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A Chebyshev-accelerated primal-dual method for distributed optimization

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arXiv 2018年

作者： Seidman, Jacob H. Fazlyab, Mahyar Pappas, George J. Preciado, Victor M. Department of Applied Mathematics and Computational Science University of Pennsylvania Department of Electrical and Systems Engineering University of Pennsylvania

We consider a distributed optimization problem over a network of agents aiming to minimize a global objective function that is the sum of local convex and composite cost functions. To this end, we propose a distributed Chebyshev-accelerated primal-dual algorithm to achieve faster ergodic convergence rates. In standard distributed primal-dual algorithms, the speed of convergence towards a global optimum (i.e., a saddle point in the corresponding Lagrangian function) is directly influenced by the eigenvalues of the Laplacian matrix representing the communication graph. In this paper, we use Chebyshev matrix polynomials to generate gossip matrices whose spectral properties result in faster convergence speeds, while allowing for a fully distributed implementation. As a result, the proposed algorithm requires fewer gradient updates at the cost of additional rounds of communications between agents. We illustrate the performance of the proposed algorithm in a distributed signal recovery problem. Our simulations show how the use of Chebyshev matrix polynomials can be used to improve the convergence speed of a primal-dual algorithm over communication networks, especially in networks with poor spectral properties, by trading local computation by communication rounds. Copyright © 2018, The Authors. All rights reserved.

关键词： Matrix algebra

Stable super-resolution of images: A theoretical study

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arXiv 2018年

作者： Eftekhari, Armin Bendory, Tamir Tang, Gongguo Institute of Electrical Engineering École Polytechnique Fédérale de Lausanne Program in Applied and Computational Mathematics Princeton University Department of Electrical Engineering Colorado School of Mines

We study the ubiquitous super-resolution problem, in which one aims at localizing positive point sources in an image, blurred by the point spread function of the imaging device. To recover the point sources, we propose to solve a convex feasibility program, which simply finds a nonnegative Borel measure that agrees with the observations collected by the imaging device. In the absence of imaging noise, we show that solving this convex program uniquely retrieves the point sources, provided that the imaging device collects enough observations. This result holds true if the point spread function of the imaging device can be decomposed into horizontal and vertical components, and if the translations of these components form a Chebyshev system, namely, a system of continuous functions that loosely behave like algebraic polynomials. Building upon recent results for one-dimensional signals [1], we prove that this super-resolution algorithm is stable (in the generalized Wasserstein metric) to model mismatch (namely, when the image is not sparse) and to additive imaging noise. In particular, the recovery error depends on the noise level and how well the image can be approximated with well-separated point sources. As an example, we verify these claims for the important case of a Gaussian point spread function. The proofs rely on the construction of novel interpolating polynomials, which are the main technical contribution of this paper, and partially resolve the question raised in [2] about the extension of the standard machinery to higher dimensions. Copyright © 2018, The Authors. All rights reserved.

关键词： Optical transfer function

Heterogeneous inputs to central pattern generators can shape insect gaits.

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arXiv 2018年

作者： Aminzare, Zahra Holmes, Philip Program in Applied and Computational Mathematics Princeton University NJ United States Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Princeton Neuroscience Institute Princeton University NJ United States

In our previous work [1], we studied an interconnected bursting neuron model for insect locomotion, and its corresponding phase oscillator model, which at high speed can generate stable tripod gaits with three legs off the ground simultaneously in swing, and at low speed can generate stable tetrapod gaits with two legs off the ground simultaneously in swing. However, at low speed several other stable locomotion patterns, that are not typically observed as insect gaits, may coexist. In the present paper, by adding heterogeneous external input to each oscillator, we modify the bursting neuron model so that its corresponding phase oscillator model produces only one stable gait at each speed, specifically: a unique stable tetrapod gait at low speed, a unique stable tripod gait at high speed, and a unique branch of stable transition gaits connecting them. This suggests that control signals originating in the brain and central nervous system can modify gait patterns.34C15, 34C60, 37G10, 92B20, 92C20 Copyright © 2018, The Authors. All rights reserved.

关键词： Neurons

Benchmarking the CoW with the TopCoW Challenge: Topology-Aware Anatomical Segmentation of the Circle of Willis for CTA and MRA

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arXiv 2023年

作者： Yang, Kaiyuan Musio, Fabio Ma, Yihui Juchler, Norman Paetzold, Johannes C. Al-Maskari, Rami Höher, Luciano Li, Hongwei Bran Hamamci, Ibrahim Ethem Sekuboyina, Anjany Shit, Suprosanna Huang, Houjing Prabhakar, Chinmay de la Rosa, Ezequiel Waldmannstetter, Diana Kofler, Florian Navarro, Fernando Menten, Martin Ezhov, Ivan Rueckert, Daniel Vos, Iris Ruigrok, Ynte Velthuis, Birgitta Kuijf, Hugo Hämmerli, Julien Wurster, Catherine Bijlenga, Philippe Westphal, Laura Bisschop, Jeroen Colombo, Elisa Baazaoui, Hakim Makmur, Andrew Hallinan, James Wiestler, Bene Kirschke, Jan S. Wiest, Roland Montagnon, Emmanuel Letourneau-Guillon, Laurent Galdran, Adrian Galati, Francesco Falcetta, Daniele Zuluaga, Maria A. Lin, Chaolong Zhao, Haoran Zhang, Zehan Ra, Sinyoung Hwang, Jongyun Park, Hyunjin Chen, Junqiang Wodzinski, Marek Müller, Henning Shi, Pengcheng Liu, Wei Ma, Ting Yalçin, Cansu Hamadache, Rachika E. Salvi, Joaquim Llado, Xavier Estrada, Uma Maria Lal-Trehan Abramova, Valeriia Giancardo, Luca Oliver, Arnau Liu, Jialu Huang, Haibin Cui, Yue Lin, Zehang Liu, Yusheng Zhu, Shunzhi Patel, Tatsat R. Tutino, Vincent M. Orouskhani, Maysam Wang, Huayu Mossa-Basha, Mahmud Zhu, Chengcheng Rokuss, Maximilian R. Kirchhoff, Yannick Disch, Nico Holzschuh, Julius Isensee, Fabian Maier-Hein, Klaus Sato, Yuki Hirsch, Sven Wegener, Susanne Menze, Bjoern Department of Quantitative Biomedicine University of Zurich Zurich Switzerland Center for Computational Health Zurich University of Applied Sciences Zurich Switzerland Department of Neuroradiology University Hospital of Zurich Zurich Switzerland Department of Neurosurgery Zhongnan Hospital of Wuhan University Wuhan China Department of Computing Imperial College London London United Kingdom Helmholtz Center Munich Germany Athinoula A. Martinos Center for Biomedical Imaging Harvard Medical School Boston United States School of Medicine Technical University of Munich Munich Germany Department of Informatics Technical University of Munich Munich Germany Helmholtz AI Helmholtz Munich Munich Germany Image Sciences Institute UMC Utrecht Utrecht Netherlands Department of Neurology UMC Utrecht Utrecht Netherlands Department of Radiology UMC Utrecht Utrecht Netherlands Department of Clinical Neurosciences Division of Neurosurgery Geneva University Hospitals Geneva Switzerland Department of Neurology University Hospital of Zurich Zurich Switzerland Department of Physiology University of Toronto Toronto Canada Department of Neurosurgery University Hospital of Zurich Zurich Switzerland Department of Diagnostic Imaging National University Hospital Singapore Department of Diagnostic and Interventional Neuroradiology University Hospital Berne University of Berne Berne Switzerland Montreal Canada Universitat Pompeu Fabra Barcelona Spain EURECOM Biot France Institute of Medical Technology Peking University Health Science Center Beijing China Hangzhou Genlight Medtech Co. Ltd. Hangzhou China Department of Artificial Intelligence Sungkyunkwan University Seoul Korea Republic of Department of Electrical and Computer Engineering Sungkyunkwan University Seoul Korea Republic of Shanghai MediWorks Precision Instruments Co. Ltd. Shanghai China Institute of Informatics HES-SO Valais-Wallis Switzerland Department of Measurement and Electronics AGH University

The Circle of Willis (CoW) is an important network of arteries connecting major circulations of the brain. Its vascular architecture is believed to affect the risk, severity, and clinical outcome of serious neuro-vascular diseases. However, characterizing the highly variable CoW anatomy is still a manual and time-consuming expert task. The CoW is usually imaged by two angiographic imaging modalities, magnetic resonance angiography (MRA) and computed tomography angiography (CTA), but there exist limited public datasets with annotations on CoW anatomy, especially for CTA. Therefore we organized the TopCoW Challenge in 2023 with the release of an annotated CoW dataset. The TopCoW dataset was the first public dataset with voxel-level annotations for thirteen possible CoW vessel components, enabled by virtual-reality (VR) technology. It was also the first large dataset with paired MRA and CTA from the same patients. TopCoW challenge formalized the CoW characterization problem as a multiclass anatomical segmentation task with an emphasis on topological metrics. We invited submissions worldwide for the CoW segmentation task, which attracted over 140 registered participants from four continents. The top performing teams managed to segment many CoW components to Dice scores around 90%, but with lower scores for communicating arteries and rare variants. There were also topological mistakes for predictions with high Dice scores. Additional topological analysis revealed further areas for improvement in detecting certain CoW components and matching CoW variant topology accurately. TopCoW represented a first attempt at benchmarking the CoW anatomical segmentation task for MRA and CTA, both morphologically and topologically. © 2023, CC BY-NC-ND.

关键词： Large datasets

Ten quick tips for deep learning in biology

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arXiv 2021年

作者： Lee, Benjamin D. Gitter, Anthony Greene, Casey S. Raschka, Sebastian Maguire, Finlay Titus, Alexander J. Kessler, Michael D. Lee, Alexandra J. Chevrette, Marc G. Stewart, Paul Allen Britto-Borges, Thiago Cofer, Evan M. Yu, Kun-Hsing Carmona, Juan Jose Fertig, Elana J. Kalinin, Alexandr A. Signal, Beth Lengerich, Benjamin J. Triche, Timothy J. Boca, Simina M. In-Q-Tel Labs School of Engineering and Applied Sciences Harvard University Department of Genetics Harvard Medical School United States Department of Biostatistics and Medical Informatics University of Wisconsin-Madison MadisonWI United States Morgridge Institute for Research MadisonWI United States Department of Systems Pharmacology and Translational Therapeutics Perelman School of Medicine University of Pennsylvania PhiladelphiaPA United States Department of Biochemistry and Molecular Genetics University of Colorado School of Medicine AuroraCO United States Center for Health AI University of Colorado School of Medicine AuroraCO United States Department of Statistics University of Wisconsin Madison United States Faculty of Computer Science Dalhousie University Canada University of New Hampshire Bioeconomy.XYZ United States Department of Oncology Johns Hopkins University United States Institute for Genome Sciences University of Maryland School of Medicine United States Genomics and Computational Biology Graduate Program University of Pennsylvania United States Department of Systems Pharmacology and Translational Therapeutics University of Pennsylvania United States Wisconsin Institute for Discovery Department of Plant Pathology University of Wisconsin-Madison United States Department of Biostatistics and Bioinformatics Moffitt Cancer Center TampaFL United States Section of Bioinformatics and Systems Cardiology Klaus Tschira Institute for Integrative Computational Cardiology University Hospital Heidelberg Germany University Hospital Heidelberg Germany Lewis-Sigler Institute for Integrative Genomics Princeton University PrincetonNJ United States Graduate Program in Quantitative and Computational Biology Princeton University PrincetonNJ United States Department of Biomedical Informatics Harvard Medical School United States Department of Pathology Brigham and Women's Hospital United States Philips Healthcare CambridgeMA United States Philips Research

Machine learning is a modern approach to problem-solving and task automation. In particular, machine learning is concerned with the development and applications of algorithms that can recognize patterns in data and use them for predictive modeling. Artificial neural networks are a particular class of machine learning algorithms and models that evolved into what is now described as deep learning. Given the computational advances made in the last decade, deep learning can now be applied to massive data sets and in innumerable contexts. Therefore, deep learning has become its own subfield of machine learning. In the context of biological research, it has been increasingly used to derive novel insights from high-dimensional biological data. To make the biological applications of deep learning more accessible to scientists who have some experience with machine learning, we solicited input from a community of researchers with varied biological and deep learning interests. These individuals collaboratively contributed to this manuscript's writing using the GitHub version control platform and the Manubot manuscript generation toolset. The goal was to articulate a practical, accessible, and concise set of guidelines and suggestions to follow when using deep learning. In the course of our discussions, several themes became clear: the importance of understanding and applying machine learning fundamentals as a baseline for utilizing deep learning, the necessity for extensive model comparisons with careful evaluation, and the need for critical thought in interpreting results generated by deep learning, among others. © 2021, CC BY.

关键词： Learning algorithms

End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems 32

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End-to-end symmetry preserving inter-atomic potential energy...

32nd Conference on Neural Information Processing Systems, NeurIPS 2018

作者： Zhang, Linfeng Han, Jiequn Wang, Han Saidi, Wissam A. Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University United States Institute of Applied Physics and Computational Mathematics China CAEP Software Center for High Performance Numerical Simulation China Department of Mechanical Engineering and Materials Science University of Pittsburgh United States Department of Chemistry Department of Physics Princeton University United States Princeton Institute for the Science and Technology of Materials Princeton University United States Department of Mathematics Princeton University United States Beijing Institute of Big Data Research China

Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES of a wide variety of systems with the accuracy of ab initio quantum mechanics models. By construction, DeepPot-SE is extensive and continuously differentiable, scales linearly with system size, and preserves all the natural symmetries of the system. Further, we show that DeepPot-SE describes finite and extended systems including organic molecules, metals, semiconductors, and insulators with high fidelity. © 2018 Curran Associates Inc..All rights reserved.

关键词： Potential energy

Communication-computation efficient gradient coding

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arXiv 2018年

作者： Ye, Min Abbe, Emmanuel Department of Electrical Engineering Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Department of Electrical Engineering Princeton University School of Mathematics Institute for Advanced Study PrincetonNJ08544 United States

This paper develops coding techniques to reduce the running time of distributed learning tasks. It characterizes the fundamental tradeoff to compute gradients (and more generally vector summations) in terms of three parameters: computation load, straggler tolerance and communication cost. It further gives an explicit coding scheme that achieves the optimal tradeoff based on recursive polynomial constructions, coding both across data subsets and vector components. As a result, the proposed scheme allows to minimize the running time for gradient computations. Implementations are made on Amazon EC2 clusters using Python with mpi4py package. Results show that the proposed scheme maintains the same generalization error while reducing the running time by 32% compared to uncoded schemes and 23% compared to prior coded schemes focusing only on stragglers (Tandon et al., ICML 2017). Copyright © 2018, The Authors. All rights reserved.

关键词： Python

HIPPYlib: An extensible software framework for large-scale inverse problems governed by pdes;Part I: Deterministic inversion and linearized Bayesian inference

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arXiv 2019年

作者： Villa, Umberto Petra, Noemi Ghattas, Omar Electrical and Systems Engineering Washington University in St. Louis St. LouisMO United States Applied Mathematics School of Natural Sciences University of California MercedCA United States Oden Institute for Computational Engineering and Sciences Department of Mechanical Engineering Department of Geological Sciences University of Texas at Austin AustinTX United States

We present an extensible software framework, hIPPYlib, for solution of large-scale deterministic and Bayesian inverse problems governed by partial differential equations (PDEs) with (possibly) infinite-dimensional parameter fields (which are high-dimensional after discretization). hIPPYlib overcomes the prohibitive nature of Bayesian inversion for this class of problems by implementing state-of-the-art scalable algorithms for PDE-based inverse problems that exploit the structure of the underlying operators, notably the Hessian of the log-posterior. The key property of the algorithms implemented in hIPPYlib is that the solution of the deterministic and linearized Bayesian inverse problem is computed at a cost, measured in linearized forward PDE solves, that is independent of the parameter dimension. The mean of the posterior is approximated by the MAP point, which is found by minimizing the negative log-posterior. This deterministic nonlinear least-squares optimization problem is solved with an inexact matrix-free Newton-CG method. The posterior covariance is approximated by the inverse of the Hessian of the negative log posterior evaluated at the MAP point. This Gaussian approximation is exact when the parameter-to-observable map is linear;otherwise, its logarithm agrees to two derivatives with the log-posterior at the MAP point, and thus it can serve as a proposal for Hessian-based MCMC methods. The construction of the posterior covariance is made tractable by invoking a low-rank approximation of the Hessian of the log-likelihood. Scalable tools for sample generation are also implemented. hIPPYlib makes all of these advanced algorithms easily accessible to domain scientists and provides an environment that expedites the development of new algorithms. hIPPYlib is also a teaching tool that can be used to educate researchers and practitioners who are new to inverse problems and the Bayesian inference *** Codes 35Q62, 62F15, 35R30, 35Q93, 65C60, 65K10, 49M15,

关键词： Differential equations

The bulk van der Waals layered magnet CrSBr is a quasi-1D material

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arXiv 2022年

作者： Klein, Julian Pingault, Benjamin Florian, Matthias Heißenbüttel, Marie-Christin Steinhoff, Alexander Song, Zhigang Torres, Kierstin Dirnberger, Florian Curtis, Jonathan B. Weile, Mads Penn, Aubrey Deilmann, Thorsten Dana, Rami Bushati, Rezlind Quan, Jiamin Luxa, Jan Sofer, Zdenek Alù, Andrea Menon, Vinod M. Wurstbauer, Ursula Rohlfing, Michael Narang, Prineha Lončar, Marko Ross, Frances M. Department of Materials Science and Engineering Massachusetts Institute of Technology CambridgeMA02139 United States John A. Paulson School of Engineering and Applied Sciences Harvard University CambridgeMA02138 United States QuTech Delft University of Technology Delft2600 GA Netherlands Department of Electrical and Computer Engineering Department of Physics University of Michigan Ann ArborMI48109 United States Institut für Festkörpertheorie Westfälische Wilhelms-Universität Münster Münster48149 Germany Institut für Theoretische Physik Universität Bremen P.O. Box 330 440 Bremen28334 Germany Bremen Center for Computational Materials Science University of Bremen Bremen28359 Germany Department of Physics City College of New York New YorkNY10031 United States College of Letters and Science UCLA Los AngelesCA90095 United States Department of Physics Technical University of Denmark Kgs. LyngbyDK-2800 Denmark MIT.nano Massachusetts Institute of Technology CambridgeMA02139 United States Department of Physics The Graduate Center City University of New York New YorkNY10016 United States Photonics Initiative CUNY Advanced Science Research Center New YorkNY10031 United States Physics Program Graduate Center City University of New York New YorkNY10026 United States Department of Inorganic Chemistry University of Chemistry and Technology Prague Technická 5 Prague 6166 28 Czech Republic Institute of Physics Center for Nanotechnology University of Münster Münster48149 Germany

Correlated quantum phenomena in one-dimensional (1D) systems that exhibit competing electronic and magnetic order are of strong interest for studying fundamental interactions and excitations, such as Tomonaga-Luttinger liquids and topological orders and defects with properties completely different from the quasiparticles expected in their higher-dimensional counterparts. However, clean 1D electronic systems are difficult to realize experimentally, particularly magnetically ordered systems. Here, we show that the van der Waals layered magnetic semiconductor CrSBr behaves like a quasi-1D material embedded in a magnetically ordered environment. The strong 1D electronic character originates from the Cr-S chains and the combination of weak interlayer hybridization and anisotropy in effective mass and dielectric screening with an effective electron mass ratio of meX/meY ∼ 50. This extreme anisotropy experimentally manifests in strong electron-phonon and exciton-phonon interactions, a Peierls-like structural instability and a Fano resonance from a van Hove singularity of similar strength of metallic carbon nanotubes. Moreover, due to the reduced dimensionality and interlayer coupling, CrSBr hosts spectrally narrow (1 meV) excitons of high binding energy and oscillator strength that inherit the 1D character. Overall, CrSBr is best understood as a stack of weakly hybridized monolayers and appears to be an experimentally attractive candidate for the study of exotic exciton and 1D correlated many-body physics in the presence of magnetic order. Copyright © 2022, The Authors. All rights reserved.

关键词： Excitons