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On the generalized Calderón formulas for closed- And open-surface elastic scattering problems

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arXiv 2021年

作者： Xu, Liwei Yin, Tao School of Mathematical Sciences University of Electronic Science and Technology of China Sichuan Chengdu611731 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 Science University of Chinese Academy of Sciences Beijing100049 China

The Calderón formulas (i.e., the combination of single-layer and hyper-singular boundary integral operators) have been widely utilized in the process of constructing valid boundary integral equation systems which could possess highly favorable spectral properties. This work is devoted to studying the theoretical properties of elastodynamic Calderón formulas which provide us with a solid basis for the design of fast boundary integral equation methods solving elastic wave problems defined on a close-surface or an open-surface in two dimensions. For the closed-surface case, it is proved that the Calderón formula is a Fredholm operator of second-kind except for certain circumstances. Regarding to the open-surface case, we investigate weighted integral operators instead of the original integral operators which are resulted from dealing with edge singularities of potentials corresponding to the elastic scattering problems by open-surfaces, and show that the Calderón formula is a compact perturbation of a bounded and invertible operator. To complete the proof, we need to use the wellposedness result of the elastic scattering problem, the analysis of the zero-frequency integral operators defined on the straight arc, the singularity decompositions of the kernels of integral operators, and a new representation formula of the hyper-singular operator. Moreover, it can be demonstrated that the accumulation point of the spectrum of the invertible operator is the same as that of the eigenvalues of the Calderón formula in the closed-surface case. Copyright © 2021, The Authors. All rights reserved.

关键词： Mathematical operators

Adaptive Surrogate Model for Failure Probability Estimation 21

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Adaptive Surrogate Model for Failure Probability Estimation

5th International Conference on Computer Science and Application engineering, CSAE 2021

作者： Qin, Yi Zhang, Yue Liu, Zexin Zhu, Xueyu Wang, Peng School of Mathematical Sciences Beihang University Haidian District Beijing China School of Integrated Circuit Science and Engineering Beihang University Haidian District Beijing China Department of Mathematics University of Utah Salt Lake CityUtah United States Scientific Computing and Imaging Institute University of Utah Salt Lake CityUtah United States Department of Mathematics University of Iowa Iowa City United States Beijing Advanced Innovation Center for Big Data and Brain Computing Beihang University Haidian District Beijing China

ISBN: (纸本)9781450389853

Estimating failure probability becomes a fundamental task in many complex engineering designs and optimizations. Yet, evaluation of failure probability via direct sampling from a given system can be computationally expensive and sometimes impossible. Although the construction of a response surface/surrogate could reduce such computational cost, reliance on its sampling alone may still yield an erroneous estimate of the failure probability. In this paper, we employ generalized polynomial chaos and develop an adaptive method whose surrogate model evolves with the additional data sampled from the underlying system as the iteration proceeds. It is more flexible by not requiring an accurate surrogate model in priori. Via three distinct numerical examples and one practical problem on a spintronic device, we demonstrate that our novel scheme provides an efficient tool to estimate system failure probability.. © 2021 Association for computing Machinery. All rights reserved.

关键词： Iterative methods

AMG Preconditioners based on Parallel Hybrid Coarsening and Multi-objective Graph Matching

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AMG Preconditioners based on Parallel Hybrid Coarsening and ...

Euromicro Conference on Parallel, Distributed and Network-Based Processing

作者： Pasqua D'Ambra Fabio Durastante S M Ferdous Salvatore Filippone Mahantesh Halappanavar Alex Pothen National Research Council (CNR) Institute for Applied Computing “M. Picone” (IAC) Napoli Italy Department of Mathematics University of Pisa Pisa Italy Pacific Northwest National Laboratory Physical and Computational Sciences Richland WA USA Dept. of Civil and Computer Engineering University of Rome Tor-Vergata Rome Italy Computer Science Department Purdue University West Lafayette IN USA

We describe preliminary results from a multi-objective graph matching algorithm, in the coarsening step of an aggregation-based Algebraic MultiGrid (AMG) preconditioner, for solving large and sparse linear systems of equations on high-end parallel computers. We have two objectives. First, we wish to improve the convergence behavior of the AMG method when applied to highly anisotropic problems. Second, we wish to extend the parallel package PSCToolkit to exploit multi-threaded parallelism at the node level on multi-core processors. Our matching proposal balances the need to simultaneously compute high weights and large cardinalities by a new formulation of the weighted matching problem combining both these objectives using a parameter $\lambda$ . We compute the matching by a parallel $2/3-\varepsilon$ -approximation algorithm for maximum weight matchings. Results with the new matching algorithm show that for a suitable choice of the parameter $\lambda$ we compute effective preconditioners in the presence of anisotropy, i.e., smaller solve times, setup times, iterations counts, and operator complexity.

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Physics-informed neural networks to learn cardiac fiber orientation from multiple electroanatomical maps

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arXiv 2022年

作者： Herrera, Carlos Ruiz Grandits, Thomas Plank, Gernot Perdikaris, Paris Costabal, Francisco Sahli Pezzuto, Simone Department of Mechanical and Metallurgical Engineering School of Engineering Pontificia Universidad Católica de Chile Santiago Chile Institute of Mathematics and Scientific Computing University of Graz Graz Austria Department of Mechanical Engineering and Applied Mechanics University of Pennsylvania Philadelphia United States Institute for Biological and Medical Engineering Schools of Engineering Medicine and Biological Sciences Pontificia Universidad Católica de Chile Santiago Chile Center for Computational Medicine in Cardiology Euler Institute Università della Svizzera italiana via Buffi 13 Lugano6900 Switzerland Gottfried Schatz Research Center Division of Biophysics Medical University of Graz Graz Austria

We propose FiberNet, a method to estimate in-vivo the cardiac fiber architecture of the human atria from multiple catheter recordings of the electrical activation. Cardiac fibers play a central role in the electromechanical function of the heart, yet they are difficult to determine in-vivo, and hence rarely truly patient-specific in existing cardiac models. FiberNet learns the fiber arrangement by solving an inverse problem with physics-informed neural networks. The inverse problem amounts to identifying the conduction velocity tensor of a cardiac propagation model from a set of sparse activation maps. The use of multiple maps enables the simultaneous identification of all the components of the conduction velocity tensor, including the local fiber angle. We extensively test FiberNet on synthetic 2-D and 3-D examples, diffusion tensor fibers, and a patient-specific case. We show that 3 maps are sufficient to accurately capture the fibers, also in the presence of noise. With fewer maps, the role of regularization becomes prominent. Moreover, we show that the fitted model can robustly reproduce unseen activation maps. We envision that FiberNet will help the creation of patient-specific models for personalized medicine. The full code is available at http://***/fsahli/FiberNet. © 2022, CC BY-NC-ND.

关键词： Inverse problems

F*** workflows: when parts of FAIR are missing

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arXiv 2022年

作者： Wilkinson, Sean R. Eisenhauer, Greg Kapadia, Anuj J. Knight, Kathryn Logan, Jeremy Widener, Patrick Wolf, Matthew Oak Ridge Leadership Computing Facility Oak Ridge National Laboratory Oak RidgeTN United States College of Computing Georgia Institute of Technology AtlantaGA United States Computational Sciences and Engineering Oak Ridge National Laboratory Oak RidgeTN United States Computer Science and Mathematics Oak Ridge National Laboratory Oak RidgeTN United States

The FAIR principles for scientific data (Findable, Accessible, Interoperable, Reusable) are also relevant to other digital objects such as research software and scientific workflows that operate on scientific data. The FAIR principles can be applied to the data being handled by a scientific workflow as well as the processes, software, and other infrastructure which are necessary to specify and execute a workflow. The FAIR principles were designed as guidelines, rather than rules, that would allow for differences in standards for different communities and for different degrees of compliance. There are many practical considerations which impact the level of FAIR-ness that can actually be achieved, including policies, traditions, and technologies. Because of these considerations, obstacles are often encountered during the workflow lifecycle that trace directly to shortcomings in the implementation of the FAIR principles. Here, we detail some cases, without naming names, in which data and workflows were Findable but otherwise lacking in areas commonly needed and expected by modern FAIR methods, tools, and users. We describe how some of these problems, all of which were overcome successfully, have motivated us to push on systems and approaches for fully FAIR workflows. © 2022, CC BY.

关键词： Computer software reusability

Capacity optimality of AMP in coded systems

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arXiv 2021年

作者： Liu, Lei Liang, Chulong Ma, Junjie Ping, Li Department of Electronic Engineering City University of Hong Kong Hong Kong School of Information Science Japan Institute of Science and Technology Nomi923-1292 Japan State Key Laboratory of Mobile Network and Mobile Multimedia Technology ZTE Corporation Shenzhen518057 China Institute of Computational Mathematics and Scientific Engineering Computing Chinese Academy of Sciences China

This paper studies a large random matrix system (LRMS) model involving an arbitrary signal distribution and forward error control (FEC) coding. We establish an area property based on the approximate message passing (AMP) algorithm. Under the assumption that the state evolution for AMP is correct for the coded system, the achievable rate of AMP is analyzed. We prove that AMP achieves the constrained capacity of the LRMS with an arbitrary signal distribution provided that a matching condition is satisfied. We provide related numerical results of binary signaling using irregular low-density parity-check (LDPC) codes. We show that the optimized codes demonstrate significantly better performance over unmatched ones under AMP. For quadrature phase shift keying (QPSK) modulation, bit error rate (BER) performance within 1 dB from the constrained capacity limit is observed. © 2021, CC BY-NC-SA.

关键词： Message passing

Adding higher-order spherical harmonics in non-spinning eccentric binary black hole merger waveform models

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arXiv 2024年

作者： Islam, Tousif Khanna, Gaurav Field, Scott E. Kavli Institute for Theoretical Physics University of California Santa Barbara Kohn Hall Lagoon Rd Santa BarbaraCA93106 United States Theoretical AstroPhysics Including Relativity and Cosmology California Institute of Technology PasadenaCA United States Department of Physics Center for Computational Research University of Rhode Island KingstonRI02881 United States Department of Physics University of Massachusetts DartmouthMA02747 United States Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States Department of Mathematics University of Massachusetts DartmouthMA02747 United States

gwNRHME is a recently developed framework that seamlessly converts a multi-modal (i.e with several spherical harmonic modes) quasi-circular waveform into multi-modal eccentric waveform if the quadrupolar eccentric waveform is known. Here, we employ the gwNRHME framework to combine a multi-modal quasi-circular waveform model NRHybSur3dq8 and quadrupolar non-spinning eccentric waveform model EccentricIMR to construct multi-modal non-spinning eccentric model NRHybSur3dq8-gwNRHME. Using a total of 35 eccentric numerical relativity (NR) simulations obtained from the SXS and RIT catalogs, we demonstrate that NRHybSur3dq8-gwNRHME model predictions agree well with NR (with typical relative L2 errors of ∼ 0.01 for the dominant quadrupolar mode) for mass ratios 1 ≤ q ≤ 4 and eccentricities up to ∼ 0.2 measured about 10 cycles before the merger. To demonstrate the modularity of the gwNRHME framework, we further combine EccentricIMR with BHPTNRSur1dq1e4 model and develop a non-spinning eccentric models named BHPTNRSur1dq1e4-gwNRHME. Finally, we develop a different variant of these models by replacing EccentricIMR with EccentricTD. Both the gwNRHME framework and associated models are available through the gwModels package. Copyright © 2024, The Authors. All rights reserved.

关键词： Spheres

Quantum Rényi Entropy Functionals for Bosonic Gaussian Systems

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arXiv 2022年

作者： Lee, Junseo Jeong, Kabgyun School of Electrical and Electronic Engineering Yonsei University Seoul03722 Korea Republic of Quantum Computing R&D Norma Inc. Seoul04799 Korea Republic of Research Institute of Mathematics Seoul National University Seoul08826 Korea Republic of School of Computational Sciences Korea Institute for Advanced Study Seoul02455 Korea Republic of

In this study, the quantum Rényi entropy power inequality of order p > 1 and power κ is introduced as a quantum analog of the classical Rényi-p entropy power inequality. To derive this inequality, we first exploit the Wehrl-p entropy power inequality on bosonic Gaussian systems via the mixing operation of quantum convolution, which is a generalized beam-splitter operation. This observation directly provides a quantum Rényi-p entropy power inequality over a quasi-probability distribution for D-mode bosonic Gaussian regimes. The proposed inequality is expected to be useful for the nontrivial computing of quantum channel capacities, particularly universal upper bounds on bosonic Gaussian quantum channels, and a Gaussian entanglement witness in the case of Gaussian amplifier via squeezing operations. © 2022, CC BY.

关键词： Quantum entanglement

Rubric-based holistic review represents a change from traditional graduate admissions approaches in physics

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Physical Review Physics Education Research 2023年第1期19卷 010134-010134页

作者： Nicholas T. Young N. Verboncoeur Dao Chi Lam Marcos D. Caballero Department of Physics and Astronomy Michigan State University East Lansing Michigan 48824 USA Department of Computational Mathematics Science and Engineering Michigan State University East Lansing Michigan 48824 USA Department of Statistics Michigan State University East Lansing Michigan 48824 USA Center for Computing in Science Education and Department of Physics University of Oslo N-0316 Oslo Norway CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA

Rubric-based admissions are claimed to help make the graduate admissions process more equitable, possibly helping to address the historical and ongoing inequities in the U.S. physics graduate school admissions process that have often excluded applicants from minoritized races, ethnicities, genders, and backgrounds. Yet, no studies have examined whether rubric-based admissions methods represent a fundamental change in the admissions process or simply represent a new tool that achieves the same outcome. To address that, we developed supervised machine learning models of graduate admissions data collected from our department over a seven-year period. During the first four years, our department used a traditional admission process and switched to a rubric-based process for the following three years, allowing us to compare which parts of the applications were driving admissions decisions. We find that faculty focused on applicants’ physics GRE scores and grade-point averages when making admissions decisions before the implementation of the rubric. While we were able to develop a sufficiently good model whose results we could trust for the data before the implementation of the rubric, we were unable to do so for the data collected after the implementation of the rubric, despite multiple modifications to the algorithms and data such as implementing Tomek Links. Our inability to model the second dataset despite being able to model the first combined with model comparison analyses suggests that rubric-based admission does change the underlying process. These results suggest that rubric-based holistic review is a method that could make the graduate admission process in physics more equitable.

关键词： Diversity & inclusion Educational policy Graduate students