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An elementary and unified proof of grothendieck's inequality

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arXiv 2017年

作者： Friedland, Shmuel Lim, Lek-Heng Zhang, Jinjie Department of Mathematics Statistics and Computer Science University of Illinois ChicagoIL60607-7045 United States Computational and Applied Mathematics Initiative Department of Statistics University of Chicago ChicagoIL60637-1514 United States Department of Statistics University of Chicago ChicagoIL60637-1514 United States Department of Mathematics University of California San DiegoCA92093-0112 United States

We present an elementary, self-contained proof of Grothendieck's inequality that unifies the real and complex cases and yields both the Krivine and Haagerup bounds, the current bestknown explicit bounds for the real and complex Grothendieck constants respectively. This article is intended to be pedagogical, combining and streamlining known ideas of Lindenstrauss-Pe lczyński, Krivine, and Haagerup into a proof that need only univariate calculus, basic complex variables, and a modicum of linear algebra as prerequisites.47A07, 46B28, 46B85, 81P40, 81P45, 03D15, 97K30, 47N10, 90C27 Copyright © 2017, The Authors. All rights reserved.

关键词： Linear algebra

Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems

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arXiv 2017年

作者： Hubmer, Simon Sherina, Ekaterina Neubauer, Andreas Scherzer, Otmar 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 Lyngby 2800 Denmark Johannes Kepler University Linz Industrial Mathematics Institute Altenbergerstraße 69 LinzA-4040 Austria University of Vienna Computational Science Center Oskar Morgenstern-Platz 1 Vienna1090 Austria Johann Radon Institute Linz Altenbergerstraße 69 LinzA-4040 Austria

We consider a problem of quantitative static elastography, the estimation of the Lamé parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically. The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lamé parameters from displacement data simulating a static elastography experiment are *** Codes 65J22, 65J15, 74G75 Copyright © 2017, The Authors. All rights reserved.

关键词： Inverse problems

Numerically testing generically reduced projective schemes for the arithmetic gorenstein property 6th

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Numerically testing generically reduced projective schemes f...

6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015

作者： Daleo, Noah S. Hauenstein, Jonathan D. Department of Mathematics Worcester State University WorcesterMA01602 United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

ISBN: (纸本)9783319328584

Let X ⊂ n be a generically reduced projective scheme. A fundamental goal in computational algebraic geometry is to compute information about X even when defining equations for X are not known. We use numerical algebraic geometry to develop a test for deciding if X is arithmetically Gorenstein and apply it to three secant varieties. © Springer International Publishing Switzerland 2016.

关键词： Algebra

Restricted power domination and zero forcing problems

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arXiv 2017年

作者： Bozeman, Chassidy Brimkov, Boris Erickson, Craig Ferrero, Daniela Flagg, Mary Hogben, Leslie Department of Mathematics Iowa State University AmesIA50011 United States Department of Computational and Applied Mathematics Rice University HoustonTX77005 United States Department of Mathematics and Computer Science Grand View University Des MoinesIA United States Department of Mathematics Texas State University San MarcosTX78666 United States Department of Mathematics Computer Science and Cooperative Engineering University of St. Thomas 3800 Montrose HoustonTX77006 United States American Institute of Mathematics 600 E. Brokaw Road San JoseCA95112 United States

Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of a graph is a set of vertices that observes every vertex in the graph, following a set of rules for power system monitoring. A practical problem of interest is to determine the minimum number of additional measurement devices needed to monitor a power network when the network is expanded and the existing devices remain in place. In this paper, we study the problem of finding the smallest power dominating set that contains a given set of vertices X. We also study the related problem of finding the smallest zero forcing set that contains a given set of vertices X. The sizes of such sets in a graph G are respectively called the restricted power domination number and restricted zero forcing number of G subject to X. We derive several tight bounds on the restricted power domination and zero forcing numbers of graphs, and relate them to other graph parameters. We also present exact and algorithmic results for computing the restricted power domination number, including integer programs for general graphs and a linear time algorithm for graphs with bounded treewidth. We also use restricted power domination to obtain a parallel algorithm for finding minimum power dominating sets in *** Codes 05C69, 05C50, 05C57, 94C15 Copyright © 2017, The Authors. All rights reserved.

关键词： Graphic methods

A family of group divisible designs with arbitrary block sizes

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arXiv 2017年

作者： Huang, Yu-Pei Liu, Chia-An Chang, Yaotsu Lee, Chong-Dao College of Applied Mathematics Beijing Normal University Zhuhai519087 China Department of Mathematical Sciences University of Delaware NewarkDE19716 United States Department of Financial and Computational Mathematics I-Shou University Taiwan84001 Taiwan Department of Communication Engineering I-Shou University Taiwan84001 Taiwan

Recently, a construction of group divisible designs (GDDs) derived from the decoding of quadratic residue (QR) codes was given. In this paper, we extend the idea to obtain a new family of GDDs, which is also involved with a well-known balanced incomplete block design (BIBD).MSC Codes 05B05 Copyright © 2017, The Authors. All rights reserved.

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Biophysics at the coffee shop: lessons learned working with George Oster

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arXiv 2019年

作者： Igoshin, Oleg Chen, Jing Xing, Jianhua Liu, Jian Elston, Timothy C. Grabe, Michael Kim, Kenneth S. Nirody, Jasmine Rangamani, Padmini Sun, Sean Wang, Hongyun Wolgemuth, Charles Departments of Bioengineering of Biosciences and of Chemistry Center for Theoretical Biological Physics Rice University HoustonTX77005 United States Department of Biological Sciences Virginia Tech BlacksburgVA24061 United States Department of Computational and Systems Biology UPMC-Hillman Cancer Center School of Medicine University of Pittsburgh PittsburghPA15261 United States Department of Cell Biology Center for Cell Dynamics School of Medicine Johns Hopkins University BaltimoreMD21205 United States Department of Pharmacology School of Medicine University of North Carolina at Chapel Hill Chapel HillNC27599 United States Cardiovascular Research Institute School of Pharmacy University of California at San Francisco San FranciscoCA94158 United States Lawrence Livermore National Laboratory LivermoreCA94550 United States Center for Studies in Physics and Biology Rockefeller University New YorkNY10065 United States Department of Mechanical and Aerospace engineering University of California at San Diego La JollaCA92093 United States Department of Mechanical Engineering Whiting School of Engineering Johns Hopkins University BaltimoreMD21218 United States Department of Applied Mathematics and Statistics University of California Santa CruzCA95064 United States Department of Physics Department of Molecular and Cellular Biology University of Arizona TucsonAZ85721 United States

Over the past 50 years, the use of mathematical models, derived from physical reasoning, to describe molecular and cellular systems has evolved from an art of the few to a cornerstone of biological inquiry. George Oster stood out as a pioneer of this paradigm shift from descriptive to quantitative biology not only through his numerous research accomplishments, but also through the many students and postdocs he mentored over his long career. Those of us fortunate enough to have worked with George agree that his sharp intellect, physical intuition and passion for scientific inquiry not only inspired us as scientists but also greatly influenced the way we conduct research. We would like to share a few important lessons we learned from George in honor of his memory and with the hope that they may inspire future generations of scientists. Copyright © 2019, The Authors. All rights reserved.

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A compact fourth-order gas-kinetic scheme for the euler and navier-stokes solutions

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arXiv 2017年

作者： Ji, Xing Pan, Liang Shyy, Wei Xu, Kun Department of Mathematics Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong Department of Mechanical and Aerospace Engineering Hong Kong University of Science and Technology Clear Water Bay Kowloon Hong Kong Institute of Applied Physics and Computational Mathematics Beijing100088 China

In this paper, a fourth-order compact gas-kinetic scheme (GKS) is developed for the compressible Euler and Navier-Stokes equations under the framework of two-stage fourth-order temporal discretization and Hermite WENO (HWENO) reconstruction. Due to the high-order gas evolution model, the GKS provides a time dependent gas distribution function at a cell interface. This time evolution solution can be used not only for the flux evaluation across a cell interface and its time derivative, but also time accurate evolution solution at a cell interface. As a result, besides updating the conservative flow variables inside each control volume, the GKS can get the cell averaged slopes inside each control volume as well through the differences of flow variables at the cell interfaces. So, with the updated flow variables and their slopes inside each cell, the HWENO reconstruction can be naturally implemented for the compact high-order reconstruction at the beginning of next step. Therefore, a compact higher-order GKS, such as the two-stages fourth-order compact scheme can be constructed. This scheme is as robust as second-order one, but more accurate solution can be obtained. In comparison with compact fourth-order DG method, the current scheme has only two stages instead of four within each time step for the fourth-order temporal accuracy, and the CFL number used here can be on the order of 0.5 instead of 0.11 for the DG method. Through this research, it concludes that the use of high-order time evolution model rather than the first order Riemann solution is extremely important for the design of robust, accurate, and efficient higher-order schemes for the compressible flows. Copyright © 2017, The Authors. All rights reserved.

关键词： Cells

On clustering network-valued data 17

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On clustering network-valued data

Proceedings of the 31st International Conference on Neural Information Processing Systems

作者： Soumendu Sundar Mukherjee Purnamrita Sarkar Lizhen Lin Department of Statistics University of California Berkeley Berkeley California Department of Statistics and Data Science University of Texas Austin Austin Texas Department of Applied and Computational Mathematics and Statistics Univeristy of Notre Dame Notre Dame Indiana

ISBN: (纸本)9781510860964

Community detection, which focuses on clustering nodes or detecting communities in (mostly) a single network, is a problem of considerable practical interest and has received a great deal of attention in the research community. While being able to cluster within a network is important, there are emerging needs to be able to cluster multiple networks. This is largely motivated by the routine collection of network data that are generated from potentially different populations. These networks may or may not have node correspondence. When node correspondence is present, we cluster networks by summarizing a network by its graphon estimate, whereas when node correspondence is not present, we propose a novel solution for clustering such networks by associating a computationally feasible feature vector to each network based on trace of powers of the adjacency matrix. We illustrate our methods using both simulated and real data sets, and theoretical justifications are provided in terms of consistency.

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Using species ranges and macroeconomic data to fill the gap in costs of biological invasions

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Nature ecology & evolution 2025年 2025 May 26页

作者： Ismael Soto Pierre Courtois Arman Pili Enrico Tordoni Eléna Manfrini Elena Angulo Céline Bellard Elizabeta Briski Miloš Buřič Ross N Cuthbert Antonín Kouba Melina Kourantidou Rafael L Macêdo Boris Leroy Phillip J Haubrock Franck Courchamp Brian Leung Faculty of Fisheries and Protection of Waters South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses University of South Bohemia in České Budějovice Vodňany Czech Republic. isma-sa@***. CEE-M University of Montpellier CNRS INRAE Instit Agro Montpellier France. School of Biological Sciences Faculty of Science Monash University Clayton Victoria Australia. Institute for Biochemistry and Biology University of Potsdam Potsdam Germany. Department of Botany Institute of Ecology and Earth Science University of Tartu Tartu Estonia. Université Paris-Saclay CNRS AgroParisTech Ecologie Société Evolution Gif sur Yvette France. Unité Biologie des Organismes et Ecosystèmes Aquatiques (BOREA UMR 8067) Muséum national d'Histoire naturelle Sorbonne Université Université de Caen Normandie CNRS IRD Université des Antilles Paris France. Estación Biológica de Doñana CSIC Seville Spain. GEOMAR Helmholtz-Zentrum für Ozeanforschung Kiel Kiel Germany. Faculty of Fisheries and Protection of Waters South Bohemian Research Center of Aquaculture and Biodiversity of Hydrocenoses University of South Bohemia in České Budějovice Vodňany Czech Republic. Institute for Global Food Security School of Biological Sciences Queen's University Belfast Belfast UK. AMURE University of Western Brittany Plouzané France. Department of Sociology Environmental and Business Economics University of Southern Denmark Esbjerg Denmark. Woods Hole Oceanographic Institution Falmouth MA USA. Marine Policy Center Woods Hole MA USA. Graduate Program in Conservation and Ecotourism Federal University of Rio de Janeiro State Rio de Janeiro Brazil. Leibniz Institute of Freshwater Ecology and Inland Fisheries (IGB) Berlin Germany. Institute of Biology Freie Universität Berlin Berlin Germany. Department of River Ecology and Conservation Senckenberg Research Institute and Natural History Museum Frankfurt Gelnhausen Germany. CAMB Center for Applied Mathematics and Bioinformatics Gulf

Biological invasions threaten global biodiversity, human well-being and economies. Many regional and taxonomic syntheses of monetary costs have been produced recently but with important knowledge gaps owing to uneven geographic and taxonomic research intensity. Here we combine species distribution models, macroeconomic data and the InvaCost database to produce the highest resolution spatio-temporal cost estimates currently available to bridge these gaps. From a subset of 162 invasive species with 'highly reliable' documented costs at the national level, our interpolation focuses on countries that have not reported any costs despite the known presence of invasive species. This analysis demonstrates a substantial underestimation, with global costs potentially estimated to be 1,646% higher for these species than previously recorded. This discrepancy was uneven geographically and taxonomically, respectively peaking in Europe and for plants. Our results showed that damage costs were primarily driven by gross domestic product, human population size, agricultural area and environmental suitability, whereas management expenditure correlated with gross domestic product and agriculture areas. We also found a lag time for damage costs of 46 years, but management spending was not delayed. The methodological predictive approach of this study provides a more complete view of the economic dimensions of biological invasions and narrows the global disparity in invasion cost reporting.

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