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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

Some observations on high-dimensional partial differential equations with barron data

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arXiv 2020年

作者： Weinan, E. Wojtowytsch, Stephan Department of Mathematics Program for Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Program for Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We use explicit representation formulas to show that solutions to certain partial differential equations lie in Barron spaces or multilayer spaces if the PDE data lie in such function spaces. Consequently, these solutions can be represented efficiently using artificial neural networks, even in high dimension. Conversely, we present examples in which the solution fails to lie in the function space associated to a neural network under *** Codes 68T07, 35C15, 65M80 Copyright © 2020, The Authors. All rights reserved.

关键词： Neural networks

A priori estimates for classification problems using neural networks

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arXiv 2020年

作者： Weinan, E. Wojtowytsch, Stephan Program for Applied and Computational Mathematics Department of Mathematics Princeton University PrincetonNJ08544 United States Program for Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We consider binary and multi-class classification problems using hypothesis classes of neural networks. For a given hypothesis class, we use Rademacher complexity estimates and direct approximation theorems to obtain a priori error estimates for regularized loss *** Codes 68T07, 60-08 Copyright © 2020, The Authors. All rights reserved.

关键词： Classification (of information)

On the banach spaces associated with multi-layer ReLU networks: Function representation, approximation theory and gradient descent dynamics

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arXiv 2020年

作者： Weinan, E. Wojtowytsch, Stephan Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We develop Banach spaces for ReLU neural networks of finite depth L and infinite width. The spaces contain all finite fully connected L-layer networks and their L2-limiting objects under bounds on the natural path-norm. Under this norm, the unit ball in the space for L-layer networks has low Rademacher complexity and thus favorable generalization properties. Functions in these spaces can be approximated by multi-layer neural networks with dimension-independent convergence rates. The key to this work is a new way of representing functions in some form of expectations, motivated by multi-layer neural networks. This representation allows us to define a new class of continuous models for machine learning. We show that the gradient flow defined this way is the natural continuous analog of the gradient descent dynamics for the associated multi-layer neural networks. We show that the path-norm increases at most polynomially under this continuous gradient flow *** Codes 68T07, 46E15, 26B35, 26B40 Copyright © 2020, The Authors. All rights reserved.

关键词： Deep neural networks

Three-Dimensional Construction of Hyperuniform, Nonhyperuniform and Antihyperuniform Random Media via Spectral Density Functions and Their Transport Properties

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arXiv 2024年

作者： Shi, Wenlong Jiao, Yang Torquato, Salvatore Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States 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 Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Rigorous theories connecting physical properties of a heterogeneous material to its microstructure offer a promising avenue to guide the computational material design and optimization. The spectral density function χ˜V(k), which can be obtained experimentally from scattering techniques, enables accurate determination of various transport and wave propagation characteristics, including the time-dependent diffusion spreadability S(t) and effective dynamic dielectric constant ϵe for electromagnetic wave propagation. Moreover, χ˜V(k) has been employed to derive sharp bounds on the fluid permeability k. Given the importance of χ˜V(k), we present here an efficient Fourier-space based computational framework to construct three-dimensional (3D) statistically isotropic two-phase heterogeneous materials corresponding to targeted spectral density functions. In particular, we employ a variety of analytical χ˜V(k) functions that satisfy all known necessary conditions to construct disordered stealthy hyperuniform, standard hyperuniform, nonhyperuniform, and antihyperuniform two-phase heterogeneous material systems at varying phase volume fractions . We show that by tuning the correlations in the system across length scales via the targeted functions, one can generate a rich spectrum of distinct structures within each of the above classes of materials. Importantly, we present the first realization of antihyperuniform two-phase heterogeneous materials in 3D, which are characterized by a power-law autocovariance function χV (r) and contain clusters of dramatically different sizes and morphologies. We also determine the diffusion spreadability S(t) and estimate the fluid permeability k associated with all of the constructed materials directly from the corresponding χ˜V(k) functions. Although it is well established that the long-time asymptotic scaling behavior of S(t) only depends on the functional form of χ˜V(k), with the stealthy hyperuniform and antihyperuniform media respectively

关键词： Spectral density

A Model of Fluid-Structure and Biochemical Interactions for Applications to Subclinical Leaflet Thrombosis

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arXiv 2022年

作者： Barrett, Aaron Brown, Jordan A. Smith, Margaret Anne Woodward, Andrew Vavalle, John P. Kheradvar, Arash Griffith, Boyce E. Fogelson, Aaron L. Department of Mathematics University of Utah Salt Lake CityUT United States Department of Mathematics University of North Carolina Chapel HillNC United States Advanced Medical Imaging Lab University of North Carolina Medical Center Chapel HillNC United States University of North Carolina School of Medicine Chapel HillNC United States Division of Cardiology Department of Medicine University of North Carolina Chapel HillNC United States Department of Biomedical Engineering University of California Irvine IrvineCA United States Department of Mathematics Applied Physical Sciences and Biomedical Engineering University of North Carolina Chapel HillNC United States Carolina Center for Interdisciplinary Applied Mathematics University of North Carolina Chapel HillNC United States Computational Medicine Program University of North Carolina Chapel HillNC United States McAllister Heart Institute University of North Carolina Chapel HillNC United States Department of Mathematics and Biomedical Engineering University of Utah Salt Lake CityUT United States

Subclinical leaflet thrombosis (SLT) is a potentially serious complication of aortic valve replacement with a bioprosthetic valve in which blood clots form on the replacement valve. SLT is associated with increased risk of transient ischemic attacks and strokes and can progress to clinical leaflet thrombosis. SLT following aortic valve replacement also may be related to subsequent structural valve deterioration, which can impair the durability of the valve replacement. Because of the difficulty in clinical imaging of SLT, models are needed to determine the mechanisms of SLT and could eventually predict which patients will develop SLT. To this end, we develop methods to simulate leaflet thrombosis that combine fluid-structure interaction and a simplified thrombosis model that allows for deposition along the moving leaflets. Additionally, this model can be adapted to model deposition or absorption along other moving boundaries. We present convergence results and quantify the model's ability to realize changes in valve opening and pressures. These new approaches are an important advancement in our tools for modeling thrombosis in which they incorporate both adhesion to the surface of the moving leaflets and feedback to the fluid-structure interaction. © 2022, CC BY-SA.

关键词： Deposition

Efficient sampling of high-dimensional free energy landscapes using adaptive reinforced dynamics

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arXiv 2021年

作者： Wang, Dongdong Zhang, Linfeng Wang, Yanze Chang, Junhan Wang, Han Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States DP Technology Beijing China College of Chemistry and Molecular Engineering Peking University Beijing100871 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China School of Mathematical Sciences Peking University Beijing China Department of Mathematics Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Beijing Institute of Big Data Research Beijing100871 China

Enhanced sampling methods such as metadynamics and umbrella sampling have become essential tools for exploring the configuration space of molecules and materials. At the same time, they have long faced a number of issues such as the inefficiency when dealing with a large number of collective variables (CVs) or systems with high free energy barriers. In this work, we show that with the clustering and adaptive tuning techniques, the reinforced dynamics (RiD) scheme can be used to efficiently explore the configuration space and free energy landscapes with a large number of CVs or systems with high free energy barriers. We illustrate this by studying various representative and challenging examples. Firstly we demonstrate the efficiency of adaptive RiD compared with other methods, and construct the 9-dimensional free energy landscape of peptoid trimer which has energy barriers of more than 8 kcal/mol. We then study the folding of the protein chignolin using 18 CVs. In this case, both the folding and unfolding rates are observed to be equal to 4.30 µs−1. Finally, we propose a protein structure refinement protocol based on RiD. This protocol allows us to efficiently employ more than 100 CVs for exploring the landscape of protein structures and it gives rise to an overall improvement of 14.6 units over the initial Global Distance Test-High Accuracy (GDT-HA) score. © 2021, CC BY.

关键词： Wave functions

First-order phase transitions in Yang-Mills theories and the density of state method

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Physical Review D 2023年第7期108卷 074517-074517页

作者： Biagio Lucini David Mason Maurizio Piai Enrico Rinaldi Davide Vadacchino Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way Swansea SA1 8EN Wales United Kingdom and Swansea Academy of Advanced Computing Swansea University Fabian Way Swansea SA1 8EN Wales United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Swansea SA2 8PP Wales United Kingdom and Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way Swansea SA1 8EN Wales United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park Swansea SA2 8PP Wales United Kingdom Interdisciplinary Theoretical and Mathematical Science Program RIKEN (iTHEMS) 2-1 Hirosawa Wako Saitama 351-0198 Japan School of Mathematics and Hamilton Mathematics Institute Trinity College Dublin 2 Ireland and Centre for Mathematical Sciences University of Plymouth Plymouth PL4 8AA United Kingdom

When studied at finite temperature, Yang-Mills theories in 3+1 dimensions display the presence of confinement/deconfinement phase transitions, which are known to be of first order—the SU(2) gauge theory being the exception. Theoretical as well as phenomenological considerations indicate that it is essential to establish a precise characterization of these physical systems in proximity of such phase transitions. We present and test a new method to study the critical region of parameter space in non-Abelian quantum field theories on the lattice, based upon the logarithmic linear relaxation (LLR) algorithm. We apply this method to the SU(3) Yang-Mills lattice gauge theory, and perform extensive calculations with one fixed choice of lattice size. We identify the critical temperature, and measure interesting physical quantities near the transition. Among them, we determine the free energy of the model in the critical region, exposing for the first time its multivalued nature with a numerical calculation from first principles, providing this novel evidence in support of a first-order phase transition. This study sets the stage for future high-precision measurements, by demonstrating the potential of the method.

关键词： Color confinement Confinement First order phase transitions Lattice field theory Lattice gauge theory Heatbath algorithm Numerical approximation & analysis

Polaronic neutron in dilute α matter: A p-wave Bose polaron

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Physical Review C 2025年第2期111卷 025802-025802页

作者： Hiroyuki Tajima Hajime Moriya Tomoya Naito Wataru Horiuchi Eiji Nakano Kei Iida Department of Physics Graduate School of Science The University of Tokyo Tokyo 113-0033 Japan RIKEN Nishina Center Wako 351-0198 Japan Research Center for Nuclear Physics Osaka University Ibaraki 567-0047 Japan Interdisciplinary Theoretical and Mathematical Science Program (iTHEMS) RIKEN Wako 351-0198 Japan Department of Physics Osaka Metropolitan University Osaka 558-8585 Japan Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP) Osaka Metropolitan University Osaka 558-8585 Japan Department of Physics Hokkaido University Sapporo 060-0810 Japan Department of Mathematics and Physics Kochi University Kochi 780-8520 Japan

We theoretically investigate quasiparticle properties of a neutron immersed in an alpha condensate, which is one of the possible states of dilute symmetric nuclear matter. The resonant p-wave neutron-alpha scattering, which plays a crucial role in forming halo nuclei, is considered. This system is similar to a Bose polaron near the p-wave Feshbach resonance that can be realized in cold-atomic experiments. Calculating the self-energy within the field-theoretical approach, we give an analytical formula for the effective mass of a polaronic neutron as a function of alpha condensation density. Moreover, two adjacent neutrons in a medium, each of which behaves like a stable polaron having an enhanced effective mass, can form a bound dineutron, with the help of S01 neutron-neutron attraction. This is in contrast to the case of the vacuum, where a dineutron is known to be unbound. Our result is useful for understanding many-body physics in astrophysical environments as well as the formation of multinucleon clusters in neutron-halo nuclei.

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