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Lattice studies of the Sp(4) gauge theory with two fundamental and three antisymmetric Dirac fermions

Physical Review D 2022年第1期106卷 014501-014501页

作者： Ed Bennett Deog Ki Hong Ho Hsiao Jong-Wan Lee C.-J. David Lin Biagio Lucini Michele Mesiti Maurizio Piai Davide Vadacchino Swansea Academy of Advanced Computing Swansea University Fabian Way SA1 8EN Swansea Wales United Kingdom Department of Physics Pusan National University Busan 46241 Korea Institute of Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu 30010 Taiwan Extreme Physics Institute Pusan National University Busan 46241 Korea Center for High Energy Physics Chung-Yuan Christian University Chung-Li 32023 Taiwan Centre for Theoretical and Computational Physics National Yang Ming Chiao Tung University 1001 Ta-Hsueh Road Hsinchu 30010 Taiwan Department of Mathematics Faculty of Science and Engineering Swansea University Fabian Way SA1 8EN Swansea Wales United Kingdom Department of Physics Faculty of Science and Engineering Swansea University Singleton Park SA2 8PP Swansea Wales United Kingdom School of Mathematics and Hamilton Mathematics Institute Trinity College Dublin 2 Ireland Centre for Mathematical Sciences University of Plymouth Plymouth PL4 8AA United Kingdom

We consider the Sp(4) gauge theory coupled to Nf=2 fundamental and nf=3 antisymmetric flavors of Dirac fermions in four dimensions. This theory serves as the microscopic origin for composite Higgs models with SU(4)/Sp(4) coset, supplemented by partial top compositeness. We study numerically its lattice realization, and couple the fundamental plaquette action to Wilson-Dirac fermions in mixed representations, by adopting a (rational) hybrid Monte Carlo method, to perform nontrivial tests of the properties of the resulting lattice theory. We find evidence of a surface (with boundaries) of first-order bulk phase transitions in the three-dimensional space of bare parameters (one coupling and two masses). Explicit evaluation of the Dirac eigenvalues confirms the expected patterns of global symmetry breaking. After investigating finite-volume effects in the weak-coupling phase of the theory, for the largest available lattice we study the mass spectra of the lightest spin-0 and spin-1 flavored mesons composed of fermions in each representation, and of the lightest half-integer spin composite particle made of fermions in different representations—the chimera baryon. This work sets the stage for future systematical studies of the nonperturbative dynamics in phenomenologically relevant regions of parameter space.

关键词： Composite models Lattice field theory Non-Abelian gauge theories Spontaneous symmetry breaking Lattice gauge theory

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The non-cutoff Vlasov-Maxwell-Boltzmann system with weak angular singularity

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Science China mathematics 2018年第1期61卷 111-136页

作者： Yingzhe Fan Yuanjie Lei Shuangqian Liu Huijiang Zhao School of Mathematics and Statistics Wuhan University School of Mathematics and Statistics Huazhong University of Science and Technology Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Department of Mathematics Jinan University Computational Science Hubei Key Laboratory Wuhan University

We establish the global existence of small-amplitude solutions near a global Maxwellian to the Cauchy problem of the Vlasov-Maxwell-Boltzmann system for non-cutoff soft potentials with weak angular singularity. This extends the work of Duan et al.(2013), in which the case of strong angular singularity is considered, to the case of weak angular singularity.

关键词： non-cutoff Vlasov-Maxwell-Boltzmann system global solutions near Maxwellians weak angular singularity time-velocity weighted energy method

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The white rat of numerical reproducibility

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AIP Conference Proceedings 2021年第1期2365卷

作者： Michael Mascagni Departments of Computer Science Mathematics and Scientific Computing Florida State University Tallahassee FL 32306-4530 USA Applied and Computational Mathematics Division National Institute of Standards and Technology (NIST) Gaithersburg MD 20899-8910 USA

We explore an application from the author’s work in neuroscience. A code used to investigate neural development modeled 100 neurons with all-to-all excitatory connectivity. We used a simple ordinary differential equation system to model each neuron, and this 100-neuron model was used to produce a paper published in the Journal of Neurophysiology. Later a colleague used our code to continue this work, and found he could not reproduce our results. This lead us to thoroughly investigate this code and we discovered that it offered many different ways to thwart reproducibility that could be explained by round-off error arising from floating-point *** reproducibility is considered a task that directly follows from the determinism in computations. However, reproducibility has become an intense concern and and issue for research. In fact, the author developed an series of international workshops on numerical reproducibility and computational reproducibility that is now a regular offering at the annual international supercomputing conferences. We will show how this particular code provides a lack of reproducibility from the following three mechanisms: (i) the introduction of floating-point errors in an inner product; (ii) introduction of floating-point errors at each an increasing number of time steps during temporal refinement (ii); and (iii) differences in the output of library mathematical functions at the level of round-off error. This code’s sensitivity makes it a very powerful tool to explore many different manifestations of numerical reproducibility. However, this code is by no means exceptional, as in neuroscience these types of models are used extensively to gain insights on the functioning of the nervous system. In addition, these types of models are widely used in many other fields of study as they just nonlinear evolution equations.

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A high accuracy nonconforming finite element scheme for helmholtz transmission eigenvalue problem

arXiv

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arXiv 2019年

作者： Xi, Yingxia Ji, Xia Zhang, Shuo School of Science Nanjing University of Science and Technology Nanjing210094 China Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

In this paper, we consider a cubic H2 nonconforming finite element scheme B3h 0 which does not correspond to a locally defined finite element with Ciarlet0s triple but admit a set of local basis functions. For the first time, we deduce and write out the expression of basis functions explicitly. Distinguished from the most nonconforming finite element methods, (δδh;δh) with non-constant coefficient;δ > 0 is coercive on the nonconforming B3h 0 space which makes it robust for numerical discretization. For fourth order eigenvalue problem, the B3h 0 scheme can provide O(h2) approximation for the eigenspace in energy norm and O(h4) approximation for the eigenvalues. We test the B3h 0 scheme on the vary-coefficient bi-Laplace source and eigenvalue problem, further, transmission eigenvalue problem. Finally, numerical examples are presented to demonstrate the effectiveness of the proposed *** Codes 31A30, 65N30 Copyright © 2019, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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EXPLAINABLE ARTIFICIAL INTELLIGENCE (XAI) 2.0: A MANIFESTO OF OPEN CHALLENGES AND INTERDISCIPLINARY RESEARCH DIRECTIONS

arXiv

引用

arXiv 2023年

作者： Longo, Luca Brcic, Mario Cabitza, Federico Choi, Jaesik Confalonieri, Roberto Ser, Javier Del Guidotti, Riccardo Hayashi, Yoichi Herrera, Francisco Holzinger, Andreas Jiang, Richard Khosravi, Hassan Lecue, Freddy Malgieri, Gianclaudio Páez, Andrés Samek, Wojciech Schneider, Johannes Speith, Timo Stumpf, Simone The Artificial Intelligence and Cognitive Load Research Lab Technological University Dublin Ireland University of Zagreb Faculty of Electrical Engineering and Computing Croatia University of Milano-Bicocca Milan Italy IRCCS Ospedale Galeazzi Sant’Ambrogio Milan Italy Kim Jaechul Graduate School of AI Korea Advanced Institute of Science & Technology Korea Republic of INEEJI Corporation Korea Republic of Department of Mathematics University of Padua Italy Derio Spain Bilbao Spain University of Pisa Pisa Italy Department of Computer Science Meiji University Tokyo Japan Department of Computer Science and Artificial Intelligence DaSCI Andalusian Institute in Data Science & Computational Intelligence University of Granada Granada Spain Human-Centered AI Lab University of Natural Resources and Life Sciences Vienna Austria School of Computing and Communications Lancaster University United Kingdom The University of Queensland Brisbane Australia Sophia Antipolis France eLaw Center for Law and Digital Technologies Leiden University Netherlands Department of Philosophy Universidad de los Andes Bogotá Colombia Center for Research & Formation in Artificial Intelligence Universidad de los Andes Bogotá Colombia Technical University of Berlin Berlin Germany Fraunhofer Heinrich Hertz Institute Berlin Germany Berlin Germany Department of Information Systems and Computer Science University of Liechtenstein Liechtenstein Liechtenstein Department of Philosophy University of Bayreuth Bayreuth Germany Center for Perspicuous Computing Saarland University Saarbrücken Germany School of Computing Science University of Glasgow United Kingdom

As systems based on opaque Artificial Intelligence (AI) continue to flourish in diverse real-world applications, understanding these black box models has become paramount. In response, Explainable AI (XAI) has emerged as a field of research with practical and ethical benefits across various domains. This paper not only highlights the advancements in XAI and its application in real-world scenarios but also addresses the ongoing challenges within XAI, emphasizing the need for broader perspectives and collaborative efforts. We bring together experts from diverse fields to identify open problems, striving to synchronize research agendas and accelerate XAI in practical applications. By fostering collaborative discussion and interdisciplinary cooperation, we aim to propel XAI forward, contributing to its continued success. Our goal is to put forward a comprehensive proposal for advancing XAI. To achieve this goal, we present a manifesto of 27 open problems categorized into nine categories. These challenges encapsulate the complexities and nuances of XAI and offer a road map for future research. For each problem, we provide promising research directions in the hope of harnessing the collective intelligence of interested stakeholders. © 2023, CC BY-SA.

关键词： Ethical technology

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The Studying of Hydrogen Diffusion Non-Stationary Processes Near a Crack in the Field of Heterogeneous Mechanical Tensions for the Encapsulated MEMS Devices

The Studying of Hydrogen Diffusion Non-Stationary Processes ...

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International Conference on Perspective Technologies and Methods in MEMS Design (MEMSTECH)

作者： Winfried Auzinger Roksolyana Stolyarchuk Yaroslav Pelekh Oksana Kozar Serhii Mentynskyi Mykola Ihnatyshyn Institute for Analysis and Scientific Computing Vienna University of Technology (TU Wien) Wien Austria Department of Computational Mathematics and Programming Lviv Polytechnic National University Lviv Ukraine Department of Mechanical Engineering Natural Sciences and Information Technologies Mukachevo State University Mukachevo Ukraine Department of Light Industry and Professional Education Mukachevo State University Mukachevo Ukraine

ISBN: (数字)9781728171807

ISBN: (纸本)9781728171814

In this paper we study an elastic-plastic isotropic body weakened by a rectilinear crack, directed along the abscissa axis, under the action of stresses symmetrical about its plane. An approximate (analytical and numerical) solution of this problem is constructed under the condition that the hydrostatic deformation of the split expansion is approximated by a parabola. The concentration of hydrogen near the top of the crack is calculated. Note that when using the above calculation formulas, at each node we get several approximations to the exact solution. In the proposed methods, only three appeals to the right-hand side of the differential equation are necessary to obtain both the third order accuracy method and the two approximations (upper and lower) of the second order of accuracy.

关键词： mathematical model elastic-plastic isotropic body hydrogen diffusion internal crack continued fractions two-sided approximations nonlinear methods diffusion of hydrogen internal cracks MEMS devices cracks Cocaine Fissure Mathematical Model Continued fraction Fields

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A hybrid WENO method with modified ghost fluid method for compressible two-medium flow problems

arXiv

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arXiv 2020年

作者： Zhao, Zhuang Chen, Yibing Qiu, Jianxian School of Mathematical Sciences Xiamen University XiamenFujian361005 China Institute of Applied Physics and Computational Mathematics Beijing100094 China School of Mathematical Sciences Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing Xiamen University XiamenFujian361005 China

In this paper, we develop a simplified hybrid weighted essentially non-oscillatory (WENO) method combined with the modified ghost fluid method (MGFM) [28] to simulate the compressible two-medium flow problems. The MGFM can turn the two-medium flow problems into two single-medium cases by defining the ghost fluids status in terms of the predicted the interface status, which makes the material interface "invisible". For the single medium flow case, we adapt between the linear upwind scheme and the WENO scheme automatically by identifying the regions of the extreme points for the reconstruction polynomial as same as the hybrid WENO scheme [50]. Instead of calculating their exact locations, we only need to know the regions of the extreme points based on the zero point existence theorem, which is simpler for implementation and saves computation time. Meanwhile, it still keeps the robustness and has high efficiency. Extensive numerical results for both one and two dimensional two-medium flow problems are performed to demonstrate the good performances of the proposed method. Copyright © 2020, The Authors. All rights reserved.

关键词： Computation theory

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Success-Driven Opinion Formation Determines Social Tensions

SSRN

引用

SSRN 2023年

作者： Chica, Manuel Perc, Matjaž Santos, Francisco C. Andalusian Research Institute DaSCI "Data Science and Computational Intelligence" University of Granada Granada18071 Spain School of Electrical Engineering and Computing The University of Newcastle CallaghanNSW2308 Australia Instituto Superior Técnico Universidade de Lisboa Porto Salvo2744-016 Portugal Faculty of Natural Sciences and Mathematics University of Maribor Koroška cesta 160 Maribor2000 Slovenia Department of Medical Research China Medical University Hospital China Medical University Taichung Taiwan Alma Mater Europaea Slovenska ulica 17 Maribor2000 Slovenia Complexity Science Hub Vienna Josefstädterstraße 39 Vienna1080 Austria Department of Physics Kyung Hee University 26 Kyungheedae-ro Dongdaemun-gu Seoul Korea Republic of

Polarization is common in politics and public opinion. It is believed to be shaped by the media as well as ideologies, and often incited by misinformation. However, little is known about the microscopic dynamics behind polarization and the resulting social tensions. By coupling together opinion formation with the strategy selection in different social dilemmas, we reveal how success at an individual level transforms to global consensus or lack thereof. When defection carries with it the fear of punishment in the absence of greed, as in the stag-hunt game, opinion fragmentation is smallest. Conversely, if defection promises a higher payoff and thus evokes also greed, like in the prisoner's dilemma and the snowdrift game, consensus is much more difficult to attain. Our research thus challenges the top-down narrative of social tensions, showing that they may well originate from fundamental principles at individual level, like the desire to prevail in pairwise evolutionary comparisons. © 2023, The Authors. All rights reserved.

关键词： Polarization

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Uplink-downlink duality between multiple-access and broadcast channels with compressing relays

arXiv

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arXiv 2020年

作者： Liu, Liang Liu, Ya-Feng Patil, Pratik Yu, Wei the Department of Electronic and Information Engineering The Hong Kong Polytechnic University Hong Kong the State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China The Edward S. Rogers Sr. Department of Electrical and Computer Engineering the University of Toronto the Department of Statistics and Data Science and the Machine Learning Department Carnegie Mellon University PittsburghPA15213 United States The Edward S. Rogers Sr. Department of Electrical and Computer Engineering University of Toronto 10 King’s College Road TorontoONM5S3G4 Canada

—Uplink-downlink duality refers to the fact that under a sum-power constraint, the capacity regions of a Gaussian multiple-access channel and a Gaussian broadcast channel with Hermitian transposed channel matrices are identical. This paper generalizes this result to a cooperative cellular network, in which remote access-points are deployed as relays in serving the users under the coordination of a central processor (CP). In this model, the users and the relays are connected over noisy wireless links, while the relays and the CP are connected over noiseless but rate-limited fronthaul links. Based on a Lagrangian technique, this paper establishes a duality relationship between such a multiple-access relay channel and broadcast relay channel, under the assumption that the relays use compression-based strategies. Specifically, we show that under the same total transmit power constraint and individual fronthaul rate constraints, the achievable rate regions of the Gaussian multiple-access and broadcast relay channels are identical, when either independent compression or Wyner-Ziv and multivariate compression strategies are used. The key observations are that if the beamforming vectors at the relays are fixed, the sum-power minimization problems under the achievable rate and fronthaul constraints in both the uplink and the downlink can be transformed into either a linear programming or a semidefinite programming problem depending on the compression technique, and that the uplink and downlink problems are Lagrangian duals of each other. Moreover, the dual variables corresponding to the downlink rate constraints become the uplink powers;the dual variables corresponding to the downlink fronthaul constraints become the uplink quantization noises. This duality relationship enables an efficient algorithm for optimizing the downlink transmission and relaying strategies based on the uplink. Copyright © 2020, The Authors. All rights reserved.

关键词： Linear programming

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Kronecker Graph Generation with Ground Truth for 4-Cycles and Dense Structure in Bipartite Graphs

Kronecker Graph Generation with Ground Truth for 4-Cycles an...

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IEEE International Symposium on Parallel and Distributed Processing Workshops and Phd Forum (IPDPSW)

作者： Trevor Steil Scott McMillan Geoffrey Sanders Roger Pearce Benjamin Priest School of Mathematics University of Minnesota Minneapolis MN USA Software Engineering Institute Carnegie Mellon University Pittsburgh PA USA Center for Applied Scientific Computing (CASC) Lawrence Livermore National Laboratory (LLNL) Livermore CA USA

ISBN: (数字)9781728174457

ISBN: (纸本)9781728174570

We demonstrate nonstochastic Kronecker graph generators produce massive-scale bipartite graphs with ground truth global and local properties and discuss their use for validation of graph analytics. Given two small connected scale-free graphs with adjacency matrices A and B, their Kronecker product graph [1] has adjacency matrix C = A ⊗ B. We first demonstrate that having one factor A non-bipartite (alternatively, adding all self loops to a bipartite A) with other factor B bipartite ensures G C is bipartite and connected. Formulas for ground truth of many graph properties (including degree, diameter, and eccentricity) carry over directly from the general case presented in previous work [2], [3]. However, the analysis of higher-order structure and dense structure is different in bipartite graphs, as no odd-length cycles exist (including triangles) and the densest possible structures are bicliques. We derive formulas to give ground truth for 4-cycles (a.k.a. squares or butterflies) at every vertex and edge in G C . Additionally, we demonstrate that bipartite communities (dense vertex subsets) in the factors A, B yield dense bipartite communities in the Kronecker product C. We additionally discuss interesting properties of Kronecker product graphs revealed by the formulas an their impact on using them as benchmarks with ground truth for various complex analytics. For example, for connected A and B of nontrivial size, G C has 4-cycles at vertices/edges associated with vertices/edges in A and B that have none, making it difficult to generate graphs with ground truth bipartite generalizations of truss decomposition (e.g. the k-wing decomposition of [4]).

关键词： Bipartite graph Generators Indexes Software engineering Benchmark testing Data analysis

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