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Comparing demographics of signatories to public letters on diversity in the mathematical sciences

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arXiv 2019年

作者： Topaz, Chad M. Cart, James Eaton, Carrie Diaz Shrout, Anelise Hanson Higdon, Jude A. İnce, Kenan Katz, Brian Lewis, Drew Libertini, Jessica Smith, Christian Michael Department of Mathematics and Statistics Williams College WilliamstownMA United States Institute for the Quantitative Study of Inclusion Diversity and Equity WilliamstownMA United States Office of Institutional Research Williams College WilliamstownMA United States Digital and Computational Studies Program Bates College LewistonME United States Department of Mathematics Westminster College Salt Lake CityUT United States Department of Mathematics and Statistics Smith College NorthamptonMA United States Department of Mathematics and Statistics University of South Alabama MobileAL United States Department of Applied Mathematics Virginia Military Institute LexingtonVA United States Department of Sociology University of Wisconsin-Madison MadisonWI United States

In its December 2019 edition, the Notices of the American Mathematical Society published an essay critical of the use of diversity statements in academic hiring. The publication of this essay prompted many responses, including three public letters circulated within the mathematical sciences community. Each letter was signed by hundreds of people and was published online, also by the American Mathematical Society. We report on a study of the signatories’ demographics, which we infer using a crowdsourcing approach. Letter A highlights diversity and social justice. The pool of signatories contains relatively more individuals inferred to be women and/or members of underrepresented ethnic groups. Moreover, this pool is diverse with respect to the levels of professional security and types of academic institutions represented. Letter B does not comment on diversity, but rather, asks for discussion and debate. This letter was signed by a strong majority of individuals inferred to be white men in professionally secure positions at highly research intensive universities. Letter C speaks out specifically against diversity statements, calling them "a mistake," and claiming that their usage during early stages of faculty hiring "diminishes mathematical achievement." Individuals who signed both Letters B and C, that is, signatories who both privilege debate and oppose diversity statements, are overwhelmingly inferred to be tenured white men at highly research intensive universities. Our empirical results are consistent with theories of power drawn from the social sciences. Copyright © 2019, The Authors. All rights reserved.

关键词： Population statistics

Plane-wave analysis of a hyperbolic system of equations with relaxation in Rd

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arXiv 2018年

作者： de Hoop, Maarten V. Liu, Jian-Guo Markowich, Peter A. Ussembayev, Nail S. Department of Computational and Applied Mathematics Rice University HoustonTX77005 United States Department of Mathematics Department of Physics Duke University DurhamNC27708 United States Applied Mathematics and Computer Science Program CEMSE Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Faculty of Mathematics University of Vienna ViennaA-1090 Austria Applied Mathematics and Computer Science Program CEMSE Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia

We consider a multi-dimensional scalar wave equation with memory corresponding to the viscoelastic material described by a generalized Zener model. We deduce that this relaxation system is an example of a non-strictly hyperbolic system satisfying Majda's block structure condition. Well-posedness of the associated Cauchy problem is established by showing that the symbol of the spatial derivatives is uniformly diagonalizable with real eigenvalues. A long-time stability result is obtained by plane-wave analysis when the memory term allows for dissipation of energy.35L40 (Primary) 74D05, 35B35 (Secondary) Copyright © 2018, The Authors. All rights reserved.

关键词： Viscoelasticity

Blind phaseless short-time fourier transform recovery

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arXiv 2018年

作者： Bendory, Tamir Edidin, Dan Eldar, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mathematics University of Missouri ColumbiaMO United States Andrew and Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa Israel

The problem of recovering a pair of signals from their blind phaseless short-time Fourier transform measurements arises in several important phase retrieval applications, including ptychography and ultra-short pulse characterization. In this paper, we prove that in order to determine a pair of generic signals uniquely, up to trivial ambiguities, the number of phaseless measurements one needs to collect is, at most, five times the number of parameters required to describe the signals. This result improves significantly upon previous papers, which required the number of measurements to be quadratic in the number of parameters rather than linear. In addition, we consider the simpler problem of recovering a pair of generic signals from their blind short-time Fourier transform, when the phases are known. In this setting, which can be understood as a special case of the blind deconvolution problem, we show that the number of measurements required to determine the two signals, up to trivial ambiguities, equals exactly the number of parameters to be recovered. As a side result, we study the classical phase retrieval problem-that is, recovering a signal from its Fourier magnitudes-when some entries of the signal are known a priori. We derive a bound on the number of required measurements as a function of the size of the set of known entries. Specifically, we show that if most of the signal's entries are known, then only a few Fourier magnitudes are necessary to determine a signal uniquely. Copyright © 2018, The Authors. All rights reserved.

关键词： Convolution

Multifunctional hyperuniform cellular networks: Optimality, anisotropy and disorder

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Multifunctional Materials 2018年第1期1卷

作者： Torquato, S. Chen, D. Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

Disordered hyperuniform heterogeneousmaterials are new, exotic amorphous states of matter that behave like crystals in themanner in which they suppress volume-fraction fluctuations at large length scales, and yet are statistically isotropic with no Bragg peaks. It has recently been shown that disordered hyperuniform dielectric two-dimensional (2D) cellular network solids possess complete photonic band gaps comparable in size to photonic crystals,while at the same timemaintaining statistical isotropy, enabling waveguide geometries not possible with photonic crystals. Motivated by these developments, we explore other functionalities of various 2D ordered and disordered hyperuniform cellular networks, including their effective thermal or electrical conductivities and *** the multifunctionality of a class of such low-density networks by demonstrating that theymaximize or virtually maximize the effective conductivities and elastic moduli. This is accomplished using themachinery of homogenization theory, including optimal bounds and cross-property bounds, and statistical *** rigorously prove that anisotropic networks consisting of sets of intersecting parallel channels in the low-density limit, ordered or disordered, possess optimal effective conductivity tensors. For a variety of different disordered networks,we showthatwhen short-range and long-range order increases, there is an increase in both the effective conductivity and elasticmoduli of the network. Moreover,we demonstrate that the effective conductivity and elasticmoduli of various disordered networks derived from disordered 'stealthy' hyperuniform point patterns possess virtually optimal *** note that the optimal networks for conductivity are also optimal for the fluid permeability associatedwith slow viscous flow through the channels as well as themean survival time associated with diffusioncontrolled reactions in the channels. In summary,we have identified ordered and disor

关键词： Transport properties

Numerical Algorithms for the Computation of Generalized Prolate Spheroidal Functions

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arXiv 2017年

作者： Lederman, Roy R. Program in Applied and Computational Mathematics Princeton University

Generalized Prolate Spheroidal Functions (GPSF) are the eigenfunctions of the truncated Fourier transform, restricted to D-dimensional balls in the spatial domain and frequency domain. Despite their useful properties in many applications, GPSFs are often replaced by crude approximations. The purpose of this paper is to review the elements of computing GPSFs and associated eigenvalues. This paper is accompanied by open-source code.42A38, 65T99, 33F05, 65D20 Copyright © 2017, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Basic Understanding of Condensed Phases of Matter via Packing Models

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arXiv 2018年

作者： Torquato, S. Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University Princeton New Jersey08544 United States

Packing problems have been a source of fascination for millenia and their study has produced a rich literature that spans numerous disciplines. Investigations of hard-particle packing models have provided basic insights into the structure and bulk properties of condensed phases of matter, including low-temperature states (e.g., molecular and colloidal liquids, crystals and glasses), multiphase heterogeneous media, granular media, and biological systems. The densest packings are of great interest in pure mathematics, including discrete geometry and number theory. This perspective reviews pertinent theoretical and computational literature concerning the equilibrium, metastable and nonequilibrium packings of hard-particle packings in various Euclidean space dimensions. In the case of jammed packings, emphasis will be placed on the "geometric-structure" approach, which provides a powerful and unified means to quantitatively characterize individual packings via jamming categories and "order" maps. It incorporates extremal jammed states, including the densest packings, maximally random jammed states, and lowest-density jammed structures. Packings of identical spheres, spheres with a size distribution, and nonspherical particles are also surveyed. We close this review by identifying challenges and open questions for future research. Copyright © 2018, The Authors. All rights reserved.

关键词： Geometry

The structure factor of primes

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arXiv 2018年

作者： Zhang, G. Martelli, F. Torquato, S. Department of Chemistry Princeton University PrincetonNJ08544 Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544

Although the prime numbers are deterministic, they can be viewed, by some measures, as pseudo-random numbers. In this article, we numerically study the pair statistics of the primes using statistical-mechanical methods, especially the structure factor S(k) in an interval M ≤ p ≤ M + L with M large, and L/M smaller than unity. We show that the structure factor of the prime-number configurations in such intervals exhibits well-defined Bragg-like peaks along with a small "diffuse" contribution. This indicates that the primes are appreciably more correlated and ordered than previously thought. Our numerical results definitively suggest an explicit formula for the locations and heights of the peaks. This formula predicts infinitely many peaks in any non-zero interval, similar to the behavior of quasicrystals. However, primes differ from quasicrystals in that the ratio between the location of any two predicted peaks is rational. We also show numerically that the diffuse part decays slowly as M and L increases. This suggests that the diffuse part vanishes in an appropriate infinite-system-size limit. Copyright © 2018, The Authors. All rights reserved.

关键词： Quasicrystals

Heterogeneous multireference alignment for images with application to 2-D classification in single particle reconstruction

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arXiv 2018年

作者： Ma, Chao Bendory, Tamir Boumal, Nicolas Sigworth, Fred Singer, Amit Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Department of Mathematics Princeton University PrincetonNJ United States Department of Cellular and Molecular Physiology Yale University School of Medicine New HavenCT United States

Motivated by the task of 2-D classification in single particle reconstruction by cryo-electron microscopy (cryo-EM), we consider the problem of heterogeneous multireference alignment of images. In this problem, the goal is to estimate a (typically small) set of target images from a (typically large) collection of observations. Each observation is a rotated, noisy version of one of the target images. For each individual observation, neither the rotation nor which target image has been rotated are known. As the noise level in cryo-EM data is high, clustering the observations and estimating individual rotations is challenging. We propose a framework to estimate the target images directly from the observations, completely bypassing the need to cluster or register the images. The framework consists of two steps. First, we estimate rotation-invariant features of the images, such as the bispectrum. These features can be estimated to any desired accuracy, at any noise level, provided sufficiently many observations are collected. Then, we estimate the images from the invariant features. Numerical experiments on synthetic cryo-EM datasets demonstrate the effectiveness of the method. Ultimately, we outline future developments required to apply this method to experimental data. Copyright © 2018, The Authors. All rights reserved.

关键词： Alignment

Nonbacktracking bounds on the influence in independent cascade models 17

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Nonbacktracking bounds on the influence in independent casca...

Proceedings of the 31st International Conference on Neural Information Processing Systems

作者： Emmanuel Abbe Sanjeev Kulkarni Eun Jee Lee Program in Applied and Computational Mathematics and The Department of Electrical Engineering Princeton University The Department of Electrical Engineering Princeton University Program in Applied and Computational Mathematics

ISBN: (纸本)9781510860964

This paper develops upper and lower bounds on the influence measure in a network, more precisely, the expected number of nodes that a seed set can influence in the independent cascade model. In particular, our bounds exploit nonbacktracking walks, Fortuin-Kasteleyn-Ginibre type inequalities, and are computed by message passing algorithms. Nonbacktracking walks have recently allowed for headways in community detection, and this paper shows that their use can also impact the influence computation. Further, we provide parameterized versions of the bounds that control the trade-off between the efficiency and the accuracy. Finally, the tightness of the bounds is illustrated with simulations on various network models.

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