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Wire Before You Walk

Wire Before You Walk

Asilomar Conference on Signals, Systems & Computers

作者： Tesfa Asmara Dhananjay Bhaskar Ian Adelstein Smita Krishnaswamy Michael Perlmutter Department of Computer Science Pomona College Claremont CA USA Mathematics and Statistics Pomona College Claremont CA USA Department of Genetics Yale School of Medicine New Haven CT USA Department of Mathematics Yale University New Haven CT USA Department of Computer Science Yale University New Haven CT USA Program for Applied Mathematics Yale University New Haven CT USA Computational Biology and Bioinformatics Program Yale University New Haven CT USA Wu Tsai Institute Yale University New Haven CT USA Department of Mathematics Boise State University Boise ID USA

Node embeddings aim to associate a vector to every vertex of a graph which can then be used for downstream tasks such as clustering, classification, or link prediction. Many popular node embeddings such as no $d$ e2vec and DeepWalk are based upon counting which nodes frequently co-occur in random walks of the graph. In this paper, we show that the performance of such algorithms can be improved by rewiring the edges of the graph through a variety of network indices before running DeepWalk. These rewirings effectively give the random walker an inductive bias and increase the accuracy of a logistic regression classifier applied to the node embedding on several benchmark data sets.

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Subdiffusive wave transport and weak localization transition in three-dimensional stealthy hyperuniform disordered systems

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Physical Review B 2022年第6期105卷 064204-064204页

作者： F. Sgrignuoli S. Torquato L. Dal Negro Department of Electrical and Computer Engineering & Photonics Center Boston University 8 Saint Mary's Street Boston Massachusetts 02215 USA Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08540 USA Division of Material Science and Engineering Boston University 15 Saint Mary's Street Brookline Massachusetts 02446 USA Department of Physics Boston University 590 Commonwealth Avenue Boston Massachusetts 02215 USA

The purpose of this work is to understand the fundamental connection between structural correlations and light localization in three-dimensional (3D) open scattering systems of finite size. We numerically investigate the transport of vector electromagnetic waves scattered by resonant electric dipoles spatially arranged in 3D space by stealthy hyperuniform disordered point patterns. Three-dimensional stealthy hyperuniform disordered systems are engineered with different structural correlation properties determined by their degree of stealthiness χ. Such fine control of exotic states of amorphous matter enables the systematic design of optical media that interpolate in a tunable fashion between uncorrelated random structures and crystalline materials. By solving the electromagnetic multiple scattering problem using Green's matrix spectral method, we establish a transport phase diagram that demonstrates a distinctive transition from a diffusive to a weak localization regime beyond a critical scattering density that depends on χ. The transition is characterized by studying the Thouless number and the spectral statistics of the scattering resonances. In particular, by tuning the χ parameter, we demonstrate large spectral gaps and suppressed subradiant proximity resonances, facilitating light localization. Moreover, consistently with previous studies, our results show a region of the transport phase diagram where the investigated scattering systems become transparent. Our work provides a systematic description of the transport and weak localization properties of light in stealthy hyperuniform structures and motivates the engineering of photonic systems with enhanced light-matter interactions for applications to both classical and quantum devices.

关键词： Anderson localization Light-matter interaction Mesoscopics Photonics Scattering theory Weak localization Metamaterials

The Role of Heterogeneity in Autonomous Perimeter Defense Problems

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arXiv 2022年

作者： Adler, Aviv Mickelin, Oscar Ramachandran, K. Sukhatme, Gaurav S. Karaman, Sertac Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology CambridgeMA United States Program in Applied and Computational Mathematics Princeton University Princeton NJ08544 United States Department of Computer Science University of Southern California Los AngelesCA90089 United States Department of Aeronautics and Astronautics Massachusetts Institute of Technology CambridgeMA02139 United States

When is heterogeneity in the composition of an autonomous robotic team beneficial and when is it detrimental? We investigate and answer this question in the context of a minimally viable model that examines the role of heterogeneous speeds in perimeter defense problems, where defenders share a total allocated speed budget. We consider two distinct problem settings and develop strategies based on dynamic programming and on local interaction rules. We present a theoretical analysis of both approaches and our results are extensively validated using simulations. Interestingly, our results demonstrate that the viability of heterogeneous teams depends on the amount of information available to the defenders. Moreover, our results suggest a universality property: across a wide range of problem parameters the optimal ratio of the speeds of the defenders remains nearly constant. Copyright © 2022, The Authors. All rights reserved.

关键词： Dynamic programming

Modeling heterogeneous materials via two-point correlation functions. II. Algorithmic details and applications

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Physical Review E 2008年第3期77卷 031135-031135页

作者： Y. Jiao F. H. Stillinger S. Torquato Department of Chemistry 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 Princeton Center for Theoretical Physics Princeton University Princeton New Jersey 08544 USA and School of Natural Sciences Institute for Advanced Study Princeton New Jersey 08540 USA

In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions S2 and introduced an efficient heterogeneous-medium (re)construction algorithm called the “lattice-point” algorithm. Here we discuss the algorithmic details of the lattice-point procedure and an algorithm modification using surface optimization to further speed up the (re)construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re)constructed, is also emphasized and discussed. We apply the algorithm to generate three-dimensional digitized realizations of a Fontainebleau sandstone and a boron-carbide/aluminum composite from the two-dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in S2 is sufficient to capture the salient structural features, we compute the two-point cluster functions of the media, which are superior signatures of the microstructure because they incorporate topological connectedness information. We also study the reconstruction of a binary laser-speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using S2 only work well for heterogeneous materials with single-scale structures. However, two-point information via S2 is not sufficient to accurately model multiscale random media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two-point correlation functions.

关键词： RECONSTRUCTING RANDOM-MEDIA TOPOLOGY OPTIMIZATION MICROSTRUCTURES COMPOSITES DESIGN TRANSPORT

Gap sensitivity reveals universal behaviors in optimized photonic crystal and disordered networks

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arXiv 2021年

作者： Klatt, Michael Andreas Steinhardt, Paul J. Torquato, Salvatore Department of Physics Princeton University PrincetonNJ08544 United States Institut für Theoretische Physik University of Erlangen-Nürnberg Staudtstr. 7 Erlangen91058 Germany Department of Chemistry Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Through an extensive series of high-precision numerical computations of the optimal complete photonic band gap (PBG) as a function of dielectric contrast α for a variety of crystal and disordered heterostructures, we reveal striking universal behaviors of the gap sensitivity S(α) ≡ d∆(α)/dα, the first derivative of the optimal gap-to-midgap ratio ∆(α). In particular, for all our crystal networks, S(α) takes a universal form that is well approximated by the analytic formula for a one-dimensional quarter-wave stack, SQWS(α). Even more surprisingly, the values of S(α) for our disordered networks converge to SQWS(α) for sufficiently large α. A deeper understanding of the simplicity of this universal behavior may provide fundamental insights about PBG formation and guidance in the design of novel photonic *** Codes 78A48, 78M50 (Primary) 82D25, 82D30, 52C99 (Secondary) © 2021, CC BY-SA.

关键词： Photonic band gap

Unsupervised particle sorting for high-resolution single-particle cryo-EM

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arXiv 2019年

作者： Zhou, Ye Moscovich, Amit Bendory, Tamir Bartesaghi, Alberto Department of Computer Science Duke University Durham United States Program in Applied and Computational Mathematics Princeton University United States School of Electrical Engineering Tel Aviv University Tel Aviv Israel Department of Biochemistry Duke University School of Medicine Durham United States Department of Electrical and Computer Engineering Duke University Durham United States

Single-particle cryo-Electron Microscopy (EM) has become a popular technique for determining the structure of challenging biomolecules that are inaccessible to other technologies. Recent advances in automation, both in data collection and data processing, have significantly lowered the barrier for non-expert users to successfully execute the structure determination workflow. Many critical data processing steps, however, still require expert user intervention in order to converge to the correct high-resolution structure. In particular, strategies to identify homogeneous populations of particles rely heavily on subjective criteria that are not always consistent or reproducible among different users. Here, we explore the use of unsupervised strategies for particle sorting that are compatible with the autonomous operation of the image processing pipeline. More specifically, we show that particles can be successfully sorted based on a simple statistical model for the distribution of scores assigned during refinement. This represents an important step towards the development of automated workflows for protein structure determination using single-particle *** Codes 62P10 Copyright © 2019, The Authors. All rights reserved.

关键词： Inverse problems

In situ characterization of nanoparticles using rayleigh scattering

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arXiv 2017年

作者： Santra, Biswajit Shneider, Mikhail N. Car, Roberto Department of Chemistry Princeton University PrincetonNJ08544 United States Mechanical and Aerospace Engineering Department Princeton University PrincetonNJ08544 United States Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We report a theoretical analysis showing that Rayleigh scattering could be used to monitor the growth of nanoparticles under arc discharge conditions. We compute the Rayleigh scattering cross sections of the nanoparticles by combining light scattering theory for gas-particle mixtures with calculations of the dynamic electronic polarizability of the nanoparticles. We find that the resolution of the Rayleigh scattering probe is adequate to detect nanoparticles as small as C60 at the expected concentrations of synthesis conditions in the arc periphery. Larger asymmetric nanoparticles would yield brighter signals, making possible to follow the evolution of the growing nanoparticle population from the evolution of the scattered intensity. Observable spectral features include characteristic resonant behaviour, shape-dependent depolarization ratio, and mass-dependent line shape. Direct observation of nanoparticles in the early stages of growth with unobtrusive laser probes should give insight on the particle formation mechanisms and may lead to better-controlled synthesis protocols. Copyright © 2017, The Authors. All rights reserved.

关键词： Rayleigh scattering

Deep learning of accurate force field of Ferroelectric HfO$_2$

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arXiv 2020年

作者： Wu, Jing Zhang, Yuzhi Zhang, Linfeng Liu, Shi Fudan University Shanghai200433 China School of Science Westlake University HangzhouZhejiang310024 China Institute of Natural Sciences Westlake Institute for Advanced Study HangzhouZhejiang310024 China Yuanpei College Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The discovery of ferroelectricity in HfO2-based thin films opens up new opportunities for using this silicon-compatible ferroelectric to realize low-power logic circuits and high-density non-volatile memories. The functional performances of ferroelectrics are intimately related to their dynamic responses to external stimuli such as electric fields at finite temperatures. Molecular dynamics is an ideal technique for investigating dynamical processes on large length and time scales, though its applications to new materials is often hindered by the limited availability and accuracy of classical force fields. Here we present a deep neural network-based interatomic force field of HfO2 learned from ab initio data using a concurrent learning procedure. The model potential is able to predict structural properties such as elastic constants, equation of states, phonon dispersion relationships, and phase transition barriers of various hafnia polymorphs with accuracy comparable with density functional theory calculations. The validity of this model potential is further confirmed by the reproduction of experimental sequences of temperature-driven ferroelectric-paraelectric phase transitions of HfO2 with isobaric-isothermal ensemble molecular dynamics simulations. We suggest a general approach to extend the model potential of HfO2 to related material systems including dopants and defects. Copyright © 2020, The Authors. All rights reserved.

关键词： Ferroelectricity

On the Particle Approximation of Lagged Feynman-Kac Formulae

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arXiv 2024年

作者： Awadelkarim, Elsiddig Caffarel, Michel Moral, Pierre Del Jasra, Ajay 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 University of Toulouse CNRS-Lab. de Chimie et Physique Quantiques Toulouse31062 France Centre de Recherche Inria Bordeaux Sud-Ouest Talence33405 France School of Data Science The Chinese University Hong Kong Shenzhen China

In this paper we examine the numerical approximation of the limiting invariant measure associated with Feynman-Kac formulae. These are expressed in a discrete time formulation and are associated with a Markov chain and a potential function. The typical application considered here is the computation of eigenvalues associated with non-negative operators as found, for example, in physics or particle simulation of rare-events. We focus on a novel lagged approximation of this invariant measure, based upon the introduction of a ratio of time-averaged Feynman-Kac marginals associated with a positive operator iterated l ∈ N times;a lagged Feynman-Kac formula. This estimator and its approximation using Diffusion Monte Carlo (DMC) have been extensively employed in the physics literature. In short, DMC is an iterative algorithm involving N ∈ N particles or walkers simulated in parallel, that undergo sampling and resampling operations. In this work, it is shown that for the DMC approximation of the lagged Feynman-Kac formula, one has an almost sure characterization of the L1-error as the time parameter (iteration) goes to infinity and this is at most of O(exp{−κl}/N), for_ κ > 0. In addition a non-asymptotic in time, and time uniform L1−bound is proved which is O(l/√N). We also prove a novel central limit theorem to give a characterization of the exact asymptotic in time variance. This analysis demonstrates that the strategy used in physics, namely, to run DMC with N and l small and, for long time enough, is mathematically justified. Our results also suggest how one should choose N and l in practice. We emphasize that these results are not restricted to physical applications;they have broad relevance to the general problem of particle simulation of the Feynman-Kac formula, which is utilized in a great variety of scientific and engineering fields. © 2024, CC BY.

关键词： Eigenvalues and eigenfunctions