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On Minor Left Prime Factorization Problem for Multivariate Polynomial Matrices

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Journal of Systems Science & Complexity 2024年第3期37卷 1295-1307页

作者： LU Dong WANG Dingkang XIAO Fanghui school of Mathematics Southwest Jiaotong UniversityChengdu 610031China KLMM Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China school of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China MOE-LCSM School of Mathematics and StatisticsHunan Normal UniversityChangsha 410081China

A new necessary and sufficient condition for the existence of minor left prime factorizations of multivariate polynomial matrices without full row rank is *** key idea is to establish a relationship between a matrix and any of its full row rank *** on the new result,the authors propose an algorithm for factorizing matrices and have implemented it on the computer algebra system *** examples are given to illustrate the effectiveness of the algorithm,and experimental data shows that the algorithm is efficient.

关键词： Free modules Grobner bases minor left prime(MLP) multivariate polynomial matrices polynomial matrix factorizations

Equilibrium Strategy of the Pursuit-Evasion Game in Three-Dimensional Space

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IEEE/CAA Journal of Automatica Sinica 2024年第2期11卷 446-458页

作者： Nuo Chen Linjing Li Wenji Mao school of Artificial Intelligence University of Chinese Academy of SciencesBeijing 100049 Institute of Automation Chinese Academy of SciencesBeijing 100190China

The pursuit-evasion game models the strategic interaction among players, attracting attention in many realistic scenarios, such as missile guidance, unmanned aerial vehicles, and target defense. Existing studies mainly concentrate on the cooperative pursuit of multiple players in two-dimensional pursuit-evasion games. However, these approaches can hardly be applied to practical situations where players usually move in three-dimensional space with a three-degree-of-freedom control. In this paper,we make the first attempt to investigate the equilibrium strategy of the realistic pursuit-evasion game, in which the pursuer follows a three-degree-of-freedom control, and the evader moves freely. First, we describe the pursuer's three-degree-of-freedom control and the evader's relative coordinate. We then rigorously derive the equilibrium strategy by solving the retrogressive path equation according to the Hamilton-Jacobi-Bellman-Isaacs(HJBI) method, which divides the pursuit-evasion process into the navigation and acceleration phases. Besides, we analyze the maximum allowable speed for the pursuer to capture the evader successfully and provide the strategy with which the evader can escape when the pursuer's speed exceeds the threshold. We further conduct comparison tests with various unilateral deviations to verify that the proposed strategy forms a Nash equilibrium.

关键词： Differential game equilibrium strategy pursuit-evasion game threedegree-of-freedom control

Structural transition,electric transport,and electronic structures in the compressed trilayer nickelate La4Ni3O10

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Science China(Physics,Mechanics & Astronomy) 2024年第11期Mechanics & Astronomy) .卷 13-19页

作者： Jingyuan Li Cui-Qun Chen Chaoxin Huang Yifeng Han Mengwu Huo Xing Huang Peiyue Ma Zhengyang Qiu Junfeng Chen Xunwu Hu Lan Chen Tao Xie Bing Shen Hualei Sun Dao-Xin Yao Meng Wang Center for Neutron Science and Technology Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices School of Physics Sun Yat-sen University Center for Materials of the Universe School of Molecular Sciences Arizona State University school of sciences Sun Yat-sen University

Atomic structure and electronic band structure are fundamental properties for understanding the mechanism of superconductivity. Motivated by the discovery of pressure-induced high-temperature superconductivity at 80 K in the bilayer Ruddlesden-Popper nickelate La3Ni2O7, the atomic structure and electronic band structure of the trilayer nickelate La4Ni3O10under pressure up to 44.3 GPa are investigated. A structural transition from the monoclinic P21/a space group to the tetragonal I4/mmm around 12.6-13.4 GPa is identified, accompanied by a drop of resistance below 7 K. Density functional theory calculations suggest that the bonding state of Ni 3dz2orbital rises and crosses the Fermi level at high pressures, which may give rise to possible superconductivity observed in resistance under pressure in La4Ni3O10. The trilayer nickelate La4Ni3O10shows some similarities with the bilayer La3Ni2O7and has unique properties, providing a new platform to investigate the underlying mechanism of superconductivity in nickelates.

关键词： La4Ni3O10 high pressure synchrotron X-ray diffraction structural transition DFT calculations

Enhancing Multi-agent Coordination via Dual-channel Consensus

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Machine Intelligence Research 2024年第2期21卷 349-368页

作者： Qingyang Zhang Kaishen Wang Jingqing Ruan Yiming Yang Dengpeng Xing Bo Xu Institute of Automation Chinese Academy of SciencesBeijing 100190China school of Future Technology University of Chinese Academy of SciencesBeijing 100049China school of Artificial Intelligence University of Chinese Academy of SciencesBeijing 100049China

Successful coordination in multi-agent systems requires agents to achieve *** works propose methods through information sharing,such as explicit information sharing via communication protocols or exchanging information implicitly via behavior ***,these methods may fail in the absence of communication channels or due to biased *** this work,we propose to develop dual-channel consensus(DuCC)via contrastive representation learning for fully cooperative multi-agent systems,which does not need explicit communication and avoids biased *** comprises two types of consensus:temporally extended consensus within each agent(inner-agent consensus)and mutual consensus across agents(inter-agent consensus).To achieve DuCC,we design two objectives to learn representations of slow environmental features for inner-agent consensus and to realize cognitive consistency as inter-agent *** DuCC is highly general and can be flexibly combined with various MARL *** extensive experiments on StarCraft multi-agent challenge and Google research football demonstrate that our method efficiently reaches consensus and performs superiorly to state-of-the-art MARL algorithms.

关键词： Multi-agent reinforcement learning contrastive representation learning consensus multi-agent cooperation cognitive consistency

Reducing Subspaces of Toeplitz Operators Induced by a Class of Non-analytic Monomials over the Unit Ball

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1767-1777页

作者： Yan Yue SHI Bo ZHANG Xu TANG Yu Feng LU school of Mathematical sciences Ocean University of ChinaQingdao 266100P.R.China school of Mathematics and Information sciences Yantai UniversityYantai 264005P.R.China school of Mathematical sciences Space Engineering UniversityBeijing 101416P.R.China school of Mathematical sciences Dalian University of TechnologyDalian 116024P.R.China

In this paper,we describe the minimal reducing subspaces of Toeplitz operators induced by non-analytic monomials on the weighted Bergman spaces and Dirichlet spaces over the unit ball B_(2).It is proved that each minimal reducing subspace M is finite dimensional,and if dim M≥3,then M is induced by a ***,the structure of commutant algebra v(T_(w)N_(z)N):={M^(*)_(w)NM_(z)N,M^(*)_(z)NM_(w)N}′is determined by N and the two dimensional minimal reducing subspaces of(T_(w)N_(z)*** also give some interesting examples.

关键词： Reducing subspace operator-weighted shifts Toeplitz operator von Neumann algebra

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Learning Top-K Subtask Planning Tree Based on Discriminative Representation Pretraining for Decision-making

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Machine Intelligence Research 2024年第4期21卷 782-800页

作者： Jingqing Ruan Kaishen Wang Qingyang Zhang Dengpeng Xing Bo Xu Institute of Automation Chinese Academy of SciencesBeijing 100190China school of Future Technology University of Chinese Academy of SciencesBeijing 100049China school of Artificial Intelligence University of Chinese Academy of SciencesBeijing 100049China

Decomposing complex real-world tasks into simpler subtasks and devising a subtask execution plan is critical for humans to achieve effective ***,replicating this process remains challenging for AI agents and naturally raises two questions:(1)How to extract discriminative knowledge representation from priors?(2)How to develop a rational plan to decompose complex problems?To address these issues,we introduce a groundbreaking framework that incorporates two main ***,our multiple-encoder and individual-predictor regime goes beyond traditional architectures to extract nuanced task-specific dynamics from datasets,enriching the feature space for ***,we innovate in planning by introducing a top-K subtask planning tree generated through an attention mechanism,which allows for dynamic adaptability and forward-looking *** framework is empirically validated against challenging benchmarks BabyAI including multiple combinatorially rich synthetic tasks(e.g.,GoToSeq,SynthSeq,BossLevel),where it not only outperforms competitive baselines but also demonstrates superior adaptability and effectiveness incomplex task decomposition.

关键词： Reinforcement learning representation learning subtask planning task decomposition pretraining.

SEMI-PROXIMAL POINT METHOD FOR NONSMOOTH CONVEX-CONCAVE MINIMAX OPTIMIZATION

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Journal of Computational Mathematics 2024年第3期42卷 617-637页

作者： Yuhong Dai Jiani Wang Liwei Zhang LSEC ICMSECAMSSChinese Academy of SciencesBeijing 100190China School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100049China Academy of Mathematics and Systems Science Chinese Academy of SciencesBeijing 100190China school of Mathematical sciences Dalian University of TechnologyDalian 116024China

Minimax optimization problems are an important class of optimization problems arising from modern machine learning and traditional research *** there have been many numerical algorithms for solving smooth convex-concave minimax problems,numerical algorithms for nonsmooth convex-concave minimax problems are *** paper aims to develop an efficient numerical algorithm for a structured nonsmooth convex-concave minimax problem.A semi-proximal point method(SPP)is proposed,in which a quadratic convex-concave function is adopted for approximating the smooth part of the objective function and semi-proximal terms are added in each *** construction enables the subproblems at each iteration are solvable and even easily solved when the semiproximal terms are cleverly *** prove the global convergence of our algorithm under mild assumptions,without requiring strong convexity-concavity *** the locally metrical subregularity of the solution mapping,we prove that our algorithm has the linear rate of *** numerical results are reported to verify the efficiency of our algorithm.

关键词： Minimax optimization Convexity-concavity Global convergence Rate of con-vergence Locally metrical subregularity

Targeting autophagy by polyphenols to prevent glycative stress-toxicity in the brain

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Neural Regeneration Research 2024年第5期19卷 941-942页

作者： Alejandro Ponce-Mora Eloy Bejarano Department of Biomedical sciences School of Health Sciences and Veterinary SchoolUniversidad Cardenal Herrera-CEUCEU UniversitiesValenciaSpain

Glycative stress-a pathological hub in brain dysfunction:The nervous system is an intricate network that requires precise and complex *** recent years,growing evidence highlights the detrimental impact of glycative stress on brain homeostasis,which disables a network of vital processes,necessary for optimal function(Gómez et al.,2021).

关键词： homeostasis stress

Magnetic proximity effect in the two-dimensional ε-Fe_(2)O_(3)/NbSe_(2)heterojunction

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Chinese Physics B 2024年第2期33卷 492-497页

作者：车冰玉胡国静朱超郭辉吕森浩刘轩冶吴康赵振潘禄禄祝轲齐琦韩烨超林晓李子安申承民鲍丽宏刘政周家东杨海涛高鸿钧 Beijing National Center for Condensed Matter Physics and Institute of Physics Chinese Academy of SciencesBeijing 100190China school of Physical sciences University of Chinese Academy of SciencesBeijing 100190China school of Materials Science and Engineering Nanyang Technological UniversitySingapore school of Physical Science and Technology Guangxi UniversityGuangxi 530004China school of Physics Beijing Institute of TechnologyBeijing 100081China

Two-dimensional(2D)magnet/superconductor heterostructures can promote the design of artificial materials for exploring 2D physics and device applications by exotic proximity ***,plagued by the low Curie temperature and instability in air,it is hard to realize practical applications for the reported layered magnetic materials at *** this paper,we developed a space-confined chemical vapor deposition method to synthesize ultrathin air-stable ε-Fe_(2)O_(3) nanosheets with Curie temperature above 350 *** ε-Fe_(2)O_(3)/NbSe_(2) heterojunction was constructed to study the magnetic proximity effect on the superconductivity of the NbSe_(2) *** electrical transport results show that the subtle proximity effect can modulate the interfacial spin–orbit interaction while undegrading the superconducting critical *** work paves the way to construct 2D heterojunctions with ultrathin nonlayered materials and layered van der Waals(vdW)materials for exploring new physical phenomena.

关键词： two-dimensional heterojunctions magnetic proximity effect non-layered magnetic nanosheet spin-orbit interaction