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The Journal of Machine Learning Research 2023年第1期24卷 13275-13327页

作者： Kun Yuan Sulaiman A. Alghunaim Xinmeng Huang Center for Machine Learning Research Peking University AI for Science Institute Beijing P. R. China Department of Electrical Engineering Kuwait University Safat Kuwait Graduate Group in Applied Mathematics and Computational Science University of Pennsylvania Philadelphia PA

We consider decentralized stochastic optimization problems, where a network of n nodes cooperates to find a minimizer of the globally-averaged cost. A widely studied decentralized algorithm for this problem is the decentralized SGD (D-SGD), in which each node averages only with its neighbors. D-SGD is efficient in single-iteration communication, but it is very sensitive to the network topology. For smooth objective functions, the transient stage (which measures the number of iterations the algorithm has to experience before achieving the linear speedup stage) of D-SGD is on the order of O(n/(1 - β)2) and O(n3/(1 - β)4) for strongly and generally convex cost functions, respectively, where 1 - β ∈ (0, 1) is a topology-dependent quantity that approaches 0 for a large and sparse network. Hence, D-SGD suffers from slow convergence for large and sparse *** this work, we revisit the convergence property of the D2/Exact-Diffusion algorithm. By eliminating the influence of data heterogeneity between nodes, D2/Exact-diffusion is shown to have an enhanced transient stage that is on the order of Õ(n/(1 - β)) and O(n3/(1-β)2) for strongly and generally convex cost functions (where Õ (·) hides all logarithm factors), respectively. Moreover, when D2/Exact-Diffusion is implemented with both gradient accumulation and multi-round gossip communications, its transient stage can be further improved to Õ (1/(1-β)1/2) and Õ(n/(1-β)) for strongly and generally convex cost functions, respectively. To our knowledge, these established results for D2/Exact-Diffusion have the best (i.e., weakest) dependence on network topology compared to existing decentralized algorithms. Numerical simulations are conducted to validate our theories.

关键词： decentralized optimization stochastic optimization transient stage

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Pump-probe scheme for optical coherence tomography using indocyanine green mixed with albumin or human plasma

Pump-probe scheme for optical coherence tomography using ind...

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Conference on Lasers and Electro-Optics (CLEO)

作者： Z. Yaqoob J.P. Fingler S. Lintner B.E. Applegate Changhuei Yang Electrical Engineering California Institute of Technology Pasadena CA USA Applied Physics California Institute of Technology Pasadena CA USA Applied & Computational Mathematics California Institute of Technology Pasadena CA USA Department of Biomedical Engineering Duke University Durham NC USA

Use of indocyanine green (ICG) in a pump-probe scheme for OCT is proposed. The study illustrates that ICG in protein solution shows unusual pump-probe imaging potential, indicating its usefulness as a contrast agent f... 详细信息

ISBN: (纸本)1557527954

关键词： Optical pumping Tomography Humans Plasmas Biomedical optical imaging High-resolution imaging Absorption Optical imaging Laser beams Pump lasers

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Minimum time control of helicopter UAVs using computational dynamic optimization

Minimum time control of helicopter UAVs using computational ...

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International Conference on Control and Automation (ICCA)

作者： K. Tang B. Wang W. Kang B. Chen Internship program Naval Postgraduate School Monterrey CA USA Department of Electrical and Computer Engineering University of Singapore Singapore Department of Applied Mathematics Naval Postgraduate School Monterrey CA USA

This paper focuses on the problem of minimum time trajectory planning for helicopter UAVs. It is formulated as a nonlinear optimal control subject to the dynamics and limitations of helicopter UAVs. The dynamical system is defined by a set of fifteen states nonlinear differential equations developed for HeLion, a UAV helicopter constructed in National University of Singapore (NUS). The problem is then solved numerically using pseudospectral method for dynamic optimization. The results show that minimum time trajectories are highly nonlinear that require complicated maneuvering.

关键词： Trajectory Helicopters Mathematical model Approximation methods Planning Aerodynamics Vectors

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computational Methods for Single-Particle Cryo-EM

arXiv

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arXiv 2020年

作者： Singer, Amit Sigworth, Fred J. Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Departments of Cellular and Molecular Physiology Biomedical Engineering and Molecular Biophysics and Biochemistry Yale University New HavenCT06520 United States

Single-particle electron cryomicroscopy (cryo-EM) is an increasingly popular technique for elucidating the three-dimensional structure of proteins and other biologically significant complexes at near-atomic resolution. It is an imaging method that does not require crystallization and can capture molecules in their native states. In single-particle cryo-EM, the three-dimensional molecular structure needs to be determined from many noisy two-dimensional tomographic projections of individual molecules, whose orientations and positions are unknown. The high level of noise and the unknown pose parameters are two key elements that make reconstruction a challenging computational problem. Even more challenging is the inference of structural variability and flexible motions when the individual molecules being imaged are in different conformational states. This review discusses computational methods for structure determination by single-particle cryo-EM and their guiding principles from statistical inference, machine learning, and signal processing that also play a significant role in many other data science applications. Copyright © 2020, The Authors. All rights reserved.

关键词： Molecules

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Fourier phase retrieval: Uniqueness and algorithms

arXiv

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arXiv 2017年

作者： Bendory, Tamir Beinerty, Robert Eldarz, Yonina C. Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States Institute of Mathematics and Scientific Computing University of Graz Heinrichstraße 36 Graz8010 Austria Andrew and Erna Viterbi Faculty of Electrical Engineering Technion - Israel Institute of Technology Haifa Israel

The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and algorithmic challenges. In general, there is no unique mapping between a one-dimensional signal and its Fourier magnitude and therefore the problem is ill-posed. Additionally, while almost all multidimensional signals are uniquely mapped to their Fourier magnitude, the performance of existing algorithms is generally not well-understood. In this chapter we survey methods to guarantee uniqueness in Fourier phase retrieval. We then present different algorithmic approaches to retrieve the signal in practice. We conclude by outlining some of the main open questions in this field. Copyright © 2017, The Authors. All rights reserved.

关键词： Fourier transforms

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Multi-index Sequential Monte Carlo ratio estimators for Bayesian Inverse problems

arXiv

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arXiv 2022年

作者： Law, Kody J.H. Walton, Neil Yang, Shangda Jasra, Ajay School of Mathematics University of Manchester ManchesterM13 9PL United Kingdom 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

We consider the problem of estimating expectations with respect to a target distribution with an unknown normalizing constant, and where even the unnormalized target needs to be approximated at finite resolution. This setting is ubiquitous across science and engineering applications, for example in the context of Bayesian inference where a physics-based model governed by an intractable partial differential equation (PDE) appears in the likelihood. A multi-index Sequential Monte Carlo (MISMC) method is used to construct ratio estimators which provably enjoy the complexity improvements of multi-index Monte Carlo (MIMC) as well as the efficiency of Sequential Monte Carlo (SMC) for inference. In particular, the proposed method provably achieves the canonical complexity of MSE−1, while single level methods require MSE−ξ for ξ > 1. This is illustrated on examples of Bayesian inverse problems with an elliptic PDE forward model in 1 and 2 spatial dimensions, where ξ = 5/4 and ξ = 3/2, respectively. It is also illustrated on more challenging log Gaussian process models, where single level complexity is approximately ξ = 9/4 and multilevel Monte Carlo (or MIMC with an inappropriate index set) gives ξ = 5/4 + ω, for any ω > 0, whereas our method is again canonical. We also provide novel theoretical verification of the product-form convergence results which MIMC requires for Gaussian processes built in spaces of mixed regularity defined in the spectral domain, which facilitates acceleration with fast Fourier transform methods via a cumulant embedding strategy, and may be of independent interest in the context of spatial statistics and machine learning. Copyright © 2022, The Authors. All rights reserved.

关键词： Inverse problems

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Single-cell stochastic gene expression kinetics with coupled positive-plus-negative feedback

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Physical Review E 2019年第5期100卷 052406-052406页

作者： Chen Jia Le Yi Wang George G. Yin Michael Q. Zhang Division of Applied and Computational Mathematics Beijing Computational Science Research Center Beijing 100193 China Department of Mathematics Wayne State University Detroit Michigan 48202 USA Department of Electrical and Computer Engineering Wayne State University Detroit Michigan 48202 USA Department of Biological Sciences Center for Systems Biology University of Texas at Dallas Richardson Texas 75080 USA MOE Key Laboratory of Bioinformatics Center for Synthetic and Systems Biology Tsinghua University Beijing 100084 China

Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation is observed upon increasing the ratio of the positive and negative feedback strengths, which reveals a strong synergistic interaction between positive and negative feedback loops. We discover that coupled positive-plus-negative feedback amplifies gene expression mean but reduces gene expression noise over a wide range of feedback strengths when promoter switching is relatively slow, stabilizing gene expression around a relatively high level. In addition, we study two types of macroscopic limits of the discrete chemical master equation model: the Kurtz limit applies to proteins with large burst frequencies and the Lévy limit applies to proteins with large burst sizes. We derive the analytic steady-state distributions of the protein abundance in a coupled gene circuit for both the discrete model and its two macroscopic limits, generalizing the results obtained by Liu et al. [Chaos 26, 043108 (2016)]. We also obtain the analytic time-dependent protein distribution for the classical Friedman-Cai-Xie random bursting model [Friedman, Cai, and Xie, Phys. Rev. Lett. 97, 168302 (2006)]. Our analytic results are further applied to study the structure of gene expression noise in a coupled gene circuit, and a complete decomposition of noise in terms of five different biophysical origins is provided.

关键词： Gene expression Stochastic processes Gene regulatory networks Markovian processes

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Rogue waves generated through quantum chaos

Rogue waves generated through quantum chaos

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International Quantum Electronics Conference, IQEC 2013

作者： Liu, Changxu Falco, Andrea Di Krauss, Thomas F. Fratalocchi, Andrea Faculty of Electrical Engineering KAUST Thuwal Saudi Arabia Faculty of Applied Mathematics and Computational Science KAUST Thuwal Saudi Arabia School of Physics and Astronomy University of St. Andrews North Haugh St. Andrews KY16 9SS United Kingdom Department of Physics University of York York YO10 5DD United Kingdom

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An Educational Perspective to Model and Controller Reduction of Dynamical Systems

An Educational Perspective to Model and Controller Reduction...

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Proceedings of the 46th IEEE Conference on Decision and Control, Pages 5052-5510

作者： Eduardo Gildin Robert H. Bishop Athanasios C. Antoulas Danny Sorensen The Institute for Computational Engineering and Sciences University of Texas Austin Austin TX USA ECE Department Rice University USA The Aerospace and Engineering Mechanics Department University of Texas Austin Austin TX USA Electrical and Computer Engineering Department Rice University Houston TX USA Computational and Applied Mathematics Rice University Houston TX USA

ISBN: (纸本)9781424414970

In this paper, and educational framework on model and controller reduction techniques arising in the study of dynamical systems is presented. The model reduction problem is posed in a projection framework, and some techniques are shown, such as balanced truncation, and moment matching by Krylov subspace, to obtain reduced-order models and controllers. The practical application of these reduced-order controllers are shown in a control laboratory setup, developed for teaching undergraduate control systems. The implementations were performed using the torsional disks apparatus controlled by LabVIEW.

关键词： Large-scale systems computational modeling Reduced order systems Laboratories Control systems Power system modeling computational fluid dynamics Circuit simulation Aerospace engineering Fluid flow control

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Decentralized and Equitable Optimal Transport

arXiv

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arXiv 2024年

作者： Lau, Ivan Ma, Shiqian Uribe, César A. The Department of Computer Science National University of Singapore Singapore The Department of Electrical and Computer Engineering Rice University HoustonTX United States The Department of Computational Applied Mathematics and Operations Research Rice University HoustonTX United States

This paper considers the decentralized (discrete) optimal transport (D-OT) problem. In this setting, a network of agents seeks to design a transportation plan jointly, where the cost function is the sum of privately held costs for each agent. We reformulate the D-OT problem as a constraint-coupled optimization problem and propose a single-loop decentralized algorithm with an iteration complexity of O(1/ϵ) that matches existing centralized first-order approaches. Moreover, we propose the decentralized equitable optimal transport (DE-OT) problem. In DE-OT, in addition to cooperatively designing a transportation plan that minimizes transportation costs, agents seek to ensure equity in their individual costs. The iteration complexity of the proposed method to solve DE-OT is also O(1/ϵ). This rate improves existing centralized algorithms, where the best iteration complexity obtained is O(1/ϵ2). Copyright © 2024, The Authors. All rights reserved.

关键词： Cost functions

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