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Creating interconnect topologies by algorithmic edge removal: MOD and SMOD graphs

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Supercomputing Frontiers and Innovations

Supercomputing Frontiers and Innovations 2015年第4期2卷 16-47页

作者： Michalewicz, Marek T. Orlowski, Lukasz P. Deng, Yuefan A-STAR Computational Resource Centre 138632 Singapore A-STAR Institute of High Performance Computing 138632 Singapore Institute for Advanced Computational Science Stony Brook University New York11794-3600 United States Department of Applied Mathematics and Statistics Stony Brook University New York11794-3600 United States

We introduce a method of constructing classes of graphs by algorithmic removal of entire groups of edges. Our approach to creating new classes of graphs is to focus entirely on the structure and properties of an adjacency matrix. At an initialisation step of the algorithm we start with a complete (fully connected) graph. In Part I we present MOD and arrested MOD graphs resulting from removal of square blocks of edges at each iteration and substitution of removed blocks with a diagonal matrix with one extra pivotal element along the main diagonal. The MOD graphs possess unique and useful properties. All important graph measures are easily expressed in analytical form and are presented in the paper. Several important properties of MOD graphs are compared very favourably with graphs representing common interconnect topologies: hypercube, 3D and 5D tori, TOFU and dragonfly. This lead us to consider MOD and arrested MOD graphs as interesting candidates for effective supercomputer interconnects. In Part II, at each iterative step we successively remove triangular shapes from the adjacency matrix. This iterative process leads to the final matrix which has two Sierpiński gaskets aligned along the main diagonal. It will be shown below that this new class of graphs is not a Sierpiński graph, since it is the adjacency matrix which has a structure of a Sierpiński gasket, and not a graph described by this matrix. We call this new class of graphs Sierpiński-Michalewicz-Or lowski-Deng (SMOD) graphs. The most remarkable property of the SMOD class of graphs, is that irrespective of the graph order, the diameter is constant and equals 2. The size of the graph, or the total number of edges, is about 10% of the size of a complete graph of the same order. We analyse important graph theoretic characteristics related to the topology such as diameter as a function of graph order, size, mean path length, ratio of the graph size to the size of a complete graph of the same order, and some spe

关键词： Graph theory

Separating the contributions of electric and magnetic fields in deflecting the probes in proton radiography with multiple proton energies

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Matter and Radiation at Extremes 2021年第3期6卷 42-54页

作者： Bao Du Hong-Bo Cai Wen-Shuai Zhang Xiao-Fang Wang Dong-Guo Kang Luan Deng En-Hao Zhang Pei-Lin Yao Xin-Xin Yan Shi-Yang Zou Shao-Ping Zhu Institute of Applied Physics and Computational Mathematics Beijing 100094China HEDPS Center for Applied Physics and TechnologyPeking UniversityBeijing 100871China IFSA Collaborative Innovation Center Shanghai Jiao Tong UniversityShanghai 200240China Department of Engineering and Applied Physics University of Science and Technology of ChinaHefei 230026China Graduate School China Academy of Engineering PhysicsBeijing 100088China Department of Engineering Physics Tsinghua UniversityBeijing 100084China STPPL Research Center of Laser FusionChina Academy of Engineering PhysicsMianyang 621900China

In proton radiography,degeneracy of electric and magnetic fields in deflecting the probe protons can prevent full interpretation of proton flux perturbations in the detection *** this paper,theoretical analyses and numerical simulations suggest that the contributions of the electric and magnetic fields can be separately obtained by analyzing the difference between the flux distributions of two discriminated proton energies in a single shot of proton *** eliminate the influence of field evolution on the separation,a strategy is proposed in which slow field evolution is assumed or an approximate estimate of field growth is *** could help achieve a clearer understanding of the radiographic process and allow further quantitative analysis.

关键词： magnetic fields assumed

Bayesian Parameter Inference for Partially Observed Diffusions using Multilevel Stochastic Runge-Kutta Methods

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arXiv 2023年

作者： Moral, Pierre Del Hu, Shulan Jasra, Ajay Ruzayqat, Hamza Wang, Xinyu Institut de Mathematiques de Bordeaux FR Bordeaux33405 France School of Mathematics and Statistics Wenlan School of Business China Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Zhongnan University of Economics and Law CN China

We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an unbiased estimator and that one must time-discretize the diffusion process. In such scenarios it has been shown how one can introduce the multilevel Monte Carlo method to reduce the cost to compute posterior expected values of the parameters for a pre-specified mean square error (MSE);see [12]. These afore-mentioned methods rely on upon the Euler-Maruyama discretization scheme which is well-known in numerical analysis to have slow convergence properties. We adapt stochastic Runge-Kutta (SRK) methods for Bayesian parameter estimation of static parameters for diffusions. This can be implemented in high-dimensions of the diffusion and seemingly under-appreciated in the uncertainty quantification and statistics fields. For a class of diffusions and SRK methods, we consider the estimation of the posterior expectation of the parameters. We prove that to achieve a MSE of O(ϵ2), for ϵ > 0 given, the associated work is O(ϵ−2). Whilst the latter is achievable for the Milstein scheme, this method is often not applicable for diffusions in dimension larger than two. We also illustrate our methodology in several numerical examples. Copyright © 2023, The Authors. All rights reserved.

关键词： Diffusion

Compressed Gradient Tracking for Decentralized Optimization Over General Directed Networks

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arXiv 2021年

作者： Song, Zhuoqing Shi, Lei Pu, Shi Yan, Ming Shanghai Center for Mathematical Sciences Fudan University Shanghai China School of Mathematical Sciences Shanghai Key Laboratory for Contemporary Applied Mathematics Fudan University Shanghai China School of Data Science Shenzhen Research Institute of Big Data The Chinese University of Hong Kong Shenzhen China Department of Computational Mathematics Science and Engineering Department of Mathematics Michigan State University East LansingMI48864 United States

In this paper, we propose two communication-efficient decentralized optimization algorithms over a general directed multi-agent network. The first algorithm, termed Compressed Push-Pull (CPP), combines the gradient tracking Push-Pull method with communication compression. We show that CPP is applicable to a general class of unbiased compression operators and achieves linear convergence rate for strongly convex and smooth objective functions. The second algorithm is a broadcast-like version of CPP (B-CPP), and it also achieves linear convergence rate under the same conditions on the objective functions. B-CPP can be applied in an asynchronous broadcast setting and further reduce communication costs compared to CPP. Numerical experiments complement the theoretical analysis and confirm the effectiveness of the proposed methods. Copyright © 2021, The Authors. All rights reserved.

关键词： Directed graphs

OPERATORS ON ANTI-DUAL PAIRS: LEBESGUE DECOMPOSITION OF POSITIVE OPERATORS

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arXiv 2019年

作者： Tarcsay, Zsigmond Department of Applied Analysis and Computational Mathematics Eötvös Loránd University Pázmány Péter sétány 1/c. BudapestH-1117 Hungary

In this paper we introduce and study absolute continuity and singularity of positive operators acting on anti-dual pairs. We establish a general theorem that can be considered as a common generalization of various earlier Lebesgue-type decompositions. Different algebraic and topological characterizations of absolute continuity and singularity are supplied and also a complete description of uniqueness of the decomposition is provided. We apply the developed decomposition theory to some concrete objects including Hilbert space operators, Hermitian forms, representable functionals, and additive set *** 46L51, 47B65, Secondary 28A12, 46K10, 47A07 Copyright © 2019, The Authors. All rights reserved.

关键词： Vector spaces

Liquid-Liquid Transition in Water from First Principles

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Physical Review Letters 2022年第25期129卷 255702-255702页

作者： Thomas E. Gartner, III Pablo M. Piaggi Roberto Car Athanassios Z. Panagiotopoulos Pablo G. Debenedetti Department of Chemistry Princeton University Princeton New Jersey 08544 USA Department of Physics Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Department of Chemical and Biological Engineering Princeton University Princeton New Jersey 08544 USA

A long-standing question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles.

关键词： Classical statistical mechanics First order phase transitions First-principles calculations Liquid-liquid phase transition Phase transitions Thermodynamics Deep learning Density functional theory Molecular dynamics

Transport effects on multiple-component reactions in optical biosensors

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arXiv 2017年

作者： Evans, Ryan M. Edwards, David A. Applied and Computational Mathematics Division Information and Technology Laboratory National Institute of Standards and Technology GaithersburgMD20899 United States Department of Mathematical Sciences University of Delaware NewarkDE19716 United States

Optical biosensors are often used to measure kinetic rate constants associated with chemical reactions. Such instruments operate in the surface-volume configuration, in which ligand molecules are convected through a fluid-filled volume over a surface to which receptors are confined. Currently, scientists are using optical biosenors to measure the kinetic rate constants associated with DNA translesion synthesis-a process critical to DNA damage repair. Biosensor experiments to study this process involve multiple interacting components on the sensor surface. This multiple-component biosensor experiment is modeled with a set of nonlinear Integrodifferential Equations (IDEs). It is shown that in physically relevant asymptotic limits these equations reduce to a much simpler set of Ordinary Differential Equations (ODEs). To verify the validity of our ODE approximation, a numerical method for the IDE system is developed and studied. Results from the ODE model agree with simulations of the IDE model, rendering our ODE model useful for parameter estimation. Copyright © 2017, The Authors. All rights reserved.

关键词： Integrodifferential equations

Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations

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arXiv 2023年

作者： Ruzayqat, Hamza Beskos, Alexandros Crisan, Dan Jasra, Ajay Kantas, Nikolas Applied Mathematics and Computational Science Program Computer Electrical and Mathematical Sciences and Engineering Division King Abdullah University of Science and Technology Thuwal23955-6900 Saudi Arabia Department of Statistical Science University College London LondonWC1E 6BT United Kingdom Department of Mathematics Imperial College London LondonSW7 2AZ United Kingdom

We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging as not only is high-dimensional, but the model for the signal yields longer-range time dependencies through the observation locations. Motivated by this model we revisit a lesser-known and provably convergent computational methodology from [4, 11, 28] that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on Linear Gaussian state space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow water model (of about 104 - 105 dimensions) with real and synthetic data. The data is provided by the National Oceanic and Atmospheric Administration (NOAA) and contains observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [-51◦,-41◦], [17◦,27◦] *** Codes 62M20, 60G35, 60J20, 94A12, 93E11, 65C40 © 2023, CC BY.

关键词： Location

Telepsychiatry:The Evaluation and Treatment of Seniors in Rural Retirement Communities

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Journal of Geriatric Medicine 2019年第2期1卷 23-31页

作者： Susanne Inez Steinberg Robert Gallop Medical Director&Psychiatrist Penn Med Princeton House Behavioral Health MoorestownNJ 08057United States Applied Statistics Program Department of MathematicsWest Chester UniversityWest ChesterPA 19383United States

Few studies examine the benefits from geriatric telepsychiatry in rural retirement ***:*** demonstrate that using telepsychiatry(a)standard approaches to psychiatric evaluation would yield diagnoses in Diagnostic and Statistical Manual of Mental Disorders(DSM-V);(b)psychotherapies and pharmacotherapy could be effectively *** examine the relationships among cognition,mood,agitation and functions at baseline and the response to treatment over ***:Prospective longitudinal ***:Geriatric Depression scale(GDS),Mini Mental State Exam(MMSE),Barthel Index(BI),Pittsburgh Agitation Scale(PAS).Setting:Video ***:Psychotherapy,***:428 Seniors over 55,met criteria for at least one DSM-V ***:Treatments were administered for a full range of psychiatric diagnoses and age-related medical *** most frequently prescribed pharmacological agents were:antidepressants(78%)antipsychotics(64%),memory enhancers(38%).Participants(66%)received psychotherapy:individual(31%),couple(7%),family(13%).Variation in the MMSE scores were observed:55%remained stable,11%declined,18%*** Scores improved from baseline to 26 weeks(p=0.02,d=0.99:95%CI 0.39-1.56).PAS scores declined from baseline to 52 weeks(McNemar’s S=11.27,p=0.0008,d=1.17:95%CI 0.63-1.68).Function(BI)at week 26 was not statistically significantly different from baseline(t(26)=1.66,p=0.11,d=0.65:95%CI-0.16-1.42).Participants maintained independence(64.5%)at 52 weeks(McNemar’s S=6.23,p=0.013,d=0.79:95%CI 0.19-1.36)Conclusion:This study demonstrates the feasibility and benefit of providing a full complement of services via telepsychiatry to seniors and provides a rationale for more comprehensive reimbursement plans.

关键词： Psychotherapy Psychopharmacology Telepsychiatry Seniors Retirement communities Nursing Homes