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arXiv 2025年

作者： Elman, Howard C. Liang, Jiaxing Sánchez-Vizuet, Tonatiuh Department of Computer Science Institute for Advanced Computer Studies University of Maryland College Park United States Department of Computational Applied Mathematics & Operations Research Rice University United States Department of Mathematics The University of Arizona United States

We explore a hybrid technique to quantify the variability in the numerical solutions to a free boundary problem associated with magnetic equilibrium in axisymmetric fusion reactors amidst parameter uncertainties. The method aims at reducing computational costs by integrating a surrogate model into a multilevel Monte Carlo method. The resulting surrogate-enhanced multilevel Monte Carlo methods reduce the cost of simulation by factors as large as 104 compared to standard Monte Carlo simulations involving direct numerical solutions of the associated Grad-Shafranov partial differential equation. Accuracy assessments also show that surrogate-based sampling closely aligns with the results of direct computation, confirming its effectiveness in capturing the behavior of plasma boundary and geometric *** Codes 65Z05, 65C05, 62P35, 35R35, 35R60 Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

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Fitting exponential: An interest in rates

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COMPUTING IN SCIENCE & ENGINEERING 2004年第3期6卷 66-69页

作者： O'Leary, DP Institute for Advanced Computer Studies and the Applied Mathematics Program at the University of Maryland

Suppose we have two chemical reactions occurring simultaneously. Then theamount y of a reactant changes due to both processes and behaves as a function of time t as y(t) =x_1e~(α_1t) + x_2e~(α_2t), where x_1, x_2, α_1, and α_2 are fixed parameters. Typically, weobserve the function y(t) for m fixed t values, perhaps t = 0, Δt, 2Δt, ..., t_(final).

关键词： chemical reactions Fixed indium Function TIME FUNCTIONS

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Multigrid methods - Managing massive meshes

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COMPUTING IN SCIENCE & ENGINEERING 2006年第5期8卷 96-103页

作者： O'Leary, Dianne P. Institute for Advanced Computer Studies and the Applied Mathematics Program at the University of Maryland

In the last issue''s installment of your homework assignment, we investigatedmultigrid methods for solving linear systems. (please see p. 10 of this issue of CiSE for moreinformation about multigrid methods, o... 详细信息

关键词： finite difference finite element multigrid finite difference finiteelement multigrid

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The direction-of-arrival problem: Coming at you

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COMPUTING IN SCIENCE & ENGINEERING 2003年第6期5卷 60-63页

作者： O'Leary, DP The Institute for Advanced Computer Studies and the Applied Mathematics Program University of Maryland

If you breadk your leg on a mountain but have a cell phone or othertransmitter with you, you would hope a rescuer could determine the direction in which to travel toreach you. Similarly, if a navy detects a transmission from a submarine, it would want to determinethe signal's direction of arrival (DOAto locate that sub. The problem is complicated if more thanone signal appears―especially if the number of signals is unknown―and even more complicated if youor the submarine is moving. Surprisingly, we will see that your rescuer can solve an eigenvalueproblem (involving the product of some unknown matricesand use that information to find you. TheDOA-finding algorithm we'll use is called Esprit. To understand the process, we also will useseveral matrix decompositions and illustrate the necessity of using update techniques for real-timecomputations.

关键词： Esapent updating technique matrices Direction of arrival estimation Navy matrix decomposition Submarine Mobile phones Leg Angle of arrival If signals mountains real-time computation United States Department of Agriculture

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Efficiently Verifiable Quantum Advantage on Near-Term Analog Quantum Simulators

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PRX Quantum 2025年第1期6卷 010341-010341页

作者： Zhenning Liu Dhruv Devulapalli Dominik Hangleiter Yi-Kai Liu Alicia J. Kollár Alexey V. Gorshkov Andrew M. Childs Joint Center for Quantum Information and Computer Science NIST/University of Maryland College Park Maryland 20742 USA Joint Quantum Institute NIST/University of Maryland College Park Maryland 20742 USA Department of Computer Science University of Maryland College Park Maryland 20742 USA Simons Institute for the Theory of Computing University of California at Berkeley California 94720 USA Applied and Computational Mathematics Division National Institute of Standards and Technology (NIST) Gaithersburg Maryland 20899 USA Department of Physics University of Maryland College Park Maryland 20742 USA Institute for Advanced Computer Studies University of Maryland College Park Maryland 20742 USA

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on single-step Feynman-Kitaev verification of an analog quantum simulation, in which the verifier need only run an O(λ2)-time classical computation, and the prover need only prepare O(1) samples of a history state and perform O(λ2) single-qubit measurements, for a security parameter λ. We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations.

关键词： Quantum computers

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Biomedical data and AI

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Science China Life Sciences 2025年第5期68卷 1536-1540页

作者： Hao Xu Shibo Zhou Zefeng Zhu Vincenzo Vitelli Liangyi Chen Ziwei Dai Ning Yang Luhua Lai Shengyong Yang Sergey Ovchinnikov Zhuoran Qiao Sirui Liu Chen Song Jianfeng Pei Han Wen Jianfeng Feng Yaoyao Zhang Zhengwei Xie Yang-Yu Liu Zhiyuan Li Fulai Jin Hao Li Mohammad Lotfollahi Xuegong Zhang Ge Yang Shihua Zhang Ge Gao Pulin Li Qi Liu Jing-Dong Jackie Han Peking-Tsinghua Center for Life Sciences (CLS) Academy for Advanced Interdisciplinary StudiesPeking University Center for Quantitative Biology (CQB) Academy for Advanced Interdisciplinary StudiesPeking University Peking University-Tsinghua University-National Institute of Biological Sciences Joint Graduate Program Academy for Advanced Interdisciplinary StudiesPeking University Department of Physics University of Chicago School of Life Sciences Southern University of Science and Technology Peking University Chengdu Academy for Advanced Interdisciplinary Biotechnologies College of Chemistry and Molecular Engineering Peking University Department of Biotherapy Cancer Center and State Key Laboratory of BiotherapyWest China HospitalSichuan University Department of Biology Massachusetts Institute of Technology Lambic Therapeutics Inc. Changping Laboratory Al for Science Institute Key Laboratory of Computational Neuroscience and Brain-Inspired Intelligence Fudan University Department of Obstetrics and Gynecology West China Second University HospitalSichuan University Peking University International Cancer Institute and Peking University-Yunnan Baiyao International Medical Institute and State Key Laboratory of Natural and Biomimetic Drugs Department of Molecular and Cellular PharmacologySchool of Pharmaceutical SciencesPeking University Health Science CenterPeking University Channing Division of Network Medicine Department of MedicineBrigham and Women's Hospital and Harvard Medical School Center for Artificial Intelligence and Modeling the Carl R.Woese Institute for Genomic BiologyUniversity of Illinois Urbana-Champaign Department of Genetics and Genome Sciences School of Medicine and Department of Computer and Data Sciences and Department of Population and Quantitative Health SciencesCase Western Reserve University Department of Biochemistry and Biophysics University of California Sanger Institute Department of Automation Tsinghua University State Key Laboratory of Multimodal Artificial Intelligence Systems I

The development of artificial intelligence(AI) and the mining of biomedical data complement each other. From the direct use of computer vision results to analyze medical images for disease screening, to now integrating biological knowledge into models and even accelerating the development of new AI based on biological discoveries, the boundaries of both are constantly expanding, and their connections are becoming closer.

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Partial solution to "image deblurring: I can see clearly now"

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Computing in Science and Engineering 2003年第4期5卷 72-74页

作者： Nagy, James G. O'Leary, Dianne P. Sagduyu, Yalin E. Mathematics Department Emory University Atlanta GA United States Applied Mathematics Program Inst. for Advanced Computer Studies University of Maryland College Park MD 20742 United States

The article discusses the partial solution to image deblurring. In this problem, the best way to choose the regularization parameter is by eye. Some nonlinear reconstruction algorithms that reduce the problem are also discussed. In many applications, one must choose the regularization parameter by automatic methods rather than by eye.

关键词： Image analysis

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CRITICAL DOUBLE PHASE PROBLEMS INVOLVING SANDWICH-TYPE NONLINEARITIES

arXiv

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arXiv 2025年

作者： Farkas, Csaba Fiscella, Alessio Ho, Ky Winkert, Patrick Sapientia Hungarian University of Transylvania Department of Mathematics and Computer Science Târgu Mures Romania Corvinus Centre for Operations Research Corvinus Institute for Advanced Studies Corvinus University of Budapest Fővám tér 8 Budapest1093 Hungary Departamento de Matemática Universidade Estadual de Campinas IMECC Rua Sérgio Buarque de Holanda 651 SP CampinasCEP 13083–859 Brazil Institute of Applied Mathematics University of Economics Ho Chi Minh City 59C Nguyen Dinh Chieu Street District 3 Ho Chi Minh City Viet Nam Technische Universität Berlin Institut für Mathematik Straße des 17.Juni 136 Berlin10623 Germany

In this paper we study problems with critical and sandwich-type growth represented by − div (|∇u|p−2∇u + a(x)|∇u|q−2∇u) = λw(x)|u|s−2u + θB (x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ RN is a bounded domain with Lipschitz boundary ∂Ω, 1 pq N1 , 0 ≤ a(·) ∈ C0,1(Ω), λ, θ are real parameters, w is a suitable weight and B: Ω × R → R is given by B(x, t):= b0(x)|t|p∗−2t + b(x)|t|q∗−2t, where r∗ := Nr/(N − r) for r ∈ {p, q}. Here the right-hand side combines the effect of a critical term given by B(·, ·) and a sandwich-type perturbation with exponent s ∈ (p, q). Under different values of the parameters λ and θ, we prove the existence and multiplicity of solutions to the problem above. For this, we mainly exploit different variational methods combined with topological tools, like a new concentration-compactness principle, a suitable truncation argument and the Krasnoselskii’s genus theory, by considering very mild assumptions on the data a(·), b0(·) and b(·). Copyright © 2025, The Authors. All rights reserved.

关键词： Perturbation techniques

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Metric Identification of Vertices in Polygonal Cacti

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computer Modeling in Engineering & Sciences 2023年第7期136卷 883-899页

作者： Xiujun Zhang Muhammad Salman Anam Rani Rashna Tanveer Usman Ali Zehui Shao School of Computer Science Chengdu UniversityChengduChina Department of Mathematics The Islamia University of BahawalpurBahawalpurPakistan Centre for Advanced Studies in Pure and Applied Mathematics Bahauddin Zakariya UniversityMultanPakistan Institute for Intelligent Information Processing South China Business College of Guangdong University of Foreign StudiesGuangzhouChina

The distance between two vertices u and v in a connected graph G is the number of edges lying in a shortest path(geodesic)between them.A vertex x of G performs the metric identification for a pair(u,v)of vertices in G if and only if the equality between the distances of u and v with x implies that u=v(That is,the distance between u and x is different from the distance between v and x).The minimum number of vertices performing the metric identification for every pair of vertices in G defines themetric dimension of *** this paper,we performthemetric identification of vertices in two types of polygonal cacti:chain polygonal cactus and star polygonal cactus.

关键词： Metric metric identification metric generator metric dimension cactus graph

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Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations

Preconditioning techniques for reduced basis methods for par...

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作者： Elman, Howard C. Forstall, Virginia Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space, and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it may be more effective to use iterative methods to solve the reduced problem. We construct preconditioners for reduced iterative methods which are derived from preconditioners for the full problem. This approach permits reduced basis methods to be practical for larger bases than direct methods allow. We illustrate the effectiveness of iterative methods for solving reduced problems by considering two examples, the steady-state diffusion and convection-diffusion-reaction equations. © 2015 Society for Industrial and applied mathematics.

关键词： Iterative methods

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