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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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Positive definiteness of real quadratic forms resulting from the variable-step approximation of convolution operators

arXiv

引用

arXiv 2020年

作者： Liao, Hong-Lin Tang, Tao Zhou, Tao Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China Division of Science and Technology BNU-HKBU United International College ZhuhaiGuangdong Province China NCMIS & LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

The positive definiteness of real quadratic forms with convolution structures plays an important role in stability analysis for time-stepping schemes for nonlocal operators. In this work, we present a novel analysis tool to handle discrete convolution kernels resulting from variable-step approximations for convolution operators. More precisely, for a class of discrete convolution kernels relevant to variable-step time discretizations, we show that the associated quadratic form is positive definite under some easy-to-check algebraic conditions. Our proof is based on an elementary constructing strategy using the properties of discrete orthogonal convolution kernels and complementary convolution kernels. To the best of our knowledge, this is the first general result on simple algebraic conditions for the positive definiteness of variable-step discrete convolution kernels. Using the unified theory, the stability for some simple non-uniform time-stepping schemes can be obtained in a straightforward *** Codes 65M06, 65M12, 65R20. © 2020, CC BY-NC-SA.

关键词： Number theory

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On the implementation of a robust and efficient finite element-based parallel solver for the compressible Navier-Stokes equations

arXiv

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arXiv 2021年

作者： Guermond, Jean-Luc Kronbichler, Martin Maier, Matthias Popov, Bojan Tomas, Ignacio Department of Mathematics Texas A&M University 3368 College StationTX77843 United States Institute for Computational Mechanics Department for Mechanical Engineering Technical University of Munich Germany Division of Scientific Computing Department of Information Technology Uppsala University Sweden Sandia National Laboratories P.O. Box 5800 MS 1320 AlbuquerqueNM87185-1320 United States

This paper describes in detail the implementation of a finite element technique for solving the compressible Navier-Stokes equations that is provably robust and demonstrates excellent performance on modern computer hardware. The method is second-order accurate in time and space. Robustness here means that the method is proved to be invariant domain preserving under the hyperbolic CFL time step restriction, and the method delivers results that are reproducible. The proposed technique is shown to be accurate on challenging 2D and 3D realistic *** Codes 35L65, 65M60, 65M12, 65N30 Copyright © 2021, The Authors. All rights reserved.

关键词： Finite element method

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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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A DISCONTINUOUS GALERKIN METHOD BY PATCH RECONSTRUCTION FOR BIHARMONIC PROBLEM

引用

Journal of computational mathematics 2019年第4期37卷 524-540页

作者： Ruo Li Pingbing Ming Zhiyuan Sun Fanyi Yang Zhijian Yang CAPT LMAM and School of Mathematical Sciences Peking University Beijing 100871 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing AMSS Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of Sciences No. 19A Yu-Quan Road Beijing 100049 China School of Mathematical Sciences Peking University Beijing 100871 China School of Mathematics and. Statistics Wuhan University Wuhan 430072 China

We propose a new discontinuous Galerkin method based on the least-squares patch reconstruction for the biharmonic problem. We prove the optimal error estimate of the proposed method. The two-dimensional and three-dimensional numerical examples are presented to confirm the accuracy and efficiency of the method with several boundary conditions and several types of polygon meshes and polyhedral meshes.

关键词： Least-squares problem Reconstructed basis function Discontinuous Galerkin method Biharmonic problem

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On energy stable, maximum-principle preserving, second order BDF scheme with variable steps for the Allen-Cahn equation

arXiv

引用

arXiv 2020年

作者： Liao, Hong-Lin Tang, Tao Zhou, Tao Department of Mathematics Nanjing University of Aeronautics and Astronautics Nanjing211106 China SUSTech International Center for Mathematics Shenzhen China Division of Science and Technology BNU-HKBU United International College ZhuhaiGuangdong Province China NCMIS LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this work, we investigate the two-step backward differentiation formula (BDF2) with nonuniform grids for the Allen-Cahn equation. We show that the nonuniform BDF2 scheme is energy stable under the time-step ratio r... 详细信息

关键词： Maximum principle

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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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Leveraging randomized compiling for the quantum imaginary-time-evolution algorithm

引用

Physical Review Research 2022年第3期4卷 033140-033140页

作者： Jean-Loup Ville Alexis Morvan Akel Hashim Ravi K. Naik Marie Lu Bradley Mitchell John-Mark Kreikebaum Kevin P. O'Brien Joel J. Wallman Ian Hincks Joseph Emerson Ethan Smith Ed Younis Costin Iancu David I. Santiago Irfan Siddiqi Quantum Nanoelectronics Laboratory Dept. of Physics University of California at Berkeley Berkeley California 94720 USA Computational Research Division Lawrence Berkeley National Lab Berkeley California 94720 USA Materials Sciences Division Lawrence Berkeley National Lab Berkeley California 94720 USA Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology Cambridge Massachusetts 02139 USA Inst. for Quantum Computing and Dept. of Applied Mathematics University of Waterloo Waterloo Ontario Canada N2L 3G1 Quantum Benchmark Inc. Kitchener Ontario Canada N2H 5G5

Recent progress in noisy intermediate-scale quantum (NISQ) hardware shows that quantum devices may be able to tackle complex problems even without error correction. However, coherent errors due to the increased complexity of these devices is an outstanding issue. They can accumulate through a circuit, making their impact on algorithms hard to predict and mitigate. Iterative algorithms like quantum imaginary time evolution are susceptible to these errors. This article presents the combination of both noise tailoring using randomized compiling and error mitigation with purification. We also show that cycle benchmarking gives an estimate of the reliability of the purification. We apply this method to the quantum imaginary time evolution of a transverse field Ising model and report an energy estimation error and a ground-state infidelity both below 1%. Our methodology is general and can be used for other algorithms and platforms. We show how combining noise tailoring and error mitigation will push forward the performance of NISQ devices.

关键词： Measurement-based quantum computing Quantum algorithms Quantum benchmarking Quantum computation Quantum control Quantum information processing Quantum simulation

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Improving the accuracy and efficiency of quantum connected moments expansions

arXiv

引用

arXiv 2021年

作者： Claudino, Daniel Peng, Bo Bauman, Nicholas P. Kowalski, Karol Humble, Travis S. Oak Ridge National Laboratory Quantum Computing Institute Oak RidgeTN37831 United States Computer Science and Mathematics Oak Ridge National Laboratory Oak RidgeTN37831 United States Pacific Northwest National Laboratory Physical Sciences Division RichlandWA99352 United States Computational Sciences and Engineering Oak Ridge National Laboratory Oak RidgeTN37831 United States

The still-maturing noisy intermediate-scale quantum (NISQ) technology faces strict limitations on the algorithms that can be implemented efficiently. In quantum chemistry, the variational quantum eigensolver (VQE) algorithm has become ubiquitous, using the functional form of the ansatz as a degree of freedom, whose parameters are found variationally in a feedback loop between the quantum processor and its conventional counterpart. Alternatively, a promising new avenue has been unraveled by the quantum variants of techniques grounded on expansions of the moments of the Hamiltonian, among which two stand out: The connected moments expansion (CMX) [Phys. Rev. Lett. 58, 53 (1987)] and the Peeters-Devreese-Soldatov (PDS) functional [J. Phys. A 17, 625 (1984);Int. J. Mod. Phys. B 9, 2899], the latter based on the standard moments . Contrasting with VQE-based methods and provided the quantum circuit prepares a state with non-vanishing overlap with the true ground state, CMX often converges to the ground state energy, while PDS is guaranteed to converge by virtue of being variational. However, for a finite CMX/PDS order, the circuit may significantly impact the energy accuracy. Here we use the ADAPT-VQE algorithm to test shallow circuit construction strategies that are not expected to impede their implementation in the present quantum hardware while granting sizable accuracy improvement in the computed ground state energies. We also show that we can take advantage of the fact that the terms in the connected moments are highly recurring in different powers, incurring a sizable reduction in the number of necessary measurements. By coupling this measurement caching with a threshold that determines whether a given term is to be measured based on its associated scalar coefficient, we observe a further reduction in the number of circuit implementations while allowing for tunable accuracy. Copyright © 2021, The Authors. All rights reserved.

关键词： Quantum chemistry

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AN OPTIMAL PIECEWISE CUBIC NONCONFORMING FINITE ELEMENT SCHEME FOR THE PLANAR BIHARMONIC EQUATION ON GENERAL TRIANGULATIONS

arXiv

引用

arXiv 2019年

作者： Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

This paper presents a nonconforming finite element scheme for the planar biharmonic equation which applis piecewise cubic polynomials (P3) and possesses O(h2) convergence rate in energy norm on general shape-regular triangulations. Both Dirichlet and Navier type boundary value problems are studied. The basis for the scheme is a piecewise cubic polynomial space, which can approximate the H4 functions with O(h2) accuracy in broken H2 norm. Besides, an equivalence (∇2h ·, ∇2h ·) = (∆h ·, ∆h ·), which is usually not true for nonconforming finite element spaces, is proved on the newly designed spaces. The finite element space does not correspond to a finite element defined with Ciarlet’s triple;however, a set of locally supported basis functions of the finite element space is still figured out. The notion of the finite element Stokes complex plays an important role in the analysis and also the construction of the basis functions. Copyright © 2019, The Authors. All rights reserved.

关键词： Finite element method

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