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Gait transitions in a phase oscillator model of an insect central pattern generator

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arXiv 2017年

作者： Aminzare, Zahra Srivastava, Vaibhav Holmes, Philip Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Princeton University NJ United States Department of Electrical and Computer Engineering Michigan State University LansingMI United States Program in Applied and Computational Mathematics Department of Mechanical and Aerospace Engineering Princeton Neuroscience Institute Princeton University NJ United States

Legged locomotion involves various gaits. It has been observed that fast running insects (cockroaches) employ a tripod gait with three legs lifted off the ground simultaneously in swing, while slow walking insects (stick insects) use a tetrapod gait with two legs lifted off the ground simultaneously. Fruit flies use both gaits and exhibit a transition from tetrapod to tripod at intermediate speeds. Here we study the effect of stepping frequency on gait transition in an ion-channel bursting neuron model in which each cell represents a hemi-segmental thoracic circuit of the central pattern generator. Employing phase reduction, we collapse the network of bursting neurons represented by 24 ordinary differential equations to 6 coupled nonlinear phase oscillators, each corresponding to a sub-network of neurons controlling one leg. Assuming that the left and right legs maintain constant phase differences (contralateral symmetry), we reduce from 6 equations to 3, allowing analysis of a dynamical system with 2 phase differences defined on a torus. We show that bifurcations occur from multiple stable tetrapod gaits to a unique stable tripod gait as speed increases. Finally, we consider gait transitions in two sets of data fitted to freely walking fruit flies.34C16, 34C60, 37G10, 92B20, 92C2034C16, 34C60, 37G10, 92B20, 92C20 Copyright © 2017, The Authors. All rights reserved.

关键词： Bifurcation (mathematics)

Data-driven model reduction and transfer operator approximation

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arXiv 2017年

作者： Klus, Stefan Nüske, Feliks Koltai, Péter Wu, Hao Kevrekidis, Ioannis Schütte, Christof Noé, Frank Department of Mathematics and Computer Science Freie Universität Berlin Germany Department of Chemical and Biological Engineering & Program in Applied and Computational Mathematics Princeton University United States Zuse Institute Berlin Germany

In this review paper, we will present different data-driven dimension reduction techniques for dynamical systems that are based on transfer operator theory as well as methods to approximate transfer operators and their eigenvalues, eigenfunctions, and eigenmodes. The goal is to point out similarities and differences between methods developed independently by the dynamical systems, fluid dynamics, and molecular dynamics communities such as time-lagged independent component analysis (TICA), dynamic mode decomposition (DMD), and their respective generalizations. As a result, extensions and best practices developed for one particular method can be carried over to other related methods. Copyright © 2017, The Authors. All rights reserved.

关键词： Dynamical systems

Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator

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arXiv 2017年

作者： Li, Qianxiao Dietrich, Felix Bollt, Erik M. Kevrekidis, Ioannis G. Institute of High Performance Computing Singapore Singapore Faculty of Mathematics Technical University of Munich Germany Department of Mathematics Clarkson University United States Department of Chemical and Biological Engineering Program in Applied and Computational Mathematics Princeton University United States

Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are becoming increasingly popular in practical applications. The EDMD improves upon the classical DMD by the inclusion of a flexible choice of dictionary of observables that spans a finite dimensional subspace on which the Koopman operator can be approximated. This enhances the accuracy of the solution reconstruction and broadens the applicability of the Koopman formalism. Although the convergence of the EDMD has been established, applying the method in practice requires a careful choice of the observables to improve convergence with just a finite number of terms. This is especially difficult for high dimensional and highly nonlinear systems. In this paper, we employ ideas from machine learning to improve upon the EDMD method. We develop an iterative approximation algorithm which couples the EDMD with a trainable dictionary represented by an artificial neural network. Using the Duffing oscillator and the Kuramoto Sivashinsky PDE as examples, we show that our algorithm can effectively and efficiently adapt the trainable dictionary to the problem at hand to achieve good reconstruction accuracy without the need to choose a fixed dictionary a priori. Furthermore, to obtain a given accuracy we require fewer dictionary terms than EDMD with fixed dictionaries. This alleviates an important shortcoming of the EDMD algorithm and enhances the applicability of the Koopman framework to practical problems. Copyright © 2017, The Authors. All rights reserved.

关键词： Machine learning

First M87 Event Horizon Telescope Results IX: Detection of Near-Horizon Circular Polarization

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arXiv 2023年

作者： Akiyama, Kazunori Alberdi, Antxon Alef, Walter Algaba, Juan Carlos Anantua, Richard Asada, Keiichi Azulay, Rebecca Bach, Uwe Baczko, Anne-Kathrin Ball, David Baloković, Mislav Bandyopadhyay, Bidisha Barrett, John Bauböck, Michi Benson, Bradford A. Bintley, Dan Blackburn, Lindy Blundell, Raymond Bouman, Katherine L. Bower, Geoffrey C. Boyce, Hope Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bronzwaer, Thomas Bustamante, Sandra Byun, Do-Young Carlstrom, John E. Ceccobello, Chiara Chael, Andrew Chan, Chi-Kwan Chang, Dominic O. Chatterjee, Koushik Chatterjee, Shami Chen, Ming-Tang Chen, Yongjun Cheng, Xiaopeng Cho, Ilje Christian, Pierre Conroy, Nicholas S. Conway, John E. Cordes, James M. Crawford, Thomas M. Crew, Geoffrey B. Cruz-Osorio, Alejandro Cui, Yuzhu Dahale, Rohan Davelaar, Jordy De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dexter, Jason Dhruv, Vedant Dihingia, Indu K. Doeleman, Sheperd S. Dougal, Sean Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fish, Vincent L. Fomalont, Ed Ford, H. Alyson Foschi, Marianna Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Fuentes, Antonio Galison, Peter Gammie, Charles F. García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gold, Roman Gómez-Ruiz, Arturo I. Gómez, José L. Gu, Minfeng Gurwell, Mark Hada, Kazuhiro Haggard, Daryl Haworth, Kari Hecht, Michael H. Hesper, Ronald Heumann, Dirk Ho, Luis C. Ho, Paul Honma, Mareki Huang, Chih-Wei L. Huang, Lei Hughes, David H. Ikeda, Shiro Impellizzeri, C.M. Violette Inoue, Makoto Issaoun, Sara James, David J. Jannuzi, Buell T. Janssen, Michael Jeter, Britton Jiang, Wu Jiménez-Rosales, Alejandra Johnson, Michael D. Jorstad, Svetlana Joshi, Abhishek V. Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, Mark Kim, Dong-Jin Kim, Jae-Young Kim, Jongsoo Kim, Junhan Kino, Motoki Koay, Jun Yi Kocherlakota, Prashant Kofuji, Yut Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Department of Physics Faculty of Science Universiti Malaya Kuala Lumpur50603 Malaysia Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Department of Physics & Astronomy The University of Texas at San Antonio One UTSA Circle San AntonioTX78249 United States Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd. Taipei10617 Taiwan Departament d’Astronomia i Astrofísica Universitat de València C. Dr. Moliner 50 Burjassot ValènciaE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 Paterna ValènciaE-46980 Spain Department of Space Earth and Environment Chalmers University of Technology Onsala Space Observatory OnsalaSE-43992 Sweden Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Yale Center for Astronomy & Astrophysics Yale University 52 Hillhouse Avenue New HavenCT06511 United States Astronomy Department Universidad de Concepción Casilla 160-C Concepción Chile Department of Physics University of Illinois 1110 West Green Street UrbanaIL61801 United States Fermi National Accelerator Laboratory MS209 P.O. Box 500 BataviaIL60510 United States Department of Astronomy and Astrophysics University of Chicago 5640 South Ellis Avenue ChicagoIL60637 United States East Asian Observatory 660 N. A’ohoku Place HiloHI96720 United States 660 N. A’ohoku Place HiloHI

Event Horizon Telescope (EHT) observations have revealed a bright ring of emission around the supermassive black hole at the center of the M87 galaxy. EHT images in linear polarization have further identified a coherent spiral pattern around the black hole, produced from ordered magnetic fields threading the emitting plasma. Here, we present the first analysis of circular polarization using EHT data, acquired in 2017, which can potentially provide additional insights into the magnetic fields and plasma composition near the black hole. Interferometric closure quantities provide convincing evidence for the presence of circularly polarized emission on event-horizon scales. We produce images of the circular polarization using both traditional and newly developed methods. All methods find a moderate level of resolved circular polarization across the image (〈|v|〉 int| ∗ © 2023, CC BY.

关键词： Circular polarization

First Sagittarius A* Event Horizon Telescope Results. VI: Testing the Black Hole Metricc

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arXiv 2023年

作者： Akiyama, Kazunori Alberdi, Antxon Alef, Walter Algaba, Juan Carlos Anantua, Richard Asada, Keiichi Azulay, Rebecca Bach, Uwe Baczko, Anne-Kathrin Ball, David Baloković, Mislav Barrett, John Bauböck, Michi Benson, Bradford A. Bintley, Dan Blackburn, Lindy Blundell, Raymond Bouman, Katherine L. Bower, Geoffrey C. Boyce, Hope Bremer, Michael Brinkerink, Christiaan D. Brissenden, Roger Britzen, Silke Broderick, Avery E. Broguiere, Dominique Bronzwaer, Thomas Bustamante, Sandra Byun, Do-Young Carlstrom, John E. Ceccobello, Chiara Chael, Andrew Chan, Chi-Kwan Chatterjee, Koushik Chatterjee, Shami Chen, Ming-Tang Chen, Yongjun Cheng, Xiaopeng Cho, Ilje Christian, Pierre Conroy, Nicholas S. Conway, John E. Cordes, James M. Crawford, Thomas M. Crew, Geoffrey B. Cruz-Osorio, Alejandro Cui, Yuzhu Davelaar, Jordy De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dexter, Jason Dhruv, Vedant Doeleman, Sheperd S. Dougal, Sean Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fish, Vincent L. Fomalont, Ed Ford, H. Alyson Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Fuentes, Antonio Galison, Peter Gammie, Charles F. García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco Gold, Roman Gómez-Ruiz, Arturo I. Gómez, José L. Gu, Minfeng Gurwell, Mark Hada, Kazuhiro Haggard, Daryl Haworth, Kari Hecht, Michael H. Hesper, Ronald Heumann, Dirk Ho, Luis C. Ho, Paul Honma, Mareki Huang, Chih-Wei L. Huang, Lei Hughes, David H. Ikeda, Shiro Impellizzeri, C.M. Violette Inoue, Makoto Issaoun, Sara James, David J. Jannuzi, Buell T. Janssen, Michael Jeter, Britton Jiang, Wu Jiménez-Rosales, Alejandra Johnson, Michael D. Jorstad, Svetlana Joshi, Abhishek V. Jung, Taehyun Karami, Mansour Karuppusamy, Ramesh Kawashima, Tomohisa Keating, Garrett K. Kettenis, Mark Kim, Dong-Jin Kim, Jae-Young Kim, Jongsoo Kim, Junhan Kino, Motoki Koay, Jun Yi Kocherlakota, Prashant Kofuji, Yutaro Koch, Patrick M. Koyama, Shoko Kramer, Carsten Kramer, Michael Krichbaum, Thomas P. Ku Massachusetts Institute of Technology Haystack Observatory 99 Millstone Road WestfordMA01886 United States National Astronomical Observatory of Japan 2-21-1 Osawa Mitaka Tokyo181-8588 Japan Black Hole Initiative at Harvard University 20 Garden Street CambridgeMA02138 United States Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Department of Physics Faculty of Science Universiti Malaya Kuala Lumpur50603 Malaysia Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Department of Physics & Astronomy The University of Texas at San Antonio One UTSA Circle San AntonioTX78249 United States Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd Taipei10617 Taiwan Departament d’Astronomia i Astrofísica Universitat de València C. Dr. Moliner 50 Burjassot ValènciaE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 València PaternaE-46980 Spain Steward Observatory Department of Astronomy University of Arizona 933 N. Cherry Ave. TucsonAZ85721 United States Yale Center for Astronomy & Astrophysics Yale University 52 Hillhouse Avenue New HavenCT06511 United States Department of Physics University of Illinois 1110 West Green Street UrbanaIL61801 United States Fermi National Accelerator Laboratory MS209 P.O. Box 500 BataviaIL60510 United States Department of Astronomy and Astrophysics University of Chicago 5640 South Ellis Avenue ChicagoIL60637 United States East Asian Observatory 660 N. A’ohoku Place HiloHI96720 United States 660 N. A’ohoku Place HiloHI96720 United States California Institute of Technology 1200 East California Boulevard PasadenaCA91125 United States Institute of Astronomy and Astrophysics Academia Sinica 645 N. A’ohoku Place HiloHI

Astrophysical black holes are expected to be described by the Kerr metric. This is the only stationary, vacuum, axisymmetric metric, without electromagnetic charge, that satisfies Einstein’s equations and does not have pathologies outside of the event horizon. We present new constraints on potential deviations from the Kerr prediction based on 2017 EHT observations of Sagittarius A∗ (Sgr A∗). We calibrate the relationship between the geometrically defined black hole shadow and the observed size of the ring-like images using a library that includes both Kerr and non-Kerr simulations. We use the exquisite prior constraints on the mass-to-distance ratio for Sgr A∗ to show that the observed image size is within ∼ 10% of the Kerr predictions. We use these bounds to constrain metrics that are parametrically different from Kerr as well as the charges of several known spacetimes. To consider alternatives to the presence of an event horizon we explore the possibility that Sgr A∗ is a compact object with a surface that either absorbs and thermally re-emits incident radiation or partially reflects it. Using the observed image size and the broadband spectrum of Sgr A∗, we conclude that a thermal surface can be ruled out and a fully reflective one is unlikely. We compare our results to the broader landscape of gravitational tests. Together with the bounds found for stellar mass black holes and the M87 black hole, our observations provide further support that the external spacetimes of all black holes are described by the Kerr metric, independent of their mass. © 2023, CC BY.

关键词： Black holes

Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics

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arXiv 2017年

作者： Zhang, Linfeng Han, Jiequn Wang, Han Car, Roberto Weinan, E. Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Institute of Applied Physics and Computational Mathematics Fenghao East Road 2 Beijing100094 China CAEP Software Center for High Performance Numerical Simulation Huayuan Road 6 Beijing100088 China Department of Chemistry Department of Physics Program in Applied and Computational Mathematics Princeton Institute for the Science and Technology of Materials Princeton University PrincetonNJ08544 United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Center for Data Science Beijing International Center for Mathematical Research Peking University Beijing Institute of Big Data Research Beijing100871 China

We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is "first principle-based" in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size. Copyright © 2017, The Authors. All rights reserved.

关键词： Molecular dynamics

Pre-processing and classification of hyperspectral imagery via selective inpainting

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Pre-processing and classification of hyperspectral imagery v...

IEEE International Conference on Acoustics, Speech and Signal Processing

作者： Victoria Chayes Kevin Miller Rasika Bhalerao Jiajie Luo Wei Zhu Andrea L. Bertozzi Wenzhi Liao Stanley Osher California Research Training Program in Computational and Applied Mathematics United States of America University of California Los Angeles Department of Mathematics United States of America Ghent University Department of Telecommunications and Information Processing Belgium

ISBN: (纸本)9781509041183

We propose a semi-supervised algorithm for processing and classification of hyperspectral imagery. For initialization, we keep 20% of the data intact, and use Principal Component Analysis to discard voxels from noisier bands and pixels. Then, we use either an Accelerated Proximal Gradient algorithm (APGL), or a modified APGL algorithm with a penalty term for distance between inpainted pixels and endmembers (APGL Hyp), on the initialized datacube to inpaint the missing data. APGL and APGL Hyp are distinguished by performance on datasets with full pixels removed or extreme noise. This inpainting technique results in band-by-band datacube sharpening and removal of noise from individual spectral signatures. We can also classify the inpainted cube by assigning each pixel to its nearest endmember via Euclidean distance. We demonstrate improved accuracy in classification over data-mining techniques like k-means, unmixing techniques like Hierarchical Non-Negative Matrix Factorization, and graph-based methods like Non-Local Total Variation.

关键词： Hyperspectral imagery (HSI) data preprocessing image inpainting image classification image enhancement Data preprocessing hyperspectral imagery Image classification image enhancement pixel Pretreatment matrix decomposition initialization Euclidean distance

On singularity formation in a Hele-Shaw model

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arXiv 2017年

作者： Constantin, Peter Elgindi, Tarek Nguyen, Huy Vicol, Vlad Department of Mathematics Princeton University PrincetonNJ08544 United States Department of Mathematics Uc San Diego San DiegoCA92093 United States Program In Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

We discuss a lubrication approximation model of the interface between two immiscible fluids in a Hele-Shaw cell, derived in [CDG+93] and widely studied since. The model consists of a single one dimensional evolution equation for the thickness 2h = 2h(x, t) of a thin neck of fluid, ∂th + ∂x(h ∂x3h) = 0, for x ∈ (−1, 1) and t ≥ 0. The boundary conditions fix the neck height and the pressure jump: h(±1, t) = 1, ∂x2h(±1, t) = P > 0. We prove that starting from smooth and positive h, as long as h(x, t) > 0, for x ∈ [−1, 1], t ∈ [0, T ], no singularity can arise in the solution up to time T. As a consequence, we prove for any P > 2 and any smooth and positive initial datum that the solution pinches off in either finite or infinite time, i.e., inf[−1,1]×[0,T∗) h = 0, for some T∗ ∈ (0, ∞]. These facts have been long anticipated on the basis of numerical and theoretical studies. August 30, 2017.35Q35, 35Q86 Copyright © 2017, The Authors. All rights reserved.

关键词：

Local-order metric for condensed-phase environments

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Physical Review B 2018年第6期97卷 064105-064105页

作者： Fausto Martelli Hsin-Yu Ko Erdal C. Oğuz Roberto Car Department of Chemistry Princeton University Princeton New Jersey 08544 USA Institut für Theoretische Physik II Heinrich-Heine-Universität D-40225 Düsseldorf Germany Department of Physics Princeton University Princeton New Jersey 08544 USA Princeton Institute for the Science and Technology of Materials Princeton University Princeton New Jersey 08544 USA Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and tending to one for environments that perfectly match the reference. The site-averaged LOM and its standard deviation define two scalar order parameters, S and δS, that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that S, δS, and the LOM provide very insightful information in the study of structural transformations, such as those occurring when ice spontaneously nucleates from supercooled water or when a supercooled water sample becomes amorphous upon progressive cooling.

关键词： Glass transition Nucleation Order parameters Phase transitions