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arXiv 2021年

作者： Sahneh, Faryad Darabi Fries, William Watkins, Joseph C. Lega, Joceline Department of Mathematics University of Arizona United States Interdisciplinary Program in Applied Mathematics University of Arizona United States Department of Epidemiology and Biostatistics University of Arizona United States BIO5 Institute University of Arizona TucsonAZ85721 United States

While a common trend in disease modeling is to develop models of increasing complexity, it was recently pointed out that outbreaks appear remarkably simple when viewed in the incidence vs. cumulative cases (ICC) plane. This article details the theory behind this phenomenon by analyzing the stochastic SIR (Susceptible, Infected, Recovered) model in the cumulative cases domain. We prove that the Markov chain associated with this model reduces, in the ICC plane, to a pure birth chain for the cumulative number of cases, whose limit leads to an independent increments Gaussian process that fluctuates about a deterministic ICC curve. We calculate the associated variance and quantify the additional variability due to estimating incidence over a finite period of time. We also illustrate the universality brought forth by the ICC concept on real-world data for Influenza A and for the COVID-19 outbreak in Arizona. Copyright © 2021, The Authors. All rights reserved.

关键词： COVID-19

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Structural properties of hyperuniform Voronoi networks

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Physical Review E 2025年第3期111卷 034123-034123页

作者： Eli Newby Wenlong Shi Yang Jiao Reka Albert Salvatore Torquato Department of Physics Pennsylvania State University University Park Pennsylvania 16802 USA Materials Science and Engineering Arizona State University Tempe Arizona 85287 USA Department of Physics Arizona State University Tempe Arizona 85287 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Disordered hyperuniform many-particle systems are recently discovered exotic states of matter, characterized by the complete suppression of normalized infinite-wavelength density fluctuations, as in perfect crystals, while lacking conventional long-range order, as in liquids and glasses. In this work, we begin a program to quantify the structural properties of nonhyperuniform and hyperuniform networks. In particular, large two-dimensional (2D) Voronoi networks (graphs) containing approximately 10,000 nodes are created from a variety of different point configurations, including the antihyperuniform hyperplane intersection process (HIP), nonhyperuniform Poisson process, nonhyperuniform random sequential addition (RSA) saturated packing, and both non-stealthy and stealthy hyperuniform point processes. We carry out an extensive study of the Voronoi-cell area distribution of each of the networks by determining multiple metrics that characterize the distribution, including their average areas and corresponding variances as well as higher-order cumulants (i.e., skewness γ1 and excess kurtosis γ2). We show that the HIP distribution is far from Gaussian, as evidenced by a high skewness (γ1=3.16) and large positive excess kurtosis (γ2=16.2). The Poisson (with γ1=1.07 and γ2=1.79) and non-stealthy hyperuniform (with γ1=0.257 and γ2=0.0217) distributions are Gaussian-like distributions, since they exhibit a small but positive skewness and excess kurtosis. The RSA (with γ1=0.450 and γ2=−0.0384) and the highest stealthy hyperuniform distributions (with γ1=0.0272 and γ2=−0.0626) are also non-Gaussian because of their low skewness and negative excess kurtosis, which is diametrically opposite of the non-Gaussian behavior of the HIP. The fact that the cell-area distributions of large, finite-sized RSA and stealthy hyperuniform networks (e.g., with N≈10,000 nodes) are narrower, have larger peaks, and smaller tails than a Gaussian distribution implies that in the thermodynamic limit th

关键词： Gaussian distribution

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Feature selection using stochastic gates 37

Feature selection using stochastic gates

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37th International Conference on Machine Learning, ICML 2020

作者： Yamada, Yutaro Lindenbaum, Ofir Negahban, Sahand Kluger, Yuval Department of Statistics and Data Science Yale University CT United States Program in Applied Mathematics Yale University CT United States School of Medicine Yale University CT United States

ISBN: (纸本)9781713821120

Feature selection problems have been extensively studied in the setting of linear estimation (e.g. LASSO), but less emphasis has been placed on feature selection for non-linear functions. In this study, we propose a method for feature selection in neural network estimation problems. The new procedure is based on probabilistic relaxation of the `0 norm of features, or the count of the number of selected features. Our `0-based regularization relies on a continuous relaxation of the Bernoulli distribution;such relaxation allows our model to learn the parameters of the approximate Bernoulli distributions via gradient descent. The proposed framework simultaneously learns either a nonlinear regression or classification function while selecting a small subset of features. We provide an information-theoretic justification for incorporating Bernoulli distribution into feature selection. Furthermore, we evaluate our method using synthetic and real-life data to demonstrate that our approach outperforms other commonly used methods in both predictive performance and feature selection. Copyright 2020 by the author(s).

关键词： Feature Selection

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Adaptive tikhonov strategies for stochastic ensemble Kalman inversion

arXiv

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arXiv 2021年

作者： Weissmann, Simon Chada, Neil K. Schillings, Claudia Tong, Xin T. Interdisciplinary Center for Scientific Computing University of Heidelberg Heidelberg69120 Germany Applied Mathematics and Computational Science Program King Abdullah University of Science and Technology Thuwal KSA 23955 Saudi Arabia Mannheim School of Computer Science and Mathematics University of Mannheim Mannheim68131 Germany Department of Mathematics National University of Singapore Singapore119077 Singapore

Ensemble Kalman inversion (EKI) is a derivative-free optimizer aimed at solving inverse problems, taking motivation from the celebrated ensemble Kalman filter. The purpose of this article is to consider the introduction of adaptive Tikhonov strategies for EKI. This work builds upon Tikhonov EKI (TEKI) which was proposed for a fixed regularization constant. By adaptively learning the regularization parameter, this procedure is known to improve the recovery of the underlying unknown. For the analysis, we consider a continuous-time setting where we extend known results such as well-posdeness and convergence of various loss functions, but with the addition of noisy observations. Furthermore, we allow a time-varying noise and regularization covariance in our presented convergence result which mimic adaptive regularization schemes. In turn we present three adaptive regularization schemes, which are highlighted from both the deterministic and Bayesian approaches for inverse problems, which include bilevel optimization, the MAP formulation and covariance learning. We numerically test these schemes and the theory on linear and nonlinear partial differential equations, where they outperform the non-adaptive TEKI and *** Codes 65M32, 60G35, 65C35, 70F17 Copyright © 2021, The Authors. All rights reserved.

关键词： Continuous time systems

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Numerical implicitization

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Journal of Software for Algebra and Geometry 2019年第1期9卷 55-63页

作者： Chen, Justin Kileel, Joe School of Mathematics Georgia Institute of Technology Atlanta GA United States Program in Applied and Computational Mathematics Princeton University Princeton NJ United States

We present the NumericalImplicitization.m2 package for Macaulay2, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This package relies on methods of numerical algebraic geometry, including homotopy continuation and monodromy. © 2019, Mathematical Sciences Publishers. All rights reserved.

关键词： homotopy continuation implicitization interpolation monodromy numerical algebraic geometry

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Unbiased Estimation Using a Class of Diffusion Processes

SSRN

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SSRN 2022年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We study the problem of unbiased estimation of expectations with respect to (w.r.t.) π a given, general probability measure on (Rd,B(Rd)) that is absolutely continuous with respect to a standard Gaussian measure. We focus on simulation associated to a particular class of diffusion processes, sometimes termed the Schrödinger-Föllmer Sampler, which is a simulation technique that approximates the law of a particular diffusion bridge process {Xt}t∈[0,1] on Rd, d ∈ N0. This latter process is constructed such that, starting at X0 = 0, one has X1 ∼ π. Typically, the drift of the diffusion is intractable and, even if it were not, exact sampling of the associated diffusion is not possible. As a result, [10, 15] consider a stochastic Euler-Maruyama scheme that allows the development of biased estimators for expectations w.r.t. π. We show that for this methodology to achieve a mean square error of O(Ε2), for arbitrary Ε > 0, the associated cost is O(Ε−5). We then introduce an alternative approach that provides unbiased estimates of expectations w.r.t. π, that is, it does not suffer from the time discretization bias or the bias related with the approximation of the drift function. We prove that to achieve a mean square error of O(Ε2), the associated cost is, with high probability, O(Ε−2|log(Ε)|2+δ), for any δ > 0. We implement our method on several examples including Bayesian inverse problems. © 2022, The Authors. All rights reserved.

关键词： Diffusion

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From Dyson models to many-body quantum chaos

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Physical Review B 2025年第3期111卷 035147-035147页

作者： Alexei Andreanov Matteo Carrega Jeff Murugan Jan Olle Dario Rosa Ruth Shir Center for Theoretical Physics of Complex Systems Institute for Basic Science (IBS) Daejeon 34126 Korea Basic Science Program Korea University of Science and Technology (UST) Daejeon 34113 Korea CNR-SPIN Via Dodecaneso 33 16146 Genova Italy The Laboratory for Quantum Gravity & Strings Department of Mathematics and Applied Mathematics University of Cape Town Cape Town 7701 South Africa The National Institute for Theoretical and Computational Sciences Private Bag X1 Matieland 7602 South Africa Max Planck Institute for the Science of Light 91058 Erlangen Germany ICTP South American Institute for Fundamental Research Instituto de Física Teórica UNESP—University of Estadual Paulista Rua Dr. Bento Teobaldo Ferraz 271 01140-070 São Paulo SP Brazil Department of Physics and Materials Science University of Luxembourg L-1511 Luxembourg Luxembourg

A deep understanding of the mechanisms underlying many-body quantum chaos is one of the big challenges in contemporary theoretical physics. We tackle this problem in the context of a set of perturbed quadratic Sachdev-Ye-Kitaev (SYK) Hamiltonians defined on graphs. This allows us to disentangle the geometrical properties of the underlying single-particle problem and the importance of the interaction terms, showing that the former is the dominant feature ensuring the single-particle to many-body chaotic transition. Our results are verified numerically with state-of-the-art numerical techniques, capable of extracting eigenvalues in a desired energy window of very large Hamiltonians. Our approach essentially provides a new way of viewing many-body chaos from a single-particle perspective.

关键词： Quantum chaos

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Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)

arXiv

引用

arXiv 2021年

作者： Gurevich, Daniel R. Golden, Matthew R. Reinbold, Patrick A.K. Grigoriev, Roman O. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Physics Georgia Institute of Technology AtlantaGA30332 United States

We show how a complete mathematical model of a physical process can be learned directly from data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality, and symmetry, a weak formulation of differential equations, and sparse regression. To illustrate this, we extract a complete system of governing equations of fluid dynamics—the Navier-Stokes equation, the continuity equation, and the boundary conditions—as well as the pressure-Poisson and energy equations, from numerical data describing a highly turbulent channel flow in three dimensions. Whether they represent known or unknown physics, relations discovered using this approach take the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects. The proposed approach offers insight into the quality of the data, serving as a useful diagnostic tool. It is also remarkably robust, yielding accurate results for very high noise levels, and should thus be well-suited for analysis of experimental data. Copyright © 2021, The Authors. All rights reserved.

关键词： Navier Stokes equations

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Generating large disordered stealthy hyperuniform systems with ultrahigh accuracy to determine their physical properties

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Physical Review Research 2023年第3期5卷 033190-033190页

作者： Peter K. Morse Jaeuk Kim Paul J. Steinhardt Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute of Materials Princeton University Princeton New Jersey 08544 USA Princeton Center for Theoretical Science Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Hyperuniform many-particle systems are characterized by a structure factor S(k) that is precisely zero as |k|→0; and stealthy hyperuniform systems have S(k)=0 for the finite range 0<|k|≤K, called the “exclusion region.” Through a process of collective-coordinate optimization, energy-minimizing disordered stealthy hyperuniform systems of moderate size have been made to high accuracy, and their novel physical properties have shown great promise. However, minimizing S(k) in the exclusion region is computationally intensive as the system size becomes large. In this paper, we present an improved methodology to generate such states using double-double precision calculations on graphical processing units (GPUs) that reduces the deviations from zero within the exclusion region by a factor of approximately 1030 for system sizes more than an order of magnitude larger. We further show that this ultrahigh accuracy is required to draw conclusions about their corresponding characteristics, such as the nature of the associated energy landscape and the presence or absence of Anderson localization, which might be masked, even when deviations are relatively small.

关键词： Exotic phases of matter

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Fault Tolerant Quantum Error Mitigation

arXiv

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arXiv 2023年

作者： Gonzales, Alvin Babu, Anjala M. Liu, Ji Saleem, Zain Byrd, Mark Intelligence Community Postdoctoral Research Fellowship Program Argonne National Laboratory LemontIL United States School of Physics and Applied Physics Southern Illinois University CarbondaleIL United States Mathematics and Computer Science Division Argonne National Laboratory LemontIL United States School of Computing Southern Illinois University CarbondaleIL United States

Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based error mitigation techniques. We also demonstrate that similar to results in fault tolerant quantum computing, code concatenation in fault-tolerant quantum error mitigation (FTQEM) can exponentially suppress the errors to arbitrary levels. For a family of circuits, we provide analytical error thresholds for FTQEM with the repetition code. These circuits include a set of quantum circuits that can generate all of reversible classical computing. The post-selection rate in FTQEM can also be increased by correcting some of the outcomes. Our threshold results can also be viewed from the perspective of quantifying the number of gate operations we can delay checking the stabilizers in a concatenated code before errors overwhelm the encoding. The benefits of FTQEM are demonstrated with numerical simulations and hardware demonstrations. Copyright © 2023, The Authors. All rights reserved.

关键词： Quantum computers

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