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Partial Differential Equations in applied mathematics 2023年 8卷

作者： Aibinu, M.O. Moyo, S. Institute for Systems Science Durban University of Technology Durban 4000 South Africa Department of Applied Mathematics and School for Data Science and Computational Thinking Stellenbosch University South Africa National Institute for Theoretical and Computational Sciences (NITheCS) South Africa

The presence of delays in a mathematical model can improve its vitality and suitability in describing several phenomena. However, in the presence of delays, nonlinear fractional differential equations are more difficult to study. This paper presents the use of a blend of variational iteration method with Sumudu transform for solving delay differential equations with Caputo derivatives of fractional variable order. Moreover, the paper introduces delays into the price adjustment equations to propose new price adjustment models with more potential for vitality and suitability. The paper assigns suitable real values to the parameters for the graphical display and comparison of the obtained solutions. The paper presents the interactions that exist among the price, demand, supply and dependence of supply and demand on the price, which can be applied to estimate the equilibrium price. © 2023 The Authors

关键词： Caputo fractional derivative Market equilibrium Model Price adjustment Sumudu transform

Biomedical data analysis in translational research: Integration of expert knowledge and interpretable models 25

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Biomedical data analysis in translational research: Integrat...

25th European Symposium on Artificial Neural Networks, computational Intelligence and Machine Learning, ESANN 2017

作者： Bhanot, G. Biehl, M. Villmann, T. Zühlke, D. Rutgers University Department of Molecular Biology and Biochemistry PiscatawayNJ08854 United States University of Groningen Johann Bernoulli Institute for Mathematics and Computer Science Nijenborgh 9 Groningen9747AG Netherlands University of Applied Sciences Computational Intelligence Group Technikumplatz 17 MittweidaD-09648 Germany Seven Principles AG Erna-Scheffler-Str. 1A KölnD-51103 Germany

ISBN: (纸本)9782875870391

In various fields of biomedical research, the availability of electronic data has increased tremendously. Not only is the amount of disease specific data increasing, but so is its structural complexity in terms of dimensionality, multi-modality and inhomogeneity. Consequently, there is an urgent need for better coordination between bio-medical and computational researchers in order to make an impact on patient care. In any such effort, the integration of expert knowledge is essential. A careful synthesis of good analytical techniques applied to relevant medical questions would make the analysis both accurate and interpretable and facilitate transdisciplinary collaboration. This article summarizes recent challenges and introduces the contributions to this ESANN special session. © ESANN 2017 - Proceedings, 25th European Symposium on Artificial Neural Networks, computational Intelligence and Machine Learning. All rights reserved.

关键词： Neural networks

Stochastic Differential Dynamic programming

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Stochastic Differential Dynamic Programming

American Control Conference

作者： Evangelos Theodorou Yuval Tassa Emo Todorov Computational Learning and Motor Control Lab Departments of Computer Science and Neuroscience University of Southern California Interdisciplinary Center for Neural Computation Hebrew University Jerusalem Israel Department of Computer Science and Engineering and the Department of Applied Mathematics University of Washington Seattle WA

ISBN: (纸本)9781424474264

Although there has been a significant amount of work in the area of stochastic optimal control theory towards the development of new algorithms, the problem of how to control a stochastic nonlinear system remains an open research topic. Recent iterative linear quadratic optimal control methods iLQG [1], [2] handle control and state multiplicative noise while they are derived based on first order approximation of dynamics. On the other hand, methods such as Differential Dynamic programming expand the dynamics up to the second order but so far they can handle nonlinear systems with additive noise. In this work we present a generalization of the classic Differential Dynamic programming algorithm. We assume the existence of state and control multiplicative process noise, and proceed to derive the second-order expansion of the cost-to-go. We find the correction terms that arise from the stochastic assumption. Despite having quartic and cubic terms in the initial expression, we show that these vanish, leaving us with the same quadratic structure as standard DDP.

关键词： dynamic programming theory of optimal control multiplicative noise Quartic stochastic derivative Additive noise correct entry dynamics Work area Handles

Kaleidoscope: An efficient, learnable representation for all structured linear maps

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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

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

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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

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

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

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

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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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

Quantum amplitude estimation algorithms on IBM quantum devices

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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

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