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Practical approach for detecting k-nonseparability of multipartite quantum states

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science China(Physics,Mechanics & Astronomy) 2025年第1期Mechanics & Astronomy) .卷 32-48页

作者： Jie Guo Jinchuan Hou Xiaofei Qi Kan He College of mathematics Taiyuan University of Technology school of mathematics and statistics Shanxi University Key Laboratory of Complex Systems and Data science of Ministry of Education Shanxi University

The instantaneous detection of entanglement in quantum states poses a significant challenge in the fields of quantum computation and quantum information, and there are no practical methods or tools to complete this task satisfactorily so far. We propose a sufficient and necessary criterion of k-nonseparability for any n-partite finite or infinite dimensional systems, 2 ≤ k ≤ n. This criterion serves as the foundation for a practical scheme designed to detect entanglement and k-nonseparability across multipartite finite-dimensional systems. To exemplify the application of our scheme, we have developed a software tool that facilitates swift and precise identification of entanglement, k-nonseparability, and genuine entanglement within n-qubit systems, specifically tailored for systems with 2 ≤ n ≤ 4.

关键词： multipartite systems entanglement states entanglement witnesses ${\bm~k}$-nonseparability

Dynamic behaviors of graphene platelets-reinforced metal foam piezoelectric beams with velocity feedback control

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Applied mathematics and Mechanics(English Edition) 2025年第1期46卷 63-80页

作者： Jie CHEN Xinyue ZHANG Mingyang FAN school of mathematics Statistics and Mechanics Beijing University of Technology College of Mechanical & Energy Engineering Beijing University of Technology

Graphene platelets(GPLs)-reinforced metal foam structures enhance the mechanical properties while maintaining the lightweight characteristics of metal foams. Further bonding piezoelectric actuator and sensor layers on the surfaces of GPLs-reinforced metal foam beams enables active vibration control, greatly expanding their applications in the aerospace industry. For the first time, this paper investigates the vibration characteristics and active vibration control of GPLs-reinforced metal foam beams with surfacebonded piezoelectric layers. The constant velocity feedback scheme is used to design the closed-loop controller including piezoelectric actuators and sensors. The effects of the GPLs on the linear and nonlinear free vibrations of the beams are numerically *** Newmark-β method combined with Newton's iteration technique is used to calculate the nonlinear responses of the beams under different load forms including harmonic loads,impact loads, and moving loads. Additionally, special attention is given to the vibration reduction performance of the velocity feedback control on the responses of the beam.

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Distinct MLT asymmetry of auroral kilometric radiation observed by the FAST satellite

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Earth and Planetary Physics 2025年第1期9卷 188-193页

作者： JiaWen Tang Sai Zhang FuLiang Xiao HongMing Yang Si Liu YiHua He Chang Yang YuYue Jin ZhouKun Deng Ping Li Archie James Johnston school of Physics and Electronic sciences Changsha University of Science and TechnologyChangsha 410114China Hunan Province Higher Education Key Laboratory of Modeling and Monitoring on the Near-Earth Electromagnetic Environments Changsha University of Science and TechnologyChangsha 410114China school of Electrical and Information Engineering Changsha University of Science and TechnologyChangsha 410114China

Auroral Kilometric Radiation(AKR)is a common radio emission,which can contribute to the magnetosphere−ionosphere−atmosphere *** emissions have been observed in all magnetic planet magnetospheres of the solar *** this study,using observations from the FAST satellite from 30 August 1996 to 9 September 2001,the distribution of AKR in altitude=500−4500 km and invariant latitude(|ILAT|)=60°−80°has been analyzed.63045 AKR samples have been identified with~48%(52%)samples on the dayside(nightside).Of considerable interest,there is a distinct MLT asymmetry with the high occurrence rate in MLT=05−08 and 18−22(02−05 and 12−17)in the northern(southern)*** distinct MLT asymmetry is associated with the direction of Bxof the interplanetary magnetic *** addition,the occurrence rate on the nightside clearly increases as the index *** study further enriches *** and understanding of AKR in the magnetosphere as well as other similar radio emissions.

关键词： asymmetry auroral kilometric radiation interplanetary magnetic field

Single-cell omics: experimental workflow, data analyses and applications

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science China Life sciences 2025年第1期68卷 5-102页

作者： Fengying Sun Haoyan Li Dongqing Sun Shaliu Fu Lei Gu Xin Shao Qinqin Wang Xin Dong Bin Duan Feiyang Xing Jun Wu Minmin Xiao Fangqing Zhao Jing-Dong J.Han Qi Liu Xiaohui Fan Chen Li Chenfei Wang Tieliu Shi Department of Clinical Laboratory the Affiliated Wuhu Hospital of East China Normal University (The Second People's Hospital of Wuhu City) Pharmaceutical Informatics Institute College of Pharmaceutical SciencesZhejiang University Key Laboratory of Spine and Spinal Cord Injury Repair and Regeneration (Tongji university) Ministry of EducationOrthopaedic DepartmentTongji HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Frontier science Center for Stem Cells School of Life Sciences and TechnologyTongji University Translational Medical Center for Stem Cell Therapy and Institute for Regenerative Medicine Shanghai East HospitalBioinformatics DepartmentSchool of Life Sciences and TechnologyTongji University Research Institute of Intelligent Computing Zhejiang Lab Shanghai Research Institute for Intelligent Autonomous Systems Center for Single-cell Omics School of Public HealthShanghai Jiao Tong University School of Medicine National Key Laboratory of Chinese Medicine Modernization Innovation Center of Yangtze River DeltaZhejiang University Center for Bioinformatics and Computational Biology Shanghai Key Laboratory of Regulatory Biologythe Institute of Biomedical Sciences and School of Life SciencesEast China Normal University Beijing Institutes of Life science Chinese Academy of Sciences Peking-Tsinghua Center for Life sciences Academy for Advanced Interdisciplinary StudiesCenter for Quantitative Biology (CQB)Peking University Zhejiang Key Laboratory of Precision Diagnosis and Therapy for Major Gynecological Diseases Women's HospitalZhejiang University School of Medicine Key Laboratory of Advanced Theory and Application in statistics and Data science-MOE School of StatisticsEast China Normal University

Cells are the fundamental units of biological systems and exhibit unique development trajectories and molecular features. Our exploration of how the genomes orchestrate the formation and maintenance of each cell, and control the cellular phenotypes of various organismsis, is both captivating and intricate. Since the inception of the first single-cell RNA technology, technologies related to single-cell sequencing have experienced rapid advancements in recent years. These technologies have expanded horizontally to include single-cell genome, epigenome,proteome, and metabolome, while vertically, they have progressed to integrate multiple omics data and incorporate additional information such as spatial sc RNA-seq and CRISPR screening. Single-cell omics represent a groundbreaking advancement in the biomedical field,offering profound insights into the understanding of complex diseases, including cancers. Here, we comprehensively summarize recent advances in single-cell omics technologies, with a specific focus on the methodology section. This overview aims to guide researchers in selecting appropriate methods for single-cell sequencing and related data analysis.

关键词： single-cell sequencing genome epigenome proteomics metabolomics multimodal spatial transcriptomics CRISPR screening

Solar flare forecasting based on a Fusion Model

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Earth and Planetary Physics 2025年第1期9卷 171-181页

作者： YiYang Li ShiYong Huang SiBo Xu ZhiGang Yuan Kui Jiang QiYang Xiong RenTong Lin school of Earth and Space science technology Hubei Luojia LaboratoryWuhan UniversityWuhan 430072China

Solar flare prediction is an important subject in the field of space *** learning technology has greatly promoted the development of this *** this study,we propose a novel solar flare forecasting model integrating Deep Residual Network(ResNet)and Support Vector Machine(SVM)for both≥C-class(C,M,and X classes)and≥M-class(M and X classes)*** collected samples of magnetograms from May 1,2010 to September 13,2018 from Space-weather Helioseismic and Magnetic Imager(HMI)Active Region Patches and then used a cross-validation method to obtain seven independent data *** then utilized five metrics to evaluate our fusion model,based on intermediate-output extracted by ResNet and SVM using the Gaussian kernel *** results show that the primary metric true skill statistics(TSS)achieves a value of 0.708±0.027 for≥C-class prediction,and of 0.758±0.042 for≥M-class prediction;these values indicate that our approach performs significantly better than those of previous *** metrics of our fusion model’s performance on the seven datasets indicate that the model is quite stable and robust,suggesting that fusion models that integrate an excellent baseline network with SVM can achieve improved performance in solar flare ***,we also discuss the performance impact of architectural innovation in our fusion model.

关键词： solar flare pace weather deep learning Fusion Model

A Decoupling-Type Strategy for the Allen-Cahn Equation on Curved Surfaces

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Journal of Mathematical Research with Applications 2025年第1期 73-83页

作者： Xiaoman XIE Qing PAN school of Computer and Communication Engineering Changsha University of Science & Technology

In this paper, we construct an efficient decoupling-type strategy for solving the Allen-Cahn equation on curved surfaces. It is based on an FEM-EIEQ(Finite Element Method and explicit-Invariant Energy Quadratization) fully discrete scheme with unconditional energy stability. Spatially the FEM is adopted, using a triangular mesh discretization strategy that can be adapted to complex regions. Temporally, the EIEQ approach is considered, which not only linearizes the nonlinear potential but also gives a new variable that we combine with the nonlocal splitting method to achieve the fully decoupled computation. The strategy can successfully transform the Allen-Cahn system into some completely independent algebraic equations and linear elliptic equations with constant coefficients, we only need to solve these simple equations at each time step. Moreover, we conducted some numerical experiments to demonstrate the effectiveness of the strategy.

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CENTRAL LIMIT THEOREM AND CONVERGENCE RATES FOR A SUPERCRITICAL BRANCHING PROCESS WITH IMMIGRATION IN A RANDOM ENVIRONMENT

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Acta Mathematica Scientia 2022年第3期42卷 957-974页

作者： Yingqiu LI Xulan HUANG Zhaohui PENG Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering School of Mathematics and StatisticsChangsha University of Science and TechnologyChangsha 410004China school of mathematics and statistics Changsha University of Science and TechnologyChangsha 410004China

We are interested in the convergence rates of the submartingale Wn=Z_(n)/Π_(n)to its limit W,where(Π_(n))is the usually used norming sequence and(Z_(n))is a supercritical branching process with immigration(Y_(n))in a stationary and ergodic environmentξ.Under suitable conditions,we establish the following central limit theorems and results about the rates of convergence in probability or in law:(i)W-W_(n) with suitable normalization converges to the normal law N(0,1),and similar results also hold for W_(n+k)-W_(n) for each fixed k∈N^(*);(ii)for a branching process with immigration in a finite state random environment,if W_(1) has a finite exponential moment,then so does W,and the decay rate of P(|W-W_(n)|>ε)is supergeometric;(iii)there are normalizing constants an(ξ)(that we calculate explicitly)such that a_(n)(ξ)(W-W_(n))converges in law to a mixture of the Gaussian law.

关键词： Branching process with immigration random environment convergence rates central limit theorem convergence in law convergence in probability

Stabilities of delay stochastic McKean-Vlasov equations in the G-framework

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science China(Information sciences) 2025年第1期 255-277页

作者： Haiyan YUAN Quanxin ZHU Department of mathematics Heilongjiang Institute of Technology Key Laboratory of Computing and Stochastic mathematics (Ministry of Education) School of Mathematics and Statistics Hunan Normal University

This article focuses on a type of stochastic Mc Kean-Vlasov equation in the G-framework(G-SMVE) and addresses the stability issue for delay stochastic Mc Kean-Vlasov equations in the G-framework(G-SMVDEs). Distribution dependence and uncertainty prevent us from directly applying the stochastic analysis method for stochastic Mc Kean-Vlasov equations(SMVEs)to G-SMVEs directly. To overcome this difficulty, we introduce definitions, including the derivative of a function with a law under the G-expectation and the Lions derivatives. Then we construct a new G-It? formula for G-SMVEs according to the G-It? formula for stochastic differential equations in the G-framework(G-SDEs) and the It? formula for SMVEs. Using the new G-It? formula and the Lyapunov functional method, we investigate the moment exponential stability and almost sure asymptotic stability of G-SMVDEs. To overcome the difficulty in obtaining the distribution dependence of the exact solution to the G-SMVDE, we introduce the empirical measure and the corresponding interacting particle system, and then prove the stability equivalence between the underlying G-SMVDE and the corresponding interacting particle system. Two examples are used to confirm our theoretical results.

关键词：

ALMOST SURE AND MOMENT EXPONENTIAL STABILITY OF PREDICTOR-CORRECTOR METHODS FOR STOCHASTIC DIFFERENTIAL EQUATIONS

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Journal of Systems science & Complexity 2012年第4期25卷 736-743页

作者： Yuanling NIU Chengjian ZHANG school of mathematics and statistics Central South University school of mathematics and statistics Huazhong University of Science and Technology

This paper deals with almost sure and moment exponential stability of a class of predictor- corrector methods applied to the stochastic differential equations of Ito-type. Stability criteria for this type of methods are derived. The methods are shown to maintain almost sure and moment exponential stability for all sufficiently small timesteps under appropriate conditions. A numerical experiment further testifies these theoretical results.

关键词： Almost sure stability moment exponential stability numerical experiment stochastic differential equations.