of articles, conferences, reports, and opinion pieces. It is suggested that grey literature is particularly difficult to identify and retrieve with some databases, such as the National Research Register, listing unpublished work \[[@r96]\]. By including unpublished evidence, it may be possible to minimise the impact of the bias towards publishing only positive results in the literature \[[@r97]\]. The validity of a systematic review is highly dependent on the results of the underlying data, and the inclusion of grey literature may help to overcome some of the problems of publication bias, which can arise due to the selective availability of data \[[@r98]\]. The most consistent difference between published and grey literature is that published research is more likely to contain results that are statistically significant and can contain effect size estimates that are about one-third larger than those of unpublished studies \[[@r99]\]. Although time-consuming and costly, literature searches which cover the grey literature in all relevant languages and databases, are normally recommended to prevent reporting biases, but this was not possible in the systematic review as resources did not allow employment of speakers of languages other than English to conduct searchers. It is not clear how much this systematic review would be affected by a lack of grey literature in non-English languages, which is therefore acknowledged as a potential sources of bias. We were not able to construct funnel plots to assess publication bias due to the small number of studies and their relative heterogeneity, which is a further limitation of this systematic review.
6.3. Quality of Included Studies
================================
Quality assessment is an integral part of a systematic review because if the results of individual studies are biased, and these are synthesised without any consideration of quality, then the results of the review will also be biased, and the quality of the evidence and conclusions generated by a systematic review depends on the quality of the primary studies that make up the review \[[@r100], [@r101]\]. We have included details of our quality assessment processes, involving independent assessment by two researchers (AE and GW), and this process gave consideration to the methodological quality of studies, including allocation concealment, randomisation and comparability of the group's baseline characteristics, treatment adherence and participation and was based on established processes \[[@r38]\]. Trials with low methodological quality and small sample sizes can result in misinterpretation of RCT's overestimated differences in effectiveness or undetected, smaller, but statistically significant differences, and we have acknowledged these issues in the detailed critical analysis above. None of the included studies were scored less than 0.6, which is an acceptable cut off point for inclusion \[[@r38]\]. Higher quality scores should indicate studies with a better methodological quality \[[@r47]\] but methodological quality is likely to remain relatively subjective, as has been the case in this systematic review.
CONCLUSIONS AND RECOMMENDATIONS
===============================
Overall, the evidence from this systematic review seems to suggest that although prednisolone appears as effective when first given, it is not as good at preventing re-presentation. There continues to be a paucity in the existing literature as to whether prednisolone is as effective as dexamethasone. Fifoot and Ting \[[@r53]\] agree and also conclude that dexamethasone and prednisone are equally effective when initially given and also are equally effective at preventing readmission, finding no difference between oral dexamethasone and oral prednisolone in case of croup score at four hours or in terms of rate of return for medical care \[[@r53]\], although they concluded that at that time there was not enough evidence either way to conclusively establish that prednisolone is as good, but early on in treatment, *i.e.* in the first 6 hours, the 'Stridor at rest' resolved promptly after prednisolone and was as effective as dexamethasone \[[@r55]\]. Even so, more investigation is needed to evaluate the comparable efficacy. It is likely that a large proportion of the children, who would have been previously admitted to the hospital, would have been treated and discharged from the emergency department after having prednisolone \[[@r55]\].
The optimum dose of prednisone to prevent relapsing symptoms and readmission is still unclear and requires further research. A comparable efficacy between a single dose of dexamethasone and single oral dose of prednisolone (1 mg/kg) for mild to moderate croup has been suggested elsewhere \[[@r102]\], but Garbutt **et al.** \[[@r54]\] concluded that when a three-day course of prednisolone is administered, the researchers found this approach to be equivalent to a single oral dose of dexamethasone (0.6/mg/kg), once again highlighting that prednisolone and dexamethasone seem equally effective when first given but relapse and re-attendance to medical care is more common with prednisolone in children with mild or moderate croup, although again there is disagreement about this elsewhere \[[@r103]\]. There is an absence of evaluative research on prednisolone compared to dexamethasone in respect to repeated doses but also a view that it would not be palatable \[[@r14], [@r24]\]. No other studies as yet have compared the effectiveness of dexamethasone and multiple doses of prednisolone for the treatment of croup in the community setting, but this systematic review indicates that clinicians might be able to feel confident giving a repeat dose of prednisolone the following day, should the child still have stridor or other residual symptoms such as a 'barking cough', particularly if they are followed up by telephone, as did Garbutt *et al* \[[@r54]\]. Prednisolone is widely regarded as an alternative to dexamethasone for croup \[[@r29]\] but there remain questions over the evidence base for dosages: as well as the regimens listed above, UK guidelines suggest a repeat dose of prednisone the following day, but only if there are residual symptoms \[[@r14]\]. The British National Formulary (BNF) \[[@r104]\] only recommend 0.15/mg/kg of dexamethasone and do not recommend prednisolone, unless the child has severe croup and is being admitted to hospital where they recommend a single dose of 0.15mg / kg dexamethasone and administer 1-2 mg/ kg of prednisolone when the former is not available. Oral prednisolone at 1-2 mg/kilo is an alternative if dexamethasone is not available but no further advice on repeat dosing is given\[[@r1]\].
There may be a possible economic benefit to using prednisolone, as prednisone is significantly cheaper than dexamethasone and seems to be more widely available. Besides, soluble prednisolone is probably more widely available and cheaper than liquid dexamethasone. For treating a 12 kg child, the prednisolone dose would cost £0.75 compared to £2.50 for 0.15 mg/kg of dexamethasone \[[@r104]\]. Even if a 2-day course of prednisolone is given, it still results in a 40% cost saving \[[@r20]\], therefore a recommendation of this systematic review is that when further studies are undertaken, cost-benefit analysis is part of the study design.
More research is needed which examines direct comparison trials of both drugs with sufficient numbers and length of trials with appropriate reliable outcomes of primary care. In general, primary care manages the vast majority of children with mild croup, with only one RCT evaluating interventions in true primary care settings \[[@r54]\]. Large trials are needed that examine single or multi dose of prednisolone at the kind of numbers with which Bjornson **et al.** \[[@r7]\] used: this would give clinicians more robust evidence that prednisolone is as effective as dexamethasone in treating croup. Trials testing a longer course of prednisolone should be done in places where dexamethasone elixir is hard to come by \[[@r35]\]. There is an argument that those conducting further research studies should standardise their outcome measures, as a minimum there needs to be some consensus as to whether the Westley or Geelhoed scoring systems, or indeed both, should be utilised.
This systematic review highlights the most available and up to date research and its methods in this area and on a practical level, we believe, shows that prednisolone is as effective when first given and that two doses are far more likely to control symptoms at that level. It is very likely that small, short doses of prednisolone are safe for children, may be well tolerated and improve symptoms quickly. Given the data reviewed, prednisolone appears to be an appropriate choice in the treatment of mild to moderate croup where dexamethasone is not available. It is no longer reasonable to conclude that the use of corticosteroids should be reserved for individuals who are hospitalised with moderate to severe croup \[[@r3]\], with prednisolone offering a convenient and familiar treatment for the primary care management of croup \[[@r54]\].
Declared none.
BNF
: The British National Formulary
NICE
: National Institute for Health and Care Excellence
PRISMA
: Preferred Reporting Items for Systematic Reviews and Meta-Analyses
RCT
: Randomised Controlled Trial
SAR
: Stridor at Rest
TOP
: Telephone Outpatient Score
CONSENT FOR PUBLICATION
=======================
Not applicable.
CONFLICT OF INTEREST
====================
The authors declare no conflict of interest, financial or otherwise.
{#F1}
######
PICO employed in this systematic review.
------- -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------
**P** **P**atient, Population, or Problem How would I describe a group of patients similar to mine? **Children with croup \< 12 years of age.**
**I** **I**ntervention, Prognostic Factor, or Exposure Which main intervention, prognostic factor, or exposure am I considering? **Prednisolone or dexamethasone**
**C** **C**omparison or Intervention (if appropriate) What is the main alternative to compare with the intervention? **Studies that examine prednisolone usage or compare prednisolone with dexamethasone**
**O** **O**utcome you would like to measure or achieve What can I hope to accomplish, measure, improve, or affect? **Measured symptom reduction, dosages and re-presentation rates.**
------- -------------------------------------------------- -------------------------------------------------------------------------------------------------------------------------------------------------------
######
Relative heterogeneity of the included studies.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Author Patient Group and Age Study Design Outcomes Key Results Study Weaknesses
----------------------------------- -------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ----------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------------------------------------------------------------------------------------------------------------------------------------
\[[@r52]\] Sparrow and Geelhoed,\ Children aged 3 months to 142 months old presenting to a single emergency department with mild to moderate croup. [Randomization and blinding]{.ul}\ Primary outcome was the magnitude and rate of reduction in Westley croup score.\ [Responses to treatment:]{.ul}\ Included patients up to the age of 12 years, although very uncommon for older children to be affected.\
2006. Double blind, randomised equivalence study.\ Clinical observations at 30 minutes after administration of steroid; hourly for the next four hours and four hourly thereafter until discharge. Criteria for discharge home were minimal stridor or chest wall retractions---that is, a croup score of 1 or 0.\ Five out of 68 (7%) children who had received dexamethasone returned for medical care *versus* 19/65 (29%) children who had received prednisolone.\ Exclusion criteria included prior administration of steroids, non-English speakers and no access to telephone. Small numbers.
[Sample size and attrition]{.ul}\ Re-attendance at medical care within 7-10 days. No significant difference between the three groups in magnitude or rate of Westley score reduction.
133. No attrition\
[Medication dosages]{.ul}\
Patients received a single dose of 0.15 mg/kg dexamethasone 0.6 dexamethasone or 1 mg/kg prednisolone.\
[Lengths of time of administration]{.ul}\
Single dose of prednisolone, 1 mg/kg, matched for potency with a single dose of dexamethasone in children with mild to moderate croup.
\[[@r53]\] Fifoot and Ting,\ Children 6 months to 6 years presenting to a single emergency department with mild or moderate croup [Randomization and blinding]{.ul}\ Primary outcome measures were the magnitude and rate of reduction in Westley croup score, rate of return for medical care with ongoing croup, and further treatment with steroids in the week following index presentation. Secondary outcome measures were the proportion of subjects requiring admission or salvage therapy, such as nebulized adrenaline, during index presentation.\ [Responses to treatment]{.ul}\ Small sample size. Large number of eligible patients not recruited. Primary outcome over short time period.
2007 Double blind, randomised trial.\ Follow-up by telephone interview at 7 days, Taussig score. No significant difference in admission rates, duration of symptoms or attendances. No significant difference between treatment groups.
[Sample size and attrition]{.ul}\
99 children with 86 patients followed up by telephone (87%).\
[Medication dosages]{.ul}\
Patients were randomised to receive 1 mg/kg prednisolone, 0.15 mg/kg dexamethasone or 0.6 mg/kg dexamethasone.\
[Lengths of time of administration]{.ul}\
Single dose.
\[[@r54]\] Garbutt *et al*, 2013 Children aged 1-8 years presenting to primary care offices with mild or moderate croup in the USA. [Randomization and blinding]{.ul}\ Additional health care within 11 days of randomization\ No difference in outcomes of either group for child or parent. Small numbers.\
Double blinded randomised comparison trial\ assessed by self-report Telephone Out Patient score.\ People with no telephone and lacking English spoken language were excluded.
[Sample size and attrition]{.ul}\ Secondary outcomes included: duration of croup symptoms; disturbed sleep; parental stress; adverse events including sleep problems, mood changes, headache or dizziness, nausea, stomach pain, and secondary infections.
Eighty-seven children randomised with 98% follow up at 11 days.\
[Medication dosages and lengths of time of administration]{.ul}\
Prednisolone 2mg/ kg per day for 3 days *versus* one dose of 0.6mg dexamethasone and two placebo doses
\[[@r55]\] Parker *et al*, 2004 Children aged 4 months to 11 years, median age 2 years presenting in an emergency department with mild or moderate croup Retrospective chart review.\ How long stridor at rest persisted after administration of prednisolone 1mg /kg.\ Average length of time from SAR to cessation was 6.5 hours.\ Retrospective chart reviews rely on completeness of contemporaneous data entry. Inter rater reliability reported as moderate. Lack of power calculation
[Randomization and blinding]{.ul}\ Westley and Geelhoed croup scores.\ Children with mild croup improved quicker although this is reported as not clinically significant.
Not undertaken\ To determine whether children with mild croup\
[Sample size and attrition]{.ul}\ had a more rapid\
188 eligible for analysis from 814 patients coded as croup.\ resolution of stridor at rest.
[Medication dosages]{.ul}\
1mg/kg prednisolone.[Lengths of time of administration]{.ul}\
Not specified but implicitly single dose only
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
| {
"pile_set_name": "PubMed Central"
} |
A boost pressure control system for an internal combustion engine is described in Patent Document 1. According to this boost pressure control system, in the case where a boost pressure needs to be raised to be made coincident with a target boost pressure as a target value thereof, the boost pressure is controlled through open-loop control while a difference between the boost pressure and the target boost pressure (this difference will be referred to hereinafter as “a boost pressure deviation”) is equal to or larger than a predetermined value, and the boost pressure is controlled through feedback control if the boost pressure deviation becomes smaller than the predetermined value. It should be noted herein that in the case where a rate of rise in the boost pressure in the control of the boost pressure through open-loop control (this control will be referred to hereinafter as “boost pressure OL control”) prior to the start of the control of the boost pressure through feedback control (this control will be referred to hereinafter as “boost pressure FB control”) is relatively large, the rate of rise in the boost pressure in boost pressure FB control is made smaller than in the case where the rate of rise in the boost pressure in boost pressure OL control prior to the start of boost pressure FB control is relatively small.
Thus, the following effects are obtained. That is, in the boost pressure control system described in Patent Document 1, while the boost pressure deviation is relatively large, the boost pressure is controlled through open-loop control. Thus, the boost pressure is raised at a relatively large rate of rise. Accordingly, this allows the boost pressure to swiftly approach the target boost pressure. Then, if the boost pressure deviation becomes relatively small, the boost pressure is controlled through feedback control. It should be noted herein that if the rate of rise in the boost pressure during boost pressure FB control is not limited at all, the possibility of the occurrence of a so-called overshoot, namely, an excess of the boost pressure far above the target boost pressure during boost pressure FB control is higher in the case where the rate of rise in the boost pressure in boost pressure OL control prior to the start of boost pressure FB control is relatively large than in the case where the rate of rise in the boost pressure in boost pressure OL control prior to the start of boost pressure FB control is relatively small. However, in the boost pressure control system described in Patent Document 1, the rate of rise in the boost pressure during boost pressure FB control is made smaller in the case where the rate of rise in the boost pressure during boost pressure OL control prior to the start of boost pressure FB control is relatively large than in the case where the rate of rise in the boost pressure during boost pressure OL control prior to the start of boost pressure FB control is relatively small. Therefore, an overshoot, namely, an excess of the boost pressure far above the target boost pressure during boost pressure FB control is restrained from occurring. That is, according to the boost pressure control system described in Patent Document 1, an effect of making it possible to make the boost pressure swiftly approach the target boost pressure and suppress an overshoot, namely, an excess of the boost pressure far above the target boost pressure is obtained. | {
"pile_set_name": "USPTO Backgrounds"
} |
[Consequence of habitual use of laxatives (author's transl)].
Though habitual, but not excessive use of laxatives can be observed frequently, no accompanying clinical symptoms have yet been described. The frequent observation of tetany and edema is striking, there is a marked decrease of potassium clearance and an incipient impairment of creatinine clearance. A secondary hyperaldosteronism can be ruled out. The electrocardiograms of 9 patients show signs of mild hypokalemia, which in 2 patients were first misinterpreted as myocardial ischemia and in one patient taken as indication of myocarditis. Oral administration of potassium normalizes the electrocardiograms. | {
"pile_set_name": "PubMed Abstracts"
} |
---
abstract: 'It has been shown by @ShchekinovVasiliev2006 (SV06) that HD molecules can be an important cooling agent in high redshift $z\ge10$ haloes if they undergo mergers under specific conditions so suitable shocks are created. Here we build upon @jpp3 who studied in detail the merger-generated shocks, and show that the conditions for HD cooling can be studied by combining these results with a suite of dark-matter only simulations. We have performed a number of dark matter only simulations from cosmological initial conditions inside boxes with sizes from $1$ to $4$ Mpc. We look for haloes with at least two progenitors of which at least one has mass $M\ge M_{cr}(z)$, where $M_{cr}(z)$ is the SV06 critical mass for HD over-cooling. We find that the fraction of over-cooled haloes with mass between $M_{cr}(z)$ and $10^{0.2}M_{cr}(z)$, roughly below the atomic cooling limit, can be as high as $\sim0.6$ at $z\approx10$ depending on the merger mass ratio. This fraction decreases at higher redshift reaching a value $\sim0.2$ at $z\approx15$. For higher masses, i.e. above $10^{0.2}M_{cr}(z)$ up to $10^{0.6}M_{cr}(z)$, above the atomic cooling limit, this fraction rises to values $\ga0.8$ until $z\approx12.5$. As a consequence, a non negligible fraction of high redshift $z\ga10$ mini-haloes can drop their gas temperature to the Cosmic Microwave Background temperature limit allowing the formation of low mass stars in primordial environments.'
author:
- |
Joaquin Prieto$^1$[^1], Raul Jimenez$^{2,1,3}$, Licia Verde$^{2,1,3}$\
$^{1}$ICC, University of Barcelona (IEEC-UB), Marti i Franques 1, E08028, Barcelona, Spain\
$^2$ ICREA\
$^3$ Theory Group, Physics Department, CERN, CH-1211, Geneva 23, Switzerland
title: 'Over-cooled haloes at $ z \ge 10$: a route to form low-mass first stars'
---
galaxies: formation — large-scale structure of the universe — stars: formation — turbulence.
Introduction
============
----------- ----------------- ------------------- -------------- ------------------ -------------------- ------------------------
Sim. Name Number of sims. Box size Part. number Part. mass $M_{cr}(z=10)/m_p$ $M_{cr,1}(z=17.5)/m_p$
$N$ $L_{\rm box}$/Mpc $N_p$ $m_p/M_\odot$ $N_{p,h}$ $N_{p,h}$
S1Mpc256 20 1 256$^3$ 5.88$\times10^3$ 3.72$\times10^3$ 1.31$\times10^3$
S2Mpc256 20 2 256$^3$ 4.70$\times10^4$ 4.66$\times10^2$ 1.64$\times10^2$
S4Mpc256 20 4 256$^3$ 3.77$\times10^5$ 5.80$\times10^1$ 2.10$\times10^1$
S1Mpc512 5 1 512$^3$ 7.35$\times10^2$ 2.98$\times10^4$ 1.05$\times10^4$
S2Mpc512 5 2 512$^3$ 5.88$\times10^3$ 3.72$\times10^3$ 1.31$\times10^3$
S4Mpc512 5 4 512$^3$ 4.70$\times10^4$ 4.66$\times10^2$ 1.64$\times10^2$
----------- ----------------- ------------------- -------------- ------------------ -------------------- ------------------------
\[table1\]
In the current $\Lambda$ Cold Dark Matter ($\Lambda$CDM) cosmological paradigm, dark matter (DM) over-densities are the building blocks of cosmic structures. These DM over-densities grow due to gravity forming DM haloes in a hierarchical way, i.e. from the smaller to the bigger ones, and mergers play an important role in this process. For the formation of the first luminous objects to become possible, the baryonic content of the haloes must be able to cool. Cooling of primordial gas is driven by molecular Hydrogen (${\rm H}_2$) which can form inside DM mini-haloes of mass $\gtrsim10^6$M$_\odot$. Once ${\rm H}_2$ formation is triggered, rovibrational transitions of the ${\rm H}_2$ molecule are able to cool the primordial gas down to temperatures of $\sim$ 200 K [@Haiman1996; @Tegmarketal1997; @Abeletal2002], see also the @BarkanaLoeb2001 review. At lower temperatures, the ${\rm H}_2$ lines become insufficient to cool the gas further.
The ${\rm H}_2$ cooling temperature floor (T$\approx 200$K) and its saturation number density ($n\approx 10^4$cm$^{-3}$ i.e. the density for Local Thermal Equilibrium at which ${\rm H}_2$ cooling is inefficient) yield a Jeans mass: $$M_J\approx 500 {\rm M}_\odot \left(\frac{T}{200 {\rm K}}\right)^{3/2} \left(\frac{10^4 {\rm cm}^{-3}}{n}\right)^{1/2}.$$ This sets a mass scale for gravitationally bounded objects in the primordial gas, suggesting that the first stars were massive [^2].
However, if the HD molecule is formed in a significant amount in primordial environments, although it has no relevant role in the first stage of ${\rm H}_2$ driven cooling it could eventually ($T\lesssim 150$K) become important [@BougleouxGalli1997; @Machidaetal2005], allowing the gas to reach temperatures as low as the Cosmic Microwave Background (CMB) temperature limit at the corresponding redshift. If HD cooling could be triggered, a lower temperature floor for the gas would decrease the Jeans mass and thus this process could favor the formation of low mass stars at high redshift.
Because the HD number density depends on the H$_2$ abundance through H$_2$ + D$^+\rightarrow$ HD + H$^+$ [@Pallaetal1995; @GalliPalla2002] and the H$_2$ abundance depends on the free electron number density through e$^-$ + H $\rightarrow$ H$^-$ + $\gamma$ followed by H$^-$ + H $\rightarrow$ H$_2$ + e$^-$ [@Peebles1968], if the gas presents a high ionization fraction it is possible to increase the HD abundance. It has been shown that such high ionization fraction conditions are common in post-shocked gas inside DM haloes [@Greifetal2008; @jpp3]. In fact, the DM halo growing process involves violent merger events. These mergers are able to produce strong shock waves which both compress the halo baryonic content and increase the ionization fraction. This drives an enhancement in the formation rate of HD molecules with the consequent over-cooling of the primordial gas, as shown in @Greifetal2008 and @jpp3.
@ShchekinovVasiliev2006 (hereafter SV06) studied the necessary (thermo-chemical) conditions for HD cooling to switch on. They argue that such conditions are fulfilled in merging DM haloes with a total system mass above a critical value, so suitable shocks form. The post-shocked gas with an enhanced HD molecular fraction is able to drop its temperature to the CMB floor of $T_{\rm CMB}\approx 2.73(1+z)$.
SV06 however only considered a straw-man head-on collision of two primordial clouds of equal mass, but, clearly the physical state of the post-shock gas depends on many factors that are not captured by this simplified scenario. @jpp3 produced numerical DM + baryons simulations that capture enough physics to study the physical state of the post-shock gas. They find that as a result of the hierarchical merging process, turbulence is generated and the production of coolants is enhanced, so much that even the HD molecule becomes an important coolant in some regions. Yet, their simulations are not sufficient to assess how generic this is, that is, how these regions are associated to the distribution of minihaloes. This is what we set up to do here.
In this paper, we use a set of DM cosmological simulations to compute the fraction of haloes able to produce over-cooling of the primordial gas due to mergers at high redshift as predicted by SV06 using the recipe developed in @jpp3. The paper is organized as follows. In §2 we describe our methodology. In §3 we show our numerical results and discuss about them. In §4 we present our summary and conclusions.
Methodology {#Methodology}
===========
In principle, to compute the fraction of haloes able to over-cool their baryonic content due to mergers at high redshifts, we would want to have multiple hydrodynamic simulations, which model both dark matter and baryonic physics and chemo-thermal evolution of primordial gas, for cosmological initial conditions, reaching a resolution of $\sim 1$pc at $z=10$. This ambitious goal was achieved in @jpp3 but only for a single 1 Mpc size box and in there the formation and baryonic matter accretion process of a single halo was simulated at full resolution: a region of 2 kpc (at $z=10$) with $\sim 2$ pc resolution (at $z=10$). The average CPU-time for one of such systems is $\sim 180000$ CPU-hrs. This makes it computationally very expensive to replicate the @jpp3 runs for multiple haloes in a cosmological context. However this complex problem can be broken in three ingredients which can be studied independently. The first ingredient is the thermo-chemical conditions for the HD cooling to switch on which were studied in SV06. The second ingredient is the physical conditions of the primordial gas (turbulence and shocks) which was studied in @jpp3. They find that post shock regions are able to produce both ${\rm H}_2$ and HD molecules very efficiently even in small mini-haloes ($M\sim 10^6 M_{\odot}$) if they accrete on, or merge with, a more massive but still relatively low mass halo ($M\sim 10^7 M_{\odot}\simeq M_{cr}$). The remaining ingredient is how frequently this happens in a cosmological context. This last step, however, can be addressed with DM-only simulations under minimal assumptions, and this is what we set up to do here.
------- ------- ------------------- ------------------- -------------------
$z_1$ $z_2$ Mass bin 1 Mass bin 2 Mass bin 3
in $10^7 M_\odot$ in $10^7 M_\odot$ in $10^7 M_\odot$
10.0 10.2 2.10 - 3.33 3.33 - 5.28 5.28 - 8.36
11.0 11.4 1.73 - 2.74 2.74 - 4.34 4.34 - 6.88
12.3 12.7 1.41 - 1.81 1.81 - 2.87 2.87 - 4.55
14.9 15.4 0.99 - 1.57 1.57 - 2.49 2.49 - 3.94
17.2 17.9 0.74 - 1.17 1.17 - 1.85 1.85 - 2.94
------- ------- ------------------- ------------------- -------------------
: Relevant redshift and mass bins. The mass bins labeled by $i=1,2,3$ have been chosen so that bin mass lower and upper boundaries are $10^{0.2(i-1)}M_{cr}(z_2)$ and $10^{0.2(i)}M_{cr}(z_2)$ respectively. The mass range spanned by the three bins covers the transition from H$_2$ cooling haloes to atomic cooling ones.
\[table2\]
----------- --------------------- --------------------- ---------------------- ---------
Mass Mass Mass Total
Sim. Name bin 1 bin 2 bin 3 Volume
$N_{OC}(N_{\rm h})$ $N_{OC}(N_{\rm h})$ $N_{OC}(N_{\rm h}) $ Mpc$^3$
S1Mpc512 5 (7) 4 (4) 3 (3) 5
S1Mpc256 25 (46) 14 (15) 11 (12) 20
S2Mpc512 88 (132) 56 (57) 37 (38) 40
----------- --------------------- --------------------- ---------------------- ---------
: Total number of OC haloes (i.e. the sum over the $N$ realizations) and total number of haloes ($N_h$) in a given mass bin with $f_{mg}=0.6$ and $m_p\le5.88\times10^3M_{\odot}$ at $z_1=10$.
\[table3\]
The critical mass to trigger HD molecular over-cooling at redshift $z$ is defined by SV06 as: $$M_{cr}^{SV06}(z)=8\times10^6\left(\frac{20}{1+z}\right)^2 M_{\odot}.$$ Following SV06 this is the total mass of the system, i.e. DM plus baryonic mass. Because we have to work with DM only simulations, we have to make an assumption regarding the baryonic matter. To take into account the gas inside the DM haloes we assume that these primordial haloes host the universal baryon fraction $$\frac{M_b}{M_{DM}+M_{b}}=\frac{\Omega_b}{\Omega_m}\equiv f_b,$$ where $M_b$, $M_{DM}$, $\Omega_b$, $\Omega_m$ and $f_{b}$ are the baryonic mass content of the halo, the dark mass content of the halo, the current average baryonic matter density in the Universe in units of the critical density, the current average DM density in the Universe in units of the critical density and the universal baryonic mass fraction of the Universe, respectively. Using this approximation, the necessary (but not yet sufficient) condition for a DM halo at redshift $z$ to become an over-cooled halo is that it must have a DM mass above a critical mass $$M_{cr}^{DM}(z)=(1-f_B)\times M_{cr}^{SV06}(z),$$ hereafter we will refer to $M_{cr}^{DM}$ as $M_{cr}$.
We use the cosmological hydrodynamical code `RAMSES` [@Teyssier2002] to perform $75$ DM-only simulations. The cosmological initial conditions are produced with the `mpgrafic` code [@Prunetetal2008] and the initial redshift for each run is set to $z_i\approx65$. The cosmological parameters are those of the concordance $\Lambda$CDM model from @Komatsu2009 [@Komatsu2010]: $\Omega_m=0.258$, $\Omega_\Lambda=0.742$ $h=0.719$, $\sigma_8=0.796$, $n_s=0.963$ and the transfer function of @EisensteinHu1998 with $\Omega_b=0.0441$.
Using the `AHF` halo finder [@AHF2009], we identified DM haloes (i.e., objects with a density contrast $\delta\ge 200$) with mass above or equal to the critical mass to enhance the HD molecular cooling $M_{cr}$, at several redshifts $z\ge10$. For reference, in the cosmology adopted here, $f_b=0.1709$, and thus $$M_{cr}(z)=6.63\times10^6\left(\frac{20}{1+z}\right)^2 M_{\odot}\,.$$ In the set-up chosen for the `AHF` halo finder the minimum particle number per halo was set to $N_{min}=20$. We adopted this low number because we are not interested in characterizing the haloes based on their internal-radial features. This corresponds closely to the minimum number of particles per critical mass halo $N_{p,h}$ at the highest redshift of interest in the lower resolution run.
Table \[table1\] shows the details of each simulation. From the first column to the last one: the simulation name, referring to both the box size and the particle number, the number of simulations $N$, the box size[^3] $L_{\rm box}$ in Mpc , the number of particles per simulation $N_p$, the particle mass $m_p$ and the number of particle per critical mass halo $N_{p,h}$ at two reference redshift $z=10$ and $z=17.5$.
![The mass scales involved. The lower solid line shows the critical mass for HD cooling $M_{cr}(z)$, the upper solid line corresponds to $T_{\rm vir}=10^4$K necessary for atomic lines cooling. The vertical bars (dotted, dashed and dot-dashed) correspond to the three mass bins considered.[]{data-label="fig:mass"}](mass.pdf){height="6cm"}
{height="12cm" width="16cm"}
{height="12cm" width="16cm"}
{height="12cm" width="16cm"}
{height="8cm" width="12cm"}
{width="2\columnwidth" height="16cm"}
As we will show in the next section, the most reliable results come from runs where $M_{cr}$ is defined by $N_{p,h}\ge1310$ particles at $z\le17.5$, i.e. runs with a particle mass $m_p\le5.88\times10^3M_{\odot}$. In these runs the DM haloes are found consistently in successive snapshots. Furthermore, it is worthwile to note that in these reliable runs the primordial perturbation distance scale $\lambda_{M_{cr}}$ associated to the critical mass $M_{cr}$ is well defined by a number of partcles ($>10$) when the simulation start.
The @jpp3 findings indicate that a necessary and sufficient condition for triggering HD cooling is that a halo with mass greater than $M_{cr}$ (recall that at the redshifts of interest $M_{cr} \sim 10^7 M_{\odot}$) undergoes a merger or accretes baryonic material funnelled in the halo along filaments. Even in sub-critical haloes ($M\sim10^6 M_{\odot}$) HD cooling can be triggered if they accrete on a critical one, as the relevant physical condition driving the turbulence is the relative velocity, which is set by the potential well created by the super-critical halo. In the super-critical halo, if it is not disrupted by a major merger, the turbulence triggered by accretion is enough enhance the creation of H$_2$ and HD and therefore kickstart over-cooling.
Informed by the above findings, here we impose the conditions for over-cooling to happen as follows.
We construct the merger trees for each simulation using the `AHF` merger tree tool, we identify DM haloes at redshift $z_2$ with mass $\geq M_{cr}(z_2)$ that subsequently undergo merging to form a bigger halo at $z_1$ (with $z_2\ge z_1$).
We define the over-cooled (OC) halo merger as the process in which an existing halo at $z_1$ has at least two progenitors, of which at least one with mass $M_{DM}\ge M_{cr}(z_2)$ and after the merger keeps at least a mass fraction $f_{mg}$ of the most massive progenitor. We vary the factor $f_{mg}$ from 0.6 to 0.9 in order to study how the OC haloes fraction depends on it.
Our parameters of the halo finder routine imply that the minimum halo mass (which sets therefore the definition of merger) is somewhat resolution-dependent ranging from $1.47\times 10^4 M_{\odot}$ in simulation S1Mpc512 to $7.54\times10^6$ in simulation S4Mpc256.
Here we want to stress that we do not impose a minimum merger mass ratio in our strategy to look for OC haloes. The method described above is suitable to address the question: [*what is the fraction of DM haloes able to over-cool their baryonic content (and thus potential site for low mass star formation) due to mergers and accretion at high redshift?*]{}. Indeed, the condition $M\ge M_{cr}$ ensures that the interaction between haloes will be strong enough to trigger the enhancement of the HD formation. On the other hand, a study based on the merger mass ratio could give us information about the amount of OC gas and then could help answer a different question: [*what is the amount of OC gas in haloes at high redshift?*]{}. Our simulation set up and our methodology cannot quantify the amount of over-cooled gas but it is suitable to estimate the fraction of OC haloes at high redshift. This is the goal of the present work.
Results and Discussion
======================
Table \[table2\] shows some example combinations of redshifts $z_1$ and $z_2$ used in building our merger tree, and the ranges of the three halo mass bins (at $z_2$) we consider. The mass bins labeled by $i=1,2,3$ have been chosen so that bin mass lower and upper boundaries are $10^{0.2(i-1)}M_{cr}(z_2)$ and $10^{0.2(i)}M_{cr}(z_2)$ respectively. Thus the three mass bins are centered around, 1.3, 2.0, and 3.2 $M_{cr}(z_2)$, respectively. With this choice, the mass range spanned by the three bins covers the transition from H$_2$ cooling mini-haloes (with virial temperature $T_{vir}\la$few$\times10^3$K and $M_{vir}\la 1.5\times10^7 M_\odot$) to atomic cooling haloes (with $T_{vir}\ga\times10^4$K and $M_{vir}\ga 1.5\times 10^7 M_\odot$). This is summarized in Fig.\[fig:mass\].
Table \[table3\] reports the total number of OC haloes $N_{OC}$ and the total number of haloes $N_{\rm h}$ at $z_1=10$ for the three different mass bins in the less restrictive case $f_{mg}=0.6$ and for the highest resolution simulations with $m_p\le5.88\times10^3M_{\odot}$. The reported number is the sum of all OC haloes (all haloes) in the $N$ simulations considered, i.e., 5 simulations of S1Mpc512, 20 for S1Mpc256 and 5 for S2Mpc512. The effective volume for finding these OC haloes is therefore 5 Mpc$^3$, 20 Mpc$^3$ and 40 Mpc$^3$, respectively.
Figures \[fig1\], \[fig2\] and \[fig3\] show the fraction of OC haloes $f_{\rm OC}^{\rm HD}$ for four different values of $f_{mg}$ and for the three halo mass bins as a function of redshift. These results are shown for our two different $N_p$ (in different columns) and different box sizes $L_{\rm box}$ (in different rows). The error bars correspond to the standard deviation between the $N$ simulations at a given redshift. The error on the mean would be smaller by a factor $\sqrt{N}$.
As we expected, the higher the $f_{mg}$ the lower the OC fraction $f_{\rm OC}^{\rm HD}$. This trend shows that after a merger process it is very difficult for the resulting halo to keep 100$\%$ of its progenitor’s mass: some of the progenitor’s mass is always removed from the parent halo after the merger. The resulting $f_{\rm OD}^{\rm HD}$ shows a very weak dependence (or no dependence at all) on $f_{mg}$ for $0.6\leq f_{mg}\leq 0.8$. Our results show a clear resolution dependence for $m_p\ge4.70\times10^4M_{\odot}$, i.e. runs S4Mpc512, S4Mpc256 and S2Mpc256. In these runs it is possible to see a monotonic growth of the OC fraction with the simulation resolution, which is particularly marked in the $f_{mg}=0.6$ case: we thus discuss numerical convergence before further interpreting Figs. \[fig1\], \[fig2\] and \[fig3\].
Numerical convergence is investigated further in Fig. \[fig4\] where it is possible to identify a mass-resolution dependent trend. Simulations S1Mpc512, S2Mpc512 (and S1Mpc256) have particle masses below $m_p= 5.88\times10^3M_{\odot}$ and thus a mass threshold for OC halo merger $M=1.2 \times 10^5$ ($M=1.47\times10^4$) or mass merger ratios below $1:65$. These simulations correspond to the (red) plus symbols, (blue) asterisk symbols and (green) “x” symbols. At this resolution results for $f_{\rm OC}^{\rm HD}$ appear to converge. On the other hand simulations S2Mpc256, S4Mpc512 and S4Mpc256 with $m_p\ge4.70\times10^4M_{\odot}$ , (magenta) open square symbols, (cyan) filled square symbols and (yellow) open circle symbols, do not show numerical convergence. This can be understood as the mass threshold for merger in these simulations is high ($> 9.4\times 10^5 M_{\odot}$) and the merger mass ratios are larger than $1:2$.
In what follows we will focus on these three higher mass resolution simulations because they have the most reliable results based on both, convergence and number of particles per DM halo.
In figure \[fig1\], corresponding to the first mass bin (see table \[table2\]), and for mass resolution $m_p\le5.88\times10^3M_{\odot}$ (i.e., top two panels, and middle right panel) our results show that at $z=10$ the fraction of OC haloes is $f_{\rm OC}^{\rm HD}\ga0.5$ in the case with $f_{mg} \lesssim 0.7$. This fraction tends to decrease at higher redshift ($z\la12.5$) but is always above 20$\%$ (for $f_{mg}\lesssim 0.7$) showing that a non negligible fraction of DM haloes in this mass bin is able to over-cool their gas content due to mergers at high redshift. At higher redshifts, i.e., $z\ga15$, the fraction decreases $f_{\rm OC}^{\rm HD}\la0.2$. This last result comes from S2Mpc512, the only simulation with data above $z\ga15$ in this mass bin.
In figure \[fig2\] we show the second mass bin centered around $M=2 M_{cr}(z_2)$. For runs with mass resolution $m_p\le5.88\times10^3M_{\odot}$ (top two panels, and middle right panel) the OC fraction at $z=10$ is $f_{\rm OC}^{\rm HD}\ga0.9$ for $f_{mg}\lesssim 0.7$ and it can reach $f_{\rm OC}^{\rm HD}\sim 1.0$. At higher redshift ($z\la12.5$) the fraction remains significant, $f_{\rm OC}^{\rm HD}\ga0.8$. As expected the OC fraction increases with the mass of the halo.
Figure \[fig3\] shows our results for the third mass bin centered around $M=3.2 M_{cr}(z_2)$. The OC fraction keeps increasing with halo mass.
In summary these figures show that a non negligible fraction of DM haloes above the critical mass $M_{cr}$ are able to over-cool their gas content due to mergers at high redshift.
To illustrate how the OC merger proceeds, figure \[fig5\] shows the evolution of two randomly chosen OC haloes from our catalog at 4 different redshift $z_1$. In the first column we show an OC halo of $M=6.41\times10^7M_\odot$ (computed at $z=10$) from the third bin mass and in the second column a $M= 2.53\times10^7M_\odot$ (computed at $z=10$) OC halo from the first mass bin. The difference in size of the objects reflects the different mass bins.
As an additional study, we have computed the probability distribution function for the halo spin parameter $\lambda$ defined by @Bullock2001 and we have found that it follows log-normal distribution characterized by a standard deviation $\sigma\approx0.5$ and an average spin parameter $\bar\lambda\approx0.04$ in good agreement with previous works, e.g. @DavisNatarajan2009. Despite of the low number of haloes in the most reliable runs (see table \[table3\]), we recover a log-normal distribution (for S1Mpc256 and S2Mpc512) characterized with the parameters shown above. This fact supports our claim on the reliability of our results.
While the N-body simulations for this work were running, new results on cosmological parameters, derived from the [*Planck*]{} satellite observations, were released [@PlanckCollaboration2013]. The [*Planck*]{}’s best fit $\Lambda$CDM cosmological parameters are somewhat different from WMAP’s ones. Because our results can be cosmology-dependent, let us elaborate on the possible effect of the [*Planck*]{} results. [*Planck*]{}’s $\Omega_m$ value is slightly higher than WMAP’s and $\Omega_b$ slightly lower. This affects directly the computation of the DM critical mass $M_{cr}(z)$ decreasing it by a $2\%$, approximately. Furthermore, because the [*Planck’s*]{} value of the Hubble constant is lower, each redshift in our calculations has to be increased by about $4\%$ and so the box size $L_{\rm box}$. Thus the changes associated to the new best fit cosmological parameters have a negligible effect on our results.
Summary and Conclusions
=======================
We have performed $75$ DM-only cosmological simulations with two different particle numbers ($256^3$ and $512^3$) and inside three different box sizes ($L_{\rm box}=$ 1Mpc, 2Mpc and 4Mpc) in order to quantify the fraction of haloes able to over-cool their baryonic content due to mergers at high redshift as predicted by @ShchekinovVasiliev2006.
As shown in @jpp3 accretion and (minor) mergers onto a halo of mass above the critical value defined by SV06, $M_{cr}(z)$ produce supersonic turbulence and a shocked environment where H$_2$ and HD molecules are formed efficiently. There, regions are able to (over)cool below the H$_2$ cooling temperature floor.
To identify the fraction of haloes where the above conditions are verified, we computed the progenitor’s mass for each halo at a given redshift inside a bin mass, specified in table \[table2\]. This mass range spans the transition between H$_2$ molecular cooling to atomic cooling haloes. Every halo with more than one progenitor of which at least one has a mass above $M_{cr}(z)$, was counted as an over-cooled (OC) halo.
Our results show that a non negligible fraction of the mini-haloes formed at $z\ge10$ over-cooled their primordial gas due to the process outlined above. The fraction of OC haloes at $z=10$ is $f_{\rm OC}^{\rm HD}\ga0.5$ for masses roughly below the atomic cooling limit: $1\times10^7\la M/M_\odot\la3\times10^7$. At higher redshift, $z\la12.5$, the fraction $f_{\rm OC}^{\rm HD}\ga0.2$ and it is below 0.2 for $z\ga15$. The fraction of OC haloes rises with halo mass. For haloes above the atomic cooling limit, $2\times10^7\la M/M_\odot\la8\times10^7$, the fraction of OC haloes at $z\la12.5$ is $f_{\rm OC}^{\rm HD}\ga0.8$.
The existence of a non negligible fraction of OC haloes at high redshift has interesting consequences for the star formation process in primordial environments. As predicted by SV06 the HD molecular cooling drops the gas temperature to the CMB limit $T_{\rm CMB}(z)\approx2.73(1+z)$ allowing the formation of low mass primordial stars [@jpp2; @jpp3]. Their low mass makes these primordial (population III) stars very long-lived opening a window for the potential detection of primordial stars in the local Universe.
Acknowledgements {#acknowledgements .unnumbered}
================
JP thanks Roberto Gonzalez and Christian Wagner for their useful and constructive comments on this work. JP, RJ and LV acknowledge support by Mineco grant FPA2011-29678- C02-02. LV is supported by European Research Council under the European CommunityÕs Seventh Framework Programme grant FP7- IDEAS-Phys.LSS.
[99]{}
Abel T., Bryan G. L. & Norman M. L., 2002, Science, 295, 93 Barkana R. & Loeb A., 2001, Phys. Rep., 349, 125 Bougleoux E. & Galli D., 1997, MNRAS, 288, 638 Bromm V., Coppi P. & Larson R. B., 2002, ApJ, 564, 23 Bullock J. S., Kolatt T. S., Kravtsov A. V., Klypin A. A., Porciani C. & Primack J. R., 2001a, ApJ, 555, 240 Davis A. J. & Natarajan P., 2009, MNRAS, 393, 1498 Eisenstein D. J. & Hu W., 1998, ApJ, 496, 605 Galli D. & Palla F., P&SS, 50, 1197 Greif T. H., Johnson, Jarrett L., Klessen R. S. & Bromm, V., 2008, MNRAS, 387, 1021 Greif T. H., Springel V., White S. D. M., Glover S. C. O., Clark P. C., Smith R. J., Klessen R. S. & Bromm V., 2011, Haiman Z., Thoul A. A. & Loeb A., 1996, ApJ, 464, 523 Knollmann S. R. & Knebe A., 2009, ApJ, 182, 608 Komatsu E., et al., 2009, ApJS, 180, 330 Komatsu E., et al., 2010, arXiv:1001.4538 Lepp S. & Shull J. M., 1983, ApJ, 270, 578 Machida M., Tomisaka K., Nakamura F. & Fujimoto M., 2005, ApJ, 622, 39 Palla F., Galli D. & Silk J., 1995, ApJ, 451, 401 Peebles P. J. E., Dicke R. H., 1968, ApJ 154, 891 arxiv.org/abs/1303.5076 Prieto J., Padoan P., Jimenez R., Infante L., 2011, ApJ, 731, L38 Prieto J. P., Infante L., Jimenez R., 2008, arXiv, arXiv:0809.2786 Prieto J., Jimenez R. & Martí J., 2012, MNRAS, 419, 3092P Prunet S. Pichon C., Aubert D., Pogosyan D., Teyssier R. & Gottloeber S., 2008, ApJs, 178, 179 Tegmark M., Silk J., Rees M. J., Blanchard A., Abel T. & Palla F., 1997, ApJ, 474, 1 Teyssier R., 2002, A&A, 385, 337 Shchekinov Yu. A. & Vasiliev E. O., 2006, MNRAS, 368, 454 Stacy A. & Bromm V., 2013, MNRAS, arXiv:1211.1889
[^1]: email:joaquin.prieto.brito@gmail.com
[^2]: But see @Greifetal2011 and @StacyBromm2013 for lower masses primordial stellar binary-multiple systems.
[^3]: Note that we adopt the value $h=0.719$ therefore here length are in Mpc and masses in $M_{\odot}$.
| {
"pile_set_name": "ArXiv"
} |
Q:
String manipulation in Clojure
I am new to Clojure. I have a java hashmap which has integer as keys and array list as values. The map is: {1=[Delhi, Goa, Mumbai], 2=[hello, world, the, world, is, awesome]}. I want to replace world with night and hello with good. I am doing something like this.
Clojure code:
(doseq [[k v] m]
(when (= k 2)
(doseq [s v]
(if (= s "world")
(def a(clojure.string/replace(s #"world" "night"))))
(if (= s "hello")
(def b(clojure.string/replace(s #"hello" "good")))))))
This doesn't work perfectly. Also when I try to print the value of a and b, it shows
#object[clojure.lang.Var$Unbound 0x31791dc5 Unbound: #'com.example.core/a] and #object[clojure.lang.Var$Unbound 0x31791dc5 Unbound: #'com.example.core/b].
How can I see the value of a i.e. night and b i.e. good. Is there any other way of string manipulation? Any help will be really appreciated.
A:
combination of update and replace would do the trick:
user> (def data {1 ["Delhi" "Goa" "Mumbai"]
2 ["hello" "world" "the" "world" "is" "awesome"]})
user> (update data 2 #(replace {"world" "night" "hello" "good"} %))
;;=> {1 ["Delhi" "Goa" "Mumbai"], 2 ["good" "night" "the" "night" "is" "awesome"]}
| {
"pile_set_name": "StackExchange"
} |
Commendatore
Commendatore (singular), Commendatori (plural), or variation, is an Italian word meaning "Commander". It may refer to:
Position, rank, title
Commander (order) (), the title of honour "Commander"
Commendatore of the Italian Republic (; ) Commander of the Italian Republic, rank in an order of honour
Commander (military), the military rank, using the affectation of Italian wording for illicit forces
Leader (person in command), a leader of a group of people, using the affectation of Italian wording for an aire of respect
People
Il Commendatore, nickname for Enzo Ferrari
Fictional characters
Il Commendatore (; aka Don Pedro), a character in the Mozart opera Don Giovanni
Arts and entertainment
Il Commendatore (sculpture), a statue in Prague
Commendatori (TV episode) 2000 television episode of The Sopranos
Other uses
Isdera Commendatore, the "Commendatore", a car model manufactured by Isdera
Palazzo del Commendatore, Rome (; ), a building in Rome
Salon del Commendatore (; ), inside the palace Palazzo del Commendatore, Rome
See also
Commander (disambiguation) | {
"pile_set_name": "Wikipedia (en)"
} |
Six months after the events depicted in The Matrix, Neo has proved to be a good omen for the free humans, as more and more humans are being freed from the matrix and brought to Zion, the one and only stronghold of the Resistance. Click the link or image above for SFMZ's highlights on The Matrix Revolutions.
The human city of Zion defends itself against the massive invasion of the machines as Neo fights to end the war at another front while also opposing the rogue Agent Smith. Click the link or image above for SFMZ's highlights on the final explosive chapter in the Matrix trilogy, The Matrix Revolutions. | {
"pile_set_name": "Pile-CC"
} |
Secondary ion mass spectrometry imaging of biological cells and tissues.
Secondary ion mass spectrometry (SIMS) is capable of providing detailed atomic and molecular characterization of the surface chemistry of (bio)molecular samples. It is one of a range of mass spectrometry imaging techniques that combine the high sensitivity and specificity of mass spectrometry with the capability to view the distribution of analytes within solid samples. The technique is particularly suited to the detection and imaging of small molecules such as lipids and other metabolites. A limit of detection in the ppm range and spatial resolution <1 μm can be obtained. Recent progress in instrumental developments, including new cluster ion beams, the implementation of tandem mass spectrometry (MS/MS), and the application of multivariate data analysis protocols promise further advances. This chapter presents a brief overview of the technique and methodology of SIMS using exemplar studies of biological cells and tissue. | {
"pile_set_name": "PubMed Abstracts"
} |
2020 ASB Classic – Men's Doubles
Ben McLachlan and Jan-Lennard Struff were the defending champions, but Struff chose not to participate.
McLachlan played alongside Luke Bambridge and successfully defended the title, defeating Marcus Daniell and Philipp Oswald in the final, 7–6(7–3), 6–3.
Seeds
Draw
Draw
References
External links
Main Draw
ASB Classic - Men's Doubles
2020 Doubles | {
"pile_set_name": "Wikipedia (en)"
} |
Postnatal growth of medial gastrocnemius motoneurons in the kitten.
Cat muscle nerves and ventral roots for the hindlimbs show a unimodal distribution of axon diameter at birth, followed, at about 20 days postnatal (dPN), by a marked change to a bimodal distribution resembling that of the adult. However, volumes calculated for motoneuron somata retrogradely labeled with HRP have been reported to be divided into two size populations at birth in the kitten. In the literature it is suggested that a dissociation between axonal and somal growth appears at a very early age. This apparent dissociation, not present in adults, prompted us to examine the somal growth patterns of kitten lumbar motoneurons. In the present report we have examined somal size development in medial gastrocnemius (MG) motor nuclei in 18 cats aged 2 dPN to adulthood using retrogradely transported horseradish peroxidase to label the motoneurons. Measurements of minimum and maximum diameter somal size, volume calculations and a double circle technique relating the diameters of an estimated spherical volume contained within the soma to that of a second spherical volume enclosing the soma clearly distinguish two subpopulations in the adult, a small and a large population. In contrast, in the kitten we show there is a unimodal distribution of small motoneuron somata at birth which at 19-23 dPN differentiates into a bimodal population. This sudden differentiation of somal size coincides with that reported for MG motoneuron axonal calibre, ruling against a neonatal dissociation of somal and axonal size distributions, and appears to correspond to the time of onset of functional characteristics and the histochemical differentiation of fiber types in the MG muscle. | {
"pile_set_name": "PubMed Abstracts"
} |
1. Technical Field
The present invention pertains to the field of cellular communication. More particularly, the present invention pertains to wireless communication of data as opposed to voice communication.
2. Discussion of Related Art
The invention concerns automatic retransmission request (ARQ) protocols for orthogonal frequency and code division multiplexing (OFCDM). The invention is a generalization of the so-called space-time adaptive retransmission (STAR) method, described e.g. in “Matrix modulation and adaptive retransmission,” by A. Hottinen and O. Tirkkonen, in Proc. IEEE ISSPA, July 2003, vol. 1, pp. 221-224. Accordingly, the invention is sometimes called Adaptive Retransmission for Frequency Spreading (ARFS).
An OFCDM signal model is as follows, in terms of baseband signals after FFT, assuming that the delay spread is smaller than the cyclic prefix, so that individual subcarriers experience frequency flat fading. Let us assume Walsh-Hadamard (WH) spreading with spreading factor S. This means that each symbol is spread over S subcarriers. Advantageously the subcarriers are interleaved, so that no subcarriers conveying a symbol are neighbors. Preferably, in the interleaving all groups of subcarriers belonging to the same spreading code are such that the distance (in frequency) between the subcarriers is as large as possible, and at a minimum, larger than a typical coherence bandwidth. Then the subcarriers over which a symbol are spread are likely to have uncorrelated or only weakly correlated channels. Also, we make the crucial assumption that in a downlink transmission at least some multicodes are transmitted to a single user. In an uplink transmission this reduces to requiring that multicode transmission is used on at least some of the spread subcarriers. In the HS-PDSCH (high speed-physical downlink shared channel), the capacity is shared primarily by time-division, but it is also possible to code multiplex a few terminals (one to four) during the TTI. The channelization codes are allocated at a fixed spreading factor (16), but the base station may assign multiple channelization codes for one terminal during a TTI thus applying multicode transmission.
Preferably, WH-spreading codes are not used to separate users. Users may be separated in time or frequency. Because of separating a user preferably not by use of a spreading code, but instead by use of time or frequency separation, the term OFCDM is used here, instead of multi-carrier CDMA (MC-CDMA). (Typically MC-CDMA is also understood as a code-division method to separate users. Here we want to stress the “multi-code” aspect of MC-CDMA, and consider the situation where many codes in overlapping dimensions are allocated to the same user. That is why we use the terminology OFCDMA instead of MC-CDMA. There is though no reason not to use the term MC-CDMA as descriptive in the case that the spreading factor is smaller than the number of subcarriers, and preferably multicodes are allocated to users from the set of codes spreading over the same subcarriers.)
For a single transmit antenna at the transmitter and a single receive antenna at the receiver, the signal model would bey=HCx+n≡x+noise (1)where y is an S×1 vector of received signals on the S subcarriers, H is an S×S diagonal matrix with the kth diagonal element representing the channel received on the kth subcarrier covered by the spreading code, C is an S×S spreading code matrix, each column being one spreading code, x is an S×1 vector of data transmitted on each spreading code, is an S×S equivalent channel matrix, and n is additive noise.
Take for example the case of WH spreading using a spreading factor S=2. The signal model in this case can be written explicitly as:
[ y 1 y 2 ] = 1 2 [ h 1 0 0 h 2 ] [ 1 1 1 - 1 ] [ x 1 x 2 ] + n = 1 2 [ h 1 0 0 h 2 ] [ x 1 + x 2 x 1 - x 2 ] + n = 1 2 [ h 1 h 1 h 2 - h 2 ] [ x 1 x 2 ] + n , where hs is the channel on subcarrier s and represents the power of the subcarrier s, the WH spreading codes are normalized by the factor 1/√{square root over (2)}, and the matrix
C = [ 1 1 1 - 1 ] is the spreading code matrix and is made up of the two spreading codes (columns of the matrix)
[ 1 1 ] and
[ 1 - 1 ] . Thus,
ℋ = 1 2 [ h 1 h 1 h 2 - h 2 ] is the equivalent channel matrix for S=2.
It is straight forward to see that despite the spreading codes being orthogonal at transmission, the received signal is not orthogonal. The correlation matrix R of the transmitted signal is the so-called Gram matrix of the equivalent channel, i.e.
R = ℋ † ℋ = 1 2 [ h 1 2 + h 2 2 h 1 2 - h 2 2 h 1 2 - h 2 2 h 1 2 + h 2 2 ] = 1 2 [ a b pm b pm a ] where a is the total power of the subcarriers, i.e.
a = ∑ s = 1 S h 2 2 and bpm is the interference between the code channels, given by:bpm=|h1|2−|h2|2.The interference vanishes and the received signal is orthogonal only if |h1|2=|h2|2, which would occur for frequency flat fading.
The simplest receiver is a matched filter receiver, indicated by † yielding output:z=†y.Written in terms of the transmitted signal and noise, the matched filter output isz=Rx+†n. If the matched filter is judged to be a sufficient receiver, symbol estimates are directly constructed from z=†y. More reliable estimates may be constructed by attempting to invert the dependence of the correlation matrix in z=Rx+†n. Thus e.g a zero-forcing (de-correlating) receiver applies the pseudo-inverse on the received signal,{circumflex over (x)}=R−1†y=x+R−1†n. The resulting symbol estimates are corrupted by colored noise. A Linear Minimum Mean Square Error estimate (LMMSE) is constructed using the pseudo-inverse with a noise estimate added to R in the inverse. (The effects of the colored noise can be mitigated by applying even more complicated detectors of the M-algorithm type, preferably based on a so-called QR-decomposition.)
In conventional ARQ, the retransmissions are exactly similar to the first transmission. If hard decision demodulation is used, the matched filtering is performed exactly as for the first transmission. After that, the matched filter outputs are summed, as well as the correlation matrices (or pseudo inverses), and the de-correlating, LMMSE or non-linear demodulation algorithm is used. For S=2, the correlation matrix for a second transmission according to conventional ARQ is:
R ~ = 1 2 [ a ~ b ~ pm b ~ pm a ~ ] where ã and {tilde over (b)}pm are the total channel power and correlation coefficients, with hs replaced by the channel {tilde over (h)}s during the retransmission. The sum of the original matched filter output and the matched filter output for the retransmission is:z+{tilde over (z)}=(R+{tilde over (R)})x+†n+† nwhere the sum of the correlation matrices is:
R + R ~ = 1 2 [ a + a ~ b pm + b ~ pm b pm + b ~ pm a + a ~ ] ,which shows the diversity advantage if the retransmission is outside the channel coherence time. The channel powers add coherently, whereas the self-interference terms add non-coherently (as real numbers). Thus the expected relative self-interference after a retransmission is smaller than before. If, however, the retransmission is within the channel coherence time, the sum correlation is just twice that for R Both channel power and self-interference add coherently. The only gain from the retransmission is that noise combines non-coherently, so the signal to interference and noise ratio (SINR) is improved.
Thus, with conventional ARQ, the complexity of detecting two transmissions is exactly twice the complexity of receiving one transmission, plus the complexity of summing the two matched filter outputs and correlation matrices/pseudo inverses. For soft output demodulation, the procedure described above may be followed with a step of combining the transmissions. Alternatively, soft outputs may be constructed from the first and second transmission separately, and the likelihood ratios may be added. The overall complexity is approximately the same.
What is needed is needed is a way to perform retransmission without adding appreciably to the complexity of the receiver processing. | {
"pile_set_name": "USPTO Backgrounds"
} |
Q:
count and count unique in a single mongo aggregate query
I have a mongo aggregate query which calculates COUNT, MIN, MAX and BLANK counts of different keys.
db.getCollection('ReportTestProcess').aggregate([
$group": {
"_id":0,
"Inititated_on_MIN": {
"$min": "$Inititated_on.v"
},
"Inititated_on_MAX": {
"$max": "$Inititated_on.v"
},
"Text_COUNT":{$sum:1},
"Text_BLANK": {
"$sum": {
"$cond": [
{
"$ifNull": [
"$Inititated_on.v",
false
]
},
0,
1
]
}
}
}])
Now I want UNIQUE_COUNT of elements along with it. The only way I could think of doing it is to group based the fields but grouping will affect the results of MIN, MAX or COUNT
A:
You can use $addToSet
Sets always keep unique values. Your code should look like.
db.getCollection('ReportTestProcess').aggregate([
$group": {
"Inititated_on_MIN": {
"$min": "$Inititated_on.v"
},
"Inititated_on_MAX": {
"$max": "$Inititated_on.v"
},
"Text_COUNT":{$sum:1},
"Text_UNIQUE": { $addToSet: "$Inititated_on.v" }
"Text_BLANK": {
"$sum": {
"$cond": [
{
"$ifNull": [
"$Inititated_on.v",
false
]
},
0,
1
]
}
}
}])
| {
"pile_set_name": "StackExchange"
} |
3 Bank of Finland Research Discussion Papers Juha Kilponen* Matti Viren* Why do growth rates differ? Evidence from cross-country data on private sector production The views expressed in this paper are those of the authors and do not necessarily reflect the views of the Bank of Finland. * and We are grateful to Jouko Vilmunen for his many useful comments and Tarja Yrjölä for helping us with the data. Viren would also like to thank the Yrjö Jahnsson Foundation for its financial support.
4 ISBN ISSN (print) ISBN ISSN (online) Helsinki 2008
5 Why do growth rates differ? Evidence from cross-country data on private sector production Bank of Finland Research Discussion Papers 13/2008 Juha Kilponen Matti Viren Monetary Policy and Research Department Abstract We estimate a standard production function with a new cross-country data set on business sector production, wages and R&D investment for a selection of 14 OECD countries including the United States. The data sample covers the years The data suggest that growth differences can largely be explained by capital deepening and an ability to produce new technology in the form of new patents. The importance of patents is magnified by the openness of the economy. We find some evidence of increasing elasticity of substitution over time, all though the results are sensitive to assumptions on the nature of technological progress. Keywords: growth, R&D, production function, patents JEL classification numbers: O40, E10, O43 3
9 1 Introduction Growth differences across western industrialized countries are widespread and persistent. For instance, recent growth data reveals striking differences in growth performance between a group of large European countries (Germany and Italy) and a group of small countries (Ireland and Nordic countries) and the US during Germany and Italy clearly lag behind the other countries. While growth rates in Germany and Italy have been roughly 2 per cent during the last 20 years, Ireland and Nordic countries have grown on average clearly much faster (see Figure 1.1). In this paper, we shed some light on the potential reasons for these growth differences by estimating different specifications of production functions with time-series-cross-section methods. Figure 1.1 Growth performance in a selection of industrialized economies 10,00 8, ,00 4,00 2,00 0,00 aut bel dkk fin fra ger ire ita net por spa swe uk usa A poor growth performance in many large European countries is often attributed to institutional features. However, the large European economies have already undergone series of structural reforms and the basic institutions that have been found important for growth in Easterly (2001) for example are already in place in all European countries. Institutional differences may thus not be a major cause for such persistently diverse growth performance. Beside institutions, there are numerous other country-specific factors that may have contributed to these differences, such as size of country, demographics and availability of natural resources. However, these features are beyond the reach of 7
10 policy. Therefore, it is natural, and in line with the empirical growth literature, 1 to focus on the features that can be influenced by policy. In what follows, we concentrate on the role of capital deepening, technological change, and possibly time varying elasticity of substitution between capital and labour. A novel feature of our analysis is the data. In contrast to most of the previous empirical work, we use the data for the business sector only. Thus, we abstract from all the complications concerning measurement of government output and government capital stock, as well as the productivity of government production. As pointed by Gollin (2002), these (and other) measurement problems may, especially in the case of developing countries, lead to highly misleading results in terms of income shares and underlying production relationships. We first illustrate that the growth differences during reflect not simply different patterns of capital accumulation and employment growth, but also different speed of technological change. We show that roughly half of the differences in growth rates can be attributed to intensity of business sector R&D investment across the countries of our sample. However, once the R&D intensity is complemented with other potential explanatory variables of technological change, such as patents and degree of openness, it turns out that the patents becomes single most important factor explaining technological change. Moreover, we find that the importance of patents is magnified by the openness of the economy. As for the role of elasticity of substitution, our findings are mixed. We find some evidence that the elasticity of substitution has increased over time. However, in the light of the sensitivity of the results to different specifications, we conclude that evidence on the varying elasticity of substitution is not very compelling. The rest of the paper is organised as follows. First, in sections 2 and 3, we illustrate the the growth rate differences and scrutinize them from point of view of basic factors of input. Then, in section 4, we proceed with estimation by setting up horse races between competing models. The last section provides concluding remarks concerning eventual policy implications. 2 Good and bad growth performers As pointed out earlier, there are considerable differences in growth rates of industrialized western countries. Figure 1.1 illustrates the case for two sample periods, and Since the data are derived from the business sector, changes in public sector output do not directly show up in the figures. 1 Basic institutions found to be important for growth have been discussed eg in Easterly (2001). 8
11 On the basis of Figure 1.1, or other similar figures, one cannot say very much about the underlying reasons for growth differences. But note that the countries that have started from relatively low levels of income seem to be among the best performers. This can be interpreted in terms of technical adaptation: these countries have been able to benefit from general technical knowledge without costly investment in R&D and education. This may also be a reason for convergence of growth rates in the data. Otherwise, our sample of countries is quite homogeneous, and so we are unable to devise a powerful test for the importance of technical adaptation. 2 In what follows, we therefore focus on other explanations, starting with the role of capital deepening. We perform a simple exercise in which we estimate a Cobb-Douglas production function with constant returns to scale restrictions for all countries, and let the rate of technical change be country-specific. By contrast, factor shares are restricted to be equal across the 14 countries in our sample. Given the estimated parameters of the production function for the period , we use the resulting regression to forecast in-sample GDP using the actual data for capital and labour inputs for the period This enables us to distinguish between bad and good performers during the ten year period starting from 1995 relative to their historical growth records. Figure 2.1 displays the actual output values together with the forecast for from this exercise. 3 We find that the growth differences apparent in Figure 1.1 also show up in the deviations between actual and forecasted values. These deviations reflect different patterns of capital accumulation and employment growth, but they also mirror any other factors not taken into account in the estimation of the basic production function. Figure 2.2 summarizes the time-series graphs. We can see that again Ireland and Italy represent the polar cases. Finland, Portugal and Sweden (together with Ireland) represent the good performers while the other countries perform more or less poorly. The United States is an interesting exception. Its forecast errors are close to zero, suggesting that nothing particular has happened in the US economy during the last 10 years. Relative to the historical growth record, the US economy has been able to keep up with its growth potential. Alternatively, it is also possible that the conflicting effects have exactly offset out each other. 2 We estimated a conventional convergence equation in terms of the US (with the data from 13 countries) where the relative output growth was explained by lagged (log) level of relative output (expressed in Euros) and time dummies (fixed time effects). The estimate of the lagged output level was , with the t-ratio of The result is consistent with the convergence property although the effect is not particularly strong. For a more thorough analysis of convergence, see eg Caselli et al (1996). 3 As pointed out in the introduction, the data are related to the business sector only, covering the period The data are annual. The output data have not been available for Greece. Most of the data are from the OECD database (including the STAN database for the R&D expenditures). The data are described in detail in Pyyhtiä (2007). 9
15 3 Decomposing the growth differences Given the deviations between actual and forecasted values of GDP, we next discuss possible causes of these deviations. The usual suspect in this context is expenditure on R&D, which proxies the country s resources devoted to technological development. We scale expenditure on R&D (for the total business sector) by GDP, in order to make it comparable across the countries. The data for the variables are derived from the OECD STAN database. 4 The first exercise which we carry out is the following: We extract the forecast errors from the previous analysis and explain their variation with R&D variables in a panel data set-up. We use least squares estimation with fixed cross-section (country) effects. The residuals are then compared with the original forecast errors, shown in Figure 3.1. Figure 3.1 Contribution of R&D to forecast errors Effect of R&D on output gap for actual-forecast deviation-r&d contribution bel dkk fin fra ger irl ita net spa swe uk us Figure 3.1 suggests that differences in R&D investment intensity across the countries explain roughly one half the deviations ( forecast errors ). In cases like Sweden, almost the whole deviation can be accounted for expenditures on R&D because this expenditure item has been exceptionally high. The opposite result is obtained for Ireland, for which the deviation in R&D expenditure is even greater reflecting the fact that Irish R&D expenditures have been exceptionally low. But had Ireland invested in R&D in line with other countries, Ireland s (private sector) GDP would have been almost 5 per cent higher. In the case of the US, the 4 Unfortunately, we havecomparable data on R&D expenditures only for the period so that we cannot adequately control for R&D for the full sample period. Thus, we can only test the hypothesis that R&D has been particularly important for the last two decades. 13
16 deviations remain small but become more negative, reflecting the very high (above sample average) value of the R&D variable. On the basis of Figure 3.1, we conclude that we have at least tentative evidence suggesting R&D plays a role in separating the good from the bad growth performers relative to their historical records. In order to obtain more definitive results, we turn to econometric analysis. 4 Estimation 4.1 Technical change We estimate the conventional Cobb-Douglas (C-D) production function with and without the R&D variable. 5 The estimates tabulated in Table 4.1 present both the full sample of 14 countries for the period , and with the R&D variables, a shorter sample ( ) for 12 countries (comparable R&D data are not available for Austria and Portugal). We let the time and cross-section variation total factor productivity be explained by common time trend and possibly by country-specific R&D intensity. The common time trend captures the idea that at least part of the technology is a public good and freely available. It could also capture any other macroeconomic time factors common to all countries of our sample. The estimated equation reads simply as log(q it ) = a 0 + αlog(l it ) + βlog(k it ) + τ t + ψrd it +ωts it + φpat it + u it (4.1) where i = 1,.14(12) denotes country, t = 1960, 2004 denotes time trend, q is private sector output (value-added), l is employment (number of employees), k is the capital stock, rd it is R&D intensity (business sector R&D expenditure/gdp), ts is a proxy for the openness of the economy (trade share), and finally pat is an indicator for the number of patents (several alternative measures are used). To test the role of the additional variables, we estimate (4.1) by a two-step procedure. First, we estimate the production function. Second, using the estimated parameters we derive the Solow residual and use it as a dependent variable in the regressions where the set of explanatory variables includes t, rd, ts, pat, and the cross-terms of rd, ts and pat. The data for R&D, trade share and patents are displayed in Figures See eg Aghion and Howitt (1998, 2005) and Grossman and Helpman (1991) on the discussion of R&D accumulation, output and productivity. 14
17 Table 4.1 CD estimation results Dependent variable α (19.25) 1 α (10.33) (12.98) (7.18) β (19.75) τ by.011 by by by by by country (14.19) country country country country country ψ (12.91) (4.37) (0.22) (4.06) (0.51) (2.36) ω (8.99) (10.97) (3.17) (5.06) ϕ (19.57) (5.78) (2.92) (4.35) rd*ts (0.68) (0.04) pat*ts (2.70) (2.20) Estimator LS,FE LS,FE GLS,FE GLS,FE SUR,FE SUR,FE SUR,FE SR,FE SUR,FE R SEE DW Dep.var log(q) Δlog(q/L) Δlog(q/L) Log(q/l) SR SR SR SR SR The dependent variables is log(q). τ is the coefficient of time trend, ψ the coefficient of the R&D variable (rd), ω the coefficient of the openness variable (ts), and φ the coefficient of the patent variable (pat). rd*ts and pat*ts represent (the coefficients of) the multiplicative terms of these variables. SR is the Solow residual from equation 2. The number of data points in the level form equation is 548. FE refers to cross-section fixed effects. t-ratios are corrected with the White's procedure. The patent variable is specified so that in equations (6) and (8) it is the number of (triadic) patents relative to total population and in equations (7) and (9) it is the country share of all (triadic patent family) patents. 15
20 Figure 4.3 Data on patents Austria Belgium Denmark Finland France Germany Greece Ireland Italy Netherlands Portugal Spain Sweden UK USA The data represent country shares of all triadic patents (data source: OECD Main Science and Technology Indicators ). We also estimate the so-called first order conditions in which log(q/l) is regressed against real wage log(w), time trend (t) and possibly the R&D variable (rd), Table The benefit of using the latter specification is that we do not need to assume the C-D production structure (in other words, the elasticity of substitution can deviate from unity). This specification takes the form log(q it /l it ) = b 0 + b 1 log(w it ) + b 2 t + b 3 rd it + b 4 tt it + b 5 pat it + e it (4.2) The data on average R&D expenditure, productivity and real wages display a fairly strong positive relationship both between the level of R&D and (labour) productivity and (labour) productivity and real wages. 6 See eg Antras (2004) and Knight et al (1993) on possibilities and problems in testing growth models with panel data. 18
21 Table 4.2 Estimates of first order condition w.r.t. labour input Dependent variable low(w) by year (16.26) (16.01) (5.09) (4.47) (5.25) (26.09) T by year (10.27) (9) (7.65) (7.07) (34.92) rd (6.73) (6.44) (0.77) (7) (7.60) Ts (3.61) (3.54) (15.54) Pat (4.79) (1.77) (6.03) rd*ts (1.40) (6.98) pat*ts (0.52) (0.76) Estimator LS, LS,FE LS,FE LS,FE LS,FE LS,FE SUR,FE TE&FE R SEE DW The dependent variable is log(q). Number of data points is 453 when the RD variable is not included. When it is included, the number is 276. FE refers to cross-section fixed effects and TE to period fixed effects. t-ratios are corrected using White s procedure. The patent variable (pat) is here specified as number of patents/population. The estimation results can be summarized as follows. In the case of the C-D production function, the estimates are generally reasonable and in line with the literature, especially when we use the first order log differences and impose constant returns to scale. The typical factor shares roughly represent the values for labour and capital respectively. When the RD variable is introduced into basic production function estimation (equation 4.1), it is always statistically significant. The coefficient (semielasticity) is estimated at roughly 0.1. In other words, if R&D intensity is increased by one percentage point, private sector productivity growth will increase by 0.l per cent. This result is thus in line with the tentative findings of the previous section. This is not, however, the full story for the RD variable. If we introduce two additional variables (and their cross-terms), trade share (ts) and number of patents (pat) the coefficient of RD decreases considerably. In fact, we cannot reject the hypothesis that the coefficients of the R&D variables are zero. In contrast, the openness and patent variables turn out to be highly significant. This suggests that while R&D investments seem to pay off it is far more important that these investments produce useful innovations, ie patents. Moreover, we find that the 19
22 importance of patents is magnified by the openness of the economy, since the cross-term between openness and patent variable is positive and significant. (See equation (9) in Table 4.1). Turning to estimation results from equation (4.2), we conclude that the coefficient of the R&D variable alone is again statistically significantly different from zero. This is true even when the coefficient of the real wage variable is allowed to change over time, ie letting the elasticity of substitution be time variant. Even in this case, the coefficient of the R&D variable has a reasonably large coefficient and a high t-ratio. 7 This finding is not surprising given previous empirical evidence on the role of R&D (cf. eg Jones and Williams, 1997). Again, we find that the openness and patent variables have statistically significant effects, even to the extent that they seem to out-perform the direct R&D effects. In this latter specification, only the cross terms of R&D, patents and openness become insignificant. In fact, signs are even negative. 4.2 Variable elasticity of substitution Different degrees of substitutability between capital and labour may provide an explanation why some countries have different technical progress than others regardless on how much they actually invest on technological development. As shown by Klump and De La Grandville (2000), when the two countries start from common initial conditions, the country with the higher elasticity of substitution will always reach a higher per capita income. 8,9 Moreover, the elasticity of substitution does not need necessarily to be equal to constant, as imposed by the estimation of Cobb-Douglas production function in the previous section. 10 Miyagiwa and Papageogiou (2007) show that in a multisector economy, the elasticity of substitution does not appear to be constant, but positively related to the capital-output ratio as a market equilibrium condition. Saam (2006), in turn, shows that the elasticity of substitution is positively related the openness of trade. The important thing is irrespectively of the mechanism 7 Due to autocorrelation, the t-values obviously do not follow the t-distribution. 8 Ky-Huyang (1991) find some support for the Klump De La Grandville hypothesis (2000) using data for South Korea and the US. 9 Klump and Preissler (2000) discuss a relationship between elasticity of substitution of the economy and the overall flexibility of production and markets, readiness to make structural and institutional changes and so on.elasticity of substitution between factors of production suggests itself as a reasonably good indicator of overall structural flexibility of the economy. 10 Willman (2002) points out that after increasing strongly in the 1970s, the share of labour income in GDP in the euro area decreased continuously in the two subsequent decades. This suggests that Cobb-Douglas production function might not be an appropriate choice for production analysis. Furthermore, Duffy and Papageorgiou (2000) report relatively large differences in factor shares across the countries. 20
23 behind the change of elasticity of substitution that the higher elasticity leads to higher output. In what follows, we next estimate attempt to estimate CES production function and see whether there is some evidence on time varying elasticity of substitution. It turns out that the results are rather sensitive on the assumption on the nature of technical change. If the rate of technical change is allowed to change over time (Figures 4.4, 4.5) we obtain the result that the elasticity of substitution has been almost constant over time (and declining rather than increasing). Instead of relying on the first order condition, another common used way of estimating the elasticity of substitution is to rely on a CES production function. Unfortunately, it is almost impossible to compute a nested model, where both the elasticity of substitution and the rate of technical change are allowed to change freely over time. However, we can estimate the usual CES production function but allowe the elasticity of substitution parameter depend linearly on time. In other words, we can write q (4.3) τt ρ ρ θ / ρ it = A( α(lite ) + (1 α)kit ) where ρ = ρ0 ρδt and A is a usual shift factor for the production function. Parameter ρ captures the trend-like behaviour in the elasticity of substitution, α is the share parameter and θ is the scale parameter. The idea that the elasticity of substitution could vary over time is by no means new. It has already been proposed by Revankar (1971). Revankar s VES production function is based on an assumption that the elasticity of substitution depends on the capital-output ratio. The VES specification has been tested in several occasions with somewhat mixed results (see, eg Kragiannis, Palivos and Papgeorgiou, 2004). We did also estimate a VES model from the panel data and found strong evidence against constant elasticity of substitution. It turned out, however, that the relationship between the elasticity of substitution and capital labour ratio (k/l) is not very robust. 11 Thus, we concentrate here on the estimates of the traditional version of the CES production function. The corresponding results are reported in Table 4.3. The estimated time-varying elasticity of substitution parameter, based on equation (4.3), is presented in Figure During the latter half of the sample, the coefficient of k/l was not significant. When estimating the VES production function we seem, in general, to have problems in identifying the effect of technical change and the effect of changing elasticity of substitution. This is because the capitaloutput ratios show an upward trend in all countries included in our sample. Consequently, various combinations of the technical change and substitution parameters produce almost identical error variance. 21
24 The estimation results are reasonable particularly when the data are normalized with country-specific sample average values. The only somewhat alarming aspect of the results is that the initial estimate of the elasticity of substitution is very low of the magnitude of 0.5. Although the estimated elasticity of substitution seems to increase over time it is still lower than one might expect on the basis of previous findings (eg Willman, 2002, Antràs, P, 2004) and what would constitute a reasonable level of substitution. Moreover, the elasticity of substitution parameters are estimated imprecisely, so that the 95% confidence intervals include values which are clearly unrealistic. Given these findings, the evidence on time varying and especially increasing elasticity of substitution is not very compelling. 12 Table 4.3 CES estimation results Parameter A (19.72) (12.36) (11.87) (45.14) α (4.21) (2.56) (2.47) (12.83) ϕ (21.35) (10.66) (5.72) (3.42) ρ (1.12) (5) (0.66) (3.71) ρ Δ (0.37) (0.40) (3.00) Θ (19.90) (234.31) σ R SEE The data is normalized with individual country sample averages in the case of columns (1) (3) and with panel average values in the case of column (4). The number of data points is 548. σ denotes the (maximum) value of the elasticity of substitution. Numbers inside parentheses are unadjusted t-ratios. 12 See eg Jones (2003 and 2005) for possible explanations for the poor performance of CES in the cross-country data. Jones s explanation is that the short-run elasticity of substitution might greatly deviate from the long-run (unitary) elasticity. 22
27 5 Concluding remarks The differences in growth performance for the selected OECD countries during the last decade or so are persistent and widespread. A large part of these differences can readily be explained by capital deepening and economic converging. The remaining part, which distinguishes between the good and bad performers, can be explained by evaluating their relative performance in terms of resources devoted to R&D and in fact by capacity to produce new technological innovations in the form of new patents. This view is based on the estimation results of this paper, suggesting that the Solow residual is largely explained by the intensity of R&D investment and beyond that ability to produce useful innovations (here gauged by triadic patents per capita). Furthermore, in an open economy framework, the benefits of R&D and patents seem to be much larger, as suggested by our finding of a positive cross-effect of triadic patents and openness of the economy. It seems that there are unused opportunities especially on the European side for keeping up with the historical growth record, as the US has done, by appropriate structural policies. In particular, the poor growth performers like Germany and Italy seem not to have used the opportunity to speed up technical change by investing in the R&D. Many small countries like the Nordics and Ireland represent the other extreme, having performed better than their historical record would have predicted. Even though the role of R&D is dominant, we cannot exclude the possibility that structural flexibility has also contributed to changes in productivity. Increased economic flexibility and investment in innovations need not be excluded alternatives for boosting economic growth: they may well be complements. Thus, investment in R&D may benefit from increased flexibility of the whole economy. In fact, the positive role of openness that is found in this study may just reflect this property. In this respect out results are consistent with Saam (2004, 2006) who shows that increased openness and increased elasticity of substitution can affect economic growth in a similar way. Testing for this possible complementarity hypothesis could indeed be challenging task for future research. Increased globalization and development of a single market in Europe would, however, easily motivate the efforts. 25
VI. Real Business Cycles Models Introduction Business cycle research studies the causes and consequences of the recurrent expansions and contractions in aggregate economic activity that occur in most industrialized
The impact of increased efficiency in the use of energy: A computable general equilibrium analysis for Spain Pablo Arocena Universidad Pública de Navarra Nafarroako Unibertsitate Publikoa OUTLINE o Motivation:
NIESR Fiscal Consolidation During a Depression Nitika Bagaria*, Dawn Holland** and John van Reenen* *London School of Economics **National Institute of Economic and Social Research October 2012 Project
Total Factor Productivity Diego Comin NewYorkUniversityandNBER August 2006 Abstract Total Factor Productivity (TFP) is the portion of output not explained by the amount of inputs used in production. The
DEPARTMENT OF ECONOMICS Unit ECON 11 Introduction to Econometrics Notes 4 R and F tests These notes provide a summary of the lectures. They are not a complete account of the unit material. You should also
Chapter 2 Population, Economic Growth, and TFP in Developed Countries Abstract In this chapter, we investigate the relationship between population size and economic growth using growth accounting and empirical
An International Look at the Growth of Modern Finance ONLINE APPENDIX Thomas Philippon and Ariell Reshef April 2013 A Historic finance income share Much of the data on financial intermediation value added
After 25 years of high unemployment. What have we learned? Olivier Blanchard October 20, Barcelona Unemployment 2 How to reduce unemployment? Many strong opinions: eliminate labor market rigidities (list
1 Conditional guidance as a response to supply uncertainty Appendix to the speech given by Ben Broadbent, External Member of the Monetary Policy Committee, Bank of England At the London Business School,
The (mis)allocation of capital Abhijit V. Banerjee Esther Duflo Kaivan Munshi September, 2002 Abstract Is capital allocated so that its marginal product is equated to the market interest rate? Is the marginal
Current Account Imbalances in the Euro Area Alan Ahearne Bruegel, Brussels and National University of Galway, Ireland Birgit Schmitz University of Bonn Jürgen von Hagen Bruegel, Brussels, University of
The Budget Deficit, Public Debt and Endogenous Growth Michael Bräuninger October 2002 Abstract This paper analyzes the effects of public debt on endogenous growth in an overlapping generations model. The
Current Account Imbalances in the Euro Area Alan Ahearne Bruegel, Brussels and National University of Galway, Ireland Birgit Schmitz University of Bonn Jürgen von Hagen Bruegel, Brussels, University of
Volume 23, Number 2, December 1998 Tests of Changes in the Elasticity of the Demand for M2 and Policy Implications: The Case of Four Asian Countries Yu Hsing * 1 This paper examines the demand for real
An Analysis of the Effect of Income on Life Insurance Justin Bryan Austin Proctor Kathryn Stoklosa 1 Abstract This paper aims to analyze the relationship between the gross national income per capita and
Financial market integration and economic growth: Quantifying the effects, Brussels 19/02/2003 Presentation of «Quantification of the Macro-Economic Impact of Integration of EU Financial Markets» by London
What Drives a Successful Fiscal Consolidation? Pablo Hernández de Cos Enrique Moral-Benito May 2012 Abstract Fiscal consolidations are currently in the agenda of fiscal authorities in many countries. Using
The Debt Challenge in Europe Alan Ahearne and Guntram Wolff October 2011 Outline The challenge: debt overhang and price adjustment. Large increase in private debt prior to the crisis. Balance-sheet adjustments
PUBLIC DEBT SIZE, COST AND LONG-TERM SUSTAINABILITY: PORTUGAL VS. EURO AREA PEERS 1. Introduction This note discusses the strength of government finances in, and its relative position with respect to other
HOW IMPORTANT IS BUSINESS R&D FOR ECONOMIC GROWTH AND SHOULD THE GOVERNMENT SUBSIDISE IT? Rachel Griffith THE INSTITUTE FOR FISCAL STUDIES Briefing Note No. 12 Published by The Institute for Fiscal Studies
Gains from Trade: The Role of Composition Wyatt Brooks University of Notre Dame Pau Pujolas McMaster University February, 2015 Abstract In this paper we use production and trade data to measure gains from
Causes of Inflation in the Iranian Economy Hamed Armesh* and Abas Alavi Rad** It is clear that in the nearly last four decades inflation is one of the important problems of Iranian economy. In this study,
International Review of Economics and Finance 9 (2000) 387 415 Stock market booms and real economic activity: Is this time different? Mathias Binswanger* Institute for Economics and the Environment, University
Insurance and the Macroeconomic Environment Casper Christophersen and Petr Jakubik 1 Abstract Insurance companies play an important role in the financial sector and the availability of insurance products
Spillover Effects of a Demand Boom in Northern Europe on Output and Employment in Southern Europe Oliver Picek 1 Enno Schröder 2 1 The New School for Social Research 2 The New School for Social Research,
This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and education use, including for instruction at the authors institution
HAS THE PRODUCTIVITY BOOM FINALLY ARRIVED? by Charles I. Plosser * William E. Simon Graduate School of Business Administration University of Rochester Shadow Open Market Committee Meeting September 26-27,
(Cover page) The Tax Burden of Typical Workers in the EU 28 2014 Edition NEW DIRECTION Page 1 of 17 James Rogers & Cécile Philippe May 2014 New Direction aims to help shift the EU onto a different course
BIS database for debt service ratios for the private nonfinancial sector Data documentation The debt service ratio (DSR) is defined as the ratio of interest payments plus amortisations to income. As such,
A Primer on Forecasting Business Performance There are two common approaches to forecasting: qualitative and quantitative. Qualitative forecasting methods are important when historical data is not available.
CENTRAL BANK OF CYPRUS EUROSYSTEM WORKING PAPER SERIES Unemployment in Cyprus: Comparison Between Two Alternative Measurement Methods George Kyriacou Marios Louca Michalis Ktoris August 2009 Working Paper
Discussion of Capital Injection, Monetary Policy, and Financial Accelerators Karl Walentin Sveriges Riksbank 1. Background This paper is part of the large literature that takes as its starting point the
Import Prices and Inflation James D. Hamilton Department of Economics, University of California, San Diego Understanding the consequences of international developments for domestic inflation is an extremely
NBER WORKING PAPER SERIES LONG-TERM DAMAGE FROM THE GREAT RECESSION IN OECD COUNTRIES Laurence M. Ball Working Paper 20185 http://www.nber.org/papers/w20185 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts
Euro area current account imbalances and income inequality Benedicta Marzinotto University of Udine Literature review Literature on current account imbalances in the euro area Inter-temporal (consumption)
Journal of Economic Integration 21(1), March 2006; 21-39 The Impact of U.S. Economic Growth on the Rest of the World: How Much Does It Matter? Vivek Arora International Monetary Fund Athanasios Vamvakidis
DOCTORAL (Ph.D) THESIS UNIVERSITY OF KAPOSVÁR FACULTY OF ECONOMIC SCIENCE Department of Finance and Economics Head of Doctors School: DR. GÁBOR UDOVECZ Doctor of the Hungarian Academy of Sciences Supervisor:
THE U.S. CURRENT ACCOUNT: THE IMPACT OF HOUSEHOLD WEALTH Grant Keener, Sam Houston State University M.H. Tuttle, Sam Houston State University 21 ABSTRACT Household wealth is shown to have a substantial
Expenditure and Outputs in the Irish Health System: A Cross Country Comparison Paul Redmond Overview This document analyzes expenditure and outputs in the Irish health system and compares Ireland to other
Stability in the Eurozone: Challenges and Solutions Ludger Schuknecht Director General Economic and Fiscal Policy Strategy; International Economy and Finance IMFS Working Lunch, Frankfurt (Main), 15 July
European Commission EU study on company car taxation: presentation of the main results Presentation in the OECD workshop on estimating support to fossil fuels, Paris 18-19 November 2010 Katri Kosonen European
Provided by the author(s) and NUI Galway in accordance with publisher policies. Please cite the published version when available. Title Are the US current account deficits really sustainable? Author(s)
Notes on the Lisbon process: An analysis of the impacts of reaching the Lisbon targets for sills, R&D and the administrative burden in the European Union Ray Barrell and Simon Kirby* NIESR Discussion Paper
The Impact of Interest Rate Shocks on the Performance of the Banking Sector by Wensheng Peng, Kitty Lai, Frank Leung and Chang Shu of the Research Department A rise in the Hong Kong dollar risk premium,
National Tax Journal, June 2012, 65 (2), 247 282 FOREIGN TAXES AND THE GROWING SHARE OF U.S. MULTINATIONAL COMPANY INCOME ABROAD: PROFITS, NOT SALES, ARE BEING GLOBALIZED Harry Grubert The foreign share
Does euro area membership affect the relation between GDP growth and public debt? Christian Dreger Hans-Eggert Reimers European University Viadrina Frankfurt (Oder) Department of Business Administration | {
"pile_set_name": "Pile-CC"
} |
/*
This file is part of:
NoahFrame
https://github.com/ketoo/NoahGameFrame
Copyright 2009 - 2020 NoahFrame(NoahGameFrame)
File creator: lvsheng.huang
NoahFrame is open-source software and you can redistribute it and/or modify
it under the terms of the License; besides, anyone who use this file/software must include this copyright announcement.
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.
*/
#include "NFComm/NFPluginModule/NFPlatform.h"
#ifdef NF_DEBUG_MODE
#if NF_PLATFORM == NF_PLATFORM_WIN
#pragma comment( lib, "SDL2d.lib" )
#elif NF_PLATFORM == NF_PLATFORM_LINUX || NF_PLATFORM == NF_PLATFORM_ANDROID
#elif NF_PLATFORM == NF_PLATFORM_APPLE || NF_PLATFORM == NF_PLATFORM_APPLE_IOS
#endif
#else
#if NF_PLATFORM == NF_PLATFORM_WIN
#pragma comment( lib, "SDL2.lib" )
#elif NF_PLATFORM == NF_PLATFORM_LINUX || NF_PLATFORM == NF_PLATFORM_ANDROID
#elif NF_PLATFORM == NF_PLATFORM_APPLE || NF_PLATFORM == NF_PLATFORM_APPLE_IOS
#endif
#endif
| {
"pile_set_name": "Github"
} |
The College of Richard Collyer
The College of Richard Collyer (colloquially Collyer's ), formerly called Collyer's School, is a co-educational sixth form college in Horsham, West Sussex, England.
Students have achieved exam results which enabled a number to progress to universities. The college is rated as being ‘outstanding’ by Ofsted, and is the only further education college in the county to have achieved this.
It is also the second oldest school in West Sussex after The Prebendal School in Chichester and the fourth oldest school in Sussex. The college is Grade II listed by English Heritage.
Admissions
Collyer's serves about 1600 students between 16 and 19 years of age. It offers AS and A-level courses in 45 different subjects, including a selection not taught at other local colleges. 20 further subjects are offered towards AVCE, BTEC, GNVQ and vocational certifications and GCSE examinations.
A wide variety of adult education classes are offered at Collyer's in the evenings. It is situated on the B2180 opposite Horsham Community Hospital, and close to the fire and police stations.
History
The College was founded in 1532 (Old Style) in the will of Richard Collyer, who was born in Horsham, and became a wealthy member of The Mercers’ Company of the City of London. The Mercers’ Company are still the school's trustees, and maintain a close relationship with the school. Collyer willed that one of his houses in the City, variously called ‘The Sonne’ or ‘The Sunne’, be sold and the proceeds used to build a school-house in Horsham for “”.
Under the terms of the will the money was not freed until 1540, and the new school was eventually opened in the early summer of 1541. The education granted to those sixty scholars, who were naturally all boys, was to be provided “freely without any money paying therefor”, with the Mercer's Company paying the masters’ salaries.
The original building was on the site of the current St Mary's Church of England Primary School, adjacent to the parish church. However, it was extended then rebuilt in 1660, in order to accommodate “neare an hundred scholars ... with diligence and good success” by 1666, such that none of Collyer's original structure survives. (Part of the 1660 building remains in structure of Arun House, in Denne Road.) In the eighteenth century it fell into disrepair, such that the Mercers’ Company surveyor reported that it would cost £1,040 to renovate, “but you will still have a very old and imperfect building.” Accordingly, in 1840 the second building was demolished (save for the part incorporated into Arun House), and a new, late-Elizabethan style structure built for the sum of £2,240.
Hurst Road Site
By the late nineteenth century, the population of Horsham had expanded to 10,000 (accelerated by the coming of the railway and its associated employment), the City and Guilds Institute (which the Mercers' Company had helped found) decreed that education needed to be extended to include the new sciences, and money needed to be found to replace the school buildings yet again. Thus after a long campaign against fees, including a petition of 1,100 signatures, the new school charter of 1889 stated that, “Tuition fees might vary between £4 and £10 p.a. and Boarding fees were not to exceed £40 a year.” A new and larger site was sorely needed.
The present site in Hurst Road was found, and the current building was designed in 1892 by Arthur Vernon, and built by Joseph Potter for a contract price of £5,795. It is now grade II listed by English Heritage. Above the entrance is a stone engraved with, “Grammar School, Founded by Richard Collier AD 1532”. (Historically the founder's name was often spelled as ‘Collier’, but from the twentieth century it has always been spelled as it is today.) The 1892 building facing Hurst Road has been extended continually as the school has expanded. This included the addition of science laboratories in 1897, a ‘Great Hall’ in 1912, and the ‘New Block’ classrooms in 1932.
In the 1890s Collyer's taught 110 boys from ages 7 to 17, both boarders and day-schoolers, and for the first time included a sixth form to study for university entrance. From 1923 the Rev. W.M. Peacock started to model the school on public school lines, introducing (among other things) four houses (see below), The Horsham Grammar School Magazine (later to become The Collyerian), and a school song. By 1926 it was a single-stream school of 220 boys with a sixth form of “less than a dozen”, and ten teaching staff.
Grammar school
Collyer's ceased to accept boarders in 1935, and the dormitories were converted into much-needed library and common-room space. Plans for adding a gymnasium and other facilities were abandoned in 1939, when the school accepted evacuees from the Mercers’ School in London, and pupil numbers soared to over 400 in three streams. (The accommodation crisis was solved by building hutted classrooms, but numbers continued to rise because of the post-war ‘baby boom’, and the huts were not demolished until the 1980s.) In 1944 it became a voluntary-aided grammar school, and its education was again made available free to the scholars. In the 1950s it had around 500 pupils, rising slowly to over 600 during the 1960s.
In the early 1960s when an Old Collyerian (OC), Dr. William W. Duckering (1861–1945) bequeathed £22,000 to the school ‘for its general purposes’. The bequest paid for a new laboratory block, gymnasium and changing rooms in 1961, and an assembly and dining hall with theatrical stage facilities, modern kitchens attached, and a ‘Small Upper Hall’ above the new foyer, all completed in 1963. The new hall was named the ‘Duckering Hall’, and the smaller hall the ‘Duckering Room’. (The final phase of building work, to be a new classroom block replacing the World War Two emergency wooden huts, was never undertaken.) Between 1960 and 1963 the playing fields were also extended, levelled, and new sports facilities were added. In 1964 a headmaster's house was built on the site, replacing the accommodation that was originally included in the 1892 school block.
In the 1960s the then headmaster, Douglas Coulson, left after it was found that he had regularly subjected pupils to canings, and two teachers were imprisoned for indecency. But the school recovered from this low point under its last headmaster, Derek Slynn.
Sixth form college
It started its transition to become a voluntary-aided sixth form college in 1976. The other three state secondary schools in Horsham (Forest Boys, Forest Girls and Horsham High School for Girls) became comprehensives. Collyer's had taken its last first form intake in the previous September, and started to expand its sixth form. Initially this was done by taking students from the two existing secondary moderns to do O-levels, and girls from Horsham High School who wanted to study A-level choices that were not offered by their previous school.
In the early 2000s, annual reports from the Office for Standards in Education (OFSTED) have deemed the school outstanding. On the strength of a recent OFSTED Grade One for Science provision, the college was awarded ‘Beacon Status’ for Science in 2005 by the Department for Education and Skills. In the same year, it achieved the status of Centre of Vocational Excellence (CoVE) for sport and recreation. A new £2 million, three storey Learning Resources Centre was unveiled during this period. In 2006 work began to extend the Sports Hall, or Cowley Building, to provide more teaching and social space.
Houses
From the 1920s the students and some teaching staff in the college have been divided into a number of different houses. All houses names are associated with the history of the college or the town. The current eight houses are:
Denne – after a local area of Horsham;
Garnet – after Thomas Garnet, a saint and Jesuit priest who attended the school in the 16th century;
Hurst – after a ward covering the western side of Horsham (see Horsham Hurst (electoral division), and also the name of the road on which the college is situated;
Mercers’ – after the Mercers' Company, a livery company based in London, a member of which founded the original school;
Pirie – After William Pirie, a previous headmaster at the college, who served for 46 years and raised standards significantly in the college. There is a small square in the town centre known as Pirie's Place, with a sculpture of Pirie in a horse-drawn cart, commemorating the achievement of the headmaster;
Richmond – After a road bordering the college;
St Leonard's – After the forest to the east of Horsham;
Whittington – After a member of the Mercer's company.
Former house names include Collyer's, Duckering and Weald.
Headmasters
The following list of the headmasters from the school's opening until 1965 was provided in the history of the school that was published in that year.
1541–1546 Richard Brokebanke
1546–1548 Nicholas Bayne
1549–1562 John Fowler
1563–1567 Thomas Hodeles
1567–1617 James Alleyn
1617–1629 Richard Nye (OC)
1629–1631 Edmund Pierson
1631–1639 Thomas Robinson
1640–1644 Rev. John Sefton
1644–1647 Rev. Thomas Smith
1647–1648 Rev. Alma Hogglebin
1648–1684 John Nisbet
1684–1685 Rev. Peregrine Peryham
1686–1699 Rev. James Wickliffe
1699 Rev. Ralph Grove
1700–1706 Rev. Alexander Hay
1706–1712 Rev. Thomas Pittis
1712 Rev. Peter Stockar
1712–1722 Rev. John Reynell
1722–1773 Rev. Francis Osgood
1773–1806 Rev. William Jameson
1806–1821 Rev. Thomas Williams
1822–1868 William Pirie
1868–1883 Richard Cragg (the younger)
1883–1890 James Williams
1890–1917 Rev. Dr. George Thompson
1917–1922 William Major
1922–1926 Rev. Canon Wilfrid Peacock
1922–1956 Philip Tharp
1956–1964 Douglas Coulson
1964–1966 Vernon Davies (acting head)
1966–1983 (Eldred) Derek Slynn
Principals
In 1976, the title was changed from Headmaster to Principal. Since then the college's principals have been:
1983–1999 David Arnold
1999–2004 Michael Marchant
2004–2014 Dr. Jacqueline Johnston
2014– Sally Bromley
Academic performance
After recovering from a country-wide low point in schooling in the eighteenth century, headmasters from William Pirie to George Thompson successively raised standards, such that in 1904, when the school had 110 pupils, six OCs held open awards at Oxford or Cambridge, and another was a City and Guilds scholar. By 1962, university education also having been made free to students, the school sent 55 students out of 80 leavers into higher education.
Notable alumni
See :Category:People educated at The College of Richard Collyer.
The College of Richard Collyer
Alex Adair, DJ, producer and remixer
Devon Endersby, first-class cricketer
Harry Enfield, contemporary British entertainer
Angie Hobbs, Professor of the Public Understanding of Philosophy at the University of Sheffield
Chris Nash, Sussex cricketer
Holly Willoughby, TV presenter
Collyer’s School
Chris Aldridge, continuity announcer and newsreader for BBC Radio 4
Wilfred Brown, tenor
William Brown, president from 1951–52 of the British Psychological Society, and director from 1936–45 of the Institute of Experimental Psychology at the University of Oxford
David Cummings, screenwriter and musician
Saint Thomas Garnet (c.1575–1608), Jesuit priest and martyr
Neil Lyndon, author and journalist
Simon Nye, writer of Men Behaving Badly
Paul Parker, Sussex cricketer
Lt.-Col. George Styles GC, commanded the 28th Commonwealth Brigade from 1958–61, and bomb disposal expert in Northern Ireland in the 1970s
Eric Thompson, actor, and voice of The Magic Roundabout
David Westwood, Chief Constable from 1999–2005 of Humberside Police
References
External links
The College of Richard Collyer
The Old Collyerians’ Association (the association for alumni)
Press release announcing 2005 OFSTED school inspection results
A Brief History of Richard Collyer’s School 1532–1964
The Mercers’ Company
Collyer’s today with up to date photographs
Contemporary photographs and text of English Heritage’s Grade II listing
Edubase
Category:Horsham
Category:Educational institutions established in the 1530s
Category:Sixth form colleges in West Sussex
Category:Learning and Skills Beacons
Category:1532 establishments in England | {
"pile_set_name": "Wikipedia (en)"
} |
Taste transduction: appetizing times in gustation.
Taste receptors cells sample the chemical composition of ingested material in order to provide the initial sensory information to facilitate decisions regarding its eventual acceptance or rejection. Ion channels, ionotropic and metabotropic receptors have been implicated in the initial events of transduction but until recently their identification has proven difficult. Recent advances in the identification and functional characterization of mammalian taste receptors has greatly increased our understanding of the pathways for the transduction of taste stimuli. This basic information will be critical to answer longstanding questions regarding the coding of taste information and may help elucidate the role of the taste system in the control of food intake. | {
"pile_set_name": "PubMed Abstracts"
} |
Yacht-Club von Deutschland
The Yacht-Club von Deutschland (YCvD), "Yacht Club of Germany", was a yacht club platform established in 1937 during Nazi rule in Germany.
History
The Sports Office of the Reich (DRL/NSRL) was founded in July 1934. As a result of its activity all German sport associations gradually lost their independence and became subject to its manipulation.
The Yacht-Club von Deutschland originated after the 1936 Summer Olympics sailing events in the Bay of Kiel. The following year the prestigious Kaiserlicher Yacht Club (Imperial Yacht Club) was forcefully merged with local smaller clubs in the Kiel area, such as the "Kieler Segelvereinigung" (KSV).
The main purpose in the creation of the Yacht-Club von Deutschland was to "bring into line" the scattered yachting and sailing clubs of North Germany's former Hanseatic League cities under a central command along with yacht clubs elsewhere in Germany. The Yacht Club of Kiel's name "Kaiserlicher Yacht Club", deemed by the Nazis not to be in tune with "the spirit of the times" ("zeitgemäß"), soon fell into oblivion and the honorary commodore's title was withdrawn from old former Emperor William II, who withered in exile in Doorn, the Netherlands.
The Yacht-Club von Deutschland was further expanded by the "incorporation" ("Einverleibung") with other German yacht clubs having a royal background. Foremost of these were the Yacht Club of Bavaria (Bayerischer Yacht-Club) and the Württembergischer Yacht Club, to form a massive pan-German entity.
After successfully organizing the 1937 Kiel Week, the Yacht-Club von Deutschland supported the Norddeutscher Regatta Verein (NRV) in the organization of the Star Class European Championship in the same year.
Upon the 1938 annexation of Austria ("Anschluss"), half of the Austrian yacht clubs were brought under the wing of the Yacht-Club von Deutschland. In 1939 many of the sailing competitions and other planned events in preparation for the 1940 Helsinki Summer Olympics were carried out in Germany, especially in Kiel, despite of the imminence of the war.
The last significant activity of the Yacht-Club von Deutschland right before the outbreak of World War II was the organization of the Star World Championship, together with the NRV. YCvD Kiel members Dr. Peter Hansohm and Christian Blankenburg ended up third in the general classification. On September 1, participants belonging mainly to nations that had become hostile were brought safely across the border into Denmark together with their boats. This operation was carried out with the assistance of the Kriegsmarine.
World War II radically altered the role of the Yacht-Club von Deutschland in the country. Even though it continued its sailing school activities among the youth for a few years, yachting was discouraged. In 1940 monetary funds for organizing sailing events, like Kiel Week, were not forthcoming. Contributors felt emboldened to deny funds to the Yacht-Club von Deutschland owing to the war-related shifting of priorities.
In the last years of the war many members of the many branches of the yacht club, among them young teenagers, had to go to fight to the fronts. A figure of the casualties is not known.
The Yacht-Club von Deutschland's short life ended with the capitulation of the Nazi government in 1945. As a Nazi organization, it was disbanded when the American Military Government issued a special law outlawing the Nazi party and all of its branches. The smaller yacht clubs that had been forcefully merged with it had to be reestablished anew after the war.
Since the Kaiser had died in 1941 and the reestablishment of the club under the name "Yacht-Club von Deutschland" was not allowed by the British occupying authorities, the former Kaiserlicher Yacht Club was reestablished as the Yacht Club of Kiel.
The Yacht-Club von Deutschland should not be confused with the Motor-Yacht-Club von Deutschland.
Publications
Mitteilungsblatt des Yacht-Clubs von Deutschland. — Kiel: NS.-Gauverl. Schleswig-Holstein. (Newsletter)
Monatsschrift des Yacht-Clubs von Deutschland e.V. (Monthly).
References
External links
Kieler Yacht-Club's site
Records of the International Star Class Yacht Racing Association/Correspondence
International Star Class Yacht Register numbers 1057 – 2116
Kiel City Archives - The Kiel Week in Nazi Propaganda (de)
Category:Nazi Party organizations
Category:1937 establishments in Germany
Category:1945 disestablishments in Germany
Category:Kiel
Category:Yacht clubs in Germany
Category:Sports organizations established in 1937
Category:Organizations disestablished in 1945 | {
"pile_set_name": "Wikipedia (en)"
} |
Q:
Infinite patterned ASCII dice
After seeing Pretty print dice faces from multiple rolls of multi-sided dices,
I decided to make an infinite ASCII dice generator.
There was one requirement, it to follow a normal dice face.
And so I decided on making two classes, the Dice and Rings.
Dice outputs the ASCII dice, holds the rings, and tells the rings how many dots to display.
The rings on the other hand are just one ring of the die.
For example a normal 6 sided dice has two 'rings', the outer 8 and the inner 1.
So Ring decide where to put the dots.
This method allows to easily extend the dice, but keep the same base layout for the dice.
That is no matter the size we will always see the same first 6 faces. (If all 6 dot's go on the same ring)
After completing the program,
some bits to me look messy for example display.
But I can't think of a way to make them easier to understand.
Or nicer to look at.
As far as I know it works with all sized dice.
But I made the algorithms with odd sized dice in mind.
from math import ceil
class Ring:
def __init__(self, ring):
self.ring = ring
self.size = self._size(ring)
self.index = self._build_index(self.size)
def build(self, amount):
indexes = set(self.index(number) for number in range(amount))
return [index in indexes for index in range(self.size)]
def fill(self):
return [True for _ in range(self.size)]
@staticmethod
def _size(ring):
# Alternate way to think about this:
# max(ring ** 2 - (ring - 2) ** 2, 1)
return max((ring - 1) * 4, 1)
@staticmethod
def _build_index(size):
increment = size // 2
columns = size // 4
columns_increment = size // 8
def column_addition(column):
return (column * columns_increment + column // 2) % columns
if not columns:
column_addition = lambda x: x
def get_index(number):
addition = column_addition(number // 4)
addition += (number % 4 > 1) * columns
return (number * increment + addition) % size
return get_index
class AsciiDice:
def __init__(self, size, icons=' O'):
self._display = self.build_display(icons)
largest_ring = ceil(size ** 0.5)
start = 1 if largest_ring % 2 else 2
self._ring = largest_ring
self.rings = list(map(
Ring,
reversed(range(start, largest_ring + 1, 2))
))
# To be overwritten in a subclass.
# The amount is _always_ even.
# This is as the odd dot is added to the last result.
def _spread_amount(self, amount):
pass
def _build(self, amount):
if amount % 2:
spread = list(self._spread_amount(amount - 1))
spread[-1] += 1
else:
spread = list(self._spread_amount(amount))
for amount, dice in zip(spread, self.rings):
if amount == dice.size:
yield dice.fill()
else:
yield dice.build(amount)
def display(self, amount):
array = [[None for _ in range(self._ring)] for _ in range(self._ring)]
rings = self._build(amount)
for r, ring in enumerate(rings):
groups = len(ring) // 4
x = r
y = r
for i, value in enumerate(ring):
array[y][x] = value
if i < groups:
y += 1
elif i < groups * 2:
x += 1
elif i < groups * 3:
y -= 1
else:
x -= 1
case = ['+' + '-'*self._ring + '+']
return case + ['|' + self._display(i) + '|' for i in array] + case
@staticmethod
def build_display(icons):
def change_icon(value):
return icons[value]
def inner(array):
return ''.join(map(change_icon, array))
return inner
class SpreadoutDice(AsciiDice):
def _spread_amount(self, amount):
rings_amount = list(map(lambda x: x.size, self.rings[:-1]))
rings_slice = len(rings_amount)
spread = [0 for _ in range(rings_slice)]
while rings_slice:
each = amount // rings_slice
if each < 4:
rings_slice -= 1
continue
each = each // 4 * 4
for ring in range(rings_slice):
spread[ring] += each
amount -= each
if spread[ring] > rings_amount[ring]:
amount += spread[ring] - rings_amount[ring]
spread[ring] = rings_amount[ring]
rings_slice -= 1
spread[0] += amount
amount = 0
if spread[0] > rings_amount[0]:
amount += spread[0] - rings_amount[0]
spread[0] = rings_amount[0]
return spread + [amount]
class OuterDice(AsciiDice):
def _spread_amount(self, amount):
for ring in self.rings:
if amount > ring.size:
yield ring.size
elif amount > 0:
yield amount
else:
yield 0
amount -= ring.size
# From here down, doesn't really need reviewed.
class PrintSideBySide:
def __init__(self, amount_dice, dice_height, separator=' '):
self.amount = amount_dice
self.height = dice_height
self.clear_buff()
self.separator = separator
def print(self):
if all(self.buff):
print('\n'.join(self.buff))
def clear_buff(self):
self.buff = ['' for _ in range(self.height)]
self._size = 0
def add(self, dice):
for index, value in enumerate(dice):
self.buff[index] += self.separator + value
self._size += 1
if self._size == self.amount:
self.print()
self.clear_buff()
if __name__ == '__main__':
size = 3
buff = PrintSideBySide(9, size + 2)
dice = OuterDice(size ** 2)
for i in range(1, size ** 2 + 1):
buff.add(dice.display(i))
buff.print()
size = 5
buff = PrintSideBySide(5, size + 2)
dice = OuterDice(size ** 2)
for i in range(1, size ** 2 + 1):
buff.add(dice.display(i))
buff.print()
buff.clear_buff()
dice = SpreadoutDice(size ** 2)
for i in range(1, size ** 2 + 1):
buff.add(dice.display(i))
buff.print()
The output for size = 3, from the above, is:
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
| | |O | |O | |O O| |O O| |O O| |O O| |OOO| |OOO|
| O | | | | O | | | | O | |O O| |OOO| |O O| |OOO|
| | | O| | O| |O O| |O O| |O O| |O O| |OOO| |OOO|
+---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+ +---+
In the above size = 5 shows how the different classes change the pattern, but is too long to put here.
A:
A couple of high-level suggestions:
No docstrings or comments! This generally makes code harder to read, review and maintain – you should get into the habit of writing them.
(Trying to debug your classes without knowing what arguments they took was quite tricky.)
Your classes should have a __repr__(). This can be really helpful for debugging. Compare and contrast:
<__main__.Ring object at 0x10125bcf8> # default repr()
Ring(3) # repr() thrown together quickly
Ring class
Setting size to a constant in your constructor is risky, because a caller could swap out the ring attribute midway through operation. (Why is another question – just trust that people will do weird things with your classes, and code defensively.)
Since the size attribute is easy to compute on the fly, I’d make it a method or perhaps a property instead. That way it won’t get out of date if the class is modified.
Likewise, the index() method is liable to get out-of-date. The optimisation from precomputing it is small – just make it a proper method.]
The variable names in the _build_index method aren’t very clear – it’s not immediately apparent what any of these variables represent. It’s also complicated by the number of functions and lambdas littering it up, which are only used once – just drop the code in directly.
The fill() method could be written more concisely:
return [True] * self.size
I haven’t quite worked out what the size attribute is for. It might be more appropriate to use the __len__ magic method, which means I can call len(Ring(foo)) and get a meaningful result. Depends on what it’s for – just a thought.
AsciiDice class
As before, you seem to be creating methods and then assigning them to attributes – for example, the self._display attribute. Just make them methods!
Using an attribute named _ring just after declaring a Ring class threw me a little – I expected this attribute to be an instance of Ring, but it seems to be just a number. That could be better named.
The list(map( to construct the rings attribute is quite hard to read; a list comprehension would be better:
self.rings = [Ring(r) for r in reversed(range(start, largest_ring + 1, 2))]
You can likewise use a list comprehension to tidy up the inner() function in the _build_display method:
return ''.join(change_icon(elem) for elem in array)
Within the _build_display method, the name of the change_icons() function is misleading – it just gets a value, whereas it sounds like it’s going to cause some changes! It should be renamed, or better, thrown away – it’s so simple that you don’t need it. Now inner() becomes:
return ''.join(icons[value] for value in array)
If the _spread_amount method is to be defined in a subclass, it should raise a NotImplementedError in the base class – this ensures a subclasser cannot forget to implement this method.
The display() method is very confusing. You can tidy up the array initialiser:
array = [[None] * self._ring] * self._ring
although pick a better name; array is hopelessly generic.
Once again we have the name ring being used for structures that don’t appear to be Ring instances – for example, we have a len() call on a class that doesn’t define __len__.
SpreadoutDice class
The list, map and lambda on the same line is unnecessarily obfuscated and confusing. Consider instead:
rings_amount = [x.size for x in self.rings[:-1]]
Isn’t that cleaner?
| {
"pile_set_name": "StackExchange"
} |
Endoscopic transvesical extramural ureterolithotomy.
The technique of endoscopic transvesical extramural ureterolithotomy for calculi impacted in the lower ureter is described. Ten patients are presented in whom calculi could not be extracted using conventional methods; 9 of the 10 calculi were successfully removed using this approach with no long-term complications. | {
"pile_set_name": "PubMed Abstracts"
} |
Q:
Flipping a Bitmap horizontally
I need to flip a Bitmap horizontally. I tried setting its scaleX property to -1.0, and that modified the Bitmap in such a way that I can see only a small portion of it (flipped) on the left side, instead of the whole flipped Bitmap. Its x property remained 0. I tried the same thing using a transformation matrix, with the same results.
What am I doing wrong?
A:
I posted a simple function to flip a bitmapdata object.
http://plasticsturgeon.com/2010/09/flipping-a-bitmapdata-image/
Here is the relevant code.
function flipBitmapData(original:BitmapData, axis:String = "x"):BitmapData
{
var flipped:BitmapData = new BitmapData(original.width, original.height, true, 0);
var matrix:Matrix
if(axis == "x"){
matrix = new Matrix( -1, 0, 0, 1, original.width, 0);
} else {
matrix = new Matrix( 1, 0, 0, -1, 0, original.height);
}
flipped.draw(original, matrix, null, null, null, true);
return flipped;
}
If you want to flip the image in a bitmap, you can flip its bitmapdata property like so:
myBitmap.bitmapData = flipBitmapData(myBitmap.bitmapData, "x");
You can switch to a vertical flip by using "y".
| {
"pile_set_name": "StackExchange"
} |
---
abstract: 'The invertibility of integral linear operators is a major problem of both theoretical and practical importance. In this paper we investigate the relation between an operator invertibility and the rank of its integral kernel to develop a local inverse theory. An operator is called locally invertible provided that any function can be recovered from its transformed image if the latter is known in an arbitrary open subset of its domain, i.e., if its image is known locally. It turns out that the local invertibility holds for any analytical kernel whose Taylor functions are linearly independent in any open subset of their domain - the so-called local linear independence condition. We also establish an equivalence between local linear independence and the so-called full rank a.e. property. The latter can be described as follows: for any finite, random sample of points, the square matrix obtained by applying, pairwise, the kernel function on them, has full rank almost surely. As an illustration, we show that the geodesic distance function on a sphere in more than one dimensions is of full rank a.e., in contrast to the Euclidean distance which is not.'
address: |
Department of Biostatistics and Computational Biology\
University of Rochester Medical Center\
601 Elmwood Ave\
Rochester, NY-14642\
author:
- Nikolay Balov
title: Local Invertibility of Integral Operators with Analytic Kernels
---
Problem Formulation and Motivation
==================================
A large class of linear inverse problems arises from the Fredholm integral equation of the first kind $$\label{eq:ram_fredholm}
\int_V \psi(x,y) f(y)dy = g(x), \textrm{ }x\in U,$$ where $U$ and $V$ are open sets in $\mathbb{R}^n$ and $f:V\to\mathbb{R}$, $g:U\to\mathbb{R}$, and $\psi:U\times V\to\mathbb{R}$ are some functions. The so-called kernel $\psi$ defines a linear operator $A_{\psi}$, allowing (\[eq:ram\_fredholm\]) to be conveniently written as $A_{\psi}f = g$. Typically, $f$ and $g$ are elements of the $L^2$-spaces $L^2(V)$ and $L^2(U)$, while $\psi$ is a Hilbert-Schmidt kernel, in which case $A_{\psi}$ is a compact linear operator. Notable examples of $A_{\psi}$ are the Laplace transformation in $\mathbb{R}$ with kernel $\psi(x,y) = \exp(-xy)$ and the closely related Fourier transformation, $\psi(x,y) = \exp(- i xy)$. Without being specific, we shall assume that (\[eq:ram\_fredholm\]) is formulated in $L^p$ sense for some $p\ge 1$.
Let us assume that for given $g$, (\[eq:ram\_fredholm\]) is solvable. Under some favorable conditions, a numerical solution of (\[eq:ram\_fredholm\]) can be obtained using a quadrature method by sampling the functions $f$, $g$ and $\psi$ at discrete sets of points. Let $\bar U=\cup_{i=1}^k \bar U_i$ and $\bar V=\cup_{j=1}^k \bar V_j$ be partitions of the closures $\bar U$ and $\bar V$ such that $U_i$ and $V_j$ are open and disjoint. Let also $\{x_i\}_{i=1}^k$ and $\{y_i\}_{i=1}^k$ be two sets of points such that $x_i\in U_i$ and $y_j\in V_j$. Then, we can discretize equation (\[eq:ram\_fredholm\]) to $$\label{eq:ram_fredholm_discrete}
\sum_{j=1}^k \psi(x_i, y_j) f(y_j) vol(V_j) = g(x_i), \textrm{ }i=1,...,k,$$ a system of linear equations. System (\[eq:ram\_fredholm\_discrete\]) can be solved for $f_k=f(y_j)_{j=1}^k$, only if the matrix $A_k = \{\psi(x_i,y_j)\}_{i,j=1}^{k}$ is invertible, or equivalently, has full rank $k$; then the solution is $\hat{f}_k(y) = \sum_{j=1}^k \hat{f}_{k,i} 1_{V_j}(y)$, for the vector $(\hat{f}_{k,j})_{j=1}^k = W_k A_k^{-1} g_k$, where $W_k = diag(1/vol(V_j))$ and $g_k=(g(x_i))_{i=1}^k$. Let us assume that $A_{\psi}$ is invertible and for a sequence of nets $\{x_i,y_j\}_{i,j=1}^{k}$, $k=1,2,...$, $A_k$ converges uniformly to $A_{\psi}$ and $g_k$ converges uniformly to $g$. Then, any convergent subsequence of $\hat{f}_k$ will approximate the solution of (\[eq:ram\_fredholm\]) (more details are given in the concluding section). Even though often, such as for compact $A_{\psi}$, $A_{\psi}^{-1}$ is unbounded and convergent subsequence of $\hat{f}_k$ may not be available, the solvability of equation (\[eq:ram\_fredholm\_discrete\]) is an interesting question by itself that is relevant to many problems with discrete nature. Usually, the sample points $(x_i,y_j)$ are chosen in a deterministic way, for example, according to uniform spacing. However, in order to formulate a more general problem regarding the invertibility of $A_k$, we introduce the following stochastic setting. Let the points $x_i$ and $y_j$ be chosen independently by some continuous distributions on $U$ and $V$, respectively. Then, the rank of $A_k$ becomes a $2k$-dimensional continuous random variable. We are interested in the question: what property of the kernel $\psi$ guarantees that for every $k$, $A_k$ has full rank almost surely (a.s.)? If this is the case, we shall say that $\psi$ has full rank almost everywhere (a.e.) in its domain.
The main focus of this paper is the characterization of the full rank a.e. kernels. We first need to define them properly. A possible approach is to simply reverse the standard, finite rank definition and say that a kernel $\psi$ has full rank, if it does not admit a finite sum representation $\psi(x,y) = \sum_{l=1}^m \phi_l(x)\xi_l(y)$ for linearly independent $\phi_l$ - finite rank linear operators are considered in all textbooks on the subject, see for example $\$70$ in [@riesz-nagy]. This approach however will be inadequate, for thus defined full rank kernels may not be of full rank in “a.e.” sense, as the following example shows. In $L^2[0,1]$, consider the functions $$c_s(x) = 1_{[\frac{s}{s+1}, \frac{s+1}{s+2})}(x) \textrm{, } s \ge 0,$$ and let $\psi(x,y) = \sum_{s=0}^{\infty} \frac{1}{s!} c_s(x) y^s$ - we call analytic in $y$ all kernels $\psi$ that admit such Taylor expansion. Note that, as defined, $c_s$ are linearly independent in $[0,1]$ and thus, $\psi(x,y)$ has no finite rank in sense of the standard definition. On the other hand, for any $k$ points $x_i$ and $y_j$, sampled uniformly in $[0,1]$, there is a positive probability for $A_k$ to have rank $1$, and hence, $\psi$ is not of full rank a.e. in $[0,1]$. Evidently, for the latter to hold, $c_s$ need to be linearly independent in a neighborhood of any point of their domain. We shall call the latter requirement on $c_s$ local linear independence. In the example above, $c_s$ are linearly independent but not locally linear independent. The main result in the paper is about rigorously showing the equivalence between the full rank a.e. property of analytical kernels and the local linear independence of their Taylor functions.
Local linear independence is a necessary condition for the solvability of some classes of integral equation problems. Our interest in this topic started with the study of the so-called variance linear operator in the domain of probability density functions. More generally, in (\[eq:ram\_fredholm\]), let $U$ and $V$ be open subsets of $\mathbb{R}^n$, and $\psi(x,y)=d(x,y)$ be a distance function in $\mathbb{R}^n$. Consider the operator $C_U$ $$(C_{U}f)(x) = \int_V d^2(x,y)f(y)dy \textrm{, } x\in U,$$ where $f\in \mathbb{P}(V)$, a class of measurable functions in $V$ with finite moments of all orders. If $d^2$ is analytic in $y\in V$, $d^2(x,y) = \sum_{s=0}^{\infty} c_s(x) y^s$, then the local linear independence of $c_s$ in $U$ will guarantee the invertibility of $C_{W}$ for any open $W\subset U$ (for more details see the concluding section). Consequently, there will be a one-to-one map between $\mathbb{P}(V)$ and the space of variance functions from the image $C_{W}(\mathbb{P}(V))$. With other words, any element of $\mathbb{P}(V)$ can be recovered if we know its variance function in an arbitrary open domain. This is what we tentatively call local invertibility. On the other hand, if $c_s$ are just linearly independent in $U$, then one needs to know the variance of $f$ everywhere in $U$ in order to recover it. Note that if only finitely many $c_s$ are non-zero, then the system $\{c_s\}_s$ can be neither linearly nor locally linear independent and no recovery is possible; this is the case with the Euclidean distance, $d^2(x,y) = ||x-y||^2$. As we show later in this paper, an example of full rank a.e. kernel is the squared spherical distance in $\mathbb{R}^n$, $d^2(x,y) = arccos^2(\frac{x.y}{||x||||y||})$. At this point we shall speculate that by establishing a one-to-one correspondence between $\mathbb{P}(V)$ and $C_{U}(\mathbb{P}(V))$, one obtains new potential tools for studying probability distributions, especially such on non-Euclidean metric spaces.
The local invertibility of integral operators may have direct practical implications. This is evident from the fact that the integral equation (\[eq:ram\_fredholm\]) and its discrete analog (\[eq:ram\_fredholm\_discrete\]) provide an abstract formulation for many remote sensing inverse problems, where the goal is to study some directly unobserved phenomena $f$ from its integral characteristic $g=A_{\psi}f$, which is measurable. Then, at least in principle, the local invertibility of $A_{\psi}$ allows the measurements on $g$ to be taken in an arbitrary domain of the measurement space and still reconstruct $f$. It is no coincidence then that all important in practice integral transformations, such as the Laplace transformation, are locally invertible.
The full rank a.e. property of integral kernels may also be of importance to some families of discrete inverse problems. Often, linear systems of equations of type (\[eq:ram\_fredholm\_discrete\]), with continuously changing sample points, arise naturally in problems such as the following variant of the $n$-body problem in astronomy. Let us assume that $\psi$ represents a gravitation field, $f$ is a mass distribution and $g$ is an observed effect of the field generated by the mass, for example, acceleration. If the gravitation field is generated by $k$ otherwise freely moving objects with positions $\{x_i\}_{i=1}^k$, one may be interested in reconstructing their mass from an instant observed effect of the accumulated force on each of them, which yields a type (\[eq:ram\_fredholm\_discrete\]) problem ($y_i$ are taken to be $x_i$). In this setting, the points $\{x_i\}_{i=1}^k$ will behave as if coming from a continuous probability distribution on the product space and the fact that the matrix $A_k$ has full rank a.s. and thus, (\[eq:ram\_fredholm\_discrete\]) is solvable, has an immediate significance.
The main body of the paper is organized in three sections. We begin, Section \[sec:finite\_rank\], with a systematization of the finite rank condition for analytic kernels by presenting some, not necessarily new, equivalent conditions for the latter (Proposition \[theorem:rank\_equivals\]). Then, in Section \[sec:lli\], we introduce the local linear independence and derive an important necessary condition (Lemma \[lemma:lli\_cond\]). In Section \[sec:full\_rank\], we define the full rank a.e. notion and present some necessary and sufficient conditions for it that hold for analytic kernels (Proposition \[theorem:psisum\_fullrank\] and Corollary \[cor:analytic\_full\_rank\_cond\]). Also there, presented is a more involved example of a full rank a.e. kernel - the spherical distance in two or more dimensions (Proposition \[theorem:full\_rank\_sphere\]). Finally, we conclude with a discussion on the usefulness and limitations of the presented results, and their possible further development.
Analytic Kernels with Finite Rank {#sec:finite_rank}
=================================
In this section we present some necessary and sufficient conditions for an analytic kernel to have finite rank. These conditions are based upon the fundamental relation between kernel rank and functional linear independence. Our goal here is not to present new facts, but to systematize some basic results and present them in a form needed in the following sections.
Let $U$ be an open subset of $\mathbb{R}^n$. A collection of functions $f_s:U \to \mathbb{R}$ is said to be linear independent in $U$ if $\sum_s \alpha_s f_s(x) = 0$, for almost all (in Lebesgue measure sense) $x\in U$ only if $\alpha_s = 0$ for all $s$. It is easy to check the following necessary condition for linear independence.
If the functions $f_1(x)$, ...,$f_k(x)$, $k\ge1$, are linearly independent in $U$, then there exist $x_1,...,x_k$ in $U$, such that $rank(\{f_i(x_j)\}_{i,j=1}^{k}) = k$. \[lemma:linindep\_functions\]
In the theory of linear operators, finite rank are said to be all kernels admitting representations in the form $\sum_{j=1}^k f_j(x)g_j(y)$, for linearly independent $f_j$ and $g_j$. We shall adopt, however, a different definition, based on the notion of matrix rank, which is equivalent to the former. The reason of not using the standard one is that our finite rank definition can be naturally extended to characterize full rank kernels as well and thus, provides more intuitive and consistent approach.
We say that a function $\psi:U\times V \to \mathbb{R}$, $U,V\subset\mathbb{R}^n$, has rank $k$ and write $rank(\psi) = k$ if for any $m\in\mathbb{N}$, $x_i\in U$ and $y_j \in V$, i, j=1,...,m, $$rank( \{\psi(x_i, y_j)\}_{i,j=1}^{m} ) \le k,$$ and $k$ is the smallest number with this property. \[ram:rank\_function\]
Recall that a function $f\in C^{\infty}(U)$ is real analytic in $U$ if it admits power series expansion in a neighborhood of any point $x\in U$. Next we extend this definition to bivariate functions or kernels in the linear operator theory context. Hereafter, we assume that $U$ and $V$ are open connected subsets of $\mathbb{R}^n$, although more general settings may be possible. We say that $\psi:U\times V \to \mathbb{R}$ is analytic in $V$, if about any $p\in V$ one can write $$\psi(x,y) = \sum_{m=0}^{\infty} \sum_{s:\sum_{i=1}^n s_i = m} c_{s_1...s_n}(x) (y_1-p_1)^{s_1}...(y_n-p_n)^{s_n}
\textrm{, }$$ for some functions $c_{s_1...s_n}$ in $U$, such that the series on the right converges to $\psi(x,y)$ for any $(x,y)\in U\times V$. For the sake of brevity, we shall write the above expansion as $$\label{eq:psi_analytic}
\psi(x,y) = \sum_{s}^{\infty} c_s(x) (y-p)^s := \sum_{l=1}^{\infty} \sum_{s:[s]=l} c_s(x) (y-p)^s$$ where $s=(s_1,...,s_n)$ is multi-index and $[s]:= s_1+...+s_n$. Any analytic $\psi(x,y)$, therefore, is infinitely differentiable in $y$ about any $p\in V$, and the series (\[eq:psi\_analytic\]) is in fact the Taylor series of $\psi$ in $y$ at $p$, thus giving $c_s(x) = \frac{1}{s!}\frac{\partial^s \psi}{\partial y^s}|_p$. We also silently assume that for all $x\in U$ and $p\in V$, the closed ball with center $p$ and radius the convergence radius of the series (\[eq:psi\_analytic\]), encloses the whole $V$. With other words, we assume that for any $p\in V$, $\psi$ admits an analytic expansion (\[eq:psi\_analytic\]) almost everywhere in $V$, except, eventually, a set of Lebesgue measure zero. If in (\[eq:psi\_analytic\]), $c_s(x)$ are analytic in $x\in U$ as well, then $\psi$ is said to be analytic in both arguments. The main results in this paper establish connections between the rank of $\psi$ and some conditions on its Taylor functions $c_s$.
We say that the vector space $span\{c_1, c_2,...\}$, that is, the space of all finite linear combinations of $c_s$, has a finite basis of size $m$, if there exist functions $c_{s_1}$, ..., $c_{c_m}$, such that all $c_s$’s are their linear combinations, i.e. $c_s\in span\{c_{s_1},...,c_{s_m}\}$ for all $s$. The next result gives some necessary and sufficient conditions for $\psi$ to have finite rank.
For any function $\psi : U\times V \to \mathbb{R}$ that is analytic in $V$, the following three conditions are equivalent
1. $rank(\psi) = k$.
2. $\psi(x,y) = \sum_{j=1}^k \phi_j(x)\xi_j(y)$ for linearly independent functions $\phi_j:U\to\mathbb{R}$ and $\xi_j\in C^{\infty}(V)$, j=1,...,k.
3. Let for arbitrary $p\in V$, $c_s$ are the Taylor functions of $\psi$ from Eq. (\[eq:psi\_analytic\]). Then, $span\{c_1, c_2,...\}$ has a finite basis of size $k$ in $U$.
\[theorem:rank\_equivals\]
Note that without the analytical requirement on $\psi$ only the link $(2) \Rightarrow (1)$ seems to be evident, because the connection $(1) \Rightarrow (2)$ goes through the Taylor expansion of $\psi$. Also, if the condition $(3)$ holds for one $p\in V$ then it inevitably holds for any other point in $V$, and therefore, to show that $\psi$ has finite rank, one only needs to show that its Taylor functions about one particular point have a finite basis.
If $\psi$ is symmetric and the representation in condition (2) of the proposition holds, then $\xi_i$ are linear combinations of $\phi_i$.Indeed, if we choose $x_j$, $j=1,...,k$, such that $rank(\{f_i(x_j)\}_{i,j=1}^{k}) = k$, then, for any $y$ we can solve the system $$\sum_{i=1}^k \phi_i(x_j)\xi_i(y) = \sum_{i=1}^k \phi_i(y)\xi_i(x_j), j=1,...,k$$ to obtain $\xi_i(y) = \sum_{i=1}^k \gamma_{ij} \phi_j(y)$.
Another immediate corollary of Proposition \[theorem:rank\_equivals\] is that for analytical $\psi$ with finite rank, $rank(\psi) = k$, the integral operator $$A_{\psi}: f \mapsto \int_V \psi(x,y)f(y)dy, \textrm{ } f:U\to \mathbb{R},$$ is of finite rank in sense of the standard definition from the integral operator theory.
Next, we present probably the simplest application of Proposition \[theorem:rank\_equivals\] showing the finite rank of the Euclidean metric. Consider the Euclidean square distance in $\mathbb{R}^n$, $
\psi(x,y) = ||x-y||^2 = \sum_{s=1}^n (x_{[s]}-y_{[s]})^2,
$ where $x_{[s]}$ are the components of $x\in \mathbb{R}^n$. Because of the global representation $$\psi(x,y) = \sum_{s=1}^n x_{[s]}^2 * 1 - 2x_{[1]} y_{[1]} ... - 2 x_{[n]} y_{[n]} + 1 * \sum_{s=1}^n y_{[s]}^2,$$ by Proposition \[theorem:rank\_equivals\], $rank(\psi) = n+2$, i.e. the Euclidean metric has finite rank of two more than the number of dimensions. Another obvious example of a finite rank kernel is the circular square distance, $\psi(x,y) = (x-y)^2$, $x,y\in \mathbb{S}^1 \equiv [0,2\pi]$. At the end of this paper we shall show that the spherical square distance in more than one dimensions is never of finite rank.
Local Linear Independence {#sec:lli}
=========================
In this section we introduce and describe the so-called local linear independence of a collection of functions, a property stronger than their linear independence. As it turns out, the rank of a bivariate analytic function is related to the local linear independence of its Taylor functions, which motivates the introduction of the latter notion. We start with its definition. \[ram\_def1\][Definition]{}
A collection of functions $f_s:U \to \mathbb{R}$ is said to be locally linear independent in $U$, if for any open subset $W$ of $U$ we have that $\sum_s \alpha_s f_s(x) = 0$ almost everywhere in $W$ if and only if $\alpha_s = 0$ for all $s$. \[def:local\_linear\_independence\]
Apparently, local linear independence implies linear independence. The reverse however is not true - a collection of functions can be linear independent in one open region but dependent in another. This is exactly the case with the functions $$f_s(x) = \left\{
\begin{array}{rl}
e^{-s/x} & \textrm{if } x > 0,\\
0 & \textrm{if } x \le 0,
\end{array} \right.$$ which are not locally linear independent, because they are linearly dependent on the negative half of the real line.
Naturally, the most important example of local linear independence is presented by the power function. \[lemma\_linindep\][Lemma]{}
\[lemma:lli\_powers\] For any distinct multi-indices $s_1,s_2,...$, the power functions $\{x^{s_l}\}_{l=1}^{\infty}$ are locally linear independent in $\mathbb{R}^n$.
In fact, the local linear independence of the power functions can be generalized to any collection of analytic functions - there is an equivalence between local linear independence and linear independence for any collection of analytic functions. The reason is that any analytic function vanishing in an open region, vanishes everywhere in its definition domain. Consequently, if a linear combination of real analytic functions vanishes in an open set, being an analytic function itself, it vanishes everywhere in its domain, and therefore the collection can not be linearly independent.
Next, we state several elementary properties of local linear independence that we are going to use later. Note that any collection of translated power functions $\{(x-a_l)^{s_l}\}_{l=1}^{\infty}$ is also locally linear independent. In fact, any bijection that have continuous inverse preserves local linear independence. \[lemma\_linindep\][Lemma]{}
\[lemma:lli\_bijection\] Let $U$ and $W$ be open subsets of $\mathbb{R}^n$ and $\mathbb{R}^k$, $k \le n$, respectfully, and $h:U\to W$ be a transformation with the property: the image of any open subset in $U$ contains an open subset in $W$. Then, for any collection $f_s: W \to \mathbb{R}$ of locally linear independent functions in $W$, $f_s\circ h$ are locally linear independent in $U$.
The assumption of Lemma \[lemma:lli\_bijection\] is satisfied by any $h:U\to W$ that has a full rank Jacobian in $U$, that is, since $k\le n$, $rank(J_h(p))=k$, $\forall p\in U$.
Although, in general, local linear independence is not preserved by forming linear combinations, there are some special cases when this is true. \[lemma\_linindep\][Lemma]{}
\[lemma:lli\_lin\_comb\] If $f_s: W \to \mathbb{R}$, s=1,...,n, are locally linear independent functions and $$g_1 \in span\{f_1\} \textrm{, } g_s \in span\{f_1,...,f_s\} \setminus span\{f_1,...,f_{s-1}\} \textrm{, } s > 0,$$ then $g_s$ are also locally linear independent.
We continue with an important connection between the local linear independence of finite sets of functions and the rank of matrices sampled from these functions. The result is analogous to that in Lemma \[lemma:linindep\_functions\] and gives a necessary condition for local linear independence. \[lemma\_linindep\][Lemma]{}
\[lemma:lli\_cond\] If the functions $f_1(x)$, ...,$f_k(x)$ are locally linear independent in $U$ and $U_i$, $i=1,...,k$, are arbitrary (non-empty) open subsets of $U$, then there exist $x_1,...,x_k$, $x_i\in U_i$, such that [$rank(\{f_i(x_j)\}_{i,j=1}^{k}) = k$]{}.
The condition in Lemma \[lemma:lli\_cond\] is only necessary. Indeed, it is clearly not-sufficient for the function $f(x) = 1_{\{x\textrm{ is rational}\}}$, $x\in (0,1)$, to be linearly independent, less locally linear independent. However, if in addition functions $f_i$ are continuous, then the condition becomes sufficient as well necessary.
Full Rank Almost Everywhere Kernels {#sec:full_rank}
===================================
We continue with an introduction of the full rank notion. As it shall become clear shortly, the definition is a natural extension of that of the finite rank and is closely related to local linear independence. \[ram\_def1\][Definition]{}
A bivariate function $\psi:U\times V \to \mathbb{R}$ is said to have full rank almost everywhere ($a.e.$) in $U\times V$ if for any number $k\in\mathbb{N}$ and open sets $U_i\subset U$ and $V_j\subset V$, $i,j=1,...,k$, there exist $x_i\in U_i$ and $y_j\in V_j$ such that $$rank( \{\psi(x_i, y_j)\}_{i,j=1}^{k} ) = k.$$ \[def:fullrank\_function\]
To say that $\psi$ has no finite rank according to Definition \[ram:rank\_function\], is not equivalent to the full rank a.e. condition. The latter implies the former, but the reverse is not true. Regarding the full rank a.e. kernel property, a close analog to Proposition \[theorem:rank\_equivals\], although weaker for it provides only a sufficient condition, is the following result. \[rank\_equivals\][Proposition]{}
\[theorem:psisum\_fullrank\] Let $\psi:U\times V \to \mathbb{R}$ admit the representation $$\label{eq:psisum}
\psi(x,y) = \sum_{s=1}^{\infty} \phi_s(x)\xi_s(y),$$ for locally linear independent $\xi_s(y)$ such that for any $k\in\mathbb{N}$, there is a set of $k$ functions $\phi_s(x)$ that are locally linear independent in $U$. Then $\psi$ has full rank a.e. in $U\times V$.
Proposition \[theorem:psisum\_fullrank\] states only a sufficient full rank condition. It turns out that for analytic in both arguments kernels, this condition becomes necessary also. In fact, the next result is a corollary of Propositions \[theorem:rank\_equivals\] and \[theorem:psisum\_fullrank\].
\[cor:analytic\_full\_rank\_cond\] If $\psi$ is analytic in $U\times V$, then $\psi$ has full rank $a.e.$ in $U\times V$ if and only if for the Taylor functions $c_s(x)$ of $\psi$ about any point $p\in V$ and every $k\in\mathbb{N}$, there is a set of $k$ functions $c_s(x)$ that are locally linear independent in $U$.
We can apply the above result to a large class of symmetric analytic functions. Let $x.y = \sum_{l=1}^n x_{[l]} y_{[l]}$ denote the dot product in $\mathbb{R}^n$. Consider the class of functions $\psi(x,y) = h(x.y)$, $(x,y)\in U\times V$, where $W=\{x.y|x\in U, y\in V\}\subset \mathbb{R}$, $0\in V$, and $h$ is analytic function in $W$ such that $h^{(s)}(0)\ne 0$ for infinitely many $s$. The Taylor functions of $\psi(x,y)$ at $y=0$ are $$c_s(x) = \frac{1}{[s]!} \frac{\partial^s}{\partial y^s} \psi(x,y)|_{y=0} = \frac{h^{(s)}(0)}{[s]!} x^s,$$ and since any finite collection of power functions is locally linear independent, for any $k$, there exist $k$ functions $c_s$ that are locally linear independent in $U$. Then, by Proposition \[theorem:psisum\_fullrank\], $\psi$ has full rank $a.e.$ in $U \times V$. As an illustration, one can show the full rank a.e. property of the Laplace kernel $\psi(x,y) = \exp(-x.y)$. Other examples of kernels of the same kind are $cos(x.y)$ and $arccos(x.y)$.
For subsets $U_l$, $l=1,...,m$, of $\mathbb{R}^n$, with $\otimes_{l=1}^{m} U_l$ we shall denote the product $U_1 \times ... \times U_m$. Let $\mu$ be the Lebesgue measure in $\mathbb{R}^n$. For the product $\otimes_{l=1}^m U_l$ of measurable $U_l$, by $\mu(\otimes_l U_l)$ we shall understand its Lebesgue (product) measure as a measurable subset of $\mathbb{R}^{nm}$. To motivate the usage of “a.e." notion in our definition of full rank, we need the following measure-theoretic result, which is of interest by itself. \[rank\_equivals\][Proposition]{}
\[theorema:f\_nullset\_zeros\] Let $f$ be an analytic function in an open subset $U$ of $\mathbb{R}^n$ such that the set $V_0 := \{x\in U| f(x) = 0\}$ has no interior points, then $V_0$ is measurable and $\mu(V_0) = 0$.
Note that if the function $\psi(x,y)$ is analytic in $U \times V$, then for any $k\ge 1$, $f(x_1,...,x_k,y_1,...,y_k) = det(\{\psi(x_i,y_j)\}_{i,j=1}^{k,k})$ is an analytic function in $(\otimes_{l=1}^{k} U \otimes_{l=1}^{k} V)$. If in addition, $\psi$ has a full rank $a.e.$ in $U\times V$, then, by the virtue of Proposition \[theorema:f\_nullset\_zeros\], we have immediately the following result. \[cor\_analytic\_full\_rank\_cond\][Corollary]{}
If $\psi: U\times V\to\mathbb{R}$ is analytic in $V$ and has full rank $a.e.$, then for any $k\ge 1$ the set $$D_k := \{(x_1,...x_k,y_1,...,y_k)\in \otimes_{l=1}^{k} U \otimes_{l=1}^{k} V \textrm{, s.t. } rank(\{\psi(x_i,y_j)\}_{i,j=1}^{k,k}) < k\}$$ has (product) measure zero, $\mu(D_k) = 0$. \[cor:full\_rank\_zero\_measure\]
Indeed, the set $D_k$ is closed and has no interior points, for otherwise $det(\{\psi(x_i,y_j)\}_{i,j=1}^{k})$ will vanish in an open subset and $\psi$ will not have full rank a.e.. Essentially, this corollary motivates the use of “a.e.” notion in the full rank definition.
Finally, we present a non-trivial example of full rank a.e. kernel - the standard distance on the unit sphere.
\[rank\_equivals\][Proposition]{}
\[theorem:full\_rank\_sphere\] The standard distance on the $n$-sphere, $\mathbb{S}^n$, $n\ge 2$, given by $$arccos(p.q), \\ p,q\in \mathbb{S}^n \subset \mathbb{R}^{n+1}$$ and its square have full rank a.e. on $\mathbb{S}^n$.
The above result has a probabilistic formulation as well: for every $k$, the square matrix with entries $arccos^2(p_i.q_j)$ of random points $p_i$ and $q_j$, $i,j=1,...,k$, on a unit sphere $\mathcal{S}^n$, $n\ge 2$, sampled independently by a continuous distribution on the sphere, is non-singular with probability one. This is evident by the completeness of the Lebesgue measure. More specifically, by continuous distribution we understand one that has a density, i.e. is absolute continuous with respect to the Lebesgue measure. Then, the probabilistic formulation above follows from Corollary \[cor:full\_rank\_zero\_measure\].
The full rank a.e. property of $arccos(x.y), \textrm{ } x,y\in \mathbb{S}^n$ can be inferred from another standard result in the linear operator theory. In the Hilbert space $L_2(\mathbb{S}^n)$ of square integrable functions on $\mathbb{S}^n$, the operator with kernel $arccos(x.y)$ is symmetric and thus $arccos(x.y) = \sum_{k\ge 1}\lambda_k\phi_k(x)\phi_k(y)$, where $\lambda_k$ and $\phi_k$ are the eigenvalues and eigenvectors of this operator (see the Theorems of Hilbert and Schmidt, [@riesz-nagy], Sec. 97). Since $\phi_k$’s form an orthonormal system in $L_2(\mathbb{S}^n)$, they are necessarily linear independent. Moreover, one can expect that they are locally linear independent, though one still has to show it. Our approach however, has an advantage in two aspects: (1) finding the Taylor functions of $arccos$ seems simpler than finding the spectral functions $\phi_k$, and (2), in general, we do not need the Hilbert space assumption.
Concluding Remarks
==================
We return to the question stated in the introduction: when can the solution of an integral equation (\[eq:ram\_fredholm\]) be approximated by discrete solutions of the linear system of equations (\[eq:ram\_fredholm\_discrete\])? The answer will be positive if, first, (\[eq:ram\_fredholm\]) has an unique solution $f$, and second, the series of solutions $\hat{f}_k$ of (\[eq:ram\_fredholm\_discrete\]) converge to $f$ in an appropriate sense, a.s. or in some $L^p$-norm. The full rank a.e. condition on the kernel $\psi$ guarantees the existence of $\hat{f}_k$, but unfortunately, is not enough for the invertibility of the operator $A_{\psi}$, for equation (\[eq:ram\_fredholm\]) may still have multiple solutions. This is illustrated by the next example. Let for $(x,y)\in(-\infty,\infty)\times(0,\infty)$ $$\psi(x,y) = 1 + \sum_{s=1}^{\infty} \frac{x^s}{s!} (\frac{y}{2s} - 1)y^{2s-1}.$$ This kernel $\psi$ has the form (\[eq:psi\_analytic\]) with Taylor functions $c_{2s-1}(x) = -\frac{x^s}{n!}$ and $c_{2s}(x) = \frac{x^s}{2sn!}$. The conditions in Proposition \[theorem:psisum\_fullrank\] for $\psi$ are satisfied and thus, $\psi$ has full rank a.e.. On the other hand, $c_s(x)$ are not linearly independent and one easily finds that $A_{\psi}$ is not invertible. Indeed, for $f(y) = e^{-y}$, we have $(A_{\psi}f)(x) = 0$, for all $x\in\mathbb{R}$, and therefore, 0 is an eigenvalue of the operator $A_{\psi}$.
The invertibility of $A_{\psi}$ however, can be guaranteed under some additional conditions. Let $\psi$ be analytic in $y\in V$ and the Taylor functions $c_s(x)$ in the analytical development (\[eq:psi\_analytic\]) of $\psi$ be linearly independent in $U$. Let $r>0$ be the convergence radius of the Taylor expansion of $\psi$ in $y$. For $r<\infty$, consider the vector space $\mathbb{P}(V)$ $$\mathbb{P}(V) := \{\textrm{all measurable } f:V\to\mathbb{R}, \textrm{ s.t. } \sup_{s\ge 1} \{ r^{-s} \int_V |f(y)y^s| dy \} < \infty \}$$ equipped with the $L^1$ norm and let $\mathbb{P}(V)=L^1(V)$, if $r=\infty$. Assume that $A_{\psi}$ is a bounded and closed operator from $\mathbb{P}(V)$ to $L^1(U)$. A sufficient condition for the latter is $\sup_{\rho\in(0,r)} \sum_{s=1}^{\infty} \rho^{s}\int_U |c_s(x)|dx < \infty$. Then, $A_{\psi}$ cannot have 0 as an eigenvalue because the equation $$(A_{\psi}f)(x) = \sum_{s=1}^{\infty} c_s(x) \int_{V} y^sf(y)dy = 0$$ has no non-zero solution for $f$; otherwise $c_s$ will not be independent. In this case, $A_{\psi}: \mathbb{P}(V) \to Im(A_{\psi}) \subset L^1(U)$ is a one-to-one map. Consequently, for any $g\in Im(A_{\psi})$, $A_{\psi}f = g$ has a unique solution $f$. If in addition $\psi$ has full rank a.e., we can construct a series of the discrete invertible operators $A_k\in\mathbb{R}^{k^2}$, $k=1,2,...$, that converge uniformly to $A_{\psi}$, $||A_{k} - A_{\psi}|| \to 0$ (recall the setup in the introduction). Let also $g_k\in\mathbb{R}^k$, such that $||g_k-g||\to 0$ and $f_k := A_{k}^{-1}g_k\in\mathbb{R}^k$. Now, for any convergent subsequence $f_{k'}$, $k'\subset k$, $||f_{k'}-f_0||\to 0$, by the uniform convergence of $A_k$, we have $||A_{k'}f_{k'} - A_{\psi}f_0|| \to 0$. On the other hand, $A_{k'}f_{k'} = g_{k'}$, and hence, $A_{\psi}f_0 = g$ and $f_0=f$. Therefore, $||f_{k'} - f||\to 0$ and we have the desired convergence to the unique solution of $A_{\psi}f = g$. Unfortunately, we cannot guarantee the existence of a convergent subsequence of $f_k$. In fact, if $A_{\psi}$ is compact, then there will be denumerable many eigenvalues concentrating at 0, $A_{\psi}^{-1}$ will be unbounded and the problem of approximating $f$ will be severely ill-posed - the ill-posedness of the Fredholm integral equations of first kind is a well known problem. Nevertheless, we find the principle possibility of inverting $A_{\psi}$ and all of its discrete approximations, the matrices $A_k$ obtained by random quadrature, to be sufficient motivation for this study and deserving some further investigations.
Note that if $\psi$ is analytic in $V$ and its Taylor functions $c_s(x)$ are locally linear independent in $U$, then $\psi$ is of full rank a.e. and any restriction $A_{\psi}|_{x\in W}$, for open $W\subset U$, is an injective operator - this is what we understand by local invertibility. With other words, any function $f\in\mathbb{P}(V)$ is possible to be recovered from $g=A_{\psi}f$, if its image $g$ is only known in some arbitrary open $W$. Even when is intractable with quadrature in practice, because of the ill-posedness, such recovery remains a principle possibility that eventually can be achieved, for example, with regularization methods targeting restricted classes of functions. As seen from the proof of Proposition \[theorem:full\_rank\_sphere\], the squared spherical distance is an analytical kernel with locally linear independent Taylor functions, and hence, is an example of full rank a.e. and locally invertible integral operator.
Bibliography
============
[10]{}
Riesz, F., and B. Sz.-Nagy, , .
Proofs
======
We show the claim by induction. Since $f_1(x)$ is not identically zero, there is $x_1\in U$ such that $f_1(x_1) \ne 0$. Let us assume that we have $k-1$ points $x_1$,...,$x_{k-1}$ in $U$, such that $det(\{f_i(x_j)\}_{i,j=1}^{k-1}) \ne 0$ and for $s=1,...,k$ define $A_s:=det(\{f_i(x_j)\}, i=1,...,k, i \ne s; j = 1,...,k-1)$. Since $A_{k-1} \ne 0$ and $f_i$ are linearly independent, we can choose $x_k\in U$ such that for $x=x_k$ $$det \left( \begin{array}{cccc}
f_1(x_1) & f_2(x_1) & ... & f_{k}(x_1) \\
... & ... & ... & ... \\
f_1(x_{k-1}) & f_2(x_{k-1}) & ... & f_{k}(x_{k-1}) \\
f_1(x) & f_2(x) & ... & f_{k}(x) \\
\end{array} \right) = \sum_{i=1}^{k} (-1)^{i+k} A_{i} f_i(x) \ne 0,$$ which proves the claim.
We shall show that $(3) \Rightarrow (2) \Rightarrow (1) \Rightarrow (3)$. Let condition $(3)$ hold and $\phi_1$, ..., $\phi_k$ be a basis of $span\{c_1, c_2,...\}$. Then, for any $s$, $c_s(x) = \sum_{i=1}^k \beta_s^i \phi_i(x)$ and $\psi(x,y) = \sum_{i=1}^k (\sum_s \beta_s^i (y-p)^s) \phi_i(x)$, provided that for any $i$ and $y\in V$, $\sum_s \beta_s^i (y-p)^s$ converges pointwise. Suppose the converse, that there exists $i_0$ and $y_0\in V $ such that $\sum_s \beta_s^{i_0} (y_0-p)^s$ does not converge. Since $\phi_i$’s are linearly independent, we can choose $x_j\in U$, $j=1,...,k$, such that $rank(A := \{\phi_i(x_j)\}_{j,i=1}^{k}) = k$. Let $||A^{-1}|| > 0$ denote the operator norm of matrix $A^{-1}$. Fix a number $\epsilon > 0$. Since all $\sum_s c_s(x_j) (y_0-p)^s$ converge absolutly, there is $N$ such that $$|\sum_{[s]=N}^M (\sum_{i=1}^k \beta_s^i \phi_i(x_j)) (y_0-p)^s| < \epsilon,$$ for any $j$ and $M\ge N$. On the other hand, by the divergence assumption, there is $M > N$, such that $$|\sum_{[s]=N}^M \beta_s^{i_0} (y_0-p)^s| \ge \sqrt{k} ||A^{-1}|| \epsilon.$$ Define the k-vectors $z=(z_1,...,z_k)^T$ and $w=(w_1, ..., w_k)^T$, where $$z_i := \sum_{[s]=N}^M \beta_s^{i} (y_0-p)^s
\textrm{ and }
w_j := \sum_{[s]=N}^M (\sum_{i=1}^k \beta_s^{i} \phi_i(x_j)) (y_0-p)^s.$$ The system $A z = w$ can be solved for $z$, $z = A^{-1}w$ and therefore $||z|| \le ||A^{-1}||\textrm{ }||w|| < \sqrt{k} ||A^{-1}|| \epsilon$, which contradicts $||z|| \ge |z_{i_0}| \ge \sqrt{k} ||A^{-1}|| \epsilon$. Hence, the initial assumption is false and all $$g_i(y) := \sum_{s=1}^{\infty} \beta_s^i (y-p)^s,$$ are well defined functions in $V$ and condition (2) holds.
That (1) follows from (2) is immediate. Apparently, the rank of $\psi$ can not be larger than $k$. Moreover, by the linear independence assumption and Lemma \[lemma:linindep\_functions\], there are $x_j\in U$ and $y_j\in V$, $j=1,...,k$, such that $rank(A := \{\phi_i(x_j)\}_{i,j=1}^k)=k$ and $rank(B = \{\xi_i(y_j)\}_{i,j=1}^k)=k$. Therefore, for $\Psi:=\{\psi(x_i,y_j)\}_{i,j=1}^{k,k}$ we have $\Psi = AB^T$, which implies $rank(\Psi) = k$.
Next we show $(1) \Rightarrow (3)$. Let $rank(\psi) = k$. For fixed $x_i \in U$, $i=1,...,k+1$, consider the set $\{\psi(x_1, y),...,\psi(x_{k+1}, y)\}$ of functions in $V$. Since for any $k+1$ points $y_j\in V$, no full rank matrix $\{\psi(x_i,y_j)\}_{i,j=1}^{k+1}$ exists, by Lemma \[lemma:linindep\_functions\], $\{\psi(x_i, y)\}_{i=1}^{k+1}$ are not linear independent. Then, there are functions $\alpha_i(\underline{x})$ of $\underline{x}=(x_1,...,x_{k+1})$, not all zero for any $\underline{x}$, such that $$\sum_{i=1}^{k+1} \alpha_i(\underline{x}) \psi(x_i, y) = 0, \forall y\in V.$$ By Taylor expanding $\psi$ in $y$ about a point $p\in V$ we obtain $$\sum_{s} \sum_{i=1}^{k+1} \alpha_i(\underline{x})c_s(x_i) (y-p)^s = 0, \forall y\in V,$$ implying $\sum_{i=1}^{k+1} \alpha_i(\underline{x}) c_s(x_i) = 0, \forall s$. The latter is true for any $x_i\in U$, $i=1,...,k+1$ and therefore, again by Lemma \[lemma:linindep\_functions\], no set of $k+1$ functions $c_s$ is linearly independent. On the other hand, there is a set of $k$ functions $c_s$ that is linearly independent, for otherwise, following $(3)\Rightarrow (2) \Rightarrow (1)$, we would have that $rank(\psi) < k$. Consequently, there exists a set of functions $\phi_1(x)$,...,$\phi_k(x)$ among $c_s$, such that for any $s$, $c_s(x) = \sum_{i=1}^k \beta_s^i \phi_i(x)$, i.e. $c_s\in span\{\phi_1,...,\phi_k\}$. Thus, the condition (3) is fulfilled.
We will show the claim by induction on the number of dimensions. Let us first convince ourselves that it is true for $n=1$ and $U=(a-\delta,a+\delta)$, $\delta>0$. If $\sum_{l=1}^{\infty} \alpha_l x^{s_l} = 0$, $\forall x\in(a-\delta,a+\delta)$, then the above power series has radius of convergence at least $\rho:=\max\{|a-\delta|, |a+\delta|\}>0$. Hence, $f := \sum_{l=1}^{\infty} \alpha_l x^{s_l}$, being an analytic function in $(-\rho, \rho)$, vanishes everywhere in $(-\rho, \rho)$, which leads to the only possible choice $\alpha_l = 0$, for all $l$.
Now, let $n>1$, $x=(x_{[1]},...,x_{[n]})$, and assume that all sets of power functions in $n-1$ dimensions are locally linear independent. If $\sum_l \alpha_l x^{s_l} = 0$ in $U\subset\mathbb{R}^n$, then the series will be absolute convergent in $U$ (we may eventually need to shrink $U$ a bit so that the closure $\bar{U}$ is entirely within the radius of convergence of the series). Consequently, we can regroup by $x_{[1]}$: $\sum_l \alpha_l x^{s_l} = \sum_{k=1}^{\infty} (\sum_{l: s_l^1=k} \alpha_l \underline{x}^{s_l^{n-1}} ) x_{[1]}^k$, where $\underline{x} := (x_{[2]},...,x_{[n]})$, $s_l=[s_l^1, s_l^{n-1}]$ and $s_l^{n-1}$ is a $(n-1)$-multi-index. Applying the argument from the first part of the proof, we have $\sum_{l: s_l^1=k} \alpha_l \underline{x}^{s_l^{n-1}} = 0$ in $U$ for every $k$. Finally, by the assumption, the only possible choice is $\alpha_l = 0$, for all $l$.
We can repeat the lines of the proof of Lemma \[lemma:linindep\_functions\] with the only change at each selection step: choosing $x_i \in U_i$ instead of $x_i \in U$.
Since $f_1(x)$ can not be identically zero in $U_1$, there is $x_1\in U_1$ such that $f_1(x_1) \ne 0$. Assuming that there are $x_i\in U_i$, $i=1,..,k-1$, such that $det(A_k := \{f_i(x_j)\}_{i,j=1}^{k-1}) \ne 0$, we can choose $x_k\in U_k$ such that for $x=x_k$ $$det \left( \begin{array}{cccc}
f_1(x_1) & f_2(x_1) & ... & f_{k}(x_1) \\
... & ... & ... & ... \\
f_1(x_{k-1}) & f_2(x_{k-1}) & ... & f_{k}(x_{k-1}) \\
f_1(x) & f_2(x) & ... & f_{k}(x) \\
\end{array} \right) = \sum_{i=1}^{k} (-1)^{i+k} A_i f_i(x) \ne 0.$$ Otherwise, if such choice is impossible, $\sum_{i=1}^{k} A_i f_i(x) = 0$, $\forall x\in U_k$ and $f_i$ would not be locally linear independent.
The convergence of the right-hand series in (\[eq:psisum\]) is assumed to be in absolute sense. Thus, $\sum_{s=1}^{\infty} |\phi_s(x)\xi_s(y)| < \infty$, for all $x\in U$ and $y\in V$.
Suppose that for a number $k$ there exist open sets $U_i\subset U$ and $V_j\subset V$, $i,j=1,...,k$, such that for all $x_i\in U_i$ and $y_j\in V_j$, $rank(\{\psi(x_i,y_j)\}_{i,j=1}^{k,k}) < k$. If we fix $x_i\in U_i$, $i=1,...,k$, then, by Lemma \[lemma:lli\_cond\], $\{\psi(x_i, y)\}_{i=1}^{k}$ are not locally linear independent functions of y in $V$. Consequently, for the fixed $\underline{x}=(x_1,...,x_{k})$, there exists an open set $W(\underline{x})\subset V$, where $\{\psi(x_i, y)|_{W(\underline{x})}\}_{i=1}^{k}$ are linearly dependent, or equivalently, there are $\alpha_i(\underline{x})$, not all zero, such that $$\sum_{i=1}^{k} \alpha_i(\underline{x}) \psi(x_i, y) = 0, \forall y\in W(\underline{x}).$$ Taking into account the given representation (\[eq:psisum\]) of $\psi$, we can write $$\sum_{s=1}^{\infty} \sum_{i=1}^{k} \alpha_i(\underline{x}) \phi_s(x_i) \xi_s(y) = 0, \forall y\in W(\underline{x}).$$ The local linear independence of $\xi_s$ then guarantees that $
\sum_{i=1}^{k} \alpha_i(\underline{x}) \phi_s(x_i) = 0, \forall s.
$ Therefore, for any choice of indices $s_1,...,s_k$, $rank(\{\phi_{s_j}(x_i)\}_{i,j=1}^{k}) < k$. Since the latter is true for any $x_i\in U_i$, $i=1,...,k$, by Lemma \[lemma:lli\_cond\], no $k$ functions $\phi_s$ would be locally linear independent in $U$, a contradiction with the proposition assumption. Therefore, $\psi$ has full rank a.e. in $U\times V$.
By $\psi$ being analytic in $U\times V$ we mean that for every $p\in V$, $\psi(x,y) = \sum_s c_s(x) (y-p)^s$, for analytic in $U$ functions $c_s(x)$. The sufficiency then follows from Proposition \[theorem:psisum\_fullrank\], which can be applied because $(y-p)^s$ are locally linear independent in $V$.
Next, we shall check the necessity. Let $\psi$ have full rank $a.e.$ in $U\times V$ and there is $p\in V$ and $k$ such that there is no a collection of $k$ Taylor functions $c_s$ that is locally linear independent. But the local linear independence of the analytic functions $c_s$ is equivalent to their simple linear independence and thus, there is not set of $k$ functions $c_s$ that is linear independent in $U$. Then, $span\{c_1, c_2,...\}$ has a finite basis of size at most $k$ in $U$ and, by Proposition \[theorem:rank\_equivals\], $rank(\psi) \le k$. This contradiction with the full rank assumption on $\psi$ proves the necessity.
For what follows, we need the following fact. \[lemma\_linindep\][Lemma]{}
\[lemma:union\_open\_sets\] Any collection $\mathcal{O}$ of (nonempty) open and disjoint subsets of $\mathbb{R}^n$ is countable.
Let $O\in\mathcal{O}$. Then there is at least one vector $q\in O$ with all rational coordinates. By applying the axiom of choice we define a map $
\theta: O \mapsto (k_1,l_1,k_2,l_2,...,k_n,l_n),
$ where $k_i$, $l_i$, $i=1,...,n$, are integers such that $q=(2^{k_1}l_1,...,2^{k_n}l_n) \in O$. $\mathcal{O}$ is countable since $\theta$ is injective map from $\mathcal{O}$ to $\mathbb{Z}^{2n}$.
Define $V_1 := \{x\in U| \frac{\partial f}{\partial x}|_{x} = 0\}$. When $n>1$, $\frac{\partial f}{\partial x}$ is a gradient vector and $\frac{\partial f}{\partial x}|_{x} = 0$ means that all partial derivatives at point $x$ vanish. Both $V_0$ and $V_1$ are closed in $U$. We shall show that $V_0\backslash V_1$ has measure zero.
By the implicit function theorem, for any point $x\in V_0\backslash V_1$ there is an open ball $B_x=B_x(r_x)$ of radius $r_x>0$ and a hypersurface $S_x$ of dimension $n-1$, the graph of a function of $n-1$ variables, such that $x\in S_x = B_x \cap V_0\backslash V_1$. We have $\mu(S_x) = 0$. Note that any two $S_x$ and $S_y$ that intersect and are images of open subsets of a common coordinate plane, say $\{x_{[i]}=0\}$, can be combined to the image of a continuous function in $\{x_{[i]}=0\}$. We have therefore the representation $V_0\backslash V_1 = \cup_{i=1}^n \cup_{\alpha\in A_i} S_{\alpha}^i$, where all $S_{\alpha}^i$ are disjoined images of continuous functions in $\{x_{[i]}=0\}$ and as such $\mu(S_{\alpha}^i) = 0$, $\forall i$ and $\forall \alpha \in A_i$.
Let $U_{\alpha}^i = \cup_{x\in S_{\alpha}^i} B_x(r_x/2)$. Then it must be that $U_{\alpha}^i \cap U_{\beta}^i = \emptyset$, $\forall \alpha\ne\beta\in A_i$. For otherwise, there would be $x\in S_{\alpha}^i$ and $y\in S_{\beta}^i$ such that $B_x(r_x/2)\cap B_y(r_y/2) \ne \emptyset$ and consequently, either $x\in B_y(r_y)$ or $y\in B_x(r_x)$. If for example $y\in B_x(r_x)$, then $y\in S_x$ and $y \in S_x \cap S_y$, and therefore $S_{\alpha}^i \cap S_{\beta}^i \ne \emptyset$, which would be a contradiction. Hence, by the virtue of Lemma \[lemma:union\_open\_sets\], for every $i$, the disjoint open sets $\{U_{\alpha}^i\}_{\alpha}$ are at most countably many, that is, the index sets $A_i$ are countable. Therefore, $\mu(V_0\backslash V_1) = 0$ and $\mu(V_0) = \mu(V_1\cap V_0)$.
We can repeat the same analysis for higher derivatives of order $l > 1$ and apply induction on $l$. Define $$V_l := \{x\in U \textrm{ s.t. } \frac{\partial^s f}{\partial x^s}|_{x} = 0 \textrm{ for all }s=(s_1,...,s_n) \textrm{ for which } [s] = l\}.$$ We claim that $\mu(V_{l-1}\backslash V_l) = 0$ for all $l>0$. We have already showed the claim for $l=1$.
For any $s=(s_1,...,s_n)\textrm{ for which }[s] = l-1$, define $$V_{l-1}^s := \{x\in U \textrm{ s.t. } \frac{\partial^s f}{\partial x^s}|_{x} = 0\}, ~
V_l^s := \{x\in U \textrm{ s.t. } \frac{\partial^{s+1} f}{\partial x^s\partial x^j}|_{x} = 0,\textrm{ for all }j=1,...,n\}$$ and observe that $V_{l-1} = \cap_{s:[s]=l-1} V_{l-1}^s$ and $V_{l} = \cap_{s:[s]=l-1} V_{l}^s$. The argument from the first part of the proof for showing $\nu_n(V_0) = \nu_n(V_1\cap V_0)$ is applicable to all pairs $(V_{l-1}^s, V_l^s)$ and consequently $\mu(V_{l-1}^s) = \mu(V_l^s\cap V_{l-1}^s)$, $\forall s,~ [s] = l-1$. Next, we use the fact that for any four measurable sets $A$, $B$, $C$ and $D$, satisfying $B\subset A$, $\mu(B)=\mu(A)$, $D\subset C$ and $\mu(D)=\mu(C)$, we have $\mu(B\cap D)=\mu(A\cap C)$, to conclude that $\mu(\cap_{[s]=l-1} V_{l-1}^s) = \mu(\cap_{[s]=l-1} (V_{l-1}^s \cap V_l^s))$. Hence we have $\mu(V_{l-1}) = \mu(V_{l-1} \cap V_l)$ and $\mu(V_{l-1}\backslash V_l) = 0$. Now, assuming that $\mu(V_0) = \mu(\cap_{m=0}^{l-1} V_m)$, from $$\mu(\cap_{m=0}^{l-1} V_m) = \mu((\cap_{m=0}^{l-1} V_m) \backslash V_l) + \mu(\cap_{m=0}^{l} V_m) = \mu(\cap_{m=0}^{l} V_m)$$ we obtain $\mu(V_0) = \mu(\cap_{m=0}^{l} V_m)$ and by the induction principle the latter is true for every $l$.
Note that $\mu(\cap_{m=0}^{l} V_m) \searrow \mu(\cap_{m=0}^{\infty} V_m)$, as $l\to\infty$. Finally, we realize that the set $\cap_{m=0}^{\infty} V_m$ should be empty, for otherwise, with all vanishing derivatives at one point, the analytic function $f$ would vanish in an open subset of $U$, a contradiction. Thus we conclude that $\mu(V_0) = \mu(\cap_{m=0}^{\infty} V_m) = 0$.
Consider the following parametrization of the north hemisphere about the north pole: $$\phi: x = (x_1,x_2,...,x_n) \in \mathbb{O}^n \to p=(x_1, x_2, ..., x_n, (1-\sum_{j=1}^n x_j^2)^{1/2}) \in \mathbb{R}^{n+1},$$ where $\mathbb{O}^n = \{x\in[0,1]^n \textrm{, } \sum_{i=1}^n x_i^2 \le 1$ is the closed $n$-ball. Then the inner product of $p=\phi(x)$ and $q=\phi(y)$ is $$p.q = \phi(x).\phi(y) = \sum_{i=1}^n x_iy_i + (1-\sum_{j=1}^n x_j^2)^{1/2}(1-\sum_{j=1}^n y_j^2)^{1/2}.$$ The proof of the desired claim is based on application of Proposition \[theorem:psisum\_fullrank\]. For the purpose we need to derive the Taylor functions $f_s(x)$ in the expansion of $arccos(p.q)$ in $y$ at $0\in\mathbb{R}^n$. Specifically, we need to show that for any $k$, there are $k$ locally linear independent $f_s(x)$ in $\mathbb{O}^n$. We will first show this property for the Taylor functions of $$\psi(x,y) = arccos(\phi(x).\phi(y)) \textrm{, } x,y\in \mathbb{O}^n,$$ and then for the square spherical distance $\psi^2$. Note that $\psi$ is analytic in $\mathbb{O}^n \times \mathbb{O}^n$.
The first simplification we are going to make is to fix $y_2 =...=y_n=0$ and consider $\psi(x,y)$ as a function of $y_1\in[0,1]$. Then, it suffices to show the local linear independence condition only for the partial derivatives $\frac{\partial^s \psi}{\partial y_1^s}$.
For brevity, denote $\underline{x} = (\sum_{i=1}^n x_i^2)^{1/2}$ and $\underline{y} = (\sum_{i=1}^n y_i^2)^{1/2}$. The form of the first few derivatives of $z=\phi(x).\phi(y)$ as a function of $y_1$ $$\frac{\partial z}{\partial y_1} = x_1 - \frac{(1-\underline{x}^2)^{1/2}}{(1-\underline{y}^2)^{1/2}} y_1 \textrm{, }
\frac{\partial^2 z}{\partial y_1^2} = -\frac{(1-\underline{x}^2)^{1/2}}{(1-\underline{y}^2)^{1/2}} - \frac{(1-\underline{x}^2)^{1/2}}{(1-\underline{y}^2)^{3/2}} y_1^2 \textrm{, }$$ can be generalized (the proof is by induction) to the following equations $$\label{eq:z_partials}
\frac{\partial z}{\partial y_1}|_{y=0} = x_1 \textrm{, }
\frac{\partial^{2k+1} z}{\partial y_1^{2k+1}}|_{y=0} = 0 \textrm{, }
\frac{\partial^{2k} z}{\partial y_1^{2k}}|_{y=0} = -a_k (1-\underline{x}^2)^{1/2} \textrm{, } k\ge 1,$$ for some integers $a_k > 0$.
On the other hand, the general form of the derivatives of $\psi(z) = arccos(z)$ $$\frac{\partial^{2s} \psi}{\partial z^{2s}} =
- \sum_{l=1}^{s} b_{2s,l} \frac{z^{2l-1}}{(1-z^2)^{(2s+2l-1)/2}} \textrm{, }$$ $$\frac{\partial^{2s+1} \psi}{\partial z^{2s+1}} =
- \sum_{l=0}^{s} b_{2s+1,l} \frac{z^{2l}}{(1-z^2)^{(2s+2l+1)/2}},$$ calculated at $z=(1-\underline{x}^2)^{1/2}$ (corresponding to $y=0$), can be summarized to $$\label{eq:psi_partials}
\frac{\partial^s \psi}{\partial z^s}|_{z=(1-\underline{x}^2)^{1/2}} = - \frac{1}{\underline{x}^s}
\sum_{l=0}^{s-1} b_{s,l} \Big( \frac{(1-\underline{x}^2)^{1/2}}{\underline{x}} \Big)^l \textrm{, } s\ge 1,$$ for some integers numbers $b_{s,l} \ge 0$ with $b_{s,s-1} > 0$. Formally, (\[eq:psi\_partials\]) can be verified by induction.
Next, we combine equations (\[eq:z\_partials\]) and (\[eq:psi\_partials\]) to express the partial derivatives of $\psi$ in $y_1$ $$\label{eq:psi_partials_y1}
\frac{\partial^s \psi}{\partial y_1^s} = \sum_{k=1}^s \frac{\partial^{k} \psi}{\partial z^{k}}
\sum_{l_1+...+l_k = s} d_{l_1l_2...l_k}
\frac{\partial^{l_1} z}{\partial y_1^{l_1}}...\frac{\partial^{l_k} z}{\partial y_1^{l_k}},$$ where $d_{l_1l_2...l_k}$ are some integers and the second sum is over all $l_1\le...\le l_k$. For example $$\frac{\partial \psi}{\partial y_1}|_{y=0} = \frac{\partial \psi}{\partial z}\frac{\partial z}{\partial y_1} = -\frac{x_1}{\underline{x}} \textrm{, }$$ $$\frac{\partial^2 \psi}{\partial y_1^2}|_{y=0} = \frac{\partial^2 \psi}{\partial z^2} \Big(\frac{\partial z}{\partial y_1}\Big)^2 +
\frac{\partial \psi}{\partial z}\frac{\partial^2 z}{\partial y_1^2}
= -\frac{(1-\underline{x}^2)^{1/2}}{\underline{x}} ((\frac{x_1}{\underline{x}})^2 - 1) \textrm{, etc.}$$ The complex form of these functions, which mix $x_1$ with $\underline{x}$, renders the verification of their local linear independence untractable. Fortunately, at this point we can do further simplifications by taking into account that $n>1$. If we fix $x_1=0$ and show that for any $k$, there are $k$ local linear independent functions $\frac{\partial^s \psi}{\partial y_1^s}|_{x_1=0, y=0} (x_2,...,x_n)$, our claim will be proven. Note that this step can not be taken if $n=1$. Indeed, we have already verified that the claim is not true for the 1-dimensional circle (recall the example at the end of Section \[sec:finite\_rank\]).
First, observe that $\frac{\partial^{2s+1} \psi}{\partial y_1^{2s+1}}|_{x_1=0, y=0} (x_2,...,x_n) = 0$, because $\frac{\partial^{2k+1} z}{\partial y_1^{2k+1}}|_{x_1=0,y=0} = 0$, for all $k\ge 0$, and all terms in Eq. (\[eq:psi\_partials\_y1\]) must have at least one odd $l_j$. Second, plugging (\[eq:z\_partials\]) and (\[eq:psi\_partials\]) in (\[eq:psi\_partials\_y1\]) and denoting $\tilde{d}_{l_1l_2...l_k} = a_{l_1} a_{l_2} ... a_{l_k} d_{(2l_1)(2l_2)...(2l_k)} $, we obtain $$\frac{\partial^{2s} \psi}{\partial y_1^{2s}}|_{x_1=0, y=0} (x_2,...,x_n) =$$ $$\sum_{k=1}^{2s} \Big[ \sum_{l=0}^{k-1} b_{k,l} \Big( \frac{(1-\underline{x}^2)^{1/2}}{\underline{x}} \Big)^l
\sum_{l_1+...+l_k = s} \tilde{d}_{l_1l_2...l_k}
\frac{1}{\underline{x}^k}
(1-\underline{x}^2)^{k/2} \Big] =
P_{s}\Big( \frac{(1-\underline{x}^2)^{1/2}}{\underline{x}} \Big),$$ where $P_{s}$ is a polynomial with integer coefficients of degree $4s-1$. Hence, by introducing the functions $h(x_2,...,x_n) = \frac{(1-\underline{x}^2)^{1/2}}{\underline{x}}$, we conclude that $$\label{eq:psi_partials_x1y1}
\frac{\partial^{2s} \psi}{\partial y_1^{2s}}|_{x_1=0, y=0} (x_2,...,x_n) \in
span\{h,...,h^{4s-1}\} \setminus span\{h,...,h^{4s-2}\} \textrm{, } s > 1.$$ Finally, by Lemmas \[lemma:lli\_bijection\] and \[lemma:lli\_lin\_comb\], we assert that indeed, for every finite set of distinct even numbers $s$, the corresponding partial derivatives (\[eq:psi\_partials\_x1y1\]) are locally linear independent. The conditions of Proposition \[theorem:psisum\_fullrank\] therefore hold and the spherical distance has full rank a.e. (in the north hemisphere).
Now we consider the square spherical distance. From the equality $$\frac{\partial^{s} \psi^2}{\partial y_1^{s}} = 2 \psi \frac{\partial^{s} \psi}{\partial y_1^{s}} +
\sum_{k=1}^{s-1} e_{k}^s \frac{\partial^{k} \psi}{\partial y_1^{k}} \frac{\partial^{s-k} \psi}{\partial y_1^{s-k}},$$ for some integers $e_k^s>0$, we conclude that at the point $(x_1=0, y=0)$ $$\frac{\partial^{2s+1} \psi}{\partial y_1^{2s+1}} (x_2,...,x_n) = 0 \textrm{, }$$ $$\label{eq:psi2_partials_even}
\frac{\partial^{2s} \psi}{\partial y_1^{2s}} (x_2,...,x_n) =
\psi((1-\underline{x}^2)^{1/2}) P_{s}\Big( \frac{(1-\underline{x}^2)^{1/2}}{\underline{x}} \Big) + Q_{s}\Big( \frac{(1-\underline{x}^2)^{1/2}}{\underline{x}} \Big),$$ where $Q_{s}=\sum_{k=1}^{s-1} e_k^s P_k P_{s-k}$ is a polynomial with integer coefficients of degree $4s-2$.
Let us assume that for some $k$, the first $k$ even derivatives (\[eq:psi2\_partials\_even\]) are not locally linear independent. Let $t=\frac{(1-\underline{x}^2)^{1/2}}{\underline{x}}$. Then, there are some $c_s$ with $c_k\ne 0$, such that $$\sum_{s=1}^k c_s \Big( P_s(t) arccos(\frac{t}{(1+t^2)^{1/2}}) + Q_{s}(t) \Big) = 0 \textrm{, } t\in W,$$ in an open (non-empty) $W\subset[0,1]$. This is equivalent to $$arccos(\frac{t}{(1+t^2)^{1/2}}) = - \frac{Q(t)}{P(t)} \textrm{, } t\in W,$$ where $P=\sum_{s=1}^k c_s P_s$ and $Q=\sum_{s=1}^k c_s Q_s$ are polynomial of degrees $4k-1$ and $4k-2$, respectively. After taking the derivatives on both sides of the above equation and applying some algebra we obtain the equality $(P(t))^2=(1+t^2)(P(t)Q'(t)-Q(t)P'(t))$. The latter however is impossible because of the degree disparity, $8k-2$ for $P^2$ and $8k-3$ for the left-hand side polynomial (we use that $degree(P(t)Q'(t)-Q(t)P'(t)) \le degree(P)+degree(Q)-2$). This proves the local linear independence of the first $k$ even derivatives (\[eq:psi2\_partials\_even\]). Due to Proposition \[theorem:psisum\_fullrank\], the square spherical distance has full rank a.e. in $\mathbb{S}^n$.
| {
"pile_set_name": "ArXiv"
} |
Q:
Inspect live objects/stack in node.js
In node.js, is there something similar to inspect.stack() and inspect.currentFrame() from Python?
Like, capturing code context/frames/inspecting live object.
A:
You can use new Error().stack to inspect the stack:
console.log(new Error().stack);
prints:
Error
at repl:1:13
at sigintHandlersWrap (vm.js:22:35)
at sigintHandlersWrap (vm.js:96:12)
at ContextifyScript.Script.runInThisContext (vm.js:21:12)
at REPLServer.defaultEval (repl.js:313:29)
at bound (domain.js:280:14)
at REPLServer.runBound [as eval] (domain.js:293:12)
at REPLServer.<anonymous> (repl.js:513:10)
at emitOne (events.js:101:20)
at REPLServer.emit (events.js:188:7)
There is node debugger that you can run with:
node debug script.js
See:
https://nodejs.org/api/debugger.html
And you can also use Chrome developer tools for live inspection of everything with:
node --inspect script.js
See:
Debugging Node.js in Chrome DevTools by Matt DesLauriers
Debugging Node.js with Chrome DevTools
by Paul Irish
| {
"pile_set_name": "StackExchange"
} |
1. Introduction {#sec1-ijms-19-00107}
===============
Renal Cell Carcinoma (RCC) is a disease found in the lining of the kidney tubules \[[@B1-ijms-19-00107]\]. It is the most prominent kidney cancer in adults, accounts for roughly 85% of all malignant kidney cancer, and can result in a number of symptoms, including weight loss, fever, hypertension, hypercalcemia, night sweats, and malaise \[[@B2-ijms-19-00107],[@B3-ijms-19-00107]\]. Although RCC is quite rare, it is still among the top ten cancers, often affecting people over 45 years old \[[@B4-ijms-19-00107]\]. More specifically, this cancer affects men more than women, with the average age of diagnosis being around 60 years \[[@B5-ijms-19-00107],[@B6-ijms-19-00107]\]. Its incidence rates have been gradually increasing by 2--4% every year over the past few decades \[[@B7-ijms-19-00107]\]. The most current cancer data estimate that nearly 64,000 new cases of renal cancer will be diagnosed in the United States, while about 14,400 people will die from complications associated with renal cancer in 2017 \[[@B8-ijms-19-00107]\]. The five-year survival rate for the patients with this disease is approximately 85% if detected and treated early, while it is only 10% when it is detected at later stages \[[@B9-ijms-19-00107]\]. An increased understanding of molecular biology and genomics of RCC have identified several signaling pathways involved in the progress of this disease \[[@B10-ijms-19-00107]\]. Significant advances in the treatment of RCC have been derived from agents approved by the FDA that target several pathways. These include inhibitors of mammalian target of rapamycin (mTOR) (e.g., everolimus and temsirolimus) and the tyrosine kinase inhibitors (TKIs) (e.g., sorafenib, sunitinib, pazopanib and axitinib). Everolimus and temsirolimus block the activation of AKT, hypoxia inducible factor α (HIFα) and p70S6 kinase by targeting mTOR complex 1 and 2 (mTORC1 and mTORC2), and in turn inhibit cell growth and survival. Sorafenib, sunitinib, pazopanib and axitinib target multiple pro-angiogenic growth factors such as vascular endothelial growth factor (VEGF) and platelet derived growth factor (PDGF), and their receptors VEGFR and PDGFR. These agents were approved by the FDA because they demonstrate clinical activity and increased survival in patients with metastatic disease \[[@B11-ijms-19-00107],[@B12-ijms-19-00107],[@B13-ijms-19-00107]\]. These drugs showed clinical benefit without adversely impacting overall quality of life and had a positive impact on specific symptoms, e.g., cough, fevers, shortness of breath, ability to enjoy life, and worry that the condition will get worse in patients with advanced RCC. However, patients eventually relapse and develop resistance to these drugs \[[@B12-ijms-19-00107],[@B14-ijms-19-00107],[@B15-ijms-19-00107]\]. To reduce the death associated with RCC, it would be important to improve methods for detection, prevention, and treatment. In this review, we will evaluate natural products traditionally studied in chemoprevention, i.e., the use of chemicals, bioactive plant compounds or dietary components to block, inhibit or reverse the development of cancer in normal or preneoplastic tissue, as therapies for the treatment of RCC.
Previous studies have found that many compounds originated from natural products could be used as both preventive and therapeutic agents. In combination with chemotherapy or alone, they have been shown to enhance the efficacy and tolerance of the chemotherapeutic agents in various cancers \[[@B16-ijms-19-00107],[@B17-ijms-19-00107],[@B18-ijms-19-00107],[@B19-ijms-19-00107],[@B20-ijms-19-00107],[@B21-ijms-19-00107],[@B22-ijms-19-00107]\]. This review article will elaborate on our current understanding of the effectiveness of naturally occurring anti-cancer agents in the treatment of RCC. We summarize studies on the effects of Epigallocatechin-3-gallate (EGCG), Englerin A, Quercetin, coumarins, curcumin, and other natural products against RCC. The structures of these natural products are shown in [Figure 1](#ijms-19-00107-f001){ref-type="fig"}.
2. Natural Products and Renal Cell Carcinoma {#sec2-ijms-19-00107}
============================================
Natural products have been used for thousands of years for their medicinal properties \[[@B23-ijms-19-00107]\], yet researchers have only recently started investigating the role they play at a molecular level. These natural products are significant because their use in ancient history can be validated and applied to modern therapy with evidenced conclusions. Indeed, nearly every major ancient civilization has used some form of natural products as traditional medicines, remedies, potions and oils with many of these bioactive natural products still being unidentified \[[@B24-ijms-19-00107]\]. The earliest records of the use of natural products for medicinal purposes can be traced to 2600 B.C., when documented oils from *Cupressus sempervirens* (cypress) and *Commiphora* species (myrrh) were used to treat illnesses \[[@B25-ijms-19-00107]\].
Recent medical history has placed natural products on the back-burner, nearly always preferring human-made drugs derived from the study of molecular biology and combinatorial chemistry \[[@B26-ijms-19-00107]\]. However, these drugs can often be extremely expensive \[[@B27-ijms-19-00107]\]. Furthermore, they usually have intolerable side effects that make them prohibitive to treat human diseases, including having the opposite of the intended effect \[[@B23-ijms-19-00107]\]. In general, herbal or natural treatments have few to no side effects while producing very favorable results in tumor treatment \[[@B23-ijms-19-00107]\]. However, the therapeutic activities of the compounds within these products have not been studied extensively in RCC. It is thus prudent to investigate the pathways affected by compounds in these natural products.
2.1. Epigallocatechin-3-Gallate {#sec2dot1-ijms-19-00107}
-------------------------------
A significant distinction between normal healthy cells and tumor cells is that the latter often circumvent the apoptosis process, allowing uncontrolled proliferation. Thus, inducing apoptosis would be an effective means of treatment. In RCC, the expression of tissue factor pathway inhibitor-2 (TFPI-2) is inversely related to the aggressiveness of these cells \[[@B28-ijms-19-00107]\]. Therefore, higher concentrations of TFPI-2 would decrease the malignancy of these cells and most likely induce apoptosis. Epigallocatechin-3-gallate (EGCG), an active and major constituent of green tea (*Camellia sinensis*), displays anti-tumor properties in several cancers, including RCC \[[@B29-ijms-19-00107],[@B30-ijms-19-00107],[@B31-ijms-19-00107],[@B32-ijms-19-00107],[@B33-ijms-19-00107],[@B34-ijms-19-00107],[@B35-ijms-19-00107]\] and inhibits tumor growth and invasiveness in RCC by upregulating expression of TFPI-2 through inhibition of DNA methyltransferase (DNMT) activity \[[@B28-ijms-19-00107]\].
A recent paper indicates that EGCG may play a preventive role in the development of RCC \[[@B36-ijms-19-00107]\]. This study evaluated the effect of tumor necrosis factor-related apoptosis-inducing ligand (TRAIL), EGCG, and a combination of both on a TRAIL-resistant RCC cell line, 786-O. The data demonstrate that EGCG alone provided a significant reduction in cell viability, but co-treatment with TRAIL provided a marked reduction in cell viability greater than that of EGCG or TRAIL alone by downregulating c-FLIP, MCl-1, and BCl-2.
Another study reported that EGCG induces apoptosis, inhibiting the proliferation and migratory potential of RCC cell lines by downregulating the expression of matrix metalloproteinase-2 (MMP-2) and matrix metalloproteinase-9 (MMP-9) \[[@B37-ijms-19-00107]\]. However, this study did not determine how the expression levels and activity of these metalloproteinases are regulated by EGCG.
It is clear through multiple, independent experiments that EGCG has proven an extremely viable treatment in vitro. A few methods to utilize EGCG arise from the data previously presented. One example was an extensive epidemiological study which reported an inverse correlation between green tea consumption and overall RCC tumor burden \[[@B38-ijms-19-00107]\]. Another approach might use EGCG in supplement with TKI or mTOR inhibitors to see if the combination particularly sensitizes the tumor cells as compared to TKI or mTOR inhibitor alone \[[@B39-ijms-19-00107],[@B40-ijms-19-00107],[@B41-ijms-19-00107],[@B42-ijms-19-00107]\]. A study by Sato et al., suggests that the restoration of connexin 32 (*Cx32*) gene, a tumor suppressor, by EGCG pretreatment enhanced the chemical sensitivity of vinblastine via the inactivation of Src and the activation of the c-Jun NH2-terminal kinase (JNK) in RCC cells \[[@B43-ijms-19-00107]\]. Overall, these studies suggest that EGCG could be used as both a preventative and therapeutic approach for renal cell carcinoma.
2.2. Englerin A {#sec2dot2-ijms-19-00107}
---------------
Englerin A is a natural product derived from the root and stem bark of *Phyllanthus engleri*, an indigenous African plant. It was identified to preferentially inhibit the cell growth and viability of RCC through a drug screen of the NCI 60 (National Cancer Institute 60) cell line panel \[[@B44-ijms-19-00107]\]. This natural product is a guaiane sesquiterpene with a tricyclic structure that has a standardized procedure for synthesis in a laboratory \[[@B45-ijms-19-00107]\].
There are multiple proposed mechanisms for the RCC growth inhibition by Englerin A which have been summarized in detail in a comprehensive review by Beutler and coworkers \[[@B46-ijms-19-00107]\]. One such proposal comes from Ramos's group, which suggests that growth of RCC cell lines can be inhibited by Englerin A through necrotic cell death rather than apoptosis \[[@B47-ijms-19-00107]\]. The authors report that apoptotic bodies, typical in apoptotic cell death, were not present after Englerin A treatment. Calcium ions have been associated with necrotic cell death \[[@B48-ijms-19-00107]\]. Ramos's group tested calcium ion content in various renal cell carcinoma cell lines and found that SF-295 cells showed little relative change in ion content while A-498 cells showed a four-fold increase in concentration \[[@B47-ijms-19-00107]\]. Although this study indicates that apoptotic bodies were not present, Williams et al., suggest otherwise \[[@B49-ijms-19-00107]\]. Not only necrosis was observed, but apoptosis and autophagy were also noticed after 24 h of treatment in A498 cells \[[@B49-ijms-19-00107]\]. In addition, their results also suggest that Englerin A-induced inhibition of RCC growth was due to cell cycle arrest by blocking G2/M transition and suppression of AKT and ERK activity.
Englerin A triggers the activity of the enzyme protein kinase C θ (PKCθ), which has been shown in vitro to phosphorylate and activate heat shock factor 1 (HSF1), resulting in insulin resistance and glucose deprivation of 786-O cells \[[@B50-ijms-19-00107]\]. However, PKCθ is not expressed in A498 cells which are the most sensitive to Englerin A \[[@B51-ijms-19-00107]\]. This finding led researchers to investigate other possible targets. Reports from two independent groups suggested that the transient receptor potential cation channel, subfamily C, member 4/5 (TRPC4/5) are characteristic to Englerin A sensitivity, and thus indicate these may be targets of Englerin A \[[@B51-ijms-19-00107],[@B52-ijms-19-00107]\]. The authors claim that Englerin A induces cell death by the elevated Ca^2+^ influx and membrane depolarization, which occurred much more frequently in cells that expressed high levels of TRPC4 on their surface \[[@B52-ijms-19-00107]\]. However, a recent finding contradicts these results and suggests that Enlerin A cytotoxicity is mediated by the influx of Na^+^ through TRPC4/TRPC1 channels \[[@B53-ijms-19-00107]\].
A hallmark of metastasis in malignancies including renal cancer is the epithelial-mesenchymal transition (EMT), followed by invasion \[[@B54-ijms-19-00107],[@B55-ijms-19-00107]\]. In our group, we sought to examine the effects of Englerin A in preventing the migration and invasion of RCC cell lines as well as to investigate whether Englerin A may inhibit the molecular changes associated with EMT induced by transforming growth factor-β1 (TGF-β1) \[[@B56-ijms-19-00107]\]. We also aimed to see whether Englerin A suppresses cancer stem cell markers and spheroid formation. Our results show that Englerin A inhibits molecular changes associated with TGF-β1-induced EMT by upregulating the epithelial markers and downregulating the mesenchymal/stem cell markers \[[@B56-ijms-19-00107]\]. We also found that Englerin A inhibits TGF-β1-induced angiogenesis. This study indicated that Englerin A might serve as a potential candidate for the treatment of renal cancer metastasis.
In a recent study, Batova and colleagues proposed a different mechanism for RCC cell death by Englerin A \[[@B57-ijms-19-00107]\]. They demonstrated that Englerin A alters lipid metabolism, induces (endoplasmic reticulum) ER stress, and in turn generates an excess of ceramides, which are lethal to RCC cells. Furthermore, Englerin A induces an acute inflammatory response.
Little work has been conducted regarding in vivo models, and those that have been conducted on mouse models indicate that the levels of Englerin A required for anti-tumor activity may be lethal \[[@B52-ijms-19-00107],[@B58-ijms-19-00107]\]. If the results of this in vivo model accurately reflect the natural product's effects, this would be a major impediment for its use in cancer treatment. However, the compound itself is certainly worth investigating. It would be extremely effective in treatment if a non-lethal derivative of Englerin A was found and implemented. Further, there is still an ongoing debate as to which mechanisms Englerin A uses to elicit anti-tumor effects. If it is found that Englerin A uses many pathways for tumor suppression, its use could be used extended to treat other tumors that use these pathways.
2.3. Quercetin {#sec2dot3-ijms-19-00107}
--------------
Quercetin (3,3',4',5,7-pentahydroxyflavone) is part of a class of pigments called flavonoids that is found in many food items, such as tea, onions, grapes, and apples \[[@B59-ijms-19-00107]\]. Quercetin itself has been shown to exhibit a chemopreventive role in several cancers including liver, lung, prostate cancers, breast and renal cancer \[[@B60-ijms-19-00107],[@B61-ijms-19-00107],[@B62-ijms-19-00107],[@B63-ijms-19-00107],[@B64-ijms-19-00107],[@B65-ijms-19-00107]\]. This natural product has proven very effective when used in combination with other compounds \[[@B66-ijms-19-00107],[@B67-ijms-19-00107]\]. Quercetin has a therapeutic effect when used with hyperoside in 786-0 renal cancer cells \[[@B66-ijms-19-00107]\]. The mechanism for this activity involves downregulation of miRNA-27a, a mechanism that we have not yet explored in this article. Most natural products we have considered trigger apoptosis or necrosis using other pathways. Meanwhile, the reduction in miRNA-27a combined with an increase in ZBTB10 (the zinc finger and BTB domain-containing protein 10) triggers a decrease in specificity protein (SP) transcription factors \[[@B66-ijms-19-00107]\]. These transcription factors are highly expressed in cancer cells, and their reduction shows the therapeutic potential of quercetin.
Methylation by catechol-*O*-methyltransferase (COMT) enzyme significantly decreased the chemopreventive activity of EGCG in several cancers \[[@B68-ijms-19-00107],[@B69-ijms-19-00107],[@B70-ijms-19-00107]\]. Quercetin has been reported to increase the activity of EGCG in terms of bioavailability in animal models by inhibiting COMT activity \[[@B65-ijms-19-00107]\].
Snail is a zinc-finger transcription factor and plays a key role in EMT, migration and metastasis \[[@B71-ijms-19-00107],[@B72-ijms-19-00107]\]. Its silencing by short hairpin RNA (shRNA) inhibits cellular proliferation, cell cycle progression, cancer cell migration and promoted apoptosis in Caki-2 cell lines \[[@B67-ijms-19-00107]\]. Quercetin together with snail silencing provides even strong suppressive effects toward these cells. Quercetin has significant therapeutic potential that can be honed through research and more thorough investigation.
Isoquercetin, which is hydrolyzed in vivo to quercetin is currently being assessed in combination with sunitinib ([clinicaltrials.gov](clinicaltrials.gov): NCT02446795). In this ongoing clinical trial, the investigators hypothesized that isoquercetin is able to reduce sunitinib-induced fatigue which is being reported in 51--63% of advanced RCC patients.
2.4. Coumarin {#sec2dot4-ijms-19-00107}
-------------
Coumarin (1,2-benzopyrone) belongs to a benzopyrone family of compounds found in different parts of plants, having the highest concentration in fruits, followed by roots, seeds, and leaves. It can also be synthesized in the laboratory \[[@B73-ijms-19-00107],[@B74-ijms-19-00107]\]. Researchers continue to show a strong interest in coumarin and its derivatives because of their diverse pharmacological and biological properties such as anti-thrombic, scavenging of reactive oxygen species, anti-mutagenic, anti-bacterial, cycloxygenase inhibition as well as an anti-tumorigenic effect \[[@B75-ijms-19-00107]\].
Multiple studies have demonstrated that coumarins possess cytostatic and cytotoxic properties, inhibiting growth in several human cancer cell lines in vitro. In some clinical trials, they have shown anti-proliferative activities against several cancers including RCC \[[@B74-ijms-19-00107],[@B76-ijms-19-00107],[@B77-ijms-19-00107],[@B78-ijms-19-00107],[@B79-ijms-19-00107],[@B80-ijms-19-00107],[@B81-ijms-19-00107]\]. Keeping in mind the anti-neoplastic action of coumarins \[[@B82-ijms-19-00107]\], Myers et al., found that coumarin in vitro inhibited the proliferation of RCC cells \[[@B83-ijms-19-00107]\]. Coumarins isolated from *Calophyllum dispar* has been used as traditional medicine to treat RCC \[[@B84-ijms-19-00107]\]. Reduction in metastatic development among patients with RCC was noted when coumarin was given orally \[[@B82-ijms-19-00107]\]. A derivative consisting of 1,2,4-triazolin-3-one attached to 4-methylcoumarin was found to have encouraging activity against RCC cell line \[[@B85-ijms-19-00107]\]. A recent derivative, coufin, a novel indolylcoumarin, showed potent anticancer activity both in 2D (monolayer culture) and 3D (tumor spheroid culture) by inhibiting microtubule formation and blocking the cell cycle at G2/M \[[@B86-ijms-19-00107]\].
Since coumarin has low toxicity, there is a scientific rationale for using coumarin with other compounds in an attempt to increase their efficacies \[[@B87-ijms-19-00107]\]. A pilot study by Marshall et al., reported a beneficial effect of coumarin and cimetidine in RCC patients \[[@B77-ijms-19-00107]\]. In a clinical study, patients with metastatic RCC were given interferon-α (IFN-α) plus coumarin and cimetidine, or IFN-α-monotherapy \[[@B88-ijms-19-00107]\]. This study claims that using coumarin plus cimetidine to IFN-α did not increase response rates or survival of the patients. Further studies need to be performed to resolve the potential therapeutic value of coumarins in combination with other agents.
2.5. Curcumin {#sec2dot5-ijms-19-00107}
-------------
Curcumin (1,7-bis(4-hydroxy-3-methoxyphenyl)-1E,6E-heptadiene-3,5-dione or diferuloyl methane), a natural polyphenolic phytochemical isolated from dried rhizomes of turmeric plant (*Curcuma longa*) has been used for centuries as traditional Indian and Chinese medicine for the treatment of a variety of diseases \[[@B89-ijms-19-00107],[@B90-ijms-19-00107],[@B91-ijms-19-00107]\]. Across a variety of studies, curcumin has shown numerous pharmacological activities, including anti-inflammatory \[[@B92-ijms-19-00107],[@B93-ijms-19-00107],[@B94-ijms-19-00107]\], antiviral \[[@B95-ijms-19-00107],[@B96-ijms-19-00107]\], anti-oxidant \[[@B94-ijms-19-00107]\], wound healing \[[@B97-ijms-19-00107]\], hepatoprotective \[[@B98-ijms-19-00107]\], and anti-microbial effects \[[@B99-ijms-19-00107],[@B100-ijms-19-00107]\]. Moreover, curcumin has been used as a chemopreventive agent and an anti-cancer therapy in several human carcinomas, including colorectal \[[@B101-ijms-19-00107]\], melanoma \[[@B102-ijms-19-00107]\], lymphoma \[[@B103-ijms-19-00107]\], breast \[[@B104-ijms-19-00107],[@B105-ijms-19-00107]\], thyroid \[[@B106-ijms-19-00107]\], head and neck \[[@B107-ijms-19-00107]\], prostate \[[@B108-ijms-19-00107]\], pancreatic \[[@B109-ijms-19-00107],[@B110-ijms-19-00107]\], ovarian \[[@B111-ijms-19-00107]\] and RCC \[[@B91-ijms-19-00107],[@B112-ijms-19-00107],[@B113-ijms-19-00107],[@B114-ijms-19-00107],[@B115-ijms-19-00107],[@B116-ijms-19-00107],[@B117-ijms-19-00107],[@B118-ijms-19-00107]\].
Curcumin has been reported to efficiently induce apoptosis in vitro in various human cancer cell lines \[[@B18-ijms-19-00107],[@B119-ijms-19-00107],[@B120-ijms-19-00107],[@B121-ijms-19-00107]\]. The mechanism(s) by which curcumin can induce apoptosis in RCC cells to remain poorly understood. Initial reports by Kim et al., suggest that curcumin induces apoptosis in Caki cells by activating caspase 3 and releasing mitochondrial cytochrome C \[[@B122-ijms-19-00107]\]. Woo et al., also suggested that curcumin induced apoptosis through the dephosphorylation of AKT, down-regulation of BCL-2, BCL-XL and inhibitor of apoptosis protein (IAP) proteins, activation of caspase 3 and release of cytochrome C \[[@B114-ijms-19-00107]\]. Zhang and groups demonstrated that curcumin significantly inhibits proliferation of RRC-949 cell lines and induces cell apoptosis, possibly via regulation of BCL-2 and BAX, and initiates cell cycle arrest in G2/M phase \[[@B116-ijms-19-00107]\]. Curcumin exposure induces apoptosis through cell cycle arrest in G1-phase and increases the volume of human kidney cells by modulating chloride ion channel \[[@B91-ijms-19-00107]\].
Moreover, curcumin has been proven to increase the efficacy of chemotherapeutic drugs. Since PI3K/AKT and mechanistic target of rapamycin (mTOR) signaling are hyper-activated in RCC, inhibition of these pathways is warranted for RCC treatment \[[@B123-ijms-19-00107]\]. Although NVP-BEZ235 inhibits PI3K/AKT and mTOR pathways, it was not sufficient to induce apoptosis in RCC cell lines \[[@B113-ijms-19-00107]\]. Curcumin significantly induces apoptosis in NVPBEZ235-treated cells through p53-dependent downregulation of MCL-1 and BCL-2 protein expression \[[@B113-ijms-19-00107]\]. However, the exact mechanism continues remains unclear.
Yes-associated protein (YAP), the effector of the Hippo signaling pathway, is reported either as an oncogene or a tumor suppressor and plays contradictory roles in the development of cancer \[[@B124-ijms-19-00107]\]. Reports from Bai et al., indicate that YAP functions as a tumor suppressor that enhances chemosensitivity via apoptosis by modulating p53 during chemotherapy \[[@B124-ijms-19-00107]\]. Short hairpin RNA-mediated knockdown of YAP significantly inhibited cell proliferation, migration, and colony formation efficiency of RCC cells in soft agar and led to significantly reduced tumor growth in mice by activating p53 signaling and inhibiting mitogen-activated protein kinase (MAPK) signaling \[[@B125-ijms-19-00107]\]. However, Xu et al., reported that combined treatment with curcumin and temsirolimus in Caki-1 and OS-RC-2 RCC cell lines markedly upregulates YAP, which binds to p53 promoter, enhances p53 expression and finally induces apoptosis by activation of cleaved poly ADP-ribose polymerase (PARP) and caspase 3, and downregulation of BCL-2 protein expression \[[@B115-ijms-19-00107]\]. Curcumin sensitizes human renal cancer cells to tumor necrosis factor-related apoptosis-inducing ligand (TRAIL)-induced apoptosis by upregulating death receptor 5 (DR5) expression and generating reactive oxygen species (ROS) \[[@B126-ijms-19-00107]\]. The results from these studies suggest that using curcumin is a potentially novel and efficient strategy to enhance the effectiveness of targeted drugs in human RCC.
Although curcumin has been successfully proven to be very effective in vitro in diminishing cancer cell proliferation, migration, and invasion, it exhibits lesser effects in vivo due to poor bioavailability, poor absorption, rapid metabolism in liver cells and intestinal wall. Several strategies such as novel drug delivery systems, blocking of metabolic pathways, and synthesis of curcumin analogs have been explored in attempting to improve the bioavailability and gain in its metabolic stability \[[@B112-ijms-19-00107],[@B127-ijms-19-00107],[@B128-ijms-19-00107],[@B129-ijms-19-00107],[@B130-ijms-19-00107],[@B131-ijms-19-00107],[@B132-ijms-19-00107]\]. We anticipate that use of curcumin or its analogs in clinics for the prevention and/or treatment of RCC and other cancers.
2.6. Resveratrol {#sec2dot6-ijms-19-00107}
----------------
Resveratrol (trans 3,4′,5-trihydroxystilbene) is a naturally occurring polyphenolic compound found in grapes and 72 additional plant species and is relatively abundant in red wines \[[@B133-ijms-19-00107]\]. It has been reported to induce apoptosis, inhibit tumor growth, and suppress angiogenesis and metastasis in various malignancies including RCC \[[@B134-ijms-19-00107]\]. The results from microarray gene expression profiling revealed that resveratrol modulates the genes related to the inhibition of cell growth and induction of apoptosis \[[@B133-ijms-19-00107]\]. It has been indicated that resveratrol significantly inhibits the RRC cell proliferation and exerts an antitumor effect by concomitant inhibition of the expression of VEGF, a vital feature of RCC microenvironment \[[@B135-ijms-19-00107]\]. In a recent study, Kim et al. \[[@B134-ijms-19-00107]\] demonstrated the pro-apoptotic and anti-invasive role of resveratrol in RCC, and their results suggest that it suppresses the activation of signal transducers and activators of transcription 3/5 (STAT3/5) proteins, which are aberrantly activated in RCC \[[@B136-ijms-19-00107]\]. Furthermore, resveratrol induced S-phase arrest and apoptosis, decreased mitochondrial membrane potential, and suppressed colony formation in RCC. They also found that resveratrol shows caspase 3-mediated apoptosis, and blockage of metastasis by downregulating the expression of BCL-2, BCL-XL, IAP1/2, survivin, COX-2, MMP2 and VEGF.
Besides, resveratrol increases sorafenib induced inhibitory effect on phosphorylation of STAT3/5, apoptosis, and in turn results in downregulation of various oncogenic gene products. In addition to its antitumor action, resveratrol can exhibit antitumor immune response. It boosts antitumor immunity in mice by efficiently suppressing regulatory T cells (Tregs), inhibiting TGF-β level, and increasing IFN-γ expressing CD8^+^ T cells \[[@B137-ijms-19-00107]\]. In agreement to these results, Chen et al., reported that resveratrol reduces Tregs cells, stimulates cytotoxic CD8^+^ T cells, increases IFN-γ and reducing the level of interleukin-6 (IL-6) and IL-10 \[[@B138-ijms-19-00107]\]. Moreover, they also revealed that resveratrol suppresses tumor growth by significantly inhibiting abnormal angiogenesis by downregulating VEGF level. Taken together, resveratrol may, therefore, be an effective antitumor therapy drug and improve outcomes for RCC patients.
2.7. Other Natural Products {#sec2dot7-ijms-19-00107}
---------------------------
There are additional natural bioactive products which possess anticancer activities against RCC. Honokiol ((3′,5-di-(2-propenyl)-1,1′-biphenyl-2,2′-diol) is a biologically active biphenolic compound isolated from *Magnolia spp*. bark, which has been extensively used in traditional Chinese medicine and shown to exhibit an anticancer effect in various cancer \[[@B139-ijms-19-00107],[@B140-ijms-19-00107],[@B141-ijms-19-00107],[@B142-ijms-19-00107],[@B143-ijms-19-00107],[@B144-ijms-19-00107]\]. However, very limited literature is available which deciphers the anticancer role of honokiol in RCC. Honokiol suppresses cell proliferation and migration of highly metastatic RCC cell line, 786-0 through activation of RhoA/ROCK/MLC signaling \[[@B145-ijms-19-00107]\]. Li et al., demonstrated that honokiol inhibits metastasis through reversing EMT and suppressing cancer stem cell (CSC) properties via modulating miR-141/ZEB2 axis \[[@B146-ijms-19-00107]\]. Another group also shows that honokiol suppresses the invasion and metastasis by upregulating the expression of metastasis suppressor genes like *KISS-1*, *TIMP4*, *KISS-1R* and *TP53*, and concomitant downregulating *CXCL12*, *CCL7*, *IL-18*, and *MMP7* expression in RCC cells \[[@B145-ijms-19-00107]\]. These studies suggest that honokiol may be a suitable therapeutic approach for RCC treatment.
Genistein (4′,5,7-trihydroxyflavone or 5,7-dihydroxy-3-(4-hydroxyphenyl)-4H-chromen-4-one) is one of the principal isoflavones found in soybeans. Many studies have shown that genistein inhibits several cancers by modulating different signaling pathways involved in cell cycle progression, apoptosis, invasion, angiogenesis and metastasis \[[@B147-ijms-19-00107],[@B148-ijms-19-00107],[@B149-ijms-19-00107],[@B150-ijms-19-00107]\]. Genistein inhibits angiogenesis in vivo by downregulating the expression of VEGF and basic fibroblast growth factor (bFGF), the two crucial players in angiogenesis in RCC \[[@B151-ijms-19-00107],[@B152-ijms-19-00107]\]. Sasamura et al., reported that genistein displays anti-proliferative action on RCC cell lines by inducing apoptosis \[[@B152-ijms-19-00107]\]. Whereas, Majid et al., revealed that anti-proliferative action of genistein is due to cell cycle arrest at G2/M phase but not due to apoptosis \[[@B153-ijms-19-00107]\]. They have reported for the first time that a tumor suppressor gene, *BTG3* (B-cell translocation gene 3) is epigenetically silenced in RCC and genistein can reactivate it by promoter demethylation and active histone modification \[[@B153-ijms-19-00107]\]. miR-1260b, which is an oncogenic miRNA, is overexpressed in RCC which promotes cell proliferation and invasion, and inhibits several tumor suppressor genes associated with Wnt-signaling-induced tumorigenesis, such as *sFRP1*, *Dkk2* and *Smad4* \[[@B154-ijms-19-00107]\]. Genistein downregulates miR-1260 expression and in turn, inhibits cell proliferation and invasion \[[@B154-ijms-19-00107]\]. These studies support that genistein can be considered a promising agent for the treatment of RCC.
Sulforaphane (SFN) is an isothiocyanate derived from cruciferous vegetables such as broccoli (*Brassica oleracea*). SFN has been shown to play a bidirectional role; it acts as a protectant in normal kidney tubular cells against nephrotoxicants secreted by these cells, whereas it exhibits a pro-apoptotic effect on cancer cells by stimulating mitochondrial metabolism \[[@B155-ijms-19-00107]\]. Moreover, studies found that SFN delays the resistance caused by chronic use of everolimus monotherapy and increases the efficacy of everolimus in RCC cell lines \[[@B156-ijms-19-00107],[@B157-ijms-19-00107]\]. Further studies are warranted to verify these results in animal models.
Amygdalin ([d]{.smallcaps}-mandelonitrile-β-[d]{.smallcaps}-glucoside-6-β-glucoside), a cyanogenic substance is found in apricots, peaches, apple, cherry, plums, and other rosaceous fruit seeds \[[@B158-ijms-19-00107]\]. Although a number of studies reported its anti-cancer properties in various cancers such as triple negative breast cancer, non-small lung cancer, prostate cancer, cervical cancer and liver cancer \[[@B158-ijms-19-00107],[@B159-ijms-19-00107],[@B160-ijms-19-00107],[@B161-ijms-19-00107]\], very limited studies have been carried out to uncover its mechanism of action in RCC. Recently, it has been reported that amygdalin inhibits the growth of RCC cells by blocking adhesion and migration via an integrin-dependent mechanism \[[@B162-ijms-19-00107],[@B163-ijms-19-00107]\].
Thymoquinone (2-methyl-5-isopropyl-1,4-benzoquinone), a monoterpene, is a natural polyphenolic compound found abundantly in the seed oil of black cumin (*Nigella sativa* L.) seeds and known to have anti-cancer properties \[[@B164-ijms-19-00107]\]. Thymoquinone has recently been reported for its role in inducing apoptosis through downregulation of c-FLIP and BCL-2 in renal carcinoma cells \[[@B165-ijms-19-00107]\]. Kahweol, a diterpene molecule from coffee beans has been reported to enhance the sensitivity to sorafenib in renal cell carcinoma cells through downregulation of MCL-1 and c-FLIP expression \[[@B166-ijms-19-00107]\].
Alpinumisoflavone is isolated from *Erythrina lysistemon* and little is known about its anti-cancer effect in RCC. Recently, Wang et al., uncovered the mechanism of its anti-cancer effect suggested that this natural compound suppresses the tumor growth and metastasis through modulating miR-101/RLIP76 signaling \[[@B167-ijms-19-00107]\].
16-hydroxycleroda-3,13-dien-15,16-olide, a clerodane diterpene (CD) isolated from *Polyalthia longifolia* var. pendula leaves has shown has been shown to inhibit the proliferation of various human cancer cell lines \[[@B168-ijms-19-00107]\]. However, the mechanism of action of CD against RCC remains unknown. A recent study elucidated the mechanism of action of CD against RCC and suggested that it inhibits the cell proliferation and induces mitochondrial-dependent apoptosis through AKT, mTOR, and MEK/ERK pathways in RCC cells \[[@B169-ijms-19-00107]\].
A very recent report demonstrates that Korean red ginseng extract can enhance the anticancer effect of sorafenib through suppressing cyclic adenosine monophosphate response element-binding protein and c-Jun activation, induce p53 phosphorylation and in turn enhances the chemosensitivity of sorafenib in RCC \[[@B170-ijms-19-00107]\].
3. Conclusions {#sec3-ijms-19-00107}
==============
There are currently many agents available for the treatment of RCC such as anti-angiogenesis drugs (TKIs and bevacizumab) and immunotherapy drugs (interleukin and interferon). Renal cell carcinoma is one of the deadliest cancers, and, despite these many therapeutic options, is not curable in advanced stages. There is a clear necessity for medicines that are effective against the tumor while sparing the patient of adverse drug reactions. As an alternative approach, nature products have been proposed, but, to date, few of these compounds have been implemented on a large-scale in the treatment of cancer patients. Recent studies have suggested that many natural compounds are quite effective in vitro, and in vivo cancer models and history has shown this class of agent has little to no adverse side effects. EGCG, Englerin A, curcumin, resveratrol, quercetin, and honokiol are a few of these natural compounds that have shown beneficial results in preclinical studies of RCC. We have summarized the anticancer mechanism of these compounds in [Table 1](#ijms-19-00107-t001){ref-type="table"}. It is prudent to continue to explore natural products as anti-tumor agents, without severe side effects, either alone or in rationally designed combination.
We greatly appreciate John Beutler (Center for Cancer Research, National Cancer Institute, Frederick, MD) for his valuable and helpful comments on this manuscript. This work was supported by Basic Research Development Award from Internal Medicine, KUMC (Inamul Haque ), the Kansas City Area Life Science grant award (Sushanta K. Banerjee), Merit review grant from Department of Veterans Affairs (Sushanta K. Banerjee, 5I01BX001989-03 and Snigdha Banerjee,1I01BX001002-04), and KUMC Van Goethem Family Endowed Funds (Sushanta K. Banerjee). Andrew K. Godwin is the Chancellors Distinguished Chair in Biomedical Sciences Endowed Professor.
Inamul Haque and Arvind Subramanian performed the literature search and wrote the manuscript; Chao H. Huang and Peter J. Van Veldhuizen helped revise the draft; Andrew K. Godwin, Snigdha Banerjee and Sushanta K. Banerjee provided their expert comments and editing.
The authors declare no conflict of interest.
{#ijms-19-00107-f001}
ijms-19-00107-t001_Table 1
######
Anticancer Indications of Natural Products in Renal Cell Carcinoma.
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Natural Products Sources Possible Targets References
--------------------- ------------------------------------------------ -------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
EGCG Green tea, plums, apple peel, onions TFPI-2, TRAIL, c-FLIP, MCL-1, BCL-2,\ \[[@B28-ijms-19-00107],[@B36-ijms-19-00107],[@B37-ijms-19-00107],[@B43-ijms-19-00107]\]
MMP-2/9, *Cx32*, Src, JNK signaling
Englerin A *Phyllanthus engleri* AKT/ERK signaling, pathway, PKCθ, HSF1, TRPC4/5, E-cadherins, Vimentin, CD44, ALDH1A1 \[[@B44-ijms-19-00107],[@B47-ijms-19-00107],[@B48-ijms-19-00107],[@B49-ijms-19-00107],[@B50-ijms-19-00107],[@B51-ijms-19-00107],[@B52-ijms-19-00107],[@B56-ijms-19-00107]\]
Quercetin Tea, onions, grapes, and apples miRNA-27a, COMT, ZBTB10, Snail \[[@B65-ijms-19-00107],[@B66-ijms-19-00107]\]
Coumarin Strawberry, sweet grass, Tonka beans, Lavender Caspase-9, G2/M phase \[[@B82-ijms-19-00107],[@B83-ijms-19-00107],[@B84-ijms-19-00107],[@B86-ijms-19-00107]\]
Curcumin Rhizomes of turmeric plant BCL-2, BCL-XL, IAP, caspase 3, cytochrome c, PARP, DR5, PI3K/AKT and mTOR signaling pathways \[[@B91-ijms-19-00107],[@B113-ijms-19-00107],[@B114-ijms-19-00107],[@B115-ijms-19-00107],[@B116-ijms-19-00107],[@B122-ijms-19-00107],[@B123-ijms-19-00107],[@B125-ijms-19-00107],[@B126-ijms-19-00107]\]
Resveratrol Grapes, red wines VEGF, STAT3/5, BCL-2, BCL-XL, IAP1/2, survivin, COX-2, MMP2, TGF-β, IFN-γ, IL-6 and IL-10 \[[@B133-ijms-19-00107],[@B135-ijms-19-00107],[@B136-ijms-19-00107],[@B137-ijms-19-00107],[@B138-ijms-19-00107]\]
Honokiol *Magnolia spp.* bark RhoA/ROCK/MLC signaling pathways, miR-141, ZEB2, KISS-1, TIMP4, KISS-1R, TP53, CXCL12, CCL7, IL-18, and MMP7 \[[@B145-ijms-19-00107],[@B146-ijms-19-00107]\]
Genistein Soybeans VEGF, bFGF, *BTG3*, miR-1260b, *sFRP1*, *Dkk2* and *Smad4* \[[@B151-ijms-19-00107],[@B152-ijms-19-00107],[@B153-ijms-19-00107],[@B154-ijms-19-00107]\]
Sulforaphane Broccoli Nrf2, PGC1α, HIF1α \[[@B155-ijms-19-00107]\]
Amygdalin apricots, peaches, apple, cherry, plums integrin α and β, FAK \[[@B162-ijms-19-00107],[@B163-ijms-19-00107]\]
Thymoquinone Black cumin c-FLIP and Bcl-2 \[[@B165-ijms-19-00107]\]
Kahweol Coffee beans Mcl-1 and c-FLIP \[[@B166-ijms-19-00107]\]
Alpinumisoflavone *Erythrina lysistemon* miR-101/RLIP76 signaling \[[@B167-ijms-19-00107]\]
Clerodane diterpene *Polyalthia longifolia* Akt, mTOR, and MEK/ERK \[[@B169-ijms-19-00107]\]
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
EGCG, Epigallocatechin-3-gallate; TFPI-2, tissue factor pathway inhibitor-2; TRAIL, tumor necrosis factor-related apoptosis-inducing ligand; c-FLIP, FLICE-like inhibitory protein; McL-1, myeloid cell leukemia 1; Bcl-2, B-cell lymphoma 2; MMP, matrix metalloproteinas; *Cx32*, connexin 32; JNK, Jun N-terminal protein kinase; ERK, extracellular signal-regulated kinase; PKCθ, protein kinase C theta; HSF1, heat sock factor 1; TRPC, transient receptor potential cation channel; ALDH1A1, Aldehyde dehydrogenase 1 family, member A1; COMT, catechol-*O*-methyltransferase; ZBTB10, zinc finger and BTB domain-containing protein 10; IAP, inhibitor of apoptosis protein; PARP, poly ADP-ribose polymerase; DR5, death receptor 5; PI3K, phosphoinositide 2-kinase; mTOR, Mechanistic target of rapamycin; VEGF, vascular endothelial growth factor, STAT3/5, Signal transducer and activator of transcription 3/5; COX-2, cyclooxygenase-2; TGF-β, transforming growth factor β; IFN-γ, interferon gamma; IL, interleukin; ROCK, Rho-associated coiled-coil kinase; MLC, myosin light chain; KISS1, Kisspeptin; TIMP4, tissue inhibitors of metalloproteinase 4; CXCL12, Chemokine (C-X-C motif) ligand 12; CCL7, Chemokine ligand 7; bFGF, basic fibroblast growth factor; *BTG3*, B-cell translocation gene 3; *sFRP1*, Secreted frizzled-related protein 1; *Dkk2*, Dickkopf WNT Signaling Pathway Inhibitor 2; Smad4, Smad Family Member 4; Nrf2, Nuclear factor E2-related factor 2; PGC1α, proliferator-activated receptor-γ co-activator-1α; HIF1α, hypoxia-inducible factor-1α; FAK, focal adhesion kinase; c-FLIP, cellular FLICE (FADD-like IL-1β-converting enzyme)-inhibitory protein; RLIP76, Ral-interacting protein of 76 kDa.
[^1]: Summer high school student.
| {
"pile_set_name": "PubMed Central"
} |
Production and characterization of the murine monoclonal antibody 2G10 to a human T4-tyrosinase epitope.
Employing as immunogen a short-term passaged, highly pigmented human melanoma cell line, we have produced the murine MoAb 2G10 of the IgG1 isotype. The antibody immunoprecipitated from 35S-methionine and 3H-glucosamine metabolically labeled human melanoma cells with a single-chain glycoprotein of 75 kD molecular weight. No such molecule could be precipitated from murine melanomas. To further investigate the fine specificity of the MoAb, immunochemical and immunohistochemical studies were performed. These studies demonstrated that MoAb 2G10 binds a significant fraction of tyrosinase activity from cell lysates, completely immunodepletes soluble cell extract of T4-tyrosinase molecules, and produces immunostaining patterns superimposable on those obtained with anti-T4-tyrosinase antibodies. Thus, MoAb 2G10 appears to recognize a human-specific determinant carried by either T4-tyrosinase or a closely related molecule. The functional relevance of this epitope remains to be evaluated. | {
"pile_set_name": "PubMed Abstracts"
} |
Background {#Sec1}
==========
Circulating thyroid hormone (TH) enters the brain via the blood--brain and blood-cerebrospinal fluid barriers \[[@CR1]\], by means of specific transporter proteins expressed in the membranes of cerebral endothelial cells and choroid plexus epithelial cells \[[@CR2], [@CR3]\]. Recent knockout mouse models provided evidence that TH entry into the brain is largely dependent on two TH transporters, monocarboxylate transporter 8 (MCT8) and organic anion-transporting polypeptide 1c1 (OATP1c1) \[[@CR4]--[@CR9]\]. We recently described that during systemic inflammation induced by bacterial lipopolysaccharide (LPS) administration, OATP1c1 and MCT8 mRNAs, as well as OATP1c1 protein markedly decrease in brain vessels \[[@CR10]\]. The downregulation of these transporters at the blood--brain barrier would suggest reduced TH uptake into the brain and consequently, lower brain TH concentration, especially during prolonged systemic inflammatory states.
Other than MCT8 and OATP1c1, however, there are additional membrane proteins that are capable of transporting TH and may contribute to TH homeostasis in the brain \[[@CR11], [@CR12]\]. Included are type 1 and 2 L-type amino acid transporters (LAT1 or *Slc7a5*; LAT2 or *Slc7a8*) that transport TH with low to medium affinity \[[@CR11], [@CR13]\] and are expressed in multiple brain cell types. In vivo mouse and rat studies demonstrated that LAT1 is expressed in microvascular cells of the blood--brain barrier \[[@CR12], [@CR14]--[@CR18]\], choroid plexus epithelial cells \[[@CR14], [@CR18]\] (in rats but not mice) and neurons \[[@CR12]\], whereas LAT2 is expressed in neurons \[[@CR12], [@CR19], [@CR20]\] and the choroid plexus \[[@CR12], [@CR19]\]. Therefore, LAT1 and LAT2 may contribute to TH transport across the blood--brain and blood-cerebrospinal fluid barriers and facilitate neuronal uptake and/or release of TH.
To determine whether upregulation of LAT1 and LAT2 compensates for the downregulation of MCT8 and OATP1c1 during inflammation and offsets the effect of reduced brain TH uptake on neurons, we examined the effect of LPS on LAT1 and LAT2 expression in the mouse and rat forebrain using in situ hybridization to study LAT1 and LAT2 mRNAs in a cell-type specific-manner, as well as immunofluorescence to study LAT1 protein levels.
Methods {#Sec2}
=======
Animals {#Sec3}
-------
The experiments were carried out on adult, male, Sprague--Dawley rats (Taconic Biosciences, Germantown, NY, USA) of similar age, weighing 220--260 g, and adult, male, C57Bl/6 mice (Taconic) of similar age, weighing 19--21 g. Animals were housed under standard conditions (lights on between 0600 and 1800 h, temperature 22 ± 1 °C, rodent chow and water ad libitum). Only male animals were used in this study to avoid the potential confounding effects of the estrous cycle on the experimental results. All experimental protocols were reviewed and approved by the Institutional Animal Care and Use Committee at Tufts Medical Center (Protocol\# B2012-171) and was carried out in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the National Institutes of Health.
Injections and tissue preparation {#Sec4}
---------------------------------
*LPS*-*injections* Animals were injected ip with LPS from *Escherichia coli* (serotype O55:B5; Sigma-Aldrich Co., St. Louis, MO, USA) between 9 and 11 a.m. LPS was dissolved in saline, and injected at a dose of 2.5 mg/kg body weight to all animals. Control animals received the same volume of saline. In our experience, different LPS serotypes such as O55:B55 and O127:B8 elicit very similar inflammatory responses in the brain, including upregulation of type 2 deiodinase \[[@CR21], [@CR22]\].
*Time course experiment for in situ hybridization in rats and mice* Groups of animals containing 4 or 5 rats or mice were injected with LPS, and 2, 4, 9, 24 or 48 h later were anesthetized with ketamine-xylazine (ketamine: 75 mg/kg body weight; xylazine: 10 mg/kg body weight), then decapitated. Control mice were euthanized at 9 h (n = 5), control rats at either 9 h (n = 3) or 24 h (n = 2), based on previous experiments. The intensity of hybridization and immunofluorescence signals were very similar in all control rats. The brains were removed, snap-frozen on powdered dry ice and 16 μm thick coronal sections from the forebrain were cut using a Leica CM3050 S cryostat (Leica Microsystems, Nussloch GmbH, Germany). Sections were thaw-mounted on Superfrost Plus slides (Fisher Scientific Co., Pittsburgh, PA, USA), air-dried and stored at −80 °C until processed for in situ hybridization or immunofluorescence.
Generation of hybridization probes {#Sec5}
----------------------------------
Template cDNA fragments were generated with RT-PCR using standard procedures. Amplification was performed on cDNA synthesized from rat and mouse brain for LAT1 and rat and mouse liver for LAT2. Fragments were cloned into pGEM^®^-T vector (Promega) and confirmed by sequencing. Probe sequences were as follows: rat LAT1 probe corresponds to nt 64--851 of \[GenBank: NM_017353.1\]; mouse LAT1 probe nt 81--868 of \[GenBank: NM_011404.3\]; rat LAT2 probe nt 621--1368 of \[GenBank: NM_053442.1\]; mouse LAT2 probe nt 657--1335 of \[GenBank: NM_016972.2\]. Antisense and sense riboprobes were synthesized using SP6 or T7 RNA polymerase (Promega) in the presence of \[35S\]-uridine 5′-(alpha-thio) triphosphate (PerkinElmer), and purified with Mini Quick Spin RNA columns (Roche Applied Sciences).
Isotopic in situ hybridization {#Sec6}
------------------------------
Isotopic in situ hybridization was performed as previously described for fresh frozen sections \[[@CR23]\] using 50,000 cpm/μl radiolabeled probe concentrations. Following stringency washes, sections were dehydrated in ascending ethanol series, air-dried and placed on Amersham Hyperfilm autoradiography film (GE Healthcare Biosciences) for 7 days. Slides were then dipped in Kodak NTB autoradiography emulsion (Carestream Health Inc) and stored at 4 °C until developed. Exposure times were as follows: 14 days for rat LAT1; 17 days for mouse LAT1; 14 days for rat LAT2 and 21 days for mouse LAT2. Autoradiograms were developed with Kodak D19 developer (Eastman Kodak Co). Sections were immersed in 0.0005 % cresyl violet acetate (Sigma-Aldrich) for 2 min to obtain fluorescent labeling of cell nuclei, dehydrated in ascending ethanol series and xylenes, and coverslipped with DPX (Sigma-Aldrich). Hybridizations with the sense transcripts for each probe did not yield any signal above a low-level of homogenous background. Darkfield images of the emulsion autoradiographs were captured using a Zeiss Axioplan 2 microscope equipped with a SPOT Slider digital camera (Diagnostic Instruments).
Isotopic LAT1 in situ hybridization combined with immunofluorescence {#Sec7}
--------------------------------------------------------------------
To confirm that LAT1 mRNA is expressed in both microvascular cells and neurons, sections from control rat and mouse brains were hybridized for LAT1 as above, then processed further for immunofluorescence. The sections were treated with the mixture of 0.5 % Triton X-100 and 0.5 % H~2~O~2~ for 15 min, rinsed in phosphate-buffered saline (PBS) (3 × 10 min), immersed in maleate buffer (pH 7.5) for 10 min and then in 1 % blocking reagent for nucleic acid hybridization (Roche). To visualize neuronal cell bodies and blood vessels, sections were incubated in the mixture of a mouse monoclonal antibody against the neuronal proteins HuC/HuD (Life Technologies; Cat\# A21271, raised against human HuC/HuD; used at 1 µg/ml) and polyclonal chicken IgY against vimentin (Millipore; Cat\# AB5733, raised against recombinant vimentin; used at 1:4000 dilution). Other sections were incubated in a rabbit polyclonal antibody against LAT1 (Cosmo Bio Co., Ltd., Tokyo, Japan; Cat\# KAL-KE026, diluted at 1 µg/ml) to label microvascular cells. The primary antibodies were detected with Alexa Fluor 488-conjugated donkey anti-mouse IgG (Life Technologies; 1:200), Cy3-conjugated donkey anti-chicken IgG (Jackson ImmunoResearch, West Grove, PA, USA) and Cy3-conjugated donkey anti-rabbit IgG (Jackson; 1:200). Sections were then dehydrated, dipped in Kodak NTB autoradiography emulsion, and the autoradiograms were developed after 17 days. The mouse HuC/D antibody and the chicken vimentin antibody have been used extensively for immunofluorescent studies (see references \[[@CR22], [@CR24]--[@CR26]\]). The HuC/D antiserum labeled neuronal cell bodies, vimentin immunostaining labeled pericytes in the brain vasculature \[[@CR27]\] as well as ependymal and meningeal cells.
Immunofluorescence {#Sec8}
------------------
For LAT1 immunofluorescence, fresh-frozen mounted sections were fixed with methanol at −20 °C for 5 min. While LAT1 immunostaining also worked well with standard 4 % paraformaldehyde fixation, methanol fixation produced more intense signal and less background staining. Sections were permeabilized with 0.25 % Triton-X-100 for 20 min, and then blocked with 2 % normal horse serum in PBS for 20 min. Sections were incubated overnight in a rabbit antiserum against human LAT1 (Cosmo Bio Co., Ltd., Cat\# KAL-KE026, diluted at 1 µg/ml), which was subsequently detected with Cy3-conjugated donkey anti-rabbit IgG (Jackson Immunoresearch, 1:200).
To demonstrate that LAT1 is expressed in endothelial cells, dual immunfluorescence was performed for LAT1 and either CD31 (or PECAM-1) or glucose transporter 1 (GLUT1), both regarded as markers for endothelial cells. To label CD31, a monoclonal rat antibody against CD31 (Cat\# 550274; clone MEC 1.3; BD Biosciences, Franklin Lakes, NJ, USA) was used at 0.3 µg/ml concentration and subsequently detected with Alexa Fluor 488-conjugated donkey anti-rat IgG (Jackson; 1:400). For GLUT1, a monoclonal mouse antibody against GLUT1 (Cat\# MABS132; clone 5B12.3; Millipore) was used at 0.5 µg/ml concentration and subsequently detected with Alexa Fluor 488-conjugated donkey anti-mouse IgG (Life Technologies; 1:400).
LAT2 immunofluorescence was performed according to the same methanol fixation protocol as above using a rabbit polyclonal antiserum against mouse LAT2 (Cat\# 0142-10; ImmunoGlobe Antikörpertechnik GmBH, Himmelstadt, Germany; diluted at 2 µg/ml), and subsequently Cy3-conjugated donkey anti-rabbit IgG (Jackson). This antiserum was used previously for immunohistochemistry in the mouse brain \[[@CR20]\].
Validation of the specificity of the LAT1 antiserum {#Sec9}
---------------------------------------------------
The LAT1 polyclonal antiserum (Cosmo-Bio Co., Cat\# KAL-KE026) was raised against the C-terminal 14 amino acids of human LAT1 (amino acid sequence: CTVLCQKLMQVVPQET) \[[@CR28]\], which differs in only one amino acid from the mouse/rat sequence. On Western blots from the rat and mouse brain (see Additional file [1](#MOESM1){ref-type="media"} for immunoblotting methods), the antibody recognized a single band corresponding to a molecular weight of approximately 46 kDa (Additional file [2](#MOESM2){ref-type="media"}), in agreement with a previous report \[[@CR14]\]. LAT1 immunofluorescence resulted in intense staining of brain vessels and generally no parenchymal labeling, in accordance with previous immunostaining studies in mice and rats \[[@CR14]--[@CR18]\]. The high specificity of the immunostaining was further confirmed by identical LAT1 immunostaining and in situ hybridization patterns in specific regions such as the subcomissural organ, where intense LAT1 immunostaining was previously reported \[[@CR15]\], and in the caudal part of the rat dorsal third ventricle, where we observed a very characteristic pattern of cells expressing high levels of LAT1 mRNA and protein surrounding the choroid plexus (see Additional file [2](#MOESM2){ref-type="media"}).
Image analysis {#Sec10}
--------------
Immunofluorescent images were captured using the following fluorescent filter sets: for Cy3, excitation of 540--590 nm, bandpass of 595 nm, and emission of 600--660 nm; for Alexa 488, excitation of 460--500 nm, bandpass of 505 nm, and emission of 510--560 nm. Semiquantitative image analysis was performed with ImageJ software (public domain at <http://rsb.info.nih.gov/ij>). In situ hybridization and immunofluorescent signals were compared between sections from a single experiment where all conditions were identical. Vascular LAT1 hybridization signal was quantified in the rat cortex where parenchymal hybridization signal is lower than in other forebrain regions, and thus, the more intense vascular signal could be easily distinguished. On darkfield images taken with a 5× objective, the intense vascular signal was separated from the low-level parenchymal signal using the threshold tool in ImageJ, and the area covered by the vascular signal was measured. LAT1 immunofluorescence in blood vessels was quantified on images taken with a 10× objective from the same regions of the mouse or rat cortex, hypothalamus and thalamus. Immunolabeled vessels were separated from the background using the threshold tool, and the average pixel intensity (brightness value) of the immunofluorescent signal was measured. Analyses from all brain regions yielded the same results, and data from the hypothalamus are presented.
Statistical analysis {#Sec11}
--------------------
Data are presented as mean ± SEM. Groups were compared by the non-parametric Kruskal--Wallis test, and then post hoc comparisons between the LPS-treated groups *vs.* the control group were made by Dunn's test.
Results {#Sec12}
=======
Distribution of LAT1 mRNA in the rat and mouse forebrain {#Sec13}
--------------------------------------------------------
LAT1 in situ hybridization patterns were highly similar in rats and mice. In general, intense hybridization signal was associated with blood vessels, including major vessels penetrating the brain surface and smaller vessels and capillaries (Figs. [1](#Fig1){ref-type="fig"}, [2](#Fig2){ref-type="fig"}B, C). This is in agreement with reported data that LAT1 mRNA is highly enriched in brain vessels \[[@CR12], [@CR18], [@CR29], [@CR30]\]. Parenchymal, non-vascular hybridization signal was generally less intense than the vascular signal, and only rarely resulted in the formation of well-defined silver grain clusters under the used experimental conditions. This parenchymal signal closely corresponded to the distribution pattern of different neuronal populations, and we confirmed that it was associated primarily with neuronal cell bodies (Fig. [1](#Fig1){ref-type="fig"}A); however, we cannot exclude that other cell types also contributed to the parenchymal signal. Neuronal LAT1 hybridization was more prominent in most hypothalamic nuclei, the medial habenular nucleus of the thalamus, certain amygdalar regions, hippocampal principal cell layers and pyriform cortex, whereas only light signal labeled most of the cortical areas and several thalamic nuclei (Fig. [2](#Fig2){ref-type="fig"}A). The choroid plexus was labeled with moderate hybridization signal in rats (Fig. [2](#Fig2){ref-type="fig"}A), while it was not labeled in mice, in agreement with previous mRNA studies \[[@CR12], [@CR14]\]. Interestingly, in the rat, cells with very intense hybridization signal were located alongside the choroid plexus of the dorsal third ventricle; caudally, these cells almost encircled the choroid plexus (see Additional file [2](#MOESM2){ref-type="media"}). Hybridization signal also labeled the subfornical and subcomissural organs (see Additional file [2](#MOESM2){ref-type="media"}), while hypothalamic tanycytes were not labeled.Fig. 1LAT1 mRNA is expressed in brain microvascular cells and neurons. **A** To confirm that LAT1 mRNA is expressed in multiple cell types, radioactive LAT1 in situ hybridization (**A1** darkfield image, silver grain accumulation represents LAT1 mRNA expression) was combined with dual immunofluorescence (**A2**) for vimentin (*red*) and HuC/D (*green*) to visualize the pericyte coverage of vessels and neuronal cell bodies, respectively. The area shown is from the rostral part of the rat hypothalamic supraoptic nucleus (SO). In the merge image (**A3**), note that silver grains form dense clusters over blood vessels (*arrows*), while a lesser degree of silver grain accumulation is present over neuronal cell bodies (*yellow arrowheads*). *oc* optic chiasm, *SO* supraoptic nucleus. **B**, **C** LAT1 in situ hybridization was co-localized with LAT1 immunofluorescence (*red*) that labels the vascular endothelium. Note that silver grain clusters that represent high LAT1 mRNA expression are formed over capillaries denoted by LAT1 immunofluorescence (*arrows* in **B3**, **C3**). Images are from the rat hypothalamic ventromedial nucleus (**B**) and the mouse hypothalamic arcuate nucleus (**C**). *Scale bar* 50 µm for all imagesFig. 2Effect of LPS on LAT1 mRNA expression in brain vessels of rats and mice. **A** X-ray film images of radioactive LAT1 in situ hybridization in rat forebrain sections. Note the reduced "graininess" of the labeling 9 h after LPS, which is especially visible in the thalamus. Neuronal labeling, well visible in the hippocampus and the hypothalamus, including the dorsomedial nucleus (DMH), is not altered. At 48 h after LPS, the "grainy" signal, which represents blood vessels, is more intense than in control brains over the entire section. *Cp* choroid plexus, *DMH* dorsomedial hypothalamic nucleus, *Hip* hippocampus, *MHb* medial habenular nucleus. *Scale bar* 2 mm. **B** Darkfield emulsion autoradiography images demonstrate the time course of LAT1 mRNA (silver grain accumulation, *white*) in the rat cortex. In the control cortex, intense hybridization signal is associated with major longitudinal vessels (*arrows*) and a multitude of small capillaries (numerous bright spots). This labeling vanishes by 4 and 9 h after LPS, only the much lower level parenchymal labeling (primarily neuronal) remains. At 48 h after LPS, hybridization signal labels a larger part of the vasculature than in controls, including major vessels (*arrows*) and capillaries. *Scale bar* 100 µm. **C** LAT1 mRNA in vessels of the mouse cortex. In the control brain, silver grains form clusters over major vessels (*arrow*) and capillaries, which disappear 9 h after LPS. 48 h after LPS, LAT1 hybridization signal in vessels is more intense than in controls. *Arrows* indicate major vessels. *Scale bar* 100 µm
Effect of LPS on LAT1 mRNA {#Sec14}
--------------------------
Following LPS administration, LAT1 mRNA decreased markedly in blood vessels of both rats and mice, in all regions of the forebrain. The time course of this response is illustrated in Figs. [2](#Fig2){ref-type="fig"} and [3](#Fig3){ref-type="fig"}; quantification of this response by image analysis is presented in Fig. [4](#Fig4){ref-type="fig"}A. In rats, vascular hybridization signal decreased at 2 h after LPS. At this point, LAT1 mRNA was not detected in major vessels, only in smaller vessels and capillaries, but fewer than in controls (Fig. [2](#Fig2){ref-type="fig"}B). Hybridization signal in vessels could only occasionally be discerned at 4 and 9 h after LPS (Figs. [2](#Fig2){ref-type="fig"}B, [3](#Fig3){ref-type="fig"}A). At 24 h, the vascular labeling re-appeared but was still lower than in control rats (Fig. [2](#Fig2){ref-type="fig"}B). Forty-eight hours after LPS administration, the vascular signal was conspicuously and markedly higher than control levels in 3 out of 4 rats. In these rats, the hybridization signal was generally more intense in individual vessels and labeled a greater portion of the vasculature than in control rats (Figs. [2](#Fig2){ref-type="fig"}A, B, [3](#Fig3){ref-type="fig"}A). One rat in the 48 h group had signal levels comparable to the control group. This difference is probably due to the variation in the timing of the recovery phase after endotoxemia, and is reminiscent of the post-endotoxemic increase of OATP1c1 mRNA levels that could occur either 24 h or 48 h after LPS \[[@CR10]\]. In mice, blood vessel-associated hybridization signal was only occasional or very light at 2 h and 24 h after LPS, and was completely absent in the 4 h and 9 h LPS groups (Figs. [2](#Fig2){ref-type="fig"}C, [3](#Fig3){ref-type="fig"}C). Similar to rats, in the 48 h LPS group, 3 mice had increased vascular LAT1 hybridization signal than controls, and 1 mouse had signal levels comparable to controls (Figs. [2](#Fig2){ref-type="fig"}C, [3](#Fig3){ref-type="fig"}C).Fig. 3LAT1 mRNA decreased in vessels but not in neurons after LPS. **A**, **B** Darkfield emulsion autoradiography images show the distribution of LAT1 mRNA (silver grain accumulation, *white*) in the rat hypothalamus. *Boxed areas* from (**A**) are shown in higher magnification in (**B**). Low-level hybridization signal is distributed across the arcuate (Arc) and ventromedial nuclei (VMH), highly resembling a neuronal expression pattern; this signal does not change following LPS administration. Well-defined silver grains clusters over capillaries disappear 9 h after LPS, but become larger and more numerous at 48 h after LPS. *3v* third ventricle, *Arc*, arcuate nucleus, *ME* median eminence, *VMH* ventromedial hypothalamic nucleus. *Scale bar* 200 µm on **A**; 100 µm on **B**. **C** LAT1 in situ hybridization signal in the hypothalamic paraventricular nucleus (PVH) of mice. While LAT1 signal in capillaries virtually disappears 9 h after LPS, the low-level neuronal LAT1 signal in the paraventricular nucleus remains visible. At 48 h after LPS, hybridization signal in vessels is markedly increased. *3v* third ventricle, *PVH* hypothalamic paraventricular nucleus; *Scale bar* 100 µmFig. 4Semiquantitative image analysis results of LAT1 in situ hybridization and LAT1 immunofluorescence. **A** LAT1 hybridization signal was quantified in the rat cortex. Values represent area covered by vascular LAT1 hybridization signal. **B**, **C** LAT1 immunofluorescence was quantified in the rat and mouse hypothalamus, ventro-lateral to the hypothalamic paraventricular nucleus. Values represent the average brightness value of the immunofluorescence. Groups were compared by the non-parametric Kruskal--Wallis test and then by Dunn's multiple comparison test. \**P* \< 0.05; \*\**P* \< 0.01; vs control; Samples sizes are n = 4 or 5 rats or mice/group
Parenchymal, neuronal LAT1 hybridization signal remained stable in forebrain regions at any time after LPS administration in both species (Figs. [2](#Fig2){ref-type="fig"}A, [3](#Fig3){ref-type="fig"}). LAT1 mRNA expression in the rat choroid plexus also did not change after LPS injection.
Effect of LPS on LAT1 protein {#Sec15}
-----------------------------
LAT1 immunofluorescence labeled brain blood vessels in both species. Using dual immunofluorescence, we demonstrated that LAT1 in vessels always colocalized with the endothelial markers CD31 or GLUT1 (Fig. [5](#Fig5){ref-type="fig"}). In both rats and mice, the overall density of labeled vessels was essentially the same following LPS treatment as in controls. In rats, the signal intensity of vessels tended to be slightly lower in the 24 h LPS group, but was not significantly different from the control group (Figs. [4](#Fig4){ref-type="fig"}B, [6](#Fig6){ref-type="fig"}A). In mice, the brightness of LAT1 immunofluorescence in vessels decreased noticeably, albeit only modestly in the 24 h and 48 h LPS groups (Fig. [6](#Fig6){ref-type="fig"}B). By image analysis, the decrease in the 24 h group was statistically significant (Fig. [4](#Fig4){ref-type="fig"}C). This reduction of labeling intensity was observed in all brain regions, including the cortex, thalamus, hypothalamus and amygdala.Fig. 5LAT1 protein is expressed in cerebral endothelial cells. **A1**--**A3** Dual immunofluorescence for the endothelial marker CD31 (*green*) and LAT1 (*red*) in the mouse brain. LAT1 always colocalized with CD31 in vessels. Some vessels that were labeled for CD31 apparently lacked or had only little LAT1 protein expression (*arrowhead*). Dual immunofluorescence for the endothelial marker GLUT1 (*green*) and LAT1 (*red*) and in the mouse (**B1**--**B3**) and the rat (**C1**--**C3**) brain. LAT1 always colocalized with GLUT1 in vessels. A fraction of vessels labeled for GLUT1 were not labeled for LAT1 (*arrowheads*). *Scale bar* 50 µmFig. 6LAT1 immunofluorescence in brain vessels of the rat and mouse hypothalamus. **A** LAT1 immunofluorescence in the rat hypothalamus at the level of the paraventricular nucleus (PVH). The intensity of labeling tended to be lower at 24 h after LPS administration. *Scale bar* 200 µm. **B** LAT1 immunofluorescence in hypothalamic vessels of mice; labeling intensity is modestly reduced at 24 and 48 h after LPS. *Scale bar* 100 µm
Interestingly, we did not observe clear LAT1 immunostaining in the rat choroid plexus, with the exception of a few occasional cells, mostly in the choroid plexus of the dorsal third ventricle. This stands in contrast to the presence of LAT1 mRNA, and a previous report that demonstrated LAT1 immunostaining in the epithelial cells of the rat lateral ventricle choroid plexus \[[@CR18]\]. However, intense LAT1 immunostaining was present in the characteristic choroid plexus-associated cells that were labeled with intense LAT1 hybridization signal (see Additional file [2](#MOESM2){ref-type="media"}).
Effect of LPS on LAT2 mRNA {#Sec16}
--------------------------
The pattern of LAT2 mRNA distribution was essentially the same in rats and mice, and corresponded to the in situ hybridization pattern described previously in mice \[[@CR12], [@CR19]\]. Intense neuronal expression was present in the cortex, hippocampus, amygdalar regions and numerous thalamic nuclei (Fig. [7](#Fig7){ref-type="fig"}A). In the hypothalamus, the paraventricular and supraoptic nuclei were intensely labeled (Fig. [7](#Fig7){ref-type="fig"}A), while most other nuclei had no or very low level of hybridization signal such as the arcuate and ventromedial nuclei. Moderate to intense expression was observed in the choroid plexus of both species (Fig. [7](#Fig7){ref-type="fig"}A). LPS did not affect LAT2 mRNA expression in either neurons or in the choroid plexus in either species (Fig. [7](#Fig7){ref-type="fig"}A--C).Fig. 7LPS had no effect on LAT2 mRNA expression in the rat and mouse brain. **A** X-ray film images of radioactive LAT2 in situ hybridization from the rat forebrain. LAT2 is expressed in several neuronal populations and the choroid plexus, but its expression did not change after LPS administration. *BLA* basolateral amygdaloid nucleus, *cp* choroid plexus, *PVH* hypothalamic paraventricular nucleus. *Scale bar* 2 mm. **B** Darkfield emulsion autoradiography images from the rat cortex show no change in neuronal LAT2 mRNA expression after LPS. *Scale bar* 200 µm. **C** Similarly, no change in LAT2 hybridization signal was observed in neurons of the basolateral amygdaloid nucleus in mice. *Scale bar* 100 µm
Using LAT2 immunofluorescence, we did not observe any difference in the pattern or intensity of LAT2-immunoreactive labeling between control and LPS-treated mice and rats. However, the LAT2 antiserum is not completely specific to LAT2 in Western blot studies from the mouse brain \[[@CR31]\], and we were unable to unambiguously confirm that the immunostaining patterns were entirely specific to LAT2.
Discussion {#Sec17}
==========
In the present study, we report that systemic inflammation, induced by bacterial endotoxin, caused a robust decrease in LAT1 mRNA expression at the blood--brain barrier of rats and mice. This was followed by an apparent rebound effect with increased LAT1 mRNA levels during the recovery from endotoxemia. A modest decrease in LAT1 protein levels was also observed in mice at 24 h following the LPS stimulus. Neither LAT1 nor LAT2 mRNA levels were altered in the choroid plexus or in neurons following LPS administration.
With respect to TH homeostasis in the brain, perhaps the most important conclusion of the present study is that the downregulation of OATP1c1 and MCT8 at the blood--brain barrier are not accompanied by a compensatory increase in either LAT1 or LAT2 expression. The most remarkable aspect of the results, however, is that LPS administration causes strikingly similar changes in LAT1, OATP1c1 and MCT8 mRNA levels at the blood--brain barrier. The downregulation of LAT1 mRNA in brain vessels occurred essentially at the same time course and with the same robustness as that of OATP1c1 and MCT8 mRNAs \[[@CR10]\]. Moreover, during the recovery phase from endotoxemia, LAT1 mRNA increased markedly in vessels, which is highly reminiscent to the rebound effect we observed for MCT8 and OATP1c1 mRNAs between 24 h and 48 h after LPS injection \[[@CR10]\]. These parallel changes are somewhat surprising since LAT1 is a high affinity amino acid transporter that accounts for the uptake of large neutral amino acids into the brain \[[@CR32], [@CR33]\], and regarded only as a secondary TH transporter \[[@CR11]\]. Thus, these data show that two different transport systems of the blood--brain barrier, one transporting primarily amino acids (LAT1) and the other primarily TH (MCT8 and OATP1c1), are regulated in a parallel manner in response to inflammation. This finding, therefore, raises the question as to whether there are other transporters at the blood--brain barrier that are similarly regulated in inflammatory conditions. Unfortunately, there are currently no reports in the literature about the in vivo effect of inflammation on major blood--brain barrier influx transporters. Interestingly, however, in a very similar LPS model to ours, organic anion transporter 3 and organic anion-transporting polypeptide 1a4 protein levels decrease in brain capillaries 24 h after LPS injection \[[@CR34]\]. Organic anion transporter 3 is regarded as a brain-to-blood efflux transporter \[[@CR35]\], while organic anion-transporting polypeptide 1a4 as both an efflux and influx transporter of anionic compounds \[[@CR36]\]. These data further indicate that multiple different transporter systems are down-regulated at the blood--brain barrier during systemic inflammation. Future studies are required to elucidate the effect of inflammation on other blood--brain barrier transporters.
Given the parallel changes in LAT1, OATP1c1 and MCT8 mRNAs in brain vessels, it is reasonable to hypothesize that the same cellular mechanism may be behind the inflammation-induced down-regulation of these genes. Since the expression of these transporters remains stable in other brain cell types \[[@CR10]\], this mechanism may be quite specific to brain endothelial cells. Interestingly, LAT1 expression is robustly induced in activated human T-cells via the nuclear factor kappa B pathway \[[@CR37]\], whereas in our LPS model, LAT1 mRNA levels decrease in spite of nuclear factor kappa B activation in cerebral endothelial cells \[[@CR38], [@CR39]\]. These data indicate that regulation of LAT1 in brain endothelial cells is different than in other cell types of the body.
In contrast to the robust effect on LAT1 mRNA, we observed only a modest decrease in LAT1 protein levels in mouse brain vessels at 24 h after LPS injection. This varies from the robust reduction in OATP1c1 protein levels observed 24 h following LPS, but is similar to MCT8 protein that remains stable in vessels \[[@CR10]\]. The time of delay between the decrease in mRNA and protein levels probably reflects the half-life of the protein, in this case suggesting a high stability for LAT1 protein in brain vessels. Indeed, a half-life of several days is not uncommon for plasma membrane proteins \[[@CR40]--[@CR47]\]. Therefore, it is conceivable that LAT1 protein in brain vessels is more robustly depleted during sustained inflammation caused by an actual bacterial infection, the course of which can take several days or weeks.
Future studies will also be necessary to determine whether LAT1 transport function in brain vessels decreases in short-term and/or prolonged inflammatory conditions. The rate of LAT1-mediated amino-acid transport across the blood--brain barrier depends on the number of functional LAT1 proteins in the luminal and abluminal surfaces of endothelial cell membranes \[[@CR18]\]. LAT1-mediated transport is considered to be saturated at physiological serum amino acid concentrations \[[@CR29], [@CR48]--[@CR50]\]. Therefore, fewer LAT1 proteins in endothelial membranes would likely result in reduced LAT1-mediated amino acid transport. It is possible that by the internalization of LAT1 from the membrane to intracellular pools, LAT1-mediated transport decreases while the amount of LAT1 protein remains stable. Determining the subcellular distribution of transporters in brain endothelial cells is challenging using conventional immunofluorescence techniques \[[@CR18]\]. As a result, we could not determine whether the distribution of LAT1 shifts between cellular compartments. Nevertheless, our results raise the possibility that LAT1 transport function could decrease, even if only days after the onset of inflammation. Since both the amino acids substrates of LAT1 and TH are necessary for normal brain function, their reduced uptake could impede certain neural processes, perhaps contributing to reduced cognitive function, a general symptom of inflammatory infections. Whether reduced LAT1 transport is an adaptive response following the initial phase of inflammation and/or during the actual recovery phase, or maladaptive, remains to be understood.
Conclusions {#Sec18}
===========
LPS-induced inflammation caused a robust decrease in LAT1 mRNA expression at the blood--brain barrier of rodents, and a modest decrease in LAT1 protein content. This finding, along with previous results on TH transporters, suggests that systemic inflammation simultaneously down-regulates the mRNA expression of different transport systems of the blood--brain barrier but the kinetics of changes at the level of transporter proteins are different. The results imply that the transport rates of various substances across the blood--brain barrier, such as amino acids and hormones, may be significantly altered during inflammation.
Additional files {#Sec19}
================
Additional file 1:Immunoblotting Methods.Additional file 2:Validation of the specificity of the LAT1 antiserum. (A) Western blot from the rat midbrain, mouse hypothalamus and mouse cortex; the LAT1 antiserum recognized a single band corresponding to a protein that migrates with the molecular weight of approximately 46 kDA. Loading control is glyceraldehyde 3-phosphate dehydrogenase (GAPDH). (B-D) LAT1 immunofluorescence and radioactive LAT1 in situ hybridization were performed in adjacent sections to show the high specificity of LAT1 immunostaining. (B, C) Both LAT1 immunofluorescence and in situ hybridization labeled the subcomissural organ (SCO) in both mice (B) and rats (C). (D) In rats, a group of cells with intense LAT1 immunofluorescent and in situ hybridization signals were located around the caudal portion of the choroid plexus of the dorsal third ventricle (d3v cp). Scale bar = 100 µm.
MCT8
: monocarboxylate transporter 8
LAT1
: [l]{.smallcaps}-type amino acid transporter 1
LAT2
: [l]{.smallcaps}-type amino acid transporter 2
OATP1c1
: organic anion-transporting polypeptide 1c1
TH
: thyroid hormone
GW designed the study, carried out the in situ hybridization and immunofluorescence experiments and drafted the manuscript. PM and BG designed and cloned the LAT1 and LAT2 fragments and revised the manuscript critically. MYB carried out the Western blot and revised the manuscript critically. RML supervised the study, helped draft the manuscript and revised it critically. All authors read and approved the final manuscript.
Acknowledgements {#d30e1121}
================
This work was supported by a Grant from the Dr. Gerald J. and Dorothy R. Friedman New York Foundation for Medical Research to RML, and a Hungarian Scientific Research Fund Grant OTKA109415 to BG.
Compliance with ethical guidelines {#d30e1126}
==================================
**Competing interests** The authors declare that they have no competing interests.
| {
"pile_set_name": "PubMed Central"
} |
Understanding intimate partner violence dynamics using mixed methods.
Trauma research has employed both quantitative and qualitative methods, but only recently, have mixed method studies begun to appear in the trauma literature. The purpose of this case series was to demonstrate the value of mixed method approaches to studying dynamics among cases involving intimate partner violence (IPV). Of the 16 women in abusive relationships who completed daily reports of the household violence and environment over an 8-week period, three cases were chosen for discussion because they provided near complete quantitative data, rich qualitative data, and a "clear" dynamic pattern. These three cases demonstrate that, through the combination of quantitative and qualitative methods, a rich picture of individual IPV dynamics can be obtained, often unique to the marital relationship and context. | {
"pile_set_name": "PubMed Abstracts"
} |
The packaging of items not only protects the item from the environment up to the point of use but also often provides information about the safe use of the item.
This is especially true for pharmaceuticals where the packaging contains information about the application of the pharmaceutical, and have a registration number to identify the pharmaceutical, expiration date for quality control, a charge or lot number to allow traceability and often also a barcode for machine readability. The packaging also provides protection of the pharmaceutical against environmental influences to prevent deterioration between the moment of production and the moment of application (administering).
A common type of packaging for one or more doses is a blister. This is basically a cavity formed around the pharmaceutical dose by two layers that are meet around the dose and form a seal where they meet. The dose can be removed from the cavity by applying pressure to one side of the cavity and either forcing the seal apart or fracturing or rupturing of one of the two layers.
A typical blister has a rupturable surface on the back of the blister made of a thin metal foil. Pharmaceuticals are known to be repackaged. In such a repackaging operation either the entire non-severed blister with multiple doses is being inserted into a new external package or the dose is being removed from the blister and put into another blister or a container of another kind.
Repackaging introduces problems in the traceability of the pharmaceuticals.
To provide room for extra information while leaving the manufacturer's packaging intact U.S. Pat. No. 8,403,212 discloses an information card for attaching to a blister holding an item such as a pharmaceutical dose. The information card comprises a rim area around an opening in the information card for attaching the information card to the blister, the opening allowing the information card to be positioned around the item. This allows additional information to be added to the blister while leaving the protective blister intact.
Such information cards allow proper tracking of the item in the blister in factories, during transport, in the shop but also for instance in a hospital environment where closed loop administration of pharmaceuticals improves patient safety.
In U.S. Pat. No. 8,403,212 an information card is attached to the manufacturer's intact packaging. The information card provides the information about the pharmaceutical with each individual dose in order to ensure the correct administering of the pharmaceutical to the patient.
As the information card disclosed in U.S. Pat. No. 8,403,212 holds a single dose it has the disadvantage that the information card must be handled individually, introducing the risk of loss. | {
"pile_set_name": "USPTO Backgrounds"
} |
"There's a theory that every time you leave an area, you always leave evidence behind, no matter what, no matter how careful you are; and that's why there's forensics" (Santy, 2007). Forensic science has seen a number of major developments over the years. Throughout its evolution, analytic techniques have become finer tuned and accurate, allowing for much greater law enforcement practices. Today, forensics relies of a plethora of techniques to help solve crimes, as seen in the case of "Welcome to Homicide."
Forensic science is not new, although it does look dramatically different that just a few decades ago. The research suggests that "forensic science resolves legal issues by applying scientific principles to them" (Hall, 1999, p 2). It is a technique used by law enforcement to help solve crimes through examining physical and biological indicators of who did what. As, such, the analysis of forensic scientists involves "a variety of sciences, mathematical principles, and problem solving methods, including the use of complex instruments; chemical, physical, and microscopic examining techniques; and reference literature" (Hall, 1999, p 3). The very first forensic lab was set up by French scientist Edmond Locard in 1910, and the discipline has grown dramatically in just over a century. Since its humble beginnings, forensic science has developed rapidly, especially since the inception of DNA testing in the mid 1980s. All these evolutions led to the type of analysis that was seen in the case study discussed here.
"Welcome to Homicide" is a real case which took place in Richmond, Virginia. In the episode, a black male had been found in the trunk of a car. The body had been there for clearly over 24 hours, and he was stripped naked. There was no visual trauma at the initial search, and the body was loosely wrapped with a comforter and trash bags with duct tape around the hands and legs. Although the initial search could not determine the exact cause of death, it definitely signified to detectives that they were dealing with a homicide case.
The episode, "Welcome to Homicide" employs modern tactics of investigation, but also some that have been used for generations. For example, the case illustrated the use of a K-9 as a way to possibly catch on a scent that would lead to further evidence. According to the research, "Europeans have been using scent-discriminating canines in criminal investigations for more than 100 years" (Stockham, Slavin, & Kift, 2004, p 1). The detective believed that the victim was murdered elsewhere and then brought to the scene of the crime. As such, the bloodhound K-9 unit was brought in to hopefully lead onto a scent. The bloodhound was given a piece of gauze that sat in the care for ten minutes to marinate in the scent. The officers had hoped that the dog would find the scent of the individual. The bloodhound tracked a scent to an apartment that was extremely close by, only a few meters away from where the car was initially found. The detectives smelled a strong odor of cleaning products, which made the situation much more suspicious. A search warrant was acquired and police units went to execute it in order to search more into the apartment. Detectives believed that the suspect found in the apartment was just using similar cleaning products that were used in the car where the victim was found, but they believed that he had no part in the murder that had taken place just outside of his apartment walls. Personally, I believe that this may not have been necessary, as it only led to a dead end. It is clear that "because human scent is easily transferred from one person or object to another, it should not be used as primary evidence" (Stockham, Slavin, & Keft, 2004, p 1). I understand that detectives were trying to use all they initially had to find more leads; yet at the same time, modern research has proven the use of K-9 units can be problematic.
Additionally, fingerprint testing was used throughout the investigation in a number of instances. Fingerprinting was a true revolution in forensic analysis. It is also known as Dactylography and its roots go as far back as ancient China (Swanson, Chamelin, & Territo, 2003). Its modern usage was revolutionized by the Henry System, which was a type of classification system that helped establish the earliest use of fingerprinting as a Western criminal investigation tactic. A cooperative network of law enforcement agencies was first established by the California Bureau of Criminal Identification in 1905, which "was set up to share information about criminal activity" (Swanson, Chamelin, & Territo, 2003, p 6). As developments in fingerprinting continued to evolve, so did the databases that kept their records for police to use in various organizations. The detectives in this particular case had the luxury of a large database, instantly accessible to fingerprint documents from around the nation. This is an example of an older method of analysis has been recently transformed by the evolution of technologies used to collect crime scene evidence. Here, the research suggests that "digital technology allows crime lab professionals to compare prints at a rate of 400,000 per second," whereas in previous generations, detectives often had to manually search and compare fingerprints without the help of computer technology (Hall, 1999, p 5). As such, the modern team in the video used fingerprinting on a number of different situations, including the car the victim was found in, as well as the suspect's house and car.
Moreover, firearms identification is another strong and traditional technique that has been used by detectives for generations, and was also used in the context of this case.
In 1913, Professor Balthazard "noted that the firing pin, breechblock, extractor, and ejector all leave marks on cartridges and that these vary among different types of weapons" (Swanson, Chamelin, & Territo, 2003, p 14). The process of "firearms examination involves matching identifying characteristics between a firearm and a projectile and between projectile and target. Typically, this includes matching bullets to the gun that fired them" (Hall, 1999, p 4). From this, computer technologies have helped the process of identifying small and unique differences on bullets pulled from crime scenes. Riffling characteristics have different widths that are unique to each fire arm. The fragments of the bullets were extracted from the victim's skull in order to determine the caliber. Investigators were able to determine that both bullets were 9 mm caliber. Additionally, the forensic examiner determined that both bullets had been fired by the same gun
There needed to be a full documentation of the crime scene prior to the car being transported to the homicide head quarters for further forensic investigation. After the vehicle was transported to the coroner's office, an autopsy took place. The medical examiner found that the victim had perished because of two gun shot wounds to the head. There was one lethal shot that went through the brain, and then another shot that went through the mouth and fractured the vertebrae. The close range of the shot indicates that the victim probably knew the person who killed him. Which wound may have been first needed to be determined by examining the nature of each wound. If the wounds are close enough, the fracture of the second blow would stop at the first fracture. However, the wounds were too far from one another to use that method. As such, there was gun power residue and stippling at the mouth, indicating that the muzzle was between two to four feet away. The medical examiner believed that the mouth shot was the first, and then the suspect shot again in the victim's head as he fell over, dead.
The car was also searched thoroughly. A search warrant was needed to search the car, which was eventually acquired. This would be the only leads that would tie in another individual to the crime. Someone had to drive the car to that particular location, and thus the search was aiming to find the driver. Pictures were taken thoroughly. Then, the entire car was swabbed in order to uncover any DNA evidence. Luminal was sprayed on the vehicle to find any evidence of blood under a UV light. There was blood found on the front of the dashboard, the stick shift, and on the wheel. The victim's own blood and fingerprints were present in the car, which is obvious because it was his car. No other definitive evidence was found in the car that would point to another individual being present for the crime.
In order to further this investigation, DNA tactics were employed. According to the research, "DNA analysis determines how frequently parts of a person's genetic code are found in the population; forensic scientists isolate that person's unique DNA to the DNA of a sample of others" (Hall, 1999, p 3). DNA is a relatively recent testing method that began to become increasingly popular in…[continue]
Other Documents Pertaining To This Topic
If the temperature is taken miles away, or if the insect that was found and studied was not exactly the same as one that had been studied before, only similar perhaps, the defense attorney will also often argue that the entomologist's testimony is only guesswork, and therefore that it is not valid and should not be admitted as evidence (Sachs, 1998). Judges have taken different approaches about whether to allow
Workplace violence in the United States has become widespread. According to the Department of Labor and Industries, homicide, is the fourth-leading cause of fatal injury. Statistics claim that workplace homicides declined one percent in 2009. Though workplace violence is a rare occurrence, recognizing the signs and emphasizing the safety of employees is paramount to preventing violence in the workplace.
The workplace culture consists of different personalities, often labeled, introvert or extrovert.
Jews desperately sought entrance into the City of Spring, but the British stood firm on their proclamation, fearing Arab backlash. "The Nazis kill us," the Jews cried, "and the British won't let us live."
In 1945, the world discovered that its greatest fear had come true: the Nazi death camps all over Europe, ripe with the massacre of the Jewish people, cemented the Zionist call in those who lived. "Israelis
Productivity-Education/Craft/Trade -- a key to being able to stop the return to the penal system is to provide training necessary to allow the individual to find work after leaving prison. Not only is it extremely tough to get a job as a convicted felon, but the skills necessary to get a job that will afford a decent living are tough to get in prison. Earning a degree either online or
Obamacare good for the economy?
The issue must be looked at from three points-of-view, One the development that goes on in the health care and how the policy ahs affected the health care industry and particularly various sections of the society, secondly the economic changes and developments that have come about in the medical care industry, and the burden and changes in the nations economy as a whole and whether
This population already had issues such as crime, poverty and unemployment in the city from which they came. When evacuees relocated to Houston these problems were simply brought with them and they were magnified because of the circumstances surrounding the relocation.
Conclusion
The purpose of this discussion was to examine the impact of citizen displacement on cities such as Houston and San Antonio, Texas. In particular we focused on the rising
The benefit of creating the term at this point is that lawmakers and prosecutors and defense lawyers will all be aware of the growth of the term as it moves through the judicial birth canal and is delivered in its full meaning, with all its parts in working order and ready to be tested at trial.
Draft Corporate Manslaughter Bill
Important as the corporate manslaughter bill is to many people, it | {
"pile_set_name": "Pile-CC"
} |
Q:
Hedetniemi's conjecture for the coloring number
Hedetniemi's conjecture is about the chromatic number of the categorical product of simple, finite, undirected graphs $G, H$ : it claims that $\chi(G\times H) = \min \{\chi(G), \chi(H)\}$.
For any simple, undirected graph $G=(V,E)$ we set $\text{col}(G) = \sup\{\delta(H): H\subseteq G\}+1$, where $\delta(\cdot)$ denotes the minimal degree. We have $\chi(G) \leq \text{col}(G)$ for any graph $G$.
Do we have $\text{col}(G\times H) = \min\{\text{col}(G), \text{col}(H)\}$ for all $G, H$?
A:
No. If $H=G=K_d$, $\text{col}(G)=d$, but $G\times G$ is a regular graph of degree $(d-1)^2$, thus $\text{col}(G\times G)\geqslant (d-1)^2+1>d$ for $d\geqslant 3$.
| {
"pile_set_name": "StackExchange"
} |
Speakers or headphones for gaming?
One of the debates I often have with fellow gamers is whether you should use external speakers or a pair of headphones while gaming. This week, I'm bringing the debate to TechSpot through the Weekend Open Forum.
I've always been an advocate of gaming through speakers. Grabbing a solid set of 5.1 channel surround speakers can give you a multi-dimensional, immersive sound experience in games. Without having the audio drivers affixed to your head, your gaming experience can be more comfortable and your ears can breathe. And with a good subwoofer, you can feel the explosions.
But there are also good points to gaming with headphones. The close proximity of drivers to your ears can give you cleaner sound, with less interference and the potential for noise cancelation. Headphones are also portable, easier to set up, have fewer wires, use less power and can contain a nearby microphone for crisp team chat.
Let me know your preferences in the comments below, and feel free to give your recommendations for the best speakers or headphones out there.
Cheap: grover 2.1 speaker system (made in china, re-branded by cdr king for Philippine market), less than 15$ , perfect for my cheap needs.
(as a person suffering from partial hearing loss, I doubt I will have a better experience if I buy/use an expensive speaker system)
When the wife is away the cat will play... I turn up the speakers all the way!!! =) When the wife is near I put the on the headphones which she bought me. I use some nice Altec Lansing speakers and Turtle Beach Seven Headphones. I love them both =)
It's all a matter of circumstances, choice and preference.
Personally I use nothing but headsets (Roccat Kave XTD stereo & HyperX Cloud). I love my gaming but I have my 95 year old mother, my wife, and often my grandkids staying with me over weekends, I can't have them listening to the foul language, violence and gunshots in a lot of my games.
If I was a young bachelor living by myself I would definitely have opted for a 5.1 channel surround sound speaker setup for gaming.
I own a Logitech Z906 speaker system and it's connected to my PVR & TV and does a stellar job by the way.
Cheap: grover 2.1 speaker system (made in china, re-branded by cdr king for Philippine market), less than 15$ , perfect for my cheap needs.
(as a person suffering from partial hearing loss, I doubt I will have a better experience if I buy/use an expensive speaker system)
Click to expand...
Wouldn't you be able to hear better with a headset?... My sister is quite deaf but she reckons headphones makes her hearing aids distort the sound.
Just as most pointed out, it all depends on the particular situation. I typically game with headphones(Sennheiser HD 600 or my Sennheiser G4me One). But, I do have a decent set of 5.1 speakers for when no-one is around and I can let them loose.
As others have stated, it's a matter of situation. Generally speaking, I prefer headphones because they provide better immersion and surround quality. If I am playing a game where that isn't important or if I need to be aware of my physical environment (phone calls, etc.), speakers are the go-to option. I also prefer to use earbuds rather than proper headphones.
If I was a young bachelor living by myself I would definitely have opted for a 5.1 channel surround sound speaker setup for gaming.
I own a Logitech Z906 speaker system and it's connected to my PVR & TV and does a stellar job by the way.
Click to expand...
I don't game much, but I am a bachelor and have a pretty nice 5.1 system for HT. Problem is, I live in a 4-plex apt, so I can't fully utilize it very often. I have some BeyerDynamic DT 880 headphones (250 ohm) for the times where I want to hear something loud but without getting the authorities called.
I currently use the Audio-Technica ATH-M40X, which is cheaper but much more balanced than the more popular, and relatively bass-heavy, M50X. Occasionally I also use Thinksound ts02 IEMs.
This is so I don't bother anyone with the sound. I've never lived by myself, I lived with my parents until finishing high school, and since starting college I rent rooms on student appartments and stuff like that. Because of this, I never really grew the habit of using speakers, and used headphones all my life.
Future plans include a Xonar DX sound card and a nice pair of open headphones, like the HD 598. But still no speakers.
I don't game much, but I am a bachelor and have a pretty nice 5.1 system for HT. Problem is, I live in a 4-plex apt, so I can't fully utilize it very often. I have some BeyerDynamic DT 880 headphones (250 ohm) for the times where I want to hear something loud but without getting the authorities called.
Click to expand...
They sound like very nice headphones especially with that high resistance but I'm a very poor example of an audiophile, the sound quality would probably escape me.
Razer Caraharias headphones for me, very comfortable to wear even when wearing glasses. I do have a logitech 5500 system but I find wearing headphones is less distracting and I can get on with the pew pew stuff.
I've spent big on the visuals but stuff all on the audio. The main sound hardware is from 1986 and it emits a hum, yet I prefer that over a headset. I dislike hardware attached to my head. Glasses are bad enough. My Logitech G930 headset is alright for those nighttime BF4 sessions. I really do need a better speaker system. I guess it's back to reading reviews...
Speakers, but I really want one of the headsets recently review here, specially the Polk Striker P1, they seemed awesome. Right now I have the Logitech live chat, they aren't great so I only use them when playing online with friends.
If I'm on my laptop I either use my Sony MDR-V6s with velour earpad swap or my new AKG K7XXs and I would use headphones on my desktop if I'm doing something competitive but otherwise I use my old set of Yamaha 2.1 speakers which are still pretty good.
I, for one, find the vibration delivered from subwoofers very unpleasant. So, I only use my 2.1 edifier x100 when the missus insists on watching my latest performance on whatever it is I'm playing at the moment.
The other 99% of the time, I'm wearing my Audio-Technica ATH-ANC7B with Noise-Cancelling enabled specifically so that I won't hear anything but my game, be it her calling me to help her with some mundane task or my neighbor lecturing her daughter on the importance of not losing the toothpaste cap...
I've seen some people complaining about headphones being uncomfortable and making their heads hot. I shave my head bald twice a week, so I've never had such problem.
But by the end of the day I'd say the sound from headphones is way more clean than any speakers I've known. | {
"pile_set_name": "Pile-CC"
} |
JAMES TURRELL : QUAKER MEETING HOUSE
If you’ve never been to the Chestnut Hill neighborhood of Philadelphia YOU. ARE. MISSING. OUT! Take a quintessential main street, add historic cobblestones, great restaurants and adorable shops and you have perfection.
The Chestnut Hill Friends Meeting House is located on Mermaid Lane, walkable from the main drag of town. It is a space for those of the Quaker faith community to meet and reflect in a peaceful setting and also provides a home to a piece by the artist James Turrell.
The Skyspace at Chestnut Hill Quaker Meeting House
20 E. Mermaid Lane
Philadelphia, PA 19118-3507
Now the meeting house serves it’s main purpose of providing a space for prayer and reflection, but it also serves as the home to one of my favorite artist’s works called Skyspace by James Turrell.
Turrell’s work focuses on the use of light, space and color providing it’s own setting for reflection. Each Sunday, the meeting house opens up it’s doors to provide a sunset light show open to people of all faiths.
“With its constantly changing effects, the Turrell encourages pure sensory absorption. You want to take in every subtle shift in what you are seeing and sensing; talk and reason just seem to get in the way.”
The show is viewed through a retractable ceiling in the sanctuary providing a open air space that coincides with a light sequence timed at sunset. You are able to sit in a pew, in the windowsills, or even lie on the floor. The space is completely silent and you can hear chirping birds, see the clouds moving through the sky, which take on the light that is being bounced around the sanctuary.
Please note that on days of inclement weather, the roof is not retracted, which provides just an indoor light sequence. Although this isn’t a fully sensory experience, it provides a completely different type of resolve and relaxation. You can make reservations online here.
It’s truly one of the most cleansing and relaxing art experiences I have ever experienced. I highly recommend going to see a Turrell exhibition whenever you are able. The mesmerizing installation is a sanctuary for anyone who values quiet contemplation and stunning visual beauty.
The Artful Epicure by T R A C Y
I strive to continuously explore new places and take in amazing art and food along the way. Always one for a contemporary art exhibit or to try a hip new restaurant and I want to take you along for the ride. Get some tips, tricks and suggestions for your upcoming travels. | {
"pile_set_name": "Pile-CC"
} |
The Goldbergs 2013 Season 6 Episode 20 (S06E20) WEB Download Torrent
The Dropouts are thrilled when they book a gig at a Flyers charity carnival, and Adam uses the opportunity to make his very first rockumentary. Since Barry doesn't want to miss out on the fun, he forces his way into the band, despite his sister's objections. Meanwhile, Beverly's concerns about Murray's health push him to the limit. | {
"pile_set_name": "Pile-CC"
} |
Q:
Storing date as integer (numeric), what are the advantages
Question 1
I am working with a system where date is stored as integer (actual numeric(8,0)) and I have noticed that other systems also store date as int such as cisco in this thread. Example
20120101 -- 01 Jan 2012
Is there any advantage of keeping numeric date system and not using SQL Datetime?
Question 2
Now I am trying to loop through numeric date to find customers between two dates. If the start and enddate encompass two months, I get thousands of records instead of just 60. Example:
create table #temp1(day int,capacity int) /* just a temp table */
declare @start int
declare @end int
set @start=20111201
set @end = 20120131
while (@start <= @end)
Begin
insert into #temp1 /* I am storing things in #temp table so data looks pretty */
exec usp_GetDailyCap @date1= @start
set @start = @start + 1;
end
select * from #temp1
This pulls 8931 records instead of 60. Is there a better way to improve the logic above so I pull only valid dates? I tried IsDate and sub-queries but that did not quite work in an efficient way.
A:
To answer your first question, I would recommend using the DATETIME data type within SQL Server. Not necessarily for performance reasons, but to leverage the RDBMS-specific functionality. For instance, you would have to re-invent a lot of logic just to do basic date math (think DATEDIFF(), DATEADD(), DATEPART() and many other functions. They are obviously tailored to the DATETIME data type and are easy to work with).
As for your second question, you are running into the exact problem that the first question (and my answer) is geared towards. You are looking at 20111201 and 20120131 as dates, and your brain is telling you that should be a difference of 60 days. Well, you're looping through based off of the delta...which is:
20120131 - 20111201 = 8930 (with the inclusive loop it'll be 8931)
In other words, your WHILE loop is executing 8931 times. This is happening because those are integer values and your loop will not jump from 20111231 straight to 20120101.
You integers aren't going to take into account the cap of years and months (i.e. your Question 2 problem).
A:
Ralph Kimball recommends storing dates as integers. He has written a lot, both online articles and books.
You can use a calendar table and issue consecutive numbers to your dates, as follows:
Date Number
20120229 1234
20120301 1235
The calendar table has to be generated, but it is a very easy task.
A:
Potential data types and their sizes/limitations:
Decimal(8,0): 5 bytes
Date: 3 bytes, 0001-01-01 through 9999-12-31
Int: 4 bytes
Pros for numeric data type:
They look pretty?
Cons for numeric data type:
Requires custom code for handling date operations
Requires custom code to manage correct dates (ie, not allowing 20120230 [Feb 30th, 2012])
Larger data footprint when compared to the Date data type.
Honestly, you're better off using the date data type IMHO.
| {
"pile_set_name": "StackExchange"
} |
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd">
<!-- NewPage -->
<html lang="en">
<head>
<!-- Generated by javadoc -->
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<title>RestServer (operator-runtime 2.1 API)</title>
<link rel="stylesheet" type="text/css" href="../../../../stylesheet.css" title="Style">
<script type="text/javascript" src="../../../../script.js"></script>
</head>
<body>
<script type="text/javascript"><!--
try {
if (location.href.indexOf('is-external=true') == -1) {
parent.document.title="RestServer (operator-runtime 2.1 API)";
}
}
catch(err) {
}
//-->
var methods = {"i0":9,"i1":9,"i2":9,"i3":10,"i4":10};
var tabs = {65535:["t0","All Methods"],1:["t1","Static Methods"],2:["t2","Instance Methods"],8:["t4","Concrete Methods"]};
var altColor = "altColor";
var rowColor = "rowColor";
var tableTab = "tableTab";
var activeTableTab = "activeTableTab";
</script>
<noscript>
<div>JavaScript is disabled on your browser.</div>
</noscript>
<!-- ========= START OF TOP NAVBAR ======= -->
<div class="topNav"><a name="navbar.top">
<!-- -->
</a>
<div class="skipNav"><a href="#skip.navbar.top" title="Skip navigation links">Skip navigation links</a></div>
<a name="navbar.top.firstrow">
<!-- -->
</a>
<ul class="navList" title="Navigation">
<li><a href="../../../../overview-summary.html">Overview</a></li>
<li><a href="package-summary.html">Package</a></li>
<li class="navBarCell1Rev">Class</li>
<li><a href="class-use/RestServer.html">Use</a></li>
<li><a href="package-tree.html">Tree</a></li>
<li><a href="../../../../deprecated-list.html">Deprecated</a></li>
<li><a href="../../../../index-all.html">Index</a></li>
<li><a href="../../../../help-doc.html">Help</a></li>
</ul>
</div>
<div class="subNav">
<ul class="navList">
<li><a href="../../../../oracle/kubernetes/operator/rest/RestConfigImpl.html" title="class in oracle.kubernetes.operator.rest"><span class="typeNameLink">Prev Class</span></a></li>
<li><a href="../../../../oracle/kubernetes/operator/rest/Scan.html" title="class in oracle.kubernetes.operator.rest"><span class="typeNameLink">Next Class</span></a></li>
</ul>
<ul class="navList">
<li><a href="../../../../index.html?oracle/kubernetes/operator/rest/RestServer.html" target="_top">Frames</a></li>
<li><a href="RestServer.html" target="_top">No Frames</a></li>
</ul>
<ul class="navList" id="allclasses_navbar_top">
<li><a href="../../../../allclasses-noframe.html">All Classes</a></li>
</ul>
<div>
<script type="text/javascript"><!--
allClassesLink = document.getElementById("allclasses_navbar_top");
if(window==top) {
allClassesLink.style.display = "block";
}
else {
allClassesLink.style.display = "none";
}
//-->
</script>
</div>
<div>
<ul class="subNavList">
<li>Summary: </li>
<li>Nested | </li>
<li>Field | </li>
<li>Constr | </li>
<li><a href="#method.summary">Method</a></li>
</ul>
<ul class="subNavList">
<li>Detail: </li>
<li>Field | </li>
<li>Constr | </li>
<li><a href="#method.detail">Method</a></li>
</ul>
</div>
<a name="skip.navbar.top">
<!-- -->
</a></div>
<!-- ========= END OF TOP NAVBAR ========= -->
<!-- ======== START OF CLASS DATA ======== -->
<div class="header">
<div class="subTitle">oracle.kubernetes.operator.rest</div>
<h2 title="Class RestServer" class="title">Class RestServer</h2>
</div>
<div class="contentContainer">
<ul class="inheritance">
<li><a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">java.lang.Object</a></li>
<li>
<ul class="inheritance">
<li>oracle.kubernetes.operator.rest.RestServer</li>
</ul>
</li>
</ul>
<div class="description">
<ul class="blockList">
<li class="blockList">
<hr>
<br>
<pre>public class <span class="typeNameLabel">RestServer</span>
extends <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></pre>
<div class="block">The RestServer runs the WebLogic operator's REST api.
<p>It provides the following ports that host the WebLogic operator's REST api:
<ul>
<li>external http port - this port can be used both inside and outside of a Kubernetes cluster.
<li>external https port - this port can be only be used outside of a Kubernetes cluster since
its SSL certificate contains the external hostnames for contacting this port.
<li>internal https port - this port can only be used inside of a Kubernetes cluster since its
SSL certificate contains the the in-cluster hostnames for contacting this port.
</ul></div>
</li>
</ul>
</div>
<div class="summary">
<ul class="blockList">
<li class="blockList">
<!-- ========== METHOD SUMMARY =========== -->
<ul class="blockList">
<li class="blockList"><a name="method.summary">
<!-- -->
</a>
<h3>Method Summary</h3>
<table class="memberSummary" border="0" cellpadding="3" cellspacing="0" summary="Method Summary table, listing methods, and an explanation">
<caption><span id="t0" class="activeTableTab"><span>All Methods</span><span class="tabEnd"> </span></span><span id="t1" class="tableTab"><span><a href="javascript:show(1);">Static Methods</a></span><span class="tabEnd"> </span></span><span id="t2" class="tableTab"><span><a href="javascript:show(2);">Instance Methods</a></span><span class="tabEnd"> </span></span><span id="t4" class="tableTab"><span><a href="javascript:show(8);">Concrete Methods</a></span><span class="tabEnd"> </span></span></caption>
<tr>
<th class="colFirst" scope="col">Modifier and Type</th>
<th class="colLast" scope="col">Method and Description</th>
</tr>
<tr id="i0" class="altColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../oracle/kubernetes/operator/rest/RestServer.html#create-oracle.kubernetes.operator.rest.RestConfig-">create</a></span>(<a href="../../../../oracle/kubernetes/operator/rest/RestConfig.html" title="interface in oracle.kubernetes.operator.rest">RestConfig</a> restConfig)</code>
<div class="block">Create singleton instance of the WebLogic Operator's RestServer.</div>
</td>
</tr>
<tr id="i1" class="rowColor">
<td class="colFirst"><code>static void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../oracle/kubernetes/operator/rest/RestServer.html#destroy--">destroy</a></span>()</code>
<div class="block">Release RestServer singleton instance.</div>
</td>
</tr>
<tr id="i2" class="altColor">
<td class="colFirst"><code>static <a href="../../../../oracle/kubernetes/operator/rest/RestServer.html" title="class in oracle.kubernetes.operator.rest">RestServer</a></code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../oracle/kubernetes/operator/rest/RestServer.html#getInstance--">getInstance</a></span>()</code>
<div class="block">Accessor for obtaining reference to the RestServer singleton instance.</div>
</td>
</tr>
<tr id="i3" class="rowColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../oracle/kubernetes/operator/rest/RestServer.html#start-oracle.kubernetes.operator.work.Container-">start</a></span>(<a href="../../../../oracle/kubernetes/operator/work/Container.html" title="class in oracle.kubernetes.operator.work">Container</a> container)</code>
<div class="block">Starts WebLogic operator's REST api.</div>
</td>
</tr>
<tr id="i4" class="altColor">
<td class="colFirst"><code>void</code></td>
<td class="colLast"><code><span class="memberNameLink"><a href="../../../../oracle/kubernetes/operator/rest/RestServer.html#stop--">stop</a></span>()</code>
<div class="block">Stops WebLogic operator's REST api.</div>
</td>
</tr>
</table>
<ul class="blockList">
<li class="blockList"><a name="methods.inherited.from.class.java.lang.Object">
<!-- -->
</a>
<h3>Methods inherited from class java.lang.<a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true" title="class or interface in java.lang">Object</a></h3>
<code><a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#equals-java.lang.Object-" title="class or interface in java.lang">equals</a>, <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#getClass--" title="class or interface in java.lang">getClass</a>, <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#hashCode--" title="class or interface in java.lang">hashCode</a>, <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#notify--" title="class or interface in java.lang">notify</a>, <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#notifyAll--" title="class or interface in java.lang">notifyAll</a>, <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#toString--" title="class or interface in java.lang">toString</a>, <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#wait--" title="class or interface in java.lang">wait</a>, <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#wait-long-" title="class or interface in java.lang">wait</a>, <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Object.html?is-external=true#wait-long-int-" title="class or interface in java.lang">wait</a></code></li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
<div class="details">
<ul class="blockList">
<li class="blockList">
<!-- ============ METHOD DETAIL ========== -->
<ul class="blockList">
<li class="blockList"><a name="method.detail">
<!-- -->
</a>
<h3>Method Detail</h3>
<a name="create-oracle.kubernetes.operator.rest.RestConfig-">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>create</h4>
<pre>public static void create(<a href="../../../../oracle/kubernetes/operator/rest/RestConfig.html" title="interface in oracle.kubernetes.operator.rest">RestConfig</a> restConfig)</pre>
<div class="block">Create singleton instance of the WebLogic Operator's RestServer. Should only be called once.</div>
<dl>
<dt><span class="paramLabel">Parameters:</span></dt>
<dd><code>restConfig</code> - - the WebLogic Operator's REST configuration. Throws IllegalStateException if
instance already created.</dd>
</dl>
</li>
</ul>
<a name="getInstance--">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>getInstance</h4>
<pre>public static <a href="../../../../oracle/kubernetes/operator/rest/RestServer.html" title="class in oracle.kubernetes.operator.rest">RestServer</a> getInstance()</pre>
<div class="block">Accessor for obtaining reference to the RestServer singleton instance.</div>
<dl>
<dt><span class="returnLabel">Returns:</span></dt>
<dd>RestServer - Singleton instance of the RestServer</dd>
</dl>
</li>
</ul>
<a name="destroy--">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>destroy</h4>
<pre>public static void destroy()</pre>
<div class="block">Release RestServer singleton instance. Should only be called once. Throws IllegalStateException
if singleton instance not created.</div>
</li>
</ul>
<a name="start-oracle.kubernetes.operator.work.Container-">
<!-- -->
</a>
<ul class="blockList">
<li class="blockList">
<h4>start</h4>
<pre>public void start(<a href="../../../../oracle/kubernetes/operator/work/Container.html" title="class in oracle.kubernetes.operator.work">Container</a> container)
throws <a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Exception.html?is-external=true" title="class or interface in java.lang">Exception</a></pre>
<div class="block">Starts WebLogic operator's REST api.
<p>If a port has not been configured, then it logs that fact, does not start that port, and
continues (v.s. throwing an exception and not starting any ports).</div>
<dl>
<dt><span class="paramLabel">Parameters:</span></dt>
<dd><code>container</code> - Container</dd>
<dt><span class="throwsLabel">Throws:</span></dt>
<dd><code><a href="https://docs.oracle.com/javase/8/docs/api/java/lang/Exception.html?is-external=true" title="class or interface in java.lang">Exception</a></code> - if the REST api could not be started for reasons other than a port was not
configured. When an exception is thrown, then none of the ports will be leftrunning,
however it is still OK to call stop (which will be a no-op).</dd>
</dl>
</li>
</ul>
<a name="stop--">
<!-- -->
</a>
<ul class="blockListLast">
<li class="blockList">
<h4>stop</h4>
<pre>public void stop()</pre>
<div class="block">Stops WebLogic operator's REST api.
<p>Since it only stops ports that are running, it is safe to call this even if start threw an
exception or didn't start any ports because none were configured.</div>
</li>
</ul>
</li>
</ul>
</li>
</ul>
</div>
</div>
<!-- ========= END OF CLASS DATA ========= -->
<!-- ======= START OF BOTTOM NAVBAR ====== -->
<div class="bottomNav"><a name="navbar.bottom">
<!-- -->
</a>
<div class="skipNav"><a href="#skip.navbar.bottom" title="Skip navigation links">Skip navigation links</a></div>
<a name="navbar.bottom.firstrow">
<!-- -->
</a>
<ul class="navList" title="Navigation">
<li><a href="../../../../overview-summary.html">Overview</a></li>
<li><a href="package-summary.html">Package</a></li>
<li class="navBarCell1Rev">Class</li>
<li><a href="class-use/RestServer.html">Use</a></li>
<li><a href="package-tree.html">Tree</a></li>
<li><a href="../../../../deprecated-list.html">Deprecated</a></li>
<li><a href="../../../../index-all.html">Index</a></li>
<li><a href="../../../../help-doc.html">Help</a></li>
</ul>
</div>
<div class="subNav">
<ul class="navList">
<li><a href="../../../../oracle/kubernetes/operator/rest/RestConfigImpl.html" title="class in oracle.kubernetes.operator.rest"><span class="typeNameLink">Prev Class</span></a></li>
<li><a href="../../../../oracle/kubernetes/operator/rest/Scan.html" title="class in oracle.kubernetes.operator.rest"><span class="typeNameLink">Next Class</span></a></li>
</ul>
<ul class="navList">
<li><a href="../../../../index.html?oracle/kubernetes/operator/rest/RestServer.html" target="_top">Frames</a></li>
<li><a href="RestServer.html" target="_top">No Frames</a></li>
</ul>
<ul class="navList" id="allclasses_navbar_bottom">
<li><a href="../../../../allclasses-noframe.html">All Classes</a></li>
</ul>
<div>
<script type="text/javascript"><!--
allClassesLink = document.getElementById("allclasses_navbar_bottom");
if(window==top) {
allClassesLink.style.display = "block";
}
else {
allClassesLink.style.display = "none";
}
//-->
</script>
</div>
<div>
<ul class="subNavList">
<li>Summary: </li>
<li>Nested | </li>
<li>Field | </li>
<li>Constr | </li>
<li><a href="#method.summary">Method</a></li>
</ul>
<ul class="subNavList">
<li>Detail: </li>
<li>Field | </li>
<li>Constr | </li>
<li><a href="#method.detail">Method</a></li>
</ul>
</div>
<a name="skip.navbar.bottom">
<!-- -->
</a></div>
<!-- ======== END OF BOTTOM NAVBAR ======= -->
<p class="legalCopy"><small><p>Copyright 2018, 2019, <a href="http://www.oracle.com">Oracle Corporation</a> and/or its affiliates. All rights reserved. <br />Licensed under the Universal Permissive License v 1.0 as shown at <a href="http://oss.oracle.com/licenses/upl">http://oss.oracle.com/licenses/upl</a>.<p></small></p>
</body>
</html>
| {
"pile_set_name": "Github"
} |
Q:
Why is ICommunicationListener.Abort() continuously invoked?
Below is Stateless Service listener code running in a local SF cluster and listening to a Service Bus Queue.
All I want is to continuously listen to queue commands in an always-on SF service. Code improvement hints are welcome!
Problem #1
Abort() is continuously called, effectively closing my connection. What is causing this behavior and how do I fix it? In my understanding Abort() is supposed to be called only in case of unhandled exceptions or forced closure, neither of which I am aware of.
Bonus Problem
Say we comment out the CloseClient call from Abort(), which allows our queue to be processed correctly. After the 1st message the CancellationToken's WaitHandle is marked as disposed and passing it into my callback throws an exception. What is causing this?
Thanks for your help!
using System;
using System.Threading;
using System.Threading.Tasks;
using Microsoft.ServiceBus.Messaging;
using Microsoft.ServiceFabric.Services.Communication.Runtime;
namespace Common
{
public class QueueListener : ICommunicationListener
{
private readonly string _connectionString;
private readonly string _path;
private readonly Action<BrokeredMessage> _callback;
private QueueClient _client;
public QueueListener(string connectionString, string path, Action<BrokeredMessage> callback)
{
// Set field values
_connectionString = connectionString;
_path = path;
// Save callback action
_callback = callback;
}
public Task<string> OpenAsync(CancellationToken cancellationToken)
{
// Connect to subscription
_client = QueueClient.CreateFromConnectionString(_connectionString, _path);
// Configure the callback options
var options = new OnMessageOptions
{
AutoComplete = false
};
// Catch and throw exceptions
options.ExceptionReceived += (sender, args) => throw args.Exception;
// Wire callback on message receipt
_client.OnMessageAsync(message =>
{
return Task.Run(() => _callback(message), cancellationToken)
.ContinueWith(task =>
{
if (task.Status == TaskStatus.RanToCompletion)
message.CompleteAsync();
else
message.AbandonAsync();
}, cancellationToken);
}, options);
return Task.FromResult(_client.Path);
}
public Task CloseAsync(CancellationToken cancellationToken)
{
CloseClient();
return Task.FromResult(_client.Path);
}
public void Abort()
{
CloseClient();
}
private void CloseClient()
{
// Make sure client is still open
if (_client == null || _client.IsClosed)
return;
// Close connection
_client.Close();
_client = null;
}
}
}
A:
The cancellation token passed to OpenAsync is not intended to be used outside of the method scope, like it is now. You're passing it to the OnMessage. OnMessage will be invoked after OpenAsync is called, but the token is disposed after OpenAsyn completes.
Create a new CancellationToken, or use this nuget package should help here.
A:
The problem was the whole concept behind creating an ICommunicationListener to interface with a Service Bus; the listener isn't listening to anything!
Refactoring the Service Bus connection into the default RunAsync() method inside the StatelessService implementation fixes the issue and allows monitoring the cancellation token as expected.
| {
"pile_set_name": "StackExchange"
} |
// ------------------------------------------------------------
// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT License (MIT). See License.txt in the repo root for license information.
// ------------------------------------------------------------
#pragma once
namespace TStoreTests
{
using namespace ktl;
using namespace Data::TStore;
using namespace TxnReplicator;
template<typename TKey, typename TValue>
class WriteTransaction :
public KObject<WriteTransaction<TKey, TValue>>,
public KShared<WriteTransaction<TKey, TValue>>
{
K_FORCE_SHARED(WriteTransaction)
public:
__declspec(property(get = get_TransactionSPtr)) TxnReplicator::Transaction::SPtr TransactionSPtr;
TxnReplicator::Transaction::SPtr get_TransactionSPtr() const
{
return transactionSPtr_;
}
__declspec(property(get = get_StoreTransactionSPtr)) KSharedPtr<Data::TStore::StoreTransaction<TKey, TValue>> StoreTransactionSPtr;
KSharedPtr<Data::TStore::StoreTransaction<TKey, TValue>> get_StoreTransactionSPtr() const
{
return storeTransactionSPtr_;
}
__declspec(property(get = get_StateProviderSPtr)) KSharedPtr<Data::TStore::Store<TKey, TValue>> StateProviderSPtr;
KSharedPtr<Data::TStore::Store<TKey, TValue>> get_StateProviderSPtr() const
{
return stateProviderSPtr_;
}
static NTSTATUS
Create(
__in Data::TStore::Store<TKey, TValue>& stateProvider,
__in TxnReplicator::Transaction& transaction,
__in Data::TStore::StoreTransaction<TKey, TValue> const & storeTransaction,
__in KAllocator& allocator,
__out SPtr& result)
{
NTSTATUS status;
SPtr output = _new(STORE_TAG, allocator) WriteTransaction(stateProvider, transaction, storeTransaction);
if (!output)
{
return STATUS_INSUFFICIENT_RESOURCES;
}
status = output->Status();
if (!NT_SUCCESS(status))
{
return status;
}
result = Ktl::Move(output);
return STATUS_SUCCESS;
}
ktl::Awaitable<LONG64> CommitAsync()
{
NTSTATUS status = co_await transactionSPtr_->CommitAsync();
Diagnostics::Validate(status);
co_return transactionSPtr_->CommitSequenceNumber;
}
ktl::Awaitable<LONG64> AbortAsync()
{
co_await suspend_never();
NTSTATUS status = transactionSPtr_->Abort();
Diagnostics::Validate(status);
co_return 0;
}
void Dispose()
{
transactionSPtr_->Dispose();
}
private:
WriteTransaction(
__in Data::TStore::Store<TKey, TValue>& stateProvider,
__in TxnReplicator::Transaction& transaction,
__in Data::TStore::StoreTransaction<TKey, TValue> const & storeTransaction);
// Hardcoded for tstore now
KSharedPtr<Data::TStore::Store<TKey, TValue>> stateProviderSPtr_;
TxnReplicator::Transaction::SPtr transactionSPtr_;
KSharedPtr<Data::TStore::StoreTransaction<TKey, TValue>> storeTransactionSPtr_;
};
template <typename TKey, typename TValue>
WriteTransaction<TKey, TValue>::WriteTransaction(
__in Data::TStore::Store<TKey, TValue>& stateProvider,
__in TxnReplicator::Transaction& transaction,
__in Data::TStore::StoreTransaction<TKey, TValue> const & storeTransaction)
:stateProviderSPtr_(&stateProvider),
transactionSPtr_(&transaction)
{
KSharedPtr<Data::TStore::StoreTransaction<TKey, TValue> const> storeTransactionCSPtr = &storeTransaction;
storeTransactionSPtr_ = (const_cast<Data::TStore::StoreTransaction<TKey, TValue>*>(storeTransactionCSPtr.RawPtr()));
}
template <typename TKey, typename TValue>
WriteTransaction<TKey, TValue>::~WriteTransaction()
{
transactionSPtr_->Dispose();
}
}
| {
"pile_set_name": "Github"
} |
6 Scientific Reasons Social Networks Are Bad for Society
We've always known that computer networks would destroy the world. We just thought they'd get super-intelligent first. Instead, we got social networks, which act as a stupidity X-ray: You suddenly see through the intelligent people your friends pretend to be to the LOLing Farmville players underneath. Some smart people decided to study these networks, and found that they're a bigger threat to society than Skynet. At least the rise of those machines forced us to band together and do things.
More real social interaction than all of MySpace.
Everyone (Correctly) Assumes You're an Egocentric Asshole
Narcissism is excessive self-love, inflated self-importance and unjustified feelings of entitlement. Along with electrons, it is the primary active ingredient in the Internet. Three years ago, psychologists decided to publish a research paper on its prevalence on social networking sites, presumably because they didn't think anyone would read the entire set of encyclopedias they could have filled, and simply publishing the words "Everything on all of them" felt too glib.
Researchers had 156 students fill out a survey called the Narcissistic Personality Inventory (NPI) that forces subjects to choose between options like, "My body is nothing special" versus "I like to look at my body," and "I can learn from other people" versus "I can solve most global problems by spitting on them." Researchers then monitored the student's Facebook activity for what they called objective and subjective factors, and compared that with how they scored on the NPI. The scientists' goal was to see if they could isolate social networking behaviors that were more narcissistic, and to boil down complex human emotions into numbers, because that's like oxygen to them.
Getty CreativeAn 8.7 on the It-normalized Birthday Trauma scale according to Science.
The scientists also got strangers to rate these profiles online, and an above-average 100 of the students were female so the scientists clearly know how to get strangers to look at things online. The nine scales used included Attractiveness, Sexiness, Provocativeness and Fun. There's a chance these "scientists" were Internet-porn's R&D division.
For users of social networking, the results were not encouraging. Narcissism ratings were higher in every single category, including how narcissistic people assume you are just for having an account. Posting large amounts of information on your profile page was both perceived as narcissistic by others, and more common among narcissists. According to the study, a typical interaction on a social networking site is like a whirlwind of self-obsessed assholery: You think you're just filling out a profile, but others (correctly) assume you're an asshole for expecting strangers to care about your forty favorite movies despite doing the exact same thing themselves. So everyone is thinking, Look at this douchebag talking about things that aren't me.
Meanwhile, people viewing your profile encourage your narcissism. For instance, another big indicator was "provocative pictures," aka "You're not fooling anyone by casually posting pictures like that." Strangers realize you desperately want people to stare at you (while staring at you).
The only negative correlation was "entertaining quotes," implying that people who post funny material online are the opposite of narcissistic. Which might mean "hate themselves." Short form: If you don't think you're inherently worth looking at, you try to be funny instead. You now understand stand-up comedy.
Thousands of Friends Means None
Photos.com
"The relationship between number of friends and interpersonal impressions on Facebook"
Journal of Computer-Mediated Communication 13 (2008) 531-549
If someone tells you they have 4,000 friends, chances are they're including you as one of them despite having just made sure it's not the case. When you hit four digits, you have a worse definition of friends than Boo Radley, and he still spent time interacting with his friends. Michigan State University researchers studied the relationship between number of friends and actual popularity, and found that the fourth digit of friends means you're likely getting the two longest digits on the hand from a good portion of them. We not only know you don't have three thousand friends, which is stupid, but we automatically know you don't even have three or you wouldn't have time to sit clicking "Add Friend" every night.
Getty CreativeGod, I wish my son would go out and take drugs. Maybe get some girls pregnant.
One-hundred and fifty-three students filled out surveys and rated fake Facebook profiles on social and physical attractiveness. These fake profiles were identical except for the number of friends listed. The scientists noticed a hill-shaped relationship between friends and attractiveness: Having more friends means you're more attractive, up to what they mysteriously failed to call the "Bullshit Threshold." At a certain point (around a thousand friends) you start looking as bad as people with only few, and even more desperate.
This is what it looks like when a scientist calls you NEEEERRRRRRD!
The scientists also analyzed the participating students. One claimed to have over 2,700 friends, and the scientists added a footnote with all the statistics re-calculated without that person. Even in a study about how many friends imaginary accounts could pretend to have, the researchers looked at this asshole and said, "They're so stupid it's throwing off our math."
Getty EditorialThey also confirmed Tila Tequila as the most unpopular person on the planet.
They're Reinstalling Sexism
Photos.com
"The Role of Friends' Appearance and Behavior on Evaluations of Individuals on Facebook: Are We Known by the Company We Keep?"
Human Communication Research 34 (2008) 28-49
Obviously, negative gender stereotypes exist on the Internet, because it's 90 percent porn. But at least they're getting paid for it. Every other woman gets it for free. Judging others by a picture is apparently a recipe for turning people into assholes -- interacting with a monitor and keyboard means people feel less empathy. They also don't bother pretending to be nice, which is a pity, because "pretending to be nice" is pretty much what made the nonwarring part of human history possible.
commons.wikipedia.orgReversing the polarity of "civil."
A group of 389 students got course credit for letting older men and women watch them use the Internet, so that's good future career training (they were all taking "communications degrees" so it's nice to have options other than communicating a request for fries with that). Just like all innocent scientific experiments involving groups of teenagers, the results were horrifying: enough sexism to make Sterling Cooper look like the Mother Goddess Freegan Collective.
If you sit on me we use less sofa material, saving the environment.
The researchers set up fake Facebook profiles for student girls who got trashed and slept with nasty slobs (it's nice to see science is only a few years behind porn technology) and their research paper explained, "Typographical errors in these messages were intentional and reflect common writing characteristics in Facebook postings." Well done, Internet, you now write so poorly, literate people have to explain it to each other. They then set up the exact same profiles with pictures of guys. The result?
Translation: guys are studs, girls are sluts, what else is new? But the scientists were worried that Facebook is resurrecting more ancient sexism than a group of cheerleaders having a sleepover in Castle Dracula. With more people interacting online every day, externality of gonads is once again becoming a disproportionately advantageous factor. Especially considering how it's a weak point in any style of combat. | {
"pile_set_name": "Pile-CC"
} |
Introduction
============
Previous studies have shown that Human's visual system can simultaneously keep track of several discrete moving objects ([@B16]; [@B18]; [@B19]; [@B20]; [@B4]). They provided evidence that in the multiple object tracking (MOT) task, observers can localize a number of independently and unpredictably moving identical targets in a field of identical distractors. Researchers also pointed out that the attentive tracking in the MOT task was object-based, that is, attention must be allocated to the objects rather than the "substance" that extended and contracted during motion ([@B20]) or the arbitrary collection of features ([@B19]). Using the dual-task paradigm of the MOT and the probe dot detection task, [@B15] found that the probe on the targets was detected better than that in the space of near-targets, and the probe on the distractors was detected worse than that in the space of near-distractors, suggesting that both the attentional enhancement of targets and the attentional inhibition of distractors during tracking are also highly localized object-based.
In the earlier MOT task, the targets and distractors are all identical. That is, observers must monitor the trajectories of the moving targets constantly to localize them. However, recent research has considered whether objects were content-addressable during attentive tracking when objects differentiated from each other with unique identities or surface features, and whether objects' identities or surface features had influence on attentive tracking. [@B14] in his study indicated that observers had difficulty identifying the targets even if they could successfully track their locations. However, the major reason of this result might be that the identities of targets were presented only briefly at the targets designation stage, but not in the tracking phase, making the maintenance of targets' identities decayed during tracking. On the contrary, later studies in which objects' identities or surface features were presented throughout the tracking phase showed that identities did exert an influence on the object-based attentive tracking, even when the identities of objects were not relevant to the task demand ([@B4]; [@B8],[@B9]; [@B5]). For instance, [@B4] used cartoon animals as tracking stimuli and found that observers' tracking performance improved when the objects were changed from identical objects or animals shared by the distractors to unique animals. That is, observers had an access to objects' identities during tracking and utilized their uniqueness to aid tracking. [@B8],[@B9]) showed that observers' tracking performance was enhanced when the objects were of unique colors or 1-digit numbers, relative to that when the objects consisted of the same features or when the targets' features paired with the distractors. And they revealed the cause to be the visual working memory mechanism operating parallel to the attentive tracking. Specifically, observers can store the targets' unique identities into the visual working memory, once one or more targets were lost during tracking, they could search for and find them back based on the initially stored identities. However, later studies provided evidence that not all uniqueness of identities could facilitate tracking. When the objects carried on complex identities, such as numbers of three- or four-digit length, complex Chinese characters and human faces, the uniqueness of identities would impair tracking ([@B17]; [@B7]). One possible explanation is that the processing of complex identities consumed extra resources and had a small capacity in visual working memory ([@B7]).
Recent studies demonstrated the feature-based grouping effect in the MOT task ([@B2]; [@B23]). They found that when all targets shared one feature and all distractors shared another---for instance, all targets were red circles and all distractors were green circles---observers' tracking performance could be enhanced. Furthermore, when the targets belonged to one semantic category (e.g., animals) and the distractors belonged to another (e.g., furniture), even when they all had unique identities, this categorical distinction between the targets and distractors could also aid location tracking and suggested a semantic category-based grouping mechanism ([@B26], [@B25], [@B24]).
In light of the above findings, objects' simple unique identities or features can facilitate location tracking in the MOT task, even when their identities or features are irrelevant to the task demand. That is, the processing of identities or features is involuntary and to some extent at an implicit level ([@B4]; [@B1]).
Previous research mainly manipulated the uniqueness of objects' simple surface features (e.g., color) or identities (e.g., unique animals) to test their effects on attentional tracking. But it is unknown which aspect of the visual objects, the local or global properties, played the main role in the uniqueness-facilitation effect. According to the global precedence hypothesis in the framework of Gestalt psychology ([@B11]; [@B22]), a visual object can be viewed as represented by a hierarchical network with two levels, the global properties corresponds to the top level of the hierarchy while the local properties corresponds to the bottom level of the hierarchy. The present study did not concentrate on the order of processing of a visual object, but mainly explored the following issues: Did a "global advantage" also exist in the MOT task? That is, could the uniqueness of global properties produce much stronger tracking facilitation effect than that of local properties? Could the uniqueness of local properties facilitate object-based tracking? To test these issues, two experiments were conducted: Experiment 1 used the Navon-type compound stimuli ([@B11]) and tested whether the global or local properties played a major role in facilitating tracking. Experiment 2 used the sparse compound stimuli to further explore the same questions.
There are the two reasons why we choose the compound stimuli as tracking stimuli in the MOT task. First, the compound stimuli can be equated across stimuli in terms of complexity, familiarity, codability and identifiability ([@B13]; [@B22]). Second, the real-world stimuli's wholistic properties and component properties vary on a number of factors, making it hard to manipulate their homogeneity or heterogeneity. On the contrary, the compound stimuli have two distinct levels of structure---global configuration and local elements, which are relative independent ([@B6]; [@B13]), thus they provide a convenient way to segregate the global and local properties and test their respective effects on tracking.
Experiment 1
============
Experiment 1 aimed to test two questions: (a) Could the uniqueness of objects' local properties facilitate tracking? (b) Did global properties or local properties play the main role in facilitating tracking? The compound stimuli were used as tracking stimuli. The uniqueness of local properties, of global properties or of both of them varied across four conditions.
Methods
-------
### Participants
The sample sizes in the present study were decided mainly by reference to previous research, in which there are usually 10--20 participants for the MOT task. Variability in the sample size of each experiment reflects the variability of available participants in the participant pool. A prior power calculation was also conducted investigating the required sample sizes ([@B3]). Since the MOT task was adapted from our previous research ([@B24]), which has found effect sizes (partial $\eta_{p}^{2}$) in repeated measures ANOVA of 0.50 or larger. To obtain a power of 90% at $\eta_{p}^{2}$ = 0.50, a sample of 5 was required.
According to standard practice, 19 students (10 female, 9 male), 18--26 years old (mean age = 22.00, *SD* = 2.11) with normal or corrected-to-normal vision, participated in the experiment. Two participants' data was excluded from analyzing for whose tracking accuracies were under 50%. All observers provided informed written consent. The study was approved by the institutional review board (ethics committee) of the Faculty of Psychology at Beijing Normal University. All observers received payment for their time.
### Equipment and Stimuli
#### Equipment
The experimental task was controlled by software written in Microsoft Visual Basic.NET (version 2013). The stimuli were presented on a Founder 17-in. CRT monitor with a resolution of 1024 pixels × 768 pixels and a refreshing rate of 85 Hz. Observers responded by pressing buttons on a keyboard and a mouse.
#### Stimuli
Moving stimuli were presented in a white, rectangle display that subtended 1024 pixels × 768 pixels (40.96° × 30.72°). A gray cross subtended 30 pixels × 30 pixels (1.2° × 1.2°) was presented in the center of the display as the fixation. The compound stimuli were lager letters (the global level) composed of small identical letters (the local level). The eight lager letters were A, E, F, H, L, S, T, and V, which consisted of the same small letters of A, E, F, H, L, S, T, and V. Thus, there were totally 64 compound stimuli. The unitary stimuli were eight capital letters. The larger letters measured 90 pixels (3.6°) vertically, and the smaller letters measured about 11 pixels (0.45°) vertically.
The stimuli moved at a constant speed of 17°/s. A repulsion technique was adopted in order to keep the stimuli from colliding. The stimuli bounced off each other when their center-to-center distance was less than 90 pixels. They also avoided the edge of the display area.
### Design
In the current study, we mainly manipulated the uniqueness of local properties or global properties between the targets and distractors through five conditions: homogeneous, local uniqueness, global uniqueness, local and global uniqueness, and unitary uniqueness. In the homogeneous condition, all stimuli as targets and distractors consisted of the same global letter composed of the same local letter, e.g., a large letter of "A" that composed of small letter of "A." The same one compound stimulus where the global letter and local letter were congruent in each trial was chosen randomly from the eight congruent large letters (A, E, F, H, L, S, T, and V). The homogeneous condition provided the performance baseline for comparison. In the local-uniqueness condition, all the eight stimuli were the same global letter, which consisted of different local letters, respectively. That is, the global properties of the stimuli were the same but their local properties were distinct. In the global-uniqueness condition, the eight stimuli were different global letters consisted of the same local letters. That is, the stimuli were the same at the local level but different at the global level. In the local-and-global uniqueness condition, the eight stimuli were different global letters which was composed of different local letters, respectively. That is, the objects' global and local properties were both distinct. In the unitary-uniqueness condition, the eight objects were different unitary letters. [Table 1](#T1){ref-type="table"} presents the details of the experiment design. The dependent variable was tracking accuracy, defined as the average proportion of correctly identified targets.
######
The five conditions of Experiment 1.
Procedures
----------
Observers sat about 55--60 cm away from the monitors while the chair was kept in a fixed position. Observers were required to reduce their head motion and to keep still during the whole experiment. Although a chin rest was not used, at this viewing distance, each pixel could be seen as subtending approximately 0.04 degrees of the visual angle. At the start of each trial, a gray fixation cross and eight pictures were displayed. No special instructions were given concerning fixation. Four of eight pictures, as the targets, flashed five times in 1 s, when the observers could identify and distinguish them from the distractors. Then all of the pictures began to move randomly and unpredictably, and the movement stopped at a random point within 5--8 s. At the same time of motion ending, the pictures were masked by gray squares subtending 90 pixels × 90 pixels (3.6° × 3.6°). The observers selected all four targets with the mouse within 20 s. The selected objects were surrounded by red frames. Observers pressed the space bar to continue to the next trial (see the sample trial procedure in [Figure 1](#F1){ref-type="fig"}). The experiment consisted of totally 100 trials (20 trials × 5 conditions) that presented randomly.
{#F1}
Results and Discussion
----------------------
[Figure 2](#F2){ref-type="fig"} presents the results of Experiment 1. A repeated measures analysis of variance (ANOVA) indicated a significant main effect \[*F*(4,64) = 37.070, *p* \< 0.001, $\eta_{p}^{2}$ = 0.699, Power (1--β) \> 99%\]. *Post hoc* tests with Bonferroni correction revealed that the tracking accuracy of observers in the local-uniqueness condition was significantly higher than the accuracy in the homogeneous condition \[local-uniqueness vs. homogeneous: *t*(16) = 3.415, *p* = 0.035 (Bonferroni adjusted *p*-value, the same below), Cohen's *d* = 0.53\], providing evidence that the distinctiveness of the objects' local properties could facilitate observers' tracking when their global properties were identical. There was no significant difference among the global-uniqueness, local-and-global uniqueness, and unitary-uniqueness conditions with pairwise comparison (all *p* = 1.000). Furthermore, the tracking accuracies in these three conditions were all significantly higher than those in the homogeneous condition and the local-uniqueness condition \[global-uniqueness vs. homogeneous: *t*(16) = 6.207, *p* \< 0.001, Cohen's *d* = 2.11; local-and-global uniqueness vs. homogeneous: *t*(16) = 8.105, *p* \< 0.001, Cohen's *d* = 1.98; unitary-uniqueness vs. homogeneous: *t*(16) = 7.676, *p* \< 0.001, Cohen's *d* = 2.40; global-uniqueness vs. local-uniqueness: *t*(16) = 5.267, *p* = 0.001, Cohen's *d* = 1.72; local-and-global uniqueness vs. local-uniqueness: *t*(16) = 6.847, *p* \< 0.001, Cohen's *d* = 1.57; unitary-uniqueness vs. local-uniqueness: *t*(16) = 6.543, *p* \< 0.001, Cohen's *d* = 2.01\]. These results suggest that the distinctiveness of global properties of compound stimuli could be recognized by observers during motion and facilitated the tracking performance to the accuracy level as in the unitary-uniqueness condition. Since observers' tracking performance in the local-and-global uniqueness condition did not improve upon the global-uniqueness condition, we inferred that observers mainly used the uniqueness of global properties to aid tracking.
{#F2}
Experiment 2
============
In Experiment 2, we used the sparse compound stimuli composed of fewer local elements to answer the same questions as in Experiment 1. Previous research has revealed that stimulus sparsity can determine the relative ease of processing global and local properties of compound stimuli. The global identities of compound stimuli with few local elements may be more difficult for observers to extract than those with many local elements ([@B10]; [@B12]; [@B6]). We tested that when the global identities were difficult to retrieve and recognize, whether the uniqueness of global properties or that of local properties could facilitate object-based tracking.
Methods
-------
### Participants
Twenty-two students (16 female, 6 male), 18--28 years old (mean age = 21.14, *SD* = 2.68) with normal or corrected-to-normal vision, participated in the experiment. None of them had participated in Experiment 1. Other particulars were the same as in Experiment 1.
### Design, Equipment, Stimuli and Procedures
The design, equipment and procedures were the same as those of Experiment 1, except that the sparse compound stimuli patterns with fewer local elements were used (see [Tables 2](#T2){ref-type="table"}, [3](#T3){ref-type="table"} for more details). The total number of local elements was decreased from 90 in Experiment 1 to 55 in Experiment 2. Furthermore, the stimuli's moving speed decreased from 17°/s in Experiment to about 14.5°/s in Experiment 2.
######
The number of the local elements in Experiments 1 and 2.
Experiment 1 Experiment 2
--- -------------- --------------
A 10 8
E 17 10
F 13 7
H 13 7
L 8 5
S 11 8
T 9 5
V 9 5
######
The five conditions of Experiment 2.
Results and Discussion
----------------------
[Figure 3](#F3){ref-type="fig"} shows the results from Experiment 2. A repeated measures ANOVA indicated a significant main effect \[*F*(4, 84) = 43.729, *p* \< 0.001, $\eta_{p}^{2}$ = 0.676, Power (1--β) \> 99%\]. *Post hoc* tests with Bonferroni correction showed that the tracking accuracy of observers in the unitary-uniqueness condition was significantly higher than the accuracies in all the other four conditions \[unitary-uniqueness vs. homogeneous: *t*(21) = 10.328, *p* \< 0.001 (Bonferroni adjusted *p*-value, the same below), Cohen's *d* = 1.71; unitary-uniqueness vs. local-uniqueness: *t*(21) = 8.930, *p* \< 0.001, Cohen's *d* = 1.66; unitary-uniqueness vs. global-uniqueness: *t*(21) = 8.262, *p* = 0.001, Cohen's *d* = 1.45; unitary-uniqueness vs. local-and-global uniqueness: *t*(21) = 7.496, *p* = 0.001, Cohen's *d* = 1.30\]. The tracking accuracy in the local-and-global uniqueness condition was significantly higher than that in the homogeneous condition \[*t*(21) = 3.884, *p* = 0.009, Cohen's *d* = 0.43\]. One exception is that, pairwise comparisons between the homogeneous, local-uniqueness, global-uniqueness and local-and-global uniqueness conditions showed no significant difference (*p*s \> 0.05). These results suggest that when both the local and global properties of the sparse compound stimuli were distinct from each other, observers' tracking performance showed a significant improvement compared to the homogeneous condition (5.09% of increment in tracking accuracy). We did not find a significant facilitation effect of the unique local properties or unique global properties under the current experiment situations. However, since the tracking loads of the present MOT task were at the moderate level (the tracking accuracies were from 69 to 75% in the four compound stimuli conditions), the results might be different when the tracking loads were lower or higher. Therefore, it would be helpful to test this issue under different tracking loads or different task difficulties in the future. Moreover, results of Experiment 2 showed different conclusions from that of Experiment 1. The detailed reasons of these discrepant results will be further discussed in the general discussion section.
{#F3}
General Discussion and Conclusion
=================================
The present study used compound stimuli and tested whether the global or local properties played the main role in the uniqueness-facilitation effect in the MOT task. In light of the results from Experiment 1, we infer that the distinctiveness of local properties can facilitate tracking when the global identities of the compound stimuli are identical, even the facilitation is small (4.15% of increment in tracking accuracy relative to the homogeneous condition). However, when the stimuli's global properties are distinct from each other---whether the local properties being unique or not---observers' tracking performance can be as good as that in the unitary-uniqueness condition. Results from Experiment 2 show that in the sparse compound stimuli situations, a uniqueness-facilitation effect was identified under the condition when both the local and global properties were distinct from each other. However, the unique local properties or unique global properties alone did not show any significant facilitation effect on observers' tracking performance in the current experiment. The present study revealed that both the unique local properties and the unique global properties could facilitate tracking when the compound stimuli consisted of many local elements, but the global properties played the main role in the uniqueness-facilitation effect.
The Effect of Unique Local Properties on Tracking
-------------------------------------------------
The present study demonstrated that when the compound stimuli with many local elements had identical global properties, their distinct local properties could slightly facilitate tracking. Specifically, when the global properties of the compound stimuli were undistinguishable, the unique local properties could be used to aid tracking. This finding suggests that in the dynamic scenes, the uniqueness of the bottom level in the hierarchical network (i.e., local properties) could be captured and utilized during tracking. However, this uniqueness-facilitation effect of the local properties seemed to be apparent only when the global properties were identical. When the global properties of the compound stimuli were distinct, observers mainly used the unique global identities to aid tracking. This claim comes from two pieces of evidence: one is that observers' tracking performance in the global-uniqueness condition was significantly better than that in the local-uniqueness condition. The other is that the tracking accuracies in the local-and-global uniqueness condition and the global-uniqueness had no significant difference. Our results also suggest that the uniqueness-facilitation effect of the local properties seems not to be additive, since the tracking accuracy in the global-uniqueness condition (82.38%) was close to the tracking accuracy in the local-and-global uniqueness condition (81.25%). Furthermore, the lack of additivity cannot be ascribed to floor/ceiling effects because observers' tracking performance in Experiment 1 ranged from 64 to 84%.
The Global Superiority Effect in the MOT Task
---------------------------------------------
As mentioned above, when the global properties of the compound stimuli were distinct from each other, observers mainly relied on the unique global identities to aid tracking (Results of Experiment 1). These results reveal a global superiority effect in the MOT task. That is, the uniqueness of the global properties or the uniqueness of the configurations plays a major role in facilitating tracking.
One might argue that the global superiority effect only exists because the size of the global configuration was much larger than that of the local elements, which is a fact of nature since the global properties are properties of a higher-level unit in the hierarchical patterns ([@B13]; [@B22]). However, the global configurations of the sparse compound stimuli in Experiment 2 had the same sizes as that of the compound stimuli in Experiment 1, but no global superiority effect was found in the global-uniqueness condition. Therefore, this alternative explanation of relative size of global and local properties could be ruled out to some extent. We conjecture that the global superiority effect is based on the same mechanism of how unique features or identities facilitate tracking ([@B8],[@B9]; [@B7]). This mechanism might consist of two stages: in the first stage, observers perceived the compound stimuli as the meaningful objects and retrieved their global identities. In the second stage, these global identities could be stored in visual working memory. When one or more targets were lost during tracking, observers could use the stored identities to find them back ([@B4]; [@B8],[@B9]). But of course, this hypothesis will need to be verified in future studies.
One issue we noticed is that results of Experiment 1 revealed a global superiority effect, while no significant facilitation effect of unique global properties on tracking was found in Experiment 2. The major difference between Experiments 1 and 2 is the adopted compound stimuli. Specifically, the compound stimuli in Experiment 1 consisted of more local elements while the compound stimuli in Experiment 2 consisted of fewer local elements. Thus, the number of local elements might exert an influence on the global superiority effect. Although lacking sufficient empirical evidence from the current study, we speculate that when the compound stimuli has many local elements, the contour of the global letters is better, making it easy for the observers to extract their identities and aid tracking. On the contrary, when the compound stimuli composes of few local elements, the contours of their global structures lack tight connection, which might constrain the observers from recognizing their global forms and retrieving their identities ([@B10]; [@B12], [@B13]). This speculation could also be further tested in our next study.
The global superiority effect in the MOT task suggests that: on one hand, observers may mainly rely on visual objects' global properties to retrieve and recognize their identities in dynamic scenes; on the other hand, the grouping principles of proximity and good continuation for contour integration ([@B21]) may also be applied in the motion scenes. While the visual elements are with proximity and good continuation (e.g., the compound stimuli with many local elements in Experiment 1), observers may be able to integrate their contours and retrieve their global identities even when the visual patterns are in a continuous and random motion.
Although the present study used compound stimuli similar to [@B11], the goal of the present study was not to explore the orders of processing of the global and local properties, or their interference with each other. Therefore, we will not discuss more about the processing mechanism of compound stimuli. Compared with real-world stimuli, the compound stimuli provide an elegant way to manipulate the distinctiveness of the local and global properties, respectively, except that, the other factors could be manipulated to be comparable across stimuli. However, the lack of external validity with the compound stimuli and the corresponding conclusions need to be further explored in future studies.
Ethics Statement
================
This study was carried out in accordance with the recommendations of 'the institutional review board (ethics committee) of the Faculty of Psychology at Beijing Normal University' with written informed consent from all subjects. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the institutional review board (ethics committee) of the Faculty of Psychology at Beijing Normal University.
Author Contributions
====================
LW and XZ conceived and designed the experiments. LW performed the experiments and analyzed the data. LW, XZ, ZL, BH, and XL contributed to the writing of the manuscript.
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.
**Funding.** This study was supported by the General Program of National Natural Science Foundation of China (Grant No. 31271083), by the Key Program of National Natural Science Foundation of China (Grant No. 61632014), and by Open Research Fund of the State Key Laboratory of Cognitive Neuroscience and Learning (Grant No. CNLZD1804).
[^1]: Edited by: Guomei Zhou, Sun Yat-sen University, China
[^2]: Reviewed by: Dan McCarthy, Western Oregon University, United States; Ken Kihara, National Institute of Advanced Industrial Science and Technology (AIST), Japan
[^3]: This article was submitted to Cognition, a section of the journal Frontiers in Psychology
| {
"pile_set_name": "PubMed Central"
} |
Tobacco use is a leading contributor to racial and socioeconomic health disparities in the US primarily due to an unequal burden of tobacco-related disease from a disproportionate share of smokers in lower socioeconomic (SES) groups in which minorities, particularly African Americans, are disproportionately represented.1-5 Although deemed effective for all smokers,6 the standard cognitive-behavioral treatment for tobacco dependence is significantly less effective for lower SES smokers.7-15 Tobacco dependence treatment, however, has the potential to reduce racial and socioeconomic disparities in achieving long-term abstinence by proactively providing our most at-risk smokers with the specific treatment components they need to achieve abstinence through the existing extensive treatment delivery system.16, 17 Our preliminary studies indicate that in addition to several socio-cultural barriers to engaging in treatment,18 there are several key factors associated with socioeconomic disparities in relapse rates and thus treatment outcomes. These factors include: stress, negative affect, smoking in response to negative affect, delay discounting, locus of control, impulsiveness, exposure to smokers in the environment, and treatment utilization (see Table 1).19, 20 Based on this and other evidence, our overall goal is to revise the standard treatment with specific, evidence-based, cognitive-behavioral strategies to address these key factors as well as target and tailor the approach to more fully meet the needs of lower SES and minority smokers, thereby reducing treatment outcome disparities. We expect: 1) The revised treatment (RT) to reduce socioeconomic disparities in treatment outcomes, and 2) Participants treated with the RT to demonstrate more improvement on each of the key factors associated with disparities than those treated with standard treatment (ST). The specific aims include: 1) Complete a revised draft of a widely utilized standard treatment manual that addresses each of the key factors with treatment components. This aim is partially accomplished (see Appendix for preliminary draft). 2) Using the PEN-3 Model,21-23 target and tailor the daft RT to more fully represent the experiences of smokers who are of lower SES and /or of minority status, particularly African American smokers. 3) Pilot test the targeted/tailored draft RT with three treatment groups (n=5-10 per group) to assess understandability and acceptability and to ensure that it can be delivered in the same timeframe as the ST. 4) Compare the effects of SES on treatment outcomes with socioeconomically and racially diverse participants treated with ST (n=110) and RT (n=110) in a randomized treatment design. 5) Compare the effects of treatment condition on each of the key factors. This innovative approach refines, improves upon, and applies theoretically derived and empirically supported concepts and strategies. If effective at reducing treatment outcome disparities, the manual-driven RT will be easily disseminable as a new standard, having a sustained and powerful impact on the field and contributing to a reduction in the magnitude of the present tobacco-related racial and socioeconomic health disparities. | {
"pile_set_name": "NIH ExPorter"
} |
Search form
Search
Cops Corner
Siesta Key
Thursday, May. 24, 2012
3 years ago
Cops Corner: Pelican Press
Share
by:
Observer Staff
May 11RUDE MANNERS
7:49 p.m. — corner of Gleason Avenue and Reid Street.Driving Under the Influence. An officer pulled over a man driving on Ocean Boulevard without a seatbelt. When the officer approached the car, he noticed the man was eating a grilled steak with his hands and smoking a cigarette at the same time. The man was asked three times to put down the steak and cigarette and exit the vehicle, however, he kept trying to bring his cigarette. He was arrested for driving under the influence and driving without a valid license.
May 12PROPERTY RIGHTS
10 p.m. — 6500 block of Sabal Drive. Criminal Mischief. A man reported that a neighbor he has quarreled with in the past did $400 worth of damage to his fence. He claimed that the neighbor referred to the fence as “ugly” and admitted to the deed. The suspect was not arrested and the man who called the police said he would review personal surveillance tapes to see if he can identify the culprit.
DOUBLE BOGEY10:20 p.m. — corner of Midnight Pass Road and Sun & Sea Island Hideaway. Driving Under the Influence. A man was pulled over for driving erratically and was arrested for driving under the influence after an officer found two fresh beer cans in his car. He explained he had had four beers and six shots of liquor at a bar after a day of golf — he also had a recorded blood alcohol content more than double the legal limit for operating a vehicle.
May 13EXCORCISM NEEDED
9:58 p.m. — 1200 block of Sea Plume Way. Impaired Person. Police encountered a woman thrashing about while lying in the middle of a roadway screaming in an unrecognizable language. An officer took her to jail after finding that no one was home while trying to return her to her residence.
May 14PRICEY PILFERING
11 p.m. — 5300 block of Siesta Cove Drive. Grand Theft. A woman reported that a $600 vacuum cleaner, $1,000 suitcase, some clothes and prescription medication were stolen from her vehicle. An officer was unable to dust for fingerprints because the vehicle owner had been touching the car before police arrived.
May 15NO PARKING
2:15 p.m. — corner of Island Circle and Las Rosas.Vehicle Crash. A woman parked at an unoccupied house less than a mile from the main Siesta Key Beach access backed into a truck causing $500 of damage to both vehicles.
EMPLOYEE OF THE MONTH4:30 p.m. — 3900 block of Higel Avenue. Trespassing. A woman reported that a man she had hired in the past for odd jobs walked by her window while she was in bed. After hearing her garage close, she saw the suspect walk by her kitchen window. A neighbor spotted the man on his bike and threatened him by saying, “You had better have a gun.” The rear hatch of the woman’s car was found open, and the suspect escaped.
TWO’S COMPANY7:15 p.m. — 900 block of Beach Road.Battery. After riding her bike to meet a male friend, a woman reported that he got angry and pushed her so hard she had to take two steps backward to avoid falling. The woman said the suspect became angry when she asked to borrow a beach chair and he said yes with the clause that she would sit next to him. The woman responded, “I will be one minute,” which sparked the tussle. | {
"pile_set_name": "Pile-CC"
} |
Q:
Do p-values assume an unlikely event has already happened?
According to this thread
What is the meaning of p values and t values in statistical tests?
a p-value essentially lets me compare the probability of tail-end (unlikely) events occurring and judging that against the significance level $\alpha$ to decide whether the null hypothesis should be rejected. In the example on this thread, Muriel Bristol visits Fisher and it essentially asks what's the probability of getting 5/6 correct guesses given the probability of her guessing correctly is $0.5$.
In the context of this, p-values make sense if I assume an unlikely event already happened. Because if such an event happens, then interpreting the significance of that event for a null hypothesis is a natural way to decide whether that hypothesis has been rejected.
My Question
Do p-values assume an unlikely event has already happened? If so, why is this part of the definition? If not, how does knowing the p-value tell me anything about why I should reject the null hypothesis?
Without knowing an unlikely event occurred, it would seem all a p-value can say is "if an unlikely event occurs, then the null hypothesis would be rejected."
A:
In frequentist statistics, it does not matter whether an event has occurred or not. P-values give an idea of how often the data would be observed given the null hypothesis is true. If you get a p-value of .15 then we would say that, if the null hypothesis is true, the data or more extreme data would occur in 15% of an infinite amount of cases.
P-values are of limited utility in general, see the statement be the American Statistical Association for more information.
| {
"pile_set_name": "StackExchange"
} |
// Copyright (c) 2019, the Dart project authors. Please see the AUTHORS file
// for details. All rights reserved. Use of this source code is governed by a
// BSD-style license that can be found in the LICENSE file.
import 'dart:io';
import 'package:analysis_server/src/services/correction/sort_members.dart';
import 'package:analyzer/dart/analysis/analysis_context_collection.dart';
import 'package:analyzer/dart/analysis/results.dart';
import 'package:analyzer/dart/analysis/session.dart';
import 'package:analyzer/file_system/file_system.dart';
import 'package:analyzer/file_system/physical_file_system.dart';
import 'package:meta/meta.dart';
import 'package:test/test.dart';
import 'utils/package_root.dart';
void main() {
group('analysis_server', () {
buildTestsForAnalysisServer();
});
group('analyzer', () {
buildTestsForAnalyzer();
});
group('analyzer_cli', () {
buildTestsForAnalyzerCli();
});
group('analyzer_plugin', () {
buildTestsForAnalyzerPlugin();
});
}
void buildTests({
@required String packagePath,
@required List<String> excludedPaths,
}) {
var provider = PhysicalResourceProvider.INSTANCE;
var pkgRootPath = provider.pathContext.normalize(packageRoot);
packagePath = _toPlatformPath(pkgRootPath, packagePath);
excludedPaths = excludedPaths.map((e) {
return _toPlatformPath(packagePath, e);
}).toList();
var collection = AnalysisContextCollection(
includedPaths: <String>[packagePath],
excludedPaths: excludedPaths,
resourceProvider: provider,
);
var contexts = collection.contexts;
if (contexts.length != 1) {
fail('The directory $packagePath contains multiple analysis contexts.');
}
buildTestsIn(contexts[0].currentSession, packagePath, excludedPaths,
provider.getFolder(packagePath));
}
void buildTestsForAnalysisServer() {
var excludedPaths = <String>[
'test/mock_packages',
// TODO(brianwilkerson) Fix the generator to sort the generated files and
// remove these exclusions.
'lib/lsp_protocol/protocol_custom_generated.dart',
'lib/lsp_protocol/protocol_generated.dart',
'lib/protocol/protocol_constants.dart',
'lib/protocol/protocol_generated.dart',
'lib/src/edit/nnbd_migration/resources/resources.g.dart',
'test/integration/support/integration_test_methods.dart',
'test/integration/support/protocol_matchers.dart',
// The following are not generated, but can't be sorted because the contain
// ignore comments in the directives, which sorting deletes.
'lib/src/edit/edit_domain.dart',
'lib/src/services/kythe/schema.dart',
'test/services/completion/dart/test_all.dart',
];
buildTests(
packagePath: 'analysis_server',
excludedPaths: excludedPaths,
);
}
void buildTestsForAnalyzer() {
buildTests(
packagePath: 'analyzer',
excludedPaths: [
'lib/src/context/packages.dart',
'lib/src/dart/error/syntactic_errors.g.dart',
'lib/src/summary/format.dart',
'test/generated/test_all.dart',
],
);
}
void buildTestsForAnalyzerCli() {
buildTests(
packagePath: 'analyzer_cli',
excludedPaths: [
'test/data',
],
);
}
void buildTestsForAnalyzerPlugin() {
// TODO(brianwilkerson) Fix the generator to sort the generated files and
// remove these exclusions.
var excludedPaths = <String>[
'lib/protocol/protocol_common.dart',
'lib/protocol/protocol_generated.dart',
'test/integration/support/integration_test_methods.dart',
'test/integration/support/protocol_matchers.dart',
];
buildTests(
packagePath: 'analyzer_plugin',
excludedPaths: excludedPaths,
);
}
void buildTestsIn(AnalysisSession session, String testDirPath,
List<String> excludedPath, Folder directory) {
var pathContext = session.resourceProvider.pathContext;
var children = directory.getChildren();
children.sort((first, second) => first.shortName.compareTo(second.shortName));
for (var child in children) {
if (child is Folder) {
if (!excludedPath.contains(child.path)) {
buildTestsIn(session, testDirPath, excludedPath, child);
}
} else if (child is File && child.shortName.endsWith('.dart')) {
var path = child.path;
if (excludedPath.contains(path)) {
continue;
}
var relativePath = pathContext.relative(path, from: testDirPath);
test(relativePath, () {
var result = session.getParsedUnit(path);
if (result.state != ResultState.VALID) {
fail('Could not parse $path');
}
var code = result.content;
var unit = result.unit;
var errors = result.errors;
if (errors.isNotEmpty) {
fail('Errors found when parsing $path');
}
var sorter = MemberSorter(code, unit);
var edits = sorter.sort();
if (edits.isNotEmpty) {
fail('Unsorted file $path');
}
});
}
}
}
String _toPlatformPath(String pathPath, String relativePosixPath) {
var pathContext = PhysicalResourceProvider.INSTANCE.pathContext;
return pathContext.joinAll([
pathPath,
...relativePosixPath.split('/'),
]);
}
| {
"pile_set_name": "Github"
} |
John Paddy Carstairs
John Paddy Carstairs (born John Keys; 11 May 1910, in London – 12 December 1970, in London) was a prolific British film director (1933–62) and television director (1962–64), usually of light-hearted subject matter. He was also a comic novelist and painter.
Biography
The son of Nelson Keys, Carstairs changed his name in order to avoid the appearance of nepotism. He directed 37 films in total. He had a long association with the character of Simon Templar (the character's creator, Leslie Charteris, dedicated the 1963 book, The Saint in the Sun to Carstairs). Aside from directing the 1939 Saint film, The Saint in London, he also directed two episodes of The Saint in the 1960s, making him the only individual (other than Charteris himself) to be connected to both the Hollywood film and British series of The Saint. Carstairs directed many British comedies including many of Norman Wisdom's films.
Death
Carstairs died of heart attack on 12 December 1970, aged 60.
Select bibliography
Honest Injun (1942)
Hadn't We the Gaiety (1945)
Kaleidoscope and a Jaundiced Eye (1946)
Selected filmography
A Honeymoon Adventure (1931, screenwriter)
The Water Gipsies (1932, screenwriter)
Nine till Six (1932, screenwriter)
The Impassive Footman (1932, screenwriter)
Love on the Spot (1932, screenwriter)
It's a Boy (1933, screenwriter)
Paris Plane (1933)
Boomerang (1934)
Gay Love (1934)
Falling in Love (1935)
It's a Cop (1934, screenwriter)
Two's Company (1936, screenwriter)
Holiday's End (1937)
Double Exposures (1937)
Night Ride (1937)
Missing, Believed Married (1937)
Incident in Shanghai (1938)
Lassie from Lancashire (1938)
The Saint in London (1939)
All Hands (1940)
Meet Maxwell Archer (1940)
Now You're Talking (1940)
The Second Mr. Bush (1940)
Dangerous Comment (1940)
Telefootlers (1941)
He Found a Star (1941)
Spare a Copper (1941)
Dancing with Crime (1947)
Sleeping Car to Trieste (1948)
Fools Rush In (1949)
The Chiltern Hundreds (1949)
Tony Draws a Horse (1950)
Talk of a Million (1951)
Made in Heaven (1952)
Treasure Hunt (1952)
Top of the Form (1953)
Trouble in Store (1953)
Up to His Neck (1954)
One Good Turn (1955)
Man of the Moment (1955)
Jumping for Joy (1956)
Up in the World (1956)
Just My Luck (1957)
The Big Money (1958)
The Square Peg (1959)
Tommy the Toreador (1959)
Sands of the Desert (1960)
A Weekend with Lulu (1961)
The Devil's Agent (1962)
References
External links
Category:1910 births
Category:1970 deaths
Category:People educated at Alleyn Court School
Category:Writers from London
Category:20th-century English painters
Category:English male painters
Category:English autobiographers
Category:English film directors
Category:English film producers
Category:German-language film directors
Category:Royal Navy personnel of World War II
Category:English male non-fiction writers | {
"pile_set_name": "Wikipedia (en)"
} |
Maturation of sympathetic neurotransmission in the rat heart. VII. Suppression of sympathetic responses by dexamethasone.
Effects of dexamethasone on development of sympathetic nerve function in the heart were evaluated by giving 1 mg/kg of dexamethasone s.c. daily for several days beginning the day after birth. Dexamethasone interfered with tyramine- and isoproterenol-induced tachycardia in the neonates but did not cause alterations in development of a marker for presynaptic sympathetic nerve terminals (synaptic vesicle uptake of [3H] norepinephrine) nor of postsynaptic beta adrenoceptor binding of [3H]dihydroalprenolol; the deficit was also unrelated to general cellular effects of the hormone. These data suggest that the subnormal chronotropic responses of the heart to sympathetic stimulation in dexamethasone-treated neonatal rats result from uncoupling of receptors from the organ response. The effects of dexamethasone on cardiac responses were specific to the neonate, as mature rats given dexamethasone did not show suppression of cardiac sympathetic action. Neonatal dexamethasone treatment also produced a deficit of adrenomedullary development with deficiencies in catecholamine levels and in catecholamine biosynthetic enzymes; deficits in phenylethanolamine N-methyltransferase activity persisted into young adulthood. | {
"pile_set_name": "PubMed Abstracts"
} |
Bitch Media - Bitch in a Boxhttp://bitchmagazine.org/taxonomy/term/10066/0
enBitch in a Box: Hostile Gift Guidehttp://bitchmagazine.org/post/bitch-in-a-box-hostile-gift-guide
<p><a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"><img src="http://bitchmagazine.org/sites/default/files/u36649/6432241749_0d1847e807_o.jpg" alt="bitch in a bo" width="447" height="74" /></a></p>
<p>This month, we’ve put together a series of <a href="http://bitchmagazine.org/tag/bitch-in-a-box">feminist gift guides</a>. They're a way to highlight fun stuff we love and creators we're excited to support. Today's list, though, is different. </p>
<p>It’s time to talk about hostile gifts.</p>
<p>A hostile gift is not merely a bad gift or an insulting gift. Rather, a hostile gift is meant to intentionally inspire perplexity, confusion, and apoplexy in the recipient. This <a href="http://bitchmagazine.org/post/bitch-in-a-box-a-hostile-gift-guide" target="_blank">second annual hostile gift guide</a> should help you not only to select a hostile gift, but also to determine whether you have received one. </p>
<p>You may have received some hostile gifts this year already—if so, please tell us about them in the comments!</p>
<p><strong>Dreamsicles</strong></p>
<p><img src="/sites/default/files/u2583/dreamsicle_doll_.jpg" alt="" width="305" height="355" /></p>
<p>Everyone knows Precious Moments. But for the truly hostile gift, these creepy Dreamsicles are your answer! </p>
<p>While the figurine style is more common, you can also find plush versions. They are available for all occasions, for every hobby lover (Dreamsicle with soccer ball!), every profession (no kidding—search for “Dreamsicle” and “fireman”). </p>
<p><strong>Anything Wrapped With Masking Tape</strong></p>
<p><img src="/sites/default/files/u2583/photo-3.jpg" alt="masking tape" width="670" height="500" /></p>
<p>To really make your giftee say, “WTF?” wrap a perfectly lovely gift using masking tape. To take it to the next level, wrap a great gift in gorgeous wrapping paper with masking tape.</p>
<p><strong>A Different Book Than the One You Give Everyone Else</strong></p>
<p><img src="/sites/default/files/u2583/iacocca_.jpg" alt="" width="160" height="160" /></p>
<p>Give all your family members the same great book—maybe something like <em>The Warmth of Other Suns</em> by Isabel Wilkerson or Can’t <em>We Talk about Something More Pleasant</em> by Roz Chast. Then, give just one person a different book (I recommend <em>Lee Iacocca: An Autobiography</em>). Don’t explain why one person is the odd one out, just let them wonder. </p>
<p><strong>A Copy of <em>Maybe It IS All in Your Head . . . and You Are NOT Crazy! </em>[Kindle Edition]</strong></p>
<p><img src="/sites/default/files/u2583/maybe_it_is.jpg" alt="" width="300" height="300" /></p>
<p>Even better when given to someone who doesn’t actually have a Kindle.</p>
<p><strong>A Really Unappealing, Homemade “Edible” Item</strong></p>
<p><img src="/sites/default/files/u2583/1116846.jpg" alt="" width="250" height="250" /></p>
<p>This is a particular effective gift if you get the recipient to “TRY A BITE” right then and there.</p>
<p><em>Have you ever received a hostile gift? Please add your ideas to the comments. </em></p>
<p><em><a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">Read the rest of our (actually nice) feminist gift guides. </a></em></p>
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader!</a></p>
<p><em><br /></em></p>
http://bitchmagazine.org/post/bitch-in-a-box-hostile-gift-guide#commentsBitch in a BoxBitch HQTue, 23 Dec 2014 20:45:28 +0000Julie Falk29747 at http://bitchmagazine.orgBitch in a Box: Gift Guide for Sober Folkshttp://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-sober-folks
<p dir="ltr"><img src="/sites/default/files/u36649/6432241749_0d1847e807_o.jpg" alt=""Bitch in a Box" Illustration" width="447" height="74" /></p>
<p dir="ltr">This month, we’re putting together a series of <a href="http://bitchmagazine.org/tag/bitch-in-a-box">feminist gift guides</a>. They're a way to highlight fun stuff we love and creators we're excited to support.</p>
<p dir="ltr">Being sober isn’t easy—especially when holiday socializing is often organized around getting drunk enough to tolerate the casual racism and homophobia of your family. Of course, the best gift you can give sober friends and family is support. We've wrangled up a list of gifts sure to please everyone from the straight-edge to the newly sober.</p>
<p dir="ltr"><strong>Fancy Non-Alcoholic Drink Recipe Book</strong></p>
<p dir="ltr"><img src="/sites/default/files/u36649/pomegranate-party-punch-by-cravings-of-a-lunatic-9.jpg" alt="Photo of pomegranate punch with cranberries." height="400" /><img src="/sites/default/files/u36649/pic_display_0.jpg" alt="Cover of "Homemade Soda"" height="400" /></p>
<p><em>Photo by <a href="http://www.cravingsofalunatic.com/2014/01/pomegranate-party-punch.html" target="_blank">Kim Beaulieu</a>. Book cover v</em><em>ia <a href="http://www.storey.com/book_detail.php?isbn=9781603427968" target="_blank">Storey</a>.</em></p>
<p dir="ltr">You know what’s badass? Coming to a party and being able to enjoy a festive drink that’s not boozy. If you’re throwing a party, be sure to include some mulled cider or fancy soda on your menu. I like whipping up a big bowl of punch. All you need is juice, citrus soda and frozen fruit to garnish and keep it chilled. Mix grapefruit and cranberry juice with plain soda water, then garnish with raspberry sorbet, lemon slices, and frozen raspberries. Easy! Pink! Delicious! Or check out Kim Beaulieu's recipe for <a href="http://www.cravingsofalunatic.com/2014/01/pomegranate-party-punch.html" target="_blank">Pomegranate Party Punch</a> on her blog.</p>
<p dir="ltr">For the whiz in the kitchen, snag a copy of <em><a href="http://www.powells.com/biblio/9781603427968" target="_blank">Homemade Soda</a></em> by Andrew Schloss. Gift it to your sober pals or use its many tricks to make both soda syrups and fermented brews like ginger beer and sarsaparilla. Bottle them in cute glass and give ‘em away.</p>
<p dir="ltr"><strong>Punk Sobriety Books and Zines</strong></p>
<p><img src="/sites/default/files/u36649/sober_living.jpg" alt="Cover of "Sober Living for the Revolution"" height="300" /><img src="/sites/default/files/u36649/towardsalessfuckedupworld_72.jpg" alt="Photo of "Towards a Less Fucked Up World"" height="300" /><img src="/sites/default/files/u36649/fillingthevoid_lg.jpg" alt="Cover of "Filling the Void"" height="300" /></p>
<p><em>Via <a href="http://www.pmpress.org/content/index.php" target="_blank">PM Press</a>,</em><em> <a href="http://www.akpress.org/towardsalessfuckedupworld.html" target="_blank">AK Press</a>, and</em><em> <a href="http://www.quimbys.com/store/1953" target="_blank">Quimbys</a>.</em></p>
<p dir="ltr"><em><a href="http://secure.pmpress.org/index.php?l=product_detail&p=162" target="_blank">Sober Living for the Revolution</a> </em>is an anthology for the straight-edge feminist in your life. In addition to contributions from <a href="http://www.dischord.com/band/minor-threat" target="_blank">Minor Threat</a> frontman Ian MacKaye and radical collective <a href="http://www.crimethinc.com/blog/" target="_blank">Crimethinc.</a>, Gabriel Kuhn’s book addresses the political legacy of straight edge culture, including associations that feed into conservatism and macho posturing in the scene. This book collects essays, manifestos, and interviews to paint a picture of a political movement that eschews drug use to foster progressive politics.</p>
<p dir="ltr">Ever described someone with frustrating behavior in your community as “having good politics, but...”? <a href="http://www.portlandbuttonworks.com/zines/towards-a-less-fucked-up-world?sort=p&limit=75" target="_blank"><em>Towards a Less Fucked Up World</em></a> is a badass zine that takes on the hypocrisy of radical communities where discussion of consent, boundaries, and healthy relationships is abundant in sober spaces but dissolves once folks get drunk. This zine looks at how cis-men access bodies through cultural norms of intoxication and how getting high can support international systems of violence and oppression, such as drug cartels.</p>
<p dir="ltr">One of my favorite zinesters, <a href="http://dorisdorisdoris.com/" target="_blank">Cindy Crabb</a>, put out an inspiring zine that addresses the transition into sobriety without religion-based support groups. For many of the folks who contributed to <em><a href="http://nervousnelly.storenvy.com/collections/49690-all-products/products/10889715-filling-the-void-interviews-about-quitting-drinking-and-using" target="_blank">Filling the Void</a></em>, the decision to stop using drugs or drinking is one that comes with the realization that healthy relationships and substance abuse are mutually exclusive. It's great for friends who are working toward sobriety.</p>
<p dir="ltr"><strong>Patches</strong></p>
<p><img src="/sites/default/files/u36649/rape_revenge_patch.jpg" alt="Black and white patch depicting a man with a fresh vasectomy wound." height="400" /><img src="/sites/default/files/u36649/next_stop_adventure.jpg" alt="" height="400" /></p>
<p dir="ltr"><em>Images and illustrations via <a href="https://www.etsy.com/shop/retirementfund" target="_blank">Matt Gauck</a>.</em></p>
<p dir="ltr">Portland-native and vegan artist Matt Gauck is a straight-edge feminist worth supporting. His shop has <a href="https://www.etsy.com/listing/186432458/ive-got-the-straightedge-xxx-ruler-patch?ref=shop_home_active_17" target="_blank">patches</a> for the punk-rock folks in your life, including this awesome <a href="https://www.etsy.com/listing/213508807/feminist-i-support-fighting-back-patch?ref=shop_home_active_2" target="_blank">rape revenge patch</a>. “If you hate it, well, think about it harder, and imagine what the person pictured here did to end up with this unwanted surgery. He deserved it,” he writes. Well said. I also recommend his zine, <em><a href="https://www.etsy.com/shop/retirementfund?section_id=14437273&ref=shopsection_leftnav_6" target="_blank">Next Stop Adventure</a></em>, for hilarious stories of Gauck’s bike tours.</p>
<p dir="ltr"><strong>Music!</strong></p>
<p><img src="/sites/default/files/u36649/replica.jpg" alt="Hardcore band Replica performs" width="600" /></p>
<p><em>Oakland hardcore band Replica. From <a href="http://www.afropunk.com/profiles/blogs/free-download-of-the-oakland-hardcore-band-replica-s-2013-eps" target="_blank">Afropunk.com</a></em></p>
<p><em><a href="http://www.afropunk.com/profiles/blogs/free-download-of-the-oakland-hardcore-band-replica-s-2013-eps" target="_blank"></a></em>For the hardcore-lover, records from bands like <a href="http://raperevenge.bandcamp.com/" target="_blank">Rape Revenge</a> (Calgary), <a href="http://r-e-p-l-i-c-a.bandcamp.com/" target="_blank">Replica</a> (Oakland), and <a href="http://punchcrew.bandcamp.com/" target="_blank">PUNCH</a> (SF) feature strong female vocals and all the blast beats you can handle. Great for exploring the genre beyond 1980’s classics like <a href="http://www.revelationrecords.com/bands/show/106" target="_blank">Chain of Strength</a>, Minor Threat, and <a href="http://www.revelationrecords.com/bands/show/114" target="_blank">Gorilla Biscuits</a>.</p>
<p><em>Read the rest of our <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides here</a></em>. </p>
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader!</a></p>
<p> </p>
http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-sober-folks#commentsBitch in a BoxBitch HQMon, 22 Dec 2014 18:30:39 +0000Jennifer Busby29677 at http://bitchmagazine.orgBitch in a Box: Queer Music Gift Guidehttp://bitchmagazine.org/post/bitch-in-a-box-queer-music-gift-guide
<p><img src="http://farm8.staticflickr.com/7019/6432241749_0d1847e807_o.jpg" alt="bitch in a box logo" width="447" height="74" /></p>
<p>This month, we’re putting together a series of <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">feminist gift guides</a>. They're a way to highlight fun stuff we love and creators we're excited to support.</p>
<p>If you're shopping for a music lover this year (or yourself), there are so many other ways to sonically please besides CDs or an iTunes gift card. While this gift guide is perfect for the giftee whose interests lie at the intersection of all things queer and music, it's a great guide for any audiophile! </p>
<p><img style="font-size: 10px;" src="/sites/default/files/images/qmgg_books.png" alt="" /></p>
<p><strong><span style="text-decoration: line-through;">Punk's</span> Print's Not Dead</strong></p>
<p>Sometimes a punk just needs to stay in for the night! Here are some great books to keep you company on cold nights. <em>Shotgun Seamstress</em>, Osa Atoe's zine for and by black punks, <a href="http://mendmydresspress.bigcartel.com/product/shotgun-seamstress-zine-anthology-by-osa-atoe" target="_blank">is now collected all in one amazing book</a> available from Mend My Dress Press. It's chock-full of profiles of artists, musicians, punks, and iconoclasts of today and yesterday alongside real talk about racism, homophobia, and classism within so-called progressive spaces—no punk bookshelf is complete without it. Speaking of which, <em>Shotgun Seamstress </em>contributor Brontez Purnell has a new graphic memoir out (and we do mean graphic in the NSFW sense). <em><a href="http://www.gimmeaction.com/books.html" target="_blank">The Cruising Diaries</a> </em>traces his early days in Oakland, CA and follows the Gravy Train!!!! member through the good, the hilarious, and the cringe-worthy. Lastly, <a href="http://www.feministpress.org/books/christy-c-road/spit-and-passion" target="_blank">Cristy C. Road's graphic memoir, <em>Spit and Passion</em></a>, which follows her adolescent love for Green Day and emerging queer identity, is another must for anyone who felt like a teenage misfit. <a href="http://bitchmagazine.org/post/smart-diggin-deep-with-cristy-c-road-art-queer-poc-zines-feminist-magazine-books-music" target="_blank">Check out our interview with Road here!</a></p>
<p><img style="font-size: 10px; margin-left: 10px; margin-right: 10px;" src="/sites/default/files/images/qmgg_box_sets.png" alt="An image of the David Bowie box set, Tegan and Sara boxset, and Sleater Kinney boxset. They each show the different packages for the collections. " width="400" /></p>
<p><strong>Go Big</strong></p>
<p>That's right—box sets. For the collector or analog-lover on your list, there are several box sets and re-releases you will want to consider. For starters, <a href="http://store.davidbowie.com/" target="_blank">David Bowie released a two LP (or three CD) collection, <em>Nothing Has Changed</em></a> this year. Spanning 2014 to 1964, the collection works its way backwards so you can appreciate the Starman's work in reverse. Gifting for a Tegan and Sara fan? <a href="http://teganandsara.warnerbrosrecords.com/so-jealous-x-book-635254.html" target="_blank">Pre-order <em>So Jealous X</em>.</a> Sixty dollars will get you not only a remastered <em>So Jealous</em>, but a bonus CD, DVD, and a beautiful book! Lastly, if you really want to make a splash, you'll want to invest in <a href="https://megamart.subpop.com/releases/sleater_kinney/start_together" target="_blank">the deluxe Sleater-Kinney box set</a>. When Sub Pop announced a special colored vinyl set of the band's work, it sold out immediately. You're still in luck though, and can pre-order the $125 vinyl collection that comes with a book of unreleased photos, a “Bury Our Friends” 7-inch, an art print, and more. Pair this with a some S-K reunion tickets and you'll be the Best Santa Ever.</p>
<p><br /><img style="margin-left: 10px; margin-right: 10px;" src="/sites/default/files/images/qmgg_tees.png" alt="Four tshirts in a grid. A yellow Thao &amp; Mirah tshirt, a purple THEESatisfaction shirt; a white Against Me! T shirt, and a dark green Hooray for the Riff Raff t shirt" width="400" /></p>
<p><strong>Tee Up</strong></p>
<p>If you know your giftee's tastes—aesthetically <em>and</em> musically—grabbing a band's t-shirt is surefire gift to please. The real fun is playing detective to find out their t-shirt size. Just visit the website of their favorite band or artist (or of the record label)! Here are some of our faves: <a href="http://killrockstars.merchtable.com/shirts-ladies/thao-and-mirah-reindeer-yellow-ladies-t-shirt#.VI52hGTF9LZ" target="_blank">Mirah and Thao</a>, <a href="https://megamart.subpop.com/tshirts/theesatisfaction/theesatisfaction_purple" target="_blank">THEESatisfaction</a>, <a href="http://totaltreble.bigcartel.com/product/against-me-heads-t-shirt" target="_blank">Against Me!</a>, and <a href="http://hurrayfortheriffraff.spinshop.com/details/220865" target="_blank">Hurray for the Riff Raff</a>.<span style="font-size: 10px;"><br /></span></p>
<p><img src="/sites/default/files/images/qmgg_etsy.png" alt="" width="690" height="497" /></p>
<p><strong>Hit Up Etsy</strong></p>
<p>One way to support independent craftsters is to head to Etsy. Simply type in your giftee's favorite artists in the search box and you'll find portraits, embroidered lyrics, shrinky dink earrings, silk-screened pillows, and other quirky tributes. Some of our favorites include this <a href="https://www.etsy.com/listing/119296533/grace-jones-art-print-pop-portrait?ref=shop_home_active_4" target="_blank">Grace Jones print from pairabirds</a>, who has several other awesome music prints; a <a href="https://www.etsy.com/listing/152316424/the-queers-punk-rock-confidential-pop?ref=sr_gallery_4&ga_search_query=queer+music&ga_search_type=all&ga_view_type=gallery" target="_blank">Queers button set from thepbrebellion</a>, and <a href="https://www.etsy.com/listing/201423919/blondie-baby-shower-gift-girl-boy-onesie?ref=sr_gallery_42&ga_search_query=blondie&ga_page=2&ga_search_type=all&ga_view_type=gallery" target="_blank">a Blondie baby onesie from monofaces</a> (which everyone needs at least one of).</p>
<p><img style="font-size: 10.3999996185303px; margin-left: 10px; margin-right: 10px;" src="/sites/default/files/images/qmgg_eclectic.png" alt="" width="400" /></p>
<p><strong>If You're Totally Stumped</strong></p>
<p>Shopping for the person who has everything? Check out these gems that they're sure to be missing. Red Hot, who uses pop culture to raise AIDs awareness, teamed up with Yep Roc records on <a href="http://www.redhot.org/" target="_blank">a tribute to Arthur Russell </a>with acts from Hot Chip to Blood Orange to Thao and the Get Down Stay Down. Great jams and a great cause! Or pick up <a href="http://www.secretlycanadian.com/onesheet.php?cat=SC221" target="_blank"><em>Turning</em>, a DVD/CD package and bring Antony and Johnsons' 2006 tour</a> to your living room. For historian buffs, <a href="http://www.paradiseofbachelors.com/products-page/cd/pob-12" target="_blank">pick up <em>Lavender Country</em></a>, a re-released 1973 work by Patrick Haggerty that's considered to be the first country album by an openly gay artist. Lastly, all gifts go well with <a href="http://feministcards.com/" target="_blank">a pack of Feminist Playing Cards</a>.</p>
<p> </p>
<p><strong><img style="margin-left: 10px; margin-right: 10px;" src="/sites/default/files/images/qmgg_mags.png" alt="" width="400" /></strong></p>
<p><strong>G</strong><strong>ive the Gift That Keeps on Giving</strong></p>
<p>Want to keep the music love going throughout the year? Give a gift subscription to <em><a href="http://shop.tomtommag.com/collections/the-mag" target="_blank">Tom Tom</a></em> and <em><a href="http://sheshredsmag.com/" target="_blank">She Shreds</a></em>. Not only will you stay up-to-date with contemporary musicians, you'll also get tips on starting the drums, bass, and guitar. Plus you'll be supporting independent, feminist media (which we're pretty big fans of here at Bitch Media.) And like Bitch, they have some sweet merch of their own! If you're looking for more ways to inspire future musicians, seek out your local Girls Rock Camp and donate today! (<a href="http://girlsrockmilwaukee.org/" target="_blank">Girls Rock Milwaukee</a> logo, pictured right).<br /></p>
<p><img style="font-size: 10.3999996185303px; margin-left: 10px; margin-right: 10px;" src="/sites/default/files/images/5333545844_1fb99f0834.jpg" alt="" width="316" height="275" /></p>
<p><strong>Make a Mix</strong></p>
<p>Mixes are the homemade pie of music—and they last longer! Plus they're perfect for when money is tight but you still have a lot of love to give. Get inspired with some mixes from Autostraddle (See: <a href="http://www.autostraddle.com/leaders-of-the-new-school-15-queer-female-hip-hop-artists-you-should-know-247819/" target="_blank">15 Queer Female Hip Hop Artists You Should Know</a>) or <a href="http://8tracks.com/bitchtapes" target="_blank">browsing the archives of Bitch's weekly feminist mixtapes</a>. <em>(Illustration via <a href="http://www.apalelandscape.co.uk/blog/?tag=design" target="_blank">A Pale Landscape</a>) </em></p>
<p><em>Read the rest of our <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides here</a></em>. </p>
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader</a>!</p>
<p> </p>
http://bitchmagazine.org/post/bitch-in-a-box-queer-music-gift-guide#commentsBitch in a BoxBitch HQWed, 17 Dec 2014 17:37:58 +0000Kjerstin Johnson29620 at http://bitchmagazine.orgBitch in a Box: Gift Guide for Social Justice Warriorshttp://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-social-justice-warriors
<p><a style="color: #6dbe45; text-decoration: none;" href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"><img src="http://farm8.staticflickr.com/7019/6432241749_0d1847e807_o.jpg" alt="bitch in a box logo" width="447" height="74" /></a></p>
<p>This month, we’re putting together a series of <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">feminist gift guides</a>. They're a way to highlight fun stuff we love and creators we're excited to support.</p>
<p>Activists, organizers, and the politicized loved ones of our lives. These social justice warriors (let's reclaim this weird pejorative and say it with pride) may be difficult to shop for because all they want for Christmas is the dismantling of this hegemonic patriarchy. And that's not something readily available on small business store shelves. What to get them? </p>
<p><a href="https://t.e2ma.net/click/390ijb/jmd9yh/jienb8" target="_blank"><img src="/sites/default/files/u71596/aisforactivist.jpg" alt="" width="386" height="400" /></a></p>
<p><em><strong>A is for Activist</strong></em></p>
<p>Forget about Christmas and just buy a stack of these picture books to keep in stock for whenever someone has a new baby. Heck, pass this beautiful book out to all of the grown-ups in your life. <em><a href="https://t.e2ma.net/click/390ijb/jmd9yh/jienb8" target="_blank">A is for Activist </a></em>is a gorgeous book (peek some <a href="http://www.aisforactivist.com/preview-the-book/" target="_blank">sample pages</a>), with important messages splayed across each playful page. It's <a href="http://bitchmagazine.org/post/a-de-activista-book-review-spanish-espanol-childrens-book" target="_blank">available in Spanish, too!</a></p>
<p><a style="color: #6dbe45; text-decoration: none;" href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"><img src="/sites/default/files/u71596/hari.jpeg" alt="http://www.harikondabolu.com/2014/02/waiting-for-2042-out-march-11th-pre-order-now/" width="400" height="400" /></a></p>
<p><strong>Hari Kondabolu's <em>Waiting for 2042</em></strong></p>
<p>A comedian with a masters degree in human rights? Yep, that's Hari Kondabolu (<a href="http://bitchmagazine.org/post/popaganda-episode-political-joke" target="_blank">listen to our interview with him here</a>). Based out of Brooklyn, a child of immigrants raised in Queens, Kondabolu's sharp commentary let's us laugh about all the effed-upedness at the intersection of race, gender, the -isms, and America. His debut comedy album, <em><a href="http://www.harikondabolu.com/2014/02/waiting-for-2042-out-march-11th-pre-order-now/" target="_blank">Waiting for 2042</a></em> (released on Kill Rock Stars!), is a reference to census projections of when white folks will be the population minority. Can't fault a guy for dreaming, right? </p>
<p><a href="https://www.buyolympia.com/q/Item=slingshot15-mini" target="_blank"><img src="/sites/default/files/u71596/slingshot_cropped.jpg" alt="" width="690" height="384" /></a></p>
<p><strong>Slingshot Organizer</strong></p>
<p>Don't know what to get the busy grassroots organizer in your life? What about an <em>organizer</em> for the organizer? In its 21st year of production, the <a href="http://slingshot.tao.ca/" target="_blank">Slingshot Collective</a> planner is packed cover to cover so folks can scribble down their days and also be inspired. There's a radical reading list, "mynstrual" calendar, tips for dealing with the police and more! There are two versions: <a href="https://www.buyolympia.com/q/Item=slingshot15-spiral" target="_blank">pocket size</a> or <a href="https://www.buyolympia.com/q/Item=slingshot15-spiral" target="_blank">full size</a>. </p>
<p><a href="https://squareup.com/market/liartownusa" target="_blank"><img src="/sites/default/files/u71596/original4.png" alt="" width="400" height="400" /></a></p>
<p><strong>Social Justice Kittens Calendar</strong></p>
<p>Perhaps what your social justice warrior really needs is a wall calendar, a <a href="http://www.readingfrenzy.com/shoppe/other_media/1332/" target="_blank">social justice kittens</a> calendar to be exact. Twelve months of squeal-worthy adorableness accompanied by little diddlies like "I drink your tears, oppressor," and, "This conversation doesn't make me feel safe." </p>
<p><img src="/sites/default/files/u71596/poster_collage.jpg" alt="" width="494" height="400" /></p>
<p><strong>Justseeds Artists' Collective art prints</strong></p>
<p>What is a grassroots movement without art? The <a href="http://justseeds.org/" target="_blank">Justseeds Artists' Collective</a> highlights the work of those creating art with a message. A <em>Bitch</em> favorite, <a href="http://bitchmagazine.org//node/21314" target="_blank">Faviana Rodriguez's</a> "<a href="http://www.justseeds.org/favianna_rodriguez/19occupysis.html" target="_blank">Occupy Sisterhood</a>" poster should be on your wall now. "<a href="http://www.justseeds.org/melanie_cervantes/20nowar.html" target="_blank">No War</a>" by Melanie Cervantes and Roger Peet's "<a href="http://www.justseeds.org/roger_peet/17giveup.html" target="_blank">Never Give Up</a>" are just a few of the gorgeous prints available from the collective. </p>
<p><img src="/sites/default/files/u71596/mugs_cropped.jpg" alt="" width="519" height="400" /></p>
<p><strong>Adventures in Feministry mugs</strong></p>
<p>Organizers and activists cannot do the good fight without the extra boost of a good energizing drink. These amazing mugs featuring feminists from the past like <a href="http://bitchmagazine.org/support-feminist-media/adventures-in-feministory-mug-phoolan-devi" target="_blank">Phoolan Devi</a>, <a href="http://bitchmagazine.org/support-feminist-media/adventures-in-feministory-mug-madam-cj-walker" target="_blank">Madam CJ Walker</a>, and <a href="http://bitchmagazine.org/support-feminist-media/adventures-in-feministory-mug-anna-julia-cooper" target="_blank">Anna Julia Cooper</a> can be filled with coffee, tea, kombucha, or your favorite spirit. </p>
<p><a href="http://www.crimethinc.com/books/rfd.html" target="_blank"><img src="/sites/default/files/u71596/recipesfordisaster_0.jpg" alt="" width="280" height="400" /></a></p>
<p><em><strong>Recipes for Disaster: An Anarchist Cookbook</strong></em></p>
<p>If the social justice warrior in your life strives to completely eschew the system, perhaps <em><a href="http://www.crimethinc.com/books/rfd.html">Recipes for Disaster: An Anarchist Cookbook</a></em> is the way to go. The CrimethInc collective has compiled and "declassified top secret anarchist tactics" with a table of contents that includes chapters such as, "How to make a bicycle," to "Sabotage." </p>
<p><img src="/sites/default/files/u2583/screen_shot_2014-12-12_at_10.49.04_am.png" alt="" width="264" height="352" /></p>
<p><strong>The only patch anyone ever needs</strong></p>
<p><a href="http://microcosmpublishing.com/catalog/patches/508/">Solidarity fist in a woman symbol patch</a>, you belong on every teenager's backpack. Get a single patch for a friend to put on their hoodie, or buy dozens of them and quilt them into a ginormous blanket of solidarity to drape over injustice.</p>
<p><img src="/sites/default/files/u71596/fightmotherfuckingsad.jpg" alt="" width="332" height="400" /></p>
<p><strong><em>The Do-It-Yourself Guide to Fighting the Big Motherfuckin' Sad</em> by Adam Gnade</strong></p>
<p>An enduring quality of activists is their capacity to give and give until they are burned out. We now discuss self-care more often, but organizers need to be reminded that before they can work to take care of the community, they need to take care of themselves. <em><a href="http://pioneerspress.com/catalog/books/4082/" target="_blank">The Do-It-Yourself Guide to Fighting the Big Motherfuckin' Sad</a></em> by Adam Gnade is a blueprint to listening and caring for yourself. </p>
<p><em>Read the rest of our <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides here</a></em>. </p>
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader</a>!</p>
http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-social-justice-warriors#commentsBitch in a BoxBitch HQFri, 12 Dec 2014 18:51:00 +0000Amy Lam29561 at http://bitchmagazine.orgBitch in a Box: A Gift Guide for Homebodieshttp://bitchmagazine.org/post/bitch-in-a-box-a-gift-guide-for-homebodies
<p class="normal"><a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"><img src="http://farm8.staticflickr.com/7019/6432241749_0d1847e807_o.jpg" alt="bitch in a box logo" width="447" height="74" /></a></p>
<p class="normal">All during December, we're publishing gift guides to highlight stuff we love and creators we want to support.</p>
<p class="normal">I am a homebody 90 percent of the time. While I enjoy socializing with friends, there is no greater love than the love homebodies have with our couches. Here is a gift guide to celebrate the art of staying indoors!</p>
<p class="normal"><img src="/sites/default/files/u2583/1928_wonder_woman_robe.jpg" alt="wonder woman robe" width="392" height="690" /></p>
<p class="normal"><strong><a href="http://www.thinkgeek.com/product/1928/" target="_blank">Wonder Woman Robe</a></strong></p>
<p class="normal">Would a sleeved throw by any other name—Snuggies, Slankets—look as sweet as this? Real talk: I used to think these things were glorified robes. Then I went to a friend’s for movie night and borrowed his, and I never wanted to give it back. So when you buy this for the geeky couch potato in your life, make sure to grab one for yourself.</p>
<p class="normal"><img src="/sites/default/files/u2583/orange_is_the_new_black_2013_season_1_dvd_cover.jpg" alt="orange is the new black" width="400" height="309" /></p>
<p><strong><a href="http://www.barnesandnoble.com/w/dvd-orange-is-the-new-black-season-one-taylor-schilling/26471581?ean=31398193913" target="_blank"><em>Orange is the New Black</em> on DVD</a></strong></p>
<p>I know what you’re thinking: who buys DVDs anymore? Turns out a lot of people do. Having physical copies of your favorite TV shows and movies is great for when a) your internet access is down or b) you want to disconnect from the online world. And if the feminist homebody in your life isn’t subscribed to Netflix, she is missing out on one of the best women-centric shows in the last five years.</p>
<p><img src="/sites/default/files/u2583/bed_desk.png" alt="" width="550" height="250" /></p>
<p class="normal"><strong><a href="http://www.bedbathandbeyond.com/store/product/plush-backrest-in-black/1016476501">Backrest</a> and a <a href="http://www.bedbathandbeyond.com/store/product/my-place-bed-desk-workstation/1015818735" target="_blank">Bed-desk</a></strong></p>
<p class="normal"><strong><a href="http://www.bedbathandbeyond.com/store/product/my-place-bed-desk-workstation/1015818735" target="_blank"></a></strong>I once used a backrest/bed-desk combo for a whole year because I couldn’t afford a real desk. It wasn’t ideal, but it was at least comfortable. Backrests are great for the homebodies in your life who don’t want to leave bed but are okay with sitting upright, and the workstation is perfect for anyone who wants to use their laptop (or do other work) in bed.</p>
<p class="normal"><img src="/sites/default/files/u2583/flameless_candles.png" alt="flameless candles" width="670" height="561" /></p>
<p class="normal"><strong><a href="http://www.lights.com/flameless-candles" target="_blank">Flameless Candles</a></strong></p>
<p class="normal">Perhaps your feminist homebody likes to host social events at home, or perhaps they like to add ambience to their rooms but don’t want to fuss with melting candle wax. In either case, flameless candles are the way to go. Just pop in some batteries, dim the house lights, and enjoy the glow.</p>
<p class="normal"><img src="/sites/default/files/u2583/tea_set.png" alt="numi tea set" width="649" height="510" /></p>
<p class="normal"><strong>A Delicious <a href="http://shop.numitea.com/Flowering-Tea/c/NumiTeaStore@FloweringTea" target="_blank">Flowering Tea Set</a></strong></p>
<p class="normal">Tea needs a few minutes to steep before it’s drinkable. For people who like to wait and watch, give them a flowering tea set. Place the leaves in the glass pot provided and watch them blossom into the most delicious drink to start or end your day.</p>
<p class="normal"><img src="/sites/default/files/u2583/male_tears_mug_0.png" alt="a mug that says male tears" width="413" height="388" /></p>
<p><strong><a href="http://www.zazzle.com/male_tears_mug-168851988639206290" target="_blank">Male Tears Mug</a></strong></p>
<p class="normal">What better way for the feminist homebody to drink flowering tea <em>and</em> show sexists we have a sense of humor than with a Male Tears mug? As an added bonus, check out the one- and five-star reviews for these and similar mugs on Amazon.</p>
<p class="normal"><img src="/sites/default/files/u2583/indie_press.png" alt="a bunch of great books" width="594" height="632" /></p>
<p><strong>Indie press books</strong></p>
<p class="normal">Left to right: <em>Forgive Me If I’ve Told You This Before</em> (Ooligan Press), <em>Clown Girl</em> (Hawthorne Books), <em>Excavation: A Memoir</em> (Future Tense Books), <em>Marielitos, Balseros, and Other Exiles</em> (Ig Publishing), <em>A Load of Hooey</em> (McSweeney’s).</p>
<p class="normal">Your feminist homebody probably likes to read. I say skip books from the Big 5 (they have enough money, trust me) and purchase some books from indie publishers, preferably from your <a href="http://www.indiebound.org/indie-store-finder" target="_blank">local independent bookstore</a>. Don’t have one? <a href="http://www.powells.com/" target="_blank">Try Powell’s</a>!</p>
<p class="normal"><img src="/sites/default/files/u2583/socks.png" alt="cute socks" width="670" height="326" /></p>
<p><strong>Cute Socks</strong></p>
<p class="normal">Puttering around the house calls for cozy socks. Portland-based <a href="http://www.sockdreams.com/" target="_blank">Sock Dreams</a> has a wide selection of adorable patterned socks, from <a href="http://www.sockdreams.com/products/sock-it-to-me-starry-night" target="_blank">Starry Night knee highs</a> to <a href="http://www.sockdreams.com/products/sloth-anklet" target="_blank">sloth anklets</a>, and not only do they have plus-sized options, they ship for free in the U.S.! For the homebody in your life, help them eliminate the need for house shoes with these <a href="http://www.sockdreams.com/products/ruby-slipper-socks" target="_blank">ruby slipper socks</a>.</p>
<p><em>Read the rest of our <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides here</a>, including a <a href="http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-young-feminists" target="_blank">gift guide for teen feminists</a>.</em></p>
<div class="content">
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader!</a></p>
</div>
http://bitchmagazine.org/post/bitch-in-a-box-a-gift-guide-for-homebodies#commentsBitch in a BoxBitch HQThu, 11 Dec 2014 20:38:20 +0000Ariana Vives29594 at http://bitchmagazine.orgBitch in a Box: Gift Guide for Children's Picture Bookshttp://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-childrens-picture-books
<p><a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"><img src="http://farm8.staticflickr.com/7019/6432241749_0d1847e807_o.jpg" alt="bitch in a box" width="447" height="74" /></a></p>
<p>It’s all too easy to accidentally pick out a well-titled, gorgeously illustrated picture book for your kids, only to find that the book perpetuates tired gender stereotypes. On the other hand, children’s books are filled with some of the most subversive characters in literature. Here are five feminist-friendly books my family has read over the years that my now-eight-year-old daughter and five-year-old son love.</p>
<p> <img src="/sites/default/files/u2583/2988487.jpg" alt="adventures of isabel cover" width="318" height="358" /></p>
<p><strong><a href="http://www.goodreads.com/book/show/2988487-adventures-of-isabel" target="_blank"><em>Adventures of Isabel</em></a> by Ogden Nash</strong></p>
<p><strong></strong>When confronted by a bear, a witch, and a questionable doctor, Isabel didn't care. As the book rhymes, “Isabel, didn't worry. Isabel didn't scream or scurry” and the bad guys get their comeuppance every time. The poem from this book is animated in <a href="https://www.youtube.com/watch?v=T9zN6jE2yUQ" target="_blank">this cute student-made short</a> (it’s a little heavy-handed that the video ends with info about the National Women’s Hotline, but that makes you feel all the more compelled to find and share books about strong girls).</p>
<p><img src="/sites/default/files/u2583/violet-the-pilot-book.jpg" alt="violet the pilot" width="518" height="400" /></p>
<p><strong><em><a href="http://www.powells.com/biblio/1-9780803731257-8" target="_blank">Violet the Pilot</a></em> by Steve Breen</strong></p>
<p>Violet is a crack mechanical engineer. With her trusty dog Orville, she not only builds her own a flying machine, but flies it, too. This book is a great gift for girls but I would also love to see this book in every little boy’s collection of planes, trains, and automobiles.</p>
<p><img src="/sites/default/files/u2583/71ejvpxtxl.jpg" alt="williams doll cover" width="339" height="450" /></p>
<p><strong><em><a href="http://www.powells.com/biblio/2-9780064430678-6" target="_blank">William’s Doll</a></em> by Charlotte Zolotow</strong></p>
<p><strong></strong>A classic memorialized in the 1972 album <em>Free to Be…You and Me</em>, this book not only validates the wishes of young boy who wants a doll—and a train set and a basketball—it is also a beautiful depiction of the relationship between a grandmother and grandson. It’s important book for boys and girls—it was four year-old girls who told my son that Hello Kitty wasn’t for him.</p>
<p><img src="/sites/default/files/u2583/flb-08.jpg" alt="" width="288" height="288" /></p>
<p><strong><em><a href="http://www.powells.com/biblio/72-9781550376852-0" target="_blank">The Munschworks Grand Treasury</a></em> by Robert Munsch</strong></p>
<p>The collection contains Munsch’s well-known feminist tale <em>The Paperbag Princess</em> along with others that should be just as much part of your library. Munsch’s books portray children of all colors, some of whom don’t match the skin of their parents.</p>
<p><img src="/sites/default/files/u2583/51ttjsk42tl.jpg" alt="ten nine eight cover" width="400" height="319" /></p>
<p><strong><em><a href="http://www.powells.com/biblio/1-9780688104801-3" target="_blank">Ten, Nine, Eight</a> by</em> Molly Bang</strong></p>
<p>This book isn’t about defying stereotypes or explicitly feminist in any way—it’s a counting book for babies and toddlers. But it’s beautifully illustrated and I am putting it on the list because basic books about numbers usually don’t portray little girls with brown skin. And as it counts down from ten, it turns into a bedtime story as well. It’s the one counting book that should be in every child’s library and is one of my favorite baby shower gifts, especially the board book version.</p>
<p><em>Read the rest of our <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides here</a>, including a <a href="http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-young-feminists" target="_blank">gift guide for teen feminists</a>.</em></p>
<div class="content">
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader!</a></p>
</div>
http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-childrens-picture-books#commentsBitch in a BoxbooksBitch HQTue, 09 Dec 2014 21:32:33 +0000Julie Falk29562 at http://bitchmagazine.orgBitch in a Box: Gift Guide for Young Feministshttp://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-young-feminists
<p><a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"></a></p>
<p><img src="http://farm8.staticflickr.com/7019/6432241749_0d1847e807_o.jpg" alt="bitch in a box" width="447" height="74" /></p>
<p>This month, we’re putting together a series of <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">feminist gift guides</a>. They're a way to highlight fun stuff we love and creators we're excited to support.</p>
<p>So you're looking for a gift for your 13-year-old niece, right? The one who loves Emma Watson, has declared she's going to run for president, and spends Friday night watching <em>Parks and Rec </em>with her friends? As a somewhat-recent teenager myself, here's what I'd recommend. </p>
<p><strong><em>Rookie Yearbook Three</em></strong> </p>
<p><img src="https://cdn.shopify.com/s/files/1/0155/4727/products/RYB3_cover.jpg?v=1404236358" alt="rookie yearbook three" width="445" height="560" /></p>
<p>Imagine if high schools taught Beyoncé 101 and your classmates included Lorde, the Fanning sisters, and Sia. With the<em> <a href="http://www.rookiemag.com/shop/rookie-yearbook-three/" target="_blank">Rookie Yearbook</a></em>, which features articles, interviews, art, and stickers, this magical feminist high school is a reality—on paper, anyway. The oversize, beautifully produced yearly anthology comprises essays and photos from <a href="http://www.rookiemag.com/">Rookie</a>, the online zine started by wunderkind <a href="http://bitchmagazine.org/post/an-interview-with-rookie-editor-tavi-gevinson" target="_blank">Tavi Gevinson</a>, as well as original content. And its chummy, accessible, and stylish content makes for a great introduction to feminist themes and theories for people of all ages.</p>
<p><strong><em>Lumberjanes</em></strong></p>
<p><strong><em><img src="http://www.boom-studios.com/media/catalog/product/cache/1/image/318x478/17f82f742ffe127f42dca9de82fb58b1/b/o/boombox_lumberjanes_001_a.jpg" alt="cover of lumberjanes" width="318" height="477" /><br /></em></strong></p>
<p>Comic book publisher BOOM describes<em> <a href="http://www.boom-studios.com/lumberjanes-01-cover-a.html" target="_blank">Lumberjanes</a></em> as “<em>Buffy the Vampire Slayer</em> meets <em>Gravity Falls</em>.” The female-created comic follows five best friends spending the summer at a scout camp where they encounter a variety of mythical creatures, from yetis to giant falcons. Eight issues of an ongoing series have been released so far, making a set of them the perfect gift to give to the girl whose BFFs like to plan their own adventures. </p>
<p><strong> “I Woke Up Like This” T-shirt</strong></p>
<p><strong><img src="/sites/default/files/u2583/bey_wokeupwhitetee_front_1.jpg" alt="i woke up like this shirt" width="460" height="690" /><br /></strong></p>
<p>Pretty much anything in the <a href="http://shop.beyonce.com/index.php/apparel.html">Beyoncé shop</a> would make a “flawless” gift, but Queen Bey’s feminist bona fides and role-model status makes this lyric the perfect one for almost any occasion.</p>
<p><strong><em>Sword and Sworcery</em></strong></p>
<p><strong><em><img src="/sites/default/files/u2583/legodesktop_small_1.png" alt="sword and sorcery logo" width="670" /><br /></em></strong></p>
<p>I’m not a videogamer, but I asked a feminist friend who studies computer science and gender studies what games he would recommend. It was a long list, to say the least, but at the top was <a href="http://www.swordandsworcery.com/"><em>Sword & Sworcery</em></a>, a game that follows a woman-warrior character on a journey through a mysterious land that incorporates both “real” and dream world. Featuring music by singer-songwriter Jim Guthrie, <em>Sword & Sworcery</em> was originally designed for iPhone and iPad, but is now available for Mac, PC, and Android.</p>
<p><strong>MaKey MaKey Kit</strong></p>
<p><strong><img src="/sites/default/files/u2583/7167036798_9e490c776f.jpg" alt="makey makey kit" width="500" height="265" /><br /></strong></p>
<p>If your budding feminist is an upstart tech nerd, there is not much that’s cooler than the <a href="http://www.makeymakey.com/" target="_blank">MaKey MaKey</a>. This fun little kit allows you to turn pretty much anything into an Internet-connected touchpad. Want to download a piano app and use bananas as the keys? Want to update your Facebook page with a keyboard made from alphabet soup? The mad science of MaKey MaKey lets it happen. (This <a href="https://www.youtube.com/watch?v=rfQqh7iCcOU" target="_blank">Youtube video</a> shows some of the amazing possibilities.) If it still sounds complicated, never fear: <a href="http://www.bbc.com/news/technology-18303012">One reviewer</a> said her four-year-old daughter was able to set up the kit with no help. </p>
<p><strong><em>The Girls' Guide to Rocking: How to Start a Band, Book Gigs, and Get Rolling to Rock Stardom </em></strong><strong>by Jessica Hopper</strong></p>
<p><strong><img src="/sites/default/files/u2583/91sa564bgxl.jpg" alt="girls guide to rocking" width="490" height="590" /><br /></strong></p>
<p>While <a href="https://twitter.com/jesshopp" target="_blank">Jessica Hopper</a> is known nowadays for her writing for Pitchfork and Rookie, as well as her upcoming book, <em>The First Collection of Criticism By A Living Female Rock Critic</em>, her <a href="http://www.powells.com/biblio/2-9780761151418-5" target="_blank">2009 guide</a> to becoming a working musician is still an inspirational and practical read. With chapters and insights on everything from choosing the right instrument to booking your own tours to translating contracts, the book offers key lessons on every aspect of life as a musician that will be pertinent well after girlhood.</p>
<p><strong>Speedball Super Value Fabric Screen Printing Kit</strong></p>
<p><strong><img src="http://upload.wikimedia.org/wikipedia/commons/4/4c/Screenprinting-example-obin.jpg" alt="screenprinting" width="670" height="420" /><br /></strong></p>
<p>A <a href="http://www.utrechtart.com/Speedball-Super-Value-Fabric-Screen-Printing-Kit-MP-44962-001-i1016030.utrecht" target="_blank">screenprinting kit</a> is pretty much a necessity for any young activist trying to get their message out. Whether they use it to make posters for their surf-rock garage band or t-shirts for their high-school math team, screenprinting screams self-reliance and classic style—there’s nothing more punk than DIY. <em>(photo via <a href="http://upload.wikimedia.org/wikipedia/commons/4/4c/Screenprinting-example-obin.jpg" target="_blank">Creative Commons</a>)</em></p>
<p><em>Read the rest of our <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides here</a>, including a gift guide for <a href="http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-crafty-people" target="_blank">people who are DIY as F*CK</a>.</em></p>
<div class="content">
<p><em>Hannah Steinkopf-Frank is a former Bitch Editorial Intern who likes to write about girl groups, her favorite 2000s TV shows, and sometimes college. See the bands she loves on Twitter <a href="https://twitter.com/hsteinkopffrank" target="_blank">@hsteinkopffrank</a>. </em></p>
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader!</a></p>
</div>
http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-young-feminists#commentsBitch in a BoxBitch HQFri, 05 Dec 2014 23:57:32 +0000Hannah Steinkopf-Frank29525 at http://bitchmagazine.orgBitch in a Box: Gift Guide for Crafty Peoplehttp://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-crafty-people
<p style="margin: 1em 0px; font-family: georgia, 'times new roman', serif; font-size: 14px; line-height: 18.003999710083px;"><a style="color: #6dbe45; text-decoration: none;" href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"><img src="http://farm8.staticflickr.com/7019/6432241749_0d1847e807_o.jpg" alt="bitch in a box logo" width="447" height="74" /></a></p>
<p>This month, we’re putting together a series of <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">feminist gift guides</a>. They're a way to highlight fun stuff we love and creators we're excited to support.</p>
<p>We all know that person who is DIY AS F*CK. It feels impossible to buy for them, because whatever you give them, they could have made it better. Do not be thwarted. Instead, get them something to nourish their craft. And hey, chances are, they’ll make you something hand hewn and awesome in return.</p>
<p><em>Please note, all of these items in this article can be found at your local hardware, craft, or sewing supply store. The links provided here are so you can get a good visual of the suggested items.</em></p>
<p><strong>Excellent Tools</strong></p>
<p><strong><img src="/sites/default/files/u2583/s100-r.jpg" alt="scissors" width="670" height="246" /></strong></p>
<p>First and foremost, all of your crafty friends will have to cut and measure something at some point. A safe bet would be to get them a really nice cut kit, including scissors, a cut mat and or other measuring devices. </p>
<p>A heavy duty, durable measuring tape is always appreciated. I like the <a href="http://www.homedepot.com/p/FATMAX-25-ft-Tape-Measure-33-725Y/100052995" target="_blank">Stanley Fat Max 25-foot tape measure</a>, which can be tossed aside in frustration without regret. Its also very brightly colored so I can find it easily.</p>
<p>A cut mat is a very handy thing to have. There are kits that you can buy, <a href="http://www.joann.com/dritz-rotary-cutting-kit-mat--ruler-and-cutter/5161526.html?mkwid=5WY7f0Pl%7Cdc&utm_source=google&utm_medium=cpc&utm_term=&utm_campaign=Shopping+-+Sewing&CS_003=10131488&CS_010=%5bProductId%5d&gclid=Cj0KEQiAhvujBRDUpomG5cq_mI0BEiQA7TYq-u8MlnYEvbwJ6MfRPXsuHB5kXhd3CIFfSNfVD2LMbvIaAhJj8P8HAQ" target="_blank">like this one</a> by Dritz, which is a great starter kit for the beginner. However, I would suggest <a href="http://www.joann.com/gingher-self-healing-rotary-mat-24inx36in/9816398.html?green=ECC8EA84-2745-568B-B01A-F4D2227CD5AD" target="_blank">getting a larger one</a>, like this <a href="http://www.joann.com/gingher-self-healing-rotary-mat-24inx36in/9816398.html?green=ECC8EA84-2745-568B-B01A-F4D2227CD5AD" target="_blank">Gingher “Self-Healing” Rotary Mat</a>. Although large and awkward to present as a gift, they are flat so can easily be stored behind a shelf or under the bed.</p>
<p>Not all scissors are created equal, and nothing is more bothersome than not being able to find a pair when you are mid project. Here are a few of my favorites: <a href="http://www.amazon.com/Fiskars-170610-1001-Amplify-RazorEdge-Fabric/dp/B00DF9W3EY/ref=zg_tr_689392011_3" target="_blank">Fiskars “RazorEdge” Fabric Shears</a>—these come in several sizes, the 10-inch ones are great for long cuts or getting through thick fabric like jeans, while the six-inch size are idea for precision cuts. Get both!</p>
<p>If you want to get your special someone the Ferrari of scissors, might I suggest any of <a href="http://www.kaiscissors.com/category.php?category_id=46" target="_blank">this array by Kai Scissors</a>. And, because nothing is more useless than dull scissors…a <a href="http://www.amazon.com/Fiskars-SewSharp-Scissors-Sharpener-98547097/dp/B0002JT0PK/ref=pd_sim_ac_3?ie=UTF8&refRID=0XK52659D43A6DCDAVA4">scissor sharpener</a> is always appreciated!</p>
<p>No crafter’s tool kit is complete without a glue gun, and might I suggest presenting it with a <a href="http://www.holsterbrands.com/hobby-holster" target="_blank">Hobby Holster</a>.</p>
<p><strong>Handy Boxes to Put Things In</strong></p>
<p><img src="/sites/default/files/u2583/il_570xn.446410332_rm9j.jpg" alt="tool box" width="570" height="393" /></p>
<p>Help give your crafter the gift of organization! A nice toolbox to put their tools and materials in is extremely helpful. Etsy has a great collection of <a href="https://www.etsy.com/search?q=tool%20box&order=most_relevant&utm_source=google&utm_medium=sem&utm_geo=US&utm_term=%20etsy%2B%20box&utm_campaign=Google%7CEtsy%7CHousewares%7CBMM&utm_ag=Box" target="_blank">outside-the -box tool storage ideas</a>. (The one above is from <a href="https://www.etsy.com/listing/128706098/wooden-tool-box-miniature-altered-cigar?ref=sr_gallery_23&ga_search_query=tool+box&ga_order=most_relevant&ga_utm_source=google&ga_utm_medium=sem&ga_utm_geo=US&ga_utm_term=+etsy%2B+box&ga_utm_campaign=Google%7CEtsy%7CHousewares%7CBMM&ga_utm_ag=Box&ga_search_type=all&ga_view_type=gallery" target="_blank">Shopworn Designs.</a>)</p>
<p>A set of four-ounce wide-mouth canning jars are also very useful for your home crafter. These can be found at most of your local hardware or grocery stores.</p>
<p><strong>Inspirational Reading</strong></p>
<p><img src="/sites/default/files/u2583/screen-shot-2014-03-02-at-15.06.02-730x390.png" alt="eliza muldoon reading her book" width="670" height="369" /></p>
<p><em><a href="http://www.powells.com/biblio/1-9781742378657-0" target="_blank">Lazing on a Sunday Crafternoon: Little Projects for People with Just a Little Time and Little Skill</a> </em>by Eliza Muldoon</p>
<p>For novice or occasional crafters, this book is ripe with inspiration for simple projects you can complete with basic things you might even have around the house. It also has some great craft projects that you can do with kids (or with kids around). (Photo above from <a href="http://www.madepeachy.com/guest-post-eliza-muldoon/" target="_blank">Made Peachy</a>.)</p>
<p><em><a href="http://www.goodreads.com/book/show/551890.Bend_the_Rules_Sewing" target="_blank">Bend The Rules Sewing</a></em> by Amy Karol</p>
<p>This is one of my personal favorites. It brings an accessible, come-as-you-are tone to the craft of sewing and some fun and simple project suggestions. </p>
<p><em><a href="http://www.goodreads.com/book/show/17326811-resin-alchemy" target="_blank">Resin Alchemy</a> </em>by Susan Lenart Kazmer </p>
<p>This book is great for the jewelry-maker you know. It has fantastic reviews and beautifully photographed step-by-step guides. </p>
<p><em><a href="http://www.goodreads.com/book/show/18124457-fabric-paper-thread" target="_blank">Fabric, Paper, Thread</a> </em>by Kristen Sutcliffe</p>
<p>For the young crafter, this book offers simple craft projects targeted at teens and anyone new to embroidery. </p>
<p><em><a href="http://www.powells.com/biblio/1-9781604693935-2" target="_blank">Succulents Simplified</a> </em>by Debra Lee Baldwin </p>
<p>This book teaches you how to grow and design with succulents. Even if you never get around to making elaborate room décor with living plants, the photography alone in this book is worth the investment.</p>
<p><strong>Some Raw Materials</strong></p>
<p><strong><img src="/sites/default/files/u2583/spoolsofthread.jpg" alt="" width="640" height="425" /><br /></strong></p>
<p>DO get your crafter small useful items, like a nice set of basic sewing tools and notions, <a href="http://moderndomesticpdx.com/products/sewing-tools-and-notions/" target="_blank">here’s a great starter list from Modern Domestic</a>, a homegrown sew shop in Northeast Portland, Oregon. </p>
<p>DO NOT get them advanced tools or specialty tools unless they specifically ask for them. A crafter can be pretty picky about the jig saw, crochet needles, or sewing machine they are after. A gift card to your local tool store would do much better!</p>
<p>DO get your crafter BASIC raw materials like Velcro, super glue, or a set of nice thread.</p>
<p>DO NOT get your crafter raw materials like yarn or fabric. This is something they’ll want to pick out for themselves. Instead, get them a gift card to your local independent fabric or yarn, or <a href="http://scrappdx.org/" target="_blank">SCRAP</a> store. They will absolutely love the experience of getting to pick out just the right material for their next project.</p>
<p><em>Read the rest of our <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides here</a></em>. </p>
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader</a>!</p>
<p> </p>
http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-crafty-people#commentsBitch in a BoxBitch HQFri, 05 Dec 2014 02:37:28 +0000Amanda Green29515 at http://bitchmagazine.orgBitch in a Box: Gift Guide for Science Nerdshttp://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-science-nerds
<p><a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"><img src="http://farm8.staticflickr.com/7019/6432241749_0d1847e807_o.jpg" alt="bitch in a box logo" width="447" height="74" /></a></p>
<p>This month, we’re putting together a series of <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">feminist gift guides</a>. They're a way to highlight fun stuff we love and creators we're excited to support. I'm kicking it off with a gift guide for science nerds—the STEM-fan in your life could use some love, after all. </p>
<p><img src="/sites/default/files/u2583/il_570xn.687064963_kn5f.jpg" alt="a blue dress covered in constellations" width="570" height="446" /></p>
<p><strong>Cute Constellation Dress</strong></p>
<p>It glows in the dark! <a href="https://www.etsy.com/listing/211734812/glow-in-the-dark-constellation-dress?ref=related-0" target="_blank">And it's handmade!</a> And the same person who sews it also makes these <a href="https://www.etsy.com/listing/211673636/gold-glitter-t-rex-heels?ref=related-0" target="_blank">glittery gold T-Rex high heels</a>. So compared to those, this dress is downright sensible. </p>
<p><img src="/sites/default/files/u2583/il_570xn.428836201_dwe8.jpg" alt="a shirt featuring various gems" width="570" height="570" /></p>
<p><strong>Lovely Mineral Gems Shirt</strong></p>
<p>I was a rockhound as a teenager, spending my summers in Eastern Oregon looking for fossils and thundereggs. <a href="https://www.etsy.com/listing/123958189/minerals-gems-womens-tshirt?ref=related-1" target="_blank">This shirt speaks to me,</a> even though wearing it will be a liability since I'm sure it will give rise to endless puns about how my shirt "rocks" or people "dig" it. </p>
<p><img src="/sites/default/files/u2583/jul098117_1.jpg" alt="digifying science cover" width="230" height="330" /></p>
<p><strong>The <em>Dignifying Science</em> Comic Book</strong></p>
<p>This <a href="https://www.comixology.com/Dignifying-Science-Stories-About-Women-Scientists/digital-comic/30385" target="_blank">143-page collection</a> tells the stories of women in a bunch of different scientific fields, including well-known people like Marie Curie and DNA researcher Rosalind Franklin to lesser-known figures like biologist Barbara McClintock. I read this in college and it blew my mind—I lent it to a couple people over the years and lost track of it somewhere along the way. Lesson learned: Get two copies so you can lend it out. </p>
<p> </p>
<p> </p>
<p><img src="/sites/default/files/u2583/ct-adas-algorithm-jpg-20141106.jpg" alt="adas algorithm book" width="500" height="281" /></p>
<p><strong>A Copy of <em>Ada's Algorithm </em></strong></p>
<p>This new book about the life and impact of mathematician and <a href="http://www.powells.com/biblio/1-9781612194080-0" target="_blank">science pioneer Ada Lovelace</a> looks great. The biography contains just the kind of moments of triumph I like to read about: Ada overcoming obstacles to get an education and make genius contributions to science. While reading the book, I will consume beverages exclusively out of Bitch's <a href="http://bitchmagazine.org/support-feminist-media/adventures-in-feministory-mug-ada-lovelace" target="_blank">Ada Lovelace mug</a>. </p>
<p><strong><img src="/sites/default/files/u2583/bat-house-on-brick-building_by_dano_cc_by_2.0.jpg" alt="a small birdhouse-looking creation with bats painted on it" width="670" height="500" /><br /></strong></p>
<p><strong>My Very Own Bat House</strong></p>
<p>Bats get a bad rap. But on a warm night last summer, I saw a backyard lecture about the importance of bats to our ecosystem and their awesomeness in general (bats make up 20 percent of mammal species worldwide! 20 percent!). I would now like to install a bat house in my backyard, to give local bats a nice place to roost while they eat all the summer mosquitos. However, I don't want to build it myself, so it would be great if a friend would <a href="http://www.nwf.org/How-to-Help/Garden-for-Wildlife/Gardening-Tips/Build-a-Bat-House.aspx" target="_blank">follow these DIY bat house instructions</a> and present me with a cozy bat home on Christmas day. <em>(photo from <a href="http://buildipedia.com/at-home/landscaping/natural-pest-control-benefits-of-bat-houses" target="_blank">Buildapedia</a>) </em></p>
<p><em><img src="/sites/default/files/u2583/baton3.gif" alt="bat detector" width="432" height="273" /><br /></em></p>
<p><strong>A Bat Detector</strong> </p>
<p>Essential for optimal use of the aforementioned bat house. It makes a <a href="http://www.batmanagement.com/Ordering/acoustic/hardware6.html" target="_blank">cool beeping noise</a> whenever bats fly close by. </p>
<p><img src="/sites/default/files/u2583/10kita.jpg" alt="" width="546" height="375" /></p>
<p><strong>A Geodesic Dome Kit</strong></p>
<p><a href="http://www.ziptiedomes.com/index.htm" target="_blank">This thing is $300</a>, but look how much fun these kids are having with it! I hope the kit comes with that Sonic shirt. Since this idea seems impractical, I will accept this <a href="https://www.etsy.com/listing/191017107/glass-half-fuller?ref=sr_gallery_35&ga_search_query=geodesic+dome&ga_ref=auto3&ga_search_type=all&ga_view_type=gallery" target="_blank">"Glass Half Fuller" print</a> as a punny substitute. </p>
<p><img src="/sites/default/files/u2583/00087147-587500_283.jpg" alt="planet earth" width="283" height="283" /></p>
<p><strong>All of <em>Planet Earth</em> on DVD</strong></p>
<p>Let's face it, I could watch this forever. I am jealous of people who have never watched the <a href="http://store.discovery.com/planet-earth-the-complete-collection-dvd/detail.php?p=87147&v=discovery_shows_life-planet-earth" target="_blank">BBC's epic documentary series</a> about nature because they get to see "Caves" and "Shallow Seas" for the first time. </p>
<p><img src="/sites/default/files/u2583/photo.jpg" alt="period table mug" width="470" height="320" /></p>
<p><strong>Japanese Periodic Table of the Elements Mug</strong></p>
<p>San Francisco-based Japanese ceramics and kitchenwear company <a href="http://www.kotobukitrading.com/product/ceramics_seto.php" target="_blank">Kotobuki</a> imports adorable stuff (<a href="http://www.kotobukitrading.com/product/ceramics_seto.php" target="_blank">like cat and panda mugs</a>) and this periodic table is no exception. It's beautiful, well-made, and maybe I'll finally memorize the periodic table just by staring at it while I'm at work. I can't for the life of me figure out how to order these online—I saw them at a Portland grocery store where I snapped the blurry photo above—but <a href="https://portal.kotobukitrading.com/pdfs/2013%20SA%20New%20Items.pdf" target="_blank">here's a PDF of the catalogue</a> and maybe you can decipher it. </p>
<p><img src="/sites/default/files/u2583/ppbs3-15237043dt.jpg" alt="" width="300" height="300" /></p>
<p><strong><em>The Bletchley Circle </em></strong></p>
<p>All year, I've been watching TV shows about hard-hitting women solving crimes. First, I got into <em>Top of the Lake</em>, then the Danish series <em>The Killing</em>. Now, <a href="http://bitchmagazine.org/post/a-female-codebreaker-finally-gets-fame-in-the-imitation-game" target="_blank">Bitch commenters tell me</a> that there's a British series about <a href="http://www.shoppbs.org/product/index.jsp?productId=19453286&cp=&sr=1&kw=bletchley+circle&origkw=bletchley+circle&parentPage=search" target="_blank">WWII mathematicians and codebreakers</a> who use their skills to crack uncrackable cases? Sign me up, please. </p>
<p><img src="https://farm5.staticflickr.com/4052/4354348514_9f514efe7a_o.jpg" alt="a blue print of a ferm" width="350" height="330" /><img src="/sites/default/files/u2583/screen_shot_2014-12-01_at_6.16.24_pm.png" alt="sunprint kit" width="309" height="281" /></p>
<p><strong>Sunprint Kit</strong></p>
<p>These <a href="http://store.lawrencehallofscience.org/Category/sunprint-kits" target="_blank">cool little kits</a> let you make cyanotype-style prints with only air, water, and sunshine. I would buy these for a kid with the noble goal of instilling them with a love of science, then never actually gift it and instead steal it for myself. So, I should have a couple on hand as a backup. </p>
<div class="content">
<p><em>Read the rest of our <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides here</a></em>. </p>
<hr />
<p>Want the best of Bitch in your inbox? <a href="http://bitchmagazine.org/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader</a>!</p>
</div>
http://bitchmagazine.org/post/bitch-in-a-box-gift-guide-for-science-nerds#commentsBitch in a BoxBitch HQTue, 02 Dec 2014 02:26:56 +0000Sarah Mirk29452 at http://bitchmagazine.orgBitch in a Box: A Hostile Gift Guidehttp://bitchmagazine.org/post/bitch-in-a-box-a-hostile-gift-guide
<p style="margin: 1em 0px; font-family: georgia, 'times new roman', serif; font-size: 14px; line-height: 18px;"><a style="color: #6dbe45; text-decoration: none;" href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank"><img src="http://farm8.staticflickr.com/7019/6432241749_0d1847e807_o.jpg" alt="feminist gift guides" width="447" height="74" /></a></p>
<p>Just for fun this week at Bitch, we’re putting together a series of <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">gift guides</a>. Our last edition of <a href="http://bitchmagazine.org/tag/bitch-in-a-box" target="_blank">Bitch in a Box</a> is a guide to hostile gifts.</p>
<p>A hostile gift (as opposed to a <a href="/post/bitch-in-a-box-gift-guide-for-hosts" target="_blank">Host Gift</a>) is a present meant for someone you don’t want to please.</p>
<p>It is not a gift for someone that is in fact intended for you (eg. Homer’s gift for Marge of a bowling ball with the name “Homer” inscribed) or a passive aggressive or mean-spirited gift that suggest the recipient needs to make changes in their life (eg. deodorant or a copy of <em>The South Beach Diet</em>). Rather a hostile gift is meant to intentionally inspire perplexity, confusion, and apoplexy.</p>
<p><strong>A plastic poinsettia</strong></p>
<p><img src="http://farm3.staticflickr.com/2857/11535579805_2b2ebc7536.jpg" alt="a poinsettia" width="500" height="500" /></p>
<p>Nothing says “crap” like <a href="http://www.christmascentral.com/p-140184-16-red-artificial-poinsettia-potted-christmas-plant-with-gold-foil-covering.aspx?CAWELAID=1648401081&catargetid=1614140047&cadevice=c&cagpspn=pla-&gclid=CJ6ei_G1v7sCFTDhQgodFl0AmQ">a cheap plastic poinsettia</a>.</p>
<p><strong>Fruitcake</strong></p>
<p><img src="http://farm4.staticflickr.com/3712/11535482285_783fd8b432.jpg" alt="fruitcake" width="500" height="333" /></p>
<p><a href="https://www.claxtonfruitcake.com/pages/bakery-catalog-item/Claxton_Fruit_Cake?previous_url_id=0" target="_blank">Fruitcake</a>, whether store bought or handmade, is a traditional hostile gift in American culture. You really can’t say “Happy holidays, I don’t really care about you” any better than with a dense, tooth-splitting, artificial-color-laden fruitcake. </p>
<p>Having said that, the Truman Capote short story <em><a href="http://en.wikipedia.org/wiki/A_Christmas_Memory" target="_blank">A Christmas Memory</a></em>, which centers on a young boy and his cousin making fruitcakes, is one of my favorite pieces of Christmas literature. Combining <a href="http://www.powells.com/biblio/9780679800408" target="_blank">a copy of this book</a> with a fruitcake turns a hostile gift into an ironic and lovely gift.</p>
<p><strong>Shoe polish</strong></p>
<p><img src="http://farm3.staticflickr.com/2853/11535558554_bf4e4493ec_n.jpg" alt="show polish" width="320" height="320" /></p>
<p>What would you say if you were given an <a href="http://www.shoecaresupplies.com/Shoe_Polish_s/59.htm?gclid=CJCNq7e-v7sCFYN_QgodMQIAig" target="_blank">off-color shoe polish</a>, such a red mahogany or banana? What could you say? A friend of mine received this gift and, I have to say, combined with a pair of used shoe trees, you have an ideal hostile gift.</p>
<p><strong>An incomplete set of dishes</strong></p>
<p><strong><img src="http://farm8.staticflickr.com/7367/11535617353_b6342e9ccb_o.jpg" alt="two owl mugs" width="400" height="400" /><br /></strong></p>
<p>If you really want to instill confusion in your gift recipient, consider purchasing of beautiful set of four wine glasses and only gifting them three. Or buying a very attractive salt and pepper set and give only the salt shaker. I recently received a set of three soup bowls for my family of four, so I can personally attest to this being an excellent hostile gift.</p>
<p>I sincerely hope you don’t have the need to purchase a hostile gift this season, and my heart goes out to you if you receive anything on this list. Please use the comments section for hostile gift ideas of your own, or to vent about gifts you may have received.</p>
<p><em>Read the rest of our <a href="/tag/bitch-in-a-box" target="_blank">gift guides here</a></em>. </p>
<hr />
<p>Want the best of Bitch in your inbox? <a href="/subscribe-to-the-weekly-reader" target="_blank">Sign up for our free weekly reader</a>!</p>
<p><a href="/issue/61" target="_blank">Read and buy <em>Bitch</em> magazine's current print issue!</a></p>
http://bitchmagazine.org/post/bitch-in-a-box-a-hostile-gift-guide#commentsBitch in a BoxBitch HQTue, 24 Dec 2013 19:14:46 +0000Julie Falk24847 at http://bitchmagazine.org | {
"pile_set_name": "Pile-CC"
} |
This proposal is to renew support for a Postdoctoral Research Training Program in Microbial Pathogenesis of Infectious Diseases. Highly successful in its first 20 years, this program has been extensively redesigned to prepare graduates to meet growing workforce needs in translational science. This program has been structured to synergize with an innovative program established for pre-doctoral students at Tufts University with support from the Howard Hughes Medical Institute (MERGE-ID). Both programs utilize a combination of required co- mentorship by a clinical researcher and a basic laboratory scientist as well as coursework and conferences specifically designed to blend a basic science orientation with medically oriented clinical research and to encourage interaction between ID clinicians and basic scientists. This program is designed to train both M.D. fellows in Infectious Diseases as well as Ph.D. fellows interested in studying microbial pathogenesis. Ph.D. trainees take a specially designed course in Medical Problem based Learning that teaches self-learning using cases from the 1st year medical school curriculum. In addition, they participate in outpatient clinics in Infectious diseases to directly observe medical care of specific diseases. M.D. trainees must take graduate level courses in Host-pathogen interactions alongside Ph.D. students in the MERGE-ID program. Although changes have been made to the structure and curriculum, the core of this program remains its outstanding faculty who share an interest in Infectious Diseases. Strengths of the faculty include investigations of: 1) virulence determinants in bacterial, viral, parasitic and fungal pathogens; 2) infections in immunocompromised hosts; 3). Interactions of the host immune system with bacterial, viral and fungal pathogens; 3) interspecies microbial interactions and the impact on infectious disease pathogenesis; 4) clinical study design. The 26 faculty are highly interactive and have a long history of collaboration as evidenced by a large number of shared publications and grants. Another major strength of the program has been the use of Personal Progress Review Committees comprised of 4 faculty members that meet every 6 months to ensure progress of the trainee. This format has allowed the program to achieve a high success rate (>75%) for its trainees in remaining in academic, industrial, or governmental research despite the fact that historically, the majority of the in trainees that have entered the program are M.D. fellows with no prior research experience. The success of the program has translated into continued highly successful recruitment, including among underrepresented minorities that comprised greater than 25% of the trainees during the most recent period. The application requests support for 4post-doctoral trainees per year. Trainees are chosen through a rigorous selection process and are supported for 2-3 years. | {
"pile_set_name": "NIH ExPorter"
} |
Image reconstruction and image quality evaluation for a 16-slice CT scanner.
We present a theoretical overview and a performance evaluation of a novel approximate reconstruction algorithm for cone-beam spiral CT, the adaptive multiple plane reconstruction (AMPR), which has been introduced by Schaller, Flohr et al. [Proc. SPIE Int. Symp. Med. Imag. 4322, 113-127 (2001)] AMPR has been implemented in a recently introduced 16-slice CT scanner. We present a detailed algorithmic description of AMPR which allows for a free selection of the spiral pitch. We show that dose utilization is better than 90% independent of the pitch. We give an overview on the z-reformation functions chosen to allow for a variable selection of the spiral slice width at arbitrary pitch values. To investigate AMPR image quality we present images of anthropomorphic phantoms and initial patient results. We present measurements of spiral slice sensitivity profiles (SSPs) and measurements of the maximum achievable transverse resolution, both in the isocenter and off-center. We discuss the pitch dependence of image noise measured in a centered 20 cm water phantom. Using the AMPR approach, cone-beam artifacts are considerably reduced for the 16-slice scanner investigated. Image quality in MPRs is independent of the pitch and equivalent to a single-slice CT system at pitch p approximately 1.5. The full width at half-maximum (FWHM) of the spiral SSPs shows only minor variations as a function of the pitch, nominal, and measured values differ by less than 0.2 mm. With 16 x 0.75 mm collimation, the measured FWHM of the smallest reconstructed slice is about 0.9 mm. Using this slice width and overlapping image reconstruction, cylindrical holes with 0.6 mm diameter can be resolved in a z-resolution phantom. Image noise for constant effective mAs is nearly independent of the pitch. Measured and theoretically expected dose utilization are in good agreement. Meanwhile, clinical practice has demonstrated the excellent image quality and the increased diagnostic capability that is obtained with the new generation of multislice CT systems. | {
"pile_set_name": "PubMed Abstracts"
} |
---
abstract: 'Parameter reduction can enable otherwise infeasible design and uncertainty studies with modern computational science models that contain several input parameters. In statistical regression, techniques for *sufficient dimension reduction* (SDR) use data to reduce the predictor dimension of a regression problem. A computational scientist hoping to use SDR for parameter reduction encounters a problem: a computer prediction is best represented by a deterministic function of the inputs, so data comprised of computer simulation queries fail to satisfy the SDR assumptions. To address this problem, we interpret SDR methods *sliced inverse regression* (SIR) and *sliced average variance estimation* (SAVE) as estimating the directions of a *ridge function*, which is a composition of a low-dimensional linear transformation with a nonlinear function. Within this interpretation, SIR and SAVE estimate matrices of integrals whose column spaces are contained in the ridge directions’ span; we analyze and numerically verify convergence of these column spaces as the number of computer model queries increases. Moreover, we show example functions that are not ridge functions but whose inverse conditional moment matrices are low-rank. Consequently, the computational scientist should beware when using SIR and SAVE for parameter reduction, since SIR and SAVE may mistakenly suggest that truly important directions are unimportant.'
author:
- Andrew Glaws
- 'Paul G. Constantine'
- 'R. Dennis Cook'
bibliography:
- 'deterministicSDR.bib'
date: 'Received: date / Accepted: date'
subtitle: 'A data-driven approach for parameter reduction in computer experiments'
title: 'Inverse regression for ridge recovery [^1] '
---
[^1]: Glaws’ work is supported by the Ben L. Fryrear Ph.D. Fellowship in Computational Science at the Colorado School of Mines and the Department of Defense, Defense Advanced Research Projects Agency’s program Enabling Quantification of Uncertainty in Physical Systems. Constantine’s work is supported by the US Department of Energy Office of Science, Office of Advanced Scientific Computing Research, Applied Mathematics program under Award Number DE-SC-0011077.
| {
"pile_set_name": "ArXiv"
} |
Q:
How does crop quality work?
I know that a higher crop quality results in more profit, and that I need to use fertilizer in order to get higher quality crops, but I'm not sure on any specific details. Specifically, I'm curious as to the following:
What are the different levels of crop quality?
How many times do I need to fertilize a crop in order to raise it's level?
How many crops can I fertilize with one bag of fertilizer?
A:
Crop quality has ten different levels from half a star, all the way up to five stars. The base quality will be what the quality of the seeds are, which are a half star when you first start out.
In order to improve quality, there are several things you can do:
Use better fields. When you first start out, you only have Gravel Fields, which aren't very good at all. As time goes on, you will gain blueprints that allow you to build better fields.
Use fertilizer every day to grow better crops. Each bag of fertilizer costs 100G, and is good for a single use, on a single crop. You'll need eight bags of fertilizer to fertilize a whole field. For best results, apply fertilizer every day. I believe it takes ~4 days to improve crop quality by half a star. This may differ for each crop; I will test and make notes as I am able. Field type probably also plays a part in it.
Important: Do NOT water it more than once a day. You can water crops twice a day, which will make them grow faster. This will adversely affect crop quality, because you won't have as many opportunities to apply fertilizer to improve crop quality. This is especially important for crops you intend to enter in the crop festival.
I suspect one of the later buildings will allow you to convert a harvested crop into a bag of seeds at the same quality level, ala. Harvest Moon DS. I have no proof, however, so take it with a grain of salt. If it's true, though, it should allow an eventual permanent five stars of all your products.
There's nothing in the tutorial that says anything about decreasing crop quality, but I bet forgetting to water them and allowing them to wilt will decrease quality; otherwise you could just keep it on the brink of death, and feed it fertilizer every day, until you were at the end of the month. Decreasing crop quality when wilting makes sense, as a counter to that. I have no real proof that that's how it work, though.
| {
"pile_set_name": "StackExchange"
} |
1. Field of the Invention
The present invention relates to data processing systems and in particular to a system in which a central processing unit has a register file for storage of often-used data to minimize the need for relatively slower accessing of a main memory of the system. More particularly, it relates to the circumstance when contents of the register file have to be saved in a main memory, and then restored therefrom, and a method of minimizing the saving and restoring of the contents of the register file in and from the main memory.
2. Description of the Prior Art
Since registers are lower in access cost than memories, the effective utilization of registers is a key design goal for enhancement of the program processing speed of a processor. However, the number of the registers that can be employed is finite.
Various systems and methods have been devised in an effort to effectively utilize the registers of a register file. For example, the system disclosed in U.S. Pat. No. 4,777,588 allocates a variable number of registers to a particular procedure that is limited to only the number that is actually required by the procedure. In addition, register classes are defined so that communication may occur between multiple procedures via variables stored in a set of "global" registers while variables required for a given procedure are stored in a set of "local" registers. Local registers may be disposed so that a set of registers used by a calling procedure overlap with the set of registers used by the called procedure. This allows convenient passing of parameters from the calling procedure to the called procedure. A stack pointer value stored in one of the register sets defines accesses to the local registers of the set. Adjusting the stack pointer values can produce the overlap so that the procedures can communicate via the registers in common. In a multi-tasking environment, to proscribe access to selected registers containing values set by a task, during the running of other tasks, a protection register is provided which contains data indicating a denial of access to a block of the register file in which the selected registers are included. Accordingly, the system can use the register file to operate on multiple tasks while maintaining the integrity of the variables of each from undesired changes occurring in the others.
A register file comprised of a plurality of register sets made up of a number of local registers is also disclosed in U.S. Pat. No. 4,811,208. At a call instruction, a register set from the file is allocated to the called procedure. At a return instruction, the allocated register set is freed for allocation to another procedure called by a subsequent call instruction. If the register file is depleted, the contents of a register set associated with a previous procedure is saved in the main memory, and that register set is allocated to the current procedure. The contents of the earlier procedure's register set is mapped into a stack frame. Unfortunately, there is no teaching or reference to a mechanism for especially storing the registers. Neither the timing of the storing or whether or how to restore is identified. | {
"pile_set_name": "USPTO Backgrounds"
} |
Patterns of fos-like immunoreactivity in the brains of parent ring doves (Streptopelia risoria) given tactile and nontactile exposure to their young.
Neuronal activation was examined by fos immunohistochemistry in ring doves (Streptopelia risoria) reunited with their young after overnight separation. In an initial study, squab-exposed parents showed more fos immunoreactivity (ir) in the preoptic area (POA) and lateral hypothalamus (LH) than squab-deprived parents. In a 2nd study, parents allowed free access to young and those separated from young by a wire mesh partition showed more fos-ir in the POA, LH, and lateral septum than box-exposed controls. Contact with young also increased fos-ir in the medial preoptic nucleus and bed nucleus of the stria terminalis, but noncontact exposure did not. Conversely, nontactile squab exposure stimulated more fos-ir in the POA than did free access to young, which suggests POA involvement in appetitive aspects of parenting. | {
"pile_set_name": "PubMed Abstracts"
} |
PeopleforBikes Praises Flawed Figueroa Bikeway Design
The bicycle industry lobby Peopleforbikes has posted the image below, identified as an official rendering, of the proposed bikeway on Figueroa Street in Los Angeles.
PeopleforBikes praises the political developments which led to this project and describes it as a “win.” My response is “what were the designers thinking, if it can be called thinking?” And “does PeopleforBikes expect to gain any credibility by supporting this?
Even putting aside general debates about “cycle tracks”… let’s just look at some specifics of the design here.
This is much less and also much more than a “protected bike lane”, PeopleforBikes’s description. Being separated from the other lanes by a barrier, it is not a bike lane but a bike path — one of substandard width. Most of the installation as shown is intended to serve bus passengers. Bicyclists get the narrow strip which is left over.
The roadway has been narrowed by one lane’s width, but more than half of it has been given over to a traffic island for a bus stop, and less than half, to the bikeway. The bikeway is not as wide as either the bicyclist or the pedestrians in the foreground are tall: only about five feet wide, between vertical curbs. Because bicyclists need to track two feet from a curb to avoid the risk of a pedal strike, the bikeway is only wide enough for a single line of bicyclists.
Bicyclists’ speeds on level roads range from approximately 8 to 25 miles per hour. One bicyclist overtaking another on this bikeway risks handlebars’ tangling, or a pedal strike. Overtaking a cargo tricycle is clearly impossible. Expect crashes, and parades of bicyclists limited to the speed of the slowest.
There is only that one bicyclist shown…if bicycle traffic were as heavy as PeopleforBikes would like, the bikeway would be clogged.
The bikeway is adjacent to a sidewalk. Expect pedestrians in the bikeway, and bicyclists riding on the sidewalk, or the bus lane, because the bikeway is slower.
The fence shown to the left of the bikeway (apparently to prevent pedestrians from crossing at an undesignated location) is nonstandard for either a pedestrian or bicycle barrier — bicyclists and pedestrians alike would topple over it. The fence is immediately adjacent to the bikeway, and that also is nonstandard.
The intersection in the foreground is signal-controlled, but the special crosswalk to the bus stop beyond the bicyclist is not. Now, imagine a crowd of pedestrians who just got off a bus, crossing in that crosswalk. If more than a few bicyclists have to wait, they will back up into the signalized crosswalk in the foreground, and into the intersection. Green paint in the crosswalk indicates, as it so often does, “we broke the rules when we designed this.”
With pedestrians in the locations shown, the bicyclist shown has to have crossed the walkway against the light. That doesn’t reflect on the design itself, but it does reflect on the people who approved the rendering, and the designers.
The striped, angled cutaway in the traffic island serves to allow large trucks and buses to turn right without dragging their wheels over the curb. But it is delimited by raised rubber barriers which might survive one or two days of wear and tear by trucks. The stripes also define the cutaway as a no-drive zone.
A truck apron is usually made of durable, slightly raised, distinctive paving. What were the designers thinking?
The tree overhanging the bikeway would drop leaves into it, an issue I brought up in an earlier post on this blog. The bikeway is shown as impeccably clean in the illustration, but it is too narrow for a standard street-cleaning machine.
I have read elsewhere that this bikeway would cross 26 intersections and 49 driveways.
The right one-foot width of the bikeway is the gutter pan, and there is a seam between it and the asphalt pavement. These seams break up, and can trap bicycle wheels. Water collects in the gutter, as also shown in videos which my friend Gary Cziko has taken from his bicycle. He describes them as follows:
1. The first video at http://vimeo.com/88343481 is a combined front and rear view while cycling on Figueroa northbound from Exposition to 7th Street, where the cycle track is planned. It was made at mid-day on a weekday with fairly light-to-moderate traffic.
2. The second video at http://vimeo.com/89685353 is rearview also northbound at evening rush hour starting a bit further south than the first video.
Gary has more to say about his videos but I’ll leave it to him to comment.
This is very much like–but is a lot longer than, and so even worse than–Austin’s Guadalupe cycletrack, which a Green Lane Project writer deemed #3 in his list of the ” best ” such facilities for 2013. It is far worse than what was in place before and has already caused crashes.
Hi, John – I appreciate the critique. For what it’s worth, I agree that the five-foot lane behind the bus stop is on the narrow side, definitely too narrow for passing or pedaling abreast. If you look at the cross-sections in the fairly detailed project description from which I pulled the image, this is the narrowest point for bike lanes on the corridor, where the 3-foot bike lane buffer includes a curb. The bus stop, according to that description, is to the left of the curb in a separate allocation of ROW. On other sections of the road, the lane and buffer range from seven feet plus a curbed buffer of up to four feet, and six feet plus a three-foot painted buffer.
The point about fallen leaves is good, and worth paying attention to (by cities and by advocates). I’m actually putting up a post today about street cleaning machines that can operate in as little as four feet.
The subtler design issues you raise are persuasive, too, and definitely worth raising with the city as it moves closer to full engineering on this project. None is a fundamental flaw with the concept, though, and certainly all of these (speed tradeoffs included) will make the street far better for biking on than it currently is for almost everyone.
The bottom line, as lucidly pointed out by Ms. Szczepanski, is that separate facilities do not relieve a cyclist, whether 8, 80, or anything in between, from being attentive, knowledgeable, aware, and knowing how to avoid a crash. Sometimes, I think cyclists relax their guard a little too much when offered their own segregated space that is marketed as “safe”. Carolyn’s concussion after hitting a pedestrian is a good counterexample–safety is still to a major extent controlled by events and your ability to master them. I’m glad Carolyn is still here to talk about her story.
On Saturday, there was a cyclist killed in Santa Fe, New Mexico, apparently while crossing the RailRunner tracks while on the Santa Fe Rail Trail. She rode right out in front of an oncoming train. Witnesses said she was wearing headphones. I implore cyclists to retain their situational awareness and practice riding skills whether on the road or on a cycletrack. I implore People for Bikes to promote cyclist education as much as they do segregated facilities. One does not displace the other. PfB’s stated goal “Riding made simple. The choice to ride a bike is yours. The responsibility to ensure safe and convenient riding opportunities is ours.” is only partially true, and I’m trying to be civil here. PfB cannot make you a safe rider and an unsafe rider can be hurt or killed on a cycletrack just as he or she can on a regular road. Trust me.
Some mistakes you only get to make once. That Santa Fe lady, a sixty year old, is dead in large part due to a lapse in awareness. Perhaps, that lack of situational awareness was due in part to thinking some other entity was responsible for her safety.
Khal — In the fourth paragraph of Carolyn Szczepanski’s article about her crash, she makes this rather sweeping claim: “Research shows that [protected bike lanes] are safer than riding in the street and reduce crashes for all road users, not just bicyclists.” ~ What do you make of that?
Impressive and thorough analysis of the proposed bike path. As a first-time visitor, I am enjoying this blog quite a little bit.
I do not want to sound cynical or world-weary (well maybe a little bit of the latter… and a lot like Joan Didion…) but I cannot imagine LA embracing any form of non-car-transit anytime soon; it would run anathema to everything with which it identifies: “freedom of the road” and such nonsense. I wish it were so, though.
As a seasoned cyclist and former inhabitant of that place of strange and unending sprawl, it just does not strike me as the region to give any sort of credence to anyone not driving a brand-new-shiny car (single occupant, naturally). Perhaps that’s the reason it’s such a narrow bike path? One group is too-often unaware of another’s risks and needs until it moves a mile on two wheels (or feet). I hope LaLaLand proves us all wrongly and that this project draws more people out of their cars and onto less wheels, ‘if you build it, they will come’ style. Moreover, it’s important to recognize that, while flawed in concept, the Figueroa plan is a step in the right direction – and what a step, too, given LA’s unending yet torrid love affair with the automobile. | {
"pile_set_name": "Pile-CC"
} |
Enzyme-Assisted Preparation of Furcellaran-Like κ-/β-Carrageenan.
Carrageenans are sulfated galactans that are widely used in industrial applications for their thickening and gelling properties, which vary according to the amount and distribution of ester sulfate groups along the galactan backbone. To determine and direct the sulfation of κ-carrageenan moieties, we purified an endo-κ-carrageenan sulfatase (Q15XH1 accession in UniprotKB) from Pseudoalteromonas atlantica T6c extracts. Based on sequence analyses and exploration of the genomic environment of Q15XH1, we discovered and characterized a second endo-κ-carrageenan sulfatase (Q15XG7 accession in UniprotKB). Both enzymes convert κ-carrageenan into a hybrid, furcellaran-like κ-/β-carrageenan. We compared the protein sequences of these two new κ-carrageenan sulfatases and that of a previously reported ι-carrageenan sulfatase with other predicted sulfatases in the P. atlantica genome, revealing the existence of additional new carrageenan sulfatases. | {
"pile_set_name": "PubMed Abstracts"
} |
Aleksandr Evgenievich Chudakov (16 June 1921 – 25 January 2001, Moscow) was a SovietRussian physicist in the field of cosmic-ray physics, known for Chudakov Effect, the effect of decreasing ionization losses for narrow electron-positron pairs and for experimentally confirming existence of the transition radiation.[1] He was also the chairman of the IUPAP Cosmic Ray Commission.
Aleksandr Chudakov was born on 16 June 1921, and graduated from Moscow State University (MSU) in 1948 .[2] In 1953 his experimental confirmation of the existence of the transition radiation, which was predicted by Ginzburg and Ilya Frank in 1945, and the effect of decreasing ionization losses for narrow electron-positron pairs, known as the Chudakov Effect, are among Chudakov's famous works. Phenomena similar to Chudakov Effect have been observed in quantum chromodynamics also.
Chudakov was the author of series of experiments carried out in the 1950s, which focused on investigation of the cosmic rays outside of the atmosphere with rockets and first satellites. As a result, during the third Soviet sputnik, he discovered the Earth's radiation belts in collaboration with S. N. Vernov.[3]
In 1961 Chudakov and G. T. Zatsepin suggested the air Chernkov method for the gamma-ray astronomy and carried out a pioneering experiment at Katsively, Crimea.[3]
From the mid-1960s Chudakov headed the design and construction of the Baksan Underground Scintillation Telescope, which was put into operation in 1978 and considered to be one of the first large multipurpose facilities for underground physics.[3] In astroparticle physics the first class results have been obtained with this telescope which is still in operation.[4] | {
"pile_set_name": "Pile-CC"
} |
Q:
can google maps on mobile phones can have plugins?
i want to use data from google maps, especialy the navigation functionality. Is this possible by plugin or wrapping the application?
I want to develop my own navigation service and use GoogleMaps for this.
A:
There are a number of samples available all over the internet which build on top of mapview. Its not a plugin architecture but based on containment model. I think you can easily achieve what you want to do.
| {
"pile_set_name": "StackExchange"
} |
Female genital cutting (FGC) is an ancient tradition unbounded by religion and practiced primarily in Africa and the regions to which Africans have immigrated. All types of FGC involve cutting neural innervation to the vulva: the clitoris, labia majora and minora. Most types include excision of the clitoris. Since the tissue of the vulva is highly innervated by nerves and their endings, I postulate here that the brain and spinal cord will respond to FGC as it would to any loss of neural targets or inputs: by rearranging neural networks. This, in turn, would affect neural signaling to target structures and modify sensory perception. Most scientific investigations of FGC have focused on its reproductive consequences. To fully appreciate its effects on the lives of women, however, an understanding beyond the reproductive system is necessary. Exploring the potential neural changes of FGC may help explain the mixed responses of the women themselves and identify new directions for research to understand their lives. A neurobiological analysis may also help us understand how cultural practices inscribe meaning on central nervous system structures, affecting mind as well as body.
Recommend
Additional Information
ISSN
1529-8795
Print ISSN
0031-5982
Pages
pp. 84-97
Launched on MUSE
2008-01-08
Open Access
No
Project MUSE Mission
Project MUSE promotes the creation and dissemination of essential humanities and social science resources through collaboration with libraries, publishers, and scholars worldwide. Forged from a partnership between a university press and a library, Project MUSE is a trusted part of the academic and scholarly community it serves. | {
"pile_set_name": "Pile-CC"
} |
/*
******************************************************************************
* *
* Copyright (C) 2003-2005, International Business Machines *
* Corporation and others. All Rights Reserved. *
* *
******************************************************************************
* file name: ulocdata.c
* encoding: US-ASCII
* tab size: 8 (not used)
* indentation:4
*
* created on: 2003Oct21
* created by: Ram Viswanadha,John Emmons
*/
#include "cmemory.h"
#include "unicode/ustring.h"
#include "unicode/ulocdata.h"
#define MEASUREMENT_SYSTEM "MeasurementSystem"
#define PAPER_SIZE "PaperSize"
/** A locale data object.
* For usage in C programs.
* @draft ICU 3.4
*/
struct ULocaleData {
/**
* Controls the "No Substitute" behavior of this locale data object
*/
UBool noSubstitute;
/**
* Pointer to the resource bundle associated with this locale data object
*/
UResourceBundle *bundle;
};
U_CAPI ULocaleData* U_EXPORT2
ulocdata_open(const char *localeID, UErrorCode *status)
{
ULocaleData *uld;
if (U_FAILURE(*status)) {
return NULL;
}
uld = (ULocaleData *)uprv_malloc(sizeof(ULocaleData));
if (uld == NULL) {
*status = U_MEMORY_ALLOCATION_ERROR;
return(NULL);
}
uld->noSubstitute = FALSE;
uld->bundle = ures_open(NULL, localeID, status);
if (U_FAILURE(*status)) {
uprv_free(uld);
return NULL;
}
return uld;
}
U_CAPI void U_EXPORT2
ulocdata_close(ULocaleData *uld)
{
if ( uld != NULL ) {
ures_close(uld->bundle);
uprv_free(uld);
}
}
U_CAPI void U_EXPORT2
ulocdata_setNoSubstitute(ULocaleData *uld, UBool setting)
{
uld->noSubstitute = setting;
}
U_CAPI UBool U_EXPORT2
ulocdata_getNoSubstitute(ULocaleData *uld)
{
return uld->noSubstitute;
}
U_CAPI USet* U_EXPORT2
ulocdata_getExemplarSet(ULocaleData *uld, USet *fillIn,
uint32_t options, ULocaleDataExemplarSetType extype, UErrorCode *status){
const char* exemplarSetTypes[] = { "ExemplarCharacters", "AuxExemplarCharacters" };
const UChar *exemplarChars = NULL;
int32_t len = 0;
UErrorCode localStatus = U_ZERO_ERROR;
if (U_FAILURE(*status))
return NULL;
exemplarChars = ures_getStringByKey(uld->bundle, exemplarSetTypes[extype], &len, &localStatus);
if ( (localStatus == U_USING_DEFAULT_WARNING) && uld->noSubstitute ) {
localStatus = U_MISSING_RESOURCE_ERROR;
}
if (localStatus != U_ZERO_ERROR) {
*status = localStatus;
}
if (U_FAILURE(*status))
return NULL;
if(fillIn != NULL)
uset_applyPattern(fillIn, exemplarChars, len,
USET_IGNORE_SPACE | options, status);
else
fillIn = uset_openPatternOptions(exemplarChars, len,
USET_IGNORE_SPACE | options, status);
return fillIn;
}
U_CAPI int32_t U_EXPORT2
ulocdata_getDelimiter(ULocaleData *uld, ULocaleDataDelimiterType type,
UChar *result, int32_t resultLength, UErrorCode *status){
const char* delimiterKeys[] = { "quotationStart",
"quotationEnd",
"alternateQuotationStart",
"alternateQuotationEnd" };
UResourceBundle *delimiterBundle;
int32_t len = 0;
const UChar *delimiter = NULL;
UErrorCode localStatus = U_ZERO_ERROR;
if (U_FAILURE(*status))
return 0;
delimiterBundle = ures_getByKey(uld->bundle, "delimiters", NULL, &localStatus);
if ( (localStatus == U_USING_DEFAULT_WARNING) && uld->noSubstitute ) {
localStatus = U_MISSING_RESOURCE_ERROR;
}
if (localStatus != U_ZERO_ERROR) {
*status = localStatus;
}
if (U_FAILURE(*status)){
ures_close(delimiterBundle);
return 0;
}
delimiter = ures_getStringByKey(delimiterBundle, delimiterKeys[type], &len, &localStatus);
ures_close(delimiterBundle);
if ( (localStatus == U_USING_DEFAULT_WARNING) && uld->noSubstitute ) {
localStatus = U_MISSING_RESOURCE_ERROR;
}
if (localStatus != U_ZERO_ERROR) {
*status = localStatus;
}
if (U_FAILURE(*status)){
return 0;
}
u_strncpy(result,delimiter,resultLength);
return len;
}
U_CAPI UMeasurementSystem U_EXPORT2
ulocdata_getMeasurementSystem(const char *localeID, UErrorCode *status){
UResourceBundle* bundle=NULL;
UResourceBundle* measurement=NULL;
UMeasurementSystem system = UMS_LIMIT;
if(status == NULL || U_FAILURE(*status)){
return system;
}
bundle = ures_open(NULL, localeID, status);
measurement = ures_getByKey(bundle, MEASUREMENT_SYSTEM, NULL, status);
system = (UMeasurementSystem) ures_getInt(measurement, status);
ures_close(bundle);
ures_close(measurement);
return system;
}
U_CAPI void U_EXPORT2
ulocdata_getPaperSize(const char* localeID, int32_t *height, int32_t *width, UErrorCode *status){
UResourceBundle* bundle=NULL;
UResourceBundle* paperSizeBundle = NULL;
const int32_t* paperSize=NULL;
int32_t len = 0;
if(status == NULL || U_FAILURE(*status)){
return;
}
bundle = ures_open(NULL, localeID, status);
paperSizeBundle = ures_getByKey(bundle, PAPER_SIZE, NULL, status);
paperSize = ures_getIntVector(paperSizeBundle, &len, status);
if(U_SUCCESS(*status)){
if(len < 2){
*status = U_INTERNAL_PROGRAM_ERROR;
}else{
*height = paperSize[0];
*width = paperSize[1];
}
}
ures_close(bundle);
ures_close(paperSizeBundle);
}
| {
"pile_set_name": "Github"
} |
Bullous pemphigoid presenting as exfoliative erythroderma.
Several unusual clinical presentations of bullous pemphigoid have been described such as localized, vesicular, vegetating, nodular, and sine bulla pemphigoid. Patients with erythroderma who fulfill diagnostic criteria for bullous pemphigoid and in whom bullae develop have been reported. We describe a patient with exfoliative erythroderma without any blistering in whom a diagnosis of bullous pemphigoid was based on examination of a biopsy specimen. Circulating antibodies to the basement membrane zone, with an epidermal pattern on salt split skin, and the presence of eosinophilic spongiosis in the skin biopsy specimen supported the diagnosis. | {
"pile_set_name": "PubMed Abstracts"
} |
Q:
Is this a good implementation of a custom locking mechanism?
I have a task where I need to implement a locking mechanism. This is what I have so far. Basically I need the lock method to try to acquire a lock and return true if lock was acquired and false otherwise. And the unlock method which tries to release the lock, and return true if successful, false otherwise.
Is this a proper way to implement this, or can it be done otherwise? What improvements can be added to this code, or in what ways can it be modified ?
Thanks in advance,
Andrei
private Long threadId;
private int lockHolds;
public synchronized boolean lock(long waitTime) throws DataStoreException {
if (lockHolds == 0) {
doLock(waitTime);
return true;
}
return false;
}
private synchronized void doLock(long waitTime) throws DataStoreException {
if (lockHolds == 0) {
lockHolds++;
this.threadId = Thread.currentThread().getId();
} else if (lockHolds > 0 && this.threadId == Thread.currentThread().getId()) {
lockHolds++;
} else {
try {
wait(waitTime);
lockHolds++;
this.threadId = Thread.currentThread().getId();
} catch (InterruptedException ie) {
ie.printStackTrace();
}
}
}
public synchronized boolean unlock() {
if (lockHolds == 0) {
return false;
}
lockHolds--;
if (lockHolds == 0) {
notify();
return true;
}
return false;
}
A:
This is wrong:
wait(waitTime);
lockHolds++;
this.threadId = Thread.currentThread().getId();
You just wait it out, then steal the lock from the currently owning thread. The thread is probably in the middle of its critical section, therefore you allow concurrent access to the critical section.
wait must always be used in a loop that repeatedly tests for the condition being awaited, to defend from spurious wakeups.
The lock() method only checks the lockHolds variable and refuses to proceed if it's non-zero, thus preventing the reentrant behavior of the lock.
Your unlock method is wrong because any thread can call it and release another thread's lock.
Although I'm not familiar with your requirements, for me it would be very odd to request a custom lock implementation but allow it to rely on both the built-in lock implementation and the built-in wait-notify mechanisms. But that part is up to you.
| {
"pile_set_name": "StackExchange"
} |
Q:
Regular expression for finding tag numbers in a list of cats
I am trying to match the tag numbers in a list of cats:
Abyssinian 987
Burmese a1a
Dragon Li 2B
987 Cat
cat 987 Toyger
cat A1A Siamese
1
The tag numbers for the list of cats would be:
987
a1a
2B
987
987
A1A
1
I've tried using the regular expression:
\b[0-9a-zA-Z]{1,3}\b
The problem is that it will match "cat" and "Li" (in Dragon Li). It should only match the tag number.
The requirements for a tag number are:
1-3 characters, it must contain at least one integer (0-9)
It can appear at any place in the string
As a side note, I am using Postgres regular expressions, which I think use POSIX regular expressions. (http://www.postgresql.org/docs/9.3/static/functions-string.html)
A:
You can use this regex:
\b(?=\w*?\d)\w{1,3}\b
Online Demo
Test: Using grep -P:
grep -oP '\b(?=\w*?\d)\w{1,3}\b' file
987
a1a
2B
987
987
A1A
1
A:
This works in PostgreSQL:
SELECT substring(cat FROM '\m(?=\w{0,2}\d)\w{1,3}\M') AS tag
FROM cat;
\m and \M .. beginning and end of a word.
(?=\w{0,2}\d).. positive lookahead
\w{1,3} .. 1-3 word characters
Assuming there is a single match in every string, substring() (without the "global" switch 'g') is better for the job than regexp_matches(), which would return an array (even for a single match).
substring() is also a bit faster.
SQL Fiddle.
| {
"pile_set_name": "StackExchange"
} |
[A new stage in the development of the membrane concept of the pathogenesis of primary hypertension: the role of cellular oncogenes in the genesis of membrane disorders].
The membrane concept of the primary (essential) hypertension pathogenesis considers the start of the disease as being linked to the characteristic disturbances of the cation-transport function. The membrane alteration result in the increase of the free calcium ion concentration in the cell cytoplasm and are the cause of both the contractile properties alteration of the vascular smooth muscle cells and the alteration of the neuromediator release in the nerve endings. The further stage in the evolution of this concept was the observation of the pathogenetic ling between the membrane "defect" in the primary hypertension and the alteration of the cell oncogenes (proto-oncogenes) function. The presence of such a link may be confirmed by both the indirect proofs considered in the paper and the results of the DNA study in rats with a spontaneous hypertension by method of RFLP analysis. | {
"pile_set_name": "PubMed Abstracts"
} |
Q:
Can someone explain some of the steps in this paper clearly?
I'm having trouble understanding the steps this paper makes to come to the conclusion $p_{f}(d) \sim e^d\sqrt{d}$
Marek Wolf, First occurrence of a given gap between consecutive primes, preprint, April 1997, IFTUWr 911/97 (Citeseer^x)
In particular, line 6 where it relates his result on the partial Brun's sums to first occurrence prime gaps. And also the following quadratic.
moreover it seems to be inconsistent with his previous paper in line (4) as it ignores some terms in line 28 of this one.
Marek Wolf, Generalized Brun's constants, preprint, March 1997, IFTUWr 910/97
(Citeseer^x)
A:
Marek Wolf's preprint First occurrence of a given gap between consecutive primes
(Preprint IFTUWr 911//97, 1997) was written in Wrocław University's Institute of Theoretical Physics (IFTUWr). The preprint employs "physical" notation, where $f\sim g$ means
$f$ and $g$ have the same order of magnitude.
(See e.g. Mathworld on the usage of the tilde symbol.)
In number-theoretic asymptotic notation, the formula should be read as
$$
p_f(d) \asymp \sqrt{d} e^{\sqrt{d}} \tag{1}
$$
(for infinitely many first-occurrence gaps of size $d$).
Wolf's recent preprint arXiv:2002.02115
clarifies this notation ambiguity (see footnote on page 12). It also generalizes the formula to first occurrences of gaps between primes in an arithmetic progression (P): $r+nq$, $n\in{\mathbb N}$.
Namely, the first occurrence of a gap $d$ between primes $p\equiv r$ (mod $q$)
is conjectured to have end-of-gap prime
$$
p \asymp \sqrt{d} e^{\sqrt{d/\varphi(q)}} \tag{2}
$$
infinitely often.
(Note that, in the derivation of this formula, omitting a small factor is okay, as long as we are not changing the order of magnitude of the result. Formulas $(1)$ and $(2)$ do not assert asymptotic equivalence of the left- and right-hand sides.)
| {
"pile_set_name": "StackExchange"
} |
The 3D display technology is to utilize a series of optical means to create optical parallax for the left and right eyes of an audience. The different images are received and a 3D effect sense is formed in the audience's brain. The 3D display technology is one of the fusion engines of industrialization and informatization, in the mean time, it is also a basic and strategic tools technology which has been widely used for the industrial community and the industrial creation community. With the 3D technology ideas, some traditional businesses, such as advertisement media, exhibition, travel investment, scientific research and teaching, games and entertainment, industrial design, geologic surveying and mapping, medical diagnosis, military affairs, scene reconstruction and etc. are given with the hopes of speeding up the industry upgrade and innovation. Meanwhile, kinds of application for life, such as 3D street view, 3D video chat, 3D shopping and etc. also can be crazy popular.
The 3D display technology can be categorized into two types of the glass type and the naked eye type. For the glass type, just as the name implied, a glass involved with the present display skill has to be worn for being able to see the 3D effect. On the contrary, for the naked eye type, no assistance of the glass is demanded and the 3D effect can be seen directly.
For these two years, the naked eye 3D technology has already become the hot spot of the digital industry. As concerning the AD player, the display to the cell phone, the TV and the computer, the vendors all over the world have been announced the naked eye 3D demonstration products and the sales volume is explosive. The naked eye 3D display is to utilize the optical parallax property of human's two eyes and a display system providing living stereoscopic image with space and depth can be achievable without any accessory equipment (such as 3D glass, helmet and etc.). The naked eye stereoscopic image has already been favored by the consumers in general with its true and real representability, beautiful and elegant atmosphere infectivity, strong and shocking visual impact.
Most of the naked eye 3D display technology at present utilizes a prism to proceed light splitting. If the switching function between the 2D display state and 3D display state needs to be equipped and the prism is no longer applicable but liquid crystal lens is demanded. However, the performance of the liquid crystal lens is worse in wide angle and a gradually changing zone of the liquid crystal exists which can leads to the interference among the adjacent pixels. | {
"pile_set_name": "USPTO Backgrounds"
} |
Q:
addObserver() method, of observer pattern and object variable lifecycle/scope, Java
when I use the method .addObserver() for example:
class ExampleOne implements Observer {
class ExampleTwo extends Observable {
ExampleOne one = new ExampleOne();
ExampleTwo two = new ExampleTwo();
two.addObserver(one)
in this case, is the connection between instance objects "two" and "one" or the class.class like a static situation, it looks to me like instance, but not sure, if this is a connection between observer and the observed then what happens if either "one" or "two" is garbage collected or goes out of scope? does that destroy the observer setup.
example of this is when a server receives a String message from the client, and the observer is used to notify when a new text message has arrived. if one of the instance variables goes out of scope and is garbage collected then there will be no more notification when messages arrive because the system will be broken. is this correct?
A:
Observable has a vector which holds the reference to all the observers that have been registered using the addObserver() method. So even if the observer goes out of scope the reference to it is still present in the observable and will not be garbage collected.
To garbage collect it call the removeObserver and then it will be garbage collected.
If Observable goes out of scope then yes, no notifications would be sent now to the observers. And the Observers can be garbage collected.
in this case, is the connection between instance objects "two" and
"one" or the class.class like a static situation
Yes everything is happening on instances and no statics are involved here.
| {
"pile_set_name": "StackExchange"
} |
---
abstract: 'When calculating stellar initial mass functions (IMFs) for young clusters, one has to take into account that most massive stars are born in multiple systems and that most IMFs are derived from data that cannot resolve such systems. It is also common to measure IMFs for clusters that are located at distances where multiple chance superpositions between members are expected to happen. In this article I model the consequences of both of those phenomena, real multiple systems and chance superpositions, on the observed color-magnitude diagrams and the IMFs derived from them. Using numerical experiments I quantify their influence on the IMF slope for massive stars and on the generation of systems with apparent masses above the stellar upper mass limit. The results in this paper can be used to correct for the biases induced by real and chance-alignment multiple systems when the effects are small and to identify when they are so large that most information about the IMF in the observed color-magnitude diagram is lost. Real multiple systems affect the observed or apparent massive-star MF slope little but can create a significant population of apparently ultramassive stars. Chance superpositions produce only small biases when the number of superimposed stars is low but, once a certain number threshold is reached, they can affect both the observed slope and the apparent stellar upper mass limit. In the second part of the paper, I apply the experiments to two well known massive young clusters in the Local Group, NGC 3603 and R136. In both cases I show that the observed population of stars with masses above 120 / can be explained by the effects of unresolved objects, mostly real multiple systems for NGC 3603 and a combination of real and chance-alignment multiple systems for R136. Therefore, the case for the reality of a stellar upper mass limit at solar or near-solar metallicities is strengthened, with a possible value even lower than 150 /. An IMF slope somewhat flatter than Salpeter or Kroupa with $\gamma$ between $-1.6$ and $-2.0$ is derived for the central region of NGC 3603, with a significant contribution to the uncertainty arising from the imprecise knowledge of the distance to the cluster. The IMF at the very center of R136 cannot be measured with the currently available data but the situation could change with new Hubble Space Telescope (HST) observations.'
author:
- 'J. Maíz Apellániz'
bibliography:
- 'general.bib'
title: 'Biases on initial mass function determinations. II. Real multiple systems and chance superpositions'
---
Introduction
============
This paper is the second one of a series where we explore the effects of different biases on the determination of the stellar initial mass function (IMF). In paper I [@MaizUbed05] we analyzed the numerical biases induced by using bins of equal width when fitting power-laws to binned data (an effect that is more general than its application to the calculation of mass functions). Those biases can be eliminated in several ways, of which a simple one is by grouping the data in equal-number bins (as opposed to equal-width bins). In this second paper I explore the effect of unresolved multiple systems, either physical or chance alignments, especially for the high-mass end of the IMF. In a future paper we will analyze the effect of random uncertainties in the mass determinations on the computed initial mass function[^1].
Binaries and the IMF
--------------------
Why worry about binaries and higher-order multiple systems when calculating the IMF of a young stellar cluster such as NGC 3603 or R136? The quick answer is because one expects most of the observed point sources in clusters beyond a few kpc to be multiple. Therefore, deriving their masses by assuming they are single stars should introduce biases in the determination of the stellar mass functions of the clusters.
@Masoetal98 studied nearby O stars from a sample that included field objects and stars in low- and intermediate-mass clusters and associations. They analyzed the observed multiple fractions as a function of environment, including both spectroscopic and visual/speckle binaries and discovered that at least 72% of the O stars in clusters and associations had detected companions. Furthermore, the period distribution had a clear bimodal structure, with one peak around 10 days and another one around $10^5$ years. They argued that such an effect was quite likely to be instrumental because binaries with periods $P$ near 1-1000 years are hard to detect and because the period distribution for B stars is quite flat[^2]. Therefore, @Masoetal98 predicted that when better spatial resolution were achieved and more intensive radial-velocity variation surveys were undertaken in the future, the gap between the two peaks might be filled and the true multiple fraction for massive stars in clusters might be found to be close to unity. Another interesting result of that paper was that the mass-ratio distribution for O binaries was flat or nearly so, i.e. massive stars tend to have companions that are more massive on average than what would be expected from a random sampling of the IMF. The shape of the secondary mass distribution function is relevant because different slopes should affect the observed or apparent mass function derived from unresolved data in different ways. @SagaRich91 calculated that the apparent MF slope for intermediate-mass stars in the random pairing case becomes significantly flatter when adding unresolved binaries but the effect is likely to be different in the flat mass-ratio case.
In the ten years after @Masoetal98 other works have validated their conclusions. @GarcMerm01 measured that 11 out of 14 O-systems in the cluster NGC 6231 are spectroscopic binaries. This means that at least 79% of its O/WR systems are multiple and at least 88% of their O/WR (and some early B) stars are in multiple systems. Their numbers are also similar for early-B stars. Also, new studies are indeed filling the Mason period gap: @Gameetal07 reported 11 new massive spectroscopic binaries and @Maizetal08b cite two new visual systems in the solar neighborhood (see also @Nelaetal04). With respect to the secondary mass distribution function, @Kouwetal05 studied intermediate-mass stars in the Sco OB2 association and found that they could exclude random pairing in binaries, since the more massive stars clearly tend to associate with other massive objects. Another recent study of Cyg OB2 by @KobuFrye07 also finds a large ($>$80%) binary fraction for massive stars. Those authors favor a secondary mass distribution function that is either (a) nearly flat or (b) a combination of a 60% Kroupa-like distribution and a 40% “twin” ($M_2 > 0.95 M_1$) component.
But what about more massive clusters? Is it possible that the multiple fraction there is significantly lower? Studying distant objects is more complicated but a recent survey by @Evanetal06 found that NGC 346 (in the SMC), NGC 2004, and N11 (in the LMC) have a minimum spectroscopic binary fraction for O- and early B-type stars of 23 to 36%. Considering that their program did not allow them to detect binaries with periods of more than several tens of days and that at the distance of the Magellanic Clouds it is very hard to resolve visual binaries, the real binary fraction should be considerably higher. Therefore, it is safe to conclude that the effect of unresolved massive binaries in the observed IMF is important and needs to be analyzed. Such an analysis is the first goal of this paper.
The stellar upper mass limit
----------------------------
From the point of view of the origin of the IMF, it has become apparent in the last decade that massive stars must form in a different way than low-mass objects because of the short time scales involved and the limiting effect of radiation pressure on the mass accretion rate [@BallZinn05; @ZinnYork07]. There are currently two viable alternatives to form a massive star: by accretion through a disk, either in a relatively isolated environment or in a more crowded one where competition for mass among different protostars may be important, and by stellar collisions followed by mergers. The second alternative can only be relevant when the stellar densities are very high, such as at the core of a dense and massive cluster, but cannot be significant in relatively low-density environments such as OB associations.
If stellar mergers are indeed important at the core of dense clusters, there should be large consequences on their stellar IMFs. @Portetal99 predicted that runaway collisions in such cores will lead to stars with masses above 100 / in a time scale of one or a few million years, which is comparable to the expected life times of those stars. The process may keep going on to the point of producing objects above 1000 / that would end up as intermediate-mass black holes [@Portetal04a]. Therefore, massive dense clusters should show an stellar upper mass limit $m_{\rm max}$ significantly higher than those of lower density or mass. Can such stellar behemoths exist? Recently, @Belketal07 and @Yungetal08 have attempted modeling of solar-metallicity stars up to 1000 /, which would be formed by mergers. However, such modeling encounters problems with the determination of the Eddington limit, its associated instabilities and interaction with rotation, and with the large extrapolation required for mass-loss rates (which are already uncertain at the present time even for run-of-the-mill main-sequence O stars). Hence, theory has not given its final word on the possible existence of such ultramassive stars.
What do observations tell us about those hypothetical ultramassive stars? Several papers on R136 and other Local Group massive young clusters [@WeidKrou04; @Fige05; @OeyClar05; @Koen06] indicate that $m_{\rm max} \approx$ 120-200 / when evolutionary tracks are used to obtain stellar masses[^3]. Some luminous blue variables (LBVs) such as $\eta$ Car could have slightly higher evolutionary masses but LBVs are notoriously difficult to observe in detail due to the existence of circumstellar material. With respect to the more accurate masses measured from the orbital motion of the stars (keplerian masses), the highest published values correspond to WR 20a, a binary with 83.0 $\pm$ 5.0 / and 82.0 $\pm$ 5.0 / (@Bonaetal04, see also @Rauwetal04). Therefore, on a first impression it appears that observations do not favor the existence of ultramassive stars at near-solar metallicity.
Unresolved multiple systems can also play a role in the identification of ultramassive stars by making e.g. a binary made out of two stars close to the stellar upper mass limit appear as a single object with an evolutionary mass well above that limit. For example, @Maizetal07 found that Pismis 24-1, formerly an ultramassive star candidate, is in reality composed of three stars with masses below 120 /. It is also possible that the observed $m_{\rm max}$ measured from evolutionary masses is affected not only by real (bound) multiple systems but also by chance alignments in the crowded environments where some of these objects are found. Analyzing the possibility that some of the objects observed close to $m_{\rm max}$ may be blended sources composed of stars of significantly lower mass is the second goal of this paper.
Experiments
===========
In order to test the effect of unresolved binaries and blending on the massive-star IMF slope and the stellar upper mass limit I have designed three numerical experiments. The first one analyzes the effect of real binaries, the second one that of chance superpositions, and the third one combines the two effects. The purpose of the experiments is to analyze the effects on a simple test IMF, provide a way to correct them, and describe the tools needed to extend the technique to other circumstances.
I design the simple case by assuming a well-sampled single stellar population with an age of 1 million years and solar metallicity. The choices for the age and metallicity are given by our desire to test our results with an analysis of NGC 3603 and R136 (note that the latter is currently thought to be of somewhat lower metallicity and may be slightly older) and by the simplicity of not having objects clearly evolved off the main sequence or even collapsed. Since we are only interested in the behavior of the top part of the IMF, for simplicity I assume that all the stars have already reached the main sequence, even though such an assumption should not valid for the low-mass stars. The $T_{\rm eff}$, $\log g$, and $\log L$ information was obtained from the Geneva evolutionary tracks and isochrones database by @LejeScha01 selecting the case with standard mass-loss rates and no rotation[^4]. For masses below 0.8 / I use the $M_V$ calibration of @Krouetal93 to extend the isochrone until 0.1 /. For the value of $m_{\rm max}$, I select the highest value available in the Geneva tracks, 120 /, which is on the low end of the possible range (for $m_{\rm max}$) for solar and near-solar metallicities. The 1-million-year isochrone was inserted into the new evolutionary synthesis module of CHORIZOS [@Maiz04c] to calculate the Johnson $U$ and $V$ absolute magnitudes[^5] as a function of mass using different synthetic spectral energy distributions (SEDs) as a function of $T_{\rm eff}$: TLUSTY [@LanzHube03; @LanzHube07], Kurucz [@CastKuru03], and Lejeune [@Lejeetal98] for the high, intermediate, and low temperature ranges, respectively. The Johnson zero points derived by @Maiz06a and modified by @Maiz07a were used. The final results are two tabulated, finely-gridded functions that give $V$ and $U-V$ as a function of mass $m$ between 0.1 and 120 /. The two functions were then extrapolated in $\log m$ up to $m = 1000$ / ($\log m = 3$). Note that $V(m)$ is a strict monotonically decreasing function over the full range of $m=0.1-1000$ / (this is true for the chosen isochrone but it is not true in general). Therefore, it is possible to invert it to produce $m(V)$, which gives the true mass[^6] that corresponds to a star of absolute magnitude $V$.
Once $V(m)$ and $U(m)-V(m)$ as a function of mass have been generated, I calculate the corresponding bidimensional single-star color-magnitude density function $g_{1{\rm s}}(U-V,V)$ by applying one of two cases: \[a\] a Kroupa IMF, which can be described as a continuous function comprised of two power law segments $dn/dm=f(m)\propto m^\gamma$, with $\gamma = -1.3$ for $m=0.1-0.5$ / and $\gamma = -2.3$ for $m=0.5-120$ /; \[b\] a flatter, top-heavy IMF, similar to Kroupa but with $\gamma = -1.3$ for $m=0.1-0.5$ / and $\gamma = -2.0$ for $m=0.5-120$ /. $g_{1{\rm s}}(U-V,V)$ can be collapsed into a one-dimensional magnitude function[^7] $G_{1{\rm s}}(V)$ without losing any information because for our isochrone $V(m)$ is a strictly monotonic function. Since both $g_{1{\rm s}}(U-V,V)$ and $G_{1{\rm s}}(V)$ are functions defined in a fine (2-D and 1-D, respectively) grid, special care has to be taken to avoid introducing numerical biases and noise due to sampling and interpolation.
Finally, in order to reproduce the blending problems associated with the strategy commonly used to derive evolutionary masses from luminosity functions, I combine individual stars into blended objects according to different rules. This is done by adding their $U$- and $V$-band luminosities and computing the resulting $V$ and $U-V$ values. From there, I generate: \[a\] a new bidimensional color-magnitude density function $g_{x}(U-V,V)$ from $g_{1{\rm s}}(U-V,V)$, where $x$ specifies the combination rule, and \[b\] the apparent mass function $f_{a,x}(m_a)$ calculated by collapsing $g_{x}(U-V,V)$ into $G_{x}(V)$ and then converting the observed absolute magnitudes into apparent masses. The last step is done by applying $m(V)$, which is a relationship derived for individual stars that is not correct for blended objects. Therefore, the derived apparent masses $m_a$ are not the real ones. In other words, I am deriving an apparent mass function (AMF) by \[a\] assuming that all the observed objects are single stars (even though they are not) and \[b\] using only the absolute magnitudes (but not their colors) to obtain the masses. The first assumption is applied in most IMF studies. The second assumption should be valid as long as all the stars are at the same distance, extinction is well known, contamination by field objects or stars of different ages is negligible, and $m(V)$ is a strictly monotonic function. Note, however, that for ages older than $\approx 2.5$ million years (when $m(V)$ is no longer monotonic) the same type of analysis can still be done measuring masses by minimizing the distance to a given isochrone.
Note also that I am not using spectral types for the calculation of the IMF. For massive stars, the main advantages of using spectral types to calculate IMFs are a better determination of the cluster age, a direct knowledge of the intrinsic color of the star (hence, usually a better extinction measurement), and an ability to derive additional luminosity/distance information. Those are all possible sources of biases, so spectroscopy indeed represents an improvement over a pure photometric analysis. However, as previously stated, for the experiments in this paper I assume that age, extinction, and distance are all well constrained by external information, so those advantages of spectroscopy are not relevant for our discussion. The additional advantage that spectroscopy has over a simple color-magnitude analysis when blended sources are present is the possibility of identifying them by their composite spectra (something that can also be done in some cases with multi-filter photometry). Note, however, that many spectra of blended sources cannot be distinguished from those of single ones for three possible reasons: \[a\] need of very high S/N data to detect the contribution from a dim companion, \[b\] absence of time-resolved data to detect spectroscopic binaries, and \[c\] similarity between the two blended spectra[^8]. In summary, spectroscopy can be and in most cases is a helpful aid to the elimination of biases in IMF determinations but it also has its costs and limitations in detecting blended sources. This paper should not be interpreted as neglecting the importance of spectroscopy for the study of the massive-star IMF but rather as a study of what can be done when spectroscopy is not available.
Experiment 1: Real binaries
---------------------------
For the first experiment I attempt to reproduce the effect of unresolved multiple systems which, for simplicity, I assume to be always binaries. The combination rules applied in this case are:
1. Each star is blended with one and only one star.
2. For a blended system with $m_1\ge m_2$, $m_2$ is randomly selected from a flat distribution in mass between 0.1 / (the lower mass limit) and $m_1$. The pairing is done while keeping the real, single-mass stellar IMF as Kroupa (case a) or top-heavy (case b).
![Color-magnitude density function $g_{1{\rm b}}(U-V,V)$ for the Kroupa case of experiment 1 (real binaries) shown as a Hess diagram. The black line shows the position of the 1 million year isochrone. The function scaling is logarithmic and the normalization is arbitrary. See the electronic version of the journal for a color version of this figure.[]{data-label="uvv_bin"}](f1.ps){width="\linewidth"}
This experiment reproduces the physical situation in which all the stars in a cluster are binaries with a flat mass-ratio distribution. As previously discussed, this is a rather accurate approximation for systems with at least one massive star but is likely to be more imprecise for lower-mass objects. For example, @Reipetal07 observe only an 8.8% binary fraction among low-mass stars in the Orion Nebula Cluster and @Solletal07 detect a binary fraction of $\approx$ 40% for globular clusters with ages less that $10^{10}$ years (of course, the situation in globular clusters is complicated by dynamical evolution, as the lower fraction detected by the same authors for older clusters show). However, since our goal is to study the top part of the resulting AMF, the validity of the approximation for low-mass objects should not concern us much. The other assumption in this experiment is that all massive binaries are unresolved. Under what circumstances is that reasonable? As previously described, in the solar neighborhood ($\lesssim 2$ kpc) $\sim 1/3$ of the massive systems in clusters/associations are spectroscopic binaries, another $\sim 1/3$ are visual/interferometric multiple systems, and the remaining $\sim 1/3$ could be undetected multiples (with periods approximately between those of the detected spectroscopic and visual/interferometric systems)[^9]. This means that even in the solar neighborhood $\sim 2/3$ of the massive binary systems would appear as point sources in a ground-based imaging study with standard imaging techniques. Using better spatial resolution (e.g. HST or non-standard techniques such as adaptive optics or lucky imaging) buys you a larger fraction of resolved systems in the solar neighborhood but once you reach several kpc, even that is not enough. For example, ACS/HRC (the imager with the best spatial resolution on HST) can still resolve objects with a magnitude difference $\Delta m \approx 1$ mag and a separation of 50 mas but that is close to the limit of its capabilities (see e.g. @Maizetal08b). At a distance of 7 kpc, 50 mas corresponds to 350 AU, which is the typical value for the separation in the visual O-systems of @Masoetal98, implying that at that distance ACS/HRC would resolve only 20-30% of the massive binary systems (if their properties are similar to those in the solar neighborhood). The LMC is hopeless, even with HST: 50 mas corresponds to 2500 AU, so only very-large separation systems are resolved. Therefore, I can conclude that this experiment represents a reasonable approximation to the conditions in many IMF studies of young clusters and associations beyond the solar neighborhood.
![(Real) IMF and AMF for experiment 1 (real binaries). The top panel shows the Kroupa case and the bottom panel the top-heavy case. The mass is expressed in solar units. The IMF is normalized to 1.0 and the AMF to 0.5.[]{data-label="imf_bin"}](f2a.ps){width=".47\linewidth"}
![(Real) IMF and AMF for experiment 1 (real binaries). The top panel shows the Kroupa case and the bottom panel the top-heavy case. The mass is expressed in solar units. The IMF is normalized to 1.0 and the AMF to 0.5.[]{data-label="imf_bin"}](f2b.ps){width=".47\linewidth"}
The resulting color-magnitude density function, $g_{1{\rm b}}(U-V,V)$ is shown in Fig. \[uvv\_bin\] for the Kroupa IMF case (the top-heavy equivalent function is not shown but is visually very similar). $g_{1{\rm b}}(U-V,V)$ is zero nearly everywhere in the color-magnitude diagram except in the narrow band between the original isochrone and a near-parallel line that is located approximately 0.75 magnitudes above it (the location of the equal-mass binaries). The band between the two lines is filled with the non-equal-mass binaries. At the low-mass extreme the band becomes narrower and detached from the isochrone because the addition of any companion changes the magnitude (and possibly the color) considerably. That effect does not take place for higher masses because the addition of a 0.1 / star is undetectable in color-magnitude with the scale of Fig. \[uvv\_bin\]. At the high-mass end an obvious extension beyond $m_{\rm max}$ is observed. The extension is nearly vertical because massive stars of this age have near-degenerate $U-V$ colors. The apparent upper mass limit, $m_{{\rm max},1{\rm b}}$ is well defined and has a value of 182 /.
![Slope change introduced by flat mass-ratio binaries (first experiment) as a function of the lower limit for the mass range ($m_{\rm lower}$) for the two IMF cases and for different values of the upper limit for the mass range ($m_{\rm upper}$). In each case the values between 1 / and 0.60$m_{\rm upper}$ are plotted. See the electronic version of the journal for a color version of this figure.[]{data-label="deltaslope_bin"}](f3.ps){width="\linewidth"}
The calculated AMFs for the Kroupa and top-heavy cases are shown in Fig. \[imf\_bin\] along with the original IMFs. The behavior in both cases is similar. For low masses, the apparent lower limit is slightly shifted towards higher values (corresponding to a 0.1 / + 0.1 / binary, since 0.1 / is the lower mass limit of our experiments) and several peaks in the AMF can be seen below 0.7 / due to the fine structure of $m(V)$[^10]. For intermediate and high masses, the AMF runs nearly parallel to the IMF at a value roughly 1/2 of the IMF (the AMF includes one half of the systems of the IMF). In order to quantify the change in slope between the IMF and the binary AMF, $\Delta\gamma$, I have fitted a power law to a number of mass ranges using the technique in Paper I. Results are plotted in Fig. \[deltaslope\_bin\]. For $m_{\rm lower}$ between 1 and 16 / and $m_{\rm upper} \ne$ 120 / there is a steepening of the MF with $\Delta\gamma$ between $-0.2$ and $0.0$ while for larger masses in most cases there a slight flattening with $\Delta\gamma$ between $0.0$ and $0.2$. $\Delta\gamma$ depends only weakly on $m_{\rm upper}$ and the IMF slope. Note that some of the small-scale structure observed in Fig. \[deltaslope\_bin\] at the 0.02 level may be of numerical origin. I conclude that for most cases [*the existence of unresolved binaries has only a small effect on the massive-star IMF slope*]{}.
The largest difference between the IMF and the AMF happens beyond $m_{\rm max}$, where a tail is formed in the AMF: these are the apparently ultramassive stars (AUMSs). In Table \[ratios\_bin\] I quantify the effect by giving the apparent number ratios between the objects above $m_{\rm max}$ and the objects in different ranges below it. There is a strong dependence on the IMF slope, since a top-heavy IMF allows a significantly larger number of objects to become AUMSs.
Figure \[uvv\_bin\] reveals another interesting issue which is relevant to IMF studies of Galactic clusters, where distance is one of the unknowns that has to be solved for. O stars are notoriously difficult to use as yardsticks because their near-degenerate optical colors place them along near-vertical lines in a color-magnitude diagram (see e.g. Fig. \[uvv\_bin\] but see also @MaizSota08 for recent progress on improving our knowledge of O-stars colors). For that reason, main-sequence B stars (which have intrinsic $U-V$ in the approximate range from $-1.3$ to $-0.1$) are more commonly used to derive distances with main-sequence fitting techniques. However, if the assumption which underlies our experiment is relevant (that most O and B stars are unresolved binaries with flat mass-ratio distributions), then it is easy to see that a direct application of main-sequence fitting to a $U-V$ vs. $V$ diagram would lead to an overestimation of the distance, because for a fixed value of $U-V$ there should be more stars close to the equal-mass binary sequence than to the main sequence itself. Note that this effect should be significantly smaller for older clusters because the binary fraction is lower there, as it is indeed observed for globular clusters (see e.g. @Solletal07). Spectroscopy can partially resolve the problem by detecting blended spectra or radial velocity variations but from Fig. \[uvv\_bin\] we can see that it should be also possible to correct for the effect by considering that there is an intrinsic spread in the observed color-magnitude diagram due to binarity (besides the ones due to differential extinction and foreground/background contamination).
Experiment 2: Chance superpositions of single stars
---------------------------------------------------
In the second experiment I model the effect of chance superpositions between single (not binary) stars within the observed clusters. Such a simulation introduces additional complications that are detector- and observation-dependent because now we have to deal with a continuous spatial distribution of stars along a 2-D detector. In other words, the observed luminosity function depends not only on the intrinsic properties of the cluster (e.g. its internal structure) but also on the the relative pixel and point-spread function (PSF) sizes, Poisson statistics, and the ability of the detector and the finding algorithm to differentiate between single- and multiple- point sources of diverse $\Delta m$. Given those considerations, the goal in this case is to obtain a toy model that allows us to approximately quantify the effect for a given region of a cluster in order to test the magnitude of the effect.
The combination rules in this case are:
1. The light from a given star falls in a single pixel (the [*fat pixel approximation*]{}).
2. The initial cluster is built by generating a fine grid in $U-V$ and $V$ and assigning to each point a value of $g_{1{\rm s}}(U-V,V)$ integrated over the size of the bin. Since $g_{1{\rm s}}(U-V,V)$ is zero outside the 1-million year isochrone, most points in the grid have no stars. The initial cluster is then defined by the non-zero values of $g_{1{\rm s}}(U-V,V)$. As with the previous experiment, we consider the two cases of a Kroupa and a top-heavy IMF.
3. $g_{2{\rm s}}(U-V,V)$ is a color-magnitude function that describes a cluster with two single stars in each pixel which are randomly paired. I generate it by convolving $g_{1{\rm s}}(U-V,V)$ with itself and assigning the result of each pair to the closest value in the ($U-V,V$) grid[^11]. Note that $g_{2{\rm s}}(U-V,V)$ does not take into consideration Poisson statistics for the stellar distribution among pixels but instead considers that each pixel contains exactly two stars.
4. $g_{4{\rm s}}(U-V,V)$ is generated by convolving $g_{2{\rm s}}(U-V,V)$ with itself, and in general, $g_{2^ns}(U-V,V)$ is generated by convolving $g_{2^{n-1}{\rm s}}(U-V,V)$ with itself. In this paper I generate the color-magnitude functions up to $n=11$ i.e. $g_{2048{\rm s}}(U-V,V)$.
Those rules should be able to simulate the general behavior of the observed color-magnitude diagram as the intrinsic stellar density or the cluster distance increases. However, there are three caveats to its direct application. The first one is that a comparison with a real case should always consider the possible additional effect of Poisson fluctuations, especially when the number of superimposed stars $N_{\rm sup}=2^n$ is small. One way to do this if the expected average number of stars per pixel, $N_{\rm px}$, falls between $2^{n-1}$ and $2^n$ would be to consider both of those cases as possible. The second caveat is that the fat pixel approximation is not valid for a well-sampled detector (PSF size several times larger than the pixel size), so an effective pixel size has to be defined by calculating the area of influence of a star i.e. the region where the presence of a star does not allow a second star to be detected but instead the fluxes from both are merged. Such an effective pixel size is in reality $\Delta m$-dependent so an average effective pixel size should be calculated. Also, the precise flux derived depends on the photometric technique (PSF fitting or aperture photometry) and the algorithm details. Once again, I stress that the purpose of this experiment is not to find the exact correction required to account for chance superpositions but rather to develop a toy model that would allow the observer to roughly quantify the effect. The third caveat is that all stars are assumed to be single. This last caveat will be addressed by the third experiment.
![Color-magnitude density functions $g_{2{\rm s}}(U-V,V)$ (left), $g_{16{\rm s}}(U-V,V)$ (center), and $g_{128{\rm s}}(U-V,V)$ (right) for the Kroupa (top row) and top-heavy (bottom row) cases of experiment 2 (chance superpositions of single stars) shown as Hess diagrams. The thick black line shows the position of the 1 million year isochrone. The function scaling is logarithmic and the normalization is arbitrary. See the author’s web site [http://www.iaa.es/$_{\mbox{\~{}}}$jmaiz]{} for animated gifs showing all the color-magnitude functions $g_{2^n{\rm s}}(U-V,V)$ from $n=0$ to $n=11$. See the electronic version of the journal for a color version of this figure.[]{data-label="uvv_chsup1"}](f4.ps){width="\linewidth"}
![Top left corner of the color-magnitude density functions $g_{2^n{\rm s}}(U-V,V)$ with $n=0,11$ for the Kroupa case of experiment 2 (chance superpositions of single stars) shown as Hess diagrams. The $n=0$ case has been smoothed in order to allow it to show some extent perpendicular to the 1 million year isochrone. The thick black line shows the position of the 1 million year isochrone and the thin lines the evolutionary tracks between 0 and 2 million years for the initial masses of 25, 40, 60, 85, and 120 /. The function scaling is logarithmic and the normalization is arbitrary. See the electronic version of the journal for a color version of this figure.[]{data-label="uvv_chsup2"}](f5.ps){width="\linewidth"}
![Top left corner of the color-magnitude density functions $g_{2^n{\rm s}}(U-V,V)$ with $n=0,11$ for the top-heavy case of experiment 2 (chance superpositions of single stars) shown as Hess diagrams. The $n=0$ case has been smoothed in order to allow it to show some extent perpendicular to the 1 million year isochrone. The thick black line shows the position of the 1 million year isochrone and the thin lines the evolutionary tracks between 0 and 2 million years for the initial masses of 25, 40, 60, 85, and 120 /. The function scaling is logarithmic and the normalization is arbitrary. See the electronic version of the journal for a color version of this figure.[]{data-label="uvv_chsup3"}](f6.ps){width="\linewidth"}
Six of the resulting full color-magnitude density functions, $g_{2^n{\rm s}}(U-V,V)$, are shown in Fig. \[uvv\_chsup1\] for $n=1,4,7$ and the two cases (Kroupa and top heavy). The top left corner (where massive stars are located) of all the functions is shown in Figs. \[uvv\_chsup2\] (Kroupa) and \[uvv\_chsup3\] (top heavy). As was the case in experiment 1, $g_{2^n{\rm s}}(U-V,V)$ is zero nearly everywhere in the color-magnitude diagram except in a narrow band. The band widens up until $n=8$ and then narrows down from that point onwards. At the same time, the lower end of the band starts climbing up the vertical coordinate starting at $n=1$. The top end starts climbing up at a lower pace but then picks up speed around $n=8$. The progression of both ends is faster for the top-heavy case than for the Kroupa case. For the final $n=11$ value the resulting Hess-diagram has been compressed to a well-defined narrow peak in the $U-V$ vs. $V$ color diagram: the distribution is completely contained in the last plot of the top-heavy case of Fig. \[uvv\_chsup3\] and almost so for the Kroupa case of Fig. \[uvv\_chsup2\].
Figures \[uvv\_chsup1\], \[uvv\_chsup2\], and \[uvv\_chsup3\] indicate that, as crowding becomes more of an issue, we progressively lose the ability to detect low-mass stars. Once a certain threshold has been attained, high-mass stars also become significantly affected by crowding. However, one should be careful in overinterpreting those Hess diagrams as color-magnitude probability distributions for the observed population of points source in a a given cluster because of the fat pixel assumption. The lower end of the observed band represents in reality those pixels which detection algorithms would simply classify as background. Therefore, a more realistic interpretation of the Hess diagrams would be that the observed point source population measured by assuming a zero background (or calculating it outside the cluster boundaries) is extracted from the top part of the 2-D function given by $g_{2^n{\rm s}}(U-V,V)$ and that the lower part represents the unobserved part of the population. The limit between the two regions is defined by the characteristics of the detector and the observations.
An interesting alternative interpretation of Figs. \[uvv\_chsup1\], \[uvv\_chsup2\], and \[uvv\_chsup3\] is that they represent the probability distribution for a cluster with $2^n$ stars, with the extension in $U-V$ and $V$ indicating the result of stochastic effects in drawing the given number of stars from an IMF. I will not explore this interpretation any further in this article; the reader is referred to @CervLuri06 for more details.
It is also useful to compare the results from $g_{1{\rm b}}$ (first experiment) and $g_{2{\rm s}}$ (second experiments)[^12]. Both functions represent the combination of two stars but with an important difference: in the first case the pairing assumes a flat mass-ratio distribution while in the second case the pairing is random. The different combination rules manifest themselves in the slope that is obtained when plotting $g_{1{\rm b}}$ or $g_{2{\rm s}}$ as a function of $V$ for a fixed $U-V$. For most values of $U-V$ in the first case the function increases towards lower values of $V$ (higher luminosities) while in the second one the behavior is the opposite. The reason is that for random pairing, once an $m_1$ is drawn in the middle or upper main sequence, chances are that $m_2$ will be significantly lower. On the other hand, for a flat mass-ratio distribution one gets a larger contribution from stars with $m_2$ only slightly lower than $m_1$, thus tilting the balance at a fixed $U-V$ towards systems with near-equal mass ratios.
![IMF and AMFs for experiment 2 (chance superpositions of single stars). The top panel shows the Kroupa case and the bottom panel the top-heavy case. The mass is expressed in solar units. The IMF is normalized to 1.0 and the AMFs to $2^{-n}$.[]{data-label="imf_chsup"}](f7.ps){width="0.61\linewidth"}
![Slope change introduced by chance superpositions of single stars (second experiment) as a function of the number of superimposed single stars for the two IMF cases and for three different mass ranges. See the electronic version of the journal for a color version of this figure.[]{data-label="deltaslope_chsup"}](f8.ps){width="\linewidth"}
The calculated AMFs for the Kroupa and top-heavy cases are shown in Fig. \[imf\_chsup\] along with the original IMFs. The overall behavior in both cases again being similar: as the number of stars increases, the left extreme of the AMF moves towards the right in approximately equal amounts in $\log m$ for each step in $n$. The right extreme has a different behavior: the population of AUMSs initially appears only as a weak tail and it is only when $n=7-8$ that a significant number is built up. From then on, the right extreme of the AMF picks up speed and starts moving towards the right, though at a lower pace than the left extreme. As a consequence, the distribution narrows in $\log m$. The narrowing process also affects the overall shape of the distribution, which for $n=11$ is already quite similar to a log-normal (especially for the top-heavy case).
Table \[ratios\_chsup\] lists the fraction of objects with apparent masses above $m_{\rm max}$ = 120 / for both the Kroupa (second column) and top-heavy cases (third column) as a function of $N_{\rm sup}$. The fraction is highly dependent on the IMF slope, with the top-heavy case showing values an order of magnitude above the Kroupa case until the point where the value becomes close to unity for the top-heavy case ($n\approx 9$). Such a dependence is not an unexpected behavior, because even a small change in $\gamma$ is sufficient to produce a large variation in the ratio of stars with masses around 100 / to low-mass stars in the real IMF (compare e.g. the two panels in Fig. \[imf\_bin\]). As also expected, flat-mass ratio binaries are significantly more efficient than chance superpositions in creating a population of AUMSs: $\approx 32$ superimposed stars are required to create the same number of those stars as those created by a single binary for the Kroupa case (the number is slightly lower for the top-heavy case).
Figure \[deltaslope\_chsup\] plots $\Delta\gamma$ the change in MF slope as a function of $N_{\rm sup}$ for three mass ranges. Three regimes can be distinguished. For low $N_{\rm sup}$, the effect in $\Delta\gamma$ is small and in most cases implies a slight steepening of order 0.1. For intermediate values, $\Delta\gamma$ starts to increase (the mass function becomes flatter) but the effect remains small and should be correctable. Finally, for large $N_{\rm sup}$, $\Delta\gamma$ becomes so large that no realistic correction is possible.
Experiment 3: Chance superpositions of binaries
-----------------------------------------------
The third experiment is a combination of the previous two. I start with the color-magnitude generated in the first experiment for flat mass-ratio binaries, $g_{1{\rm b}}(U-V,V)$, and I convolve it with itself to derive $g_{2{\rm b}}(U-V,V)$. $g_{4{\rm b}}(U-V,V)$ is then generated by convolving $g_{2{\rm s}}(U-V,V)$ with itself and the process is repeated until $n=11$ i.e. $g_{2048{\rm b}}(U-V,V)$. This experiment should provide the most realistic representation of the observed color-magnitude density function and AMF of a distant cluster, always keeping in mind the first two caveats previously discussed.
![Color-magnitude density functions $g_{2{\rm b}}(U-V,V)$ (left), $g_{16{\rm b}}(U-V,V)$ (center), and $g_{128{\rm b}}(U-V,V)$ (right) for the Kroupa (top row) and top-heavy (bottom row) cases of experiment 3 (chance superpositions of binaries) shown as Hess diagrams. The thick black line shows the position of the 1 million year isochrone. The function scaling is logarithmic and the normalization is arbitrary. See the author’s web site [http://www.iaa.es/$_{\mbox{\~{}}}$jmaiz]{} for animated gifs showing all the color-magnitude functions $g_{2^n{\rm b}}(U-V,V)$ from $n=0$ to $n=11$. See the electronic version of the journal for a color version of this figure.[]{data-label="uvv_chsupbin1"}](f9.ps){width="\linewidth"}
![Top left corner of the color-magnitude density functions $g_{2^n{\rm b}}(U-V,V)$ with $n=0,11$ for the Kroupa case of experiment 3 (chance superpositions of binaries) shown as Hess diagrams. The $n=0$ case has been smoothed in order to allow it to show some extent perpendicular to the 1 million year isochrone. The thick black line shows the position of the 1 million year isochrone and the thin lines the evolutionary tracks between 0 and 2 million years for the initial masses of 25, 40, 60, 85, and 120 /. The function scaling is logarithmic and the normalization is arbitrary. See the electronic version of the journal for a color version of this figure.[]{data-label="uvv_chsupbin2"}](f10.ps){width="\linewidth"}
![Top left corner of the color-magnitude density functions $g_{2^n{\rm b}}(U-V,V)$ with $n=0,11$ for the top-heavy case of experiment 3 (chance superpositions of binaries) shown as Hess diagrams. The $n=0$ case has been smoothed in order to allow it to show some extent perpendicular to the 1 million year isochrone. The thick black line shows the position of the 1 million year isochrone and the thin lines the evolutionary tracks between 0 and 2 million years for the initial masses of 25, 40, 60, 85, and 120 /. The function scaling is logarithmic and the normalization is arbitrary. See the electronic version of the journal for a color version of this figure.[]{data-label="uvv_chsupbin3"}](f11.ps){width="\linewidth"}
As I did for the second experiment, I show six of the resulting full color-magnitude density functions, $g_{2^n{\rm b}}(U-V,V)$ in Fig. \[uvv\_chsupbin1\] for $n=1,4,7$ and the two cases (Kroupa and top heavy). The top left corner (where massive stars are located) of all the functions is shown in Figs. \[uvv\_chsupbin2\] (Kroupa) and \[uvv\_chsupbin3\] (top heavy). Those three figures are quite similar to the equivalent ones for the second experiment. The most prominent differences are: \[a\] the non-zero regions of $g_{2^n{\rm b}}(U-V,V)$ are more extended in their short direction (in the diagrams, from the lower left to the upper right) compared to the non-zero regions of $g_{2^n{\rm s}}(U-V,V)$ due to the additional widening introduced by binaries; and \[b\] the extension of $g_{2^n{\rm b}}(U-V,V)$ in its long direction (from the lower right to the upper left) is similar to that of $g_{2^n{\rm s}}(U-V,V)$ but it is slightly displaced towards lower magnitudes (higher luminosities) due to the additional factor of two in the number of superimposed objects. The latter effect is especially noticeable for large values of $n$ (compare the lower right panels of Figs. \[uvv\_chsup2\] and \[uvv\_chsupbin2\] or those of Figs. \[uvv\_chsup3\] and \[uvv\_chsupbin3\]). Note, however, that a comparison of the two experiments assuming the same number of superimposed individual stars implies using $g_{2^n{\rm s}}(U-V,V)$ and $g_{2^{n-1}{\rm b}}(U-V,V)$. If the comparison is done in that way one finds that for large $n$ the top parts of the non-zero regions of the two functions end near a similar value (with the $g_{2^{n-1}{\rm b}}(U-V,V)$ one only slightly higher in luminosity) and that the low-luminosity tail of $g_{2^{n-1}{\rm b}}(U-V,V)$ is significantly more extended than that of $g_{2^n{\rm s}}(U-V,V)$.
![AMFs for experiment 3 (chance superpositions of binaries). The top panel shows the Kroupa case and the bottom panel the top-heavy case. The mass is expressed in solar units. All AMFs are normalized to $2^{-(n+1)}$.[]{data-label="imf_chsupbin"}](f12.ps){width="0.62\linewidth"}
![Slope change introduced by chance superpositions of binaries (third experiment) as a function of the number of superimposed binaries for the two IMF cases and for three different mass ranges. See the electronic version of the journal for a color version of this figure.[]{data-label="deltaslope_chsupbin"}](f13.ps){width="\linewidth"}
The calculated AMFs for the third experiment are shown in Fig. \[imf\_chsupbin\], with the overall behavior in both cases being similar to the equivalent ones for the second experiment. A more detailed comparison shows that for low values of $n$ the behavior beyond $m_{\rm max}$ is quite different: both experiments start by developing a tail from their $n=0$ case but since each initial distribution has a very different apparent upper mass limit (for experiment 2 it is the real $m_{\rm max}$ while for experiment 3 it is $m_{{\rm max},1{\rm b}}$) the fraction of stars above the limit starts from a much higher value for experiment 3 and grows at a significantly slower pace (see Table \[ratios\_chsup\]). For large values of $n$ the left side of $g_{2^{n-1}{\rm b}}(U-V,V)$ is quite similar to that of $g_{2^{n-1}{\rm s}}(U-V,V)$ while its right side is similar to $g_{2^n{\rm s}}(U-V,V)$.
Figure \[deltaslope\_chsupbin\] plots the change in MF slope $\Delta\gamma$ as a function of $N_{\rm sup}$ for three mass ranges. The same three regimes as in Fig. \[deltaslope\_chsup\] can be distinguished. For low $N_{\rm sup}$, the effect in $\Delta\gamma$ is small and can be approximated by the value derived from the first experiment. For intermediate values, $\Delta\gamma$ increases moderately (the mass function becomes flatter) and the effect remains correctable. Finally, for large $N_{\rm sup}$, $\Delta\gamma$ becomes very large and no realistic correction is possible.
Sample applications
===================
In this section I apply the results of the experiments above to the IMFs derived from HST observations for two of the best studied massive young clusters in the Local Group, NGC 3603 and R136. In order to do that, two preliminary steps are required:
1. Derive the radius of an effective pixel. As previously mentioned, the value depends not only on the detector properties but also on $\Delta m$. Indeed, ACS/HRC on HST can separate low $\Delta m$ objects only 2 pixels apart [@Maizetal08a] (effective radius of 1 pixel) but for large $\Delta m$ the effective radius can grow to 4-5 pixels (similar values apply to the PC of WFPC2). As a compromise, we adopt a value of 2.5 pixels.
2. Determine the average number of stars per effective pixel, $N_{\rm epx}$, given by:
$$N_{\rm epx} = \left(\frac{d}{10\;{\rm pc}}\right)^2 10^{-0.4(m_{V,{\rm epx}}-M_{V,1})}.
\label{Nepx}$$
In Eqn. \[Nepx\], $d$ is the distance to the object, $m_{V,{\rm epx}}$ is the averaged $V$-band extinction-corrected measured magnitude in a single effective pixel, and $M_{V,1}$ is the absolute magnitude of a “1-star cluster” derived from evolutionary synthesis (calculated by deriving $M_V$ for a large cluster with e.g. $N=10^6$ stars and then adding $2.5\log N$). If needed, $V$-based values can be substituted by those from other passband.
NGC 3603
--------
NGC 3603 is the massive young cluster with the lowest extinction in the Galaxy. @Moffetal94 described it as a Galactic clone of R136 without the halo due to their similarities in age, stellar content, and central density. Note, however, that most of the mass of 30 Doradus is located outside R136, making it significantly more massive than NGC 3603. A study with HST spectroscopy by @Drisetal95, recently extended from the ground by @Meleetal07, indicates that NGC 3603 contains the highest concentration of well-classified O2/3 + WNha stars in the Galaxy.
I show in Table \[NGC3603data\] the literature data for the distance and extinction to the core of NGC 3603. The values for the extinction are quite homogeneous and here we adopt $A_V = 4.50$. Also, at the location of the central cluster there is little point-to-point variation in the extinction [@Moff83; @Melnetal89; @Meleetal07], so the assumption of a constant foreground screen appears reasonable[^13]. The disagreement on the distance to NGC 3603 is larger. Different methods and observations yield values between $\approx$ 6 kpc and $\approx$ 8 kpc (see @Meleetal07 for a discussion). In order to consider the different possibilities, I adopt three possible distances of 6, 7, and 8 kpc, which I refer to as the short, intermediate, and long distances, respectively. Regarding the age of the core of NGC 3603, it was previously thought to be $\approx$ 3 million years based on the presence of WR stars but now it is believed that those objects are still in their core hydrogen-burning stage (i.e. they are WNha stars, see e.g. @Crow07) and the currently favored age is 1 million years [@Stoletal04; @SungBess04], which I adopt.
[lll]{} \[NGC3603data\] @Moff83 & 7.0 $\pm$ 0.5 & 4.46 $\pm$ 0.28\
@Melnetal89 & 7.2 & 4.47 $\pm$ 0.40\
@Eiseetal98 & & 4.60\
@dePretal99 & 6.1 $\pm$ 0.6 &\
@Nurnetal02 & 7.7 $\pm$ 0.2 &\
@Stoletal04 & 6.0 $\pm$ 0.3 & 4.50 $\pm$ 0.60\
@SungBess04 & 6.9 $\pm$ 0.6 & 4.44\
@Meleetal07 & 7.6 & 4.66\
![ACS/HRC F550M DRZ frame of NGC 3603. The three WNha objects are marked and circles with radii of 3 and 6 centered on the cluster have been drawn. A square-root scale between 0 and 800 counts has been used in order to show both the bright and the dim stars. The pixel size is 0025, the field size is 293$\times$254 (1172 px $\times$ 1016 px), and the vertical direction is 124 East of North.[]{data-label="ngc3603_f550m"}](f14.ps){width="\linewidth"}
NGC 3603 was observed with HST/ACS on 29 December 2005 under GO program 10602 using both the WFC and HRC detectors and several filters. Here I use the HRC F550M data, combined with the literature information described above for the distance, extinction, and age, to study the blending effect created by real multiple systems and chance alignments on the NGC 3603 IMF. In a future paper we will use all the data to do a more thorough analysis that will include independent measurements of the distance and extinction. Four F550M exposures of 2 s each were obtained with a dithering pattern that covers the gap produced by the HRC occulting finger. The exposure time was chosen in order to avoid saturation of the brightest stars. MULTIDRIZZLE was used to generate a common geometrically-undistorted cosmic-ray-corrected drizzled (DRZ) frame, see Fig. \[ngc3603\_f550m\], as well as to clean the individual geometrically-distorted flat-fielded (FLT) frames from cosmic rays and hot pixels.
JMAPHOT, a crowded-field photometry package specifically designed for HST images was used for the data reduction. First, a search is performed in the DRZ frame to find all the sources above a certain S/N threshold. JMAPHOT finds the sources in order from bright to dim and, after each one is found, a model (the drizzled PSF for point sources, simple kernels for extended sources and possible leftover cosmic rays and hot pixels) is subtracted from the data and a correction applied to the weight map before the next source is searched for. This technique allows for the exclusion of false positives caused by complex PSFs with secondary peaks and for the detection of some of the otherwise false negatives close to bright sources. Once a source list is built, the coordinates are transformed back to each of the distorted, cleaned FLT frames and PSF photometry is performed on each one of them. Positions and fluxes of each star are fitted simultaneously; also, stars with close neighbors are grouped together and fitted at the same time. Several passes are performed to eliminate the small contributions from distant stars and to improve the initial PSF model (derived from @AndeKing04 with wings from Tiny Tim, @Kris95) by calculating the PSF residuals. Aperture and charge-transfer efficiency corrections are applied to the flux from each individual FLT frame and the four values are finally combined to derive the observed VEGAMAG magnitude for each object.
Several steps are needed to convert the observed magnitudes into masses. First, F550M values are transformed into the Johnson $V$ band by adding 0.120 mag, as calculated for the appropriate input SED and extinction using the synthetic photometry package in CHORIZOS[^14]. Second, $5\log d -5$ is subtracted to obtain the absolute magnitudes $V$ for each of the short, intermediate, and long distances. Finally, I use $m(V)$ to obtain the corresponding apparent masses. The first three rows in Table \[ngc3603\_results\] give the values I obtain for the three brightest objects in NGC 3603: A1, B, and C.
![AMFs for NGC 3603 assuming a distance of 6.0 kpc (top), 7.0 kpc (middle), and 8.0 kpc (bottom). In each case the data, the power-law fit in the 8-120 / range, and the top-heavy 2-binaries AMF are shown. Masses are in /. See the electronic version of the journal for a color version of this figure.[]{data-label="ngc3603_imf"}](f15.ps){width="0.395\linewidth"}
[lccc]{} \[ngc3603\_results\] $M_{\rm A1}$ (/) & 159 & 189 & 217\
$M_{\rm B}$ (/) & 147 & 176 & 203\
$M_{\rm C}$ (/) & 105 & 130 & 152\
$\gamma_{\rm equal\; number}$ & $-$1.98 $\pm$ 0.16 & $-$1.98 $\pm$ 0.14 & $-$1.83 $\pm$ 0.12\
$\gamma_{\rm equal\; width}$ & $-$2.33 $\pm$ 0.49 & $-$2.68 $\pm$ 0.42 & $-$2.37 $\pm$ 0.39\
$\gamma_{\rm IMF}$ & $-$1.90 $\pm$ 0.16 & $-$1.90 $\pm$ 0.14 & $-$1.74 $\pm$ 0.12\
$N_{\rm epx}$ (3) & 0.64 & 0.88 & 1.15\
$N_{\rm epx}$ (6) & 0.21 & 0.29 & 0.38\
$N_{>120 M_\odot,{\rm 2s}}$ & 0.01 & 0.01 & 0.01\
$N_{>120 M_\odot,{\rm 1b}}$ & 2.40 & 2.83 & 3.07\
In order to derive the AMF I first eliminate those objects with observed masses below 8 /. Using such a large cutoff allows us not to worry about incompleteness due to low S/N, since an 8 / isolated star has a S/N of $\approx 35$ in a single FLT frame and of $\approx 70$ in the combined DRZ frame[^15]. Also, since I want to compare the results with the experiments in the previous section, those stars with apparent masses above 120 / (A1, B, and, for the two longest distances, C) are also excluded i.e. only the 8-120 / range is used for the power-law fit. No contamination correction is applied given the small size of the field, the high density of stars in the cluster, and that most such objects should be dimmer than the equivalent to the 8 / cutoff. Finally, the AMF is fitted using bins with an equal number of objects, as prescribed in Paper I. Different numbers of bins were tried but the slopes were left essentially unchanged, as expected from the results in that paper. The results for 10 bins are shown in Table \[ngc3603\_results\] and plotted in Fig. \[ngc3603\_imf\]. For comparison purposes, a fit with 10 bins of equal width was also attempted and, as expected, the obtained slopes were significantly different due to the bias inherent in such a method. Also, the measured uncertainties using bins of equal width were a factor of three larger (see Table \[ngc3603\_results\]). Note that for the three distances $\gamma_{\rm equal\; number}$ is compatible (less than 1 sigma in two cases, less than 1.5 sigmas in the other) with the value we have used for our top-heavy experiments ($\gamma = -2.0$)[^16], so that will be the assumed slope for the rest of this subsection.
Finally, to correct for the effects of unresolved binaries and/or chance superpositions, we need to calculate $N_{\rm epx}$ using Eqn. \[Nepx\]. With the evolutionary synthesis module of CHORIZOS I obtain that the absolute $V$ magnitude of a solar-metallicity 1-million-year old top-heavy “1-star cluster” is $-0.75$. The other quantity needed is the observed average magnitude in an effective pixel, which will depend on the aperture radius chosen. The DRZ field has a size of 293$\times$254 but 69% of the flux is contained within a radius of 3 and 94% within a radius of 6. Therefore, the area enclosed within those two radii provide reasonable descriptions of the center of NGC 3603 and of the region that contains most of the light from the core, respectively. The resulting $N_{\rm epx}$ are shown in Table \[ngc3603\_results\]. Depending on the distance and radius selected, I find that, on average, each point source in NGC 3603 contains at most 1.15 individual stars due to chance superpositions with the assumption that all systems are single and not unresolved binaries. Therefore, chance superpositions are not an important issue for the NGC 3603 HRC data and, indeed, most effective pixels should be empty. Of course, if most point sources are binaries the results of the first experiment are still relevant.
What do our experiments tell us about the corrections required to analyze the AMF in terms of the real IMF of NGC 3603? With the observed values of $N_{\rm epx}$, $f_{a,1{\rm b}}$ (1 binary) should be the closest approximation to reality if indeed most stars are binaries (note that for binaries the values of $N_{\rm epx}$ have to be reduced by a factor of two and that those values represent the average number of binaries per effective pixel). As a comparison, I also discuss the case of $f_{a,2{\rm s}}$ (2 single stars), which is less realistic but is the closest choice among the results of the second experiment. Regarding $\Delta\gamma$, both AMFs indicate that the measured slope for the range 8-120 / will be slightly steeper than the real IMF ($\Delta\gamma = -0.086$ $f_{a,2{\rm s}}$ and by $\Delta\gamma = -0.087$ for $f_{a,1{\rm b}}$). Applying the correction $-\Delta\gamma$ we arrive at the final values for the IMF slope, $\gamma_{\rm IMF}$, shown in Table \[ngc3603\_results\]. For the short and intermediate distances, I obtain a slope close to the $-2.0$ while for the long distance the slope is slightly steeper. The values are in good agreement with the recent result by @Stoletal06, who measured an IMF for NGC 3603 with $\gamma$ = -1.89 $\pm$ 0.14 between 7 and 20 (note, however, that their $m_{\rm lower}$ is significantly lower than 8 /).
The result is different for the expected number of ultramassive objects, $N_{>120 M_\odot}$, shown in Table \[ngc3603\_results\]. For the single-star case, the expected number is almost zero. For the binary case, the predicted numbers are $\sim$2 for the short distance and $\sim$3 for the intermediate and long distances. In other words, [*if the real stellar upper mass limit is 120 /, we would expect two or three stars with apparent masses beyond that limit if most objects are unresolved binaries*]{} and that is precisely the number that is observed.
What else do we know about A1, B, and C, the three brightest point sources in NGC 3603? @Drisetal95 identified them as the source of the Wolf-Rayet part of the composite WR+O integrated spectrum of the core, as had been already partially suggested by @Walb73b. Since hydrogen is present and there is intrinsic absorption in the high-order Balmer lines, they are classified as WN6ha, implying that they are the more luminous and massive cousins of the O3 stars in their immediate vicinity. Therefore, from the point of view of their spectral classification they are good candidates to have masses above 120 / if such stars really exist. However, it is also possible that they are unresolved multiple systems composed of individual stars with masses in the range 70-120 / which, from what we currently know, should have the same or similar spectral type (see e.g. @Bonaetal04 and note that their values are present-day masses, not initial ones).
One way to decide which of the two options is correct is to search for radial velocity variations and possible eclipses, which is what @Moffetal04 did. They found that A1 is an eclipsing binary with a 3.7724 day period. Olivier Schnurr and Tony Moffat (private communication) have recently measured the radial velocity variations of A1 and obtained masses of 114 $\pm$ 30 / and 84 $\pm$ 15 /, respectively. Interestingly, if we take those masses to be the initial ones, a 114 / + 84 / unresolved object should have an apparent mass of 157 /; assuming some stellar mass loss during their lifetimes may add up to a few tens of solar masses to that value. The observed evolutionary masses lie between 159 / and 217 /, which is in very good agreement with the Schnurr and Moffat result.
Schnurr and Moffat (in preparation) have also found that C is a binary with an 8.92 day period, so at least two of the WN objects in NGC 3603 are not single. B shows no signs of radial velocity variations so far but that does not mean that it is not a binary, since most massive binaries have separations (and some, also inclinations) that make their motions hard to detect. On the other hand, both A1 and C are overluminous in X-rays [@Moffetal02], usually a sign of binarity since intense X-ray emission is produced in wind-wind interactions but B is normal. Then again, that does not preclude B from being a binary with a separation large enough not to emit extra X-rays but still small enough not to have its two components resolved by ACS/HRC.
In summary, our analysis of NGC 3603 has found out that the existence of 2-3 objects with apparent masses above 120 / would be expected as the result of the observed number of stars in the cluster and its IMF below that limit without having to invoke the existence of stars with real masses above 120 /. The underlying hypothesis is that most or all massive stars in NGC 3603 are members of binary systems. Independent data have shown that indeed two of those stars are binaries and the currently available results for the third one leave room for the decision to go either way. The measurement of $\gamma$ could be revised slightly when the additional ACS data are processed. When we do that in a future paper, we will apply CHORIZOS to calculate individual extinction corrections for each star, derive a distance from the data, and do a comparison between the resulting color-magnitude diagram with the one in Fig. \[uvv\_bin\].
R136
----
From a historical point of view, R136 (HD 38268), the core of 30 Doradus, is an excellent case study on the problems caused by multiplicity, either real or induced by chance superpositions. @Walb73b, noting the WR features in its spectrum, compared it to NGC 3603 and suggested that it could be a Trapezium-like system made out of Wolf-Rayet and other early-type O stars. On the other hand, @Cassetal81 dismissed that the central object, R136a, could be made out of “30 O3 or WN3 within a space of 0.5 arcsec (0.1 pc)” and proposed instead that it was a single supermassive star with 2500 /. A few years later that alternative was shown to be false first by @MoffSegg83 by detecting spectral variations within R136 and later by @WeigBaie85 by using speckle interferometry to resolve R136a into eight individual sources, something which was later confirmed with HST [@Weigetal91].
Several later HST studies have analyzed the stellar composition of R136, of which the most complete is that of @MassHunt98. They obtained FOS spectroscopy of all the bright point sources in the core and combined it with PC (WFPC2) photometry to derive a color-magnitude diagram of the massive stars. In a follow-up paper, @Massetal02 observed four spectroscopic eclipsing binaries and measured their masses. They also detected another five eclipsing binaries, indicating that massive binaries are also common in R136. From their data, @MassHunt98 measured a Salpeter- or Kroupa-like IMF with $\gamma$ between $-2.3$ and $-2.4$ for the range 15-120 /. That value, however, does not correspond to R136 alone but also includes the inner part of the 30 Doradus halo. In any case, for lack of better information, it will be the value assumed here.
R136 is roughly seven times farther away than NGC 3603. Also, 30 Doradus has never been observed with ACS (either WFC or HRC) and the best data currently available were obtained with the PC on WFPC2 (that was what @MassHunt98 used), which has a factor of 1.6 lower pixel size than HRC. Therefore, if R136 and NGC 3603 had similar stellar densities at their centers, one would expect crowding to be $(1.6\times 7)^2 \approx 125$ times worse in the former. The difference in resolution is readily apparent when one compares Figs. \[ngc3603\_f550m\] and \[r136\_f555w\].
Let us quantify how important crowding is within a 1-radius circle centered on R136. Doing aperture photometry on the F555W data, obtaining $A_V$ from the data in @MassHunt98, and using CHORIZOS to estimate the conversion to the $V$ passband, I derive an extinction-corrected $m_V$ of 9.29. Assuming an effective pixel radius of 2.5 real pixels I obtain $m_{V,{\rm epx}}$ = 14.01. For assumed values of 1 million years (age)[^17], LMC (metallicity), and Kroupa (IMF), the value $M_{V,1} = 0.79$ is obtained. Finally, assuming a distance of 50 kpc, Eqn. \[Nepx\] yields $N_{\rm epx} = 129$. The value is relatively robust to small variations in the assumed parameters. Therefore, the $n=7$ results of the second experiment (if binaries are not abundant in R136) and the $n=6$ results of the third experiment (if binaries dominate) should be the reference for the analysis of the PC data of R136. This means that all the objects within the circle in Fig \[r136\_f555w\] have to be the superposition of a large number of stars (the majority of them being of low mass).
Using $f_{a,64{\rm b}}$ we obtain that 1.6% of the 77 effective pixels within 1 are expected to contain one object above 120 /. The equivalent value for $f_{a,128{\rm s}}$ is 0.6%. This translates into 1.3 and 0.5 stars, respectively[^18]. How does this compare with the observations? Using the currently preferred low-temperature-scale values of @MassHunt98, the three most massive stars in the region are R136a1, a2, and a3, with masses of 136 /, 122 /, and 120 /, respectively. Those observed masses agree very well with the values predicted by the experiments in this paper, especially if binaries dominate. It is also interesting to point out that three of the four most massive objects with spectral types in the larger region explored by @MassHunt98 are within the 1 radius considered here. One explanation would be that the most massive stars form preferentially in very dense environments. However, there are five other stars with similar spectral types (WNha and O3 If\*/WN) outside the most crowded regions with masses only slightly lower (between 103 / and 120 /). Hence, a reasonable alternative is that all of those stars have similar masses and that the extra measured mass in R136a1, a2, and a3 is simply due to the increased likelihood of chance superpositions there.
R136 was the cluster used by @WeidKrou04 and @Koen06 and one of the clusters in the sample used by @OeyClar05 to derive an $m_{\rm max}$ around 150 / (with varying degree of uncertainty around the value). All of those works used the @MassHunt98 values for the masses which, even for the low-temperature scale, include at least a star with a mass of 136 / (R136a1). Of course, the existence of a single star with such a mass invalidates the possibility that $m_{\rm max}$ is lower than that value. However, if, as we have seen, the certain existence of chance superpositions and the likelihood that R136a1 is a binary[^19] (as most massive stars are) are considered, then the real mass of the heaviest component in R136a1 could be 120 / or even less.
What about deriving the true IMF slope from the observed AMF at the center of R136? Figs. \[deltaslope\_chsup\] and \[deltaslope\_chsupbin\] indicate that $\Delta\gamma$ is in the range between 0.8 and 1.5 for 8-120 / in the region within 1. That correction is too large and too dependent on the assumptions to be applied with confidence, so with the current data it is not possible to know the real IMF slope at the very center of R136. However, note that if a factor of 2 in (linear) effective pixel size is achieved, a dramatic change takes place. The relevant functions then are $f_{a,32{\rm s}}$ and $f_{b,16{\rm s}}$ and $\Delta\gamma$ becomes $\approx 0.10$, which is a believable correction. Note also that in such a case, with $\approx 300$ effective pixels and with a S/N large enough to have 100-150 of them populated with detected stars, the number of observed objects will be enough to derive a bias-free meaningful IMF ($\sigma_\gamma \le$ 0.2) if the techniques in Paper I are used (see section 5 in @MaizUbed05).
Our summary for R136 is similar to that for NGC 3603. Even though there are stars with apparent masses above 120 /, their detection can be explained by unresolved stars with real masses below that value. The main differences are that here the measured values are only slightly above the limit and that here the unresolved stars are a combination of chance superpositions and (likely) real multiple systems. $\gamma$ cannot be reliably measured with the current data for the innermost regions of R136 but a moderate improvement in the quality (within the capabilities of HRC/ACS) should be sufficient to do the job.
Discussion
==========
I have presented in this paper a simple method to quantify the effect of unresolved multiple systems and chance alignments on the heavy part of the mass functions of young stellar clusters and applied it to NGC 3603 and R136. Unresolved multiple systems introduce an intrinsic spread in the observed color-magnitude diagrams and can produce a population of AUMSs in a rich cluster. On the other hand, their effect on the apparent massive star MF slope is relatively small. Chance alignments can also produce AUMSs but only for large $N_{\rm sup}$. As opposed to unresolved multiple systems, their effect on the AMF slope can be large.
To my knowledge, no similar method had been previously developed for those same circumstances. For the effect of binaries in the IMF of low-mass stars in the field and in globular clusters, see @Krouetal91 and @Solletal07, respectively. For a similar (but more restricted) analysis to the one in this paper applied to intermediate-age clusters, see @SagaRich91. Previous analyses for young clusters sometimes include a simplified correction with equal-mass binaries (e.g. @Stoletal06) but in most cases binaries are included in the incompleteness analysis. An incompleteness test adds a large number of fake stars to the observed field and runs the output through the star detection algorithm to see how many of the fake objects are recovered. The percentage of unrecovered objects is then used to calculate an incompleteness correction. Such an analysis in reality is measuring two different effects: the weakest objects (those close to the detection limit) may be missed, even in an uncrowded region, either because Poisson/background fluctuations or read noise place them below the detection limit or because the details of the detection algorithm make it stop before reaching it. Alternatively, some brighter objects are missed because they are located close to an even brighter star that hides them under its PSF. The first effect (low S/N objects) should be quantifiable by studying the detector properties and the expected S/N as a function of magnitude. The second effect is more complex because it depends on the PSF (which may be or may be not well characterized) and, more importantly, the stellar distribution. For that reason, incompleteness tests need to be run on a specific dataset. Furthermore, a classical incompleteness test does not address the issue that the added fake stars may significantly modify the measured magnitude of the detected, brighter star, and, thus, alter the results of the mass function. The technique presented here does not attempt to substitute the correction of the first effect (low S/N objects) provided by incompleteness tests but only the second. It does so by \[a\] correcting the measured slope after it is fitted to the observed mass function rather than modifying the observed mass function before fitting it and \[b\] including the effect of the different mass detected when two stars are superimposed and not only counting the fraction of undetected objects. It also has the advantage of being easily quantifiable and applicable to the planning of future observations.
Having analyzed in detail NGC 3603 and R136, it is interesting to point out that no end-products of runaway collisions are seen there despite those two clusters being mentioned as likely candidates for them by @Portetal04a. There are several possible explanations: \[a\] Runaway collisions do take place but the remaining products evolve so fast that those in NGC 3603 and R136 have already become black holes (this would require lifetimes of $\approx$ 1 million years). \[b\] Core collapse happens at a later stage, so the required time and density conditions are not satisfied in these clusters and ultramassive objects form only as a result of the merger of evolved objects. \[c\] Core collapse never happens and ultramassive objects never form. \[d\] The output of a massive stellar merger that would lead to an ultramassive stars is so unstable that it loses its excess mass almost immediately. Regarding the latter possibility, it is notorious that very massive stars are very difficult to model and that our current knowledge of them is limited. Nevertheless, we know that there could be different mechanisms at work that would impede the formation of an ultramassive star via a merger: the resulting object may be directly above Eddington’s limit [@GlebPols07], so close to it that strange-mode instabilities overwhelm it [@Town07], or may always rotate so fast that it surpasses the $\Omega\Gamma$ limit [@MaedMeyn00].
This article provides further evidence for the existence of a stellar upper mass limit at solar or near-solar metallicities. Furthermore, the analyzed data indicate that $m_{\rm max}$ may be as low as 120 /. The situation for Population III stars is expected to be different, likely because the reduced opacity should place Eddington’s limit at higher luminosities and, hence, masses (see e.g. @ZinnYork07 and references therein).
Support for this work was provided by the Spanish Government Ministerio de Educación y Ciencia through grant AYA2004-08260-C03, grant AYA2007-64712, and the Ramón y Cajal Fellowship program and co-financed with FEDER funds. I would like to thank Tony Moffat and Phil Massey for providing me access to their work before publication; Nolan Walborn, Tony Moffat, and an anonymous referee for useful comments to previous versions of the manuscript; and Enrique Pérez and Miguel Cerviño for fruitful conversations on this topic.
[^1]: Most of the analysis in these papers is also applicable to the calculation of the present-day mass function (PDMF).
[^2]: Such a distribution, expressed in terms of separation $r$ instead of $P$, is close to $f(\log r) \propto (\log r)^0$ and is known as Öpik’s law, after @Opik24.
[^3]: Those values are called evolutionary masses and refer to the initial mass of the star.
[^4]: In the last years much work has been done on new evolutionary tracks and isochrones with rotation and possibly-reduced mass-loss rates due to clumping corrections. The present work can be easily adapted to those other conditions but the effects on our results are expected to be relatively minor.
[^5]: For the sake of notation simplicity and since at this point I am not discussing distance effects, I write $M_U$ and $M_V$ simply as $U$ and $V$, respectively.
[^6]: Throughout this paper $m$ is considered to be the initial stellar mass, not the mass when the star is 1 million years old.
[^7]: In this paper I use magnitude functions instead of luminosity functions; the conversion between one and the other is straightforward.
[^8]: For example, the spectra of the two components of WR 20a [@Bonaetal04] are almost indistinguishable and if it were not for the large velocity variations induced by their proximity it would be almost impossible to identify the spectrum as a composite.
[^9]: It should be pointed out that the overlap between spectroscopic and visual/interferometric systems is very small, see @Boyaetal07 and @Nortetal07 for examples.
[^10]: The conversion from a magnitude or luminosity function to a IMF involves $dm/dV$, whose numerical behavior may be odd when using coarsely-gridded tabular information to derive it. The observed structures may or may not be real but since our concern is with the high-mass end of the AMF, we will not discuss them any further.
[^11]: As previously noted, special care was taken to avoid roundoff errors.
[^12]: Note that the function scaling in Figs. \[uvv\_bin\] and \[uvv\_chsup1\] is different.
[^13]: Strong extinction variations exist at larger radii but those do not concern us here.
[^14]: The value depends on the exact SED and $A_V$ but the added uncertainty is of the order of only a few thousandths of a magnitude, which is good enough for our purposes.
[^15]: Note that most incompleteness analyses deal with two different types of non-detections, those due to low S/N of the object and those due to the proximity of bright sources. Since the latter is already taken care of by our experiments, we only need to worry about the former.
[^16]: Of course, the observed $\gamma$ is that of the AMF, not the IMF, but, as we will see below, both should be very similar in this case.
[^17]: R136 could hardly be significantly younger than that because it has already cleared of dense gas a large region around it. Also, if its age were older than 2 million years, its most massive stars would no longer be of WNha type.
[^18]: Note that the expected number of ultramassive stars is lower for R136 than for NGC 3603, despite the facts that the regions considered here have the same extinction-corrected absolute magnitude and that R136 is more crowded. The explanation resides in the different IMFs used for the calculation, Kroupa for R136 and top-heavy for NGC 3603.
[^19]: Note that R136a1+a2 is not likely to be a bound system, as they are separated by at least 15000 AU.
| {
"pile_set_name": "ArXiv"
} |
---
abstract: |
Motivated in part by the several observed anomalies involving CP asymmetries of B and $B_s$ decays, we consider the Standard Model with a 4th sequential family (SM4) which seems to offer a rather simple resolution. We initially assume T-invariance by taking the up and down-quark $4 \times 4$ mass matrix to be real. Following Friedberg and Lee (FL), we then impose a “hidden" symmetry on the unobserved (“hidden") up and down-quark SU(2) states. The hidden symmetry for four generations ensures the existence of two zero-mass eigenstates, which we take to be the $(u,c)$ and $(d,s)$ states in the up and down-quark sectors, respectively. Then, we simultaneously break T-invariance and the hidden symmetry by introducing two phase factors in each sector. This breaking mechanism generates the small quark masses $m_u,~m_c$ and $m_d,~m_s$, which, along with the orientation of the hidden symmetry, determine the size of CP-violation in the SM4. For illustration we choose a specific physical picture for the hidden symmetry and the breaking mechanism that reproduces the observed quark masses, mixing angles and CP-violation, and at the same time allows us to further obtain very interesting relations/predictions for the mixing angles of $t$ and $t^\prime$. For example, with this choice we get $V_{td} \sim (V_{cb}/V_{cd} - V_{ts}/V_{us}) + {\cal O}(\lambda^2)$ and $V_{t^\prime b} \sim V_{t^\prime d} \cdot (V_{cb}/V_{cd})$, $V_{t b^\prime} \sim V_{t^\prime d} \cdot (V_{ts}/V_{us})$, implying that $V_{t^\prime d} > V_{t^\prime b},V_{t b^\prime}$. We furthermore find that the Cabibbo angle is related to the orientation of the hidden symmetry and that the key CP-violating quantity of our model at high-energies, $J_{SM4} \equiv {\rm Im} \left( V_{tb} V_{t^\prime b}^\star V_{t^\prime b^\prime} V_{t b^\prime}^\star \right)$, which is the high-energy analogue of the Jarlskog invariant of the SM, is proportional to the light-quark masses and the measured CKM angles: $| J_{SM4} | \sim A^3 \lambda^5 \times ( \sqrt{ m_u/m_t }
+ \sqrt{ m_c/m_{t^\prime} }
- \sqrt{ m_d/m_b }
+ \sqrt{ m_s/m_{b^\prime}}) \sim
10^{-5}$, where $A \sim 0.81$ and $\lambda=0.2257$ are the Wolfenstein parameters. Other choices for the orientation of the hidden symmetry and/or the breaking mechanism may lead to different physical outcomes. A general solution, obtained numerically, will be presented in a forthcoming paper.
---
[**Extended Friedberg Lee hidden symmetries, quark masses and CP-violation with four generations**]{}
Shaouly Bar-Shalom$^{a}$[^1], David Oaknin$^{a}$[^2], Amarjit Soni$^b$[^3]
*$^a$Physics Department, Technion-Institute of Technology, Haifa 32000, Israel*
*$^b$Theory Group, Brookhaven National Laboratory, Upton, NY 11973, USA*
Introduction
============
In spite of the success of the Standard Model (SM) in explaining almost all of the observed phenomena in particle physics, it does not address some fundamental issues, such as the hierarchy problem, dark matter, the matter anti-matter asymmetry in the universe etc. Also unexplained are the issues in flavor physics, such as the hierarchy of fermion masses and the number of families. There are strong indications, from both the theoretical and experimental points of views, that some of these unresolved questions are related to some new physics, maybe at the near by TeV-scale. It is, therefore, hoped that, with the LHC turning on very soon, we will get a first hand glimpse of the new physics at the TeV scale and new hints from nature to some of these issues and, in particular to the physics of flavor.
In this paper we wish to study some of the fundamental unresolved issues of flavor within a simple extension of the SM, in which a fourth sequential family of fermions is added - the SM4. Indeed, the four generations scenario can play an important role in flavor physics [@oldsoni], and has recently gained some new interest as it might shed new light on baryogenesis and on CP-violation in K in B, $B_s$ decays [@hou2006; @soni4gen; @CPbaryo1; @CPbaryo2; @kribs]. This model, which can be regarded as an effective low energy description of some higher energy and more fundamental underlying theory, retains all the features of the SM with three generations (which from here on we will denote as SM3), except that it brings into existence the new heavy fermionic members $t^\prime$ and $b^\prime$, which form the 4th quark doublet and a similar leptonic doublet, where the “neutrino" of the 4th family must also be rather heavy, with mass $\gsim M_Z/2$. This may well be an important clue that the underlying nature of the 4th family may be quite different from the 1st three families. This line of thinking may in fact lead to a dark matter candidate [@0310006].
The addition of the fourth generation to the SM3 means that the CKM matrix can now potentially have six independent real parameters/angles and three physical CP-violating phases [@jarlskog]. The two additional phases (with respect to the SM3) provide new sources of CP-violation and may, thus, give rise to new CP-violating effects. Indeed, in a recent paper [@soni4gen], it was shown that a fourth family of quarks with $m_{t^\prime}$ in the range of $\sim 400 - 600$ GeV provides a simple and perhaps rather natural explanation for the several indications of new physics [@newsoni] that have been observed involving CP asymmetries in b-quark systems, and this in fact forms an important motivation for our work. Such heavy fermionic states point to the interesting possibility that the 4th family may play a role in dynamical electroweak symmetry breaking (EWSB), since the mechanism of dynamical mass generation seems to require such heavy masses [@dynEWSB; @dynEWSB2]. In addition, as mentioned above, the new CP-violating phases may play an important role in generating the baryon asymmetry in the universe [@CPbaryo1; @CPbaryo2], which is difficult to address within the SM3.
We note in passing that a 4th generation of quarks (and leptons) with such heavy masses is not ruled out by precision electroweak constraints, but rather requires that correspondingly the Higgs has to be heavier, $\gsim$ 300 GeV [@kribs].
In a recent paper [@FL] that also partly motivated the present work, Friedberg and Lee (FL) suggested a very interesting new approach for the generation of CP-violation and quark masses in the SM3: that a weakly broken symmetry which is operational in the SU(2) (weak) fermionic states relates the smallness of CP-violation to the smallness of the light-quark masses $m_d$ and $m_u$. More specifically, they imposed a “hidden" symmetry on the weak states of the quarks (named henceforward as the “hidden" frame), which is then weakly broken by small CP-phases that generate the non-zero masses for the light-quarks u and d. They found a very interesting relation between CP-violation and the light-quark masses: $$J_{SM} \propto \sqrt{\frac{m_d m_s}{m_b^2}} \label{FLrelation}~,$$ where $J_{SM}$ is the Jarlskog invariant responsible for CP-violation in the SM3 [@jarlskog].
The main appealing feature of the FL mechanism is that the CP-violating phases are the small parameters that control the breaking of the hidden symmetry and are, therefore, the generators of the small masses of the first generation quarks. Unlike the conventional SM3 picture, the FL mechanism gives a physical meaning to the rotations of the quark fields (i.e., from the weak basis to the physical mass eigenstates basis) in the up and down quark sector separately, since there is an independent hidden symmetry for each sector.
As we will show in this paper, the idea of FL and their main result in Eq. \[FLrelation\] is extremely interesting when applied to the SM4 case and our extension will lead it to predictive power . In particular, with an appropriate choice of a hidden symmetry, it allows to generate [*all four masses*]{} of the $u,d,c$ and $s$-quarks in terms of the masses of the four heavy quarks $b,t,b^\prime$ and $t^\prime$ and the new CP-phases. It also gives distinct predictions for the 4th generation mixing angles and for the size of CP-violation in this theory, subject to the constraints coming from existing data on the SM3’s $3 \times 3$ CKM matrix and quark masses. Thus, the hidden symmetry framework for the SM4 case can be directly tested in collider experiments. In particular, we give distinct predictions for the new mixing angles and for the size of the new CP-violating quantities associated with the dynamics of the 4th generation quarks.
On the other hand, the construction of a hidden symmetry for the SM4 case, and the generation of the four light-quark masses in conjunction with T-violation, is more challenging and rather intricate and analytically involved than in the case of the SM3. This is mainly due to the fact that the phase-space of the hidden symmetry in the SM4 case is much broader and that, as opposed to the FL mechanism for the SM3 where the CP-phases generate only the masses of the 1st generation fermions, here we use the new CP-phases (of the SM4) as generators of all four light-quark masses $m_d,m_u,m_s,m_c$, which makes it more difficult to find a physical solution. To put it in another way, our hidden symmetry for the SM4 case defines a plane in which the theory is invariant whereas for three families the symmetry is “one-dimensional", i.e., defines a direction/vector.
In order to spell out our notation and the general formalism of the hidden symmetry and its breaking mechanism within the SM4, we first consider the $4 \times 4$ up and down-quark Yukawa terms in the SM4 (after EWSB):
$$\begin{aligned}
{\cal M}(q^{u,d}) =
\left(q^{u,d}_1,~q^{u,d}_2,~q^{u,d}_3,~q^{u,d}_4 \right) M(q^{u,d})
\left( \begin{array}{c}
q^{u,d}_1 \\ q^{u,d}_2 \\ q^{u,d}_3 \\ q^{u,d}_4 \end{array} \right) ~,\end{aligned}$$
where $q^{u,d}_i$, $i = 1-4$, are the hidden SU(2) quark states of the SM4, and $M(q^{u,d})$ are the corresponding mass matrices in the hidden frame basis.
As our zeroth-approximation we assume invariance under time reversal, thus taking $M_0(q^{u,d})$ (the subscript $0$ will henceforward denote the zeroth-order quantities) to be real and symmetric. We can then extend FL’s idea to the case of the SM4 by “doubling" the hidden symmetry in each quark sector (in the following we drop the indices $u$ and $d$, where unless stated otherwise, it is understood that the discussion below applies to both up and down sectors):
$$\begin{aligned}
&&q_1 \to q_1 + \delta^1_z z + \delta^1_t t~, \nonumber \\
&&q_2 \to q_2 + \delta^2_z z + \delta^2_t t ~, \nonumber \\
&&q_3 \to q_3 + \delta^3_z z + \delta^3_t t ~, \nonumber \\
&&q_4 \to q_4 + \delta^4_z z + \delta^4_t t \label{HS} ~,\end{aligned}$$
where $z$ and $t$ are space-time independent constants of Grassmann algebra anticomuting with the Dirac field operators, and $\delta^i_z,~\delta^i_t$ are c-numbers.
Since $M_0(q)$ is a real symmetric $4 \times 4$ matrix, it is characterized in general by 10 real parameters. However, imposing the hidden symmetry in Eq. \[HS\] eliminates 2 of the 10 parameters. The hidden symmetry of Eq. \[HS\] ensures (under the invariance of ${\cal M}_0(q^{u,d})$) the existence of two massless quark states in each sector, which we will identify as $m_u$ and $m_c$ (in the up-quark sector) and as $m_d$ and $m_s$ (in the down-quark sector). The corresponding two massless eigenvectors of $M_0(q)$ are thus identified as the zeroth-order $u$ and $c$ states, $v_u^0$ and $v_c^0$ (with $m_u^0,~m_c^0=0$) and in the down-quark sector as the zeroth-order $d$ and $s$ states, $v_d^0$ and $v_s^0$ (with $m_d^0,~m_s^0=0$). That is, since nature proves to have a large hierarchical mass structure in the quark sector, we will consider the SM4 in the chiral limit for the first two generations of quarks - $m_{u,d,c,s} =0$. Accordingly, the two massive eigenvectors are identified as the zeroth-order $t$ and $t^\prime$ states (or $b$ and $b^\prime$ states) $v_t^0$ and $v_{t^\prime}^0$ , (or $v_b^0$ and $v_{b^\prime}^0$) with masses (i.e., eigenvalues) $m^0_t,~m^0_{t^\prime}$ (or $m^0_b,~m^0_{b^\prime}$). In particular, it is easy to show that in the hidden basis $\{q_1,q_2,q_3,q_4\}$ the massless eigenvectors span a 2-dimensional subspace of the form:
$$\begin{aligned}
v_u^0,v_c^0 \in \left( \begin{array}{c}
\delta^1_z \\ \delta^2_z \\ \delta^3_z \\ \delta^4_z \end{array} \right) ,
\left( \begin{array}{c}
\delta^1_t \\ \delta^2_t \\ \delta^3_t \\ \delta^4_t \end{array} \right) ~,\end{aligned}$$
and similarly in the down-quark sector.
The next step towards establishing the complete physical picture of quark masses and mixings is to simultaneously break T-invariance and the hidden symmetry by inserting two new phase factors into $M_0$, in each sector. In the following we will construct a general framework that defines the hidden symmetry in the SM4 scenario in a form that emphasizes the underlying geometrical picture, and, then, give a concrete physical example for the breaking mechanism.
Hidden symmetry, T-invariance and the zeroth-order spectrum for the SM4
=======================================================================
In a generalization of the FL idea to the case of the SM4, let us assume, at the first stage that the zeroth-order mass matrix $M_0$ is real and invariant under the following translational symmetry (we will denote this symmetry as Hidden Symmetry 1, HS1) $$\begin{aligned}
\nonumber
q_1 & \rightarrow & q_1 + c_\theta z ~,\nonumber \\
q_2 & \rightarrow & q_2 + s_\theta c_\phi z ~,\nonumber \\
q_3 & \rightarrow & q_3 + s_\theta s_\phi c_\omega z ~, \nonumber \\
q_4 & \rightarrow & q_4 + s_\theta s_\phi s_\omega z \label{HS1} ~.\end{aligned}$$ where $c_\theta,s_\theta = \cos\theta, \sin\theta$ etc., and $z$ is a space-time independent constant of Grassmann algebra anticomuting with the Dirac fields.
This symmetry guarantees that the vector $$\begin{aligned}
Q_1 = c_\theta q_1 + s_\theta c_\phi q_2 + s_\theta s_\phi c_\omega q_3 + s_\theta s_\phi s_\omega q_4 \label{Q0} ~,\end{aligned}$$ is a massless eigenstate of the theory, as under the HS1 it transforms as $Q_1 \rightarrow Q_1 + z$. On the other hand, the three orthogonal (to $Q_1$) vectors $$\begin{aligned}
Q_2 &=& -s_\theta q_1 + c_\theta c_\phi q_2 + c_\theta s_\phi c_\omega q_3 + c_\theta s_\phi s_\omega q_4 \nonumber \\
Q_3 &=& -s_\phi q_2 + c_\phi c_\omega q_3 + c_\phi s_\omega q_4 \nonumber \\
Q_4 &=& -s_\omega q_3 + c_\omega q_4 \label{Q123}~,\end{aligned}$$ are invariant under the HS1, i.e., $Q_i \to Q_i$ for $i=2,3,4$. The rotation from the hidden frame $\{q_1,q_2,q_3,q_4\}$ to the HS1 frame $\{Q_1,Q_2,Q_3,Q_4\}$ can be written as $Q_i = R_{ij} q_j$, thus defining the real unitary matrix $R$:
$$\begin{aligned}
R =\left( \begin{array}{cccc}
c_\theta & s_\theta c_\phi & s_\theta s_\phi c_\omega & s_\theta s_\phi s_\omega \\
-s_\theta & c_\theta c_\phi & c_\theta s_\phi c_\omega & c_\theta s_\phi s_\omega \\
0 & -s_\phi & c_\phi c_\omega & c_\phi s_\omega \\
0 & 0 & -s_\omega & c_\omega
\end{array} \right) \label{Rmatrix}~.\end{aligned}$$
Demanding translational invariance under HS1 of Eq. \[HS1\], $M_0$ has only one massless eigenstate (the state $Q_1$). Thus, in order to enforce the chiral limit for the first two generations, we will demand that the zeroth-order mass matrix is invariant under an additional translation operation, which is operational in the HS1 frame $\{Q_1,Q_2,Q_3,Q_4\}$ and which we will name Hidden Symmetry 2 (HS2). Without loss of generality, we assume that HS2 is orthogonal to HS1 as follows:
$$\begin{aligned}
\nonumber
Q_1 & \rightarrow & Q_1 ~, \nonumber \\
Q_2 & \rightarrow & Q_2 + c_\zeta t ~, \nonumber\\
Q_3 & \rightarrow & Q_3 + s_\zeta c_\eta t ~, \nonumber \\
Q_4 & \rightarrow & Q_4 + s_\zeta s_\eta t \label{HS2} ~.\end{aligned}$$
The additional symmetry HS2 guarantees that the vector $$P_1 = c_\zeta Q_2 + s_\zeta c_\eta Q_3 + s_\zeta s_\eta Q_4
\label{P0} ~,$$ which is orthogonal to $Q_1$, is also massless.
The most general form of the Yukawa term ${\cal M}_{0}$ that is invariant under the independent translations in both directions HS1 and HS2, can then be written as: $$\begin{aligned}
{\cal M}_{0} = \alpha | c_\eta Q_4 - s_\eta Q_3 |^2 +
\beta | c_\zeta Q_4 - s_\zeta s_\eta Q_2 |^2 + \gamma | c_\zeta Q_3 - s_\zeta c_\eta Q_2|^2
\label{zeroth_order_matrx}~,\end{aligned}$$ and this defines the quark mass matrix $M_0$. Recall that, since $M_0$ is invariant under HS1 and HS2, two of its four eigenstates, i.e., $Q_1$ and $P_1$, are necessarily massless.
Before deriving the full zeroth-order system (i.e., 2 non-zero masses and 4 states), we wish to point out the mapping of our double hidden symmetry (HS1 and HS2) to the generic parameterizations of the hidden symmetry in Eq. \[HS\]. In particular, using the definition for HS1 and HS2 in Eqs. \[HS1\] and \[HS2\], respectively, and the fact that $q = R^{-1}Q$, we obtain the overall hidden symmetry for the SM4 case: $$\begin{aligned}
\nonumber
q_1 & \rightarrow & q_1 + c_\theta z - s_\theta c_\zeta t ~, \nonumber \\
q_2 & \rightarrow & q_2 + s_\theta c_\phi z + \left[c_\theta c_\phi c_\zeta - s_\phi s_\zeta c_\eta \right] t ~, \nonumber \\
q_3 & \rightarrow & q_3 + s_\theta s_\phi c_\omega z +
\left[c_\theta s_\phi c_\omega c_\zeta + c_\phi c_\omega s_\zeta c_\eta - s_\omega s_\zeta s_\eta \right] t ~, \nonumber \\
q_4 & \rightarrow & q_4 + s_\theta s_\phi s_\omega z +
\left[c_\theta s_\phi s_\omega c_\zeta + c_\phi s_\omega s_\zeta c_\eta + c_\omega s_\zeta s_\eta \right] t \label{fullHS} ~,\end{aligned}$$ from which one can extract the hidden symmetry parameters $\delta_z^i$ and $\delta_t^i$ of Eq. \[HS\], as a function of the angles which define the orientations of HS1 and HS2 with respect to the hidden frame $\{ q_1,q_2,q_3,q_4 \}$.
Note that the expression for ${\cal M}_{0}$ in Eq. \[zeroth\_order\_matrx\] contains five angles: the two (explicit) angles $\zeta,\eta$ associated with the orientation of HS2 with respect to the HS1 frame $\{Q_1, Q_2, Q_3, Q_4 \}$ and the three angles $\theta,\phi,\omega$ associated with the orientation of HS1 with respect to the hidden frame $\{q_1, q_2, q_3, q_4 \}$, which enter through the rotation $Q=Rq$. Thus, along with the parameters $\alpha,\beta$ and $\gamma$, ${\cal M}_{0}$ in Eq. \[zeroth\_order\_matrx\] is parameterized by 8 real parameters (in each sector) as required when imposing the double hidden symmetry (see discussion above). However, there is one non-physical angle in [*each sector*]{} which results from the fact that the two orthogonal states $Q_1,P_1$ are massless at zeroth-order and are, therefore, indistinguishable. This can be easily understood by considering the geometrical interpretation of the hidden symmetry in the SM4 case. In particular, the double hidden symmetry (HS1+HS2) defines a plane in the hidden frame $\{q_1, q_2, q_3, q_4 \}$ under which the theory is invariant. This is the plane spanned by the two orthogonal vectors $Q_1$ and $P_1$. We, therefore, have the freedom to make any unitary transformation in the $Q_1-P_1$ plane/subspace (in both up and down-quark sectors) without affecting the physical picture. This allows us to eliminate one angle in each of the $(v_d^0,v_s^0)$ and $(v_u^0,v_c^0)$ subspaces. Thus, without loss of generality we find it convenient to choose $\omega=\pi/2$ in both sectors, which sets $Q_4=q_3$ and $Q_1,Q_2,Q_3 \perp q_3$. This is analogous to a gauge condition in a vector field theory as also identified in [@FL]. Note that even though at each sector the massless states $(v_d^0,v_s^0)$ and $(v_u^0,v_c^0)$ are indistinguishable at the zeroth-order, as we will see in the next section, after breaking the hidden symmetry this degeneracy is removed, and those (now massive) states become well defined.
We are now ready to derive the mass spectrum and the $4 \times 4$ CKM matrix at zeroth-order, i.e., without T-violation. Recall that, by construction, there are two massless states, given by $Q_1$ and $P_1$. In order to find the 2 massive states we can apply the original FL formulae for three generations to the $\{ Q_2, Q_3, Q_4 \}$ subspace. As in [@FL], we find that the eigensystem of $M_{0}$ depends only on two linear combinations of $\alpha,\beta,\gamma$, so that one of these three parameters can be “gauged away". Following the choice of FL in [@FL], we eliminate the parameter $\gamma$ using the “gauge" condition (i.e., this has no effect on the physical outcome): $$\begin{aligned}
\frac{\beta}{\gamma} = 1 \label{gauge1}~.\end{aligned}$$
Using this condition, we diagonalize the mass matrix $M_0$ and find that the two massive states are: $$\begin{aligned}
P_2 &=& -s_\zeta Q_2 + c_\zeta c_\eta Q_3 + c_\zeta s_\eta Q_4 ~, \nonumber \\
P_3 &=& -s_\eta Q_3 + c_\eta Q_4 \label{P23}~,\end{aligned}$$ with masses: $$\begin{aligned}
m_{P_2}&=& \beta ~, \\
m_{P_3}&=&\alpha + c_\zeta^2 \beta =
\alpha + c_\zeta^2 m_{P_2} \label{M23}~.\end{aligned}$$
Note that, for $m_{P_3} >> m_{P_2}$ and/or $c_\zeta \to 0$ we have $m_{P_3} \approx \alpha$ and $m_{P_2} \approx \beta$ (see below).
Thus the complete set of eigenstates of $M_0$ at zeroth-order becomes quite simple, as it is given by $\{ Q_1, P_1, P_2, P_3 \}$ with masses $\{ 0, 0, m_{P_2}, m_{P_3} \}$, which we hanceforward identify (in each sector) as the zeroth-order quark states: $$\begin{aligned}
\{ v_d^0, v_s^0, v_b^0, v_{b^\prime}^0 \}
&\equiv& \{ Q_1^d, P_1^d, P_2^d, P_3^d \} \label{rel1}~, \\
\{ v_u^0, v_c^0, v_t^0, v_{t^\prime}^0 \}
&\equiv& \{ Q_1^u, P_1^u, P_2^u, P_3^u \} \label{rel2}~,\end{aligned}$$ with masses $m_d^0=m_s^0=m_u^0=m_c^0=0$ and: $$\begin{aligned}
&&m_b^0 =\beta_d,~ m_{b^\prime}^0 \approx \alpha_d ~, \nonumber \\
&&m_t^0 =\beta_u,~ m_{t^\prime}^0 =
\alpha_u + c_{\zeta_u}^2 m_t^0 \label{zeromasses}~,\end{aligned}$$ where the superscripts $d$ and $u$ distinguish between the parameters in the down-quark and up-quark sectors, respectively. Note that since T-violation is responsible for generating the light-quark masses, it is a small perturbation to the T-invariant zeroth-order spectrum. Thus for all practical purposes we can set: $m_b \approx m_b^0$, $m_{b^\prime} \approx m_{b^\prime}^0$, $m_t \approx m_t^0$ and $m_{t^\prime} \approx m_{t^\prime}^0$ (see also below).
Using the orientation of the HS1 frame $Q_i$ with respect to the hidden frame $q_i$, i.e., $Q=Rq$ with $R$ given in Eq. \[Rmatrix\], and the orientation of the states $P_{2},P_{3}$ with respect to the $\{ Q_2, Q_3, Q_4 \}$ subframe (as given in Eq. \[P23\]), we can write the set of four eigenstates in each sector in terms of the weak (hidden) states $q_i$ (as required in order to derive the zeroth-order (real) $4\times 4$ CKM matrix): $$\begin{aligned}
\left( \begin{array}{c}
v_d^0 \\ v_s^0 \\ v_b^0 \\ v_{b^\prime}^0 \end{array} \right) =
\left( \begin{array}{c}
R^d_{1i} \\ A^d_i \\ B^d_i \\ C^d_i \end{array} \right) q^d_i ~,~
\left( \begin{array}{c}
v_u^0 \\ v_c^0 \\ v_t^0 \\ v_{t^\prime}^0 \end{array} \right) =
\left( \begin{array}{c}
R^u_{1i} \\ A^u_i \\ B^u_i \\ C^u_i \end{array} \right) q^u_i \label{rel3} ~,\end{aligned}$$ where the superscripts $u$ and $d$ are again added in order to distinguish between the angles associated with the up and down-quark sectors, respectively. Also, $$\begin{aligned}
A^d_i &\equiv& \cos\zeta_d \cdot R^d_{2i} + \sin\zeta_d\cdot \cos\eta_d\cdot R^d_{3i} + \sin\zeta_d\cdot \sin\eta_d\cdot R^d_{4i} \label{ai} ~ \\
B^d_i &\equiv& -\sin\zeta_d \cdot R^d_{2i} + \cos\zeta_d\cdot\cos\eta_d\cdot R^d_{3i} + \cos\zeta_d\cdot \sin\eta_d\cdot R^d_{4i} \label{bi} ~, \\
C^d_i &\equiv& -\sin\eta_d\cdot R^d_{3i} + \cos\eta_d\cdot R^d_{4i} \label{ci}~,\end{aligned}$$ and similarly for $A^u_i,B^u_i,C^u_i$ using $R^u$ and $\zeta_u,\eta_u$.
Then denoting by $D_0 = (v_d^0, v_s^0, v_b^0, v_{b^\prime}^0 )$ and $U_0 = (v_u^0, v_c^0, v_t^0, v_{t^\prime}^0)$ the unitary matrices that diagonalize the real and symmetric mass matrices in the down and up-quark sectors, respectively: $$\begin{aligned}
D_0^\dagger M_0(q^d) D_0 &=& {\rm diag}(0,0,m_b^0,m_{b^\prime}^0) ~, \\
U_0^\dagger M_0(q^u) U_0 &=& {\rm diag}(0,0,m_t^0,m_{t^\prime}^0) ~,\end{aligned}$$ we can obtain the $4\times 4$ zeroth-order CKM matrix of the SM4 (i.e., without T-violation): $$\begin{aligned}
V^0(CKM) = U_0^\dagger D_0 \label{CKM0}~.\end{aligned}$$ The general expression for $V^0(CKM)$ in terms of the angles that define the hidden symmetry in the up and down-quark sectors is rather complicated to be written here. Let us, therefore, choose a specific physical orientation of the hidden symmetry, where the direction of HS2 is partly fixed by the angle $\zeta$ with the choice $\zeta =\omega=\pi/2$ in each sector (recall that we have fixed the angle $\omega = \pi/2$ in a manner similar to choosing a gauge). This orientation is physically viable in the sense that it reproduces the observed light-quark masses and the measured CKM mixing angles. It will be used in the next sections to demonstrate the general mechanism for breaking the hidden symmetry and T-invariance and the corresponding generation of the light-quark masses.
In particular, using Eqs. \[rel1\]-\[CKM0\] with $\zeta =\omega=\pi/2$ we obtain: $$\begin{aligned}
V_{ud}^0 &=& c_{\theta_u} c_{\theta_d} + s_{\theta_u} s_{\theta_d} \cos(\phi_u-\phi_d) ~,\nonumber\\
V_{us}^0 &=& s_{\theta_u} c_{\eta_d} \sin(\phi_u-\phi_d) ~, \nonumber \\
V_{ub}^0 &=& c_{\theta_u} s_{\theta_d} - s_{\theta_u} c_{\theta_d} \cos(\phi_u-\phi_d) ~,\nonumber\\
V_{ub^\prime}^0 &=& - s_{\theta_u} s_{\eta_d} \sin(\phi_u-\phi_d) ~,\nonumber\\
V_{cd}^0&=&- s_{\theta_d} c_{\eta_u} \sin(\phi_u-\phi_d) ~,\nonumber\\
V_{cs}^0 &=& s_{\eta_u} s_{\eta_d} + c_{\eta_u} c_{\eta_d} \cos(\phi_u-\phi_d) ~,\nonumber\\
V_{cb}^0&=& c_{\eta_u} c_{\theta_d} \sin(\phi_u-\phi_d) ~,\nonumber\\
V_{cb^\prime}^0 &=& s_{\eta_u} c_{\eta_d} - c_{\eta_u} s_{\eta_d} \cos(\phi_u-\phi_d) ~,\nonumber\\
V_{td}^0&=& c_{\theta_d} s_{\theta_u} - s_{\theta_d} c_{\theta_u} \cos(\phi_u-\phi_d) ~,\nonumber\\
V_{ts}^0&=& -c_{\eta_d} c_{\theta_u} \sin(\phi_u-\phi_d) ~,\nonumber\\
V_{tb}^0 &=& s_{\theta_u} s_{\theta_d} + c_{\theta_u} c_{\theta_d} \cos(\phi_u-\phi_d) ~,\nonumber\\
V_{tb^\prime}^0&=& s_{\eta_d} c_{\theta_u} \sin(\phi_u-\phi_d) ~,\nonumber\\
V_{t^\prime d}^0&=& s_{\theta_d} s_{\eta_u} \sin(\phi_u-\phi_d) ~,\nonumber\\
V_{t^\prime s}^0&=&s_{\eta_d} c_{\eta_u} - c_{\eta_d} s_{\eta_u} \cos(\phi_u-\phi_d) ~,\nonumber\\
V_{t^\prime b}^0&=& - s_{\eta_u} c_{\theta_d} \sin(\phi_u-\phi_d) ~,\nonumber\\
V_{t^\prime b^\prime}^0 &=& c_{\eta_d} c_{\eta_u} + s_{\eta_d} s_{\eta_u} \cos(\phi_u-\phi_d) \label{CKMel}~.\end{aligned}$$
From these expressions we can find the size of some of the hidden symmetry angles in terms of the observed $3 \times 3$ CKM elements and, also, several interesting and surprising relations/predictions for the mixing angles of the 4th generation quarks with the first 3 generations: $$\begin{aligned}
- \tan\theta_u &=& \frac{V_{us}}{V_{ts}} = \frac{V_{ub^\prime}}{V_{tb^\prime}} \label{eqV1}~,\\
- \tan\theta_d &=& \frac{V_{cd}}{V_{cb}} = \frac{V_{t^\prime d}}{V_{t^\prime b}} \label{eqV2}~,\\
- \tan\eta_u &=& \frac{V_{t^\prime d}}{V_{cd}} ~,\\
- \tan\eta_d &=& \frac{V_{u b^\prime}}{V_{us}} \label{eqV4} ~,\end{aligned}$$ implying $V_{t^\prime d} > V_{t^\prime b}$ and $V_{ub^\prime} > V_{tb^\prime}$ - opposite to the hierarchical pattern as observed in the SM3’s $3 \times 3$ block.
In addition, taking $V_{ts}^2/V_{us}^2 \sim V_{cb}^2/V_{cd}^2 \ll 1$, $V_{ud} \sim 1 - \lambda^2/2$ and $V_{cs} \sim 1 - \lambda^2/2$, where $\lambda \sim 0.2257$ is the Wolfenstein parameter [@PDG], we find that $\phi_u-\phi_d$ is the Cabibbo angle (i.e., the Wolfenstein parameter) with: $$\begin{aligned}
\sin(\phi_u - \phi_d) &\sim& \lambda \sim 0.2257 ~, \\
\cos(\phi_u - \phi_d) &\sim& V_{ud} - {\cal O}(\lambda^2) ~,\end{aligned}$$ and $$\begin{aligned}
c_{\theta_d} &\sim& \frac{V_{cb}}{V_{cd}} \sim {\cal O}(\lambda) \label{ctetd}~\\
c_{\theta_u} &\sim& \frac{V_{ts}}{V_{us}} \sim {\cal O}(\lambda) \label{ctetu}~\\
\cos(\eta_u - \eta_d) &\sim& V_{cs} - {\cal O}(\lambda^2) \label{ceta}~,\end{aligned}$$ also implying that $\eta_u \sim \eta_d$. This in turn gives: $$\begin{aligned}
V_{t^\prime b^\prime} &\sim& V_{cs} ~\\
V_{u b^\prime} &\sim& V_{t^\prime d} \label{vubprime}~.\end{aligned}$$
Furthermore, for the top-quark mixing angles we get: $$\begin{aligned}
V_{tb} &\sim& 1 - {\cal O}(\lambda^2) ~,\\
V_{td} &\sim& \left( \frac{V_{cb}}{V_{cd}} - \frac{V_{ts}}{V_{us}} \right) + {\cal O}(\lambda^2) \label{eqV6} ~,
$$
In the next sections we will use this physical setup to break T-invariance and derive the CP-violating parameters of the model.
T-violation and hidden symmetry breaking mechanism
==================================================
There are, of course, several ways to break the hidden symmetry without breaking T-invariance. Here we wish to extend the attractive mechanism for the simultaneous breaking of both the hidden symmetry and T-invariance, that was suggested by Friedberg and Lee in [@FL] in the SM3 case, and formulate the general breaking mechanism for the SM4 case.
In particular, when the hidden symmetry and T-invariance are broken simultaneously, the massless states $v_d^0,v_s^0,v_u^0,v_c^0$ (which were protected by the hidden symmetry) acquire a mass which is directly related to the size of the phases responsible for T-violation: two CP-violating phases in the up-quark sector are needed to generate the masses $m_u$ and $m_c$, while two CP-violating phases in the down-quark sector generate the masses $m_d$ and $m_s$. Since we know that $m_{u,c} << m_{t,t^\prime}$ and $m_{d,s} << m_{b,b^\prime}$, we can treat the effect of T-violation as a perturbation to the zeroth-order (T-invariant) approximation in both the down and up-quark sectors.
In what follows we will describe the breaking mechanism using the generic notation outlined in the previous section, which holds for both down and up-quark sectors. The application of the results below to a specific sector is straight forward.
In order to break the hidden symmetry we rewrite the zeroth-order Yukawa term ${\cal M}_0$ in terms of its eigenstates:
$$\begin{aligned}
{\cal M}_0 = \sum_i m_i^0 |v_i^0|^2 = m_{P_2} |P_2|^2 + m_{P_3} |P_3|^2~,\end{aligned}$$
where we have used the fact that $m_{Q_1}=m_{P_1}=0$. This gives (see Eqs. \[rel1\],\[rel2\] and \[rel3\]): $$\begin{aligned}
(M_0)_{ij} = m_{P_2} B_i B_j + m_{P_3} C_i C_j \label{M0bc}~,\end{aligned}$$ where we have dropped the superscripts $d$ or $u$ in the coefficients $B^{d,u}_i$ and $C^{d,u}_i$ (as defined in Eqs. \[bi\] and \[ci\]), so that the expression above applies to both down and up sectors. T-invariance and the hidden symmetry can then be broken by inserting a phase in any one of the non-diagonal entries of $(M_0)_{ij}$ as follows: $$\begin{aligned}
(\Delta M)_{ij} = \left( m_{P_2} B_i B_j + m_{P_3} C_i C_j \right) \cdot
\left( e^{i \delta_{ij}} - 1 \right) ~, j > i ~;~
(\Delta M)_{ji} = (\Delta M)_{ij}^\star
\label{deltaM}~,\end{aligned}$$ such that $$\begin{aligned}
M = M_0 + \Delta M ~.\end{aligned}$$ We assume that $\delta_{ij} \ll 1$, hence, $\Delta M \ll M_0$ so that $\Delta M$ can be treated as a perturbation. As we shall demonstrate in the next section, in the minimal setup, two such phase insertions (in each sector) are required in different locations in $M_0$ in order to break both HS1 and HS2 and to generate the observable masses of the first 2 light generations of quarks. Thus, we can write the overall T-violating term as: $$\begin{aligned}
\Delta M \equiv \Delta M_z + \Delta M_t ~,\end{aligned}$$ where $\Delta M_z$ and $\Delta M_t$ contain the new phases that break HS1 and HS2, respectively, each given by the generic form in Eq. \[deltaM\]. The T-violating mass term $\Delta M$ then shifts the zeroth-order masses and states. Using perturbation theory, these shifts are given in the general case without degeneracies by:
$$\begin{aligned}
\Delta m_q &\equiv& m_q - m_q^0 = (v_q^0)^\dagger \Delta M v_q^0 \label{dmass}~,\end{aligned}$$
$$\begin{aligned}
\Delta v_q &\equiv& v_q- v_q^0 = \sum_{q\neq q^\prime} \frac{(v_{q^\prime}^0)^\dagger
\Delta M v_q^0}{m_q^0-m_{q^\prime}^0} v_{q^\prime}^0 \label{dvec}~,\end{aligned}$$
where $m_q^0$ and $v_q^0$ are the zeroth-order masses and states (i.e., $v_q^0$ and $v_{q^\prime}^0$ stands for any one of the vectors $Q_1,P_1,P_2,P_3$ in either the up or down-sectors), $\Delta m_q$ are the mass shifts due to the breaking of the hidden symmetry and $\Delta v_q$ contains the imaginary terms which are $\propto i \sin\delta_{ij}$ from which the physical T-violating elements of the $4 \times 4$ CKM matrix are constructed.
In our case, however, the states $Q_1$ and $P_1$ are degenerate. Thus, in order to find the physical masses ($m_{\pm}$) and their corresponding physical states ($v_{\pm}$) in the $Q_1 - P_1$ subspace, we need to diagonalize the following $2 \times 2$ perturbation mass matrix in the $Q_1-P_1$ subspace: $$\begin{aligned}
\Delta m(Q_1,P_1) =\left( \begin{array}{cc}
Q_1^\dagger \Delta M Q_1 & Q_1^\dagger \Delta M P_1 \\
P_1^\dagger \Delta M Q_1 & P_1^\dagger \Delta M P_1 \end{array} \right) \equiv
\left( \begin{array}{cc}
\Delta m_{QQ} & \Delta m_{QP} \\
\Delta m_{PQ} & \Delta m_{PP} \end{array} \right)
\label{deltaQP}~,\end{aligned}$$ where $ \Delta m_{QP} = (\Delta m_{PQ})^\dagger$ and $\Delta m_{QQ},~\Delta m_{PP}$ are real. That is, after breaking T-invariance, the physical masses and states of the first two generations are given by: $$\begin{aligned}
m_\pm &=& \frac{\Delta m_{QQ} +\Delta m_{PP}}{2}
\left[ 1 \pm \sqrt{1 - \frac{4 \left( \Delta m_{QQ} \Delta m_{PP} -
\Delta m_{QP} \Delta m_{PQ} \right)}{\left( \Delta m_{QQ} +\Delta m_{PP} \right)^2}} \right] \label{mpm}~,\end{aligned}$$ and $$\begin{aligned}
v_+ &=& \frac{1}{\sqrt{ \left| \Delta m_{QP} \right|^2 + \left(m_+ - \Delta m_{QQ} \right)^2}}
\left[ \Delta m_{QP} Q_1 + \left(m_+ - \Delta m_{QQ} \right) P_1 \right] \nonumber ~\\
v_- &=& \frac{1}{\sqrt{ \left|\Delta m_{PQ} \right|^2 + \left(m_- - \Delta m_{PP} \right)^2}}
\left[ \left(m_- - \Delta m_{PP} \right) Q_1 + \Delta m_{PQ} P_1 \right] \label{vpm}~.\end{aligned}$$ The corresponding corrections/shifts to the physical states are still calculated from Eq. \[dvec\], where now $v_q^0,v_{q^\prime}^0 \in \{v_-,v_+,P_2,P_3\}$. In particular, let us further define the “perturbation matrix": $$\begin{aligned}
(v_q^0)^\dagger \Delta M v_{q^\prime}^0 \equiv i P_{q q^\prime}
\label{pijdef}~,\end{aligned}$$ where $q \neq q^\prime$ and, to ${\cal O}(\delta)$, $P_{q q^\prime}$ are real and $P_{q^\prime q} = - P_{q q^\prime}$. That is, $(v_{q^\prime}^0)^\dagger \Delta M v_q^0 = \left[(v_q^0)^\dagger \Delta M v_{q^\prime}^0 \right]^\dagger = -i P_{q q^\prime}$, where $q,q^\prime \in d,s,b,b^\prime$ in the down-quark sector and $q,q^\prime \in u,c,t,t^\prime$ in the up-quark sector. Also note that the perturbation matrix is diagonal in the $(v_- - v_+)$ subspace to ${\cal O}(\delta)$ (i.e., $P_{d s} = P_{sd} \approx {\cal O}(\delta^2)$ and $P_{uc} = P_{cu} \approx {\cal O}(\delta^2)$).
In the next section, for simplicity we will consider the case where the perturbation is diagonal in the $Q_1-P_1$ subspace, i.e., $\Delta m_{QP} =0$ in Eq. \[deltaQP\], so that $v_-=Q_1$ and $v_+ = P_1$. In this simple case we can use Eqs. \[dvec\] and \[pijdef\] to obtain the ${\cal O}(\delta)$ shifts, $\Delta v_q$, to the zeroth-order states $(v_d^0, v_s^0, v_b^0, v_{b^\prime}^0 )$ and $(v_u^0, v_c^0, v_t^0, v_{t^\prime}^0)$ (as defined in Eqs. \[rel3\]-\[ci\]): $$\begin{aligned}
\begin{array}{cc}
\Delta v_d = i \left( \frac{P_{d b}}{m_b} v_b^0 +
\frac{P_{d b^\prime}}{m_{b^\prime}} v_{b^\prime}^0 \right) &
\Delta v_u = i \left( \frac{P_{u t}}{m_t} v_t^0 +
\frac{P_{u t^\prime}}{m_{t^\prime}} v_{t^\prime}^0 \right) \\
\Delta v_s = i \left( \frac{P_{s b}}{m_b} v_b^0 +
\frac{P_{s b^\prime}}{m_{b^\prime}} v_{b^\prime}^0 \right) &
\Delta v_c = i \left( \frac{P_{c t}}{m_t} v_t^0 +
\frac{P_{c t^\prime}}{m_{t^\prime}} v_{t^\prime}^0 \right) \\
\Delta v_b = i \left( \frac{P_{d b}}{m_b} v_d^0 +
\frac{P_{s b}}{m_b} v_s^0 +
\frac{P_{b b^\prime}}{m_{b^\prime} - m_b} v_{b^\prime}^0 \right) &
\Delta v_t = i \left( \frac{P_{u t}}{m_t} v_u^0 +
\frac{P_{c t}}{m_t} v_c^0 +
\frac{P_{t t^\prime}}{m_{t^\prime} - m_t} v_{t^\prime}^0 \right) \\
\Delta v_{b^\prime} = i \left( \frac{P_{d b^\prime}}{m_{b^\prime}} v_d^0 +
\frac{P_{s b^\prime}}{m_{b^\prime}} v_s^0 +
\frac{P_{b b^\prime}}{m_{b^\prime} - m_b} v_{b}^0 \right) &
\Delta v_{t^\prime} = i \left( \frac{P_{u t^\prime}}{m_{t^\prime}} v_u^0 +
\frac{P_{c t^\prime}}{m_{t^\prime}} v_c^0 +
\frac{P_{t t^\prime}}{m_{t^\prime} - m_t} v_{t}^0 \right)
\label{deltav}
\end{array}\end{aligned}$$ such that, to ${\cal O}(\delta)$, the physical states are given by $v_q = v_q^0 + \Delta v_q$. The corresponding ${\cal O}(\delta)$ corrections to $v_q^0$ in the general case where the perturbation is not diagonal in the $Q_1-P_1$ subspace, can be easily derived from the expressions for $v_\pm$ in Eq. \[vpm\] and the shifts $\Delta v_q$ in Eq. \[deltav\] above. For example, $$\begin{aligned}
\Delta v_- &=& \frac{1}{\sqrt{ \left|\Delta m_{PQ} \right|^2 + \left(m_- - \Delta m_{PP} \right)^2}}
\left[ \left(m_- - \Delta m_{PP} \right) \cdot \Delta v_d + \Delta m_{PQ} \cdot \Delta v_s \right]\end{aligned}$$ where $\Delta v_{d,s}$ are given in Eq. \[deltav\].
The physical (T-violating) $4 \times 4$ CKM matrix elements are, therefore, given symbolically by ($u$ and $d$ stand for any of the up and down-quark states, respectively): $$\begin{aligned}
V_{ud} = (v_u)^\dagger \cdot v_d = V_{ud}^0 + (\Delta v_u)^\dagger \cdot v_d^0 +
v_u^0 \cdot \Delta v_d ~,\end{aligned}$$ where $V_{ud}^0 = (v_u^0)^T \cdot v_d^0$ is the zeroth-order CKM matrix elements and the terms $[ (\Delta v_u)^\dagger \cdot v_d^0 ],~[v_u^0 \cdot \Delta v_d]$, which are also functions of the zeroth-order CKM elements, are readily obtained from Eq. \[deltav\] above. For example, in the simple case where $v_-=Q_1$ and $v_+ = P_1$, $V_{ud}$ (i.e., now the (11) elements of $V$) is given by $$\begin{aligned}
V_{ud} = V_{ud}^0 + i \left[
\frac{P_{d b}}{m_b} V_{u b}^0 +
\frac{P_{d b^\prime}}{m_{b^\prime}} V_{u b^\prime}^0
-
\frac{P_{u t}}{m_t} V_{td}^0 -
\frac{P_{u t^\prime}}{m_{t^\prime}} V_{t^\prime d}^0
\right] + {\cal O}(\delta^2) \label{Vudfull}~.\end{aligned}$$
Note that the zeroth-order elements $V_{ud}^0$, given in Eq. \[CKMel\], are a good approximation to the magnitude of the physical CKM angles (i.e., up to corrections of ${\cal O}(\delta^2)$, where $\delta$ is any one of the CP-violating phases).
A physical framework for T-violation
====================================
In the previous two sections we have described the general features of the hidden symmetry and the generic mechanism of breaking T-invariance and generating the corresponding light-quark masses in coincidence with the breaking of the hidden symmetry in the case of SM4. In this section we would like to give a concrete physical example (i.e., compatible with all relevant known data) which is relatively simple analytically, therefore, providing insight for the physical picture. Our chosen setup below illustrates the power of this mechanism in predicting the new mixing angles and phases associated with the 4th generation of quarks and the size of CP-violation of the theory.
As in the previous section, here also we consider a specific orientation for the hidden symmetry, where the direction of HS2 is partly fixed by setting $\zeta = \pi/2$ in each sector. The hidden symmetry is then broken by inserting the phases in the $12$ and $34$ elements of the mass matrix $M_0$, such that:
$$\begin{aligned}
\Delta M_z = (\Delta M)_{12} ~,~ \Delta M_t = (\Delta M)_{34} ~,\end{aligned}$$
where $(\Delta M)_{ij}$ is defined in Eq. \[deltaM\]. Note that with $\omega=\zeta=\pi/2$ we have $B_1 = s_\theta$, $B_2 = -c_\theta c_\phi$, $B_3=0$, $B_4 = -c_\theta s_\phi$, $C_1=0$, $C_2 = s_\eta s_\phi$, $C_3 = - c_\eta$ and $C_4 = - s_\eta c_\phi$ (see Eqs. \[bi\] and \[ci\]). Thus, the overall T-violating term, $\Delta M = \Delta M_z + \Delta M_t$, is given by: $$\begin{aligned}
\Delta M =\left( {\tiny{ \begin{array}{cccc}
0 & - m_{P_2} s_\theta c_\theta c_\phi \left( e^{i \delta_{12}} - 1 \right) & 0 & 0 \\
- m_{P_2} s_\theta c_\theta c_\phi \left( e^{-i \delta_{12}} - 1 \right) & 0 & 0 & 0 \\
0 & 0 & 0 & m_{P_3} s_\eta c_\eta c_\phi \left( e^{i \delta_{34}} - 1 \right) \\
0 & 0 & m_{P_3} s_\eta c_\eta c_\phi \left( e^{-i \delta_{34}} - 1 \right) & 0 \end{array} }} \right) \label{deltaMzeta}~.\end{aligned}$$ For simplicity and without loss of generality, we will further take $s_{\phi} \ll 1$ for $\phi =\phi_d \sim \phi_u$ (recall that $\cos(\phi_u - \phi_d) \sim V_{ud} \sim 1$ implying $\phi_u \sim \phi_d$, see previous section), which allows us to obtain a relatively compact analytical picture. In particular, one simplification that arises with this choice, is that the perturbation in the $Q_1-P_1$ subspace, $\Delta m(Q_1,P_1)$ in Eq. \[deltaQP\], is approximately diagonal so that $m_- \approx \Delta m_{QQ}$, $m_+ \approx \Delta m_{PP}$ and the corresponding states are $v_- \approx Q_1$, $v_+ \approx P_1$ in each sector. In particular, $\Delta M$ in Eq. \[deltaMzeta\] generates the following light-quark masses (we now add the superscripts $d$ and $u$ to distinguish between the angles in the down and up-quark sectors): $$\begin{aligned}
m_d &\approx& 2 m_b s_{\theta_d}^2 c_{\theta_d}^2 \left( 1 - \cos\delta_{12}^d \right) \label{md}~,\\
m_s &\approx& 2 m_{b^\prime} s_{\eta_d}^2 c_{\eta_d}^2 \left( 1 - \cos\delta_{34}^d \right) \label{ms}~,\\
m_u &\approx& 2 m_t s_{\theta_u}^2 c_{\theta_u}^2 \left( 1 - \cos\delta_{12}^u \right) \label{mu}~,\\
m_c &\approx& 2 m_{t^\prime} s_{\eta_u}^2 c_{\eta_u}^2 \left( 1 - \cos\delta_{34}^u \right) \label{mc}~.\end{aligned}$$ where (see Eq. \[zeromasses\] and set $\zeta = \pi/2$): $$\begin{aligned}
m_b \approx \beta_d,~m_{b^\prime} \approx \alpha_d,~m_t \approx \beta_u,
~m_{t^\prime} \approx \alpha_u ~.\end{aligned}$$
As expected, we cannot reproduce the physical light-quark mass spectrum if any of the phases $\delta_{ij}$ above vanishes. Note also that, since $\eta_u \sim \eta_d$ and $\theta_u \sim \theta_d$ (see Eqs. \[ctetd\] and \[ceta\]), we can also use the expressions in Eqs. \[md\]-\[mc\] for the light-quark mass terms to relate the phases in one sector to the phases in the other sector: $$\begin{aligned}
\frac{\delta_{12}^d}{\delta_{12}^u} &\sim & \sqrt{\frac{m_d m_t}{m_u m_b}} \sim 10 ~,\\
\frac{\delta_{34}^d}{\delta_{34}^u} &\sim & \sqrt{\frac{m_s m_{t^\prime}}{m_c m_{b^\prime}}} \sim 0.3~,\end{aligned}$$ where we have taken $m_{t^\prime}/m_{b^\prime} \sim 1$.
Finally, for our chosen orientation with $\zeta=\pi/2$ and $\phi << 1$, the $P_{q q^\prime}$ elements required to calculate the imaginary terms of the $4 \times 4$ CKM elements (see Eqs. \[pijdef\]-\[Vudfull\]) are given by (to first order in $\delta_{ij}$): $$\begin{aligned}
P_{d b} &=& m_b s_{\theta_d} c_{\theta_d} \sin\delta_{12}^d ~, \nonumber \\
P_{s b^\prime} &=& m_{b^\prime} s_{\eta_d} c_{\eta_d} \sin\delta_{34}^d ~, \nonumber\\
P_{u t} &=& m_t s_{\theta_u} c_{\theta_u} \sin\delta_{12}^u ~, \nonumber\\
P_{c t^\prime} &=& m_{t^\prime} s_{\eta_u} c_{\eta_u} \sin\delta_{34}^u
\label{pij} ~,\end{aligned}$$ and all other $P_{q q^\prime}$ elements vanish. Using the expressions for the light-quark masses in Eqs. \[md\]-\[mc\], we can re-express the elements of the perturbation matrix $P_{q q^\prime}$ in Eq. \[pij\] above in terms of the CP-phases and the light-quark masses: $$\begin{aligned}
P_{d b} &\approx& \sqrt{m_d m_b} \cos\left( \frac{1}{2} \delta_{12}^d \right) ~, \nonumber\\
P_{s b^\prime} &\approx& \sqrt{m_s m_{b^\prime}} \cos\left( \frac{1}{2} \delta_{34}^d \right) ~, \nonumber\\
P_{u t} &\approx& \sqrt{m_u m_t} \cos\left( \frac{1}{2} \delta_{12}^u \right) ~, \nonumber\\
P_{c t^\prime} &\approx& \sqrt{m_c m_{t^\prime}} \cos\left( \frac{1}{2} \delta_{34}^u \right) \label{pij2}~,\end{aligned}$$
CP-invariants with four generations
===================================
As in the SM3, CP-violation in the SM4 can also be parameterized using CP-invariants a la the Jarlskog invariant $J_{SM}$ of the SM3 [@jarlskog]. Indeed, as was shown in [@jarlskog], the invariant CP-violation measure in the four quark families case can be expressed in terms of four “copies" similar to $J_{SM}$ (out of which only three are independent): $J_{123},~J_{124},~J_{134}$ and $J_{234}$, where the indices indicate the generation number, i.e., in this language one identifies $J_{SM}$ with $J_{123}$ even though these two CP-invariants are not quite the same as $J_{SM}$ is no longer a valid CP-quantity in the SM4.
A generic derivation of the four $J_{ijk}$ copies in terms of the quark masses and CKM mixing angles is quite complicated and we are unable to give it in a compact analytical format. There are several useful general formulations in the literature for the parametrization of CP-violation in the SM4 [@jarlskog; @CPinvariants], but none is at the level of simplification required for an analytical study of CP-violation in our model. A numerical calculation/study of the CP-violating quantities in our model is, however, straight forward following the prescription of the previous sections. This will be presented elsewhere [@our-2nd-FLpaper].
On the other hand, as was observed more than 10 years ago [@branco] and noted again recently in [@CPbaryo1], in the chiral limit $m_{u,d,s,c} \to 0$, CP-violation in the SM4 effectively “shrinks" to the CP-violation picture of a three generation model involving the 4th generation heavy quarks. This chiral limit, which is in the spirit of our current study, is clearly applicable at high-energies of the EW-scale and above. Moreover, it allows us to derive a compact analytical estimate for the expected size of CP-violation in our model.[^4]
As was shown in [@branco], in the chiral limit there is no CP-violation within the three families SM3 and so all CP-violating effects are attributed to the new physics - in our case, to the fourth generation of quarks. The key CP-violating quantity in this limit can be written as [@branco]: $$\begin{aligned}
J_{SM4} = {\rm Im} \left( V_{tb} V_{t^\prime b}^\star V_{t^\prime b^\prime} V_{t b^\prime}^\star \right)
~,
\label{b2} ~.\end{aligned}$$ since this is the only CP-violating quantity that survives when one takes the limit $m_{u,d,s,c} \to 0$.
Thus, in order to get some insight for the expected size of CP-violation in our model, it is sufficient to derive an estimate for $J_{SM4}$. In particular, we will calculate $J_{SM4}$ for the specific orientation used in the previous section, i.e., for the case $\zeta=\pi/2$ and $\phi \ll 1$.
Using the $P_{q q^\prime}$ factors of Eq. \[pij2\] and based on Eq. \[Vudfull\], we can calculate (to ${\cal O}(\delta)$) the relevant complex CKM elements which enter $J_{SM4}$ in Eq. \[b2\]: $$\begin{aligned}
V_{tb} &\approx& V_{tb}^0 + i \left[ V_{td}^0 \sqrt{ \frac{m_d}{m_b} }
\cos\left(\frac{1}{2} \delta_{12}^d \right) -
V_{ub}^0 \sqrt{ \frac{m_u}{m_t} }
\cos\left(\frac{1}{2} \delta_{12}^u \right) \right] ~, \\
V_{t^\prime b} &\approx& V_{t^\prime b}^0 + i \left[ V_{t^\prime d}^0 \sqrt{ \frac{m_d}{m_b} }
\cos\left(\frac{1}{2} \delta_{12}^d \right) -
V_{cb}^0 \sqrt{ \frac{m_c}{m_{t^\prime}} }
\cos\left(\frac{1}{2} \delta_{34}^u \right) \right] ~, \\
V_{t b^\prime} &\approx& V_{t b^\prime}^0 + i \left[ V_{t s}^0 \sqrt{ \frac{m_s}{m_{b^\prime}} }
\cos\left(\frac{1}{2} \delta_{34}^d \right) -
V_{u b^\prime}^0 \sqrt{ \frac{m_u}{m_{t}} }
\cos\left(\frac{1}{2} \delta_{12}^u \right) \right] ~, \\
V_{t^\prime b^\prime} &\approx& V_{t^\prime b^\prime}^0 + i \left[ V_{t^\prime s}^0 \sqrt{ \frac{m_s}{m_{b^\prime}} }
\cos\left(\frac{1}{2} \delta_{34}^d \right) -
V_{c b^\prime}^0 \sqrt{ \frac{m_c}{m_{t^\prime}} }
\cos\left(\frac{1}{2} \delta_{34}^u \right) \right] ~.\end{aligned}$$ We can now estimate the size of CP-violation in our model, which can emanate in high-energy processes involving $t^\prime$ and $b^\prime$ exchanges. In particular, since the zeroth-order CKM elements are a good approximation for the magnitude of physical elements, we set $V_{ij}^0 \sim V_{ij}$ and use the results and relations obtained for the CKM elements in the previous sections (see Eqs. \[eqV1\]-\[eqV6\]): $V_{tb} \sim 1$, $V_{t^\prime b^\prime} \sim V_{cs} \sim 1$, $V_{t^\prime b} \sim V_{u b^\prime} \times (V_{cb}/V_{cd})$ and $V_{t b^\prime} \sim V_{u b^\prime} \times (V_{ts}/V_{us})$. We then obtain: $$\begin{aligned}
J_{SM4} \approx
&& V_{u b^\prime} \frac{V_{ts}}{V_{us}} \times \left[
V_{c b} \sqrt{ \frac{m_c}{m_{t^\prime}} }
\cos\left(\frac{1}{2} \delta_{34}^u \right) -
V_{u b^\prime} \sqrt{ \frac{m_d}{m_{b}} }
\cos\left(\frac{1}{2} \delta_{12}^d \right) \right] + \nonumber \\
&&V_{u b^\prime} \frac{V_{cb}}{V_{cd}} \times \left[
V_{u b^\prime} \sqrt{ \frac{m_u}{m_{t}} }
\cos\left(\frac{1}{2} \delta_{12}^u \right) -
V_{ts} \sqrt{ \frac{m_s}{m_{b^\prime}} }
\cos\left(\frac{1}{2} \delta_{34}^d \right) \right]
\label{moreb2}~.\end{aligned}$$ Setting $V_{cb} \sim - V_{ts} \sim A \lambda^2$ and $V_{ts}/V_{us} \sim V_{cb}/V_{cd} \sim - A \lambda$ and (consistent with their measured values [@PDG], where $A \sim 0.81$ and $\lambda = 0.2257$ is the Wolfenstein parameter), and taking $V_{u b^\prime} \sim V_{cb} \sim A \lambda^2$ and $m_{t^\prime} \sim 2 m_t$, $m_{b^\prime} \sim m_{t^\prime} - 55~{\rm GeV}$, consistent with the electroweak precision tests [@kribs; @0902.4883], we obtain: $$\begin{aligned}
\left| J_{SM4} \right| \sim A^3 \lambda^5 \times
\left[
\sqrt{ \frac{m_u}{m_{t}} }
+
\sqrt{ \frac{m_c}{m_{t^\prime}} }
-
\sqrt{ \frac{m_d}{m_{b}} }
+
\sqrt{ \frac{m_s}{m_{b^\prime}} }
\right] \sim
10^{-5} \label{jsm4} ~,\end{aligned}$$ where we have used $\cos(\delta_{12}^d/2) \sim \cos(\delta_{34}^d/2) \sim \cos(\delta_{12}^u/2) \sim \cos(\delta_{34}^u/2) \sim 1$ for the numerical estimate (see below). Indeed, with the above chosen values for the CKM elements and the 4th generation quark masses, all the four phases are fixed by the requirement that they reproduce the corresponding light-quark masses as given in Eqs. \[md\]-\[mc\]. In particular, according to Eqs.\[md\]-\[mc\] and the relations between the hidden symmetry angles and the CKM elements as given by Eqs. \[eqV1\]-\[eqV4\], we have: $$\begin{aligned}
\cos\left(\delta_{23}^u \right) &\sim& 1 - \frac{m_c}{2 m_{t^\prime} \frac{V_{u b^\prime}^2}{V_{cd}^2}} \sim 0.945 ~, \\
\cos\left(\delta_{12}^d \right) &\sim& 1 -\frac{m_d}{2 m_{b}
\frac{V_{c b}^2}{V_{cd}^2} } \sim 0.98 ~, \\
\cos\left(\delta_{23}^d \right) &\sim& 1 -\frac{m_s}{2 m_{b^\prime}
\frac{V_{u b^\prime}^2}{V_{us}^2} } \sim 0.995 ~, \\
\cos\left(\delta_{12}^u \right) &\sim& 1 -\frac{m_u}{2 m_{t}
\frac{V_{ts}^2}{V_{us}^2} } \sim 0.9998 ~,\end{aligned}$$ consistent with our perturbative description of CP-violation.
From Eq. \[jsm4\] we see that as the CP-violating phases $\delta_{12}^d,\delta_{34}^u \to 0$, both $m_d$ and $m_c$ approach zero and, therefore, also $J_{SM4} \to 0$. Note also that, for our chosen orientation of the hidden symmetry, we have $J_{SM4} \sim 10^{-5} \sim J_{SM}$, i.e., the SM4 analogue of the SM3’s Jarlskog invariant at high-energies and the original measured SM3’s Jarlskog invariant are of similar size. These results demonstrate the highly predictive power of our model for the description of CP-violation and the generation of the light-quark masses in the SM4. In particular, once the magnitude of the mixing angles and the masses of the 4th generation quarks are measured, our model gives a very distinct prediction for the expected size of CP-violation in the SM4, which can be directly confirmed at high-energy collider experiments. In a forthcoming paper [@our-2nd-FLpaper], we will perform a full numerical study and scan the complete range of the free parameter space of our model, subject to the relevant existing data. We will also suggest ways to test our model in the upcoming LHC and the future machines such as a Super-B factory and the International Linear Collider.
Summary
=======
Motivated by the recent hints of CP anomalies in the B-system and by the idea of Friedberg and Lee (FL) in [@FL], we have presented a new framework for CP-violation and the generation of the light-quark masses in the SM with four families - the SM4.
We have applied the basic ingredients of the FL mechanism to the SM4 case, by constructing an extended (double) hidden symmetry suitable for four families which defines the zeroth-order states in the up and down-quarks sectors and which ensures T-invariance. We then outlined the breaking mechanism of both the hidden symmetry and T-invariance in the SM4 case, from which we obtained the CP-violating measure and the physical states in this model. We have shown that this mechanism, when applied to the SM4, can be highly predictive and can be tested in future experiments. In particular, we gave one physically relevant example for the predictive power of our model by choosing a specific orientation of the hidden symmetry. This allowed us to analytically derive the physical (observed) quark states, and to give a prediction for the size of the mixing angles between the 4th generation and the 1st three generations of the SM3 and for the size of CP-violation associated with the 4th generation quarks.
A complete numerical study of our model, which explores the full phase-space of viable hidden symmetries for the SM4 and the corresponding range of the expected size of CP-violation and of the 4th generation mixing angles, is in preparation and will be presented in [@our-2nd-FLpaper].
[***Acknowledgments:***]{} We thank Gad Eilam for discussions. The work of AS is supported in part by the US DOE contract No. DE-AC02-98CH10886.
[99]{}
W.S. Hou, R.S. Willey and A.Soni, Phys. Rev. Lett. [**58**]{}, 1608 (1987) \[Erratum-ibid. [**60**]{}, 2337 (1988); W.S. Hou, A.Soni and H. Steger, Phys. Rev. Lett. [**59**]{}, 1521 (1987); W.S. Hou, A. Soni and H. Steger Phys. Lett. [**B192**]{}, 441 (1987).
Wei-Shu Hou, Makiko Nagashima, Andrea Soddu, Phys. Rev. [**D72**]{}, 115007 (2005); Wei-Shu Hou, Makiko Nagashima, Andrea Soddu, Phys. Rev. Lett. [**95**]{}, 141601 (2005); A. Arhib and W.S. Hou, JHEP [**0607**]{}, 009 (2006); Wei-Shu Hou, Hsiang-nan Li, Satoshi Mishima, Makiko Nagashima, Phys. Rev. Lett. [**98**]{}, 131801 (2007);
A. Soni, A. Kumar Alok, A. Giri, R. Mohanta and S. Nandi, arXiv:0807.1971.
W.S. Hou, arXiv:0803.1234; W.S. Hou, arXiv:0810.3396.
R. Fok and G.D. Kribs, Phys. Rev. [**D78**]{}, 075023 (2008).
Graham D. Kribs, Tilman Plehn, Michael Spannowsky, Timothy M.P. Tait, Phys. Rev. [**D76**]{}, 075016 (2007).
See [*e.g.*]{}, G.E. Volovik, Pisma Zh. Eksp. Teor. Fiz. [**78**]{}, 1203 (2003), JETP Lett. [**78**]{}, 691 (2003).
C. Jarlskog, Phys. Rev. [**D36**]{}, 2128 (1987).
E. Lunghi and A. Soni, arXiv:0903.5059 \[hep-ph\]; E. Lunghi and A. Soni, Phys. Lett. [**B666**]{}, 162 (2008); E. Lunghi and A. Soni, JHEP [**0709**]{}, 053 (2007).
H. Pagels and D. Stoker, Phys. Rev. [**D20**]{}, 2947 (1979); Hong-Jian He, Christopher T. Hill, Timothy M.P. Tait, Phys. Rev. [**D65**]{}, 055006 (2002); B. Holdom, JHEP [**0608**]{}, 076 (2006); G. Burdman and L.D. Rold, JHEP [**0712**]{}, 086 (2007).
For unitarity issues assosiated with such heavy quarks, see: M.S. Chanowitz, Phys. Lett. [**B352**]{}, 376 (1995); M.S. Chanowitz, M. Furman and I. Hinchliffe, Phys. Lett. [**B78**]{}, 285 (1982).
R. Friedberg and T.D. Lee, Ann. of Phys. [**323**]{}, 1087 (2008); R. Friedberg and T.D. Lee, Ann. of Phys. [**323**]{}, 1677 (2008).
C. Amsler [*et al.*]{}, “The Review of Particle Physics" Phys. Lett. [**B667**]{}, 1 (2008).
S. Bar-Shalom, D. Oaknin and A. Soni, in preperation.
C. Jarlskog and R. Stora, Phys. Lett. [**B208**]{}, 268 (1988); M. Gronau, A. Kfir and R. Loewy, Phys. Rev. Lett. [**56**]{}, 1538 (1986); O.W. Greenberg, Phys. Rev. [bf D32]{}, 1841 (1985); D.D. Wu, Phys. Rev. [bf D33]{}, 860 (1986); F. del Aguila and J.A. Aguilar-Saavedra, Phys. Lett. [bf B386]{}, 241 (1996).
F. del Aguila, J.A. Aguilar-Saavedra and G.C. Branco, Nucl. Phys. [**B510**]{}, 39 (1998).
M. Bobrowski, A. Lenz, J. Riedl and J. Rohrwild, arXiv:0902.4883 \[hep-ph\].
[^1]: Electronic address: shaouly@physics.technion.ac.il
[^2]: Electronic address: d1306av@gmail.com
[^3]: Electronic address: soni@bnl.gov
[^4]: Note that, although their is no CP-violation in our model in the chiral limit $m_{u,d,s,c} \to 0$ (which is our zeroth-order approximation), we can use the CP-violating quantities obtained in [@branco] in this limit, since those are given in terms of the physical mixing angles. In our model, the imaginary parts of these mixing angles are proportional to the very small light-quark masses.
| {
"pile_set_name": "ArXiv"
} |
Antibodies to Tamm-Horsfall protein in patients with acute pyelonephritis.
The role of antibodies to Tamm-Horsfall protein in the diagnosis of acute pyelonephritis was studied. Antibodies to Tamm-Horsfall protein were also determined in a group of normal subjects. Patients with acute pyelonephritis were divided into subgroups according to the concurrent presence of vesicoureteral reflux or nephrolithiasis. No statistically significant differences (p > 0.05) were observed for any class of antibodies (IgG, IgA and IgM) between the groups of healthy subjects and patients with acute pyelonephritis, regardless of the presence or absence of vesicoureteral reflux or nephrolithiasis. Values for different antibody classes showed that IgM antibodies were the most abundant in all the groups examined. A difference in the values of IgM relative to IgA and IgG antibodies was found to be statistically significant in the patient group only (p < 0.05). In patients with vesicoureteral reflux, there was no statistically significant difference (p > 0.05) between the values of IgM and of other antibody classes. In these patients, however, the highest values of all the three antibody classes were obtained, although these differences were also not statistically significant (p > 0.05). The results pointed to the need of further studies of the role of antibodies to Tamm-Horsfall protein in the diagnosis and pathogenesis of tubulointerstitial nephritis. | {
"pile_set_name": "PubMed Abstracts"
} |
Urinary tract infection in children: diagnosis and treatment.
Urinary tract infection (UTI) is a fairly frequent occurrence in children. Diagnosis should be made quickly and accurately by Gram staining and culture of an uncontaminated urine specimen. A first, uncomplicated UTI should be treated with sulfonamides or nitrofurantoin. Careful follow-up is necessary because of the high risk of recurrence. Sensitivity studies and specific antimicrobial therapy are indicated in any patient with recurrence and in patients with anatomic urinary tract abnormalities. Long-term prophylaxis may be needed. | {
"pile_set_name": "PubMed Abstracts"
} |
1. Introduction {#sec1}
===============
Bladder cancer is one of the most common urinary malignancies and represents approximately 90%-95% of urothelial carcinomas \[[@B1]\]. There was an estimated 76,960 newly diagnosed cases (58,950 men and 18,010 women) in the USA in 2016 \[[@B2]\]. Although the accuracy of current diagnostic methods has greatly improved, the 5-year overall survival (OS) remains unsatisfying, especially for metastatic bladder cancer \[[@B1], [@B2]\]. Furthermore, bladder cancer has a high recurrence rate (50%), and 15-40% of cases develop into a muscle-invasive form of the disease \[[@B3], [@B4]\]. Therefore, a reliable and readily accessible preoperative prognostic biomarker is required to determine the optimal therapeutic strategies.
A growing number of studies have shown that inflammation has been closely involved in tumorigenesis and cancer progression and also has been found to correlate with the prognosis \[[@B5]\]. Based on the accumulating evidence, inflammation-based models, such as the C-reactive protein/albumin ratio, albumin-to-globulin ratio (AGR), inflammation-based index (IBI), and neutrophil-to-lymphocyte ratio (NLR), and the platelet-to-lymphocyte ratio (PLR) have been developed to predict oncological outcomes in a variety of human cancers \[[@B6]--[@B9]\]. The lymphocyte-to-monocyte ratio (LMR) has been associated with worse prognoses in various cancers such as hepatocellular carcinoma, colorectal cancer, and lung adenocarcinoma \[[@B10]--[@B12]\]. However, because of the inconsistent results, whether LMR is associated with the prognosis in the bladder remains controversial \[[@B13]--[@B15]\]. Therefore, this study was conducted to evaluate the prognostic value of LMR and analyze the relationships between LMR and clinicopathological parameters in patients with bladder cancer.
2. Materials and Methods {#sec2}
========================
2.1. Search Strategies {#sec2.1}
----------------------
The MEDLINE, EMBASE, Cochrane Library, and CNKI databases were comprehensively searched up to September 20th, 2018. Studies focused on the correlation of LMR and bladder cancer were taken into retrieved. Studies were selected using the following keywords: "bladder cancer," "bladder carcinoma," "bladder adenocarcinoma," "bladder tumor," "bladder neoplasms," "transitional cell carcinoma," "ureteral neoplasms," or "urethral neoplasms" and "LMR," "lymphocyte to monocyte ratio," "lymphocyte monocyte ratio," or "lymphocyte-to-monocyte ratio." The references of retrieved studies were also checked to avoid missing relevant studies. For the detailed search strategies, please refer to the supplementary material file ([available here](#supplementary-material-1){ref-type="supplementary-material"}).
2.2. Selection Criteria {#sec2.2}
-----------------------
The criteria for inclusion were as follows: (1) studies focused on bladder cancer patients, (2) studies that evaluated the prognostic value of LMR, (3) a reported cut-off value for LMR, and (3) available hazard ratios (HRs) with 95% CIs for OS, RFS, or CSS. Articles were excluded if they were duplicate publications or reviews, data was not usable, or the studies were only performed on animals.
2.3. Data Extraction and Quality Assessment {#sec2.3}
-------------------------------------------
Data extraction and quality evaluation were independently operated by two investigators. Any discrepancies between the two investigators were resolved by discussion until reaching a consensus. General information was gathered as follows: the first authors\' name, year of publication, age, geographical regions, number of patients, distribution of gender, sample size, tumor stage, differentiation, lymph node metastasis, distant metastasis, treatment type, tumor size, cut-off values, survival outcome, follow-up period, and concomitant Cis (carcinoma in situ).
The methodological quality of included studies was independently assessed according to the Newcastle-Ottawa Scale (NOS) \[[@B16]\], which included three primary domains: Selection, Comparability, and Outcome. Studies with an NOS score of ≥6 were deemed high-quality studies.
2.4. Statistical Analysis {#sec2.4}
-------------------------
We used Stata 13.0 statistical software (Stata, College Station) to estimate HRs for OS, RFS, and CSS and odds ratios (ORs) for clinicopathological parameters. As for prognostic variables (e.g., OS, DFS, and RFS), the hazard ratio (HR) and corresponding 95% confidence interval (CI) were directly extracted from published studies. Otherwise, they were indirectly calculated from survival curves if only survival curves were available in some studies \[[@B17], [@B18]\]. The heterogeneity among studies was assessed using Cochran\'s *Q* test and Higgins *I* ^2^ statistic; the fixed effect model was used in case of the absence of significant heterogeneity (*P* \> 0.10 or/and *I* ^2^ \< 50%); otherwise, the random effect model was chosen. We then performed subgroup analyses to examine the potential source of heterogeneity. To validate the robustness of the pooled results, sensitivity analyses were performed by removing each study. Publication bias was evaluated using Egger\'s test. All *P* values were two-sided, and the difference was considered significant when the *P* value was less than 0.05.
3. Results {#sec3}
==========
3.1. Study Characteristics {#sec3.1}
--------------------------
A total of 123 records were initially retrieved from four common databases ([Figure 1](#fig1){ref-type="fig"}). Meanwhile, 2 articles were identified through references. After the removal of duplicates, 96 articles remained for further evaluation. As shown in [Figure 1](#fig1){ref-type="fig"}, after screening titles and abstracts, 76 duplicate articles were excluded. The remaining articles were carefully evaluated by evaluating the full texts, and 11 articles were excluded. Finally, a total of 9 studies were included in the meta-analysis \[[@B13]--[@B15], [@B19]--[@B24]\].
[Table 1](#tab1){ref-type="table"} displays the characteristics of included studies. All included studies were retrospective cohort trials and released from years 2014 to 2018. These studies were carried out in six countries, including Lebanon, UK, China, Japan, Austria, and Poland. The treatments were surgery and mixed methods. Cut-off values of LMR ranged from 1.8 to 4. All cases in the eligible studies were classified into two groups (high and low). Eight studies reported the association between LMR and OS, and 3 studies reported RFS and CSS. NOS scores of all the studies were at least 6 or more ([Table 1](#tab1){ref-type="table"}).
4. Meta-Analysis {#sec4}
================
4.1. Impact of LMR on OS {#sec4.1}
------------------------
Eight studies, including 5,368 patients, were included in this meta-analysis of OS. The pooled results showed significant differences in OS among the higher LMR groups and lower LMR groups (HR: 0.63, 95% CI: 0.50-0.80, *P* \< 0.001, [Figure 2](#fig2){ref-type="fig"}). To further explore the prognostic value of LMR in bladder cancer, subgroup analysis based on the main features was performed. Results for subgroup analyses are shown in [Table 2](#tab2){ref-type="table"}. The results indicated that elevated LMR significantly predicted favourable OS in patient mixed stages (HR = 0.63; 95% CI = 0.49-0.80; *P* \< 0.001). Pooled HRs for OS were stratified by the cut-off value for LMR. The result showed that patients with LMR ≥ 3 had significantly increased OS (HR: 0.56, 95% CI: 0.35-0.88, *P* = 0.011). However, no prognostic value was observed in patients with LMR \< 3 (HR: 0.65, 95% CI: 0.41-1.04, *P* = 0.075). Moreover, the ethnicity, treatment, and analysis method also did not affect the significant predictive value of LMR in bladder cancer patients.
4.2. Impact of LMR on RFS and CSS {#sec4.2}
---------------------------------
Three studies with 4,536 patients investigated the association between LMR and RFS. The pooled HR was 0.59, which indicated that elevated LMR was significantly associated with favourable RFS ([Figure 3](#fig3){ref-type="fig"}). There were three studies with a total of 4,459 patients investigating the predictive value of LMR for CSS. As shown in [Figure 4](#fig4){ref-type="fig"}, a statistically significant difference was observed between the higher LMR groups and the lower LMR groups (HR: 0.76, 95% CI: 0.70-0.83, *P* \< 0.001). The result revealed that patients with a high LMR had a significantly favourable CSS compared with those with a low LMR.
4.3. Associations between LMR and Clinicopathological Parameters {#sec4.3}
----------------------------------------------------------------
Meta-analyses for the association between LMR and clinicopathological parameters were conducted, and the results are presented in [Table 3](#tab3){ref-type="table"}. Compared with high LMR, low LMR was highly correlated with age (≥60 vs. \<60; OR = 2.07, 95% CI: 1.22-3.50, *P* = 0.007), differentiation (low vs. moderate/high; OR = 1.60, 95% CI: 1.10-2.32, *P* = 0.01), T stage (III-IV vs. I-II; OR = 1.13, 95% CI: 1.01-1.28, *P* = 0.04), lymph node metastasis (yes vs. no; OR = 1.22, 95% CI: 1.06-1.39, *P* = 0.005), and concomitant Cis (yes vs. no; OR = 0.88, 95% CI: 0.78-0.99, *P* = 0.03). However, there was no obvious relationship between the LMR and gender (male vs. female; OR = 1.18, 95% CI: 0.68-2.04, *P* = 0.56), smoking status (always/current vs. never; OR = 0.95, 95% CI: 0.63-1.45, *P* = 0.82), tumor size (\>3 cm vs. \<3 cm; OR = 1.86, 95% CI: 0.74, 4.71, *P* = 0.19), distant metastasis (yes vs. no; OR = 1.46, 95% CI: 0.37-5.73, *P* = 0.59), and multiplicity (multiple vs. solitary; OR = 1.04, 95% CI: 0.68-1.58, *P* = 0.86).
4.4. Sensitivity Analysis and Publication Bias {#sec4.4}
----------------------------------------------
A sensitivity analysis was performed by omitting the enrolled studies in turn to investigate the stability of the results. The results indicated that the pooled results were relatively reliable and steady ([Figure 5](#fig5){ref-type="fig"}).
No obvious publication bias was found among studies ([Figure 6](#fig6){ref-type="fig"}), which were also demonstrated in Egger\'s test for OS (*P* \> ∣*t*∣ = 0.055).
5. Discussion {#sec5}
=============
Recently, more and more studies focused on the correlation between inflammation and cancers revealed that tumor initiation, progression, and metastasis were affected by host systemic inflammatory response as well as tumor microenvironment \[[@B5], [@B25], [@B26]\]. To the best of our knowledge, our study is the first and most comprehensive meta-analysis that systematically analyzed the prognostic value of pretreatment LMR in bladder cancer survivors. A prognostic effect for LMR on OS, RFS, and CSS was found after pooling the results. Therefore, LMR could serve as biomarker for the prognosis of bladder cancer patients. Additionally, the correlations between LMR and clinicopathological parameters were evaluated. Low LMR was highly correlated with age (≥60), differentiation (low), T stage (III-IV), lymph node metastasis (yes), and concomitant Cis (yes).
LMR, as a composite inflammatory-based prognostic system, has shown great prognostic value in multiple cancers. However, the underlying molecular mechanisms have not been adequately illuminated. Lymphocytes play a major role in suppressing cancer cell proliferation and migration \[[@B27]\]. Tumor-infiltrating lymphocytes (TILs) are vital components of the antitumor immune microenvironment and are involved in several stages of tumor progression \[[@B28], [@B29]\]. Cytotoxic lymphocytes, mainly cytotoxic T cells, are essential for eliminating residual cancer cells and are being applied in immunotherapy \[[@B30], [@B31]\]. Monocytes are thought to have an impact on tumorigenesis through differentiation to tumor-associated macrophages (TAMs). TAMs are recruited to the tumor site by obtaining the signal from tumor-derived chemotactic factors \[[@B32]\]. Therefore, the amount and percentage of monocytes could be representative for TAMs reflecting the tumor burden. Recent studies reported that increased infiltration of TAMs was associated with the outcome of various cancers \[[@B33], [@B34]\]. Thus, LMR may represent a balance between the antitumor immune reaction and the tumor promotion function.
There were several limitations of this study. First, the cut-off value of LMR applied in the enrolled studies was not uniform. This might have made a significant contribution to the substantial heterogeneity. Second, all of the included studies were retrospective. Third, excessive heterogeneity existed among the included studies. However, subgroup analyses showed that the heterogeneity diminished or disappeared in Caucasian patients and patients receiving surgery.
6. Conclusions {#sec6}
==============
Our meta-analysis confirmed that low pretreatment LMR was associated with shorter OS, RFS, CSS, and worse clinicopathological features in patients with bladder cancer. Therefore, LMR could serve as a promising prognostic factor of bladder cancer.
Conflicts of Interest
=====================
The authors report no conflicts of interest in this work.
Authors\' Contributions
=======================
JYM, GH, and QL conceived, designed, and performed the experiments and analyzed the data. All authors contributed the reagents/materials/analysis tools and wrote the paper. Jian-ying Ma and Gang Hu contributed equally to this work.
Supplementary Materials {#supplementary-material-1}
=======================
######
The search strategies of this meta-analysis.
######
Click here for additional data file.
{#fig1}
{#fig2}
{#fig3}
{#fig4}
{#fig5}
{#fig6}
######
Characteristics of the studies included in the meta-analysis.
Author Year Country Ethnicity Follow-up (months) Treatment No. of patients Stage Cut-off value Survival analysis Analysis Confounding factors adjusted for NOS score
----------- ------ --------- ----------- -------------------- ----------- ----------------- ------- --------------- ------------------- ---------- ----------------------------------------------------------- -----------
Temraz 2014 Lebanon Caucasian 24 Mixed 68 Mixed 2.81 OS/RFS UV NA 8
Lee 2015 UK Caucasian NA Surgery 226 Early 1.8 OS MV Age, grade, tumor size, NLR, PLR 7
Zhang 2015 China Asian 50.8 Mixed 124 Mixed 4 OS MV Age, sex, BMI, AC, concomitant Cis, T stage, LNM, DM, PLR 8
Yoshida 2015 Japan Asian 72 (27.6-111.6) Mixed 181 Mixed 3.51 OS MV T stage, N stage, grade, LVI, margin, AC, LVI 7
Lucca 2016 Austria Caucasian NA Surgery 310 Early 3.3 OS MV T stage, grade, concomitant Cis, LVI, NLR, PLR, GPS, PNI 6
D\'Andrea 2017 Austria Caucasian 42.4 (18.3-85.1) Surgery 4198 Mixed 3.5 OS/RFS/CSS MV Gender, age, margin, concomitant Cis, LNM, LVI, AC, NLR 8
Miyake 2017 Japan Asian 22 (10--64) Mixed 117 Mixed 3.3 OS/CSS UV NA 6
Rajwa 2018 Poland Caucasian 14 (7-40) Surgery 144 Mixed 2.44 OS/CSS MV T stage, LNM, grade, tumor necrosis, NLR, PLR 8
Wang 2018 China Asian NA Mixed 270 Early 4 RFS UV NA 7
Abbreviations: OS: overall survival; RFS: recurrence-free survival; CSS: cancer-specific survival; MV: multivariate; Cis: carcinoma in situ; AC: adjuvant chemotherapy; NLR: neutrophil-lymphocyte ratio; PLR: platelet-lymphocyte ratio; LNM: lymph node metastasis; DM: distant metastasis; LVI: lymphovascular invasion; GPS: Glasgow prognostic score; PNI: prognostic nutritional index; PMI: psoas muscle index; NA: not available.
######
Pooled hazard ratios (HRs) for OS according to subgroup analyses.
Subgroup No. of studies No. of patients HR (95% CI) *P* value Heterogeneity
----------------- ---------------- ----------------- ------------------ ----------- --------------- -------
Overall 8 5,368 0.63 (0.50-0.80) \<0.001 65.9 0.005
Ethnicity
Asian 2 422 0.46 (0.25-0.87) 0.016 73.3 0.023
Caucasian 5 4,946 0.80 (0.71-0.89) \<0.001 8.2 0.360
Disease stage
Early 2 536 0.61 (0.20-1.82) 0.377 0 0.705
Mixed 6 4,832 0.63 (0.49-0.80) \<0.001 75.3 0.001
Treatment
Surgery 4 4,878 0.81 (0.74-0.89) \<0.001 0 0.883
Mixed 4 482 0.45 (0.27-0.73) 0.001 62.3 0.047
Cut-off for LMR
≥3 5 4,930 0.56 (0.35-0.88) 0.011 76.6 0.002
\<3 3 438 0.65 (0.41-1.04) 0.075 41.7 0.180
Analysis method
Univariate 2 185 0.46 (0.27-0.79) 0.005 0 0.488
Multivariate 6 5,183 0.67 (0.53-0.86) 0.001 65.9 0.005
######
Meta-analysis of the association between LMR and clinicopathological features of bladder cancer.
Characteristics No. of studies No. of patients OR (95% CI) *P* Heterogeneity
------------------------------------------- ---------------- ----------------- ------------------ ------- --------------- ------
Age (≥60 vs. \<60) 3 626 2.07 (1.22-3.50) 0.007 42 0.18
Gender (male vs. female) 4 4,818 1.18 (0.68-2.04) 0.56 70 0.02
Smoking status (always/current vs. never) 2 394 0.95 (0.63-1.45) 0.82 0 0.80
Differentiation (low vs. moderate/high) 5 4,886 1.60 (1.10-2.32) 0.01 35 0.19
Tumor size (\>3 cm vs. \<3 cm) 2 496 1.86 (0.74-4.71) 0.19 71 0.06
T stage (III-IV vs. I-II) 3 4,390 1.13 (1.01-1.28) 0.04 0 0.79
Lymph node metastasis (yes vs. no) 3 4,390 1.22 (1.06-1.39) 0.005 0 0.67
Distant metastasis (yes vs. no) 1 124 1.46 (0.37-5.73) 0.59 --- ---
Multiplicity (multiple vs. solitary) 2 496 1.04 (0.68-1.58) 0.86 0 0.49
Concomitant Cis (yes vs. no) 2 4,322 0.88 (0.78-0.99) 0.03 0 0.87
Cis: carcinoma in situ.
[^1]: Academic Editor: Massimiliano M. Corsi Romanelli
| {
"pile_set_name": "PubMed Central"
} |
Q:
Reordering Treenodes in C#.NET
I have a Visual Studio 2005 C#.NET GUI application. I want to provide the flexibility to reorder the treenodes in the treeview just by dragging and dropping them wherever desired. Is that possible by using any property of the treeview class? Or do I have to do it the hard way by writing events for mouseup and then sensing the dragging of the node etc etc. Any help would be apreciated.
Thanks,
Viren
A:
Seem that microsoft itself answered at least a part of your question : kb 307968: How to add TreeView drag-and-drop functionality in a Visual C# application.
| {
"pile_set_name": "StackExchange"
} |
-
featured designs.
Converting A Garage To A Room
Converting A Garage To A Room
Garden Flooring
Kitchen Design Gallery
Archive with tag: converting a loft
collection of galleries from Awesome Home Design like Converting A Loft. and other designs you might like Kitchen Designs Small Spaces. Landscape For Gardens. Bedroom Designs Images. Simple Living Room Designs. Aston Matthews. Temporary Garden Fencing. Modern Designs Interior. | {
"pile_set_name": "Pile-CC"
} |
### Localized Resource
[toc]
### Finite State Machine
### *DOWNLOADING => LOCALIZED*
| {
"pile_set_name": "Github"
} |
Rick Atkinson
Lawrence Rush "Rick" Atkinson IV (born November 16, 1952) is an American author, most recently of The British Are Coming: The War for America, Lexington to Princeton, 1775–1777, the first volume in the Revolution Trilogy. He has won Pulitzer Prizes in history and journalism.
After working as a newspaper reporter, editor, and foreign correspondent for The Washington Post, Atkinson turned to writing military history. His seven books include narrative accounts of five different American wars.
His Liberation Trilogy, a history of the American role in the liberation of Europe in World War II, concluded with the publication of The Guns at Last Light in May 2013. In 2010, he received the $100,000 Pritzker Military Library Literature Award for Lifetime Achievement in Military Writing. In 2019, Atkinson was named a Vincent J. Dooley Distinguished Fellow by the Georgia Historical Society, an honor that recognizes national leaders in the field of history as both writers and educators whose research has enhanced or changed the way the public understands the past.
Life and career
Atkinson was born in Munich to Margaret (née Howe) and Larry Atkinson, who was a U.S. Army officer. He grew up on military posts around the world, including stints in Salzburg, Georgia, Idaho, Pennsylvania, California, Hawaii, Kansas, and Virginia. Turning down an appointment to West Point, he instead attended East Carolina University on a full scholarship, graduating with a bachelor of arts degree in English in 1974. He received a master of arts degree in English language and literature from the University of Chicago in 1975.
While visiting his parents for Christmas at Fort Riley, Kansas, in 1975, Atkinson found a job as a newspaper reporter for The Morning Sun in Pittsburg, Kansas, covering crime, local government, and other topics in southeast Kansas, an area known as “the Little Balkans” for its ethnic diversity and fractious politics. In April 1977, he joined the staff of The Kansas City Times, working nights in suburban Johnson County, Kansas, before moving to the city desk and eventually serving as a national reporter; in 1981, he joined the newspaper's bureau in Washington, D.C. He won the Pulitzer Prize for national reporting in 1982 for a "body of work" that included a series about the West Point class of 1966, which lost more men in Vietnam than any other Military Academy class. He also contributed to the newspaper's coverage of the Hyatt Regency walkway collapse in Kansas City, Missouri, for which the paper's staff in 1982 was awarded a Pulitzer Prize for local spot news reporting.
In November 1983, Atkinson was hired as a reporter on the national staff of The Washington Post. He subsequently wrote about defense issues, the 1984 presidential election–he covered Rep. Geraldine Ferraro, the first woman vice-presidential candidate for a major party—and various national topics. In 1985, he became deputy national editor, overseeing coverage of defense, diplomacy, and intelligence. In 1988, he returned to reporting on the Post's investigative staff, writing about topics as varied as public housing in the District of Columbia and the secret history of Project Senior C.J., which became the B-2 stealth bomber. In 1991, he was the newspaper's lead writer during the Persian Gulf War. Two years later he joined the foreign staff as bureau chief in Berlin, covering not only Germany and NATO, but also spending considerable time in Somalia and Bosnia. He returned from Europe in 1996 to become assistant managing editor for investigations; in that role, he headed a seven-member team that for more than a year scrutinized shootings by the District of Columbia police department, resulting in “Deadly Force,” a series for which the Post was awarded the Pulitzer Prize for Public Service.
Atkinson left the newspaper world in 1999 to write about World War II, a consuming interest that began with his birth in Germany and was rekindled during his three-year tour in Berlin. Subsequently, he twice rejoined the Post for reporting forays, first in 2003, when for two months he accompanied General David Petraeus and the 101st Airborne Division during the invasion of Iraq, and again in 2007, when he made trips to Iraq and Afghanistan while writing “Left of Boom,” an investigative series about the proliferation of roadside bombs in modern warfare, which won the Gerald R. Ford Award for Distinguished Reporting on National Defense. He held the Omar N. Bradley Chair of Strategic Leadership at the United States Army War College and Dickinson College in 2004–2005, and remains an adjunct faculty member at the war college.
Atkinson is a presidential counselor at the National World War II Museum in New Orleans, a member of the Society of American Historians, and an inductee in the Academy of Achievement, for which he also serves as a board member. He serves on the governing commission of the National Portrait Gallery.
Works
Atkinson's first book, written while on leave from the Post, was The Long Gray Line: The American Journey of West Point’s Class of 1966. A 1989 review in Time magazine called it "brilliant history", and
Business Week reviewer Dave Griffiths called it "the best book out of Vietnam to date".
Author James Salter, reviewing the book for The Washington Post Book World, wrote, "Enormously rich in detail and written with a novelist's brilliance, the pages literally hurry before one." In 1993, Atkinson wrote Crusade: The Untold Story of the Persian Gulf War. In a review, The Wall Street Journal wrote, "No one could have been better prepared to write a book on Desert Storm, and Atkinson's Crusade does full justice to the opportunity."
Publication of The Liberation Trilogy began in 2002 with An Army at Dawn: The War in North Africa, 1942–1943, acclaimed by The Wall Street Journal as "the best World War II battle narrative since Cornelius Ryan’s classics, The Longest Day and A Bridge Too Far." While with the 101st Airborne Division south of Baghdad in April 2003, Atkinson learned that the book had been awarded the Pulitzer Prize for history. The trilogy's second volume, The Day of Battle: The War in Sicily and Italy, 1943–1944, published in 2007, drew praise from The New York Times as "a triumph of narrative history, elegantly written...and rooted in the sight and sounds of battle." Volume three, The Guns at Last Light: The War in Western Europe, 1944–1945, was published by Henry Holt and Co. in May 2013, and was ranked #1 on the New York Times Hardcover Nonfiction and Combined Print & E-Book Nonfiction bestseller lists. A review in The New York Times called the book "a tapestry of fabulous richness and complexity...Atkinson is a master of what might be called 'pointillism history,' assembling the small dots of pure color into a vivid, tumbling narrative... The Liberation Trilogy is a monument achievement."</ref>
As a result of his time with Gen. Petraeus and the 101st Airborne, Atkinson also wrote In the Company of Soldiers: A Chronicle of Combat, which The New York Times Book Review called "intimate, vivid, and well-informed", and which Newsweek cited as one of the ten best books of 2004. Atkinson was the lead essayist in Where Valor Rests: Arlington National Cemetery, published by the National Geographic Society in 2007. He is the editor and introductory essayist for Cornelius Ryan, an anthology of work by the journalist and military historian published by Library of America in May 2019.
In 2013, Atkinson began researching the Revolution Trilogy, with the first volume, The British Are Coming, published in May 2019 by Henry Holt and edited, as all of Atkinson's books have been, by John Sterling. The first book in the "The Revolution Trilogy", The British Are Coming: The War for America, Lexington to Princeton, 1775-1777 was released in 2019. The New York Times selected The British Are Coming for its "100 Notable Books of 2019."
Awards
1982 Pulitzer Prize, National Reporting
1983 Livingston Award for Young Journalists
1989 George Polk Award for National Reporting
1989 John Hancock Award for Excellence in Business Writing, with David Maraniss
1989 Morton Mintz Award for Investigative Reporting
1999 Pulitzer Prize for public service, awarded to The Post for articles on shootings by the District of Columbia police department
2003 Pulitzer Prize in History, An Army at Dawn
2003 Society for Military History Distinguished Book Award
2007 Gerald R. Ford Award for Distinguished Reporting on National Defense
2008 American Academy of Achievement's Golden Plate Award
2009 Axel Springer Prize and fellowship, the American Academy, Berlin
2009 John Reagan "Tex" McCrary Award, Congressional Medal of Honor Society
2010 Pritzker Military Library Literature Award for Lifetime Achievement in Military Writing
2013 Norwich University, Honorary Doctor of Military History
2013 New York Military Affairs Symposium, lifetime achievement award
2014 Samuel Eliot Morison Prize for lifetime achievement, Society for Military History
2014 Society of Midland Authors, best adult nonfiction book of the year
2015 Peggy V. Helmerich Distinguished Author Award
2019 Vincent J. Dooley Distinguished Fellow, honor bestowed by the Georgia Historical Society
Bibliography
(Liberation Trilogy #1) (2003 Pulitzer Prize for History)
(Liberation Trilogy #2)
(Liberation Trilogy #3)
(The Young Readers Adaptation of The Guns of Last Light)
(The Young Readers Adaptation of The Guns at Last Light)
Notes and references
External links
Website for The Revolution Trilogy
Website for The Liberation Trilogy
Rick Atkinson interview on Counterpoint Radio with Marcus W. Orr Center for the Humanities at the University of Memphis.
Pulitzer Biography in 2003
Reviews of An Army At Dawn and The Day of Battle (Advanced Readers Copy)
Interview on In the Company of Soldiers on March 17, 2004, at the Pritzker Military Museum & Library
Interview on The Day of Battle on October 18, 2007 at the Pritzker Military Museum & Library
Presentation by Rick Atkinson on April 28, 2011 at the Pritzker Military Museum & Library
Interview with Max Hastings at the Pritzker Military Museum & Library
Lecture on Guns at Last Light on May 16, 2013 at Pritzker Military Museum & Library
Booknotes interview with Atkinson on Army at Dawn, November 17, 2002
In Depth interview with Atkinson, June 2, 2013
Category:1952 births
Category:Living people
Category:People from Munich
Category:American military writers
Category:East Carolina University alumni
Category:Pulitzer Prize for History winners
Category:Pulitzer Prize for National Reporting winners
Category:American male journalists
Category:Berlin Prize recipients
Category:The Washington Post people
Category:University of Chicago alumni
Category:Military brats | {
"pile_set_name": "Wikipedia (en)"
} |
Q:
Unable to get rating bar to align with text View
I am trying to create a scrollable list with ratingbars and textviews.
However I am unable to get them to align correctly. I would like even spacing between all textviews and rating bars..
I have tried to use the layout_below but this does not produce what I would like, I have also tried dragging, but this also does not create the wanted effect.
Any help would be appreciated :)
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
xmlns:app="http://schemas.android.com/apk/res-auto"
xmlns:tools="http://schemas.android.com/tools"
android:layout_width="match_parent"
android:layout_height="match_parent"
android:background="@color/colorPrimaryDark"
tools:context="uk.co.neverendingsport.neverendingsport.LoginActivity">
<Button
android:layout_width="match_parent"
android:layout_height="wrap_content"
android:text="Continue"
android:layout_alignParentBottom="true"
android:layout_alignParentStart="true"
android:layout_marginBottom="13dp"
android:id="@+id/button" />
<TextView
android:id="@+id/textView4"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:text="Select Sports"
android:textSize="30sp"
android:textStyle="bold"
android:layout_alignParentTop="true"
android:layout_centerHorizontal="true" />
<RelativeLayout
android:layout_width="wrap_content"
android:layout_height="match_parent"
android:layout_below="@+id/textView4"
android:layout_alignParentStart="true">
<TextView
android:id="@+id/footballTextView"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:text="Football"
android:textSize="30sp"
android:layout_above="@+id/cyclingRatingBar"
android:layout_alignParentStart="true" />
<RatingBar
android:id="@+id/footballRatingBar"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignParentTop="true"
android:layout_alignParentEnd="true" />
<TextView
android:id="@+id/cyclingTextView"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:text="Cycling"
android:textSize="30sp"
android:layout_above="@+id/badmintonTextView"
android:layout_alignParentStart="true"
android:layout_marginBottom="10dp" />
<RatingBar
android:id="@+id/cyclingRatingBar"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_below="@+id/footballRatingBar"
android:layout_alignParentEnd="true" />
<TextView
android:id="@+id/badmintonTextView"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:text="Badminton"
android:textSize="30sp"
android:layout_below="@+id/cyclingRatingBar"
android:layout_alignParentStart="true"
android:layout_marginBottom="10dp"/>
<RatingBar
android:id="@+id/badmintonRatingBar"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_above="@+id/runningTextView"
android:layout_alignParentEnd="true" />
<TextView
android:id="@+id/runningTextView"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:text="Running"
android:textSize="30sp"
android:layout_below="@+id/badmintonTextView"
android:layout_alignParentStart="true"
android:layout_marginBottom="10dp"/>
<RatingBar
android:id="@+id/runningRatingBar"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_below="@+id/badmintonRatingBar"
android:layout_alignParentEnd="true" />
<TextView
android:id="@+id/swimmingTextView"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:text="Swimming"
android:textSize="30sp"
android:layout_below="@+id/runningTextView"
android:layout_alignParentStart="true"
android:layout_marginBottom="10dp"/>
<RatingBar
android:id="@+id/swimmingRatingBar"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_below="@+id/runningRatingBar"
android:layout_alignParentEnd="true" />
<TextView
android:id="@+id/golfTextView"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:text="Golf"
android:textSize="30sp"
android:layout_below="@+id/swimmingTextView"
android:layout_alignParentStart="true"
android:layout_marginBottom="10dp"/>
<RatingBar
android:id="@+id/golfRatingBar"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_below="@+id/swimmingRatingBar"
android:layout_alignParentEnd="true" />
</RelativeLayout>
</RelativeLayout>
Image of current layout
A:
Here is the answer that works fine for me
<?xml version="1.0" encoding="utf-8"?>
<RelativeLayout xmlns:android="http://schemas.android.com/apk/res/android"
android:layout_width="match_parent"
android:layout_height="match_parent">
<TextView
android:id="@+id/textView2"
style="@style/Base.TextAppearance.AppCompat.Large"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignParentTop="true"
android:layout_centerHorizontal="true"
android:text="Select Sports" />
<TextView
android:id="@+id/textView6"
style="@style/Base.TextAppearance.AppCompat.Large"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignBottom="@+id/ratingBar"
android:layout_alignParentLeft="true"
android:layout_alignParentStart="true"
android:layout_marginBottom="17dp"
android:layout_toLeftOf="@+id/ratingBar"
android:layout_toStartOf="@+id/ratingBar"
android:text="Football" />
<RatingBar
android:id="@+id/ratingBar"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignParentEnd="true"
android:layout_alignParentRight="true"
android:layout_below="@+id/textView2" />
<RatingBar
android:id="@+id/ratingBar2"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignParentEnd="true"
android:layout_alignParentRight="true"
android:layout_below="@+id/ratingBar" />
<RatingBar
android:id="@+id/ratingBar3"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignLeft="@+id/ratingBar2"
android:layout_alignStart="@+id/ratingBar2"
android:layout_below="@+id/ratingBar2" />
<RatingBar
android:id="@+id/ratingBar4"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignLeft="@+id/ratingBar3"
android:layout_alignStart="@+id/ratingBar3"
android:layout_below="@+id/ratingBar3" />
<TextView
android:id="@+id/textView7"
style="@style/Base.TextAppearance.AppCompat.Large"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_above="@+id/ratingBar3"
android:layout_alignParentLeft="true"
android:layout_alignParentStart="true"
android:layout_marginBottom="17dp"
android:layout_toLeftOf="@+id/textView2"
android:text="Cycling" />
<TextView
android:id="@+id/textView8"
style="@style/Base.TextAppearance.AppCompat.Large"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_above="@+id/ratingBar4"
android:layout_alignParentLeft="true"
android:layout_alignParentStart="true"
android:layout_marginBottom="14dp"
android:layout_toLeftOf="@+id/ratingBar3"
android:text="Badminton" />
<TextView
android:id="@+id/textView9"
style="@style/Base.TextAppearance.AppCompat.Large"
android:layout_width="wrap_content"
android:layout_height="wrap_content"
android:layout_alignBottom="@+id/ratingBar4"
android:layout_alignParentLeft="true"
android:layout_alignParentStart="true"
android:layout_marginBottom="16dp"
android:layout_toLeftOf="@+id/ratingBar4"
android:text="Running" />
</RelativeLayout>]
final output
First of all you need to add rating bar to parent layout and later textview to the parent layout
| {
"pile_set_name": "StackExchange"
} |
Q:
Update YAML Route Files as same as Connected mode, while working in Disconnected Mode
How can I update my YAML files for local disconnected mode development from Sitecore, as same as Connected mode. As We have a team who is working on Sitecore and another team is working on front-end in disconnected mode. I know we can use :connected mode for development but I need the same data in disconnected mode also.
How can I update that .yml files.
A:
There are no tools built into the JSS SDK to retrieve and store Layout Service data as files.
When disconnected data is imported into Sitecore, it is "expanded" to reflect the data schemas you have defined in disconnected mode. In other words, component definitions, route data, content data and everything else you define in disconnected mode become templates, renderings, data source items, etc... in Sitecore.
At that point, it becomes extremely difficult to "export" everything that has been expanded and make it available again as disconnected data in the same/similar structure as you defined it originally in disconnected mode. And make that data import-able again. This is especially true for shared data/components.
If you have backend/frontend teams working in tandem on a JSS site / Sitecore instance, it is recommended that you try to use Connected mode in this scenario. Also, once Sitecore becomes the "source of truth" for your data, be sure to exercise caution if importing templates/components/renderings (e.g. disconnected data) into Sitecore so as not to break anything the backend team may have implemented.
All of that said, your JSS app is essentially built to consume and render data made available via Layout Service. And you are not required to use the mock Layout Service that the sample apps use. There is nothing preventing you from saving Layout Service data queried from Sitecore into a JSON file. Once you have that data locally (disconnected), you might consider building your own service layer to fetch "raw" Layout Service data from the JSON file(s) you saved.
For instance, wherever you currently call dataApi.fetchRouteData, you can add a conditional statement, e.g.
if (inDisconnectedMode) {
fetchRouteDataFromLocalFile();
} else {
dataApi.fetchRouteData();
}
Related question (but similar answer: Any way to remove disconnected manifest processing?)
UPDATE (2019-04-26)
If you absolutely need to export JSS app data/definitions from Sitecore into disconnected data (as opposed to working in Connected mode), you may want to consider Umbrella for Sitecore JSS: https://github.com/macaw-interactive/umbrella-for-sitecore-jss
| {
"pile_set_name": "StackExchange"
} |
J. J. Birden
LaJourdain J. Birden Sr. (born June 16, 1965) is a former professional American football player who was selected by the Cleveland Browns in the 8th round of the 1988 NFL Draft.
A 5'10", 157-lb. wide receiver, Birden graduated from Lakeridge High School in Lake Oswego, Oregon, and the University of Oregon. He played in 9 NFL seasons for the Kansas City Chiefs and Atlanta Falcons from 1988 to 1996.
College statistics
1985: 3 catches for 39 yards
1987: 19 catches for 399 yards and 1 touchdown; his quarterback was Bill Musgrave
After football
Following his football career, Birden became an executive for Xocai with Team X 88. Later he became a distributor of Isagenix health and wellness products and continues to represent Isagenix. Birden has also travelled extensively as a motivational and opportunity speaker and trainer for companies large and small; team building seminars, as well as youth group life skill development meetings.
Birden and his wife Raina have three children and five adopted children. They live in Scottsdale, Arizona.
In 2010, Birden was inducted into the University of Oregon's Athletic Hall of Fame for his performance on the Ducks' 1985 Track and Field NCAA Championship team.
References
External links
NFL.com player page
JJ Birden's Personal Website
Isagenix Top Leader
JJ's bestselling book, "When Opportunity Knocks 8 Surefire Ways to Take Advantage!
Category:1965 births
Category:Living people
Category:American football wide receivers
Category:Atlanta Falcons players
Category:Kansas City Chiefs players
Category:Oregon Ducks football players
Category:Lakeridge High School alumni
Category:Sportspeople from Lake Oswego, Oregon
Category:Sportspeople from Portland, Oregon
Category:Players of American football from Oregon | {
"pile_set_name": "Wikipedia (en)"
} |
Jeff Jospeh was manning the playback controls from way across the room and he accomplished this longer-than-USB-comfortably-allows connection from his laptop to the Aeris DAC using the Inex Innovation USB to Toslink converter. | {
"pile_set_name": "Pile-CC"
} |
Q:
Google script to edit entire column of spreadsheet?
I am new to google scripts so I am going through the documentation in hopes of finding out how to write the script I need. So far everything I read says that it can't access data outside of it's own cell.
The information is in a google spreadsheet, if excel has a easier solution I can move to that.
The idea is that this script would go through a column some 1000 strings and go to the end of the line and walk backward deleting each character until it passes the first "-", once that occurs it would move to the next row.
Can someone point me in the right direction?
Thank you
A:
Works for the example you provided in a comment, otherwise not tested:
In new Google Sheets
Edit
Find and Replace...
Find (.+)(-[^-].+)
Replace with $1
Search select your range
Search using regular expressions tick
Replace all.
| {
"pile_set_name": "StackExchange"
} |
62 F.3d 342
Ellis Wayne FELKER, Petitioner-Appellant,v.Albert G. THOMAS, Warden, Respondent-Appellee.
No. 94-8224.
United States Court of Appeals,Eleventh Circuit.
Aug. 9, 1995.
August F. Siemon, III, Atlanta, GA, Frank Derrickson, Decatur, GA, for appellant.
Susan V. Boleyn, State of Georgia Law Dept., Atlanta, GA, for appellee.
Appeal from the United States District Court for the Middle District of Georgia.
ON PETITION FOR REHEARING
AND SUGGESTION OF
REHEARING EN BANC
Before BIRCH, BLACK and CARNES, Circuit Judges.
PER CURIAM:
1
Because no member of this panel nor any other judge in regular active service on this Court has requested that this Court be polled about the suggestion of rehearing en banc (Fed.R.App.P. 35; 11th Cir.R. 35-5), that suggestion is denied, as is the petition for rehearing. However, the initial panel opinion, published at 52 F.3d 907 (11th Cir.1995), is extended as follows:
2
In his petition for rehearing, Felker argues that we have failed to give proper deference to the state court factfindings relating to the Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), issue. We affirmed the denial of relief as to the Brady claim on two independently adequate grounds. One was that Felker had not established, and cannot establish, that the evidence in question was suppressed, because if that evidence is true, Felker himself was aware of it before trial. None of the state court factfindings is in any way inconsistent with that independently adequate basis for denying relief on the claim.
3
Felker's arguments about the state court factfindings go only to our alternative holding that the allegedly suppressed evidence was immaterial, anyway. Felker, 52 F.3d at 910-11. We stated in our opinion that Felker's alibi for Wednesday, November 25, 1981, began when the police arrived at his house, which was at 7:00 p.m. Id. at 909-10. As Felker points out, one part of the Georgia Supreme Court's opinion, which did not address the Brady issue, states that the police arrived at Felker's house that evening at "approximately 5:30 p.m." Felker v. State, 252 Ga. 351, 314 S.E.2d 621, 627 (1984). We were bound to accept that factfinding as correct unless we concluded that it is not "fairly supported by the record." Sumner v. Mata, 449 U.S. 539, 550, 101 S.Ct. 764, 770, 66 L.Ed.2d 722 (1981). That is exactly what we concluded, albeit implicitly.
4
Our examination of the record revealed that there were only three witnesses who testified concerning the time the police officers arrived at Felker's house on Wednesday, November 25, 1981. Two were detectives. Detective Pond testified that he was initially informed about the case at the police station at about 5:30 or 6:00 p.m. that night. He also testified that he did not have a record of the time that he and detective Upshaw had arrived at Felker's house, but he thought that it was about 5:30 or 6:00 p.m. that evening. However, when Felker's attorney asked Detective Pond during cross-examination if it could have been nearer to 7:00 p.m. that evening when they arrived at Felker's house, Detective Pond testified: "I guess it's a possibility because I can't recall the exact time." By contrast, Detective Upshaw had no problem recalling the exact time that he and Detective Pond went to Felker's house. During cross-examination by Felker's attorney he testified as follows:
BY MR. HASTY:
5
Q: Sergeant Upshaw, I believe the night that you did this investigation, November the 25th, that was right at seven p.m. you went to Mr. Felker's house?
6
A: Yes, sir.
7
Q: And you're positive of the time?
8
A: Yes, sir. 7:02 to be exact.
9
Q: 7:02?
10
A: Yes, sir, because we called it out on the radio, police radio; went back and checked the log.
11
The only other witness to testify about the arrival of the detectives was Felker himself. He stated that he did not know when the detectives arrived that evening, except that it was after dark.
12
Having carefully considered all of the evidence on the issue, we find that the Georgia Supreme Court's statement that the two officers arrived at Felker's house at approximately 5:30 p.m. on Wednesday, November 25, 1981, is not "fairly supported by the record." Instead, it is contradicted by the record, which establishes that the two officers arrived at Felker's house at 7:02 p.m. that evening.
13
Even if we accepted the state court's finding that the detectives arrived at Felker's house between 5:30 p.m. and 6:00 p.m. that evening, the result still would be the same. Nothing about the timing of the detectives' arrival changes the fact that Felker himself personally knew about the allegedly suppressed evidence, if it was true, 52 F.3d at 910, nor does the time of their arrival change the fact that the allegedly suppressed evidence flatly contradicted Felker's own sworn testimony about when he was last with the victim, id. at 910-11.*
*
Felker also argues that we should have credited the Georgia Supreme Court's finding concerning the testimony of Dr. Whitaker, the medical examiner, about when the bruises were inflicted on the victim. The Georgia Supreme Court said "Dr. Whitaker concluded that the bruises had been inflicted 4 to 6 hours prior to death." 314 S.E.2d at 627. Actually, the record reveals that Dr. Whitaker testified that three of the four bruises on the victim's body were "fresh," which he said meant that they were inflicted between zero and four to six hours before death. He testified that the fourth bruise, which was not fresh, was probably inflicted four to six hours before death but that "there is a possibility it could have been 10 years also." Neither Dr. Whitaker nor any other witness testified that that bruise was inflicted by the killer
Moreover, Dr. Whitaker's testimony was evidence that was presented, not suppressed. The only evidence allegedly suppressed was evidence tending to show that the victim had been at a western wear store (with Felker) the Wednesday afternoon of her death. Dr. Whitaker's testimony concerning the victim's bruises does not change the fact that Felker personally knew about the allegedly suppressed evidence, nor does it change the fact that that evidence would have directly contradicted Felker's own sworn testimony. Accordingly, we need not decide whether the state court's characterization of Dr. Whitaker's testimony is fairly supported by the record.
| {
"pile_set_name": "FreeLaw"
} |
Experimental validation of Monte Carlo dose calculations about a high-intensity Ir-192 source for pulsed dose-rate brachytherapy.
Despite widespread use of high-intensity Ir-192 remotely afterloaded sources, no published measured or calculated dose-rate tables for currently used source designs are available. For a pulsed dose-rate Ir-192 source, both transverse axis (0.5-10 cm) and two-dimensional polar dose-rate profiles (1.5, 3, and 5 cm) were measured with thermoluminescent dosimetry in a solid water phantom. Dose rates were normalized to measured air-kerma strength, and the source geometry was verified by pinhole autoradiography and transmission radiography. At each measurement point, dose rates were calculated by a Monte Carlo photon transport (MCPT) code, which realistically modeled the experimental phantom, source, and detector geometry. Agreement between MCPT absolute dose-rate calculations and measurements averaged 3% and was less than 5%, demonstrating that Monte Carlo simulation is an accurate and powerful tool for two-dimensional dosimetric characterization of high activity Ir-192 sources. | {
"pile_set_name": "PubMed Abstracts"
} |
The children's eating behavior inventory: reliability and validity results.
Eating and mealtime problems are common in childhood. They occur across a broad age span, in normally developing children and in a wide variety of developmental and medical disorders. There is no currently available standard instrument by which to assess these problems. The Children's Eating Behavior Inventory (CEBI) was developed according to a conceptual framework based upon a transactional/systemic understanding of parent-child relationships. It was completed by 206 mothers of nonclinic children and 110 mothers of clinic children. Results of test-retest and internal reliability testing indicate that the CEBI meets criteria for instrument reliability. Construct validity is demonstrated by the significant difference between the clinic and nonclinic groups in the mean total eating problem score and in the mean number of items perceived to be a problem. | {
"pile_set_name": "PubMed Abstracts"
} |
The anatomical study of mammalian white matter structure and arrangement has evolved over the past two centuries. There have been three major revolutions facilitating neuroanatomical study of white matter: Early development of post-mortem preparation techniques like Klingler\'s (Ludwig and Klingler, [@B7]) to readily visualize the gross orientation of larger white fibers in dissection specimens; introduction of neurochemical tracing techniques to permit cortical-connectivity analysis in non-human primates in the second half of the twentieth century (Lanciego and Wouterlood, [@B6]); and most recently, development of *in vivo* diffusion magnetic resonance (MR) tractography in the 1990\'s, which has grown to become the premier white matter research technique. Unfortunately, and for varying reasons, the anatomical classification and nomenclature of white matter architecture, particularly of the association fasciculi, has been subject to considerable heterogeneity, conflicting theories, and disagreements between researchers. Nevertheless, attempts have been made to unify the classification and nomenclature of the human white matter fasciculi.
Recently, Mandonnet et al. ([@B9]) proposed a global classification for the long-range human association fasciculi on a hierarchical basis, using the insular sulcus as a demarcating boundary of larger dorsal and ventral systems (Mandonnet et al., [@B9]). Each system contained particular, well-known bundles interconnecting cortical areas, which received novel numerical classification e.g., the arcuate fasciculus is known as the superior longitudinal system IV. Though this attempt to unify the anatomy is commendable, we believe, however, that their proposal potentially adds more confusion to the current scenario. From our perspective, the major shortcoming of this nomenclature is that it does not adequately dispel the archaic, conflicting notions of white matter anatomy compounded over the years, but rather "paints over" them while leaving the fundamental controversies unaddressed, or possibly causing greater confusion.
Though it is unfeasible to discuss every association tract discussed in the current classification, we use our own recently published data regarding several relevant tracts (Fernández-Miranda et al., [@B2]; Wang et al., [@B17]; Panesar et al., [@B12], [@B11],[@B13]) to argue our point: The superior longitudinal fascicle (SLF) was first divided into 4 subsegments (SLF I to IV) based on primate neurochemical tracer data (Petrides and Pandya, [@B14]), and later reinforced by a diffusion tensor imaging (DTI) study (Makris et al., [@B8]). These initial studies included the arcuate fasciculus (AF) as the "SLF-IV" or "perisylvian-SLF," a proposal later propagated by others (Catani et al., [@B1]; Martino et al., [@B10]). The present authors propose the AF to be considered as the "superior longitudinal system (SLS) IV." In our view, this is problematic: The AF cannot be regarded as a longitudinal tract as it is an "arcuate-shaped" tract; in fact, the AF is a lateral fronto-temporal fascicle with no parietal connections (Fernández-Miranda et al., [@B2]), while the SLF is a lateral fronto-parietal fascicle with no temporal connections (Wang et al., [@B17]). From an anatomical (morphological and topographical) perspective, defining an "arcuate" tract as a "longitudinal" tract is misleading.
Furthermore, the literature generally shows that the AF has strong leftward-lateralization in terms of its subdivisions, volume, and connectivity profiles, while the "superior longitudinal fasciculus proper" (excluding AF) (Thiebaut de Schotten et al., [@B16]; Wang et al., [@B17]), is rightward-lateralized in terms of subdivision, connectivity, and volume. Based upon comparisons between human and simian AF morphology, Rilling et al. ([@B15]) proposed the human AF to be evolutionarily differentiated to sub-serve lexical-semantic functionality (Rilling et al., [@B15]). This view was further elaborated upon and reinforced with our dedicated tractographic and dissection study (Fernández-Miranda et al., [@B2]). As the structural characteristics of white matter likely reflect evolutionary divergence, underpinned by functional specialization (Glasser and Rilling, [@B3]; Rilling et al., [@B15]), this adds further evidence that these anatomo-functionally differentiated should not be grouped together.
In our advanced fiber tractography study of the SLF (Wang et al., [@B17]), we were unable to find the so-called SLF-I, which in theory travels adjacent to SLF-II to interconnect the superior frontal gyrus with the superior parietal lobule. We did find fibers interconnecting these two regions, but they were traveling medial to the corona radiata in the mesial aspect of the hemisphere. We subsequently proposed these fibers to be part of the cingulum fiber system rather than the SLF. However, multiple authors have continued preserving the inappropriate nomenclature derived from primate studies for no good reason. Our study showed that the SLF can be practically classified in dorsal and ventral components, which correlate with the SLF-II and III, but offer additional anatomical information in their description while adhering to modern anatomical nomenclature systems.
The same issues arise when considering the proposed nomenclature for the "inferior longitudinal system (ILS)" which includes both the inferior fronto-occipital fasciculus (IFOF) and the uncinate fasciculus (UF). According to the authors, the "ILS IV" is synonymous with the UF. Recent tractographic studies have demonstrated a unique, subdivided morphology of the UF (Hau et al., [@B5], [@B4]; Panesar et al., [@B12]). According to the proposed "ILS" nomenclature, the various subcomponents of the IFOF, in concordance with our previous findings (Panesar et al., [@B12]) are accounted for, yet the subdivisions of the UF are not ([Figure 1](#F1){ref-type="fig"}).
![All tractography conducted in DSI studio (<http://dsi-studio.labsolver.org>) using the HCP 842 atlas (Yeh et al., [@B19]) as a template. AF tracts were created according to the method described in (Fernández-Miranda et al., [@B2]), while SLF tracts were created according to the methodology used by Wang et al. ([@B17]). IFOF and UF tracts were created using the method from Panesar et al. ([@B12]). This tractography template represents "averaged" healthy white matter tractographic anatomy of 842 subjects from the Human Connectome Project. Visible in this picture are the dorsal (dAF) and ventral (vAF) AF components, the dorsal (dSLF) and ventral (vSLF) SLF components. Deep and ventral to these tracts are the IFOF consisting of the dorsomedial (DM IFOF), ventromedial (VM IFOF) and ventrolateral (VL) subfascicles. The UF also traverses through the ventral external capsule and is comprised of the ventrolateral (VL UF) and ventromedial (VM UF) sub-fascicles.](fnana-13-00061-g0001){#F1}
Fiber tracts should not be grouped with other fasciculi on the sole basis of spatial proximity, but on the basis of distinct connectivity. In addition, the present proposal carries on with tract sub-classifications that originated from animal studies and were later "validated" with DTI studies. The classifications, from our point of view, are inaccurate and inappropriate for human brain anatomy, especially in light of new tractography findings. We strongly recommend against the use of numerical subsegments (I to IV), and we favor using a topographic classification (dorsal-ventral, medial-lateral), which has a long tradition and is better understood by neuroanatomists as the names themselves provide anatomical information, as opposed to numeric classifications that provide no additional information.
Finally, we highlight technical factors that may potentially confound this classification proposal. At this point, the differences between DTI and more advanced white matter tractography modalities such as high-angular resolution diffusion imaging (HARDI) or generalized Q-sampling imaging (GQI) are well-recognized. In a recent dissection and tractography study into the short vertical association tracts of the posterior hemisphere, we demonstrated that GQI-based tractography could reliably demonstrate the unique spatial separation between the two components within what Mandonnet et al. refer to as the posterior transverse system, and which we refer to as the "temporo-parietal aslant tract" (temporo-parietal course) and vertical occipital fasciculus (occipito-occipital course), respectively (Panesar et al., [@B11]). Yeatman et al. ([@B18]) first questioned whether these two fasciculi were indeed separated, a discrete "band of fibers" or whether they appeared unified due to shortcomings of the DTI method. In our study, we demonstrated that the temporo-parietal aslant tract and vertical occipital fasciculus were indeed spatially separated. The band of fibers bridging the two fascicles may be comprised of U-fibers or may be comprised of false continuities from other fasciculi, arising from tensor-based tractography.
In conclusion, we congratulate the authors for the efforts toward a unified classification of the white matter tracts, but at the same time we encourage them and all other experts in the field to consider the points of concern raised here, and to utilize a more practical, anatomically-oriented, and academically-accurate classification of the human fiber tracts.
Author Contributions {#s1}
====================
Both authors SP and JF-M contributed equally to the manuscript: JF-M: main idea and editing. SP: writing and figure creation.
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.
[^1]: Edited by: Hans J. ten Donkelaar, Radboud University Nijmegen, Netherlands
[^2]: Reviewed by: Michela Ferrucci, University of Pisa, Italy; Giorgio Innocenti, Karolinska Institute (KI), Sweden
| {
"pile_set_name": "PubMed Central"
} |
T.C. Memo. 2009-308
UNITED STATES TAX COURT
JAMES SCOTT SPARKMAN, Petitioner v.
COMMISSIONER OF INTERNAL REVENUE, Respondent
Docket Nos. 9278-08L, 9279-08L. Filed December 28, 2009.
James Scott Sparkman, pro se.
Jonathan J. Ono, for respondent.
MEMORANDUM OPINION
GOEKE, Judge: These consolidated cases involve respondent’s
efforts to collect income taxes and section 66721 trust fund
recovery penalties through lien and levy. Jurisdiction is based
upon section 6330(d). Petitioner’s sole argument is that he does
1
Unless otherwise indicated, all section references are to
the Internal Revenue Code.
- 2 -
not owe the income tax liabilities. As we will explain, this
argument is not available to petitioner in this collection case,
and we uphold respondent’s determinations.
Background
Petitioner was a resident of Hawaii when the petitions were
filed. Before trial, respondent filed motions to show cause why
proposed facts in evidence should not be accepted as established
in these two consolidated dockets. After consideration of
petitioner’s reply to the motions, the facts proposed were
accepted as established, and the exhibits attached to the motions
were deemed admitted into evidence. There is no other
stipulation of facts, but petitioner testified at trial.
Respondent’s collection efforts involve these liabilities:
Tax Period Type of Tax Assessed Amount Due
1996 Income $51,962.71
1997 Income 54,210.54
1998 Income 32,753.04
1999 Income 117,933.12
2000 Income 44,470.51
200203 Sec. 6672 298.64
200303 Sec. 6672 4,753.35
200306 Sec. 6672 2,933.75
On October 5, 2006, respondent issued to petitioner a Notice
of Federal Tax Lien Filing and Your Right to a Hearing Under IRC
6320 (NFTL). A notice of intent to levy was issued to petitioner
- 3 -
on August 12, 2006, in response to which he submitted a timely
request for a collection due process (CDP) hearing. Petitioner
timely submitted his request for a CDP hearing to respondent in
response to the NFTL. Petitioner’s request for a CDP hearing
contained the following statements:
Several months ago 7-14-2006 I requested a payment plan
no response. I never breached any prior payment plan.
I have also requested a CDP hearing 4 times now. More
importantly I do not owe the tax assessed. The case is
in 9th Circuit Appeals.
Your agent omitted evidence at trial. Your agent
fabricated evidence at trial. I told your office not
to file a lien several times yet IRS did anyway. This
has been noted and will be dealt with per code 7433.
Petitioner’s delinquent income tax liabilities for years
1996 through 2000 arose from assessments that were made following
the issuance of a statutory notice of deficiency to him on March
28, 2003. Petitioner timely filed a petition with this Court in
response to the notice of deficiency. Sparkman v. Commissioner,
docket No. 8400-03. After a trial was conducted on June 22,
2004, the Court filed a Memorandum Findings of Fact and Opinion
in docket No. 8400-03 on June 13, 2005. Sparkman v.
Commissioner, T.C. Memo. 2005-136. A decision in docket No.
8400-03 was entered on December 15, 2005, finding that petitioner
was liable for the following:
- 4 -
Additions to Tax
Tax Year Deficiency Sec. 6651(a)(1) Sec. 6662(a)
1996 $22,364 $5,591.00 $2,516.00
1997 23,665 5,916.25 2,753.20
1998 15,290 3,822.50 1,613.20
1999 61,028 9,154.20 10,704.80
2000 29,490 --- 3,460.60
Petitioner timely filed a notice of appeal in the case at
docket No. 8400-03, and the case was appealed to the U.S. Court
of Appeals for the Ninth Circuit. The Court of Appeals filed its
opinion on December 10, 2007, and entered a judgment in that case
on February 1, 2008, affirming the decision of this Court.
Sparkman v. Commissioner, 509 F.3d 1149 (9th Cir. 2007). No
petition for certiorari was timely filed in docket No. 8400-03.
Respondent assessed income tax deficiencies and additions to
tax for the years 1996 through 2000 in May and June 2006,
pursuant to the decision of the Court in docket No. 8400-03. The
income tax liability for 2000 was assessed on July 3, 2006.
For the taxable quarterly periods ending March 31, 2002,
March 31, 2003, and June 30, 2003, respondent determined that
petitioner was liable for trust fund recovery penalties under
section 6672 as a person required to collect, account for, and
pay over withheld employment taxes for a business entity known as
Mercury Solar. Respondent assessed the section 6672 penalties
against petitioner on August 16, 2004. Before the assessment
- 5 -
respondent sent petitioner by certified mail a Letter 1153, Trust
Funds Recovery Penalty Letter, dated May 10, 2004, which provided
him with an opportunity to appeal or protest the proposed section
6672 penalties. Petitioner received the Letter 1153 on May 12,
2004, but submitted no timely appeal or protest. Forms 4340,
Certificate of Assessments, Payments, and Other Specified
Matters, were issued to petitioner with respect to the assessed
section 6672 penalties.
After considering petitioner’s request for a CDP hearing, on
March 20, 2009, respondent’s Appeals Office issued a Notice of
Determination Concerning Collection Action(s) Under Section 6320
and/or 6330 (notice of determination). The notice of
determination stated in part:
We have discussed the taxpayer’s appeal with him on
several occasions. In each of these discussions and in
written correspondence, the taxpayer has steadfastly
held to the position that he does not owe the
individual income tax amounts assessed against him.
Most recently, he states this position in a letter
dated March 2, 2008. He has also stated on a number of
occasions that he feels that the proposed levy action
is not legal since he had appealed the decision by the
United States Tax Court to the Ninth Circuit Court of
Appeals.
We have advised the taxpayer that IRC § 6330(c)(2)(b)
does not allow a taxpayer to challenge the existence or
the amount of the liability if the taxpayer had a prior
opportunity to dispute the liability. We have noted
that the taxpayer’s assessments were made based on a
decision by the United States Tax Court. This clearly
gave the taxpayer an opportunity to dispute the amount
of the liability. We also advised the taxpayer that he
could have forestalled assessment and collection of the
tax as determined by the Tax Court by filing an appeal
- 6 -
bond. Since he did not do so, assessment and
subsequent proposed collection action was appropriate.
We also advised the taxpayer that based on
documentation we received from the administrative case
file relating to assertion of the Trust Fund Recovery
Penalty, the postal records indicate he received Letter
1153 but he did not make a timely appeal of the
proposed assertion of the Trust Fund Recovery Penalty.
Accordingly, IRC § 6330(c)(2)(b) does not allow a
taxpayer to challenge the existence or the amount of
the liability when he had a prior opportunity to
dispute the liability.
We have also given the taxpayer a reasonable period of
time to discuss a collection alternative for payment of
his accounts. Consideration of a collection
alternative has been difficult since the taxpayer
continues to take the position that the income tax
assessed against him is not correct. He made it clear
in his letter of March 2, 2008, that he expects Appeals
will process his amended tax returns and allow the
depreciation he claimed on his amended returns. He
completely ignores the decisions by the courts. In
fact, he states that the Ninth Circuit Court of Appeals
merely “rubber stamped” the decision by the Tax Court.
However, even if the taxpayer acknowledged liability
for the amounts assessed against him, we are unable to
determine the taxpayer’s ability to pay his delinquent
accounts. The financial information provided by the
taxpayer does not lead to a collection alternative.
The taxpayer provided a Collection Information
Statement for Individuals, Form 433-A dated May 30,
2007. The primary concern with the information on Form
433-A is that the taxpayer indicates he has living
expenses of $10,500 but listed income of only $1,600
per month. Included in his living expenses are
mortgage payments on two properties totaling $8,100 per
month and a car payment of $850 per month. Since these
payments cannot be made on income of $1,600 per month,
we believe that we have an incomplete picture of the
taxpayer’s actual financial condition. Incomplete
financial information does not enable us to determine
an appropriate collection alternative.
* * * * * * *
- 7 -
We have determined that the * * * [filing of the notice
of Federal tax lien] was appropriate under the
circumstances presented in this case. We have given
the taxpayer a reasonable period of time to discuss the
issues he raised in his appeal. The fact that the
taxpayer has not * * * [presented any basis for
withdrawing the lien] and has not provided complete
financial information leaves us unable to determine an
appropriate collection alternative. We are left with
no alternative to sustaining * * * [the filing of the
notice of Federal tax lien] * * *.
A similar notice of determination was issued regarding
respondent’s attempt to levy.
In filing his petition for lien or levy action under section
6320(c) or 6330(d), petitioner continued to contest his assessed
income tax deficiencies and alleged, in part:
This was not justice but a legal stunt or at best an
error which I sought to correct with a due process
hearing. The LIEN and LEVY are unjust and not correct
they were obtained by illegal, negligent and fraudulent
IRS collection maneuvering. IRS Collection due process
agent did not take a new objective view of the case.
Discussion
Section 6320(a) requires the Secretary to notify the
taxpayer in writing of the filing of an NFTL and of the
taxpayer’s right to an administrative hearing on the matter.
Section 6330 provides a similar hearing opportunity before a
proposed levy. Section 6320(b) affords the taxpayer the right to
a fair hearing with respect to an NFTL before an impartial
hearing officer. Section 6320(c) requires that the
administrative hearing be conducted pursuant to section 6330(c),
(d), and (e).
- 8 -
At the hearing a taxpayer may raise any relevant issues,
including appropriate spousal defenses, challenges to the
appropriateness of the collection action, and possible collection
alternatives. Sec. 6330(c)(2)(A). A taxpayer is precluded,
however, from contesting the existence or amount of the
underlying tax liability unless the taxpayer did not receive a
notice of deficiency for the tax liability in question or did not
otherwise have an opportunity to dispute the tax liability. See
sec. 6330(c)(2)(B); Sego v. Commissioner, 114 T.C. 604, 609
(2000).
On the basis of petitioner’s request for a CDP hearing, the
petition filed, and his position at trial, petitioner is
attempting to contest his assessed income tax liabilities. As a
statutory matter he is precluded under section 6330(c)(2)(B) from
doing so in this proceeding since a notice of deficiency was
issued to him. Furthermore, not only did petitioner receive a
notice of deficiency for his delinquent income tax liabilities
for the years 1996 through 2000; he also litigated the
liabilities in this Court and appealed the adverse decision to
the Court of Appeals for the Ninth Circuit, which affirmed this
Court’s holding. Petitioner’s arguments regarding his income tax
- 9 -
liabilities are precluded in these collection cases.2 See
Stroube v. Commissioner, 130 T.C. 257 (2008). Such a challenge
in these cases is also precluded by res judicata.
Following a hearing, the Appeals Officer must issue a notice
of determination regarding the validity of the filed Federal tax
lien or proposed levy. If the taxpayer disagrees with the
Appeals Office’s determination, the taxpayer may seek judicial
review by appealing to this Court. Sec. 6330(d). Where the
validity of the underlying tax liability is properly at issue,
the Court reviews the determination regarding the underlying tax
liability de novo. Sego v. Commissioner, supra at 610; Goza v.
Commissioner, 114 T.C. 176, 181-182 (2000). Where the validity
of the underlying tax liability is not properly at issue, the
Court reviews the determination of the Appeals Office for abuse
of discretion. Sego v. Commissioner, supra at 610; Goza v.
Commissioner, supra at 182.
Section 6672(a) imposes a penalty (commonly known as a trust
fund recovery penalty) on any person required to collect,
truthfully account for, and pay over tax who willfully fails to
do so or who willfully attempts to evade or defeat any such tax.
At trial petitioner did not contest his section 6672 trust
fund recovery penalty assessments. Nevertheless, he may not do
2
Petitioner, in conjunction with these cases, also filed a
motion for leave to file a motion to vacate the decision in
docket No. 8400-03. This motion was denied on Sept. 10, 2009.
- 10 -
so in any event because he previously received by certified mail
from respondent a Letter 1153, which proposed the assessment of
the subject penalties and provided him with an opportunity to
appeal or protest said assessments. For purposes of section
6330(c)(2)(B), petitioner has previously had an opportunity to
dispute the underlying section 6672 penalties. See Mason v.
Commissioner, 132 T.C. ___, ___ (2009) (slip op. at 30).
In conclusion, respondent did not abuse his discretion
regarding the proposed collection actions and may proceed by
means of the NFTL and the proposed levy to collect petitioner’s
tax liabilities for the years in issue.
To reflect the foregoing,
Decisions will be entered for
respondent.
| {
"pile_set_name": "FreeLaw"
} |
1. Introduction {#sec1-ijms-18-02160}
===============
DNA methylation is an important epigenetic modification in mammalians and occurs predominately at CpG dinucleotides in the genome. At CpG sites, cytosine is modified by an enzyme called DNA methyltransferase (DNMT) and a methyl group is added at the 5-position. De novo methylation is catalyzed by DNMT3A and DNMT3B. In double-stranded DNA, methylated CpGs are short palindromic sequences, and methyl groups which are located in the large grove of the double helix are recognized by methyl-CpG binding domain-containing proteins (e.g., MBD2). These proteins recruit chromatin silencing complexes that result in condensation of the chromosomal region. During semi-conservative DNA replication, unmethylated CpGs on the newly synthesized daughter strand are methylated by DNMT1. This maintenance DNA methyltransferase is recruited to the hemi-methylated CpG sequences with the help of several co-factors including PCNA and UHRF1 \[[@B1-ijms-18-02160],[@B2-ijms-18-02160]\].
In mammalians CpG and GC-rich regions, so-called CpG islands are often localized at regulatory regions like gene promoters and imprinting centers. Unmethylated CpG island promoters are in an open chromatin configuration and are correlated with active gene transcription. However, hypermethylated CpG islands consist of epigenetic inactive chromatin regions. During aging and carcinogenesis, several CpG island promoters become aberrantly methylated. Hypermethylation of tumor suppressor genes (TSG) is a hallmark of their inactivation in the pathogenesis of cancer. One of the most frequently hypermethylated CpG islands of a TSG is located in the promoter region of the *Ras Association Domain Family 1A* (*RASSF1A*) gene \[[@B3-ijms-18-02160],[@B4-ijms-18-02160]\].
2. The Ras Association Domain Family 1 (*RASSF1*) Gene {#sec2-ijms-18-02160}
======================================================
In lung cancer, deletion of a region in 3p21.3 of chromosome 3 has frequently been reported \[[@B5-ijms-18-02160]\]. Chromosomal deletions of this region have also been found in other cancer entities (in tissues of e.g., breast, head and neck, kidney and gastrointestinal tract) \[[@B6-ijms-18-02160]\]. In the minimal deletion region, we and others have discovered the *Ras Association Domain Family 1* gene ([Figure 1](#ijms-18-02160-f001){ref-type="fig"}) \[[@B4-ijms-18-02160],[@B7-ijms-18-02160]\]. Initially, we termed the gene *Ras effector homologue* 3p21, since its protein sequences exhibited homologies to the murine *novel Ras effector 1* (*Nore1*) \[[@B8-ijms-18-02160]\]. However, the HUGO gene nomenclature committee renamed it to *Ras Association Domain Family 1* (*RASSF1*) gene and human *NORE1* was later renamed *RASSF5*.
Subsequently, we identified two main isoforms of *RASSF1*, that were transcribed by two distinct CpG island promoters: *RASSF1A* and *RASSF1C* ([Figure 1](#ijms-18-02160-f001){ref-type="fig"}). A third variant initially named *RASSF1B* was only expressed at very low levels, and its biological function was not further investigated \[[@B4-ijms-18-02160]\]. The transcript of *RASSF1A* contains six exons (1α, 2αβ, 3, 4, 5 and 6) and is translated to a protein with 340 aa ([Figure 2](#ijms-18-02160-f002){ref-type="fig"}). The *RASSF1C* variant is transcribed from an intragenic CpG island and consists of 5 exons (2γ, 3, 4, 5 and 6). On protein level, *RASSF1A* and *RASSF1C* both encode a C-terminal Ras Association domain (RA) ([Figure 2](#ijms-18-02160-f002){ref-type="fig"}). The rat sarcoma genes (*Ras*) are a family of small GTPases that function as proto-oncogenes by regulating mitogen-induced signaling pathways. In contrast to RASSF5/NORE1, which interacts with several Ras proteins, the direct interaction of RASSF1 with Ras proteins is rather weak \[[@B9-ijms-18-02160]\]. Most likely, the interaction of RASSF1A with Ras is indirect through binding to the endogenous RASSF5 \[[@B9-ijms-18-02160]\]. The RA domain of RASSF1 is also defined as an ubiquitin-like domain (UBQ) \[[@B10-ijms-18-02160]\]. A domain that is only present in the RASSF1A protein is the protein kinase C conserved region 1 (C1) ([Figure 2](#ijms-18-02160-f002){ref-type="fig"}). The C1 domain has been characterized as a binding site for phorbol esters and diacylglycerol, which act as tumor promoters \[[@B4-ijms-18-02160]\].
The *RASSF1* isoforms and *RASSF5* encode a C-terminal SARAH (Sav/Rassf/Hpo) domain that is a characteristic coiled-coil structure ([Figure 2](#ijms-18-02160-f002){ref-type="fig"}). It is a small helical module that is important in signal-transduction networks and serves for protein-protein interactions \[[@B11-ijms-18-02160]\]. This SARAH domain is also found in the regulatory protein WW45 (human homologue of the *Drosophila* protein Salvador/Sav) and the serine/threonine kinase STK3 and STK4 (human homologues of the *Drosophila* kinase Hippo/hpo) \[[@B11-ijms-18-02160],[@B12-ijms-18-02160],[@B13-ijms-18-02160]\]. STK3 and STK4 are also often termed MST1 and MST2 (mammalian STE20-like protein kinase), respectively. Mutation in the *Drosophila Hpo* gene leads to organ overgrowth which was termed the hippopotamus (Hippo) phenotype \[[@B14-ijms-18-02160]\]. In mammals MST1/2 kinases regulate the Hippo pathway through phosphorylation of the large tumor suppressor kinases (LATS) which in turn phosphorylate the transcriptional regulator YAP1 (Yes-associated protein 1) \[[@B15-ijms-18-02160]\]. YAP1 was initially characterized as a protein that interacts with the src-family tyrosine kinase YES1 (homologue of the Yamaguchi sarcoma viral oncogene) and acts as a proto-oncogene \[[@B16-ijms-18-02160],[@B17-ijms-18-02160]\]. Deregulation of the Hippo pathway results in tissue overgrowth and cancer in mammalians. In this signaling network, RASSF1A acts as an upstream activator through its interaction with MST1/2 and WW45 \[[@B13-ijms-18-02160],[@B18-ijms-18-02160]\]. *RASSF1A* is the only tumor suppressor gene that is frequently inactivated in this pathway \[[@B19-ijms-18-02160],[@B20-ijms-18-02160],[@B21-ijms-18-02160]\]. Thus reexpression of RASSF1A induces cell cycle arrest \[[@B22-ijms-18-02160],[@B23-ijms-18-02160]\] and also activates the YAP1 target gene *ANKRD1* \[[@B19-ijms-18-02160]\]. Activation of *ANKRD1* was absent in HeLa cells that harbor an unmethylated *RASSF1A* promoter and express *RASSF1A* \[[@B19-ijms-18-02160]\].
3. Hypermethylation of *RASSF1A* in Human Cancers {#sec3-ijms-18-02160}
=================================================
Initially, we observed that the *RASSF1A* CpG island promoter is frequently hypermethylated in lung cancer \[[@B4-ijms-18-02160]\]. Hypermethylation of *RASSF1A* was revealed not only in non-small cell lung cancer but also in small cell lung cancer \[[@B4-ijms-18-02160],[@B24-ijms-18-02160],[@B25-ijms-18-02160],[@B26-ijms-18-02160]\]. Interestingly, aberrant methylation of the *RASSF1C* CpG island promoter was not observed \[[@B4-ijms-18-02160],[@B24-ijms-18-02160]\]. During the last two decades, it turned out that *RASSF1A* is frequently inactivated in all types of human cancers and promoter methylation of *RASSF1A* has been revealed in cancers from breast \[[@B27-ijms-18-02160]\], liver \[[@B28-ijms-18-02160]\], pancreas \[[@B29-ijms-18-02160]\], prostate \[[@B30-ijms-18-02160]\], renal cell \[[@B31-ijms-18-02160],[@B32-ijms-18-02160]\], brain \[[@B33-ijms-18-02160]\], gastric \[[@B34-ijms-18-02160]\], head and neck \[[@B20-ijms-18-02160]\], pheochromocytoma \[[@B35-ijms-18-02160]\], thyroid \[[@B36-ijms-18-02160]\] and others \[[@B31-ijms-18-02160],[@B37-ijms-18-02160],[@B38-ijms-18-02160]\]. *RASSF1A* hypermethylation is also found in skin cancers including melanoma and Merkel cell carcinoma \[[@B39-ijms-18-02160],[@B40-ijms-18-02160],[@B41-ijms-18-02160]\]. Hypermethylation of *RASSF1A* has been also observed in osteosarcoma and soft tissue sarcomas \[[@B42-ijms-18-02160],[@B43-ijms-18-02160]\]. However, in other cancer entities like cervix carcinoma and colon carcinoma *RASSF1A* hypermethylation is also present but less frequent (\<20%) \[[@B31-ijms-18-02160],[@B44-ijms-18-02160]\]. In blood cancer, *RASSF1A* hypermethylation was frequently found in Hodkin's lymphoma, but was not revealed in chronic myeloid leukemia \[[@B45-ijms-18-02160],[@B46-ijms-18-02160]\]. Interestingly, *RASSF1A* hypermethylation has been correlated with different hallmarks of advanced pathogenesis of cancer, for example with increased progression, advanced staging or metastatic properties \[[@B36-ijms-18-02160],[@B47-ijms-18-02160],[@B48-ijms-18-02160]\]. It has also been reported that *RASSF1A* methylation correlated with a poorer prognosis of cancer patients \[[@B42-ijms-18-02160],[@B48-ijms-18-02160]\]. It has been suggested that *RASSF1A* is one of the most frequently hypermethylated tumor suppressor genes in human cancers and may serve as biomarker for cancer detection \[[@B48-ijms-18-02160],[@B49-ijms-18-02160]\].
Interestingly, we found that normal human mammary epithelial cells, when grown in cell culture for several passages, displayed a senescence-associated hypermethylation of the *RASSF1A* promoter \[[@B50-ijms-18-02160]\]. This indicates that the *RASSF1A* promoter is susceptible to its epigenetic silencing. Recently, we revealed that for tandem-oriented genes, the downstream gene is significantly higher methylated when the transcriptional end site of the upstream gene is in proximity (\<1 kb distance) with the transcriptional start site \[[@B51-ijms-18-02160]\]. The *RASSF1A* promoter is located only 200 bp downstream of the last exon of the *ZMYND10* gene ([Figure 1](#ijms-18-02160-f001){ref-type="fig"}). *ZYMND10* encodes a protein containing a MYND-type zinc finger domain, that likely functions in assembly of the dynein motor \[[@B52-ijms-18-02160]\]. In lung cancer, we observed a hypomethylation of the *ZYMND10* promoter and increased expression of its transcript \[[@B51-ijms-18-02160]\]. This data suggest that through its genomic organization *RASSF1A* is prone to epigenetic silencing. Additionally, in cancer we and others observed that aberrant expression of DNMT1, DNMT3A, DNMT3B and histone deacetylases (HDAC) is involved in the inactivation process of *RASSF1A* \[[@B51-ijms-18-02160],[@B53-ijms-18-02160],[@B54-ijms-18-02160],[@B55-ijms-18-02160],[@B56-ijms-18-02160]\].
4. Demethylation of *RASSF1A* by Treatment of Cancer Cells with Cytidine Analogues {#sec4-ijms-18-02160}
==================================================================================
In contrast to mutated tumor suppressor genes that express aberrant proteins, epigenetically silenced genes are rather infrequently mutated and their reactivation has been postulated as a cure for cancer malignancies \[[@B57-ijms-18-02160],[@B58-ijms-18-02160]\]. Thus, different inhibitors of DNA methylation have been tested, and specifically cytidine analogues are employed in therapy for specific blood cancers \[[@B59-ijms-18-02160],[@B60-ijms-18-02160]\]. In general, these synthetic analogues lead to passive demethylation by inhibiting the methylation of the newly synthetized DNA strand during DNA replication. In contrast to cytidine, which harbors a carbon at position 5 of the base, 5-aza-cytidine and 5-aza-2′-deoxycytidine contain a nitrogen at this position and therefore cannot be methylated by DNMTs. 5-aza-cytidine (trade name: Vidaza or Azadine) and 5-aza-2′-deoxycytidine (trade name: Decitabin or Dacogen) have been approved for the treatment of the myelodysplastic syndrome and other forms of blood cancers \[[@B61-ijms-18-02160],[@B62-ijms-18-02160]\]. Another cytidine analogue that is now in clinical trials for blood cancers is Guadecitabine (SGI-110) \[[@B63-ijms-18-02160]\]. Guadectiabine is a 5-aza-2′-deoxycytidine and 2′-deoxyguanosine containing dinucleotide that is largely resistant to degradation by cytidine deaminase \[[@B64-ijms-18-02160]\].
On molecular level, 5-aza-cytidine and 5-aza-2′-deoxycytidine reactivate the expression of *RASSF1A* in different cancer cell lines \[[@B4-ijms-18-02160],[@B32-ijms-18-02160]\]. Usually, treatment of cancer cells for several days with 1--10 μM of 5-aza-cytidine or 5-aza-2′-deoxycytidine leads to the reexpression of the *RASSF1A* transcript \[[@B27-ijms-18-02160]\]. Consistently, demethylation of the *RASSF1A* promoter was also observed. Treatment of an ovarian cancer cell line with 5 μM SGI-110 (5-aza-2′-deoxycytidine containing dinucleotdide) for two days induced *RASSF1A* hypomethylation and reexpression \[[@B65-ijms-18-02160]\]. Zebularine is yet another DNMT inhibitor and nucleoside analogue of cytidine that reactivates *RASSF1A* \[[@B60-ijms-18-02160],[@B66-ijms-18-02160]\]. It lacks the amino group at position 4 of cytidine and also inhibits cytidine deaminases \[[@B67-ijms-18-02160]\]. A number of studies have provided evidence that several natural compounds found in food and herbs can inhibit DNMT activity or downregulate DNMT expression ([Table 1](#ijms-18-02160-t001){ref-type="table"}) and modulate DNA methylation of tumor suppressor genes, like *RASSF1A* or *p16/CDKNA2* \[[@B68-ijms-18-02160],[@B69-ijms-18-02160]\]. However, there is no naturally occurring substance that function as a cytidine analogue for DNA demethylation.
5. Effects of Methyl Donors and Vitamins on *RASSF1A* Methylation {#sec5-ijms-18-02160}
=================================================================
Folate, methionine, cobalamin (vitamin B12), betaine and choline are natural compounds that serve as natural methyl donor for the DNA methylation reaction \[[@B87-ijms-18-02160],[@B88-ijms-18-02160]\]. These compounds function as precursors to generate S-adenosyl-methionine (SAM) which is then used as a substrate by DNMT to methylated DNA \[[@B88-ijms-18-02160]\]. Dietary methyl donors were shown to have epigenetic effects in mice studies which showed that high maternal intake of folic acid, vitamin B12, choline and betaine can silence a transposable element through its increased methylation \[[@B89-ijms-18-02160]\]. In breast cancer, both positive (hypermethylation) and inverse (hypomethylation) correlations with high intake of methyl donors were observed \[[@B90-ijms-18-02160]\].
Some of these methyl donors were studied regarding their effect on the methylation level of *RASSF1A* ([Table 1](#ijms-18-02160-t001){ref-type="table"}). It has been reported that dietary folate and alcohol intake could be associated with changes in promoter hypermethylation (*RASSF1A* and other TSG) in patients with sporadic colorectal cancer \[[@B91-ijms-18-02160]\]. This study indicated that folate has a protective role against promoter methylation \[[@B91-ijms-18-02160]\]. In another study, the methylation level of a panel of ten genes including *RASSF1A* in blood cells of monozygotic twins with discordant smoking habits was analyzed and the methylation index was correlated with plasma levels of folic acid, vitamin B12 and homocysteine \[[@B70-ijms-18-02160]\]. The increased methylation index of overall promoter methylation (e.g., decreased methylation of *RARB* and *CDH1*), displayed a significant inverse correlation with plasma folic acid levels both in smokers and in non-smokers \[[@B70-ijms-18-02160]\]. However, RASSF1A methylation levels were not significantly lower in subjects with higher plasma folic acid levels (\>4.6 ng/mL) \[[@B70-ijms-18-02160]\]. Other data for lung cancer suggested that smoking, sex, and alcohol intake had a strong influence on the methylation levels of single genes (*RASSF1A* and *MTHFR*), whereas folate intake had no significant influence on their methylation states \[[@B92-ijms-18-02160]\]. The *methylene tetrahydrofolate reductase* (*MTHFR*) gene encodes an enzyme in the folate cycle and is important for generating the active form of folate, which is then used in the methionine cycle to synthesize the methly-donor SAM (S-adenosyl-methionine) for the DNA methylation reaction \[[@B93-ijms-18-02160]\]. Interestingly genetic polymorphisms of *MTHFR* have been associated with an increased risk of cancer \[[@B93-ijms-18-02160],[@B94-ijms-18-02160]\] and hypermethylation of *RASSF1A* \[[@B95-ijms-18-02160],[@B96-ijms-18-02160]\]. Others have investigated the effect of methionine on *RASSF1A* methylation levels \[[@B71-ijms-18-02160],[@B72-ijms-18-02160]\]. Vineis et al. examined the association between DNA methylation patterns of candidate genes and the level of methionine in the blood of lung cancer patients \[[@B72-ijms-18-02160]\]. They report that folate levels were correlated with increased methylation of *RASSF1A* and *MTHFR*, but methionine levels were associated with decreased methylation of *RASSF1A* \[[@B72-ijms-18-02160]\].
Vineis et al. also analyzed vitamin Bs with the methylation of *RASSF1A* and other TSG. Their data suggest that increased vitamin B12 levels are correlated with a decrease of *RASSF1A* methylation in former smorkers \[[@B72-ijms-18-02160]\]. In breast cancer patients, the level of dietary methyl donors was correlated with the promoter hypermethylation status of *retinoic acid receptor-beta (RARB)*, *BRCA1* and *RASSF1A* \[[@B71-ijms-18-02160]\]. There was no association with nutritional intakes and *RASSF1A* methylation, but high dietary intake of folate increased the chance of demethylation-dependent expression of *BRCA1* \[[@B71-ijms-18-02160]\]. In another study, randomized breast cancer patients received daily supplements of co-enzyme Q10, riboflavin and niacin (vitamins B2 and B3, respectively) along with tamoxifen \[[@B97-ijms-18-02160]\]. A significant decrease in *RASSF1A* methylation was found in patients treated with nutritional supplements compared to control patients \[[@B97-ijms-18-02160]\]. The exact mechanism that regulates preferential modulations of DNA methylation levels of a specific set of genes by methyl donors and vitamin Bs in specific cancer types is still enigmatic \[[@B72-ijms-18-02160]\]. Other vitamins that target DNMT are retinoic acid (vitamin A) \[[@B98-ijms-18-02160]\] and cholecalciferol (vitamin D3) \[[@B99-ijms-18-02160]\], but these were not tested for their effects on the *RASSF1A* methylation level in cancer cells.
6. Impact of Naturally Occurring Polyphenols on *RASSF1A* Methylation {#sec6-ijms-18-02160}
=====================================================================
Several natural occurring compounds are derivates of polyphenols including resveratrol, curcumin, genistein and epigalloctechin-3-gallate (EGCG) and these regulate DNMT activity or expression \[[@B100-ijms-18-02160],[@B101-ijms-18-02160]\]. Some of these substances have been tested for the capacity to reactivate *RASSF1A* ([Table 1](#ijms-18-02160-t001){ref-type="table"}). Scoccianti et al. have analyzed a group of smokers who were on a normal isocaloric diet or a diet enriched with flavonoids of green tea and soy products \[[@B102-ijms-18-02160]\]. They analyzed the methylation level of *RASSF1A* and other regions (e.g., LINE1 with 72% methylation level) in white blood cells of smokers before and after four weeks of diet. The methylation level of *RASSF1A* was not affected by these diets, since it was rather unmethylated. However, repetitive poly-A retrotransposons (LINE1) showed a small but significant increase (1--2%) in their methylation levels \[[@B102-ijms-18-02160]\].
The green tea polyphenol EGCG inhibits DNMTs and reactivates silenced TSG and DNA repair genes (*p16* and *MLH*1, respectively) through their demethylation in cancer cell lines \[[@B73-ijms-18-02160]\]. Fang et al. also compared the demethylation capacity of EGCG to 5-aza-2′-deoxycytidine and showed that a treatment with 50 μM EGCG is comparable to 8.7 μM 5-aza-2′-deoxycytidine \[[@B73-ijms-18-02160]\]. The effect of EGCG on the reactivation or demethylation of *RASSF1A* has not been reported ([Table 1](#ijms-18-02160-t001){ref-type="table"}). Resveratrol and curcumin function as antioxidants, but also regulate DNMT activity \[[@B103-ijms-18-02160]\]. Resveratrol has been tested for its capacity to reactive TSG in cancer cells \[[@B74-ijms-18-02160],[@B99-ijms-18-02160]\]. It has been reported that resveratrol demethylates *RASSF1A* in women with increased breast cancer risk \[[@B74-ijms-18-02160]\]. Women with an increased breast cancer risk were treated with trans-resveratrol twice a day for 12 weeks. Methylation assessment of four cancer-related genes including *RASSF1A* was performed on mammary ductoscopy specimens and *RASSF1A* methylation decreased with increasing levels of serum trans-resveratrol \[[@B74-ijms-18-02160]\].
Curcumin is a polyphenol isolated from turmeric which inhibits DNMT and is a potential chemo-preventive substance \[[@B104-ijms-18-02160],[@B105-ijms-18-02160]\]. It has also been demonstrated that curcumin (10--20 μM for 72 h) can enhance the expression level of *RASSF1A* and decrease its promoter methylation in breast cancer MCF7 cells \[[@B76-ijms-18-02160]\]. Curcumin also reactivates *RARB* by decreasing its DNA methylation level in lung cancer cell lines \[[@B75-ijms-18-02160]\].
Several polyphenols from the soy bean, including the isoflavones genistein and daidzein, were tested for their capacity to reactivate TSG \[[@B77-ijms-18-02160],[@B78-ijms-18-02160],[@B101-ijms-18-02160]\]. It has been shown that these isoflavones regulate DNMT expression or inhibit DNMT activity \[[@B69-ijms-18-02160],[@B101-ijms-18-02160],[@B106-ijms-18-02160]\]. In prostate cancer cells the demethylation effects of genistein and daidzein were compared to 5-aza-cytidine for *RASSF1A* and other hypermethylated promoters \[[@B78-ijms-18-02160]\]. After treatment by soy isoflavones, demethylation of certain promoter regions (*GSTP1* and *EPHB2*) occurred ([Table 1](#ijms-18-02160-t001){ref-type="table"}), but this was not observed for *RASSF1A* \[[@B78-ijms-18-02160]\]. Vardi et al. also compared the demethylation capacity of genistein to 5-aza-cytidine in prostate cancer cell lines and showed that 40 μM genistein is comparable to 2 μM 5-aza-cytidine treatment \[[@B78-ijms-18-02160]\]. Qin et al. treated premenopausal women daily with isoflavones through one menstrual cycle and analyzed the methylation of *RASSF1A* and other cancer-related genes in intraductal samples \[[@B77-ijms-18-02160]\]. They reported that isoflavones induced dose-specific changes in *RARB* and *CCND2* (*cyclin D2*) methylation. High genistein levels correlated with increased methylation of *RARB* and *CCND2* \[[@B77-ijms-18-02160]\]. Again, *RASSF1A* methylation was not significantly affected by this treatment, indicating that genistein is not involved in selective demethylation of the *RASSF1A* locus ([Table 1](#ijms-18-02160-t001){ref-type="table"}).
Emodin is a natural polyphenol and anthraquinone derivate from *Rheum palmatum* \[[@B107-ijms-18-02160]\]. Zhang et al. utilized 40 μM emodin to treat pancreatic cancer cells for three days and analyzed the effect on the methylation levels of *RASSF1A* \[[@B80-ijms-18-02160]\]. They reported the demethylation of *RASSF1A*, *p16* and *preproenkepahlin* (*ppENK*) and that emodin downregulates DNMT levels ([Table 1](#ijms-18-02160-t001){ref-type="table"}). Subsequently they showed that *RASSF1A* demethylation by 40 μM emodin is comparable to 1 μM 5-aza-2′-deoxycytidine treatment and *RASSF1A* demethylation is enhanced by co-treatment with emodin and 5-aza-2′-deoxycytidine \[[@B79-ijms-18-02160]\].
Peperomin E is another natural polyphenol that has been utilized to study the reactivation of *RASSF1A* ([Table 1](#ijms-18-02160-t001){ref-type="table"}). Peperomin E is a bioactive secolignan from the plant *peperomia dindygulensis* \[[@B108-ijms-18-02160]\]. Peperomin E binds to the active pocket of DNMT1 and reduces DNMT1 levels \[[@B81-ijms-18-02160]\]. Wang et al. treated lung cancer cells with 0.5--2 μM peperomin E for 48 h and analyzed the methylation and expression of *RASSF1A* and other TSG \[[@B81-ijms-18-02160]\]. It was shown that the treatment with 2 μM of peperomin E resulted in the demethylation and reexpression of *RASSF1A*, *p16*, *APC* and *RUNX3* in A549 lung cancer cells \[[@B81-ijms-18-02160]\]. Wang et al. also showed that the treatment with 2 μM peperomin E is comparable to 2 μM of 5-aza-2′-deoxycytidine in its demethylation capacity \[[@B81-ijms-18-02160]\]. They propose that peperomin E may serve as a potential chemotherapeutic agent for non-small cell lung cancer, since it also promotes apoptosis and cell cycle arrest \[[@B81-ijms-18-02160]\].
Dioscin is a polyphenolic component isolated from *Phyllanthus amarus* which exhibits anti-oxidative activity \[[@B109-ijms-18-02160]\]. This substance was utilized to treat bladder cancer cell lines and to analyze its effect on the *RASSF1A* and *DAPK1* expression and methylation \[[@B82-ijms-18-02160]\]. After 48 h of treatment with 5 and 25 μg/mL dioscin, bladder cancer cells showed induced *RASSF1A* levels and this increase was correlated with *RASSF1A* demethylation \[[@B82-ijms-18-02160]\]. However, the impact of dioscin on DNMT expression and activity was not analyzed ([Table 1](#ijms-18-02160-t001){ref-type="table"}).
7. Effects of Other Natural Compounds on *RASSF1A* Methylation {#sec7-ijms-18-02160}
==============================================================
Mahanine is a carbazole alkaloid from plants (e.g., curry tree/*Murraya koenigii*) with antioxidative activity \[[@B110-ijms-18-02160]\]. It has also been shown that mahanine inhibits DNMT activity \[[@B83-ijms-18-02160],[@B84-ijms-18-02160]\]. Mahanine (1--3 μg/mL) was utilized to treat cancer cells and to reactive *RASSF1A* expression. *RASSF1A* rexpression was observed in prostate, breast and lung cancer cell lines \[[@B84-ijms-18-02160],[@B85-ijms-18-02160]\]. Further data suggest that mahanine is involved in demethylation of the *RASSF1A* promoter \[[@B83-ijms-18-02160]\].
Phenethyl isothiocyanate (PEITC) is a natural compound from cruciferous vegetables that possesses anti-cancer activities \[[@B111-ijms-18-02160]\]. Boyanapalli et al. treated prostate cancer cells with 5 μM PEITC for 5 days and analyzed the *RASSF1A* methylation and expression levels \[[@B86-ijms-18-02160]\]. They reported that this treatment induced *RASSF1A* expression by its promoter demethylation ([Table 1](#ijms-18-02160-t001){ref-type="table"}). Boyanapallli et al. also showed that demethylation of *RASSF1A* by treatment with 5 μM of PEITC is comparable to 2.5 μM of 5-aza-2′-deoxycytidine \[[@B86-ijms-18-02160]\]. Furthermore, it was shown that PEITC significantly reduced DNMT1, DNMT3A and DNMT3B protein levels \[[@B86-ijms-18-02160]\]. However, other genomic regions have not been analyzed so far.
8. Conclusions {#sec8-ijms-18-02160}
==============
Several natural occurring substances have already been utilized to study their epigenetic activity and to analyze the effect on *RASSF1A* reactivation ([Table 1](#ijms-18-02160-t001){ref-type="table"}). The role of methyl donors (e.g., folate and vitamin B12) on the regulation of methylation levels of *RASSF1A* should be analyzed in further detail and the precise mechanism that modulates this methylation needs to be elucidated. It has also been reported that vitamin A and vitamin D regulate DNMT expression and revert the epigenetic silencing of TSG. Thus it would be interesting to test these substances and others for *RASSF1A* demethylation and to elucidate the pathways involved in the reactivation process. Several polyphenols, like EGCG and genistein, inhibit DNMT activity and the treatment with these polyphenols lead to demethylation of certain TSG. However, methylation of *RASSF1A* was not affected by some of these compounds (e.g., genistein). In contrast, conventional demethylating agents such as synthetic cytidine analogues (e.g., 5-aza-2′-deoxycytidine) lead to reactivation of *RASSF1A*. Mahanine and peperomin E are also compounds that reactivate *RASSF1A* by inhibiting DNMT activity. The selective mechanism of some substances (e.g., methyl donors), that on the one hand side promote demethylation of certain TSG but on the other hand cause hypermethylation of other regions (e.g., retrotransponsons), remains enigmatic. Further efforts are needed to address distinct pathways responsible for selective demethylation of TSG like *RASSF1A*.
This work was supported by the German Center for Lung Research (DZL).
The authors declare no conflict of interest. The founding sponsors had no role in the writing of the manuscript.
RASSF
Ras Association Domain Family
TSG
tumor suppressor gene
DNMT
DNA methyltransferase
HDAC
histone deacetylase
EGCG
epigalloctechin-3-gallate
LINE1
long interspersed nuclear element 1
PEITC
phenethyl isothiocyanate
aa
amino acids
{#ijms-18-02160-f001}
{#ijms-18-02160-f002}
ijms-18-02160-t001_Table 1
######
Natural compounds tested for *RASSF1A* reactivation in cancer.
Compound Effect on *RASSF1A* Effect on Other Genes Mechanism References
------------- --------------------------------------------------------------------------------------------------------- ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- ---------------------------- --------------------------------------------------------------------
folate no effect \[[@B70-ijms-18-02160],[@B71-ijms-18-02160]\], increased methylation \[[@B72-ijms-18-02160]\] decreased methylation of *RARB* \[[@B70-ijms-18-02160],[@B71-ijms-18-02160]\], *BRCA1* \[[@B71-ijms-18-02160]\] and *CDH1* \[[@B70-ijms-18-02160]\], increased *MTHFR* methylation \[[@B72-ijms-18-02160]\] methyl donor \[[@B70-ijms-18-02160],[@B71-ijms-18-02160],[@B72-ijms-18-02160]\]
methionine decreased methylation decreased methylation of *p16* and *MTHFR* methyl donor \[[@B72-ijms-18-02160]\]
vitamin B12 decreased methylation increased *MTHFR* methylation \[[@B72-ijms-18-02160]\] methyl donor \[[@B71-ijms-18-02160],[@B72-ijms-18-02160]\]
EGCG ^a^ not analyzed decreased methylation of *p16*, *RARB*, *MGMT* and *MLH1* inhibits DNMT ^b^ activity \[[@B73-ijms-18-02160]\]
reseveratol decreased methylation no effect on *p16*, *APC* and *CCND2* methylation downregulation of DNMT \[[@B74-ijms-18-02160]\]
curcumin decreased methylation decreased methylation of *RARB* \[[@B75-ijms-18-02160]\] downregulation of DNMT \[[@B76-ijms-18-02160]\]
genistein no effect increased methylation of *RARB* and *CCND2* \[[@B77-ijms-18-02160]\], decreased methylation of *GSTP1* and *EPHB2* \[[@B78-ijms-18-02160]\] inhibits DNMT \[[@B77-ijms-18-02160],[@B78-ijms-18-02160]\]
emodin decreased methylation decreased methylation of *p16* and *ppEN*K downregulation of DNMT \[[@B79-ijms-18-02160],[@B80-ijms-18-02160]\]
peperomin E decreased methylation decreased methylation of *p16*, *APC* and *RUNX3* inhibits DNMT activity \[[@B81-ijms-18-02160]\]
dioscin decreased methylation decreased methylation of *DAPK1* antioxidant \[[@B82-ijms-18-02160]\]
mahanine decreased methylation not reported inhibits DNMT activity \[[@B83-ijms-18-02160],[@B84-ijms-18-02160],[@B85-ijms-18-02160]\]
PEITC ^c^ decreased methylation not reported downregulation of DNMT \[[@B86-ijms-18-02160]\]
^a^ epigalloctechin-3-gallate; ^b^ DNA methyltransferase; ^c^ phenethyl isothiocyanate.
| {
"pile_set_name": "PubMed Central"
} |
Why A New Federal Harassment Law Is A Bad Idea
Azhar Majeed writes for FIRE (Foundation for Individual Rights in Education, defending free speech rights for all on campuses) that Senator Frank Lautenberg is trying to enact a new law against harassment and cyberbullying on campus. Problem is, it could do damage to free speech rights on campus.
Plus, Debra J. Saunders writes for SFGate that Rutgers, where Tyler Clementi recently killed himself after being videotaped being sexual with another guy, already has such a policy in place -- with offenses potentially leading to expulsion:
The list includes "intentionally or recklessly endangering the welfare of any individual" - but more to the point, "making or attempting to make an audio or video recording of any person(s) on University premises in bathrooms, showers, bedrooms, or other premises where there is an expectation of privacy with respect to nudity and/or sexual activity." Under "prohibited conduct," Rutgers lists "cyberbullying."
"I was a little puzzled" by the Lautenberg press release, Robert L. Shibley, senior vice president of the Foundation for Individual Rights in Education (FIRE), told me. "As terrible as the Tyler Clementi case was - and it was - it was already forbidden by harassment policies that every university in America has on the books."
And: "You don't need a new law to know that that's illegal." In fact, New Jersey prosecutors have charged two students with two counts each of invasion of privacy.
Shibley is concerned, and rightly so, that a new law would "attempt to ban speech that is protected by the First Amendment." Wouldn't be the first time a student code of conduct was used to stifle politically incorrect speech. In 2007, a San Francisco State student board filed a complaint against conservative students who held an "anti-terrorism rally" at which they stepped on Hamas and Hezbollah flags because they exhibited "hateful religious intolerance."
When I mentioned that Rutgers already has the policies Lautenberg advocated, spokeswoman Gail Ribas responded, "It would be a national law."
No, it would be a national imposition. It would be another feel-good bill that a headline-happy senator offered without appearing to have asked himself if the law is redundant, necessary or likely to help. Like so much that comes out of Washington these days, it would be clutter.
Comments
"I'll just propose this law, get some headlines, then it will never make it to a vote." He's basically campaigning.
Worse, what if the law does make it onto the books? Yet another unneeded law adding to the already far too huge complex of laws already on the books.
There needs to be some disincentive for creating new laws. Something to make Congress stop and think: "do we really, really need this?" The best suggestion I have seen is simply to limit the total laws on the books. Something like one million plain-english words of law that can apply to individuals, and another one million for businesses. If you want a new law, then you have to throw an old one out.
One million words is a tiny, tiny fraction of what currently exists. But it is the upper limit of what you can expect a normal person to be aware of - about 10 thin novels, or 4 really fat ones. And State and local laws are still to be added in.
bradley13
at October 23, 2010 12:49 AM
Not surprised. Tragic as Tyler Clementi's case was, it was still one incident. I've reached the point where, if something like this happens - one tragic event that the media seizes upon drags out like one of Meatloaf's romantic ballads - I simply wait for the inevitable public outcry for new, redundant laws.
I haven't been surprised by this since Matthew Shepard. Tragic and appalling, certainly, but demanding new laws is an overreaction. Wyoming and the nation already have laws against kidnapping, assault, battery, detaining someone against their will, and murder, homicide, manslaughter, etc. Henderson and McKinney were brought to justice without new laws, laws, laws.
So by the time Tyler Clementi came around, it was just a matter of time before the demand for laws, laws, laws.
Never mind that the idiots who streamed Clementi's romantic tryst are already charged with two counts of invasion of privacy. The justice system appears to be working as intended. If somehow, these two jerks get off scot-free, I might understand the demand for new laws, but please, give the system a chance first.
And lets not forget that if Clementi had chosen to laugh this off instead of killing himself, none of us would have heard about it anyway.
Patrick
at October 23, 2010 1:07 AM
Hey, you do this to yourself. You (of course, not me) insist that your legislators make more laws!
Lawmaking is a capitalist venture. Everybody thinks that more means better!
Radwaste
at October 23, 2010 6:16 AM
The problem that I have with this law is that it will be used for nefarious purposes.
Already -- if you want to campaign for open or concealed carry on campus you are shouted down. Gun owners are dangerous.
It is my understanding that the two students that violated Clementi's privacy will not be charged with anything really except for invading privacy since the state/local laws did not have appropriate protections against the specified behaviour. They cannot be charged by a prosecutor for violating the law at the college. The college can act on college laws and their actions are simply limited to grades and suspension/expulsion.
Local laws have not kept up with all the available ways modern technology can be used to invade privacy, harass, bully, intimidate etc.
So new laws probably are needful. I am not certain if the proposed law is one of them.
LauraGr
at October 23, 2010 7:10 AM
Laura, I don't think that's correct. According to this article, they could be facing five years in prison for "third and fourth degree invasion of privacy" (and I have no idea what that's supposed to mean, committing invasion of privacy to the third and fourth degree).
I've been hearing, although I can't find an article about it right now, that they'll be facing two counts each.
I have no issue with this...unless these two clowns get off on a technicality or something.
Patrick
at October 23, 2010 7:22 AM
Patrick, I think you and I basically said the same thing. They will be charged with invading his privacy.
They will not be charged with anything else because there are no other relevant laws that can be used in this instance.
I could be wrong. I'm ignorant about many subjects but I am willing to learn. I'll need to finish my coffee first, though.
LauraGr
at October 23, 2010 7:30 AM
No one wants to hear this, but most cases of bullying are reciprocal. They're the result of a mutual antagonism and only become bullying when one party gets the upper hand. That's not to say that there aren't incidents where the bullying becomes egregious and one party is clearly in the wrong, but they aren't as easy to define as people assume. There isn't a class of perfect bully victims out their for us to save.
I've followed this issue for a while through my sister, who's a school counselor in NJ. What's apparent is that there's an element among anti-bullying activists that see bullying as a catch-all for their social agenda. They're not only interested in physical bullying and deliberate emotional harm. They want to prescribe all sorts of speech and expression, and behavior, to the point that they're basically dictating the content of all personal communication, and even who you must communicate with.
For instance, they regard exclusion as a form of bullying, and so they want to prevent children from forming tight groups of friends. This is where the anti-best-friend agenda comes from.
Their list of bullying behaviors is endless, because they are defined by the potential subjective impression of the self identified victim. You'll also notice that they tend to track the interests of the activists. One woman that my sister has dealt with is fixated on 'food choices'. She's convinced that kids are being bullied over the food in their lunches. Not surprisingly, she also sees 'food choices' as the underpinning of all sorts of other social problems as well, like war and aggression.
lola
at October 23, 2010 8:29 AM
Wyoming and the nation already have laws against kidnapping, assault, battery, detaining someone against their will, and murder, homicide, manslaughter, etc.
This is why I don't like hate crime legislation. If it's against the law to kidnap and murder anyone, it doesn't matter why you did it or to whom you did it. You did it and should be punished according to the law.
Hate crime legislation is the law is saying some people are more valuable than others and that their murder demands extra punishment.
Conan the Grammarian
at October 23, 2010 1:47 PM
Conan: Hate crime legislation is the law is saying some people are more valuable than others and that their murder demands extra punishment.
I do share your opposition to hate crime legislation...I'm not sure I agree with the message it sends, though.
While I can understand the particularly despicable nature of bias crime -- you go out and kill someone that you probably don't even know who probably never did anything to you, as opposed to someone you might have a grievance against.
Bias crime suggests that the perpetrator would do something similar to all members of this particular category.
I'm not going to get into the "punishing thought" argument, though. We've punished people based on motives for as long as we've had laws in this country, ergo, we've always punished thought.
It just seems to me that if know someone killed someone else, deliberately, and can determine that it was premeditated, we've sufficiently scrutinized the case.
It's not that it suggests that some people are more valuable than others...it's presuming that you would do the same thing to someone else of the same category.
Let's not start presupposing what a person will do if they haven't actually done it, and no evidence exists that they're going to. Yes, these thugs killed Matthew Shepard, and yes, they did it because he was gay. Would they do the same thing to other gays if they didn't get caught? Maybe...I don't know. But Bias Crime Legislation accusingly points the finger and says, "Yes, they would!"
Unless you can find concrete evidence that they were indeed planning to kill someone else, gay or not, I'm against charging people with crimes they haven't committed.
I wonder how many of us would be in jail simply for wanting to kill someone.
...if Clementi had chosen to laugh this off instead of killing himself, none of us would have heard about it anyway.
I don't know. Some things you can't just laugh off. Being made into the star of a secretly-taped Internet porn video by your college roommate is one of them.
But suicide isn't the answer. You can file a civil lawsuit, a complaint with the university, or even criminal charges (if applicable).
Conan the Grammarian
at October 23, 2010 2:14 PM
I wouldn't have expected him to laugh it off, really. But then again, what he did do was out of proportion as well. I simply took it to the other extreme. Your suggestions are much more realistic.
Patrick
at October 23, 2010 2:38 PM
" There isn't a class of perfect bully victims out their for us to save."
I can't agree here. There is a certain class of people that you can peg as being bully fodder, and another certain class that are bullies. Most people, thank god, are in between. I've never (which is not to say it's never happened) heard of a football player being bullied to the extreme that it makes news. But the effiminate/butch/scrawny/smart "different" kid? Yep. And call me crazy, but I think a kid has the right to grow up liking Dungeons and Dragons (totally dating myself here) as opposed to sports without being tormented for it.
At my 1st graders school, they have an inclusive policy. Classes line up for lunch, walk in, and sit at the class table in the order they come in, in. No saving seats, no sitting by friends from another class. They also-as much as possible-break up classes year to year so no clique stays together. I've railed against this to my DH as my daughters got separated from their special friends. And I see that "vulnerable" students are also probably losing their support system, but in this area, I can't fault schools for trying. And there IS no "popular crowd" at this school.
DO we need new laws? Maybe-technology advances. That's about as definitive as I can get on this. It's tough.
momof4
at October 23, 2010 8:18 PM
> There is a certain class of people that
> you can peg as being bully fodder
No, or you'd have "pegged" them already. The purpose of civilization is not to give everyone a 100% unremarkable position in life, as if we all had the same personalities, vigor and drive.
Crid [CridComment at gmail]
at October 24, 2010 2:08 AM
Dungeons and Dragons (totally dating myself here)
Er, I still play D&D. My half-orc fighter is badass.
The purpose of civilization is not to give everyone a 100% unremarkable position in life, as if we all had the same personalities, vigor and drive.
None of momof4's school's policies would do that, anyway. People will always find a way to be remarkable, or not.
Bullying isn't just a phase all kids go through that builds character or some such nonsense. If I had to worry every time I got up to use the bathroom at work that some of my co-workers were going to jump me on the way there, I would have a problem with that. Adults don't take bullying among children very seriously because we're not afraid of those bullies.
MonicaP
at October 24, 2010 5:27 PM
> People will always find a way to be
> remarkable, or not.
That is SO, SO not true. That's the psychotic belief of the Obama Administration, whose endlessly burdensome taxation policies presume that there will always be an unseen fountain of wealth out there.... Unseen to them at least, because none of them have ever created any wealth.
No... You're wrong. Impulses in society to perfectly, PRISSILY shelter the weak and idiots from pain and challenge will always, always interrupt the feedback loops which allow ALL people to better serve their fellows.
You are mistaken. If you want to protect the timid and the daft from bullies, it's OK by me. Beyond that, keep your hands to yourself.
Crid [CridComment at gmail]
at October 25, 2010 5:17 AM
I was bullied in grade school. Nothing physical, but constant taunts about pretty much everything else. And there was a point when I was 10 that I wanted to kill myself over it. I'm very grateful I didn't as I like myself these days.
Bullying is not always done just because the person is a dick (though it might be). A lot of the time bullies themselves have self esteem issues and they're acting out because they need to feel better about themselves. Or they're trying to look cool to their peers.
While it's tragic that somebody might kill themselves over bullying (even in these extreme cases), you have to keep in mind that THEY MADE THAT CHOICE. Was it the best option? Not so much.
However, instead of imposing laws on our free speech (there's too many already!) The best we can do is make sure that "vulnerable" people (nerds/homosexuals/etc.) have a strong support system. If bullies are so identifiable as jocks (/sarcasm), shouldn't potential victims be? To me this not not mean more useless legislation.
This means that we, as individuals, treat each other as human beings. Yes, there are bad people out there (and they're always making the news!) but there are lots of good people as well. If you take the time to stop and look around, sometimes you can be the person who makes a difference in somebody else's life.
However, I refuse to advocate anything that imposes on free speech. "I may not agree with what you say, but I will defend to the death your right to stay it." Free speech does not exist to protect popular ideas, it exists to protect unpopular ones.
Cheryl
at October 25, 2010 12:30 PM
If it comes from Lautenberg, you're pretty safe in concluding that it's bad. He's one of the biggest big-government nanny-state dirtbags out there. | {
"pile_set_name": "Pile-CC"
} |
Real Estate Development Project Modeling (Marquee) – Webinar
May 27 @ 8:30 am - May 28 @ 5:00 pm
Description
This advanced hands-on course reviews real estate project development concepts and focuses on the skills required to design and create a model to help finance professionals evaluate a real estate development investment. Using a mixed-use development case study, the course reviews concepts including model design, logic, project timing and various financing structures. PLEASE NOTE, all course times are EDT. | {
"pile_set_name": "Pile-CC"
} |
Cardi B Not Hiding from Baby Talk, Drawing Attention to Her Belly
Cardi B isn't SAYING she's pregnant, but she's sure playing it up to max at New York Fashion Week. Cardi showed up at the Marc Jacobs show Wednesday night in a colorful dress that included a giant bow tied right over her belly. She's no fool and...Read more ...
Join us from 10am EST as we stream live from the Tory Burch Fall/Winter 2018 fashion show.Read more ...
All About the Bold Beauty Look at Marc Jacobs' Fall/Winter 2018 Fashion Show
Marc Jacobs is no stranger to creating some of the boldest, most talked-about and at times controversial looks for his New York Fashion Week runway shows. And this season is no different.
From gigantic colored dreadlocks to grungy top hats to colorful head scarves , the designer and Redken Global Creative Director and lead hairstylist Guido Palau always push the boundaries when it comes to the models' hairstyles each season. This time, Jacobs wanted to play with hair accessories again, and put almost all of the models in hijab-like colorful scarves wrapped around their head and neck and...Read more ...
Love Story, Now Playing at Story
NEW YORK - Story, the Chelsea neighborhood retailer that changes its theme every four to eight weeks, is celebrating Valentine's Day through March 11 with Love Story. But founder Rachel Shechtman isn't clobbering consumers over the head with clichés employed by other retailers such as cheeky greeting cards, heart-shaped chocolates, red roses and risqué lingerie.
Rather, she conjured up a love story with multiple meanings. There's loving Story, the store, and the way Shechtman lovingly chose brands for the concept. Also, gifts that will be beloved, and most importantly, self-love.
“It's not...Read more ...
Esteban Cortazar RTW Fall 2018
In 2002, Esteban Cortazar launched his namesake label in New York, but for the past 12 years has been based out of, and shown, in Paris. For his fall collection,”I'd been toying a lot with the idea of celebrating the different cities where I've grown, where I've nurtured my brand,” the Peruvian-born designer explained. That notion is what inspired his return to NYFW. In particular, his fall line was a love letter to South America. “A tapestry of different ideas, different experiences,” he said backstage of the many ideas that went into the collection.
Cortazar said wool and cashmere blend...Read more ...
We rounded up the best hair and makeup looks from NYFW Fall 2018, like the graphic eyes at Sies Marjan and Jeremy Scott and the claw clips at Alexander Wang.Read more ...
The Coolest Beauty Looks You Probably Missed At NYFW
A brief recap of what we learned at Fall/Winter 2018 New York Fashion Week: Western fringe can work on your manicure , millennial pink is officially out , and athleisure hair is the new tousled beach wave. But those are just the trends we spotted backstage or on the actual runway - and there's one crucial part of the scene, low-key packed with beauty inspiration, that hasn't been accounted for. Yet. Now's the time to turn your attention to the front row, because with over 300 shows on the official fashion calendar and audiences so large even insiders find themselves in standing-room only...Read more ...
Jeremy Scott Fall 2018: New York Fashion Week
Jeremy Scott NYFW FW18
If a humanoid alien dropped to Earth today and needed to be at school in an hour, I imagine they would look just like this collection. In a blatant act of rebellion towards fall/winter grays and jewel tones, Jeremy Scott's FW18 collection, like many others this season, has decided pastels and neon are for winter. And why not? They look pleasing against a dreary snowy day.
The neon bob wigs caused a storm of social media twittering and, I'm guessing, a flurry of salon appointments, if only to obtain the shocking red orange color that we've seen at Alexander Wang. Some...Read more ...
Vivienne Hu Fall 2018: New York Fashion Week
Vivienne Hu NYFW FW18
New York based womenswear label, Vivienne Hu, is pleased to unveil the latest collection for Autumn/ Winter 2018 with a runway show held on Tuesday, February 13that Spring Studios in Tribeca for New York Fashion Week.For the first time since the brand launched in 2012, Creative Director Vivienne Hu looked to her Chinese heritage, particularly the historic DunHuangMogao Grottoes, for inspiration when creating this latest, vibrant offering.
Vivienne Hu: NYFW FW18
Known as the Thousand Buddha Grottoes, the Mogao caves sit at a cultural and religious crossroads on the...Read more ...
Vivienne Tam Fall 2018: New York Fashion Week
Vivienne Tam NYFW FW18
The collection is inspired by a spiritual expedition through the Himalayas to Tibet, evoking the infinite essence of love, and the discovery of its vibrant topography, art, culture and indigenous people. Exploration of this mystical landscape imbued with a sense of timelessness, finds expression in a compelling collection that imagines the urban traveler's journey over the mountainous terrain in pilgrimage.
Vivienne Tam: NYFW FW18
The collection, rendered in varying hues of burnt orange, gradations of earthy khaki, red, burgundy, brown, blue, deep turquoise and Tara...Read more ...
Puppy Power: Anthony Rubio Fall 2018: New York Fashion Week
Anthony Rubio NYFW FW18
Pet couturier Anthony Rubio is no stranger to the runways, having done runway shows for nearly ten years with the last five during fashion week. He had a plan in place to break the stigma and barriers presenting his canine couture as escorted by human models wearing his women's wear fashions at the historic Angel Orensanz Center, originally a Synagogue built in 1850.
Anthony Rubio: NYFW FW18
From Anthony Rubio
The ideas and inspirations for my Fall/Winter 2018 collection for New York Fashion Week just fell on my lap. The new Lunar New Year is The Year Of The Dog. I...Read more ...
Prabal Gurung Fall 2018: New York Fashion Week
Prabal Gurung NYFW FW18
The power of the woman was celebrated in Prabal Gurung's AW18 collection. Many shades of vibrant pink, red and purplegraced the runway, some in the form of cashmere oversized slouchy knits, some elegant draped saris. Baggy jumpers were teamed with flowing skirts, spaghetti strapped dressed were embellished with sequins or feathers and colour blocking was apparent in every look.
Prabal Gurung: NYFW FW18
Not for the timid, this was a collection designed to empower women by giving them outfits that were bold and brazen. Inspired by strong women activists in Northern...Read more ...
Chocheng Fall 2018: New York Fashion Week
Chocheng NYFW FW18
Inspired by the glamourous and unconventional beauty from the 1958 film “Auntie Mame”, CHOCHENG's Fall Winter 18 collection was a modern take on classic British tailoring and crisp equestrian jackets. Titled “Mame”, the brand put out 34 looks in beautiful fabrics comprisedof cotton boucles, Scottish cashmeres and silk tulles.
Presented in Greenwich Village, CHOCHENG created another collection appealing to the brand's following. A clientele who value not only quality craftsmanship, but also have a strong stance on sustainability.
Chocheng: NYFW FW18
Known for using 100%...Read more ...
Oxford Fashion Studio Group Show: Rachel Pollack, Tadazzleme, Shabeeg, Mirochoa, and B. Zarina NYFW FW18
In the airy Studio 450, where the light of day oozed out of the city, Oxford Fashion Studio presented a group show of emerging designers. These kinds of showcases are always a delight, since you never know where you'll find the designer next and perhaps you'll be able to fondly look back at their stint in a smaller venue as an emerging designer. It's a wonderful space to watch the beginnings of a designer's evolution.
Oxford Fashion Studio Group Show: Rachel Pollack, Tadazzleme...Read more ...
Yuna Yang Fall 2018: New York Fashion Week
Yuna Yang NYFW FW18
Models sashayed through the halls of the Margo Feiden Gallery in Greenwich Village presenting Yuna Yang's bespoke womenswear collection.
“Love Yourself”, the title of her collection, was embellished across the front of hats, on the backs of jackets and down the sides of sleeves. According to press notes, she “wanted to send a message about the importance of loving yourself. Every woman, regardless of race and status, should be treated fairly and equally”. Aresonating message that coincides with the current changing landscape, not just in fashion, but throughout every...Read more ...
Interview With Pamella Roland: Fall 2018
Pamella Roland: Fall / New York
When asked about the inspiration behind this collection, designer Pamella DeVos proudly stated just one word- “Prague”.
A trip to Prague that was originally just for her son's hockey game resulted in an opportunity to gain great inspiration for this collection as she was able to explore the city in depth. The jewel toned colors that she saw throughout Prague are very much reflected in the collection with ruby, amethyst, sapphire, and emerald as the focus of this season's color palette. Baroque motifs are translated into luxe fil coupes and jacquards to...Read more ...
Zadig & Voltaire Fall 2018: New York Fashion Week
Zadig & Voltaire NYFW FW18
French brand Zadig & Voltaire has always exemplified the very best of Paris cool-the lived-in denim, the tossed-on jacket, the wrinkled shirt. And now, showing in New York yet again, the brand is yet again gracing us with the pleasure of a ready to wear that already looks like it's been worn.
Zadig & Voltaire: NYFW FW18
Some of the best of the FW18 trends were on full display: Prince of Wales check, lumberjack check, monochrome reds, oversized and distressed sweaters, gothic accents, and feathers in hair reminiscent of the kind that actually caused quite a stir...Read more ...
Michael Kors Celebrates Individuality with Fall '18 Collection
Known for his classic American style, Michael Kors took a slight detour for fall-winter 2018. Instead of the usual, Kors celebrated individuality with a youthful presentation. Grunge, prep, and hip-hop references came together for an eclectic outing. The big hero of the season was undoubtedly tartan. Available in a variety of colors, the timeless print...Read more ...
Here's Round 3 of the Best Street Style From New York Fashion Week Fall/Winter 2018
Our first round of New York Fashion Week street style centered around furry layers , while round two showcased boots alongside the biggest names in fashion. Our third roundup sees Off-White™ take the lead the fashion set's go-to label, with representation from an array of other recognizable imprints.
Street style favorites like Kiko Mizuhara , Aleali May and Christina Paik all made appearances towards the tail-end of New York Fashion Week, showcasing gear from the likes of Gucci and Cactus Plant Flea Market. Indeed, floral patterns are still a go-to for many fashion week attendees...Read more ... | {
"pile_set_name": "Pile-CC"
} |