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arXiv 2019年

作者： Tang, Shanshan Li, Bo Yu, Haijun Software Development Center Industrial and Commercial Bank of China No. 16 Building of ZhongGuanCun Software Park Haidian District Beijing100193 China Huawei Technologies Co. Ltd Bai Ruida Apartment Bantian Street Longgang District Shenzhen518129 China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

In a previous study [B. Li, S. Tang and H. Yu, Commun. Comput. Phy. 27(2):379-411, 2020], it is shown that deep neural networks built with rectified power units (RePU) as activation functions can give better approximation for sufficient smooth functions than those built with rectified linear units, by converting polynomial approximations using power series into deep neural networks with optimal complexity and no approximation error. However, in practice, power series approximations are not easy to obtain due to the associated stability issue. In this paper, we propose a new and more stable way to construct RePU deep neural networks based on Chebyshev polynomial approximations. By using a hierarchical structure of Chebyshev polynomial approximation in frequency domain, we obtain efficient and stable deep neural network construction, which we call ChebNet. The approximation of smooth functions by ChebNets is no worse than the approximation by deep RePU nets using power series. On the same time, ChebNets are much more stable. Numerical results show that the constructed ChebNets can be further fine-tuned to obtain much better results than those obtained by tuning deep RePU nets constructed by power series approach. As spectral accuracy is hard to obtain by direct training of deep neural networks, ChebNets provide a practical way to obtain spectral accuracy, it is expected to be useful in real applications that require efficient approximations of smooth functions. © 2019, CC BY-NC-ND.

关键词： Chebyshev polynomials

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Ab initio vibrational free energies including anharmonicity for multicomponent alloys

arXiv

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arXiv 2019年

作者： Grabowski, Blazej Ikeda, Yuji Körmann, Fritz Freysoldt, Christoph Duff, Andrew Ian Shapeev, Alexander Neugebauer, Jörg Department for Computational Materials Design Max-Planck-Institut für Eisenforschung GmbH Max-Planck-Str. 1 Düsseldorf40237 Germany Department of Materials Science and Engineering Delft University of Technology Mekelweg 2 Delft2628 CD Netherlands Scientific Computing Department STFC Daresbury Laboratory Hartree Centre Warrington United Kingdom Skolkovo Institute of Science and Technology Skolkovo Innovation Center Nobel St. 3 Moscow143026 Russia

A density-functional-theory based approach to efficiently compute numerically exact vibrational free energies|including anharmonicity|for chemically complex multicomponent alloys is developed. It is based on a combination of thermodynamic integration and a machine-learning potential. We demonstrate the performance of the approach by computing the anharmonic free energy of the prototypical five-component VNbMoTaW refractory high entropy alloy. Copyright © 2019, The Authors. All rights reserved.

关键词： Computation theory

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Harmonized-Multinational qEEG norms (HarMNqEEG)

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NEUROIMAGE 2022年 256卷 119190-119190页

作者： Li, Min Wang, Ying Lopez-Naranjo, Carlos Hu, Shiang Reyes, Ronaldo Cesar Garcia Paz-Linares, Deirel Areces-Gonzalez, Ariosky Hamid, Aini Ismafairus Abd Evans, Alan C. Savostyanov, Alexander N. Calzada-Reyes, Ana Villringer, Arno Tobon-Quintero, Carlos A. Garcia-Agustin, Daysi Yao, Dezhong Dong, Li Aubert-Vazquez, Eduardo Reza, Faruque Razzaq, Fuleah Abdul Omar, Hazim Abdullah, Jafri Malin Galler, Janina R. Ochoa-Gomez, John F. Prichep, Leslie S. Galan-Garcia, Lidice Morales-Chacon, Lilia Valdes-Sosa, Mitchell J. Trondle, Marius Zulkifly, Mohd Faizal Mohd Rahman, Muhammad Riddha Bin Abdul Milakhina, Natalya S. Langer, Nicolas Rudych, Pavel Koenig, Thomas Virues-Alba, Trinidad A. Lei, Xu Bringas-Vega, Maria L. Bosch-Bayard, Jorge F. Valdes-Sosa, Pedro Antonio [a]The Clinical Hospital of Chengdu Brain Science Institute MOE Key Lab for Neuroinformation School of Life Science and Technology University of Electronic Science and Technology of China Chengdu China [b]Cuban Center for Neurocience La Habana Cuba [c]McGill Centre for Integrative Neuroscience Ludmer Centre for Neuroinformatics and Mental Health Montreal Neurological Institute Canada [d]Department of Neurosciences School of Medical Sciences Universiti Sains Malaysia Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [e]Brain and Behaviour Cluster School of Medical Sciences Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [f]Hospital Universiti Sains Malaysia Universiti Sains Malaysia Health Campus Kota Bharu Kelantan 16150 Malaysia [g]Humanitarian Institute Novosibirsk State University Novosibirsk 630090 Russia [h]Laboratory of Psychophysiology of Individual Differences Federal State Budgetary Scientific Institution Scientific Research Institute of Neurosciences and Medicine Novosibirsk 630117 Russia [i]Laboratory of Psychological Genetics at the Institute of Cytology and Genetics Siberian Branch of the Russian Academy of Sciences Novosibirsk 630090 Russia [j]University of Pinar del Río “Hermanos Saiz Montes de Oca” Pinar del Río Cuba [k]Department of Neurology Max Planck Institute for Human Cognitive and Brain Sciences Leipzig Germany [l]Department of Cognitive Neurology University Hospital Leipzig Leipzig Germany [m]Center for Stroke Research Charité-Universitätsmedizin Berlin Berlin Germany [n]Grupo Neuropsicología y Conducta - GRUNECO Faculty of Medicine Universidad de Antioquia Colombia [o]Research Department Institución Prestadora de Servicios de Salud IPS Universitaria Colombia [p]The Cuban center aging longevity and health Havana Cuba [q]Research Unit of NeuroInformation Chinese Academy of Medical Sciences Chengdu 2019RU035 China [r]School of Electrical Engineering Zhengzhou University Zhengzhou 4500

This paper extends frequency domain quantitative electroencephalography (qEEG) methods pursuing higher sensitivity to detect Brain Developmental Disorders. Prior qEEG work lacked integration of cross-spectral information omitting important functional connectivity descriptors. Lack of geographical diversity precluded accounting for site-specific variance, increasing qEEG nuisance variance. We ameliorate these weaknesses. (i) Create lifespan Riemannian multinational qEEG norms for cross-spectral tensors. These norms result from the HarMNqEEG project fostered by the Global Brain Consortium. We calculate the norms with data from 9 countries, 12 devices, and 14 studies, including 1564 subjects. Instead of raw data, only anonymized metadata and EEG cross spectral tensors were shared. After visual and automatic quality control, developmental equations for the mean and standard deviation of qEEG traditional and Riemannian DPs were calculated using additive mixed-effects models. We demonstrate qEEG "batch effects " and provide methods to calculate harmonized z-scores. (ii) We also show that harmonized Riemannian norms produce z-scores with increased diagnostic accuracy predicting brain dysfunction produced by malnutrition in the first year of life and detecting COVID induced brain dysfunction. (iii) We offer open code and data to calculate different individual z-scores from the HarMNqEEG dataset. These results contribute to developing bias-free, low-cost neuroimaging technologies applicable in various health settings.

关键词： Quantitative EEG EEG cross-spectrum Riemannian geometry Batch effects Z-score Harmonization Malnutrition Covid induced brain dysfunction Developmental Brain Chart

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Influence of the vacuum polarization effect on the motion of charged particles in the magnetic field around a Schwarzschild Black Hole

arXiv

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arXiv 2019年

作者： Pavlović, Petar Saveliev, Andrey Sossich, Marko Department of Physics Ramashna Mission Vivekananda Educational and Research Institute Belur MathWest Bengal711202 India Institute of Physics Mathematics and Information Technology Immanuel Kant Baltic Federal University Ul. Aleksandra Nevskogo 14 Kaliningrad236016 Russia Faculty of Computational Mathematics and Cybernetics Lomonosov Moscow State University GSP-1 Leninskiye Gory 1-52 Moscow119991 Russia Faculty of Electrical Engineering and Computing Department of Physics University of Zagreb Unska 3 Zagreb10 000 Croatia

The consequences of the vacuum polarization effect in magnetic fields around a Schwarzschild Black Hole (SBH) on the motion of charged particles are investigated in this work. Using the weak electromagnetic field approximation, we discuss the non-minimal coupling between magnetic fields and gravity caused by the vacuum polarization and study the equations of motion for the case of a magnetic field configuration which asymptotically approaches a dipole magnetic field. It is shown that the presence of non-minimal coupling can significantly influence the motion of charged particles around Black Holes. In particular, the vacuum polarization effect, leading to strong amplification or suppression of the magnetic field strength around the event horizon (depending on the sign of the coupling parameter), can affect the scattering angle and minimal distance for the electrons moving in the gravitational field of the Black Hole as well as the dependence of these parameters on the asymptotic magnetic field strength, initial distance and the Black Hole mass. It is further demonstrated that the non-minimal coupling between gravity and astrophysical magnetic fields, caused by the vacuum polarization, can cause significant changes of the parameter space corresponding to bound trajectories around the Black Hole. In certain cases, the bounded or unbounded character of a trajectory is determined solely by the presence of non-minimal coupling and its strength. These effects could in principle be used as observational signatures of the vacuum polarization effect and also to constrain the value of the coupling parameter. Copyright © 2019, The Authors. All rights reserved.

关键词： Gravitation

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Lattice QCD and Particle Physics

arXiv

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arXiv 2022年

作者： Kronfeld, Andreas S. Bhattacharya, Tanmoy Blum, Thomas Christ, Norman H. DeTar, Carleton Detmold, William Edwards, Robert Hasenfratz, Anna Lin, Huey-Wen Mukherjee, Swagato Orginos, Konstantinos Brower, Richard Cirigliano, Vincenzo Davoudi, Zohreh Jóo, Bálint Jung, Chulwoo Lehner, Christoph Meinel, Stefan Neil, Ethan T. Petreczky, Peter Richards, David G. Bazavov, Alexei Catterall, Simon Dudek, Jozef J. El-Khadra, Aida X. Engelhardt, Michael Fleming, George T. Giedt, Joel Gupta, Rajan Hansen, Maxwell T. Izubuchi, Taku Karsch, Frithjof Laiho, Jack Liu, Keh-Fei Meyer, Aaron S. Rinaldi, Enrico Savage, Martin Schaich, David Shanahan, Phiala E. Sharpe, Stephen R. Sufian, Raza Syritsyn, Sergey Van de Water, Ruth S. Wagman, Michael L. Weinberg, Evan Witzel, Oliver Aubin, Christopher Boyle, Peter Chandrasekharan, Shailesh Cloët, Ian C. Constantinou, Martha Cushman, Kimmy DeGrand, Thomas Fodor, Zoltan Foreman, Sam Gottlieb, Steven Hoying, Daniel Jang, Yong-Chull Jay, William I. Jin, Xiao-Yong Kelly, Christopher Kuti, Julius Lamm, Henry Lin, Meifeng Lin, Yin Lytle, Andrew T. Mackenzie, Paul Mandula, Jeffrey Meurice, Yannick Monahan, Christopher Morningstar, Colin Osborn, James C. Park, Sungwoo Simone, James N. Strelchenko, Alexei Tomii, Masaaki Vaquero, Alejandro Vranas, Pavlos Wang, Bigeng Wilcox, Walter Yoon, Boram Zhao, Yong Theory Division Fermi National Accelerator Laboratory BataviaIL60510 United States Group T-2 Los Alamos National Laboratory Los AlamosNM87545 United States Department of Physics University of Connecticut StorrsCT06269 United States RIKEN BNL Research Center Brookhaven National Laboratory UptonNY11973 United States Department of Physics Columbia University New YorkNY10027 United States Department of Physics and Astronomy University of Utah Salt Lake CityUT84112 United States Center for Theoretical Physics Massachusetts Institute of Technology CambridgeMA02139 United States The NSF Institute for Artificial Intelligence and Fundamental Interactions Theory Center Thomas Jefferson National Accelerator Facility Newport NewsVA23606 United States Department of Physics University of Colorado BoulderCO80309 United States Department of Physics and Astronomy Michigan State University East LansingMI48824 United States Physics Department Brookhaven National Laboratory UptonNY11973 United States Department of Physics College of William & Mary WilliamsburgVA23187 United States Department of Physics Center for Computational Science Boston University BostonMA02215 United States Institute of Nuclear Theory University of Washington SeattleWA98195 United States Department of Physics Maryland Center for Fundamental Physics University of Maryland College ParkMD20742 United States Oak Ridge Leadership Computing Facility Oak Ridge National Laboratory Oak RidgeTN37831 United States Fakultät für Physik Universität Regensburg RegensburgD-93040 Germany Department of Physics University of Arizona TucsonAZ85721 United States Department of Computational Mathematics Science and Engineering Michigan State University East LansingMI48824 United States Department of Physics Syracuse University SyracuseNY13244 United States Department of Physics University of Illinois Urbana-Champaign UrbanaIL61801 United States Department of Physics New Mexic

Lattice field theory provides a mathematically rigorous definition of quantum field theory, including gauge theories. The rigor provides a platform for computation of strongly-coupled gauge theories, not only quantum chromodynamics (QCD) at long-distances but also strongly-coupled sectors that might lie beyond the Standard Model (BSM) of particle physics. Indeed, the interpretation of many experiments in particle physics, nuclear physics, and astrophysics relies, often crucially, on results from lattice QCD or BSM. In quark-flavor physics, lattice QCD is essential for grounding theoretical predictions. Together with experimental measurements, lattice QCD is used to determine many of the fundamental parameters of the Standard Model's flavor sector: five out of six quark masses and the three mixing angles and CP-violating phase of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. Further Standard-Model predictions requiring lattice QCD are for processes that could reveal signatures of new physics. This area of lattice QCD has become a precision science, as has the determination of the strong coupling, αs, which is key in many areas, for example for understanding Higgs-boson decay to gluons. Lattice-QCD calculations of the hadronic contributions to the anomalous magnetic moment of the muon are another area for which precision is both mandatory and achievable. While these contributions can be estimated via a combination of certain measurements and general theoretical concepts, a direct ab initio calculation from QCD is desirable to confirm robustly the tantalizingly large discrepancy between experiment and the Standard Model. Other indirect searches for new physics are complementary to quark-flavor physics and the muon anomalous magnetic moment. Lattice QCD is an essential tool for understanding newly discovered hadrons with quark content different from the usual baryons and mesons. Lattice-QCD calculations are needed to interpret bounds on electric dipole moments, proton dec

关键词： Calculations

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Functional a posteriori error estimates for boundary element methods

arXiv

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arXiv 2019年

作者： Kurz, Stefan Pauly, Dirk Praetorius, Dirk Repin, Sergey Sebastian, Daniel TU Wien Institute for Analysis and Scientific Computing Wiedner Hauptstraße 8-10/E101/4 Vienna1040 Austria TU Darmstadt Centre for Computational Engineering Dolivostraße 15 Darmstadt64293 Germany Universität Duisburg-Essen Fakultät für Mathematik Thea-Leymann-Straße 9 Essen45141 Germany University of Jyväskylä Building Agora Mattilanniemi 2 Jyväskylä40100 Finland Russian Academy of Sciences Steklov Institute of Mathematics 191011 Fontanka 27 St. Petersburg Russia

Functional error estimates are well-estabilished tools for a posteriori error estimation and related adaptive mesh-refinement for the finite element method (FEM). The present work proposes a first functional error estimate for the boundary element method (BEM). One key feature is that the derived error estimates are independent of the BEM discretization and provide guaranteed lower and upper bounds for the unknown error. In particular, our analysis covers Galerkin BEM as well as collocation, which makes our approach of particular interest for people working in engineering. Numerical experiments for the Laplace problem confirm the theoretical *** Codes 65N38, 65N15, 65N50 Copyright © 2019, The Authors. All rights reserved.

关键词： Boundary element method

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Data-driven polynomial chaos expansions: A weighted least-square approximation

arXiv

引用

arXiv 2018年

作者： Guo, Ling Liu, Yongle Zhou, Tao Department of Mathematics Shanghai Normal University Shanghai China Department of Mathematics Southern University of Science and Technology Shenzhen China LSEC Institute of Computational Mathematics and Scientific Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China

In this work, we combine the idea of data-driven polynomial chaos expansions with the weighted least-square approach to solve uncertainty quantification (UQ) problems. The idea of data-driven polynomial chaos is to use statistical moments of the input random variables to develop an arbitrary polynomial chaos expansion, and then use such data-driven bases to perform UQ computations. Here we adopt the bases construction procedure by following [1], where the bases are computed by using matrix operations on the Hankel matrix of moments. Different from previous works, in the postprocessing part, we propose a weighted least-squares approach to solve UQ problems. This approach includes a sampling strategy and a least-squares solver. The main features of our approach are two folds: On one hand, our sampling strategy is independent of the random input. More precisely, we propose to sampling with the equilibrium measure, and this measure is also independent of the data-driven bases. Thus, this procedure can be done in prior (or in a off- line manner). On the other hand, we propose to solve a Christoffel function weighted least-square problem, and this strategy is quasi-linearly stable - the required number of PDE solvers depends linearly (up to a logarithmic factor) on the number of (data-driven) bases. This new approach is thus promising in dealing with a class of problems with epistemic uncertainties. Several numerical tests are presented to show the effectiveness of our approach. Copyright © 2018, The Authors. All rights reserved.

关键词： Uncertainty analysis

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STABILITY ANALYSIS FOR NONLINEAR SCHRODINGER EQUATIONS WITH NONLINEAR ABSORBING BOUNDARY CONDITIONS

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Journal of computational mathematics 2017年第1期35卷 1-18页

作者： Jiwei Zhang Zhenli Xu Xiaonan Wu Desheng Wang Applied and Computational Mathematics Division Beijing Computational Science Research Center China Department of Mathematics Institute of Natural Sciences and MOE Key Lab of Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai 200240 China Department of Mathematics Hong Kong Baptist University Kowloon Hong Kong China Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 Singapore

Local absorbing boundary conditions （LABCs） for nonlinear Schr6dinger equations have been constructed in papers [PRE 78（2008） 026709; and PRE 79 （2009） 046711] using the so-called unified approach. In this paper, we present stability analysis for the reduced problem with LABCs on the bounded computational domain by the energy estimate, and discuss a class of modified versions of LABCs. To prove the stability analysis of the re- duced problem, we turn to the technique of some auxiliary variables which reduces the higher-order derivatives in LABCs into a family of equations with lower-order derivatives. Furthermore, we extend the strategy to the stability analysis of two-dimensional problems by carefully dealing with the LABCs at corners. Numerical examples are given to demon- strate the effectiveness of our boundary conditions and validate the theoretical analysis.

关键词： Nonlinear SchrSdinger equations Energy estimates Absorbing boundaryconditions.

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Plane wave methods for quantum eigenvalue problems of incommensurate systems

arXiv

引用

arXiv 2018年

作者： Zhou, Yuzhi Chen, Huajie Zhou, Aihui Institute of Applied Physics and Computational Mathematics Bejing100088 China School of Mathematical Sciences Beijing Normal University Beijing100875 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China

We propose a novel numerical algorithm for computing the electronic structure related eigenvalue problem of incommensurate systems. Unlike the conventional practice that approximates the system by a large commensurate supercell, our algorithm directly discretizes the eigenvalue problem under the framework of a plane wave method. The emerging ergodicity and the interpretation from higher dimensions give rise to many unique features compared to what we have been familiar with in the periodic system. The numerical results of 1D and 2D quantum eigenvalue problems are presented to show the reliability and efficiency of our scheme. Furthermore, the extension of our algorithm to full Kohn-Sham density functional theory calculations are discussed. Copyright © 2018, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Regularity results for the time-harmonic maxwell equations with impedance boundary condition

arXiv

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arXiv 2018年

作者： Lu, Peipei Wang, Yun Xu, Xuejun Department of Mathematics Soochow University SuZhou215006 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences People's Republic of China School of Mathematical Sciences Tongji University Shanghai China

This paper considers the time-harmonicMaxwell equationswith impedance boundary condition. We present H2-norm bound and other high-order norm bounds for strong solutions. The H2-estimate have been derived in [M. Dauge, M. Costabel and S. Nicaise, Tech. Rep. 10-09, IRMAR (2010)] for the case with homogeneous boundary condition. Unfortunately, their method can not be applied to the inhomogeneous case. The main novelty of this paper is that we follow the spirit of the H1- estimate in [R. Hiptmair, A. Moiola and I. Perugia, math. Models Methods Appl. Sci., 21(2011), pp. 2263-2287] and modify the proof by applying two inequalities of Friedrichs' type to make the H1-estimate move into H2-estimate and Wm,p-estimate. Finally, the dependence of the regularity estimates on the wave number is obtained, which will play an important role in the convergence analysis of the numerical solutions for the time-harmonicMaxwell equations. Copyright © 2018, The Authors. All rights reserved.

关键词： Boundary conditions

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