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Faithful geometric measures for genuine tripartite entanglement

Physical Review A 2024年第1期110卷 L010402-L010402页

作者： Xiaozhen Ge Lijun Liu Yong Wang Yu Xiang Guofeng Zhang Li Li Shuming Cheng Department of Control Science and Engineering Department of Applied Mathematics The Department of Mathematics and Computer Science State Key Laboratory for Mesoscopic Physics School of Physics Frontiers Science Center for Nano-optoelectronics and Collaborative Innovation Center of Quantum Matter Shanghai Institute of Intelligent Science and Technology Institute for Advanced Study

We present a faithful geometric picture for genuine tripartite entanglement of discrete, continuous, and hybrid quantum systems. We first find that the triangle relation Ei|jkα≤Ej|ikα+Ek|ijα holds for all subadditive bipartite entanglement measure E, all permutations under parties i,j,k, all α∈[0,1], and all pure tripartite states. Then, we rigorously prove that the nonobtuse triangle area, enclosed by side Eα with 0<α≤1/2, is a measure for genuine tripartite entanglement. Finally, it is significantly strengthened for qubits that given a set of subadditive and nonsubadditive measures, some state is always found to violate the triangle relation for any α>1, and the triangle area is not a measure for any α>1/2. Our results pave the way to study discrete and continuous multipartite entanglement within a unified framework.

关键词： Entanglement measures Quantum correlations in quantum information Quantum correlations, foundations & formalism Resource theories

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Magnetic ordering of the Mo3O8-type cluster Mott insulator Na3Sc2(MoO4)2Mo3O8 with spin-1/2 triangular lattice prepared via optimal synthesis

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Physical Review Materials 2024年第8期8卷 084409-084409页

作者： Yuya Haraguchi Daigo Ishikita Hiroko Aruga Katori Department of Applied Physics and Chemical Engineering

We detail the optimized synthesis of the Mo3O8-type cluster Mott insulator (CMI) Na3Sc2(MoO4)2Mo3O8, which has been considered a candidate for realizing the spin liquid ground state. The optimized Na3Sc2(MoO4)2Mo3O8, characterized by x-ray diffraction, energy-dispersive x-ray spectroscopy, and magnetic and heat capacity measurements exhibited an effective magnetic moment close to the ideal 1.73 μB for S = 1/2 spin and magnetic ordering at ∼5 K. These observations categorize Na3Sc2(MoO4)2Mo3O8 as the second Mo3O8-type CMI to achieve a magnetic ground state, following Li2InMo3O8. They highlight the stabilization of the magnetic ground state over the theoretically anticipated quantum spin liquid state through precise valence and chemical disorder tuning. Our findings challenge the existing theory that the magnetic ground state of Mo3O8-type CMIs is determined by the breathing parameter, instead showing that magnetic order is suppressed by spin defects. This study underscores the crucial role of chemical precision in investigating quantum magnetism. It suggests that precise tuning of valence states could induce magnetic ordering in previously nonmagnetic Mo3O8-type CMIs. Additionally, the negative findings regarding the existence of quantum spin liquids highlight the need for applied research and a reevaluation of our fundamental understanding of electronic states from both theoretical and experimental aspects.

关键词： Magnetic order Quantum spin liquid Specific heat Mott insulators Triangular lattice Magnetization measurements

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Stable reproducibility of turbulence dynamics by machine learning

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Physical Review Fluids 2024年第10期9卷 104601页

作者： Satoshi Matsumoto Masanobu Inubushi Susumu Goto Graduate School of Engineering Science Department of Applied Mathematics Department of Applied Mathematics and Theoretical Physics

We investigate the stability and accuracy of a machine-learning-based turbulence closure model. To this end, we construct a turbulence closure model for a shell model, which is a toy model of turbulence, based on the inference of sub-grid scale (SGS) variables using a recurrent neural network, and conduct an extensive parameter survey of the constructed model. The model stably and accurately reproduces the statistics of grid-scale variables when the cutoff wave number κc is higher than 0.2η−1, where η denotes the Kolmogorov length. This is because in this case, SGS variables are subordinate to grid-scale ones. On the other hand, when κc is lower than 0.2η−1, the model becomes stochastically unstable. However, an appropriate regularization in the inference step of SGS variables realizes a sufficiently long lifetime of the model.

关键词： Turbulence Turbulence modeling Chaotic systems Machine learning

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Research on Multi-Scale Feature Fusion Network Algorithm Based on Brain Tumor Medical Image Classification

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Computers, Materials & Continua 2024年第6期79卷 5313-5333页

作者： Yuting Zhou Xuemei Yang Junping Yin Shiqi Liu Graduate School China Academy of Engineering PhysicsBeijing100000China Department of Computational Mathematics Beijing Institute of Applied Physics and Computational MathematicsBeijing100000China National Key Laboratory of Computational Physics Beijing100088China Shanghai Zhangjiang Institute of Mathematics Shanghai201203China

Gliomas have the highest mortality rate of all brain *** classifying the glioma risk period can help doctors make reasonable treatment plans and improve patients’survival *** paper proposes a hierarchical multi-scale attention feature fusion medical image classification network(HMAC-Net),which effectively combines global features and local *** network framework consists of three parallel layers:The global feature extraction layer,the local feature extraction layer,and the multi-scale feature fusion layer.A linear sparse attention mechanism is designed in the global feature extraction layer to reduce information *** the local feature extraction layer,a bilateral local attention mechanism is introduced to improve the extraction of relevant information between adjacent *** the multi-scale feature fusion layer,a channel fusion block combining convolutional attention mechanism and residual inverse multi-layer perceptron is proposed to prevent gradient disappearance and network degradation and improve feature representation *** double-branch iterative multi-scale classification block is used to improve the classification *** the brain glioma risk grading dataset,the results of the ablation experiment and comparison experiment show that the proposed HMAC-Net has the best performance in both qualitative analysis of heat maps and quantitative analysis of evaluation *** the dataset of skin cancer classification,the generalization experiment results show that the proposed HMAC-Net has a good generalization effect.

关键词： Medical image classification feature fusion transformer

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Strain-induced band-gap widening in (100) β−Ga2O3 thin films grown on θ−Al2O3 buffer layers

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Physical Review Materials 2025年第3期9卷 L031601-L031601页

作者： Kazuki Koreishi Takeyoshi Onuma Takuto Soma Akira Ohtomo Department of Chemical Science and Engineering Institute of Science Tokyo 2-12-1 Ookayama Meguro Tokyo 152-8552 Japan Department of Applied Physics Kogakuin University 2665-1 Nakano Hachioji Tokyo 192-0015 Japan

We report on the impact of compressive strain on (100)-oriented β−Ga2O3 epitaxial thin films grown on partially strain-relaxed monoclinic θ−Al2O3 buffer layers by oxygen-radical-assisted pulsed-laser deposition. Reflection high-energy electron diffraction was used to monitor the in-plane lattice spacing during the deposition. This observation revealed that the tensile strain in the θ−Al2O3 buffer layer on the (100) β−Ga2O3 substrate gradually relaxed by the formation of misfit dislocations, whereas the β−Ga2O3 epilayer adapted the lattice spacing of the θ−Al2O3 buffer layer up to −3% lattice mismatch along the b-axis direction. The widening of the band gap of β−Ga2O3 with increasing compressive strain was observed from both reflection electron energy-loss spectroscopy and polarized optical reflectance measurements. Experimental results are supported by results from density functional theory calculations.

关键词： Energy gap

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A Bregman-Style Improved ADMM and its Linearized Version in the Nonconvex Setting:Convergence and Rate Analyses

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Journal of the Operations Research Society of China 2024年第2期12卷 298-340页

作者： Peng-Jie Liu Jin-Bao Jian Hu Shao Xiao-Quan Wang Jia-Wei Xu Xiao-Yu Wu School of Mathematics Jiangsu Center for Applied MathematicsChina University of Mining and TechnologyXuzhou 221116JiangsuChina School of Mathematics and Physics Center for Applied Mathematics of GuangxiGuangxi Minzu UniversityNanning 530006GuangxiChina Department of Civil and Environmental Engineering The Hong Kong Polytechnic UniversityHong KongChina School of Mathematics and Computational Science Xiangtan UniversityXiangtan 411105HunanChina

This work explores a family of two-block nonconvex optimization problems subject to linear *** first introduce a simple but universal Bregman-style improved alternating direction method of multipliers(ADMM)based on the iteration framework of ADMM and the Bregman ***,we utilize the smooth performance of one of the components to develop a linearized version of *** to the traditional ADMM,both proposed methods integrate a convex combination strategy into the multiplier update *** each proposed method,we demonstrate the convergence of the entire iteration sequence to a unique critical point of the augmented Lagrangian function utilizing the powerful Kurdyka–Łojasiewicz property,and we also derive convergence rates for both the sequence of merit function values and the iteration ***,some numerical results show that the proposed methods are effective and encouraging for the Lasso model.

关键词： Nonconvex optimization Alternating direction method of multipliers Kurdyka-Lojasiewicz property Convergence rate

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Optical Solitons for the Dispersive Concatenation Model with Differential Group Delay

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Nonlinear Optics Quantum Optics 2025年第1-2期61卷 71-97页

作者： Arnous, Ahmed H. Biswas, Anjan Yildirim, Yakup Alshomrani, Ali Saleh Department of Physics and Engineering Mathematics Higher Institute of Engineering El–Shorouk Academy Cairo Egypt Department of Mathematics and Physics Grambling State University GramblingLA71245–2715 United States Department of Mathematics King Abdulaziz University Jeddah21589 Saudi Arabia Department of Applied Sciences Cross–Border Faculty of Humanities Economics and Engineering Dunarea de Jos University of Galati 111 Domneasca Street Galati800201 Romania Department of Mathematics and Applied Mathematics Sefako Makgatho Health Sciences University Medunsa 0204 South Africa Department of Computer Engineering Biruni University Istanbul34010 Turkey Mathematics Research Center Near East University Nicosia99138 Cyprus Faculty of Arts and Sciences University of Kyrenia Kyrenia99320 Cyprus

This paper retrieves optical soliton solutions to the dispersive concatenation model with differential group delay that is with Kerr law of nonlinearity. The enhanced direct algebraic method has made this recovery possible. A full spectrum of optical solitons are presented. The intermediary functions that framed the pathway to the soliton solutions are Weierstrass’ elliptic functions and Jacobi’s elliptic functions. The parameter constraints that guarantees the existence of such solitons are also presented. ©2025 Old City Publishing, Inc.

关键词： Group delay

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Theoretical Prediction of Superconductivity in Boron Kagome Monolayer:MB3(M=Be,Ca,Sr)and the Hydrogenated CaB3

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Chinese physics Letters 2023年第1期40卷 53-59页

作者：杨柳李牙平刘浩东焦娜倪美燕路洪艳张平 C.S.Ting School of Physics and Physical Engineering Qufu Normal UniversityQufu 273165China Institute of Applied Physics and Computational Mathematics Beijing 100088China Texas Center for Superconductivity and Department of Physics University of HoustonHoustonTexas 77204USA

Using first-principles calculations, we predict a new type of two-dimensional(2D) boride MB3(M = Be,Ca, Sr), constituted by boron kagome monolayer and the metal atoms adsorbed above the center of the boron hexagons. The band structures show that the three MB3compounds are metallic, thus the possible phononmediated superconductivity is explored. Based on the Eliashberg equation, for BeB3, CaB3, and SrB3, the calculated electron–phonon coupling constants λ are 0.46, 1.09, and 1.33, and the corresponding superconducting transition temperatures Tc are 3.2, 22.4, and 20.9 K, respectively. To explore superconductivity with higher transition temperature, hydrogenation and charge doping are further considered. The hydrogenated CaB3, i.e.,HCaB3, is stable, with the enhanced λ of 1.39 and a higher Tc of 39.3 K. Moreover, with further hole doping at the concentration of 5.8 × 1011hole/cm2, the Tc of HCaB3can be further increased to 44.2 K, exceeding the Mc Millan limit. The predicted MB3and HCaB3provide new platforms for investigating 2D superconductivity in boron kagome lattice since superconductivity based on monolayer boron kagome lattice has not been studied before.

关键词： boron doping superconductivity

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Machine learning for the identification of phase transitions in interacting agent-based systems: A Desai-Zwanzig example

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Physical Review E 2024年第1期110卷 014121-014121页

作者： Nikolaos Evangelou Dimitris G. Giovanis George A. Kevrekidis Grigorios A. Pavliotis Ioannis G. Kevrekidis Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Department of Civil and Systems Engineering Department of Mathematics

Deriving closed-form analytical expressions for reduced-order models, and judiciously choosing the closures leading to them, has long been the strategy of choice for studying phase- and noise-induced transitions for agent-based models (ABMs). In this paper, we propose a data-driven framework that pinpoints phase transitions for an ABM—the Desai-Zwanzig model—in its mean-field limit, using a smaller number of variables than traditional closed-form models. To this end, we use the manifold learning algorithm Diffusion Maps to identify a parsimonious set of data-driven latent variables, and we show that they are in one-to-one correspondence with the expected theoretical order parameter of the ABM. We then utilize a deep learning framework to obtain a conformal reparametrization of the data-driven coordinates that facilitates, in our example, the identification of a single parameter-dependent ordinary differential equation (ODE) in these coordinates. We identify this ODE through a residual neural network inspired by a numerical integration scheme (forward Euler). We then use the identified ODE—enabled through an odd symmetry transformation—to construct the bifurcation diagram exhibiting the phase transition.

关键词： Bifurcations Collective dynamics Dynamical systems High dimensional systems Multiple time scale dynamics Data mining Machine learning

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Curl Constraint-Preserving Reconstruction and the Guidance it Gives for Mimetic Scheme Design

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Communications on applied mathematics and Computation 2023年第1期5卷 235-294页

作者： Dinshaw S.Balsara Roger Käppeli Walter Boscheri Michael Dumbser Physics and ACMS Departments University of Notre DameNotre DameINUSA Seminar for Applied Mathematics(SAM) Department of MathematicsETH ZürichCH-8092 ZurichSwitzerland Department of Mathematics and Computer Science University of FerraraFerraraItaly Laboratory of Applied Mathematics Department of CivilEnvironmental and Mechanical EngineeringUniversity of TrentoTrentoItaly

Several important PDE systems,like magnetohydrodynamics and computational electrodynamics,are known to support involutions where the divergence of a vector field evolves in divergence-free or divergence constraint-preserving ***,new classes of PDE systems have emerged for hyperelasticity,compressible multiphase flows,so-called firstorder reductions of the Einstein field equations,or a novel first-order hyperbolic reformulation of Schrödinger’s equation,to name a few,where the involution in the PDE supports curl-free or curl constraint-preserving evolution of a vector *** study the problem of curl constraint-preserving reconstruction as it pertains to the design of mimetic finite volume(FV)WENO-like schemes for PDEs that support a curl-preserving involution.(Some insights into discontinuous Galerkin(DG)schemes are also drawn,though that is not the prime focus of this paper.)This is done for two-and three-dimensional structured mesh problems where we deliver closed form expressions for the *** importance of multidimensional Riemann solvers in facilitating the design of such schemes is also *** two dimensions,a von Neumann analysis of structure-preserving WENOlike schemes that mimetically satisfy the curl constraints,is also *** shows the tremendous value of higher order WENO-like schemes in minimizing dissipation and dispersion for this class of *** results are also presented to show that the edge-centered curl-preserving(ECCP)schemes meet their design *** paper is the first paper that invents non-linearly hybridized curl-preserving reconstruction and integrates it with higher order Godunov *** its very design,this paper is,therefore,intended to be forward-looking and to set the stage for future work on curl involution-constrained PDEs.

关键词： PDEs Numerical schemes Mimetic

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