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arXiv 2020年

作者： Dao, Tri Sohoni, Nimit S. Gu, Albert Eichhorn, Matthew Blonder, Amit Leszczynski, Megan Rudra, Atri Ré, Christopher Department of Computer Science Stanford University United States Institute for Computational and Mathematical Engineering Stanford University United States Center for Applied Mathematics Cornell University United States Department of Computer Science and Engineering University at Buffalo SUNY United States

Modern neural network architectures use structured linear transformations, such as low-rank matrices, sparse matrices, permutations, and the Fourier transform, to improve inference speed and reduce memory usage compared to general linear maps. However, choosing which of the myriad structured transformations to use (and its associated parameterization) is a laborious task that requires trading off speed, space, and accuracy. We consider a different approach: we introduce a family of matrices called kaleidoscope matrices (K-matrices) that provably capture any structured matrix with near-optimal space (parameter) and time (arithmetic operation) complexity. We empirically validate that K-matrices can be automatically learned within end-to-end pipelines to replace hand-crafted procedures, in order to improve model quality. For example, replacing channel shuffles in ShuffleNet improves classification accuracy on ImageNet by up to 5%. K-matrices can also simplify hand-engineered pipelines—we replace filter bank feature computation in speech data preprocessing with a learnable kaleidoscope layer, resulting in only 0.4% loss in accuracy on the TIMIT speech recognition task. In addition, K-matrices can capture latent structure in models: for a challenging permuted image classification task, a K-matrix based representation of permutations is able to learn the right latent structure and improves accuracy of a downstream convolutional model by over 9%. We provide a practically efficient implementation of our approach, and use K-matrices in a Transformer network to attain 36% faster end-to-end inference speed on a language translation task. Copyright © 2020, The Authors. All rights reserved.

关键词： Matrix algebra

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Critical pore radius and transport properties of disordered hard- and overlapping-sphere models

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Physical Review E 2021年第1期104卷 014127-014127页

作者： Michael A. Klatt Robert M. Ziff Salvatore Torquato Department of Physics Princeton University Princeton New Jersey 08544 USA Institut für Theoretische Physik FAU Erlangen-Nürnberg Staudtstr. 7 91058 Erlangen Germany Center for the Study of Complex Systems and Department of Chemical Engineering University of Michigan Ann Arbor Michigan 48109 USA Department of Chemistry Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Transport properties of porous media are intimately linked to their pore-space microstructures. We quantify geometrical and topological descriptors of the pore space of certain disordered and ordered distributions of spheres, including pore-size functions and the critical pore radius δc. We focus on models of porous media derived from maximally random jammed sphere packings, overlapping spheres, equilibrium hard spheres, quantizer sphere packings, and crystalline sphere packings. For precise estimates of the percolation thresholds, we use a strict relation of the void percolation around sphere configurations to weighted bond percolation on the corresponding Voronoi networks. We use the Newman-Ziff algorithm to determine the percolation threshold using universal properties of the cluster size distribution. The critical pore radius δc is often used as the key characteristic length scale that determines the fluid permeability k. A recent study [Torquato, Adv. Wat. Resour. 140, 103565 (2020)] suggested for porous media with a well-connected pore space an alternative estimate of k based on the second moment of the pore size 〈δ2〉, which is easier to determine than δc. Here, we compare δc to the second moment of the pore size 〈δ2〉, and indeed confirm that, for all porosities and all models considered, δc2 is to a good approximation proportional to 〈δ2〉. However, unlike 〈δ2〉, the permeability estimate based on δc2 does not predict the correct ranking of k for our models. Thus, we confirm 〈δ2〉 to be a promising candidate for convenient and reliable estimates of the fluid permeability for porous media with a well-connected pore space. Moreover, we compare the fluid permeability of our models with varying degrees of order, as measured by the τ order metric. We find that (effectively) hyperuniform models tend to have lower values of k than their nonhyperuniform counterparts. Our findings could facilitate the design of porous media with desirable transport properties via targete

关键词： Geophysical networks Materials Patterns in complex systems

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arXiv

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arXiv 2023年

作者： Stickler, Megan Ott, William Kilpatrick, Zachary P. Josic, Krešimir Karamched, Bhargav R. Department of Mathematics University of Houston HoustonTX United States Department of Applied Mathematics University of Colorado-Boulder BoulderCO United States Department of Biology and Biochemistry University of Houston HoustonTX United States Department of Mathematics Florida State University TallahasseeFL United States Institute of Molecular Biophysics Florida State University TallahasseeFL United States Program in Neuroscience Florida State University TallahasseeFL United States

Normative models are often used to describe how humans and animals make decisions. These models treat deliberation as the accumulation of uncertain evidence that terminates with a commitment to a choice. When extended to social groups, such models often assume that individuals make independent observations. However, individuals typically gather evidence from common sources, and their observations are rarely independent. Here we ask: For a group of ideal observers who do not exchange information, what is the impact of correlated evidence on decision accuracy? We show that even when agents are identical, correlated evidence causes decision accuracy to depend on temporal decision order. Surprisingly, the first decider is less accurate than a lone observer. Early deciders are less accurate than late deciders. These phenomena occur despite the fact that the rational observers use the same decision criterion, so they are equally confident in their decisions. We analyze discrete and continuum evidence-gathering models to explain why the first decider is less accurate than a lone observer when evidence is correlated. Pooling the decisions of early deciders using a majority rule does not rescue accuracy in the sense that such pooling results in only modest accuracy gain. Although we analyze an idealized model, we believe that our analysis offers insights that do not depend on exactly how groups integrate evidence and form *** Codes 92F05 © 2023, CC BY.

关键词： Decision making

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Differentially private stochastic optimization: New results in convex and non-convex settings

arXiv

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arXiv 2021年

作者： Bassily, Raef Guzmán, Cristóbal Menart, Michael The Ohio State University United States Department of Applied Mathematics University of Twente Netherlands Institute for Mathematical and Computational Engineering Pontificia Universidad Católica de Chile Chile Department of Computer Science & Engineering The Ohio State University United States

We study differentially private stochastic optimization in convex and non-convex settings. For the convex case, we focus on the family of non-smooth generalized linear losses (GLLs). Our algorithm for the 2setting achieves optimal excess population risk in near-linear time, while the best known differentially private algorithms for general convex losses run in super-linear time. Our algorithm for the 1setting has nearly-optimal excess population risk Õ(log d/nϵ), and circumvents the dimension dependent lower bound of [AFKT21] for general non-smooth convex losses. In the differentially private non-convex setting, we provide several new algorithms for approximating stationary points of the population risk. For the 1-case with smooth losses and polyhedral constraint, we provide the first nearly dimension independent rate, Õ(log2/3d/(nϵ)1/3) in linear time. For the constrained 2-case with smooth losses, we obtain a linear-time algorithm with rate Õ(1/n1/3+ d1/5/(nϵ)2/5). Finally, for the 2-case we provide the first method for non-smooth weakly convex stochastic optimization with rate Õ(1/n1/4+ d1/6/(nϵ)1/3) which matches the best existing non-private algorithm when d = O(√n). We also extend all our results above for the non-convex 2setting to the psetting, where 1 © 2021, CC BY.

关键词： Clustering algorithms

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Optimal control theory applied to the anti-viral treatment of AIDS

Optimal control theory applied to the anti-viral treatment o...

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IEEE Conference on Decision and Control

作者： J.A.M. Felippe de Souza M.A.L. Caetano T. Yoneyama Departament of Electromechanical Engineering Universidade da Beira Interior Covilha Portugal Department of Statistical Computational and Applied Mathematics Universidade Estadual Paulista (UNESP) Sao Paulo Brazil Department of Eletronics Engineering Instituto Technologico de Aeronautica Sao Paulo Brazil

ISBN: (纸本)0780366387

This work deals with a particular application of the optimal control theory to a model related to HIV infection dynamics. The mathematical model adopted in this work was proposed by Nowak et al. (1996), and describes the dynamics of viral concentration in terms of interaction with CD4 cells and the cytoroxic T lymphocytes, which are responsible for the immune defence of the organism. The control variable is the drug dose which, in turn, affects the rate of infection of CD4 cells by HIV virus. The cost function to be minimized is a weighted sum of the final viral load and the accumulated side effects. Simulation results show that the optimal control scheme can achieve improved quality of the treatment in terms of reduction in the viral load and quantity of administered drugs, but has the inconvenience related to the necessity of frequent and periodic laboratory analysis to provide feedback information to adjust the doses.

关键词： Optimal control Acquired immune deficiency syndrome Human immunodeficiency virus Drugs Mathematical model Immune system Organisms Cost function Analytical models Laboratories

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Multiple Magnetic Pole Reversals and Mössbauer Studies in Molecular-based Mixed Valency Ferrimagnet {[N(n-C4H9)4][MIIFeIII(C2O4)3]}n (M=Zn, Fe)

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Physics Procedia 2012年 25卷 375-381页

作者： Qing Lin Chenglong Lei Guodong Tang Qingmei Zhang Xinlong Dong Fupei Liang Ruijun Wang Siliang Zeng Yun He College of Physics and Technology Guangxi Normal University Guilin 541004 China Department of Information Technology Hainan Medical College Haikou 571101 China College of Chemistry and Chemical Engineering Guangxi Normal University Guilin 541004China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

The Molecule magnets Materials {[N(n-C4H9)4][MIIFeIII(C2O4)3]}n (M=Zn Fe) were investigated by magnetic measurements and Mössbauer spectroscopy .In the complex {[N(n-C4H9)4][ZnII0.03FeII0.97 FeIII(C2O4)3]}n detailed investigation of the ferromagnetism behaviour, and a compensation temperature has found with the field being less than 1KOe. And the 57Fe Mössbauer measurements had been carried out in {[N(n-C4H9)4][FeIIFeIII(C2O4)3]}n to investigate the mixed valency character and antiferromagnetic coupling. Some ferrimagnets consisting of magnetic anisotropy ions and two or more types of antiferromagnetically ordered magnetic ions exhibit this behavior. As the temperature was lowered to 40 K, the FeIII doublet subspectrum almost completely turns into a sextet subspectrum. The hyperfine magnetic field increases as the temperature decreasing.

关键词： Molecule-based magnet Oxalate Mössbauer spectroscopy spin glass

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Quantum amplitude estimation algorithms on IBM quantum devices

arXiv

引用

arXiv 2020年

作者： Rao, Pooja Yu, Kwangmin Lim, Hyunkyung Jin, Dasol Choi, Deokkyu Department of Mathematics Stony Brook University Stony BrookNY11794 United States Computational Science Initiative Brookhaven National Laboratory UptonNY11973 United States Department of Applied Mathematics and Statistics Stony Brook University Stony BrookNY11794 United States Department of Chemistry Stony Brook University Stony BrookNY11794 United States

Since the publication of the Quantum Amplitude Estimation (QAE) algorithm by Brassard et al., 2002, several variations have been proposed, such as Aaronson et al., 2019, Grinko et al., 2019, and Suzuki et al., 2020. The main difference between the original and the variants is the exclusion of Quantum Phase Estimation (QPE) by the latter. This difference is notable given that QPE is the key component of original QAE, but is composed of many operations considered expensive for the current NISQ era devices. We compare two recently proposed variants (Grinko et al., 2019 and Suzuki et al., 2020) by implementing them on the IBM Quantum device using Qiskit, an open source framework for quantum computing. We analyze and discuss advantages of each algorithm from the point of view of their implementation and performance on a quantum computer. Copyright © 2020, The Authors. All rights reserved.

关键词： Quantum theory

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Time-dependent information transmission in a model regulatory circuit

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Physical Review E 2013年第2期88卷 022708-022708页

作者： F. Mancini C. H. Wiggins M. Marsili A. M. Walczak International School for Advanced Studies (SISSA) Trieste Italy Department of Applied Physics and Applied Mathematics Center for Computational Biology and Bioinformatics Columbia University New York New York 10027 USA The Abdus Salam International Centre for Theoretical Physics (ICTP) Trieste Italy CNRS and Laboratoire de Physique Théorique de l’École Normale Supérieure Paris France

Many biological regulatory systems respond with a physiological delay when processing signals. A simple model of regulation which respects these features shows how the ability of a delayed output to transmit information is limited: at short times by the time scale of the dynamic input, at long times by that of the dynamic output. We find that topologies of maximally informative networks correspond to commonly occurring biological circuits linked to stress response and that circuits functioning out of steady state may exploit absorbing states to transmit information optimally.

关键词： GENE regulatory networks STRESS (Physiology) SIGNAL processing TOPOLOGY INFORMATION networks DYNAMICAL systems

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Tunable spin states in two-dimensional magnet CrI

arXiv

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arXiv 2017年

作者： Zheng, Fawei Zhao, Jize Liu, Zheng Li, Menglei Zhou, Mei Zhang, Shengbai Zhang, Ping Institute of Applied Physics and Computational Mathematics Beijing100088 China Beijing Computational Science Research Center Beijing100193 China Institute for Advanced Study Tsinghua University Beijing100084 China Department of Physics Capital Normal University Beijing100048 China Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute TroyNY12180-3590 United States

The recent discovery of ferromagnetic single-layer CrI3 creates ample opportunities for studying fundamental properties of atomically-thin magnets. By using first-principles calculations and model analysis, we show that a lateral strain and/or charge doping can have unexpected effects on the magnetic properties of CrI3. In particular, strain tunes the magnetic order and anisotropy: (1) a compressive strain leads to a phase transition from a ferromagnetic insulator to an antiferromagnetic insulator, while (2) a tensile strain can flip the magnetic orientation from off-plane to in-plane. Interestingly, we find that the phase boundary for the first transition is insensitive to charge doping, whereas that of the second one can be significantly modulated by electron doping. Copyright © 2017, The Authors. All rights reserved.

关键词： Chromium compounds

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Theoretical calculation of the cross sections of dielectronic recombination on He+

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Physical Review A 1999年第6期60卷 4510-4510页

作者： Yu Zou Li-Bo Zhao Quan-Yu Fang China Center for Advanced Science and Technology (World Laboratory) P.O. Box 8730 Beijing 100080 People’s Republic of China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 People’s Republic of China Department of Applied Physics Beijing University of Aeronautics and Astronautics Beijing 100083 People’s Republic of China

The relativistic multichannel theory has been applied to calculations of cross sections of dielectronic recombination on He+. A first-order approximation is adopted for the radiative process. A correction based on isolated resonance approximation is used for the very narrow resonances among the 2lnl′ states to include the radiation width. Twelve partial cross sections are calculated for both the 2lnl′ and 3lnl′ resonance states with n<~5. The convolved cross sections for the n<~3 states are in good agreement with those of the observations. A quantitative discrepancy for the n=4 and n=5 states may be attributed to the l dependence of the field ionization and the radiative decay during the time of flight.

关键词： Hydrogenlike helium Ions

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