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Designer Pair Statistics of Disordered Many-Particle Systems with Novel Properties

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arXiv 2023年

作者： Wang, Haina Torquato, Salvatore Department of Chemistry Princeton University PrincetonNJ08544 United States Department of Chemistry Department of Physics Princeton Materials Institute Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States

Knowledge of exact analytical functional forms for the pair correlation function g2(r) and its corresponding structure factor S(k) of disordered many-particle systems is limited. For fundamental and practical reasons, it is highly desirable to add to the existing data base of analytical functional forms for such pair statistics. Here, we design a plethora of such pair functions in direct and Fourier spaces across the first three Euclidean space dimensions that are realizable by diverse many-particle systems with varying degrees of correlated disorder across length scales, spanning a wide spectrum of hyperuniform, typical nonhyperuniform and antihyperuniform ones. This is accomplished by utilizing an efficient inverse algorithm that determines equilibrium states with up to pair interactions at positive temperature that precisely match targeted forms for both g2(r) and S(k). Among other results, we realize an example with the strongest hyperuniform property among known positive-temperature equilibrium states, critical-point systems (implying unusual 1D systems with phase transitions) that are not in the Ising universality class, systems that attain self-similar pair statistics under Fourier transformation, and an experimentally feasible polymer model. We show that our pair functions enable one to achieve systems with a wide range of translational order and self-diffusion coefficients D, which are inversely related to one another. One can design other realizable pair statistics via linear combinations of our functions or by applying our inverse procedure to other desirable functional forms. Our approach facilitates the inverse design of materials with desirable physical and chemical properties by tuning their pair statistics. © 2023, CC BY.

关键词： Statistics

Scaling positive random matrices: Concentration and asymptotic convergence

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arXiv 2020年

作者： Landa, Boris Program in Applied Mathematics Department of Mathematics Yale University United States

It is well known that any positive matrix can be scaled to have prescribed row and column sums by multiplying its rows and columns by certain positive scaling factors (which are unique up to a positive scalar). This procedure is known as matrix scaling, and has found numerous applications in operations research, economics, image processing, and machine learning. In this work, we investigate the behavior of the scaling factors and the resulting scaled matrix when the matrix to be scaled is random. Specifically, letting Ã∈ RM×N be a positive and bounded random matrix whose entries assume a certain type of independence, we provide a concentration inequality for the scaling factors of Ã around those of A = E[Ã]. This result is employed to bound the convergence rate of the scaling factors of Ã to those of A, as well as the concentration of the scaled version of Ã around the scaled version of A in operator norm, as M, N → ∞. When the entries of Ã are independent, M = N, and all prescribed row and column sums are 1 (i.e., doubly-stochastic matrix scaling), both of the previously-mentioned bounds are O(√log N/N) with high probability. We demonstrate our results in several *** Codes 60B20, 60F10, 65F35 Copyright © 2020, The Authors. All rights reserved.

关键词： Operations research

RELATIVE SIMPLICITY OF THE UNIVERSAL COVERINGS OF TRANSFORMATION GROUPS AND TSUBOI’S METRIC

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arXiv 2024年

作者： Kawasaki, Morimichi Kimura, Mitsuaki Kodama, Hiroki Matsuda, Yoshifumi Matsushita, Takahiro Orita, Ryuma Department of Mathematics Faculty of Science Hokkaido University North 10 West 8 Kita-ku Hokkaido Sapporo060-0810 Japan Department of Mathematics Osaka Dental University 8-1 Kuzuha-hanazono-cho Osaka Hirakata573-1121 Japan Center for Mathematical Engineering Musashino University 3-3-3 Ariake Koto-ku Tokyo135-8181 Japan Interdisciplinary Theoretical and Mathematical Sciences Program RIKEN 2-1 Hirosawa Saitama Wako-shi351-0198 Japan Department of Mathematical Sciences College of Science and Engineering Aoyama Gakuin University 5-10-1 Fuchinobe Chuo-ku Kanagawa Sagamihara252-5258 Japan Department of Mathematical Sciences Faculty of Science Shinshu University Nagano390-8621 Japan Department of Mathematics Faculty of Science Niigata University Niigata950-2181 Japan

Many transformation groups on manifolds are simple, but their universal coverings are not. In the present paper, we study the concept of relatively simple group, that is, a group with the maximum proper normal subgroup. We show that many examples of universal coverings of transformation groups are relatively simple, including the universal covering (formula presented) of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold (M, ω). Tsuboi constructed a metric space M(G) for a simple group G. We generalize his construction to relatively simple groups, and study their large scale geometric structure. In particular, Tsuboi’s metric space of (formula presented) is not quasi-isometric to the half line for every closed symplectic manifold (M, ω).MSC Codes 20A05, 20E32, 51F30, 53D22, 53D40, 57S05 Copyright © 2024, The Authors. All rights reserved.

关键词： Hamiltonians

Optimizing Hammerstein-Wiener Model for Forecasting Confirmed Cases of Covid-19

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IAENG International Journal of applied mathematics 2022年第1期52卷 1页

作者： Abdullahi, Sunusi Bala Ibrahim, Abdulkarim Hassan Abubakar, Auwal Bala Kambheera, Abhiwat General Investigation Zonal Criminal Investigation Section Force Criminal Investigation and Intelligence Department Nigeria Police Abuja900211 Nigeria Department of Applied Mathematics King Mongkut’s University of Technology Thonburi Bangkok Thailand Department of Mathematical Sciences Faculty of Physical Sciences Bayero University Kano700241 Nigeria Mathematics and Computing Science Program Faculty of Science and Technology Phetchabun Rajabhat University Phetchabun 67000 Thailand

Noise poses challenge to nonlinear Hammerstein-Wiener (HW) subsystem model application, because HW subsystem need large number of parameter interactions. However, flexibility, soft computing, and automatic adjustment to dynamic observation for best model fitting make it potential for forecasting nonlinear data. In this article, we adopted improved HW inference from Levenberg-Marquardt optimization algorithm to optimize HW subsystem and to select best model parameters. Therefore, the adopted model is tested on COVID-19 confirmed reported cases, to estimate transmission rate of COVID-19 virus for period from 15th March 2020 to 29th April 2020. Model validation is carried out on small dataset, which outperforms some existing models. The adopted model is further evaluated using statistical metrics and reported best accuracy of 0.127 and 0.998 for Mean Absolute percentage error (MAPE) and coefficient of determination (R2) respectively, with best model complexity of 1.86. The obtained results are promising enough in predicting spread of COVID-19 virus and may inspire as guidance to relax lockdown restriction policies. © 2022, IAENG International Journal of applied mathematics. All Rights Reserved.

关键词： COVID-19

Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI 41

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Position: Bayesian Deep Learning is Needed in the Age of Lar...

41st International Conference on Machine Learning, ICML 2024

作者： Papamarkou, Theodore Skoularidou, Maria Palla, Konstantina Aitchison, Laurence Arbel, Julyan Dunson, David Filippone, Maurizio Fortuin, Vincent Hennig, Philipp Hernández-Lobato, José Miguel Hubin, Aliaksandr Immer, Alexander Karaletsos, Theofanis Khan, Mohammad Emtiyaz Kristiadi, Agustinus Li, Yingzhen Mandt, Stephan Nemeth, Christopher Osborne, Michael A. Rudner, Tim G.J. Rügamer, David Teh, Yee Whye Welling, Max Wilson, Andrew Gordon Zhang, Ruqi Department of Mathematics The University of Manchester Manchester United Kingdom Eric and Wendy Schmidt Center Broad Institute of MIT and Harvard Cambridge United States Spotify London United Kingdom Computational Neuroscience Unit University of Bristol Bristol United Kingdom Centre Inria de l'Université Grenoble Alpes Grenoble France Department of Statistical Science Duke University United States Statistics Program KAUST Saudi Arabia Helmholtz AI Munich Germany Department of Computer Science Technical University of Munich Munich Germany Munich Center for Machine Learning Munich Germany Tübingen AI Center University of Tübingen Tübingen Germany Department of Engineering University of Cambridge Cambridge United Kingdom Department of Mathematics University of Oslo Oslo Norway Bioinformatics and Applied Statistics Norwegian University of Life Sciences Ås Norway Department of Computer Science ETH Zurich Switzerland Chan Zuckerberg Initiative CA United States Center for Advanced Intelligence Project RIKEN Tokyo Japan Vector Institute Toronto Canada Department of Computing Imperial College London London United Kingdom Department of Computer Science UC Irvine Irvine United States Department of Mathematics and Statistics Lancaster University Lancaster United Kingdom Department of Engineering Science University of Oxford Oxford United Kingdom Center for Data Science New York University New York United States Department of Statistics LMU Munich Munich Germany DeepMind London United Kingdom Department of Statistics University of Oxford Oxford United Kingdom Informatics Institute University of Amsterdam Amsterdam Netherlands Courant Institute of Mathematical Sciences Center for Data Science Computer Science Department New York University New York United States Department of Computer Science Purdue University West Lafayette United States

In the current landscape of deep learning research, there is a predominant emphasis on achieving high predictive accuracy in supervised tasks involving large image and language datasets. However, a broader perspective reveals a multitude of overlooked metrics, tasks, and data types, such as uncertainty, active and continual learning, and scientific data, that demand attention. Bayesian deep learning (BDL) constitutes a promising avenue, offering advantages across these diverse settings. This paper posits that BDL can elevate the capabilities of deep learning. It revisits the strengths of BDL, acknowledges existing challenges, and highlights some exciting research avenues aimed at addressing these obstacles. Looking ahead, the discussion focuses on possible ways to combine large-scale foundation models with BDL to unlock their full potential. Copyright 2024 by the author(s)

关键词： Contrastive Learning

Recent Methodological Advances in Federated Learning for Healthcare

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arXiv 2023年

作者： Zhang, Fan Kreuter, Daniel Chen, Yichen Dittmer, Sören Tull, Samuel Shadbahr, Tolou Preller, Jacobus Rudd, James H.F. Aston, John A.D. Schönlieb, Carola-Bibiane Gleadall, Nicholas Roberts, Michael Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom ZeTeM University of Bremen Bremen Germany Research Program in Systems Oncology Faculty of Medicine University of Helsinki Helsinki Finland Addenbrooke’s Hospital Cambridge University Hospitals NHS Trust Cambridge United Kingdom Department of Medicine University of Cambridge Cambridge United Kingdom Department of Pure Mathematics and Mathematical Statistics University of Cambridge Cambridge United Kingdom Department of Haematology University of Cambridge Cambridge United Kingdom

For healthcare datasets, it is often not possible to combine data samples from multiple sites due to ethical, privacy or logistical concerns. Federated learning allows for the utilisation of powerful machine learning algorithms without requiring the pooling of data. Healthcare data has many simultaneous challenges which require new methodologies to address, such as highly-siloed data, class imbalance, missing data, distribution shifts and non-standardised variables. Federated learning adds significant methodological complexity to conventional centralised machine learning, requiring distributed optimisation, communication between nodes, aggregation of models and redistribution of models. In this systematic review, we consider all papers on Scopus that were published between January 2015 and February 2023 and which describe new federated learning methodologies for addressing challenges with healthcare data. We performed a detailed review of the 89 papers which fulfilled these criteria. Significant systemic issues were identified throughout the literature which compromise the methodologies in many of the papers reviewed. We give detailed recommendations to help improve the quality of the methodology development for federated learning in healthcare. © 2023, CC BY.

关键词： Paper

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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Efficient Power Transfer via Induced Virtual Critical Coupling in an Overcoupled Silicon Nitride Microresonator

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Efficient Power Transfer via Induced Virtual Critical Coupli...

Conference on Lasers and Electro-Optics (CLEO)

作者： Jakob Hinney Seunghwi Kim Graydon J. K. Flatt Ipshita Datta Andrea Alù Michal Lipson Department of Electrical Engineering Columbia University New York NY USA Photonics Initiative Advanced Science Research Center City University of New York New York NY USA Department of Applied Physics and Applied Mathematics Columbia University New York NY USA Physics Program Graduate Center City University of New York New York NY USA

We induce virtual critical coupling in an overcoupled photonic microresonator using complex-frequency pulses. We observe efficient cavity storage as an incident pulse of time constant 138 ps suppresses the resonant tr... 详细信息

ISBN: (纸本)9781957171258

关键词： Continuous wave operation Coupled mode theory Electrooptical modulators Optical resonators Pulse shaping Silicon nitride

Double diffusion structure of logarithmically damped wave equations with a small parameter

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arXiv 2021年

作者： Piske, Alessandra Charão, Ruy Coimbra Ikehata, Ryo Graduate Program in Pure and Applied Mathematics Department of Mathematics Federal University of Santa Catarina Florianopolis88040-270 Brazil Department of Mathematics Division of Educational Sciences Graduate School of Humanities and Social Sciences Hiroshima University Higashi-Hiroshima739-8524 Japan

We consider a wave equation with a nonlocal logarithmic damping depending on a small parameter 0 1/2. We study the Cauchy problem for this model in Rnto the case θ ∈ (0, 1/2), and we obtain an asymptotic profile and optimal estimates in time of solutions as t → ∞ in L2-sense. An important discovery in this research is that in the case when n = 1, we can present a threshold θ∗= 1/4 of the parameter θ ∈ (0, 1/2) such that the solution of the Cauchy problem decays with some optimal rate for θ ∈ (0,θ∗) as t → ∞, while the L2-norm of the corresponding solution never decays for θ ∈ [θ∗, 1/2), and in particular, in the case θ ∈ [θ∗, 1/2) it shows an infinite time L2-blow up of the corresponding solutions. The former (i.e., θ ∈ (0, θ∗) case) indicates an usual diffusion phenomenon, while the latter (i.e., θ ∈ [θ∗, 1/2) case) implies, so to speak, a singular diffusion phenomenon. Such a singular diffusion in the one dimensional case is a quite novel phenomenon discovered through our new model produced by logarithmic damping with a small parameter θ. It might be already prepared in the usual structural damping case such as (-Δ)θutwith θ ∈ (0, 1/2), however unfortunately nobody has ever just pointed out even in the structural damping *** Codes 35B40, 35L05, 35B20, 35R12, 35S05 © 2021, CC BY.

关键词： Damping