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Generating large disordered stealthy hyperuniform systems with ultra-high accuracy to determine their physical properties

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arXiv 2023年

作者： Morse, Peter K. Kim, Jaeuk Steinhardt, Paul J. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Institute of Materials Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

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 30 for systems sizes more than an order of magnitude larger. We further show that this ultra-high 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. © 2023, CC BY.

关键词： Physical properties

THE COMPLEX INTERPLAY BETWEEN RISK TOLERANCE AND THE SPREAD OF INFECTIOUS DISEASES

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arXiv 2024年

作者： Nguyen, Maximilian Freedman, Ari Cheung, Matthew Saad-Roy, Chadi Espinoza, Baltazar Grenfell, Bryan Levin, Simon Lewis-Sigler Institute Princeton University PrincetonNJ08544 United States Department of Ecology and Evolutionary Biology Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Miller Institute for Basic Research in Science Department of Integrative Biology University of California Berkeley BerkeleyCA United States Biocomplexity Institute University of Virginia CharlottesvilleVA United States

Risk-driven behavior provides a feedback mechanism through which individuals both shape and are collectively affected by an epidemic. We introduce a general and flexible compartmental model to study the effect of heterogeneity in the population with regards to risk tolerance. The interplay between behavior and epidemiology leads to a rich set of possible epidemic dynamics. Depending on the behavioral composition of the population, we find that increasing heterogeneity in risk tolerance can either increase or decrease the epidemic size. We find that multiple waves of infection can arise due to the interplay between transmission and behavior, even without the replenishment of susceptibles. We find that increasing protective mechanisms such as the effectiveness of interventions, the number of risk-averse people in the population, and the duration of intervention usage reduces the epidemic overshoot. When the protection is pushed past a critical threshold, the epidemic dynamics enter an underdamped regime where the epidemic size exactly equals the herd immunity threshold. Lastly, we can find regimes where epidemic size does not monotonically decrease with a population that becomes increasingly risk-averse. Copyright © 2024, The Authors. All rights reserved.

关键词： Epidemiology

A provable initialization and robust clustering method for general mixture models

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arXiv 2024年

作者： Jana, Soham Fan, Jianqing Kulkarni, Sanjeev Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN United States Department of Operations Research and Financial Engineering Department of Electric and Computer Engineering Princeton University PrincetonNJ United States

Clustering is a fundamental tool in statistical machine learning in the presence of heterogeneous data. Most recent results focus primarily on optimal mislabeling guarantees when data are distributed around centroids with sub-Gaussian errors. Yet, the restrictive sub-Gaussian model is often invalid in practice since various real-world applications exhibit heavy tail distributions around the centroids or suffer from possible adversarial attacks that call for robust clustering with a robust data-driven initialization. In this paper, we present initialization and subsequent clustering methods that provably guarantee near-optimal mislabeling for general mixture models when the number of clusters and data dimensions are finite. We first introduce a hybrid clustering technique with a novel multivariate trimmed mean type centroid estimate to produce mislabeling guarantees under a weak initialization condition for general error distributions around the centroids. A matching lower bound is derived, up to factors depending on the number of clusters. In addition, our approach also produces similar mislabeling guarantees even in the presence of adversarial outliers. Our results reduce to the sub-Gaussian case in finite dimensions when errors follow sub-Gaussian distributions. To solve the problem thoroughly, we also present novel data-driven robust initialization techniques and show that, with probabilities approaching one, these initial centroid estimates are sufficiently good for the subsequent clustering algorithm to achieve the optimal mislabeling rates. Furthermore, we demonstrate that the Lloyd algorithm is suboptimal for more than two clusters even when errors are Gaussian and for two clusters when error distributions have heavy tails. Both simulated data and real data examples further support our robust initialization procedure and clustering *** Codes 62H30 (Primary), 62G35, 62G05 (Secondary) Copyright © 2024, The Authors. All rights reserved.

关键词： Adversarial machine learning

Ab Initio Generalized Langevin Equation

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arXiv 2022年

作者： Xie, Pinchen Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States AI for Science Institute Beijing China Center for Machine Learning Research School of Mathematical Sciences Peking University Beijing China

We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multi-scale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of collective variables by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude, and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency. © 2022, CC BY.

关键词： Molecular dynamics

MULTI-TARGET DETECTION WITH ROTATIONS

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arXiv 2021年

作者： Bendory, Tamir Lan, Ti-Yen Marshall, Nicholas F. Rukshin, Iris Singer, Amit School of Electrical Engineering Tel Aviv University Tel Aviv Israel Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Department of Mathematics Oregon State University Corvallis OR USA Program in Applied and Computational Mathematics Princeton University Princeton NJ USA Program in Applied and Computational Mathematics and the Department of Mathematics Princeton University Princeton NJ USA

We consider the multi-target detection problem of estimating a two-dimensional target image from a large noisy measurement image that contains many randomly rotated and translated copies of the target image. Motivated by single-particle cryo-electron microscopy, we focus on the low signal-to-noise regime, where it is difficult to estimate the locations and orientations of the target images in the measurement. Our approach uses autocorrelation analysis to estimate rotationally and translationally invariant features of the target image. We demonstrate that, regardless of the level of noise, our technique can be used to recover the target image when the measurement is sufficiently large. Copyright © 2021, The Authors. All rights reserved.

关键词： Signal to noise ratio

Precise determination of pair interactions from pair statistics of many-body systems in and out of equilibrium

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Physical Review E 2022年第4期106卷 044122-044122页

作者： Salvatore Torquato Haina Wang Department of Chemistry Department of Physics Princeton Institute of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA School of Natural Sciences Institute for Advanced Study 1 Einstein Drive Princeton New Jersey 08540 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA

The determination of the pair potential v(r) that accurately yields an equilibrium state at positive temperature T with a prescribed pair correlation function g2(r) or corresponding structure factor S(k) in d-dimensional Euclidean space Rd is an outstanding inverse statistical mechanics problem with far-reaching implications. Recently, Zhang and Torquato [Phys. Rev. E 101, 032124 (2020)] conjectured that any realizable g2(r) or S(k) corresponding to a translationally invariant nonequilibrium system can be attained by a classical equilibrium ensemble involving only (up to) effective pair interactions. Testing this conjecture for nonequilibrium systems as well as for nontrivial equilibrium states requires improved inverse methodologies. We have devised an optimization algorithm to precisely determine effective pair potentials that correspond to pair statistics of general translationally invariant disordered many-body equilibrium or nonequilibrium systems at positive temperatures. This methodology utilizes a parameterized family of pointwise basis functions for the potential function whose initial form is informed by small-, intermediate- and large-distance behaviors dictated by statistical-mechanical theory. Subsequently, a nonlinear optimization technique is utilized to minimize an objective function that incorporates both the target pair correlation function g2(r) and structure factor S(k) so that the small intermediate- and large-distance correlations are very accurately captured. To illustrate the versatility and power of our methodology, we accurately determine the effective pair interactions of the following four diverse target systems: (1) Lennard-Jones system in the vicinity of its critical point, (2) liquid under the Dzugutov potential, (3) nonequilibrium random sequential addition packing, and (4) a nonequilibrium hyperuniform “cloaked” uniformly randomized lattice. We found that the optimized pair potentials generate corresponding pair statistics that accur

关键词： Nonequilibrium statistical mechanics Optimization problems Structural properties Complex materials

Algebraic Constraints and Algorithms for Common Lines in Cryo-EM

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arXiv 2024年

作者： Muller, Tommi Duncan, Adriana L. Verbeke, Eric J. Kileel, Joe Mathematical Institute University of Oxford OxfordOX2 6GG United Kingdom Department of Mathematics University of Texas at Austin AustinTX78712 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Oden Institute University of Texas at Austin AustinTX78712 United States

We revisit the topic of common lines between projection images in single particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain 2n × n matrix storing properly-scaled basis vectors for the common lines between n projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated to the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental *** Codes 90C26, 14Q30 © 2024, CC BY.

关键词： Clustering algorithms

Designer Pair Statistics of Disordered Many-Particle Systems with Novel Properties

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arXiv 2023年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Materials Institute Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States

Knowledge of exact analytical functional forms for the pair correlation function g2(r) and its corresponding structure factor S(k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing data base of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperature that precisely match targeted forms for both g2(r) and S(k). Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve systems with a wide range of translational order and self-diffusion coefficients D, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics. © 2023, CC BY.

关键词： Statistics

Liquid-Liquid Transition in Water from First Principles

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Physical Review Letters 2022年第25期129卷 255702-255702页

作者： Thomas E. Gartner, III Pablo M. Piaggi Roberto Car Athanassios Z. Panagiotopoulos Pablo G. Debenedetti Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

关键词： Classical statistical mechanics First order phase transitions First-principles calculations Liquid-liquid phase transition Phase transitions Thermodynamics Deep learning Density functional theory Molecular dynamics