pinecone/core-2020-05-10-deduplication huggingface dataset:
Arithmetic Spectral Transitions for the Maryland Model

We give a precise description of spectra of the Maryland model $
(h_{\lambda,\alpha,\theta}u)_n=u_{n+1}+u_{n-1}+ \lambda \tan
\pi(\theta+n\alpha)u_n$ for all values of parameters. We introduce an
arithmetically defined index $\delta (\alpha, \theta)$ and show that for
$\alpha\notin\mathbb{Q},\,$
$\sigma_{sc}(h_{\lambda,\alpha,\theta})=\overline{\{e:\gamma_{\lambda}(e)
<\delta (\alpha, \theta) \}}$ and
$\sigma_{pp}(h_{\lambda,\alpha,\theta})=\{e:\gamma_{\lambda}(e) \geq \delta
(\alpha, \theta) \}$. Since
$\sigma_{ac}(h_{\lambda,\alpha,\theta})=\emptyset,\;$ this gives complete
description of the spectral decomposition for {\it all} values of parameters
$\lambda,\alpha,\theta$, making it the first case of a family where arithmetic
spectral transition is described without any parameter exclusion. The set of
eigenvalues can be explicitly identified for all parameters, using the {\it
quantization condition}. We also establish, for the first time for this or any
other model, a quantization condition for singular continuous spectrum (an
arithmetically defined measure zero set that supports singular continuous
measures) for all parameters.Comment: CPAM to appea
Uniqueness of tangent cones for two-dimensional almost-minimizing currents

We consider two-dimensional integer rectifiable currents that are almost area minimizing and show that their tangent cones are everywhere unique. Our argument unifies a few uniqueness theorems of the same flavor, which are all obtained by a suitable modification of White's original theorem for area-minimizing currents in the euclidean space. This note is also the first step in a regularity program for semicalibrated two-dimensional currents and spherical cross sections of three-dimensional area-minimizing cones
Axial compression of a thin elastic cylinder: bounds on the minimum
  energy scaling law

We consider the axial compression of a thin elastic cylinder placed about a
hard cylindrical core. Treating the core as an obstacle, we prove upper and
lower bounds on the minimum energy of the cylinder that depend on its relative
thickness and the magnitude of axial compression. We focus exclusively on the
setting where the radius of the core is greater than or equal to the natural
radius of the cylinder. We consider two cases: the "large mandrel" case, where
the radius of the core exceeds that of the cylinder, and the "neutral mandrel"
case, where the radii of the core and cylinder are the same. In the large
mandrel case, our upper and lower bounds match in their scaling with respect to
thickness, compression, and the magnitude of pre-strain induced by the core. We
construct three types of axisymmetric wrinkling patterns whose energy scales as
the minimum in different parameter regimes, corresponding to the presence of
many wrinkles, few wrinkles, or no wrinkles at all. In the neutral mandrel
case, our upper and lower bounds match in a certain regime in which the
compression is small as compared to the thickness; in this regime, the minimum
energy scales as that of the unbuckled configuration. We achieve these results
for both the von K\'arm\'an-Donnell model and a geometrically nonlinear model
of elasticity.Comment: Minor edits made, for consistency and readabilit
Multi- to one-dimensional transportation

Fix probability densities $f$ and $g$ on open sets $X \subset \mathbf{R}^m$
and $Y \subset \mathbf{R}^n$ with $m\ge n\ge1$. Consider transporting $f$ onto
$g$ so as to minimize the cost $-s(x,y)$. We give a non-degeneracy condition
(a) on $s \in C^{1,1}$ which ensures the set of $x$ paired with [$g$-a.e.]
$y\in Y$ lie in a codimension $n$ submanifold of $X$. Specializing to the case
$m>n=1$, we discover a nestedness criteria relating $s$ to $(f,g)$ which allows
us to construct a unique optimal solution in the form of a map $F:X
\longrightarrow \overline Y$. When $s\in C^2 \cap W^{3,1}$ and $\log f$ and
$\log g$ are bounded, the Kantorovich dual potentials $(u,v)$ satisfy $v \in
C^{1,1}_{loc}(Y)$, and the normal velocity $V$ of $F^{-1}(y)$ with respect to
changes in $y$ is given by $V(x) = v"(f(x))-s_{yy}(x,f(x))$. Positivity (b) of
$V$ locally implies a Lipschitz bound on $f$; moreover, $v \in C^2$ if
${F^{-1}(y)}$ intersects $\partial X \in C^1$ transversally (c). On subsets
where (a)-(c) can be be quantified, for each integer $r \ge1$ the norms of $u,v
\in C^{r+1,1}$ and $F \in C^{r,1}$ are controlled by these bounds, $||\log
f,\log g, \partial X ||_{C^{r-1,1}}, ||\partial X||_{C^{1,1}}$,
$||s||_{C^{r+1,1}}$, and the smallness of $F^{-1}(y)$. We give examples showing
regularity extends from $X$ to part of $\bar X$, but not from $Y$ to $\bar Y$.
We also show that when $s$ remains nested for all $(f,g)$, the problem in
$\mathbf{R}^m \times \mathbf{R}$ reduces to a supermodular problem in
$\mathbf{R} \times \mathbf{R}$
Volume estimates on the critical sets of solutions to elliptic PDEs

In this paper we study solutions to elliptic linear equations
$L(u)=\partial_i(a^{ij}(x)\partial_j u) + b^i(x) \partial_i u + c(x) u=0$,
either on $R^n$ or a Riemannian manifold, under the assumption of Lipschitz
control on the coefficients $a^{ij}$. We focus our attention on the critical
set $Cr(u)\equiv\{x:|\nabla u|=0\}$ and the singular set
$S(u)\equiv\{x:u=|\nabla u|=0\}$, and more importantly on effective versions of
these. Currently, under the coefficient control we have assumed, the strongest
results in the literature say that the singular set is n-2-dimensional, however
at this point it has not even been shown that $H^{n-2}(S)<\infty$ unless the
coefficients are smooth. Fundamentally, this is due to the need of an
$\epsilon$-regularity theorem which requires higher coefficient control as the
frequency increases. We introduce new techniques for estimating the critical
and singular set, which avoids the need of any such $\epsilon$-regularity.
Consequently, we prove that if the frequency of u is bounded by $\Lambda$ then
we have the estimates $H^{n-2}(C(u))\leq C^{\Lambda^2}$, $H^{n-2}(S(u))\leq
C^{\Lambda^2}$, depending on whether the equation is critical or not. More
importantly, we prove corresponding estimates for the {\it effective} critical
and singular sets. Even under the assumption of analytic coefficients these
results are much sharper than those currently in the literature. We also give
applications of the technique to the nodal set of solutions, and to give
estimates on the corresponding eigenvalue problem
On equilibrium shapes of charged flat drops

Equilibrium shapes of two-dimensional charged, perfectly conducting liquid
drops are governed by a geometric variational problem that involves a perimeter
term modeling line tension and a capacitary term modeling Coulombic repulsion.
Here we give a complete explicit solution to this variational problem. Namely,
we show that at fixed total charge a ball of a particular radius is the unique
global minimizer among all sufficiently regular sets in the plane. For sets
whose area is also fixed, we show that balls are the only minimizers if the
charge is less than or equal to a critical charge, while for larger charge
minimizers do not exist. Analogous results hold for drops whose potential,
rather than charge, is fixed
Message-passing algorithms for synchronization problems over compact
  groups

Various alignment problems arising in cryo-electron microscopy, community
detection, time synchronization, computer vision, and other fields fall into a
common framework of synchronization problems over compact groups such as Z/L,
U(1), or SO(3). The goal of such problems is to estimate an unknown vector of
group elements given noisy relative observations. We present an efficient
iterative algorithm to solve a large class of these problems, allowing for any
compact group, with measurements on multiple 'frequency channels' (Fourier
modes, or more generally, irreducible representations of the group). Our
algorithm is a highly efficient iterative method following the blueprint of
approximate message passing (AMP), which has recently arisen as a central
technique for inference problems such as structured low-rank estimation and
compressed sensing. We augment the standard ideas of AMP with ideas from
representation theory so that the algorithm can work with distributions over
compact groups. Using standard but non-rigorous methods from statistical
physics we analyze the behavior of our algorithm on a Gaussian noise model,
identifying phases where the problem is easy, (computationally) hard, and
(statistically) impossible. In particular, such evidence predicts that our
algorithm is information-theoretically optimal in many cases, and that the
remaining cases show evidence of statistical-to-computational gaps.Comment: 35 pages, 11 figure
Quantitative isoperimetry \`a la Levy-Gromov

On a Riemannian manifold with a positive lower bound on the Ricci tensor, the
distance of isoperimetric sets from geodesic balls is quantitatively controlled
in terms of the gap between the isoperimetric profile of the manifold and that
of a round sphere of suitable radius. The deficit between the diameters of the
manifold and of the corresponding sphere is bounded likewise. These results are
actually obtained in the more general context of (possibly non-smooth) metric
measure spaces with curvature-dimension conditions through a quantitative
analysis of the transport-rays decompositions obtained by the localization
method.Comment: 31 pages. Final version to appear in Comm. Pure Applied Math. From
  the previous version, we added some more background in the introduction and
  updated the bibliograph
Semiclassical regularization of Vlasov equations and wavepackets for
  nonlinear Schr\"odinger equations

We consider the semiclassical limit of nonlinear Schr\"odinger equations with
wavepacket initial data. We recover the Wigner measure of the problem, a
macroscopic phase-space density which controls the propagation of the physical
observables such as mass, energy and momentum. Wigner measures have been used
to create effective models for wave propagation in random media, quantum
molecular dynamics, mean field limits, and the propagation of electrons in
graphene. In nonlinear settings, the Vlasov-type equations obtained for the
Wigner measure are often ill-posed on the physically interesting spaces of
initial data. In this paper we are able to select the measure-valued solution
of the 1+1 dimensional Vlasov-Poisson equation which correctly captures the
semiclassical limit, thus finally resolving the non-uniqueness in the seminal
result of [Zhang, Zheng \& Mauser, Comm. Pure Appl. Math. (2002) 55,
doi:10.1002/cpa.3017]. The same approach is also applied to the
Vlasov-Dirac-Benney equation with small wavepacket initial data, extending
several known results
Breather Solutions of the Nonlinear Wave Equation

We construct series solutions to all orders for breathers of Klein-Gordon
equations, in powers of an amplitude parameter epsilon, under a sign condition
on the coefficients of the expansion of the nonlinearity. All terms may be
computed thanks to the properties of a 1D Schr\"odinger equation with
two-soliton potential. We prove that this series is free of poles in the unit
disc of the complex epsilon plane if and only if the equation is essentially
equivalent to the sine-Gordon equation. This appears to be the only result that
explains both what makes the sine-Gordon equation special from a PDE point of
view, and at the same time, why approximate, long-lived breathers exist. In a
related paper (Classical and Quantum Gravity, 25 (2008) 245004 ) we have
extended this approach to address the soliton star problem in General
Relativity
Amenamevir: Studies of Potential CYP2C8- and CYP2B6-Mediated Pharmacokinetic Interactions With Montelukast and Bupropion in Healthy Volunteers

Amenamevir (formerly ASP2151) induces cytochrome P450 (CYP)2B6 and CYP3A4 and inhibits CYP2C8. We conducted 2 studies, 1 using montelukast as a probe to assess CYP2C8 and the other bupropion to assess CYP2B6. The montelukast study examined the effect of amenamevir on the pharmacokinetics of montelukast in 24 healthy men: each subject received montelukast 10 mg alone, followed by montelukast 10 mg with amenamevir 400 mg, or vice versa after a washout period. In the bupropion study, 24 subjects received a single dose of 150 mg bupropion on days 1, 15, 22, and 29, and repeated once‐daily doses of 400 mg amenamevir on days 6‐15. Amenamevir increased peak concentration and area under the concentration‐time curve of montelukast by about 22% (ratio 121.7%, 90%CI [114.8, 129.1]; 121% [116.2, 128.4], respectively) with a similar increase in hydroxymontelukast (ratio 121.4%, 90%CI [106.4, 138.5]; 125.6 % [111.3, 141.7]). Amenamevir reduced peak concentration and area under the concentration‐time curve of bupropion by 16% (84.29%, 90%CI [78.00, 91.10]; 84.07%, 90%CI [78.85, 89.63]), with recovery after 1 week; the pharmacokinetics of the primary metabolite hydroxybupropion was unaffected. Thus, amenamevir increased plasma concentrations of montelukast and decreased those of bupropion, but it did not do so enough to require dose adjustment of coadministered substrates of either CYP2C8 or CYP2B6Maruh
Amenamevir: Studies of Potential CYP3A-Mediated Pharmacokinetic Interactions With Midazolam, Cyclosporine, and Ritonavir in Healthy Volunteers.

Amenamevir (formerly ASP2151) is a helicase‐primase inhibitor being developed for the treatment of herpesvirus infection. Amenamevir is both a substrate and inducer of cytochrome P450 (CYP) 3A4. Three studies were done in healthy volunteers to investigate potential CYP3A pharmacokinetic interactions with the following drugs: (1) Midazolam (probe substrate for CYP3A): After 10 days’ pretreatment with amenamevir 400 mg daily, geometric mean maximum concentration of drug in blood plasma (Cmax) and area under the plasma drug concentration‐time curve from time zero to infinity (AUC0‐∞) of midazolam 7.5 mg were about 68% and 51%, respectively, of those after midazolam alone. (2) Cyclosporine (substrate and inhibitor of CYP3A): After 5 days’ pretreatment with cyclosporine 100 mg twice daily, geometric mean Cmax of amenamevir after 400‐mg and 1200‐mg single doses was, respectively, about 66% and 69%, and AUC0‐∞ about 82% and 79%, of those after amenamevir alone. (3) Ritonavir (inhibitor of CYP3A): When given with single doses of ritonavir 600 mg, geometric mean Cmax of amenamevir after 400‐mg and 1200‐mg single doses was, respectively, about 1.4 and 1.6 times higher, and geometric mean AUC0‐∞ about 2.6 and 3.3 times higher, than after amenamevir alone. Amenamevir has the potential to be involved in CYP3A‐mediated pharmacokinetic interactions in clinical practice.Maruh
Heterogeneous Strong Computation Migration

The continuous increase in performance requirements, for both scientific
computation and industry, motivates the need of a powerful computing
infrastructure. The Grid appeared as a solution for inexpensive execution of
heavy applications in a parallel and distributed manner. It allows combining
resources independently of their physical location and architecture to form a
global resource pool available to all grid users. However, grid environments
are highly unstable and unpredictable. Adaptability is a crucial issue in this
context, in order to guarantee an appropriate quality of service to users.
Migration is a technique frequently used for achieving adaptation. The
objective of this report is to survey the problem of strong migration in
heterogeneous environments like the grids', the related implementation issues
and the current solutions.Comment: This is the pre-peer reviewed version of the following article:
  Milan\'es, A., Rodriguez, N. and Schulze, B. (2008), State of the art in
  heterogeneous strong migration of computations. Concurrency and Computation:
  Practice and Experience, 20: 1485-1508, which has been published in final
  form at http://onlinelibrary.wiley.com/doi/10.1002/cpe.1287/abstrac
Job submission to grid computing environments

The  problem of   enabling scientist users to submit  jobs  to grid  computing environments \ud
will  eventually  limit  the  usability  of   grids.  The  eMinerals  project  has  tackled  this \ud
problem by developing  the  “my_condor_submit”  (MCS)  tool,  which  provides  a  simple \ud
scriptable  interface  to Globus, a  flexible  interaction with  the Storage Resource  Broker, \ud
metascheduling with load balancing within a grid environment, and automatic metadata \ud
harvesting.  This paper provides an overview of  MCS together with some  use cases.  We \ud
also describe the use of MCS within parameter-sweep studies
Parallel Tiled QR Factorization for Multicore Architectures

As multicore systems continue to gain ground in the High Performance
Computing world, linear algebra algorithms have to be reformulated or new
algorithms have to be developed in order to take advantage of the architectural
features on these new processors. Fine grain parallelism becomes a major
requirement and introduces the necessity of loose synchronization in the
parallel execution of an operation. This paper presents an algorithm for the QR
factorization where the operations can be represented as a sequence of small
tasks that operate on square blocks of data. These tasks can be dynamically
scheduled for execution based on the dependencies among them and on the
availability of computational resources. This may result in an out of order
execution of the tasks which will completely hide the presence of intrinsically
sequential tasks in the factorization. Performance comparisons are presented
with the LAPACK algorithm for QR factorization where parallelism can only be
exploited at the level of the BLAS operations.Comment: 19 pages 14 figure
Speeding up simulation applications using WinGrid

The vision of grid computing is to make computational power, storage capacity, data and applications available to users as readily as electricity and other utilities. Grid infrastructures and applications have traditionally been geared towards dedicated, centralized, high performance clusters running on UNIX “flavour” operating systems (commonly referred to as cluster-based grid computing). This can be contrasted with desktop-based grid computing which refers to the aggregation of non-dedicated, de-centralized, commodity PCs connected through a network and running (mostly) the Microsoft Windows operating system. Large scale adoption of such Windows-based grid infrastructure may be facilitated via grid-enabling existing Windows applications. This paper presents the WinGrid approach to grid enabling existing Windows-based Commercial-Off-The-Shelf (COTS) simulation packages (CSPs).  Through the use of two case studies developed in conjunction with  a major automotive company and a leading investment bank respectively, the contribution of this paper is the demonstration of how experimentation with the CSP Witness (Lanner Group) and the CSP Analytics (SunGard Corporation) can achieve speedup when using WinGrid middleware on both dedicated and non-dedicated grid nodes. It is hoped that this research would facilitate wider acceptance of desktop grid computing among enterprises interested in a low-intervention technological solution to speeding up their existing simulations
Dimensions of coupling in middleware

It is well accepted that different types of distributed architectures require different degrees of coupling. For example, in client-server and three-tier architectures, application components are generally tightly coupled, both with one another and with the underlying middleware. Meanwhile, in off-line transaction processing, grid computing and mobile applications, the degree of coupling between application components and with the underlying middleware needs to be minimized. Terms such as ‘synchronous’, ‘asynchronous’, ‘blocking’, ‘non-blocking’, ‘directed’, and ‘non-directed’ are often used to refer to the degree of coupling required by an architecture or provided by a middleware. However, these terms are used with various connotations. Although various informal definitions have been provided, there is a lack of an overarching formal framework to unambiguously communicate architectural requirements with respect to (de-)coupling. This article addresses this gap by: (i) formally defining three dimensions of (de-)coupling; (ii) relating these dimensions to existing middleware; and (iii) proposing notational elements to represent various coupling integration patterns. This article also discusses a prototype that demonstrates the feasibility of its implementation
Modelling and analysis of the AMBA bus using CSP and B

In this paper, we present a formal model and analysis of the Advanced Microcontroller Bus Architecture (AMBA) Advanced High-performance Bus (AHB). The model is given in CSP parallel to B an integration of the process algebra CSP and the state-based formalism B. We describe the theory behind the integration of CSP and B, and present the model in this theory. Analysis is performed using the model-checker ProB. The contribution of this paper may be summarized as follows: presentation of a formal model of the AMBA AHB protocol such that it may be used for analysis of co-design systems incorporating the bus, an evaluation of the integration of CSP and B in the production of such a model, and a demonstration and evaluation of ProB in performing this analysis. Copyright (C) 2009 John Wiley & Sons, Ltd
Energy-aware scheduling of bag-of-tasks applications on master-worker platforms

International audienceWe consider the problem of scheduling an application composed of independent tasks on a fully heterogeneous master-worker platform with communication costs. We introduce a bi-criteria approach aiming at maximizing the throughput of the application while minimizing the energy consumed by participating resources. Assuming arbitrary super-linear power consumption laws, we investigate different models, with energy overheads and memory constraints. Building upon closed-form expressions for the uni-processor case, we derive asymptotically optimal solutions for all models
An object-oriented BSP library for multicore programming

We show that the bulk synchronous parallel (BSP) model, originally designed for distributed-memory systems, is also applicable for shared-memory multicore systems and, furthermore, that BSP libraries are useful in scientific computing on these systems. A proof-of-concept MulticoreBSP library has been implemented in Java, and is used to show that BSP algorithms can attain proper speedups on multicore architectures. This library is based on the BSPlib implementation, adapted to an object-oriented setting. In comparison, the number of function primitives is reduced, while the overall design simplicity is improved. We detail applying the BSP model and library on the sparse matrix–vector (SpMV) multiplication problem, and show by performing numerical experiments that the resulting BSP SpMV algorithm attains speedups, in one case reaching a speedup of 3.5 for 4 threads. Whereas not described in detail in this paper, algorithms for the fast Fourier transform and the dense LU decomposition are also investigated; in one case, attaining superlinear speedups of 5 for 4 threads. The predictability of BSP algorithms in the case of the SpMV is also investigated.status: publishe