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17th European Signal Processing Conference, EUSIPCO 2009

作者： Jafarpour, Sina Polatkan, Güngör Brevdo, Eugene Hughes, Shannon Brasoveanu, Andrei Daubechies, Ingrid Princeton University Departments of Electrical Engineering Computer Science and Mathematics Program in Applied and Computational Mathematics Princeton NJ 08544 United States

Wavelet transforms and machine learning tools can be used to assist art experts in the stylistic analysis of paintings. A dual-tree complex wavelet transform, Hidden Markov Tree modeling and Random Forest classifiers are used here for a stylistic analysis of Vincent van Gogh's paintings with results on two stylometry challenges that concern "dating, resp. extracting distinguishing features". © EURASIP, 2009.

关键词： Decision trees

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Anomalous suppression of large-scale density fluctuations in classical and quantum spin liquids

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arXiv 2025年

作者： Chen, Duyu Samajdar, Rhine Jiao, Yang Torquato, Salvatore Materials Research Laboratory University of California Santa BarbaraCA93106 United States Department of Physics Princeton University PrincetonNJ08544 United States Princeton Center for Theoretical Science Princeton University PrincetonNJ08544 United States Materials Science and Engineering Arizona State University TempeAZ85287 United States Department of Physics Arizona State University TempeAZ85287 United States Department of Chemistry Princeton University PrincetonNJ08544 United States Princeton Materials Institute Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics PrincetonNJ08544 United States

Classical spin liquids (CSLs) are intriguing states of matter that do not exhibit long-range magnetic order and are characterized by an extensive ground-state degeneracy. Adding quantum fluctuations, which induce dynamics between these different classical ground states, can give rise to quantum spin liquids (QSLs). QSLs are highly entangled quantum phases of matter characterized by fascinating emergent properties, such as fractionalized excitations and topological order. One such exotic quantum liquid is the Z2 QSL, which can be regarded as a resonating valence bond (RVB) state formed from superpositions of dimer coverings of an underlying lattice. In this work, we unveil a hidden large-scale structural property of archetypal CSLs and QSLs known as hyperuniformity, i.e., normalized infinite-wavelength density fluctuations are completely suppressed in these systems. In particular, we first demonstrate that classical ensembles of close-packed dimers and their corresponding quantum RVB states are perfectly hyperuniform in general. Subsequently, we focus on a ruby-lattice spin liquid that was recently realized in a Rydberg-atom quantum simulator, and show that the QSL remains effectively hyperuniform even in the presence of a finite density of spinon and vison excitations, as long as the dimer constraint is still largely preserved. Moreover, we demonstrate that metrics based on the framework of hyperuniformity can be used to distinguish the QSL from other proximate quantum phases. These metrics can help identify potential QSL candidates, which can then be further analyzed using more advanced, computationally-intensive quantum numerics to confirm their status as true QSLs. © 2025, CC BY-NC-ND.

关键词： Quantum entanglement

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Majorana's stellar representation for the quantum geometric tensor of symmetric states

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Communications in Theoretical Physics 2022年第6期74卷 31-38页

作者： Xingyu Zhang Jiancheng Pei Libin Fu Xiaoguang Wang Zhejiang Institute of Modern Physics Department of PhysicsZhejiang UniversityHangzhou 310027China National Laboratory of Science and Technology on Computational Physics Institute of Applied Physics and Computational MathematicsBeijing 100088China Graduate School of China Academy of Engineering Physics Beijing 100193China

Majorana's stellar representation provides an intuitive picture in which quantum states in highdimensional Hilbert space can be observed using the trajectory of Majorana *** consider the Majorana's stellar representation of the quantum geometric tensor for a spin state up to spin-3/*** real and imaginary parts of the quantum geometric tensor,corresponding to the quantum metric tensor and Berry curvature,are therefore obtained in terms of the Majorana ***,we work out the expressions of quantum geometric tensor for arbitrary spin in some important *** results will benefit the comprehension of the quantum geometric tensor and provide interesting relations between the quantum geometric tensor and Majorana's stars.

关键词： quantum geometric tensor Berry curvature quantum metric tensor Majorana's stellar representation

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NUMERICAL STUDY OF A 2-POINT CORRELATION-FUNCTION AND LIOUVILLE FIELD PROPERTIES IN 2-DIMENSIONAL QUANTUM-GRAVITY

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MODERN PHYSICS LETTERS A 1991年第12期6卷 1115-1131页

作者： AGISHTEIN, ME BENAV, R MIGDAL, AA SOLOMON, S Program in Applied and Computational Mathematics Fine Hall Princeton University Princeton NJ 08544–1000 USA Nuclear Physics Department Weizmann Institute of Science Rehovot 76100 Israel Physics Department and Program in Applied and Computational Mathematics Fine Hall Princeton University Princeton NJ 08544–1000 USA Physics Department Hebrew University Jerusalem Israel

Two-point Green's function is measured on the manifolds of a 2-dimensional quantum gravity. The recursive sampling technique is used to generate the triangulations, lattice sizes being up to hundred thousand triangles. The grid Laplacian was inverted by means of the algebraic multi-grid solver. The free field model of the Quantum Gravity assumes the Gaussian behavior of Liouville field and curvature. We measured histograms as well as six momenta of these fields. Our results support the Gaussian assumption.

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Motor cortex repetitive transcranial magnetic stimulation in fibromyalgia: a multicentre randomised controlled trial

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British Journal of Anaesthesia 2025年第6期134卷 1756-1764页

作者： Silva, Valquíria A. Baptista, Abrahão F. Fonseca, Alessandra S. Carneiro, Adriana M. Brunoni, André R. Carrilho, Paulo.E.M. Lins, Catarina C. Kubota, Gabriel T. Fernandes, Ana Mércia B.L. Lapa, Jorge.D.S. dos Santos, Lucas M. Sasso, Ivo Monte-Silva, Katia Poindessous-Jazat, Frédérique Mori, Nobuhiko Miki, Kenji Baltar, Adriana Tanaka, Clarice Teixeira, Manoel J. Hosomi, Koichi Bouhassira, Didier Attal, Nadine Ciampi de Andrade, Daniel LIM 62 - Pain Center Department of Neurology São Paulo Brazil Service of Interdisciplinary Neuromodulation (SIN) Department and Institute of Psychiatry São Paulo Brazil Medical-Surgical Nursing Department University of São Paulo São Paulo Brazil Center for Mathematics Computation and Cognition Federal University of ABC São Paulo Brazil Mood Disorder Program (Pro-GRUDA) Department of Psychiatry University of São Paulo São Paulo Brazil Medicine School “Professor Orival Alves” State University of Western Paraná (UNIOESTE) Paraná Brazil Neurosurgery Unit Hospital de Cirurgia Sergipe Aracaju Brazil Department of Medicine Federal University of Sergipe Sergipe São Cristóvão Brazil LIM 54 - Physiotherapy Research Laboratory University of São Paulo São Paulo Brazil Applied Neuroscience Laboratory Universidade Federal de Pernambuco Cidade Universitária Pernambuco Brazil UVSQ-Paris-Saclay University Ambroise Paré Hospital Boulogne-Billancourt U987 France Department of Neurosurgery Osaka University Graduate School of Medicine Osaka Japan Faculty of Health Science Osaka Yukioka College of Health Science Osaka Japan Center for Pain Management Hayaishi Hospital Osaka Japan Center for Neuroplasticity and Pain (CNAP) Department of Health Science and Technology University of Aalborg Gistrup Denmark

Background: Despite affecting 2–4% of the population worldwide, fibromyalgia often remains refractory to treatment. Here we report the first international randomised double-blind, sham-controlled trial developed to assess the efficacy of repetitive transcranial magnetic stimulation (rTMS) as an add-on therapy for fibromyalgia. Methods: Women aged ≥18 yr with fibromyalgia refractory to best available treatment were enrolled in Brazil, France, and Japan, and randomised to 10 Hz motor cortex (M1) rTMS, 3000 pulses day⁻¹, or sham stimulation. This included 10 induction sessions over 2 weeks, followed by weekly maintenance (6 weeks), and fortnightly extended maintenance (8 weeks). Primary outcome was ≥50% pain reduction at week 8 compared with baseline. Secondary outcomes included pain interference, mood, global impression of change, and Fibromyalgia Impact Questionnaire (FIQ) scores at weeks 8 and 16. Results: We randomised 101 women (mean age 48 [range 25-83] yr) into active (n=52) or sham (n=49) arms. Bayesian analysis revealed a 99.4% probability of ≥50% pain reduction at week 8 in the active group vs sham (odds ratio [OR] 3.04;95% credible interval [95% CrI] 1.26–8.06), with a number needed to treat of 4.54. Frequentist analysis confirmed that relative pain reduction was higher in the active than in the sham group (40.4% vs 18.4%, P=0.028). At week 16, this probability reduced to 34.2% (OR 0.815;95% CrI 0.313–2.1), but the likelihood of FIQ score reduction was 79.1%. The intervention appeared safe. Conclusions: Add-on M1-repetitive transcranial magnetic stimulation reduced pain intensity up to 8 weeks in women with fibromyalgia. Although analgesic effects waned, functional improvements remained during extended maintenance at week 16. © 2025 The Authors

关键词： chronic pain clinical trial fibromyalgia neuromodulation transcranial magnetic stimulation

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Quadratic Finite Volume Element Schemes over Triangular Meshes for a Nonlinear Time-Fractional Rayleigh-Stokes Problem

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Computer Modeling in Engineering & sciences 2021年第5期127卷 487-514页

作者： Yanlong Zhang Yanhui Zhou Jiming Wu Graduate School of China Academy of Engineering Physics Beijing100088China School of Data and Computer Science Sun Yat-Sen UniversityGuangzhou510275China Institute of Applied Physics and Computational Mathematics Beijing100088China

In this article,we study a 2D nonlinear time-fractional Rayleigh-Stokes problem,which has an anomalous subdiffusion term,on triangular meshes by quadratic finite volume element ***-fractional derivative,defined by Caputo fractional derivative,is discretized through L2−1σformula,and a two step scheme is used to approximate the time first-order derivative at time tn−α/2,where the nonlinear term is approximated by using a matching linearized difference scheme.A family of quadratic finite volume element schemes with two parameters are proposed for the spatial discretization,where the range of values for two parameters areβ1∈(0,1/2),β2∈(0,2/3).For testing the precision of numerical algorithms,we calculate some numerical examples which have known exact solution or unknown exact solution by several kinds of quadratic finite volume element schemes,and contrast with the results of an existing quadratic finite element scheme by drawing diversified comparison plots and showing the detailed data of L2 error results and convergence *** results indicate that,L2 error estimate of one scheme with parameters β_(1)=(3−√3)/6,β2=(6+√3−√21+6√3)/9 is O(h^(3)+△t^(2)),and L^(2) error estimates of other schemes are O(h^(2)+△t^(2)),where h and △t denote the spatial and temporal discretization parameters,respectively.

关键词： Quadratic finite volume element schemes anomalous sub-diffusion term L2 error estimate quadratic finite element scheme

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STOCHASTIC CONTROLLED AVERAGING FOR FEDERATED LEARNING WITH COMMUNICATION COMPRESSION 12

STOCHASTIC CONTROLLED AVERAGING FOR FEDERATED LEARNING WITH ...

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12th International Conference on Learning Representations, ICLR 2024

作者： Huang, Xinmeng Li, Ping Li, Xiaoyun LinkedIn BellevueWA98004 United States The Graduate Group of Applied Mathematics and Computational Science The University of Pennsylvania United States

Communication compression has been an important topic in Federated Learning (FL) for alleviating the communication overhead. However, communication compression brings forth new challenges in FL due to the interplay of compression-incurred information distortion and inherent characteristics of FL such as partial participation and data heterogeneity. Despite the recent development, the existing approaches either cannot accommodate arbitrary data heterogeneity or partial participation, or require stringent conditions on compression. In this paper, we revisit the seminal stochastic controlled averaging method by proposing an equivalent but more efficient/simplified formulation with halved uplink communication costs, building upon which we propose two compressed FL algorithms, SCALLION and SCAFCOM, to support unbiased and biased compression, respectively. Both the proposed methods outperform the existing compressed FL methods in terms of communication and computation complexities. Moreover, SCALLION and SCAFCOM attain fast convergence rates under arbitrary data heterogeneity without any additional assumptions on compression errors. Experiments show that SCALLION and SCAFCOM outperform recent compressed FL methods under the same communication budget. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Stochastic systems

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On Local Wellposedness of the Schrodinger-Boussinesq System

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Journal of Partial Differential Equations 2022年第4期35卷 360-381页

作者： SHAO Jjie GUO Boling Department of Mathematics Nanjing University of Science and TechnologyNanjing210094China Institute of Applied Physics and Computational Mathematics Beijing 100088China The Graduate School of China Academy of Engineering Physics Beijing 100088China

In this paper we prove that the Schrodinger-Boussinesq system with solution(u,v,(-∂xx)-^(2/1)vt)is locally wellposed in H^(s)×H^(s)×Hs^(-1),s≥-1/*** local wellposedness is obtained by the transformation from the problem into a nonlinear Schrodinger type equation system and the contraction mapping theorem in a suitably modified Bourgain type space inspired by the work of Kishimoto,*** result improves the known local wellposedness in H^(s)×H^(s)×H^(s-1),s>-1/4 given by Farah.

关键词： Schrodinger-Boussinesq system Cauchy problem local wellposedness low regularity.

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ANALYSIS ON A NUMERICAL SCHEME WITH SECOND-ORDER TIME ACCURACY FOR NONLINEAR DIFFUSION EQUATIONS

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Journal of computational mathematics 2021年第5期39卷 777-800页

作者： Xia Cui Guangwei Yuan Fei Zhao Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsP.O.Box 8009-26Beijing 100088China College of Science North China University of TechnologyBeijing 1OO144China Graduate School of China Academy of Engineering Physics Beijing 100088China

A nonlinear fully implicit finite difference scheme with second-order time evolution for nonlinear diffusion problem is *** scheme is constructed with two-layer coupled discretization(TLCD)at each time *** does not stir numerical oscillation,while permits large time step length,and produces more accurate numerical solutions than the other two well-known second-order time evolution nonlinear schemes,the Crank-Nicolson(CN)scheme and the backward difference formula second-order(BDF2)*** developing a new reasoning technique,we overcome the difficulties caused by the coupled nonlinear discrete diffusion operators at different time layers,and prove rigorously the TLCD scheme is uniquely solvable,unconditionally stable,and has second-order convergence in both s-pace and *** tests verify the theoretical results,and illustrate its superiority over the CN and BDF2 schemes.

关键词： Nonlinear diffusion problem Nonlinear two-layer coupled discrete scheme Second-order time accuracy Property analysis Unique existence Convergence

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GAUGE METHOD FOR VISCOUS INCOMPRESSIBLE FLOWS

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Communications in Mathematical sciences 2003年第2期1卷 317-332页

作者： Weinan, E. Liu, Jian-Guo Department of Mathematics and Program in Applied and Computational Mathematics Princeton University Princeton 08544 NJ United States Institute for Physical Science and Technology and Department of Mathematics University of Maryland College Park 20742 MD United States

We present a new formulation of the incompressible Navier-Stokes equation in terms of an auxiliary field that differs from the velocity by a gauge transformation. The gauge freedom allows us to assign simple and specific boundary conditions for both the auxiliary field and the gauge field, thus eliminating the issue of pressure boundary condition in the usual primitive variable formulation. The resulting dynamic and kinematic equations can then be solved by standard methods for heat and Poisson equations. A normal mode analysis suggests that in contrast to the classical projection method, the gauge method does not suffer from the problem of numerical boundary layers. Thus the subtleties in the spatial discretization for the projection method are removed. Consequently, the projection step in the gauge method can be accomplished by standard Poisson solves. We demonstrate the efficiency and accuracy of the gauge method by several numerical examples, including the flow past cylinder © 2003 International Press

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