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Nonstandard finite element de Rham complexes on cubical meshes

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arXiv 2018年

作者： Gillette, Andrew Hu, Kaibo Zhang, Shuo Department of Mathematics University of Arizona 617 N. Santa Rita Ave. TucsonAZ United States Department of Mathematics University of Oslo PO Box 1053 Blindern OsloNO 0316 Norway LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences National Centre for Mathematics and Interdisciplinary Sciences Chinese Academy of Sciences Beijing100190 China

MSC Codes 65N30We propose two general operations on finite element differential complexes on cubical meshes that can be used to construct and analyze sequences of "nonstandard" convergent methods. The first operation, called DoF-transfer, moves edge degrees of freedom to vertices in a way that reduces global degrees of freedom while increasing continuity order at vertices. The second operation, called serendipity, eliminates interior bubble functions and degrees of freedom locally on each element without affecting edge degrees of freedom. These operations can be used independently or in tandem to create nonstandard complexes that incorporate Hermite, Adini and "trimmed-Adini" elements. We show that the resulting elements provide convergent, non-conforming methods for problems requiring stronger regularity and satisfy a discrete Korn inequality. We discuss potential benefits of applying these elements to Stokes, biharmonic and elasticity problems. Copyright © 2018, The Authors. All rights reserved.

关键词： Finite element method

Toward single particle reconstruction without particle picking: Breaking the detection limit

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arXiv 2018年

作者： Bendory, Tamir Boumal, Nicolas Leeb, William Levin, Eitan Singer, Amit The School of Electrical Engineering Tel Aviv University Tel Aviv Israel Lausanne Switzerland School of Mathematics University of Minnesota MinneapolisMN United States Department of Computing and Mathematical Sciences California Institute of Technology PasadenaCA United States The Program in Applied and Computational Mathematics Department of Mathematics Princeton University PrincetonNJ United States

Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method to resolve biological macromolecules. In a cryo-EM experiment, the microscope produces images called micrographs. Projections of the molecule of interest are embedded in the micrographs at unknown locations, and under unknown viewing directions. Standard imaging techniques first locate these projections (detection) and then reconstruct the 3-D structure from them. Unfortunately, high noise levels hinder detection. When reliable detection is rendered impossible, the standard techniques fail. This is a problem, especially for small molecules. In this paper, we pursue a radically different approach: we contend that the structure could, in principle, be reconstructed directly from the micrographs, without intermediate detection. The aim is to bring small molecules within reach for cryo-EM. To this end, we design an autocorrelation analysis technique that allows to go directly from the micrographs to the sought structures. This involves only one pass over the micrographs, allowing online, streaming processing for large experiments. We show numerical results and discuss challenges that lay ahead to turn this proof-of-concept into a complementary approach to state-of-the-art algorithms. Copyright © 2018, The Authors. All rights reserved.

关键词： X ray crystallography

Comparative and demographic analysis of orang-utan genomes (vol 469, pg 529, 2011)

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NATURE 2022年第7924期608卷 E36-E36页

作者： Locke, Devin P. Hillier, LaDeana W. Warren, Wesley C. Worley, Kim C. Nazareth, Lynne V. Muzny, Donna M. Yang, Shiaw-Pyng Wang, Zhengyuan Chinwalla, Asif T. Minx, Pat Mitreva, Makedonka Cook, Lisa Delehaunty, Kim D. Fronick, Catrina Schmidt, Heather Fulton, Lucinda A. Fulton, Robert S. Nelson, Joanne O. Magrini, Vincent Pohl, Craig Graves, Tina A. Markovic, Chris Cree, Andy Dinh, Huyen H. Hume, Jennifer Kovar, Christie L. Fowler, Gerald R. Lunter, Gerton Meader, Stephen Heger, Andreas Ponting, Chris P. Marques-Bonet, Tomas Alkan, Can Chen, Lin Cheng, Ze Kidd, Jeffrey M. Eichler, Evan E. White, Simon Searle, Stephen Vilella, Albert J. Chen, Yuan Flicek, Paul Ma, Jian Raney, Brian Suh, Bernard Burhans, Richard Herrero, Javier Haussler, David Faria, Rui Fernando, Olga Darre, Fleur Farre, Domenec Gazave, Elodie Oliva, Meritxell Navarro, Arcadi Roberto, Roberta Capozzi, Oronzo Archidiacono, Nicoletta Della Valle, Giuliano Purgato, Stefania Rocchi, Mariano Konkel, Miriam K. Walker, Jerilyn A. Ullmer, Brygg Batzer, Mark A. Smit, Arian F. A. Hubley, Robert Casola, Claudio Schrider, Daniel R. Hahn, Matthew W. Quesada, Victor Puente, Xose S. Ordonez, Gonzalo R. Lopez-Otin, Carlos Vinar, Tomas Brejova, Brona Ratan, Aakrosh Harris, Robert S. Miller, Webb Kosiol, Carolin Lawson, Heather A. Taliwal, Vikas Martins, Andre L. Siepel, Adam RoyChoudhury, Arindam Ma, Xin Degenhardt, Jeremiah Bustamante, Carlos D. Gutenkunst, Ryan N. Mailund, Thomas Dutheil, Julien Y. Hobolth, Asger Schierup, Mikkel H. Ryder, Oliver A. Yoshinaga, Yuko de Jong, Pieter J. Weinstock, George M. Rogers, Jeffrey Mardis, Elaine R. Gibbs, Richard A. Wilson, Richard K. The Genome Center at Washington University Washington University School of Medicine Saint Louis Missouri USA Human Genome Sequencing Center Department of Molecular and Human Genetics Baylor College of Medicine One Baylor Plaza Houston Texas USA MRC Functional Genomics Unit and Department of Physiology Anatomy and Genetics University of Oxford Le Gros Clark Building Oxford UK Wellcome Trust Centre for Human Genetics Oxford UK Department of Genome Sciences University of Washington School of Medicine Seattle Washington USA IBE Institut de Biologia Evolutiva (UPF-CSIC) Universitat Pompeu Fabra PRBB Doctor Aiguader 88 Barcelona Spain Howard Hughes Medical Institute Seattle Washington USA CIBIO Centro de Investigação em Biodiversidade e Recursos Genéticos Universidade do Porto Campus Agrário de Vairão Vairão Portugal Instituto de Tecnologia Química e Biológica Universidade Nova de Lisboa Oeiras Portugal ICREA (Institució Catalana de Recerca i Estudis Avançats) and INB (Instituto Nacional de Bioinformática) PRBB Doctor Aiguader 88 Barcelona Spain Wellcome Trust Sanger Institute Wellcome Trust Genome Campus Cambridge UK European Bioinformatics Institute Wellcome Trust Genome Campus Hinxton Cambridge UK Center for Biomolecular Science and Engineering University of California Santa Cruz California USA Center for Comparative Genomics and Bioinformatics Penn State University University Park Pennsylvania USA Department of Biology University of Bari Bari Italy Department of Biology University of Bologna Bologna Italy Department of Biological Sciences Louisiana State University Baton Rouge Louisiana USA Center for Computation and Technology Department of Computer Sciences Louisiana State University Baton Rouge Louisiana USA Institute for Systems Biology Seattle Washington USA Department of Biology and School of Informatics and Computing Indiana University Bloomington Indiana USA Instituto Universitario de Oncologia Departamento de Bioquimica y Biol

SPT clusters with DES and HST weak lensing. II. Cosmological constraints from the abundance of massive halos

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Physical Review D 2024年第8期110卷 083510页

作者： S. Bocquet S. Grandis L. E. Bleem M. Klein J. J. Mohr T. Schrabback T. M. C. Abbott P. A. R. Ade M. Aguena A. Alarcon S. Allam S. W. Allen O. Alves A. Amon A. J. Anderson J. Annis B. Ansarinejad J. E. Austermann S. Avila D. Bacon M. Bayliss J. A. Beall K. Bechtol M. R. Becker A. N. Bender B. A. Benson G. M. Bernstein S. Bhargava F. Bianchini M. Brodwin D. Brooks L. Bryant A. Campos R. E. A. Canning J. E. Carlstrom A. Carnero Rosell M. Carrasco Kind J. Carretero F. J. Castander R. Cawthon C. L. Chang C. Chang P. Chaubal R. Chen H. C. Chiang A. Choi T-L. Chou R. Citron C. Corbett Moran J. Cordero M. Costanzi T. M. Crawford A. T. Crites L. N. da Costa M. E. S. Pereira C. Davis T. M. Davis J. DeRose S. Desai T. de Haan H. T. Diehl M. A. Dobbs S. Dodelson C. Doux A. Drlica-Wagner K. Eckert J. Elvin-Poole S. Everett W. Everett I. Ferrero A. Ferté A. M. Flores J. Frieman J. Gallicchio J. García-Bellido M. Gatti E. M. George G. Giannini M. D. Gladders D. Gruen R. A. Gruendl N. Gupta G. Gutierrez N. W. Halverson I. Harrison W. G. Hartley K. Herner S. R. Hinton G. P. Holder D. L. Hollowood W. L. Holzapfel K. Honscheid J. D. Hrubes N. Huang J. Hubmayr E. M. Huff D. Huterer K. D. Irwin D. J. James M. Jarvis G. Khullar K. Kim L. Knox R. Kraft E. Krause K. Kuehn N. Kuropatkin F. Kéruzoré O. Lahav A. T. Lee P.-F. Leget D. Li H. Lin A. Lowitz N. MacCrann G. Mahler A. Mantz J. L. Marshall J. McCullough M. McDonald J. J. McMahon J. Mena-Fernández F. Menanteau S. S. Meyer R. Miquel J. Montgomery J. Myles T. Natoli A. Navarro-Alsina J. P. Nibarger G. I. Noble V. Novosad R. L. C. Ogando Y. Omori S. Padin S. Pandey P. Paschos S. Patil A. Pieres A. A. Plazas Malagón A. Porredon J. Prat C. Pryke M. Raveri C. L. Reichardt J. Roberson R. P. Rollins C. Romero A. Roodman J. E. Ruhl E. S. Rykoff B. R. Saliwanchik L. Salvati C. Sánchez E. Sanchez D. Sanchez Cid A. Saro K. K. Schaffer L. F. Secco I. Sevilla-Noarbe K. Sharon E. Sheldon T. Shin C. Sievers G. Smecher M. Smith T. Somboonpanyakul M. Sommer B. Stalder A. A. Stark J. Stephen V. Straz University Observatory Faculty of Physics Universität Innsbruck Institut für Astro- und Teilchenphysik Technikerstraße 25/8 6020 Innsbruck Austria High-Energy Physics Division Argonne National Laboratory 9700 South Cass Avenue Lemont Illinois 60439 USA Kavli Institute for Cosmological Physics University of Chicago 5640 South Ellis Avenue Chicago Illinois 60637 USA Max Planck Institute for Extraterrestrial Physics Gießenbachstraße 1 85748 Garching Germany Argelander-Institut für Astronomie Auf dem Hügel 71 53121 Bonn Germany Cerro Tololo Inter-American Observatory NSF’s National Optical-Infrared Astronomy Research Laboratory Casilla 603 La Serena Chile School of Physics and Astronomy Cardiff University Cardiff CF24 3YB United Kingdom Laboratório Interinstitucional de e-Astronomia—LIneA Rua Gal. José Cristino 77 Rio de Janeiro Rio de Janeiro—20921-400 Brazil Fermi National Accelerator Laboratory P. O. Box 500 Batavia Illinois 60510 USA Kavli Institute for Particle Astrophysics and Cosmology Stanford University 452 Lomita Mall Stanford California 94305 USA Department of Physics Stanford University 382 Via Pueblo Mall Stanford California 94305 USA SLAC National Accelerator Laboratory 2575 Sand Hill Road Menlo Park California 94025 USA Department of Physics University of Michigan Ann Arbor Michigan 48109 USA Institute of Astronomy University of Cambridge Madingley Road Cambridge CB3 0HA United Kingdom Kavli Institute for Cosmology University of Cambridge Madingley Road Cambridge CB3 0HA United Kingdom School of Physics University of Melbourne Parkville Victoria 3010 Australia NIST Quantum Devices Group 325 Broadway Mailcode 817.03 Boulder Colorado 80305 USA Department of Physics University of Colorado Boulder Colorado 80309 USA Institut de Física d’Altes Energies (IFAE) The Barcelona Institute of Science and Technology Campus UAB 08193 Bellaterra (Barcelona) Spain Institute of Cosmology and Gravitation University of Portsmouth Portsmouth

We present cosmological constraints from the abundance of galaxy clusters selected via the thermal Sunyaev-Zel’dovich (SZ) effect in South Pole Telescope (SPT) data with a simultaneous mass calibration using weak gravitational lensing data from the Dark Energy Survey (DES) and the Hubble Space Telescope (HST). The cluster sample is constructed from the combined SPT-SZ, SPTpol ECS, and SPTpol 500d surveys, and comprises 1,005 confirmed clusters in the redshift range 0.25–1.78 over a total sky area of 5200 deg2. We use DES Year 3 weak-lensing data for 688 clusters with redshifts z<0.95 and HST weak-lensing data for 39 clusters with 0.6

关键词： Cosmological parameters Dark energy Large scale structure of the Universe Galaxy clusters

A minimal mechanosensing model predicts keratocyte evolution on flexible substrates

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arXiv 2018年

作者： Zhang, Zhiwen Rosakis, Phoebus Hou, Thomas Y. Ravichandran, Guruswami Department of Mathematics The University of Hong Kong Pokfulam Road Hong Kong SAR Hong Kong Department of Mathematics and Applied Mathematics University of Crete Heraklion Crete70013 Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology-Hellas Voutes Crete70013 Greece Computing and Mathematical Sciences California Institute of Technology PasadenaCA91125 United States Division of Engineering and Applied Science California Institute of Technology PasadenaCA91125 United States

A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behavior of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and traveling waves in the lamellipodium leading edge (iii) response to mechanical stress externally applied to the substrate (tensotaxis), (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis) and (v) the configuration of substrate wrinkles induced by contractile forces applied by the keratocyte. Copyright © 2018, The Authors. All rights reserved.

关键词： Substrates

Tangible reduction in learning sample complexity with large classical samples and small quantum system

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arXiv 2019年

作者： Song, Wooyeong Wieśniak, Marcin Liu, Nana Pawlowski, Marcin Lee, Jinhyoung Kim, Jaewan Bang, Jeongho Department of Physics Hanyang University Seoul04763 Korea Republic of Seoul02792 Korea Republic of Institute of Theoretical Physics and Astrophysics Faculty of Mathematics Physics and Informatics University of Gdańsk Gdańsk80-308 Poland International Centre for Theory of Quantum Technologies University of Gdańsk Gdańsk80-308 Poland Institute of Natural Science Shanghai Jiao Tong University Shanghai200240 China Ministry of Education Key Laboratory in Scientific and Engineering Computing Shanghai Jiao Tong University Shanghai200240 China University of Michigan-Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Computational Sciences Korea Institute for Advanced Study Seoul02455 Korea Republic of Electronics and Telecommunications Research Institute Daejeon34129 Korea Republic of

Quantum computation requires large classical datasets to be embedded into quantum states in order to exploit quantum parallelism. However, this embedding requires considerable resources in general. It would therefore be desirable to avoid it, if possible, for noisy intermediate-scale quantum (NISQ) implementation. Accordingly, we consider a classical-quantum hybrid architecture, which allows large classical input data, with a relatively small-scale quantum system. This hybrid architecture is used to implement a sampling oracle. It is shown that in the presence of noise in the hybrid oracle, the effects of internal noise can cancel each other out and thereby improve the query success rate. It is also shown that such an immunity of the hybrid oracle to noise directly and tangibly reduces the sample complexity in the framework of computational learning theory. This NISQ-compatible learning advantage is attributed to the oracle’s ability to handle large input features. Copyright © 2019, The Authors. All rights reserved.

关键词： Quantum optics

Upper bounds for relative entropy of entanglement based on convex hull approximation

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arXiv 2019年

作者： Hou, Shi-Yao Cao, Chenfeng Zhou, D.L. Zeng, Bei College of Physics and Electronic Engineering Center for Computational Sciences Sichuan Normal University Chengdu610068 China Center for Quantum Computing Peng Cheng Laboratory Shenzhen518055 China Department of Physics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong China Institute of Physics Beijing National Laboratory for Condensed Matter Physics Chinese Academy of Sciences Beijing100190 China School of Physical Sciences University of Chinese Academy of Sciences Beijing100049 China CAS Central of Excellence in Topological Quantum Computation Beijing100190 China Songshan Lake Materials Laboratory Dongguan Guangdong523808 China Department of Mathematics & Statistics University of Guelph GuelphON Canada Institute for Quantum Computing University of Waterloo WaterlooON Canada

Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement ERis an important quantity due to its clear geometric meaning, easy compatibility with different system sizes, and various applications in many other related quantity calculations. Lower bounds of ERwere previously found based on distance to the set of positive partial transpose states. We propose a method to calculate upper bounds of ERbased on the convex hull approximation of the set of separable states. We apply our method to calculate ERfor composite systems of various sizes, and compare with the previous known lower bounds, obtaining promising results. Our method adds a new tool for entanglement measure calculation and deepens our understanding for the structure of separable states. Copyright © 2019, The Authors. All rights reserved.

关键词： computational geometry

Verification benchmarks for single-phase flow in three-dimensional fractured porous media

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arXiv 2020年

作者： Berre, Inga Boon, Wietse M. Flemisch, Bernd Fumagalli, Alessio Gläser, Dennis Keilegavlen, Eirik Scotti, Anna Stefansson, Ivar Tatomir, Alexandru Brenner, Konstantin Burbulla, Samuel Devloo, Philippe Duran, Omar Favino, Marco Hennicker, Julian Lee, I-Hsien Lipnikov, Konstantin Masson, Roland Mosthaf, Klaus Chiara Nestola, Maria Giuseppina Ni, Chuen-Fa Nikitin, Kirill Schädle, Philipp Svyatskiy, Daniil Yanbarisov, Ruslan Zulianp, Patrick Department of Mathematics University of Bergen Allégaten 41 Bergen5007 Norway Department of Mathematics KTH Royal Institute of Technology Lindstedtsvägen 25 Stockholm11428 Sweden Department of Hydromechanics and Modelling of Hydrosystems University of Stuttgart Pfaffenwaldring 61 Stuttgart70569 Germany Laboratory for Modeling and Scientific Computing MOX Politecnico di Milano p.za Leonardo da Vinci 32 Milano20133 Italy Department of Applied Geology Geosciences Center University of Göttingen Goldschmidtstrasse 3 Göttingen37077 Germany Department of Earth Sciences Uppsala University Villavägen 16 UppsalaS-75236 Sweden University of Côte d’Azur CNRS INRIA LJAD Nice France Institute of Applied Analysis and Numerical Simulation University of Stuttgart Pfaffenwaldring 57 Stuttgart70569 Germany FEC Universidade Estadual de Campinas Cidade Universitária R. Josiah Willard Gibbs 85 Campinas-SPCEP 13083-839 Brazil Institute of Earth Sciences University of Lausanne Building Geopolis UNIL-Mouline Lausanne1015 Switzerland Section de Mathématiques Université de Genève 2-4 rue du Lièvre CP 64 Genève1211 Switzerland Graduate Institute of Applied Geology National Central University Taiwan Center for Environmental Studies National Central University Taiwan Los Alamos National Laboratory New Mexico United States Department of Environmental Engineering Technical University of Denmark Bygningstorvet Building 115 Kgs. Lyngby2800 Denmark Numerical Simulation in Science Medicine and Engineering Group Institute of Computational Science Università della Svizzera italiana. Via G. Buffi 13 Lugano Ticino6900 Switzerland Marchuk Institute of Numerical Mathematics of Russian Academy of Sciences Moscow Russia ETH Zürich Geothermal Energy and Geofluids Group Institute of Geophysics Zürich8092 Switzerland

Flow in fractured porous media occurs in the earth’s subsurface, in biological tissues, and in man-made materials. Fractures have a dominating influence on flow processes, and the last decade has seen an extensive development of models and numerical methods that explicitly account for their presence. To support these developments, we present a portfolio of four benchmark cases for single-phase flow in three-dimensional fractured porous media. The cases are specifically designed to test the methods’ capabilities in handling various complexities common to the geometrical structures of fracture networks. Based on an open call for participation, results obtained with 17 numerical methods were collected. This paper presents the underlying mathematical model, an overview of the features of the participating numerical methods, and their performance in solving the benchmark cases. Copyright © 2020, The Authors. All rights reserved.

关键词： Numerical methods

Two-scale sparse finite element approximations

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Science China mathematics 2016年第4期59卷 789-808页

作者： LIU Fang ZHU JinWei School of Statistics and Mathematics Central University of Finance and Economics The State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and ScientificEngineering ComputingAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

To reduce computational cost,we study some two-scale finite element approximations on sparse grids for elliptic partial differential equations of second order in a general *** any tensor product domain ?R^d with d = 2,3,we construct the two-scale finite element approximations for both boundary value and eigenvalue problems by using a Boolean sum of some existing finite element approximations on a coarse grid and some univariate fine grids and hence they are cheaper *** applications,we obtain some new efficient finite element discretizations for the two classes of problem:The new two-scale finite element approximation on a sparse grid not only has the less degrees of freedom but also achieves a good accuracy of approximation.

关键词： combination discretization eigenvalue finite element postprocessing two-scale