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arXiv 2022年

作者： Aiola, Simone Akrami, Yashar Basu, Kaustuv Boylan-Kolchin, Michael Brinckmann, Thejs Bryan, Sean Casey, Caitlin M. Chluba, Jens Clesse, Sébastien Cyr-Racine, Francis-Yan Di Mascolo, Luca Dicker, Simon Essinger-Hileman, Thomas Farren, Gerrit S. Fedderke, Michael A. Ferraro, Simone Fuller, George M. Galitzki, Nicholas Gluscevic, Vera Grin, Daniel Han, Dongwon Hasselfield, Matthew Hložek, Renée Holder, Gil Hotinli, Selim C. Jain, Bhuvnesh Johnson, Bradley Johnson, Matthew Klaassen, Pamela MacInnis, Amanda Madhavacheril, Mathew Mandal, Sayan Mauskopf, Philip Meerburg, Daan Meyers, Joel Miranda, Vivian Mroczkowski, Tony Mukherjee, Suvodip Münchmeyer, Moritz Munoz, Julian Naess, Sigurd Nagai, Daisuke Namikawa, Toshiya Newburgh, Laura Nguyên, Hô Nam Niemack, Michael Oppenheimer, Benjamin D. Pierpaoli, Elena Raghunathan, Srinivasan Schaan, Emmanuel Sehgal, Neelima Sherwin, Blake Simon, Sara M. Slosar, Anže Smith, Kendrick Spergel, David Switzer, Eric R. Trivedi, Pranjal Tsai, Yu-Dai van Engelen, Alexander Wandelt, Benjamin D. Wollack, Edward J. Wu, Kimmy Center for Computational Astrophysics Flatiron Institute 162 5th Avenue New YorkNY10010 United States CERCA ISO Department of Physics Case Western Reserve University 10900 Euclid Avenue ClevelandOH44106 United States Department of Physics Imperial College London Blackett Laboratory Prince Consort Road LondonSW7 2AZ United Kingdom Laboratoire de Physique de l’École Normale Supérieure ENS Université PSL CNRS Sorbonne Université ParisF-75005 France Observatoire de Paris Université PSL Sorbonne Université LERMA Paris750 France Argelander Institute for Astronomy University of Bonn Auf dem Hügel 71 BonnD-53121 Germany Department of Astronomy The University of Texas at Austin 2515 Speedway Stop C1400 AustinTX78712 United States Dipartimento di Fisica e Scienze della Terra Universitá degli Studi di Ferrara via Giuseppe Saragat 1 Ferrara44122 Italy Sezione di Ferrara Via Giuseppe Saragat 1 Ferrara44122 Italy School of Earth and Space Exploration Arizona State University 781 Terrace Mall TempeAZ85287 United States Jodrell Bank Centre for Astrophysics Alan Turing Building University of Manchester ManchesterM13 9PL United Kingdom Université Libre de Bruxelles Boulevard du Triomphe Brussels1050 Belgium Department of Physics and Astronomy University of New Mexico 210 Yale Blvd NE AlbuquerqueNM87106 United States Astronomy Unit Department of Physics University of Trieste via Tiepolo 11 Trieste34131 Italy INAF Osservatorio Astronomico di Trieste via Tiepolo 11 Trieste34131 Italy IFPU - Institute for Fundamental Physics of the Universe Via Beirut 2 Trieste340 Italy Department of Physics and Astronomy University of Pennsylvania 209 South 33rd Street PhiladelphiaPA19104 United States NASA/Goddard Space Flight Center GreenbeltMD20771 United States Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom Department of Physics and Astronomy Haverford College 370 Lancaste

CMB-HD is a proposed millimeter-wave survey over half the sky that would be ultra-deep (0.5 µK-arcmin) and have unprecedented resolution (15 arcseconds at 150 GHz). Such a survey would answer many outstanding questions about the fundamental physics of the Universe. Major advances would be 1.) the use of gravitational lensing of the primordial microwave background to map the distribution of matter on small scales (k ∼ 10 hMpc-1), which probes dark matter particle properties. It will also allow 2.) measurements of the thermal and kinetic Sunyaev-Zel’dovich effects on small scales to map the gas density and velocity, another probe of cosmic structure. In addition, CMB-HD would allow us to cross critical thresholds: 3.) ruling out or detecting any new, light ( © 2022, CC BY.

关键词： Telescopes

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Limited angle acousto-electrical tomography

arXiv

引用

arXiv 2017年

作者： Hubmer, Simon Knudsen, Kim Li, Changyou Sherina, Ekaterina Johannes Kepler University Linz Doctoral Program Computational Mathematics Altenbergerstraße 69 LinzA-4040 Austria Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark School of Electronics and Information Northwestern Polytechnical University Xian China Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby2800 Denmark

This paper considers the reconstruction problem in Acousto-Electrical Tomography, i.e., the problem of estimating a spatially varying conductivity in a bounded domain from measurements of the internal power densities resulting from different prescribed boundary conditions. Particular emphasis is placed on the limited angle scenario, in which the boundary conditions are supported only on a part of the boundary. The reconstruction problem is formulated as an optimization problem in a Hilbert space setting and solved using Landweber iteration. The resulting algorithm is implemented numerically in two spatial dimensions and tested on simulated data. The results quantify the intuition that features close to the measurement boundary are stably reconstructed and features further away are less well reconstructed. Finally, the ill-posedness of the limited angle problem is quantified numerically using the singular value decomposition of the corresponding linearized problem.65J22, 35R30, 65M32 Copyright © 2017, The Authors. All rights reserved.

关键词： Boundary conditions

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Spatiotemporal Dynamics and Reliable Computations in Recurrent Spiking Neural Networks

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Physical Review Letters 2017年第1期118卷 018103-018103页

作者： Ryan Pyle Robert Rosenbaum Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre Dame Indiana 46556 USA Interdisciplinary Center for Network Science and Applications University of Notre Dame Notre Dame Indiana 46556 USA

Randomly connected networks of excitatory and inhibitory spiking neurons provide a parsimonious model of neural variability, but are notoriously unreliable for performing computations. We show that this difficulty is overcome by incorporating the well-documented dependence of connection probability on distance. Spatially extended spiking networks exhibit symmetry-breaking bifurcations and generate spatiotemporal patterns that can be trained to perform dynamical computations under a reservoir computing framework.

关键词： Neuronal network activity Neuronal networks Spiking neurons Cortical networks

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Inference for Differential Equation Models using Relaxation via Dynamical Systems

arXiv

引用

arXiv 2017年

作者： Lee, Kyoungjae Lee, Jaeyong Dass, Sarat Department of Applied and Computational Mathematics and Statistics University of Notre Dame United States Department of Statistics Seoul National University Korea Republic of Department of Fundamental and Applied Sciences Universiti Teknologi PETRONAS Malaysia

Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The estimation of parameters of ODE based models is essential for understanding its dynamics, but the lack of an analytical solution of the ODE makes the parameter estimation challenging. The aim of this paper is to propose a general and fast framework of statistical inference for ODE based models by relaxation of the underlying ODE system. Relaxation is achieved by a properly chosen numerical procedure, such as the Runge-Kutta, and by introducing additive Gaussian noises with small variances. Consequently, filtering methods can be applied to obtain the posterior distribution of the parameters in the Bayesian framework. The main advantage of the proposed method is computation speed. In a simulation study, the proposed method was at least 14 times faster than the other methods. Theoretical results which guarantee the convergence of the posterior of the approximated dynamical system to the posterior of true model are presented. Explicit expressions are given that relate the order and the mesh size of the Runge-Kutta procedure to the rate of convergence of the approximated posterior as a function of sample size. Key words: Ordinary differential equation, Dynamic model, Runge-Kutta Method, Extended Liu and West filter62F15 (Primary) 62L12, 65L06 (Secondary) Copyright © 2017, The Authors. All rights reserved.

关键词： Ordinary differential equations

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Physical, optical and luminescence properties of Sm 3+ doped lithium aluminium phosphate glass system

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Materials Today: Proceedings 2018年第7期5卷 15066-15071页

作者： N. Chanthima Y. Tariwong M. Djamal J. Kaewkhao N. Sangwaranatee Center of Excellence in Glass Technology and Materials Science (CEGM) Nakhon Pathom Rajabhat University Nakhon Pathom 73000 Thailand Physics Program Faculty of Science and Technology Nakhon Pathom Rajabhat University Nakhon Pathom 73000 Thailand Department of Physics Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung 40132 Indonesia Applied Physics Faculty of Science and Technology Suan Sunandha Rajabhat University Bangkok 10300 Thailand

Sm 3+ doped lithium aluminium phosphate glasses have been investigated in different concentration of Sm 3+ ions. The physical, optical and luminescence properties were studied to evaluate their potential to using as orange color emitting materials. The result of physical properties indicated that the density, the molar volume and the refractive index of glass samples were increased with an increase of Sm 2 O 3 content. The absorption spectra of glass samples were recorded in the wavelength range of 250-2000 nm. The absorption bands centered at 401, 473, 947, 1080, 1232, 1379, 1482 and 1532 nm have been observed. From the photoluminescence spectra, the glasses are showed strong emission at 597 nm which corresponds to 4 G 5/2 → 6 H 7/2 transition under excitation wavelength at 401 nm. The optimal concentration of Sm 2 O 3 in lithium aluminium phosphate glasses was 0.5 mol%.

关键词： Luminescence properties Phosphate glass Physical properties Samarium

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Accurate solutions of polynomial eigenvalue problems

arXiv

引用

arXiv 2017年

作者： YOU, YILING RODRIGUEZ, JOSE ISRAEL LIM, LEK-HENG Department of Statistics University of Chicago ChicagoIL United States Computational and Applied Mathematics Initiative Department of Statistics University of Chicago ChicagoIL United States

Quadratic eigenvalue problems (QEP) and more generally polynomial eigenvalue problems (PEP) are among the most common types of nonlinear eigenvalue problems. Both problems, especially the QEP, have extensive applications. A typical approach to solve QEP and PEP is to use a linearization method to reformulate the problem as a higher dimensional linear eigenvalue problem. In this article, we use homotopy continuation to solve these nonlinear eigenvalue problems without passing to higher dimensions. Our main contribution is to show that our method produces substantially more accurate results, and finds all eigenvalues with a certificate of correctness via Smale's α-theory. To explain the superior accuracy, we show that the nonlinear eigenvalue problem we solve is better conditioned than its reformulated linear eigenvalue problem, and our homotopy continuation algorithm is more stable than QZ algorithm | theoretical findings that are borne out by our numerical experiments. Our studies provide yet another illustration of the dictum in numerical analysis that, for reasons of conditioning and stability, it is sometimes better to solve a nonlinear problem directly even when it could be transformed into a linear problem with the same solution mathematically. Copyright © 2017, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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SPT-SZ MCMF: An extension of the SPT-SZ catalog over the DES region

arXiv

引用

arXiv 2023年

作者： Klein, M. Mohr, J.J. Bocquet, S. Aguena, M. Allen, S.W. Alves, O. Ansarinejad, B. Ashby, M.L.N. Bacon, D. Bayliss, M. Benson, B.A. Bleem, L.E. Brodwin, M. Brooks, D. Bulbul, E. Burke, D.L. Canning, R.E.A. Carlstrom, J.E. Rosell, A. Carnero Carretero, J. Chang, C.L. Conselice, C. Costanzi, M. Crites, A.T. da Costa, L.N. Pereira, M.E.S. Davis, T.M. De Vicente, J. Desai, S. de Haan, T. Dobbs, M.A. Doel, P. Ferrero, I. Flores, A.M. Frieman, J. George, E.M. Giannini, G. Gladders, M.D. Gonzalez, A.H. Grandis, S. Gruen, D. Gruendl, R.A. Gutierrez, G. Halverson, N.W. Hinton, S.R. Holder, G.P. Hollowood, D.L. Holzapfel, W.L. Honscheid, K. Hrubes, J.D. Huang, N. James, D.J. Khullar, G. Kim, K. Knox, L. Kraft, R. Kéruzoré, F. Lee, A.T. Luong-Van, D. Mahler, G. Mantz, A. Marrone, D.P. Marshall, J.L. McDonald, M. McMahon, J.J. Mena-Fernández, J. Menanteau, F. Meyer, S.S. Miquel, R. Myles, J. Padin, S. Pieres, A. Malagón, A.A. Plazas Pryke, C. Reichardt, C.L. Reil, K. Roberson, J. Romer, A.K. Romero, C. Ruhl, J.E. Saliwanchik, B.R. Salvati, L. Sanchez, E. Saro, A. Schaffer, K.K. Schrabback, T. Schubnell, M. Sevilla-Noarbe, I. Sharon, K. Shirokoff, E. Smith, M. Somboonpanyakul, T. Stalder, B. Stanford, S.A. Stark, A.A. Strazzullo, V. Suchyta, E. Swanson, M.E.C. Tarle, G. To, C. Vanderlinde, K. Vieira, J.D. von der Linden, A. Weaverdyck, N. Williamson, R. Wiseman, P. Young, M. University Observatory Faculty of Physics Ludwig-Maximilians-Universität Scheinerstr. 1 Munich81679 Germany Max Planck Institute for Extraterrestrial Physics Giessenbachstrasse Garching85748 Germany Laboratório Interinstitucional de e-Astronomia - LIneA Rua Gal. José Cristino 77 RJ Rio de Janeiro20921-400 Brazil Kavli Institute for Particle Astrophysics and Cosmology Stanford University 452 Lomita Mall StanfordCA94305 United States Department of Physics Stanford University 382 Via Pueblo Mall StanfordCA94305 United States SLAC National Accelerator Laboratory 2575 Sand Hill Road Menlo ParkCA94025 United States Department of Physics University of Michigan Ann ArborMI48109 United States School of Physics University of Melbourne ParkvilleVIC3010 Australia Center for Astrophysics Harvard & Smithsonian CambridgeMA02138 United States Institute of Cosmology and Gravitation University of Portsmouth PortsmouthPO1 3FX United Kingdom Kavli Institute for Astrophysics and Space Research Massachusetts Institute of Technology 77 Massachusetts Avenue CambridgeMA02139 United States Department of Physics University of Cincinnati CincinnatiOH45221 United States Department of Astronomy and Astrophysics University of Chicago ChicagoIL60637 United States Kavli Institute for Cosmological Physics University of Chicago ChicagoIL60637 United States Fermi National Accelerator Laboratory BataviaIL60510-0500 United States HEP Division Argonne National Laboratory ArgonneIL60439 United States Department of Physics and Astronomy University of Missouri 5110 Rockhill Road Kansas CityMO64110 United States Department of Physics & Astronomy University College London Gower Street LondonWC1E 6BT United Kingdom Max Planck Institute for Extraterrestrial Physics Giessenbachstr. 1 Garching85748 Germany Kavli Institute for Particle Astrophysics & Cosmology Stanford University P. O. Box 2450 StanfordCA94305 United States SLAC National Accelerator Laboratory

We present an extension to a Sunyaev-Zel’dovich Effect (SZE) selected cluster catalog based on observations from the South Pole Telescope (SPT);this catalog extends to lower signal-to-noise than the previous SPT-SZ catalog and therefore includes lower mass clusters. Optically derived redshifts, centers, richnesses and morphological parameters together with catalog contamination and completeness statistics are extracted using the multi-component matched filter algorithm (MCMF) applied to the S/N>4 SPT-SZ candidate list and the Dark Energy Survey (DES) photometric galaxy catalog. The main catalog contains 811 sources above S/N=4, has 91% purity and is 95% complete with respect to the original SZE selection. It contains 50% more total clusters and twice as many clusters above z = 0.8 in comparison to the original SPT-SZ sample. The MCMF algorithm allows us to define subsamples of the desired purity with traceable impact on catalog completeness. As an example, we provide two subsamples with S/N>4.25 and S/N>4.5 for which the sample contamination and cleaning-induced incompleteness are both as low as the expected Poisson noise for samples of their size. The subsample with S/N>4.5 has 98% purity and 96% completeness, and will be included in a combined SPT cluster and DES weak-lensing cosmological analysis. We measure the number of false detections in the SPT-SZ candidate list as function of S/N, finding that it follows that expected from assuming Gaussian noise, but with a lower amplitude compared to previous estimates from simulations. Copyright © 2023, The Authors. All rights reserved.

关键词： Galaxies

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Gradient-augmented hybrid interface capturing method for incompressible two-phase flow

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Chinese Physics B 2016年第6期25卷 283-289页

作者：付峥吴士玉刘凯欣 Institution of Applied Physics and Computational Mathematics Beijing 100094 China LTCS and Department of Mechanics & Aerospace Engineering College of Engineering Peking University Beijing 100871 China Center for Applied Physics and Technology Peking University Beijing 100871 China

Motivated by inconveniences of present hybrid methods,a gradient-augmented hybrid interface capturing method（GAHM） is presented for incompressible two-phase flow.A front tracking method（FTM） is used as the skeleton of the GAHM for low mass loss and *** eulerian level set values are calculated from the FTM interface,and are used for a local interface *** reconstruction avoids marker particle redistribution and enables an automatic treatment of interfacial topology *** cubic Hermit interpolation is employed in all steps of the GAHM to capture subgrid structures within a single spacial *** performance of the GAHM is carefully evaluated in a benchmark *** show significant improvements of mass loss,clear subgrid structures,highly accurate derivatives（normals and curvatures） and low *** GAHM is further coupled with an incompressible multiphase flow solver,Super CE/SE,for more complex and practical *** updated solver is evaluated through comparison with an early droplet research.

关键词： interface capturing hybrid method mass loss incompressible two-phase flow

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Evaluating and tuning n-fold integer programming

arXiv

引用

arXiv 2018年

作者： Altmanova, Katerina Knop, Dusan Koutecky, Martin Department of Applied Mathematics Charles University Prague Czech Republic Algorithmics and Computational Complexity Faculty IV Tu Berlin Germany Department of Theoretical Computer Science Faculty of Information Technology Czech Technical University in Prague Prague Czech Republic Faculty of Industrial Engineering and Management Technion-Israel Institute of Technology Haifa Israel Computer Science Institute of Charles University Charles University Prague Czech Republic

In recent years, algorithmic breakthroughs in stringology, computational social choice, scheduling, etc., were achieved by applying the theory of so-called n-fold integer programming. An n-fold integer program (IP) has a highly uniform block structured constraint matrix. Hemmecke, Onn, and Romanchuk [Math. programming, 2013] showed an algorithm with runtime O(rst+r2s)n3, where is the largest coefficient, r, s, and t are dimensions of blocks of the constraint matrix and n is the total dimension of the IP;thus, an algorithm efficient if the blocks are of small size and with small coefficients. The algorithm works by iteratively improving a feasible solution with augmenting steps, and n-fold IPs have the special property that augmenting steps are guaranteed to exist in a not-Too-large neighborhood. However, this algorithm has never been implemented and evaluated. We have implemented the algorithm and learned the following along the way. The original algorithm is practically unusable, but we discover a series of improvements which make its evaluation possible. Crucially, we observe that a certain constant in the algorithm can be treated as a tuning parameter, which yields an efficient heuristic (essentially searching in a smaller-Than-guaranteed neighborhood). Furthermore, the algorithm uses an overly expensive strategy to find a "best" step, while finding only an "approximately best" step is much cheaper, yet sufficient for quick convergence. Using this insight, we improve the asymptotic dependence on n from n3 to n2 log n. Finally, we tested the behavior of the algorithm with various values of the tuning parameter and different strategies of finding improving steps. First, we show that decreasing the tuning parameter initially leads to an increased number of iterations needed for convergence and eventually to getting stuck in local optima, as expected. However, surprisingly small values of the parameter already exhibit good behavior while significantly lowering the ti

关键词： Integer programming

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Noisy Hegselmann-Krause systems: Phase transition and the 2R-conjecture 55

Noisy Hegselmann-Krause systems: Phase transition and the 2R...

引用

55th IEEE Conference on Decision and Control, CDC 2016

作者： Wang, Chu Li, Qianxiao Weinan, E. Chazelle, Bernard Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States Nokia Bell Labs 600 Mountain Avenue Murray HillNJ07974 United States Department of Mathematics Program in Applied and Computational Mathematics Princeton University NJ08540 United States Department of Computer Science Princeton University PrincetonNJ08540 United States

ISBN: (纸本)9781509018376

The classic Hegselmann-Krause (HK) model for opinion dynamics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of the agents within a fixed distance R. In this work, we investigate the effects of noise in the continuous-time version of the model as described by its mean-field Fokker-Planck equation. In the presence of a finite number of agents, the system exhibits a phase transition from order to disorder as the noise increases. We introduce an order parameter to track the phase transition and resolve the corresponding phase diagram. The system undergoes a phase transition for small R but none for larger R. Based on the stability analysis of the mean-field equation, we derive the existence of a forbidden zone for the disordered phase to emerge. We also provide a theoretical explanation for the well-known 2R conjecture, which states that, for a random initial distribution in a fixed interval, the final configuration consists of clusters separated by a distance of roughly 2R. Our theoretical analysis confirms previous simulations and predicts properties of the noisy HK model in higher dimension. © 2016 IEEE.

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