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arXiv 2017年

作者： Gao, Xu Ombao, Hernando Gillen, Daniel Department of Statistics University of California IrvineCA United States Department of Cognitive Sciences University of California IrvineCA United States Program on Applied Mathematics and Computational Science King Abdullah University of Science and Technology Saudi Arabia

A common approach to analyzing categorical correlated time series data is to fit a gen- eralized linear model (GLM) with past data as covariate inputs. There remain challenges to conducting inference for short time series length. By treating the historical data as covariate inputs, standard errors of estimates of GLM parameters computed using the empirical Fisher information do not fully account the auto-correlation in the data. To overcome this serious limitation, we derive the exact conditional Fisher information matrix of a general logistic autoregressive model with endogenous covariates for any series length T . Moreover, we also develop an iterative computational formula that allows for relatively easy implementation of the proposed estimator. Our simulation studies show that confidence intervals derived using the exact Fisher information matrix tend to be narrower than those utilizing the empirical Fisher information matrix while maintaining type I error rates at or below nominal levels. Further, we establish that the exact Fisher information matrix approaches, as T tends to infinity, the asymptotic Fisher information matrix previously derived for binary time series data. The developed exact conditional Fisher information matrix is applied to time-series data on respiratory rate among a cohort of expectant mothers where it is found to pro- vide narrower confidence intervals for functionals of scientific interest and lead to greater statistical power when compared to the empirical Fisher information matrix. Copyright © 2017, The Authors. All rights reserved.

关键词： Time series

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Space-time signaling based on Kerdock and Delsafte-Goethals codes

Space-time signaling based on Kerdock and Delsafte-Goethals ...

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IEEE International Conference on Communications (ICC)

作者： A.R. Calderbank S.N. Diggavi N. Al-Dhahir Program in Applied and Computational Mathematics Princeton University Princeton NJ USA School of Computer and Communication Sciences Swiss Federal Institute of Technology Lausanne Switzerland Department of Electrical Engineering University of Technology Dallas TX USA

This paper designs space-time codes for standard PSK and QAM signal constellations that have flexible rate, diversity and require no constellation expansion. Central to this construction are binary partitions of the PSK and QAM constellations that appear in codes designed for the Gaussian channel. The space-time codes presented here are designed by separately specifying the different levels of the binary partition in the space-time array. The individual levels are addressed by either the binary symmetric matrices associated with codewords in a Kerdock code or other families of binary matrices. Binary properties of these sets are sufficient to verify the diversity property of the codewords in the complex domain. Larger sets of binary symmetric matrices (such as the set used in Delsarte-Goethals codes) are used to trade diversity protection for increased rate.

关键词： Space time codes Phase shift keying Quadrature amplitude modulation Constellation diagram Symmetric matrices Binary phase shift keying Quadrature phase shift keying Transmitting antennas Fading mathematics

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computational Methods for Single-Particle Electron Cryomicroscopy

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Biomedical Data Science 1000年第1期3卷 163-190页

作者： Amit Singer Fred J. Sigworth 1Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA email: amits@math.princeton.edu 2Departments of Cellular and Molecular Physiology Biomedical Engineering and Molecular Biophysics and Biochemistry Yale University New Haven Connecticut 06520 USA email: fred.sigworth@yale.edu

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional (3D) structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the 3D molecular structure needs to be determined from many noisy 2D tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing, which also play a significant role in many other data science applications.

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mechanoChemML: A software library for machine learning in computational materials physics

arXiv

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arXiv 2021年

作者： Zhang, X. Teichert, G.H. Wang, Z. Duschenes, M. Srivastava, Siddhartha Livingston, E. Holber, J. Shojaei, M. Faghih Sundararajan, A. Garikipati, K. Department of Mechanical Engineering University of Michigan United States Applied Physics Program University of Michigan United States Department of Mathematics University of Michigan United States Michigan Institute for Computational Discovery & Engineering University of Michigan United States

We present mechanoChemML, a machine learning software library for computational materials physics. mechanoChemML is designed to function as an interface between platforms that are widely used for machine learning on one hand, and others for solution of partial differential equations-based models of physics. Of special interest here, and the focus of mechanoChemML, are applications to computational materials physics. These typically feature the coupled solution of material transport, reaction, phase transformation, mechanics, heat transport and electrochemistry. Central to the organization of mechanoChemML are machine learning workflows that arise in the context of data-driven computational materials physics. The mechanoChemML code structure is described, the machine learning workflows are laid out and their application to the solution of several problems in materials physics is outlined. © 2021, CC BY-NC-SA.

关键词： Partial differential equations

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Uncertainty quantification by random measures and fields

arXiv

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arXiv 2020年

作者： Bastian, Caleb Deen Rabitz, Herschel Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Massive Dynamics PrincetonNJ08542 United States Department of Chemistry Princeton University PrincetonNJ08544 United States

We present a general framework for uncertainty quantification that is a mosaic of interconnected models. We define global first and second order structural and correlative sensitivity analyses for random counting measures acting on risk functionals of input-output maps. These are the ANOVA decomposition of the intensity measure and the decomposition of the random measure variance, each into subspaces. Orthogonal random measures furnish sensitivity distributions. We show that the random counting measure may be used to construct positive random fields, which admit decompositions of covariance and sensitivity indices and may be used to represent interacting particle systems. The first and second order global sensitivity analyses conveyed through random counting measures elucidate and integrate different notions of uncertainty quantification, and the global sensitivity analysis of random fields conveys the proportionate functional contributions to covariance. This framework complements others when used in conjunction with for instance algorithmic uncertainty and model selection uncertainty *** Codes 60G57, 60G60, 60G55 © 2020, CC-BY-NC-ND.

关键词： Uncertainty analysis

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DeePKS+ABACUS as a Bridge between Expensive Quantum Mechanical Models and Machine Learning Potentials

arXiv

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arXiv 2022年

作者： Li, Wenfei Ou, Qi Chen, Yixiao Cao, Yu Liu, Renxi Zhang, Chunyi Zheng, Daye Cai, Chun Wu, Xifan Wang, Han Chen, Mohan Zhang, Linfeng AI for Science Institute Beijing100080 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States HEDPS CAPT College of Engineering School of Physics Peking University Beijing100871 China Department of Physics Temple University PhiladelphiaPA19122 United States Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Huayuan Road 6 Beijing100088 China DP Technology Beijing100080 China

Recently, the development of machine learning (ML) potentials has made it possible to perform large-scale and long-time molecular simulations with the accuracy of quantum mechanical (QM) models. However, for high-level QM methods, such as density functional theory (DFT) at the meta-GGA level and/or with exact exchange, quantum Monte Carlo, etc., generating a sufficient amount of data for training a ML potential has remained computationally challenging due to their high cost. In this work, we demonstrate that this issue can be largely alleviated with Deep Kohn-Sham (DeePKS), a ML-based DFT model. DeePKS employs a computationally efficient neural network-based functional model to construct a correction term added upon a cheap DFT model. Upon training, DeePKS offers closely-matched energies and forces compared with high-level QM method, but the number of training data required is orders of magnitude less than that required for training a reliable ML potential. As such, DeePKS can serve as a bridge between expensive QM models and ML potentials: one can generate a decent amount of high-accuracy QM data to train a DeePKS model, and then use the DeePKS model to label a much larger amount of configurations to train a ML potential. This scheme for periodic systems is implemented in a DFT package ABACUS, which is open-source and ready for use in various applications. © 2022, CC BY.

关键词： Density functional theory

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Model reduction for agent-based social simulation: Coarse-graining a civil violence model

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Physical Review E 2012年第6期85卷 066106-066106页

作者： Yu Zou Vladimir A. Fonoberov Maria Fonoberova Igor Mezic Ioannis G. Kevrekidis Department of Chemical and Biological Engineering and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Aimdyn Inc. 1919 State Street Suite 207 Santa Barbara California 93101 USA Department of Mechanical Engineering University of California Santa Barbara Santa Barbara California 93106 USA

Agent-based modeling (ABM) constitutes a powerful computational tool for the exploration of phenomena involving emergent dynamic behavior in the social sciences. This paper demonstrates a computer-assisted approach that bridges the significant gap between the single-agent microscopic level and the macroscopic (coarse-grained population) level, where fundamental questions must be rationally answered and policies guiding the emergent dynamics devised. Our approach will be illustrated through an agent-based model of civil violence. This spatiotemporally varying ABM incorporates interactions between a heterogeneous population of citizens [active (insurgent), inactive, or jailed] and a population of police officers. Detailed simulations exhibit an equilibrium punctuated by periods of social upheavals. We show how to effectively reduce the agent-based dynamics to a stochastic model with only two coarse-grained degrees of freedom: the number of jailed citizens and the number of active ones. The coarse-grained model captures the ABM dynamics while drastically reducing the computation time (by a factor of approximately 20).

关键词： VIOLENCE SOCIAL dynamics STOCHASTIC models CITIZENS SOCIAL interaction DEGREES of freedom

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Characterizing the hyperuniformity of ordered and disordered two-phase media

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Physical Review E 2021年第1期103卷 012123-012123页

作者： Jaeuk Kim Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

The hyperuniformity concept provides a unified means to classify all perfect crystals, perfect quasicrystals, and exotic amorphous states of matter according to their capacity to suppress large-scale density fluctuations. While the classification of hyperuniform point configurations has received considerable attention, much less is known about the classification of hyperuniform two-phase heterogeneous media, which include composites, porous media, foams, cellular solids, colloidal suspensions, and polymer blends. The purpose of this article is to begin such a program for certain two-dimensional models of hyperuniform two-phase media by ascertaining their local volume-fraction variances σV2(R) and the associated hyperuniformity order metrics B¯V. This is a highly challenging task because the geometries and topologies of the phases are generally much richer and more complex than point-configuration arrangements, and one must ascertain a broadly applicable length scale to make key quantities dimensionless. Therefore, we purposely restrict ourselves to a certain class of two-dimensional periodic cellular networks as well as periodic and disordered or irregular packings of circular disks, some of which maximize their effective transport and elastic properties. Among the cellular networks considered, the honeycomb networks have minimal values of the hyperuniformity order metrics B¯V across all volume fractions. On the other hand, for all packings of circular disks examined, the triangular-lattice packings have the smallest values of B¯V for the possible range of volume fractions. Among all structures studied here, the triangular-lattice packing of circular disks have the minimal values of the order metric for almost all volume fractions. Our study provides a theoretical foundation for the establishment of hyperuniformity order metrics for general two-phase media and a basis to discover new hyperuniform two-phase systems with desirable bulk physical properties by inverse d

关键词： Patterns in complex systems

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Characterization of void space, large-scale structure, and transport properties of maximally random jammed packings of superballs

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Physical Review Materials 2022年第2期6卷 025603-025603页

作者： Charles Emmett Maher Frank H. Stillinger Salvatore Torquato Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Dense, disordered packings of particles are useful models of low-temperature amorphous phases of matter, biological systems, granular media, and colloidal systems. The study of dense packings of nonspherical particles enables one to ascertain how rotational degrees of freedom affect packing behavior. Here, we study superballs, a large family of deformations of the sphere, defined in three dimensions by |x1|2p+|x2|2p+|x3|2p≤1, where p∈(0,∞) is a deformation parameter indicating to what extent the shape deviates from a sphere. As p increases from the sphere point (p=1), the superball tends to a cuboidal shape and approaches a cube in the p→∞ limit. As p→0.5, it approaches an octahedron, becomes a concave body with octahedral symmetry for p<0.5, and approaches a three-dimensional cross in the limit p→0. Previous characterization of superball packings has shown that they have a maximally random jammed (MRJ) state, whose properties (e.g., packing fraction ϕ, average contact number Z¯) vary nonanalytically as p diverges from unity. Here, we use an event-driven molecular dynamics algorithm to produce MRJ superball packings with 0.85≤p≤1.50. To supplement the previous work on such packings, we characterize their large-scale structure by examining the behaviors of their structure factors S(Q) and spectral densities χ̃V(Q), as the wave number Q tends to zero, and find that these packings are effectively hyperuniform for all values of p examined. We show that the mean width w¯ is a useful length scale to make distances dimensionless in order to compare systematically superballs of different shape. Moreover, we compute the complementary cumulative pore-size distribution F(δ) and find that the pore sizes tend to decrease as |1−p| increases. From F(δ), we estimate how the fluid permeability, mean survival time, and principal diffusion relaxation time vary as a function of p. Additionally, we compute the diffusion “spreadability” S(t) [Torquato, Phys. Rev. E 104, 054102 (2021)] of

关键词： Granular packing

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Marginal stability in jammed packings: Quasicontacts and weak contacts

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Physical Review E 2014年第2期90卷 022114-022114页

作者： Yoav Kallus Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Department of Chemistry Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and Princeton Institute of the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA

Maximally random jammed (MRJ) sphere packing is a prototypical example of a system naturally poised at the margin between underconstraint and overconstraint. This marginal stability has traditionally been understood in terms of isostaticity, the equality of the number of mechanical contacts and the number of degrees of freedom. Quasicontacts, pairs of spheres on the verge of coming in contact, are irrelevant for static stability, but they come into play when considering dynamic stability, as does the distribution of contact forces. We show that the effects of marginal dynamic stability, as manifested in the distributions of quasicontacts and weak contacts, are consequential and nontrivial. We study these ideas first in the context of MRJ packing of d-dimensional spheres, where we show that the abundance of quasicontacts grows at a faster rate than that of contacts. We reexamine a calculation of Jin et al. [Phys. Rev. E 82, 051126 (2010)], where quasicontacts were originally neglected, and we explore the effect of their inclusion in the calculation. This analysis yields an estimate of the asymptotic behavior of the packing density in high dimensions. We argue that this estimate should be reinterpreted as a lower bound. The latter part of the paper is devoted to Bravais lattice packings that possess the minimum number of contacts to maintain mechanical stability. We show that quasicontacts play an even more important role in these packings. We also show that jammed lattices are a useful setting for studying the Edwards ensemble, which weights each mechanically stable configuration equally and does not account for dynamics. This ansatz fails to predict the power-law distribution of near-zero contact forces, P(f)∼fθ.

关键词： SPHERE packings POWER law (mathematics) computational complexity NP-hard problems BRAVAIS lattice

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