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A demonstration of improved constraints on primordial gravitational waves with delensing

Physical Review D 2021年第2期103卷 022004-022004页

作者： P. A. R. Ade Z. Ahmed M. Amiri A. J. Anderson J. E. Austermann J. S. Avva D. Barkats R. Basu Thakur J. A. Beall A. N. Bender B. A. Benson F. Bianchini C. A. Bischoff L. E. Bleem J. J. Bock H. Boenish E. Bullock V. Buza J. E. Carlstrom C. L. Chang J. R. Cheshire, IV H. C. Chiang T-L. Chou R. Citron J. Connors C. Corbett Moran J. Cornelison T. M. Crawford A. T. Crites M. Crumrine A. Cukierman T. de Haan M. Dierickx M. A. Dobbs L. Duband W. Everett S. Fatigoni J. P. Filippini S. Fliescher J. Gallicchio E. M. George T. St. Germaine N. Goeckner-Wald D. C. Goldfinger J. Grayson N. Gupta G. Hall M. Halpern N. W. Halverson S. Harrison S. Henderson J. W. Henning S. R. Hildebrandt G. C. Hilton G. P. Holder W. L. Holzapfel J. D. Hrubes N. Huang J. Hubmayr H. Hui K. D. Irwin J. Kang K. S. Karkare E. Karpel S. Kefeli S. A. Kernasovskiy L. Knox J. M. Kovac C. L. Kuo K. Lau A. T. Lee E. M. Leitch D. Li A. Lowitz A. Manzotti J. J. McMahon K. G. Megerian S. S. Meyer M. Millea L. M. Mocanu L. Moncelsi J. Montgomery A. Nadolski T. Namikawa T. Natoli C. B. Netterfield H. T. Nguyen J. P. Nibarger G. Noble V. Novosad R. O’Brient R. W. Ogburn, IV Y. Omori S. Padin S. Palladino S. Patil T. Prouve C. Pryke B. Racine C. L. Reichardt C. D. Reintsema S. Richter J. E. Ruhl B. R. Saliwanchik K. K. Schaffer A. Schillaci B. L. Schmitt R. Schwarz C. D. Sheehy C. Sievers G. Smecher A. Soliman A. A. Stark B. Steinbach R. V. Sudiwala G. P. Teply K. L. Thompson J. E. Tolan C. Tucker A. D. Turner C. Umiltà T. Veach J. D. Vieira A. G. Vieregg A. Wandui G. Wang A. C. Weber N. Whitehorn D. V. Wiebe J. Willmert C. L. Wong W. L. K. Wu H. Yang V. Yefremenko K. W. Yoon E. Young C. Yu L. Zeng C. Zhang Cardiff University Cardiff CF10 3XQ United Kingdom SLAC National Accelerator Laboratory 2575 Sand Hill Road Menlo Park California 94025 USA Kavli Institute for Particle Astrophysics and Cosmology Stanford University 452 Lomita Mall Stanford California 94305 USA Department of Physics and Astronomy University of British Columbia Vancouver British Columbia V6T 1Z1 Canada Fermi National Accelerator Laboratory MS209 P.O. Box 500 Batavia Illinois 60510 USA NIST Quantum Devices Group 325 Broadway Mailcode 817.03 Boulder Colorado 80305 USA Department of Physics University of Colorado Boulder Colorado 80309 USA Department of Physics University of California Berkeley California 94720 USA Harvard-Smithsonian Center for Astrophysics 60 Garden Street Cambridge Massachusetts 02138 USA California Institute of Technology MS 249-17 1216 E. California Blvd. Pasadena California 91125 USA High Energy Physics Division Argonne National Laboratory 9700 S. Cass Avenue Argonne Illinois 60439 USA Kavli Institute for Cosmological Physics University of Chicago 5640 South Ellis Avenue Chicago Illinois 60637 USA Department of Astronomy and Astrophysics University of Chicago 5640 South Ellis Avenue Chicago Illinois 60637 USA School of Physics University of Melbourne Parkville Victoria 3010 Australia Department of Physics University of Cincinnati Cincinnati Ohio 45221 USA Jet Propulsion Laboratory Pasadena California 91109 USA Department of Physics Harvard University Cambridge Massachusetts 02138 USA Minnesota Institute for Astrophysics University of Minnesota Minneapolis Minnesota 55455 USA Department of Physics University of Chicago 5640 South Ellis Avenue Chicago Illinois 60637 USA Enrico Fermi Institute University of Chicago 5640 South Ellis Avenue Chicago Illinois 60637 USA Department of Physics McGill University 3600 Rue University Montreal Quebec H3A 2T8 Canada School of Mathematics Statistics and Computer Science University of KwaZulu-Natal Dur

We present a constraint on the tensor-to-scalar ratio, r, derived from measurements of cosmic microwave background (CMB) polarization B-modes with “delensing,” whereby the uncertainty on r contributed by the sample variance of the gravitational lensing B-modes is reduced by cross-correlating against a lensing B-mode template. This template is constructed by combining an estimate of the polarized CMB with a tracer of the projected large-scale structure. The large-scale-structure tracer used is a map of the cosmic infrared background derived from Planck satellite data, while the polarized CMB map comes from a combination of South Pole Telescope, bicep/Keck, and Planck data. We expand the bicep/Keck likelihood analysis framework to accept a lensing template and apply it to the bicep/Keck dataset collected through 2014 using the same parametric foreground modeling as in the previous analysis. From simulations, we find that the uncertainty on r is reduced by ∼10%, from σ(r)=0.024 to 0.022, which can be compared with a ∼26% reduction obtained when using a perfect lensing template or if there were zero lensing B-modes. Applying the technique to the real data, the constraint on r is improved from r0.05<0.090 to r0.05<0.082 (95% C.L.). This is the first demonstration of improvement in an r constraint through delensing.

关键词： Cosmic microwave background Inflation Large scale structure of the Universe

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Comparison of Polarized Radiative Transfer Codes used by the EHT Collaboration

arXiv

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arXiv 2023年

作者： Prather, Ben S. Dexter, Jason Moscibrodzka, Monika Pu, Hung-Yi Bronzwaer, Thomas Davelaar, Jordy Younsi, Ziri Gammie, Charles F. Gold, Roman Wong, And George N. 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 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 De Laurentis, Mariafelicia Deane, Roger Dempsey, Jessica Desvignes, Gregory Dhruv, Vedant Doeleman, Sheperd S. Dougal, Sean Dzib, Sergio A. Eatough, Ralph P. Emami, Razieh Falcke, Heino Farah, Joseph Fish, Vincent L. Fomalont, Ed Alyson Ford, H. Fraga-Encinas, Raquel Freeman, William T. Friberg, Per Fromm, Christian M. Fuentes, Antonio Galison, Peter García, Roberto Gentaz, Olivier Georgiev, Boris Goddi, Ciriaco 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 Violette Impellizzeri, C.M. 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 K CCS-2 Los Alamos National Laboratory P.O. Box 1663 Los AlamosNM87545 United States JILA Department of Astrophysical and Planetary Sciences University of Colorado BoulderCO80309 United States Department of Astrophysics IMAPP Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Department of Physics National Taiwan Normal University No. 88 Sec.4 Tingzhou Rd. Taipei116 Taiwan Center of Astronomy and Gravitation National Taiwan Normal University No. 88 Sec. 4 Tingzhou Road Taipei116 Taiwan Institute of Astronomy and Astrophysics Academia Sinica 11F of Astronomy-Mathematics Building AS/NTU No. 1 Sec. 4 Roosevelt Rd Taipei10617 Taiwan Department of Astronomy Columbia Astrophysics Laboratory Columbia University 550 W 120th Street New YorkNY10027 United States Center for Computational Astrophysics Flatiron Institute 162 Fifth Avenue New YorkNY10010 United States Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Mullard Space Science Laboratory University College London Holmbury St. Mary Dorking SurreyRH5 6NT United Kingdom Institut für Theoretische Physik Goethe-Universität Frankfurt Max-von-Laue-Straße 1 Frankfurt am MainD-60438 Germany Department of Physics University of Illinois 1110 West Green Street UrbanaIL61801 United States Department of Astronomy University of Illinois at Urbana-Champaign 1002 West Green Street UrbanaIL61801 United States NCSA University of Illinois 1205 W Clark St UrbanaIL61801 United States CP3-Origins University of Southern Denmark Campusvej 55 Odense MDK-5230 Denmark School of Natural Sciences Institute for Advanced Study 1 Einstein Drive PrincetonNJ08540 United States Princeton Gravity Initiative Princeton University PrincetonNJ08544 United States 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 Harvard University 20 Gar

Interpretation of resolved polarized images of black holes by the Event Horizon Telescope (EHT) requires predictions of the polarized emission observable by an Earth-based instrument for a particular model of the black hole accretion system. Such predictions are generated by general relativistic radiative transfer (GRRT) codes, which integrate the equations of polarized radiative transfer in curved spacetime. A selection of ray-tracing GRRT codes used within the EHT collaboration is evaluated for accuracy and consistency in producing a selection of test images, demonstrating that the various methods and implementations of radiative transfer calculations are highly consistent. When imaging an analytic accretion model, we find that all codes produce images similar within a pixel-wise normalized mean squared error (NMSE) of 0.012 in the worst case. When imaging a snapshot from a cell-based magnetohydrodynamic simulation, we find all test images to be similar within NMSEs of 0.02, 0.04, 0.04, and 0.12 in Stokes I, Q, U, and V respectively. We additionally find the values of several image metrics relevant to published EHT results to be in agreement to much better precision than measurement uncertainties. © 2023, CC BY.

关键词： Mean square error

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P-71: On the Origin and Significance of Melting Dimensionality in ELA of Si films

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SID Symposium Digest of Technical Papers 2018年第1期49卷

作者： Wenkai Pan Vernon Wong Miao Yu Ruobing Song Insung Choi James S. Im Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New York NY United States

Our recent investigations have revealed that substantially 2D melting transpires during the ELA process. In this paper, we first present the experimental finding that shows how this behavior at least stems intrinsically from the presence in the material of melt-prone grain boundaries and superheating-permitting Si-oxide interface. We also point out, and substantiate with numerical simulation results, that the manifested dimensionality of melting can figure in affecting (1) the energy utilization efficiency of the ELA method, as well as (2) the microstructural uniformity of the resulting polycrystalline materials.

关键词： Excimer-laser annealing laser crystallization materials processing phase transformations melting and solidification

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First Sagittarius A* Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole in the Center of the Milky Way

arXiv

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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 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 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

We present the first Event Horizon Telescope (EHT) observations of Sagittarius A* (Sgr A∗), the Galactic center source associated with a supermassive black hole. These observations were conducted in 2017 using a global interferometric array of eight telescopes operating at a wavelength of λ = 1.3 mm. The EHT data resolve a compact emission region with intrahour variability. A variety of imaging and modeling analyses all support an image that is dominated by a bright, thick ring with a diameter of 51.8 ± 2.3 µas (68% credible interval). The ring has modest azimuthal brightness asymmetry and a comparatively dim interior. Using a large suite of numerical simulations, we demonstrate that the EHT images of Sgr A∗ are consistent with the expected appearance of a Kerr black hole with mass ∼4 × 106 M☉, which is inferred to exist at this location based on previous infrared observations of individual stellar orbits as well as maser proper motion studies. Our model comparisons disfavor scenarios where the black hole is viewed at high inclination (i > 50◦), as well as non-spinning black holes and those with retrograde accretion disks. Our results provide direct evidence for the presence of a supermassive black hole at the center of the Milky Way galaxy, and for the first time we connect the predictions from dynamical measurements of stellar orbits on scales of 103 − 105 gravitational radii to event horizon-scale images and variability. Furthermore, a comparison with the EHT results for the supermassive black hole M87∗ shows consistency with the predictions of general relativity spanning over three orders of magnitude in central mass. © 2023, CC BY.

关键词： Telescopes

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Clustering with T-SNE, provably

arXiv

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arXiv 2017年

作者： Linderman, George C. Steinerberger, Stefan Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States

t-distributed Stochastic Neighborhood Embedding (t-SNE), a clustering and visualization method proposed by van der Maaten &Hinton in 2008, has rapidly become a standard tool in a number of natural sciences. Despite its overwhelming success, there is a distinct lack of mathematical foundations and the inner workings of the algorithm are not well understood. The purpose of this paper is to prove that t-SNE is able to recover well-separated clusters;more precisely, we prove that t-SNE in the 'early exaggeration' phase, an optimization technique proposed by van der Maaten &Hinton (2008) and van der Maaten (2014), can be rigorously analyzed. As a byproduct, the proof suggests novel ways for setting the exaggeration parameter a and step size h. Numerical examples illustrate the effectiveness of these rules: in particular, the quality of embedding of topological structures (e.g. the swiss roll) improves. We also discuss a connection to spectral clustering methods. Copyright © 2017, The Authors. All rights reserved.

关键词： Stochastic systems

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Triangles capturing many lattice points

arXiv

引用

arXiv 2017年

作者： Marshall, Nicholas F. Steinerberger, Stefan Program in Applied Mathematics Yale University New HavenCT06511 United States Department of Mathematics Yale University New HavenCT06511 United States

We study a combinatorial problem that recently arose in the context of shape optimization: among all triangles with vertices (0, 0), (x, 0), and (0, y) and fixed area, which one encloses the most lattice points from Z>02? Moreover, does its shape necessarily converge to the isosceles triangle (x = y) as the area becomes large? Laugesen and Liu suggested that, in contrast to similar problems, there might not be a limiting shape. We prove that the limiting set is indeed nontrivial and contains infinitely many elements. We also show that there exist 'bad' areas where no triangle is particularly good at capturing lattice points and show that there exists an infinite set of slopes y/x such that any associated triangle captures more lattice points than any other fixed triangle for infinitely many (and arbitrarily large) areas;this set of slopes is a fractal subset of [1/3, 3] and has Minkowski dimension at most 3/4. Copyright © 2017, The Authors. All rights reserved.

关键词： Shape optimization

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Structural variability from noisy tomographic projections

arXiv

引用

arXiv 2017年

作者： Andén, Joakim Singer, Amit Center for Computational Biology Flatiron Institute New YorkNY United States Department of Mathematics and Program in Applied and Computational Mathematics Princeton University NJ United States

In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low-rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For n images of size N-by-N pixels, we propose an algorithm for calculating this covariance estimator with computational complexity O(nN4 + √κN6 log N), where the condition number κ is empirically in the range 10-200. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in 6D. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of the 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed non-consistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrix estimation, we incorporate a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.92C55, 68U10, 44A12, 65R32, 62G05, 62H30, 62J10, 62J07 Copyright © 2017, The Authors. All rights reserved.

关键词： Conjugate gradient method

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Author Correction: Hysteresis control of epithelial-mesenchymal transition dynamics conveys a distinct program with enhanced metastatic ability

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Nature communications 2019年第1期10卷 527页

作者： Toni Celià-Terrassa Caleb Bastian Daniel D Liu Brian Ell Nicole M Aiello Yong Wei Jose Zamalloa Andres M Blanco Xiang Hang Dmitriy Kunisky Wenyang Li Elizabeth D Williams Herschel Rabitz Yibin Kang Department of Molecular Biology Princeton University Princeton NJ 08544 USA. Cancer Program IMIM (Hospital del Mar Medical Research Institute) 08003 Barcelona Spain. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA. cbastian@princeton.edu. Lewis-Sigler Institute of Integrative Genomics Princeton University Princeton NJ 08544 USA. Department of Mathematics Princeton University Princeton NJ 08544 USA. School of Biomedical Sciences Translational Research Institute Queensland University of Technology (QUT) Brisbane QLD 4102 Australia. Program in Applied and Computational Mathematics Princeton University Princeton NJ 08544 USA. Department of Chemistry Princeton University Princeton NJ 08544 USA. Department of Molecular Biology Princeton University Princeton NJ 08544 USA. ykang@princeton.edu.

The original version of this Article contained an error in the spelling of the author Daniel D. Liu, which was incorrectly given as Daniel Liu. This has now been corrected in both the PDF and HTML versions of the Arti...

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Polarimetric geometric modeling for mm-VLBI observations of black holes

arXiv

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arXiv 2023年

作者： Roelofs, Freek Johnson, Michael D. Chael, Andrew Janssen, Michael Wielgus, Maciek Broderick, Avery E. 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 Broguiere, Dominique Bronzwaer, Thomas Bustamante, Sandra Byun, Do-Young Carlstrom, John E. Ceccobello, Chiara 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 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. Jeter, Britton Jiang, Wu Jiménez-Rosales, Alejandra 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, Center for Astrophysics Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Radboud University P.O. Box 9010 Nijmegen6500 GL Netherlands Black Hole Initiative Harvard University 20 Garden Street CambridgeMA02138 United States Princeton Gravity Initiative Princeton University Jadwin Hall PrincetonNJ08544 United States Max-Planck-Institut für Radioastronomie Auf dem Hügel 69 BonnD-53121 Germany Perimeter Institute for Theoretical Physics 31 Caroline Street North WaterlooONN2L 2Y5 Canada Department of Physics and Astronomy University of Waterloo 200 University Avenue West WaterlooONN2L 3G1 Canada Waterloo Centre for Astrophysics University of Waterloo WaterlooONN2L 3G1 Canada 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 Instituto de Astrofísica de Andalucía-CSIC Glorieta de la Astronomía s/n GranadaE-18008 Spain Department of Physics Faculty of Science Universiti Malaya Kuala Lumpur50603 Malaysia 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 València BurjassotE-46100 Spain Observatori Astronòmic Universitat de València C. Catedrático José Beltrán 2 València PaternaE-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 Universit

The Event Horizon Telescope (EHT) is a millimeter very-long-baseline interferometry (VLBI) array which has imaged the apparent shadows of the supermassive black holes M87∗ and Sagittarius A∗. Polarimetric data from these observations contain a wealth of information on the black hole and accretion flow properties. In this work, we develop polarimetric geometric modeling methods for mm-VLBI data, focusing on approaches that fit data products with differing degrees of invariance to broad classes of calibration errors. We establish a fitting procedure using a polarimetric "m-ring" model to approximate the image structure near a black hole. By fitting this model to synthetic EHT data from general relativistic magnetohydrodynamic (GRMHD) models, we show that the linear and circular polarization structure can be successfully approximated with relatively few model parameters. We then fit this model to EHT observations of M87∗ taken in 2017. In total intensity and linear polarization, the m-ring fits are consistent with previous results from imaging methods. In circular polarization, the m-ring fits indicate the presence of event-horizon-scale circular polarization structure, with a persistent dipolar asymmetry and orientation across several days. The same structure was recovered independently of observing band, used data products, and model assumptions. Despite this broad agreement, imaging methods do not produce similarly consistent results. Our circular polarization results, which imposed additional assumptions on the source structure, should thus be interpreted with some caution. Polarimetric geometric modeling provides a useful and powerful method to constrain the properties of horizon-scale polarized emission, particularly for sparse arrays like the EHT. © 2023, CC BY.

关键词： Polarimeters

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

arXiv

引用

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

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