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arXiv 2024年

作者： Simard, Olivier Dawid, Anna Tindall, Joseph Ferrero, Michel Sengupta, Anirvan M. Georges, Antoine Collège de France PSL University 11 place Marcelin Berthelot Paris75005 France CPHT CNRS École Polytechnique IP Paris PalaiseauF-91128 France Center for Computational Quantum Physics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States 〈aQaL〉 Applied Quantum Algorithms – Leiden Institute of Advanced Computer Science Lorentz Insitute for Theoretical Physics Universiteit Leiden Netherlands Center for Computational Mathematics Flatiron Institute 162 5th Avenue New YorkNY10010 United States Department of Physics and Astronomy Rutgers University PiscatawayNJ08854 United States DQMP Université de Genève 24 quai Ernest Ansermet GenèveCH-1211 Switzerland

Quantum simulators have the potential to solve quantum many-body problems that are beyond the reach of classical computers, especially when they feature long-range entanglement. To fulfill their prospects, quantum simulators must be fully controllable, allowing for precise tuning of the microscopic physical parameters that define their implementation. We consider Rydberg-atom arrays, a promising platform for quantum simulations. Experimental control of such arrays is limited by the imprecision on the optical tweezers positions when assembling the array, hence introducing uncertainties in the simulated Hamiltonian. In this work, we introduce a scalable approach to Hamiltonian learning using graph neural networks (GNNs). We employ the Density Matrix Renormalization Group (DMRG) to generate ground-state snapshots of the transverse field Ising model realized by the array, for many realizations of the Hamiltonian parameters. Correlation functions reconstructed from these snapshots serve as input data to carry out the training. We demonstrate that our GNN model has a remarkable capacity to extrapolate beyond its training domain, both regarding the size and the shape of the system, yielding an accurate determination of the Hamiltonian parameters with a minimal set of measurements. We prove a theorem establishing a bijective correspondence between the correlation functions and the interaction parameters in the Hamiltonian, which provides a theoretical foundation for our learning algorithm. Our work could open the road to feedback control of the positions of the optical tweezers, hence providing a decisive improvement of analog quantum simulators. Copyright © 2024, The Authors. All rights reserved.

关键词： Optical tweezers

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General Matrix Representation For Generalized B-Splines and its Application

SSRN

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SSRN 2023年

作者： Guo, Huayuan Liu, Minchao Qin, Guiming Qin, Kaihuai He, Kunlun Medical Big Data Research Center Medical Innovation Research Division Chinese PLA General Hospital. Beijing100853 China Medical Artificial Intelligence Research Center Medical Innovation Research Division Chinese PLA General Hospital Beijing100853 China Department of Information Medical Supplies Center of Chinese PLA General Hospital Beijing100853 China Institute of Applied Physics and computational Mathematics Beijing100091 China Department of Computer science and technology Tsinghua University Beijing100084 China

Classical B-splines based on deBoor-Cox algorithm is widely used, but its recursive calculation is time-consuming and its shape control capability still needs to be improved. To address the problem, by incorporated both core functions and Toeplitz matrix theory into the deBoor-Cox recursive formula, a novel set of basis matrix formula to calculate generalized B-splines of arbitrary order is proposed to realize the general matrix representation of three types of curves, including non-uniform generalized B-splines,uniform generalized B-splines and generalized piecewise Bézier. Furthermore, based on this general matrix, we developed the shape-controllable algorithms for curve generation and curve/surface interpolation. Experiments show that our basis matrix method outperforms classical method in terms of computational time and shape controllability for curve and surface modeling. Therefore, this novel method can further enrich the B-splines modeling theory and has good application potential. © 2023, The Authors. All rights reserved.

关键词： Matrix algebra

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Q-functions, synchronization, and Arnold tongues for coupled stochastic oscillators

arXiv

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arXiv 2025年

作者： Kreider, Max Lindner, Benjamin Thomas, Peter J. Department of Mathematics Applied Mathematics and Statistics Case Western Reserve University ClevelandOH44106 United States Bernstein Center for Computational Neuroscience Berlin Berlin10115 Germany Department of Physics Humboldt Universität zu Berlin BerlinD-12489 Germany Department of Mathematics Applied Mathematics and Statistics Department of Biology Department of Dataand Computer Science Department of Electrical Control and Systems Engineering Case Western Reserve University ClevelandOH44106 United States

Phase reduction is an effective theoretical and numerical tool for studying synchronization of coupled deterministic oscillators. Stochastic oscillators require new definitions of asymptotic phase. The Q-function, i.e. the slowest decaying complex mode of the stochastic Koopman operator (SKO), was proposed as a means of phase reduction for stochastic oscillators. In this paper, we show that the Q-function approach also leads to a novel definition of "synchronization" for coupled stochastic oscillators. A system of coupled oscillators in the synchronous regime may be viewed as a single (higher-dimensional) oscillator. Therefore, we investigate the relation between the Q-functions of the uncoupled oscillators and the higher-dimensional Q-function for the coupled system. We propose a definition of synchronization between coupled stochastic oscillators in terms of the eigenvalue spectrum of Kolmogorov’s backward operator (the generator of the Markov process, or the SKO) of the higher dimensional coupled system. We observe a novel type of bifurcation reflecting (i) the relationship between the leading eigenvalues of the SKO for the coupled system and (ii) qualitative changes in the cross-spectral density of the coupled oscillators. Using our proposed definition, we observe synchronization domains for symmetrically-coupled stochastic oscillators that are analogous to Arnold tongues for coupled deterministic oscillators. Copyright © 2025, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Decoding the Functional Interactome of Non-model Organisms with PHILHARMONIC 29th

Decoding the Functional Interactome of Non-model Organisms...

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29th International Conference on Research in computational Molecular Biology, RECOMB 2025

作者： Sledzieski, Sam Versavel, Charlotte Singh, Rohit Ocitti, Faith Devkota, Kapil Kumar, Lokender Shpilker, Polina Roger, Liza Yang, Jinkyu Lewinski, Nastassja Putnam, Hollie Berger, Bonnie Klein-Seetharaman, Judith Cowen, Lenore Center for Computational Biology Flatiron Institute New YorkNY United States Department of Computer Science Tufts University MedfordMA United States Departments of Biostatistics and Bioinformatics Duke University DurhamNC United States School of Biotechnology Faculty of Applied Sciences and Biotechnology Shoolini University Himachal Pradesh Solan173229 India School of Molecular Sciences and School of Ocean Futures Arizona State University TempeAZ United States Department of Mechanical Engineering Seoul National University Seoul Korea Republic of Department of Chemical and Life Science Engineering Virginia Commonwealth University RichmondVA United States Department of Biological Sciences University of Rhode Island KingstonRI United States Computer Science and Artificial Intelligence Laboratory and Department of Mathematics MIT CambridgeMA United States School of Molecular Sciences and College of Health Solutions Arizona State University PhoenixAZ United States

ISBN: (纸本)9783031902512

We introduce PHILHARMONIC, a computational framework that couples deep learning de novo network inference with robust unsupervised spectral clustering algorithms to uncover functional relationships and high-level organization in non-model organisms. Our novel clustering approach produces highly informative functional modules by de-noising the predicted network. We also develop a novel algorithm called ReCIPE, which aims to reconnect disconnected clusters, increasing functional enrichment and biological interpretability. We initially perform remote homology-based functional annotation by leveraging hmmscan and GODomainMiner to assign initial functions to proteins at large evolutionary distances;our clusters then enable us to newly assign functions to uncharacterized proteins through "function by association." We validate the ability of PHILHARMONIC to recover gold-standard functional enrichments in the well-annotated fruit fly D. melanogaster, and apply it to investigate stress response in the reef-building coral P. damicornis and its algal symbiont C. goreaui. Easy to run end-to-end and requiring only a sequenced proteome, PHILHARMONIC is an engine for biological hypothesis generation and discovery in non-model organisms. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Deep learning

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On the Age of Status Updates in Unreliable Multi-Source M/G/1 Queueing Systems

arXiv

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arXiv 2022年

作者： SenthilKumar, Muthukrishnan Dadlani, Aresh Moradian, Masoumeh Khonsari, Ahmad Tsiftsis, Theodoros A. The Department of Applied Mathematics and Computational Sciences Psg College of Technology Coimbatore641004 India The Faculty of Arts - Interdisciplinary Studies University of Alberta EdmontonABT6G 2E7 Canada The Department of Electrical and Computer Engineering Nazarbayev University Astana010000 Kazakhstan The School of Computer Science Institute for Research in Fundamental Sciences Tehran Iran The Department of Electrical and Computer Engineering University of Tehran Iran The Institute for Research in Fundamental Sciences Tehran Iran The School of Intelligent Systems Science and Engineering Jinan University Zhuhai Campus Zhuhai519070 China

The timeliness of status message delivery in communications networks is subjective to time-varying wireless channel transmissions. In this paper, we investigate the age of information (AoI) of each source in a multi-source M/G/1queueingupdatesystem with active server failures. In particular, we adopt the method of supplementary variables to derive a closed-form expression for the average AoI in terms of system parameters, where the server repair time follows a general distribution and the service time of packets generated by independent sources is a general random variable. Numerical results are provided to validate the effectiveness of the proposed packet serving policy under different parametric settings. © 2022, CC BY.

关键词： Real time systems

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A deterministic Susceptible–Infected–Recovered model for studying the impact of media on epidemic dynamics

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Healthcare Analytics 2023年 3卷 100189-100189页

作者： Fome, Anna D. Rwezaura, Herieth Diagne, Mamadou L. Collinson, Shannon Tchuenche, Jean M. Department of Economics Mathematics and Statistics Jordan University College Morogoro Tanzania Mathematics Department University of Dar es Salaam P.O. Box 35062 Dar es Salaam Tanzania Département de Mathématiques UFR des Sciences et Technologies Université de Thiès BP 967 Thiès Senegal Centre for Disease Modelling York University Canada School of Computational and Communication Sciences and Engineering Nelson Mandela African Institution of Science and Technology P.O. Box 447 Arusha Tanzania School of Computer Science and Applied Mathematics University of the Witwatersrand Private Bag 3 Wits 2050 Johannesburg South Africa

It is important to understand how the provision of information influences individuals’ behavior and its impact on disease transmission dynamics. We formulate a simple deterministic Susceptible–Infected–Recovered (SIR) model with vital dynamics and incorporate, one at a time, four media functions used in previous studies to mimic media reporting of a disease outbreak to investigate their impact on the dynamics of an epidemic. The most sensitive model parameter for the epidemic outcome at initial disease transmission and disease prevalence are obtained through normalized forward-sensitivity analyses. Media reporting does not impact initial disease transmission but affects the effective reproduction number as the media coverage begins. Numerical results show that the epidemic will affect a large proportion of the population with no media functions. Still, the epidemic time line may be short. In contrast, the key epidemiological quantities (such as age at infection, peak magnitude, peak time, end of the epidemic, and final epidemic size) vary depending on the media function used. The choice of the media function in a pandemic is critical. The media reporting on the spread of disease during pandemics should be done with care since it could counter-intuitively lead to under or overestimating the disease outbreak. © 2023 The Author(s)

关键词： Deterministic model Disease outbreak Epidemic dynamics Media coverage Sensitivity analysis Susceptible–infected–recovered

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Canada needs to rapidly escalate public health interventions for its COVID-19 mitigation strategies

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Infectious Disease Modelling 2020年第1期5卷 316-322页

作者： Francesca Scarabel Lorenzo Pellis Nicola Luigi Bragazzi Jianhong Wu Laboratory for Industrial and Applied Mathematics Department of Mathematics and StatisticsYork UniversityTorontoOntarioM3J1P3Canada CDLab-Computational Dynamics Laboratory Department of MathematicsComputer Science and PhysicsUniversity of Udinevia delle scienze 20633100UdineItaly School of Mathematics University of ManchesterManchesterM139PLUK Fields-CQAM Laboratory of Mathematics for Public Health York UniversityTorontoOntarioCanadaM3J 1P3

Background:After the declaration of COVID-19 pandemic on March 11th,2020,local transmission chains starting in different countries including Canada are forcing governments to take decisions on public health interventions to mitigate the spread of the ***:We conduct data-driven and model-free estimations for the growth rates of the COVID-19 epidemics in Italy and Canada,by fitting an exponential curve to the daily reported *** use these estimates to predict epidemic trends in Canada under different scenarios of public health ***:In Italy,the initial growth rate(0.22)has reduced to 0.1 two weeks after the lockdown of the country on March 8th,*** corresponds to an increase of the doubling time from about 3.15 to almost 7 *** comparison,the growth rate in Canada has increased from 0.13 between March 1st and 13th,to 0.25 between March 13th to *** current growth rate corresponds to a doubling time of 2.7 days,and therefore,unless further public health interventions are escalated in Canada,we project 15,000 cases by March ***,the case number may be reduced to 4000 if escalated public health interventions could instantly reduce the growth rate to 0.1,the same level achieved in ***:Prompt and farsighted interventions are critical to counteract the very rapid initial growth of the COVID-19 epidemic in *** plans must take into account the delayed effect of interventions by up to 2-weeks and the short doubling time of 3e4 days.

关键词： Canada doubling starting

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An Optimisation Model for Designing Social Distancing Enhanced Physical Spaces

An Optimisation Model for Designing Social Distancing Enhanc...

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2020 International Conference on Internet of Things and Intelligent Applications, ITIA 2020

作者： Ugail, Hassan Aggarwal, Riya Iglesias, Andres Suarez, Patricia Maqsood, Muazzam Aadil, Farhan Campuzano, Almudena Gleghorn, Sarah Mehmood, Irfan Taif, Khasrouf University of Bradford Centre for Visual Computing United Kingdom University of Newcastle Australia School of Engineering Australia University of Cantabria Applied Mathematics and Computational Sciences Spain Comsats University Islamabad Department of Computer Science Pakistan University of Amsterdam Netherlands Skipton Girls' High School United Kingdom

ISBN: (纸本)9781728193014

In the wake of the COVID-19 pandemic, social distancing has become an essential element of our daily lives. As a result, the development of technological solutions for the design and re-design of physical spaces with the necessary physical distancing measures is an important problem that must be addressed. In this paper, we show how automatic design optimisation can be used to simulate the layout of physical spaces subject to a given social distancing requirement. We use a well known mathematical technique based on the circle packing to address this challenge. Thus, given the dimensions and the necessary constraints on the physical space, we formulate the design as a solution to a constrained nonlinear optimisation problem. We then solve the optimisation problem to arrive at a number of feasible design solutions from which the user can pick the most desirable option. By way of examples, in this paper, we show how the proposed model can be practically applied. © 2020 IEEE.

关键词： COVID-19

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Extending the limit of molecular dynamics with ab initio accuracy to 10 billion atoms

arXiv

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arXiv 2022年

作者： Guo, Zhuoqiang Lu, Denghui Yan, Yujin Hu, Siyu Liu, Rongrong Tan, Guangming Sun, Ninghui Jiang, Wanrun Liu, Lijun Chen, Yixiao Zhang, Linfeng Chen, Mohan Wang, Han Jia, Weile Institute of Computing Technology Chinese Academy of Sciences Beijing China University of Chinese Academy of Sciences Beijing China State Key Laboratory of Computer Architecture ICT Chinese Academy of Sciences Beijing China HEDPS CAPT College of Engineering Peking University Beijing China AI for Science Institute Beijing China Osaka University Osaka Japan Princeton University Princeton United States DP Technology Beijing China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics Beijing China

High-performance computing, together with a neural network model trained from data generated with first-principles methods, has greatly boosted applications of ab initio molecular dynamics in terms of spatial and temporal scales on modern supercomputers. Previous state-of-the-art can achieve 1 − 2 nanoseconds molecular dynamics simulation per day for 100-million atoms on the entire Summit supercomputer. In this paper, we have significantly reduced the memory footprint and computational time by a comprehensive approach with both algorithmic and system innovations. The neural network model is compressed by model tabulation, kernel fusion, and redundancy removal. Then optimizations such as acceleration of customized kernel, tabulation of activation function, MPI+OpenMP parallelization are implemented on GPU and ARM architectures. Testing results of the copper system show that the optimized code can scale up to the entire machine of both Fugaku and Summit, and the corresponding system size can be extended by a factor of 134 to an © 2022, CC BY-NC-SA.

关键词： Supercomputers

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Pass-Efficient randomized lu algorithms for computing low-rank matrix approximation

arXiv

引用

arXiv 2020年

作者： Zhang, Bolong Mascagniy, Michael Department of Computer Science Florida State University FL United States Applied and Computational Mathematics Division NIST GaithersburgMD United States

Low-rank matrix approximation is extremely useful in the analysis of data that arises in scientific computing, engineering applications, and data science. However, as data sizes grow, traditional low-rank matrix approximation methods, such as singular value decomposition (SVD) and column pivoting QR decomposition (CPQR), are either prohibitively expensive or cannot provide sufficiently accurate results. A solution is to use randomized low-rank matrix approximation methods such as randomized SVD , and randomized LU decomposition on extremely large data sets. In this paper, we focus on the randomized LU decomposition method. First, we employ a reorthogonalization procedure to perform the power iteration of the existing randomized LU algorithm to compensate for the rounding errors caused by the power method. Then we propose a novel randomized LU algorithm, called PowerLU, for the fixed low-rank approximation problem. PowerLU allows for an arbitrary number of passes of the input matrix, v = 2. Recall that the existing randomized LU decomposition only allows an even number of passes. We prove the theoretical relationship between PowerLU and the existing randomized LU. Numerical experiments show that our proposed PowerLU is generally faster than the existing randomized LU decomposition, while remaining accurate. We also propose a version of PowerLU, called PowerLU FP, for the fixed precision low-rank matrix approximation problem. PowerLU FP is based on an efficient blocked adaptive rank determination Algorithm 4.1 proposed in this paper. We present numerical experiments that show that PowerLU FP can achieve almost the same accuracy and is faster than the randomized blocked QB algorithm by Martinsson and Voronin. We finally propose a single-pass algorithm based on LU factorization. Tests show that the accuracy of our single-pass algorithm is comparable with the existing single-pass *** Codes 65F99, 65C99 Copyright © 2020, The Authors. All rights reserved.

关键词： Singular value decomposition

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