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arXiv 2020年

作者： Stone, James M. Tomida, Kengo White, Christopher J. Felker, Kyle G. Department of Astrophysical Sciences Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Earth and Space Science Osaka University Toyonaka Osaka560-0043 Japan Kavli Institute for Theoretical Physics University of California Santa Barbara Santa BarbaraCA93107 United States School of Natural Sciences Institute for Advanced Study PrincetonNJ08544 United States Astronomical Institute Tohoku University Sendai Miyagi980-8578 Japan Argonne National Laboratory LemontIL60439 United States

The design and implementation of a new framework for adaptive mesh refinement (AMR) calculations is described. It is intended primarily for applications in astrophysical fluid dynamics, but its flexible and modular design enables its use for a wide variety of physics. The framework works with both uniform and nonuniform grids in Cartesian and curvilinear coordinate systems. It adopts a dynamic execution model based on a simple design called a "task list" that improves parallel performance by overlapping communication and computation, simplifies the inclusion of a diverse range of physics, and even enables multiphysics models involving different physics in different regions of the calculation. We describe physics modules implemented in this framework for both non-relativistic and relativistic magnetohydrodynamics (MHD). These modules adopt mature and robust algorithms originally developed for the Athena MHD code and incorporate new extensions: support for curvilinear coordinates, higher-order time integrators, more realistic physics such as a general equation of state, and diffusion terms that can be integrated with super-time-stepping algorithms. The modules show excellent performance and scaling, with well over 80% parallel efficiency on over half a million threads. The source code has been made publicly available. Copyright © 2020, The Authors. All rights reserved.

关键词： Magnetohydrodynamics

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

arXiv

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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

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TWO-SAMPLE TEST OF COMMUNITY MEMBERSHIPS OF WEIGHTED STOCHASTIC BLOCK MODELS

arXiv

引用

arXiv 2018年

作者： Li, Yezheng Li, Hongzhe Program in Applied Mathematics and Computational Science University of Pennsylvania PhiladelphiaPA19104 United States University of Pennsylvania PhiladelphiaPA19104 United States

Suppose two networks are observed for the same set of nodes, where each network is assumed to be generated from a weighted stochastic block model. This paper considers the problem of testing whether the community memberships of the two networks are the same. A test statistic based on singular subspace distance is developed. Under the weighted stochastic block models with dense graphs, the limiting distribution of the proposed test statistic is developed. Simulation results show that the test has correct empirical type 1 errors under the dense graphs. The test also behaves as expected in empirical power, showing gradual changes when the intra-block and inter-block distributions are close and achieving 1 when the two distributions are not so close, where the closeness of the two distributions is characterized by Renyi divergence of order 1/2. The Enron email networks are used to demonstrate the proposed *** Codes 62E20, 62F03, 62H15, 91D30, 62F05 Copyright © 2018, The Authors. All rights reserved.

关键词： Clustering algorithms

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Smooth graph signal interpolation for big data

arXiv

引用

arXiv 2018年

作者： Heimowitz, Ayelet Eldar, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Faculty of Math and Computer Science Weizmann Institute of Science Rehovot Israel

In this paper we present the Markov variation, a smoothness measure which offers a probabilistic interpretation of graph signal smoothness. This measure is then used to develop an optimization framework for graph signal interpolation. Our approach is based on diffusion embedding vectors and the connection between diffusion maps and signal processing on graphs. As diffusion embedding vectors may be expensive to compute for large graphs, we present a computationally efficient method, based on the Nyström extension, for interpolation of signals over a graph. We demonstrate our approach on the MNIST dataset and a dataset of daily average temperatures around the US. We show that our method outperforms state of the art graph signal interpolation methods on both datasets, and that our computationally efficient reconstruction achieves slightly reduced accuracy with a large speedup. Copyright © 2018, The Authors. All rights reserved.

关键词： computational efficiency

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Robust preconditioning for space-time isogeometric analysis of parabolic evolution problems

arXiv

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arXiv 2018年

作者： Hofer, Christoph Langer, Ulrich Neumüller, Martin Doctoral Program 'Computational Mathematics' Johannes Kepler University Altenbergerstr. 69 LinzA-4040 Austria Institute of Computational Mathematics Johannes Kepler University Altenbergerstr. 69 LinzA-4040 Austria Johann Radon Institute for Computational and Applied Mathematics Austrian Academy of Sciences Altenbergerstr. 69 LinzA-4040 Austria

We propose and investigate new robust preconditioners for space-time Isogeometric Analysis of parabolic evolution problems. These preconditioners are based on a time parallel multigrid method. We consider a decomposition of the space-time cylinder into time-slabs which are coupled via a discontinuous Galerkin technique. The time-slabs provide the structure for the timeparallel multigrid solver. The most important part of the multigrid method is the smoother. We utilize the special structure of the involved operator to decouple its application into several spatial problems by means of generalized eigenvalue or Schur decompositions. Some of these problems have a symmetric saddle point structure, for which we present robust preconditions. Finally, we present numerical experiments confirming the robustness of our space-time IgA solver. Copyright © 2018, The Authors. All rights reserved.

关键词： Galerkin methods

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Hard convex lens-shaped particles: Characterization of dense disordered packings

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Physical Review E 2019年第6期100卷 062902-062902页

作者： Giorgio Cinacchi Salvatore Torquato Departamento de Física Teórica de la Materia Condensada Instituto de Física de la Materia Condensada (IFIMAC) Instituto de Ciencias de Materiales “Nicolás Cabrera” Universidad Autónoma de Madrid Ciudad Universitaria de Cantoblanco E-28049 Madrid Spain Department of Chemistry and Department of Physics Institute for the Science and Technology of Materials Program for Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Among the family of hard convex lens-shaped particles (lenses), the one with aspect ratio equal to 2/3 is “optimal” in the sense that the maximally random jammed (MRJ) packings of such lenses achieve the highest packing fraction ϕMRJ≃0.73 [G. Cinacchi and S. Torquato, Soft Matter 14, 8205 (2018)]. This value is only a few percent lower than ϕDKP=0.76210⋯, the packing fraction of the corresponding densest-known crystalline (degenerate) packings [G. Cinacchi and S. Torquato, J. Chem. Phys. 143, 224506 (2015)]. By exploiting the appreciably reduced propensity that a system of such optimal lenses has to positionally and orientationally order, disordered packings of them are progressively generated by a Monte Carlo method–based procedure from the dilute equilibrium isotropic fluid phase to the dense nonequilibrium MRJ state. This allows us to closely monitor how the (micro)structure of these packings changes in the process of formation of the MRJ state. The gradual changes undergone by the many structural descriptors calculated here can coherently and consistently be traced back to the gradual increase in contacts between the hard particles until the isostatic mean value of ten contact neighbors per lens is reached at the effectively hyperuniform MRJ state. Compared to the MRJ state of hard spheres, the MRJ state of such optimal lenses is denser (less porous), more disordered, and rattler-free. This set of characteristics makes them good glass formers. It is possible that this conclusion may also hold for other hard convex uniaxial particles with a correspondingly similar aspect ratio, be they oblate or prolate, and that, by using suitable biaxial variants of them, that set of characteristics might further improve.

关键词： Granular packing Jamming Colloids Disordered systems Granular materials Lyotropic liquid crystals Monte Carlo methods

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Volume growth, curvature, and buser-type inequalities in graphs

arXiv

引用

arXiv 2018年

作者： Benson, Brian Ralli, Peter Tetali, Prasad Department of Mathematics University of California RiversideCA United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States School of Mathematics Georgia Institute of Technology AtlantaGA United States

We study the volume growth of metric balls as a function of the radius in discrete spaces, and focus on the relationship between volume growth and discrete curvature. We improve volume growth bounds under a lower bound on the so-called Ollivier curvature, and discuss similar results under other types of discrete Ricci curvature. Following recent work in the continuous setting of Riemannian manifolds (by the first author), we then bound the eigenvalues of the Laplacian of a graph under bounds on the volume growth. In particular, λ2of the graph can be bounded using a weighted discrete Hardy inequality and the higher eigenvalues of the graph can be bounded by the eigenvalues of a tridiagonal matrix times a multiplicative factor, both of which only depend on the volume growth of the graph. As a direct application, we relate the eigenvalues to the Cheeger isoperimetric constant. Using these methods, we describe classes of graphs for which the Cheeger inequality is tight on the second eigenvalue. We also describe a method for proving Buser's Inequality in graphs, particularly under a lower bound assumption on curvature. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics

引用

Physical Review Letters 2018年第14期120卷 143001-143001页

作者： Linfeng Zhang Jiequn Han Han Wang Roberto Car Weinan E Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA and Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing 100871 People’s Republic of China

We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is first-principles based in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DPMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size.

关键词： Classical statistical mechanics Density functional theory First-principles calculations Interatomic & molecular potentials Learning Neuronal networks Potential energy surfaces Solid-state chemistry Thermal properties Van der Waals interaction Molecular dynamics

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Hyperuniform states of matter

arXiv

引用

arXiv 2018年

作者： Torquato, Salvatore Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

Hyperuniform states of matter are correlated systems that are characterized by an anomalous suppression of long-wavelength (i.e., large-length-scale) density fluctuations compared to those found in garden-variety disordered systems, such as ordinary fluids and amorphous solids. All perfect crystals, perfect quasicrystals and special disordered systems are hyperuniform. Thus, the hyperuniformity concept enables a unified framework to classify and structurally characterize crystals, quasicrystals and the exotic disordered varieties. While disordered hyperuniform systems were largely unknown in the scientific community over a decade ago, now there is a realization that such systems arise in a host of contexts across the physical, materials, chemical, mathematical, engineering, and biological sciences, including disordered ground states, glass formation, jamming, Coulomb systems, spin systems, photonic and electronic band structure, localization of waves and excitations, self-organization, fluid dynamics, number theory, stochastic point processes, integral and stochastic geometry, the immune system, and photoreceptor cells. Such unusual amorphous states can be obtained via equilibrium or nonequilibrium routes, and come in both quantum-mechanical and classical varieties. The connections of hyperuniform states of matter to many different areas of fundamental science appear to be profound and yet our theoretical understanding of these unusual systems is only in its infancy. The purpose of this review article is to introduce the reader to the theoretical foundations of hyperuniform ordered and disordered systems. Special focus will be placed on fundamental and practical aspects of the disordered kinds, including our current state of knowledge of these exotic amorphous systems as well as their formation and novel physical properties. Copyright © 2018, The Authors. All rights reserved.

关键词： Ground state

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Regularized matrix data clustering and its application to image analysis

arXiv

引用

arXiv 2018年

作者： Gao, Xu Shen, Weining Ombao, Hernando Department of Statistics University of California IrvineCA United States Program on Applied Mathematics & Computational Science King Abdullah University of Science and Technology Saudi Arabia

In this paper, we propose a regularized mixture probabilistic model to cluster matrix data and apply it to brain signals. The approach is able to capture the sparsity (low rank, small/zero values) of the original signals by introducing regularization terms into the likelihood function. Through a modified EM algorithm, our method achieves the optimal solution with low computational cost. Theoretical results are also provided to establish the consistency of the proposed estimators. Simulations show the advantages of the proposed method over other existing methods. We also apply the approach to two real datasets from different experiments. Promising results imply that the proposed method successfully characterizes signals with different patterns while yielding insightful scientific interpretation. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

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