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arXiv 2021年

作者： Maher, Charles Emmett Stillinger, Frank H. Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics 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

The study of hard-particle packings is of fundamental importance in physics, chemistry, cell biology, and discrete geometry. Much of the previous work on hard-particle packings concerns their densest possible arrangements. By contrast, we examine kinetic effects inevitably present in both numerical and experimental packing protocols. Specifically, we determine how changing the compression/shear rate of a two-dimensional packing of noncircular particles causes it to deviate from its densest possible configuration, which is always periodic. The adaptive shrinking cell (ASC) optimization scheme maximizes the packing fraction of a hard-particle packing by first applying random translations and rotations to the particles and then isotropically compressing and shearing the simulation box repeatedly until a possibly jammed state is reached. We use a stochastic implementation of the ASC optimization scheme to mimic different effective time scales by varying the number of particle moves between compressions/shears. We generate dense, effectively jammed, monodisperse, two-dimensional packings of obtuse scalene triangle, rhombus, curved triangle, lens, and "ice cream cone" (a semicircle grafted onto an isosceles triangle) shaped particles, with a wide range of packing fractions and degrees of order. To quantify these kinetic effects, we introduce the kinetic frustration index K, which measures the deviation of a packing from its maximum possible packing fraction. To investigate how kinetics affect short- and long-range ordering in these packings, we compute their spectral densities χV (k) and characterize their contact networks. We find that kinetic effects are most significant when the particles have greater asphericity, less curvature, and less rotational symmetry. This work may be relevant to the design of laboratory packing protocols. Copyright © 2021, The Authors. All rights reserved.

关键词： Kinetic theory

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

arXiv

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arXiv 2021年

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 ¯) 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 χV (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 these packings and find that the long-time power-law scaling indicates these packings are hyperuniform with a small-Q power law scaling of the spectral density χV (Q) ∼ Qα with an exponent α that ranges from 0.64 at th

关键词： Spheres

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Local number fluctuations in ordered and disordered phases of water across temperatures: Higher-order moments and degrees of tetrahedrality

arXiv

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arXiv 2024年

作者： Klatt, Michael A. Kim, Jaeuk Gartner, Thomas E. Torquato, Salvatore Institute for AI Safety and Security Wilhelm-Runge-Str. 10 Ulm89081 Germany Institute for Material Physics in Space Köln51170 Germany Department of Physics Ludwig-Maximilians-Universität München Schellingstr. 4 Munich80799 Germany Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08544 United States Department of Chemical & Biomolecular Engineering Lehigh University BethlehemPA18015 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

The isothermal compressibility (i.e., the asymptotic number variance) of equilibrium liquid water as a function of temperature is minimal near ambient conditions. This anomalous non-monotonic temperature dependence is due to a balance between thermal fluctuations and the formation of tetrahedral hydrogen-bond networks. Since tetrahedrality is a many-body property, it will also influence the higher-order moments of density fluctuations, including the skewness and kurtosis. To gain a more complete picture, we examine these higher-order moments that encapsulate many-body correlations using a recently developed, advanced platform for local density fluctuations. We study an extensive set of simulated phases of water across a range of temperatures (80 K to 1600 K) with various degrees of tetrahedrality, including ice phases, equilibrium liquid water, supercritical water, and disordered nonequilibrium quenches. We find clear signatures of tetrahedrality in the higher-order moments, including the skewness and excess kurtosis, that scale for all cases with the degree of tetrahedrality. More importantly, this scaling behavior leads to non-monotonic temperature dependencies in the higher-order moments for both equilibrium and non-equilibrium phases. Specifically, at near-ambient conditions, the higher-order moments vanish most rapidly for large length scales, and the distribution quickly converges to a Gaussian in our metric. However, at non-ambient conditions, higher-order moments vanish more slowly and hence become more relevant especially for improving information-theoretic approximations of hydrophobic solubility. The temperature non-monotonicity that we observe in the full distribution across length-scales could shed light on water's nested anomalies, i.e., reveal new links between structural, dynamic, and thermodynamic anomalies. © 2024, CC BY-NC-ND.

关键词： Higher order statistics

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On the Lagrangian-Eulerian Coupling in the Immersed Finite Element/Difference Method

arXiv

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arXiv 2021年

作者： Lee, Jae H. Griffith, Boyce E. Department of Mathematics University of North Carolina Chapel HillNC United States Department of Mechanical Engineering Johns Hopkins University BaltimoreMD United States Institute for Computational Medicine Johns Hopkins University BaltimoreMD United States Departments 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 School of Medicine Chapel HillNC United States McAllister Heart Institute University of North Carolina School of Medicine Chapel HillNC United States

The immersed boundary (IB) method is a non-body conforming approach to fluid-structure interaction (FSI) that uses an Eulerian description of the momentum, viscosity, and incompressibility of a coupled fluid-structure system and a Lagrangian description of the deformations, stresses, and resultant forces of the immersed structure. Integral transforms with Dirac delta function kernels couple the Eulerian and Lagrangian variables, and in practice, discretizations of these integral transforms use regularized delta function kernels. Many different kernel functions have been proposed, but prior numerical work investigating the impact of the choice of kernel function on the accuracy of the methodology has often been limited to simplified test cases or Stokes flow conditions that may not reflect the method’s performance in applications, particularly at intermediate-to-high Reynolds numbers, or under different loading conditions. This work systematically studies the effect of the choice of regularized delta function in several fluid-structure interaction benchmark tests using the immersed finite element/difference (IFED) method, which is an extension of the IB method that uses a finite element structural discretizations combined with a Cartesian grid finite difference method for the incompressible Navier-Stokes equations. Whereas the conventional IB method spreads forces from the nodes of the structural mesh and interpolates velocities to those nodes, the IFED formulation evaluates the regularized delta function on a collection of interaction points that can be chosen to be denser than the nodes of the Lagrangian mesh. This opens the possibility of using structural discretizations with wide node spacings that would produce gaps in the Eulerian force in nodally coupled schemes (e.g., if the node spacing is comparable to or broader than the support of the regularized delta function). Earlier work with this methodology suggested that such coarse structural meshes can yield imp

关键词： Fluid structure interaction

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Iterative quantum optimization of spin glass problems with rapidly oscillating transverse fields

arXiv

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arXiv 2024年

作者： Barton, Brandon Sagal, Jacob Feeney, Sean Grattan, George Patnaik, Pratik Oganesyan, Vadim Carr, Lincoln D. Kapit, Eliot Quantum Engineering Program Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Applied Mathematics and Statistics Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Center for Computational Quantum Physics Flatiron Institute 162 5th Avenue New YorkNY10010 United States Department of Physics Colorado School of Mines 1523 Illinois St GoldenCO80401 United States Department of Computer Science Colorado School of Mines 1500 Illinois St GoldenCO80401 United States Department of Physics and Astronomy College of Staten Island City University of New York Staten IslandNY10314 United States Physics program and Initiative for the Theoretical Sciences The Graduate Center City University of New York New YorkNY10016 United States

In this work, we introduce a new iterative quantum algorithm, called Iterative Symphonic Tunneling for Satisfiability problems (IST-SAT), which solves quantum spin glass optimization problems using high-frequency oscillating transverse fields. IST-SAT operates as a sequence of iterations, in which bitstrings returned from one iteration are used to set spin-dependent phases in oscillating transverse fields in the next iteration. Over several iterations, the novel mechanism of the algorithm steers the system toward the problem ground state. We benchmark IST-SAT on sets of hard MAX-3-XORSAT problem instances with exact state vector simulation, and report polynomial speedups over trotterized adiabatic quantum computation (TAQC) and the best known semi-greedy classical algorithm. When IST-SAT is seeded with a sufficiently good initial approximation, the algorithm converges to exact solution(s) in a polynomial number of iterations. Our numerical results identify a critial Hamming radius(CHR), or quality of initial approximation, where the time-to-solution crosses from exponential to polynomial scaling in problem size. By combining IST-SAT with future classical or quantum approximation algorithms, larger gains may be achieved. The mechanism we present in this work thus presents a new path toward achieving quantum advantage in optimization. © 2024, CC BY.

关键词： Combinatorial optimization

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Local two-sample testing over graphs and point-clouds by random-walk distributions

arXiv

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arXiv 2020年

作者： Landa, Boris Qu, Rihao Chang, Joseph Kluger, Yuval Program in Applied Mathematics Yale University Department of Pathology Yale University School of Medicine Department of Statistics and Data Science Yale University Interdepartmental Program in Computational Biology and Bioinformatics Yale University Department of Immunology Yale School of Medicine

Rejecting the null hypothesis in two-sample testing is a fundamental tool for scientific discovery. Yet, aside from concluding that two samples do not come from the same probability distribution, it is often of interest to characterize how the two distributions differ. Given samples from two densities f1and f0, we consider the task of localizing occurrences of the inequality f1> f0. To avoid the challenges associated with high-dimensional space, we propose a general hypothesis testing framework where hypotheses are formulated adaptively to the data by conditioning on the combined sample from the two densities. We then investigate a special case of this framework where the notion of locality is captured by a random walk on a weighted graph constructed over this combined sample. We derive a tractable testing procedure for this case employing a type of scan statistic, and provide non-asymptotic lower bounds on the power and accuracy of our test to detect whether f1> f0in a local sense. Furthermore, we characterize the test's consistency according to a certain problem-hardness parameter, and show that our test achieves the minimax detection rate for this parameter. We conduct numerical experiments to validate our method, and demonstrate our approach on two real-world applications: detecting and localizing arsenic well contamination across the United States, and analyzing two-sample single-cell RNA sequencing data from melanoma *** Codes 62G10 Copyright © 2020, The Authors. All rights reserved.

关键词： Random processes

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Modeling liquid water by climbing up Jacob’s ladder in density functional theory facilitated by using deep neural network potentials

arXiv

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arXiv 2021年

作者： Zhang, Chunyi Tang, Fujie Chen, Mohan Zhang, Linfeng Qiu, Diana Y. Perdew, John P. Klein, Michael L. Wu, Xifan Department of Physics Temple University PhiladelphiaPA19122 United States HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mechanical Engineering and Materials Science Yale University New HavenCT06520 United States Department of Chemistry Temple University PhiladelphiaPA19122 United States Institute for Computational Molecular Science Temple University PhiladelphiaPA19122 United States

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. In order to generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water towards the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. © 2021, CC BY.

关键词： Deep neural networks

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Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI 41

Position: Bayesian Deep Learning is Needed in the Age of Lar...

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41st International Conference on Machine Learning, ICML 2024

作者： Papamarkou, Theodore Skoularidou, Maria Palla, Konstantina Aitchison, Laurence Arbel, Julyan Dunson, David Filippone, Maurizio Fortuin, Vincent Hennig, Philipp Hernández-Lobato, José Miguel Hubin, Aliaksandr Immer, Alexander Karaletsos, Theofanis Khan, Mohammad Emtiyaz Kristiadi, Agustinus Li, Yingzhen Mandt, Stephan Nemeth, Christopher Osborne, Michael A. Rudner, Tim G.J. Rügamer, David Teh, Yee Whye Welling, Max Wilson, Andrew Gordon Zhang, Ruqi Department of Mathematics The University of Manchester Manchester United Kingdom Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge United States Spotify London United Kingdom Computational Neuroscience Unit University of Bristol Bristol United Kingdom Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University United States Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany Department of Computer Science Technical University of Munich Munich Germany Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge United Kingdom Department of Mathematics University of Oslo Oslo Norway Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative CA United States Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London United Kingdom Department of Computer Science UC Irvine Irvine United States Department of Mathematics and Statistics Lancaster University Lancaster United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Center for Data Science New York University New York United States Department of Statistics LMU Munich Munich Germany DeepMind London United Kingdom Department of Statistics University of Oxford Oxford United Kingdom Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences Center for Data Science Computer Science Department New York University New York United States Department of Computer Science Purdue University West Lafayette United States

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential. Copyright 2024 by the author(s)

关键词： Contrastive Learning

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computational Methods for Single-Particle Cryo-EM

arXiv

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arXiv 2020年

作者： Singer, Amit Sigworth, Fred J. Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Departments of Cellular and Molecular Physiology Biomedical Engineering and Molecular Biophysics and Biochemistry Yale University New HavenCT06520 United States

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional 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 three-dimensional molecular structure needs to be determined from many noisy two-dimensional 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 that also play a significant role in many other data science applications. Copyright © 2020, The Authors. All rights reserved.

关键词： Molecules

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

arXiv

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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

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