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Density peak clustering using tensor network

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Science China(Information sciences) 2024年第3期67卷 321-322页

作者： Xiao SHI Yun SHANG Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences National Center for mathematics and Interdisciplinary sciences Key Laboratory of ManagementDecision and Information SystemsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences

Tensor networks have been a powerful tool in simulating many-body physics and have recently gained recognition in the machine learning community due to their remarkable representation capabilities. However, using tens... 详细信息

关键词： Tensors

Threshold Selection and Resource Allocation for Quantized Identification

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Journal of systems Science & Complexity 2024年第1期37卷 204-229页

作者： WANG Ying LI Xin ZHAO Yanlong ZHANG Ji-Feng Key Laboratory of systems and Control Institute of Systems ScienceAcademy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100049China

This paper is concerned with the optimal threshold selection and resource allocation problems of quantized identification, whose aims are improving identification efficiency under limited resources. Firstly, the first-order asymptotically optimal quantized identification theory is extended to the weak persistent excitation condition. Secondly, the characteristics of time and space complexities are established based on the Cramér-Rao lower bound of quantized systems. On these basis, the optimal selection methods of fixed thresholds and adaptive thresholds are established under aperiodic signals, which answer how to achieve the best efficiency of quantized identification under the same time and space complexity. In addition, based on the principle of maximizing the identification efficiency under a given resource, the optimal resource allocation methods of quantized identification are given for the cases of fixed thresholds and adaptive thresholds, respectively, which show how to balance time and space complexity to realize the best identification efficiency of quantized identification.

关键词： Quantized output resource allocation system identification threshold selection.

A stochastic gradient-based two-step sparse identification algorithm for multivariate ARX systems

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Control Theory and Technology 2024年第2期22卷 213-221页

作者： Yanxin Fu Wenxiao Zhao Key Laboratory of systems and Control Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing100049China

We consider the sparse identification of multivariate ARX systems, i.e., to recover the zero elements of the unknown parameter matrix. We propose a two-step algorithm, where in the first step the stochastic gradient (SG) algorithm is applied to obtain initial estimates of the unknown parameter matrix and in the second step an optimization criterion is introduced for the sparse identification of multivariate ARX systems. Under mild conditions, we prove that by minimizing the criterion function, the zero elements of the unknown parameter matrix can be recovered with a finite number of observations. The performance of the algorithm is testified through a simulation example.

关键词： ARX system Stochastic gradient algorithm Sparse identification Support recovery Parameter estimation Strong consistency

H?lder continuous weak solutions of the 2D Boussinesq equation with thermal diffusion

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Science China mathematics 2024年第8期67卷 1777-1806页

作者： Tianwen Luo Tao Tao Liqun Zhang Yau Mathematical sciences Center Tsinghua University School of mathematics Shandong University Institute of mathematics Academy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

We show the existence of H?lder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy. More precisely, for any smooth e(t):[0, 1]→■ and ... 详细信息

关键词： 2D Boussinesq equation with thermal diffusion Hölder continuous periodic weak solutions prescribed kinetic energy

2-local unstable homotopy groups of indecomposable A32-complexes

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Science China mathematics 2024年第3期67卷 607-626页

作者： Zhongjian Zhu Jianzhong Pan College of mathematics and Physics Wenzhou University Hua Loo-Keng Key Laboratory of mathematics Institute of MathematicsAcademy of Mathematics and Systems ScienceChinese Academy of Sciences School of Mathematical sciences University of Chinese Academy of Sciences

In this paper,we calculate the 2-local unstable homotopy groups of indecomposable A32-complexes.The main technique used is analysing the homotopy property of J(A,X),defined by Gray(1973) for a CW-pair(X,A),which is ho... 详细信息

关键词： homotopy groups A 2 n -complexes fibration sequence relative James construction 55P15

Understanding Human and Machine Interaction from Decision Perspective: An Empirical Study Based on the Game of Go

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Journal of systems Science & Complexity 2024年第2期37卷 647-667页

作者： ZHAO Ping LI Xuerong WANG Shouyang academy of mathematics and systems Science Chinese Academy of SciencesBeijing 100190China School of Mathematical sciences University of Chinese Academy of SciencesBeijing 100190China

The authors aim to interpret human and AI interactions from the decision perspective.The authors decompose the interaction analysis into the following main components in the context of interactions:Individual behavior patterns,interaction relationships,and comprehensive analysis.The authors interpret intertemporal decisions from a physical perspective and employ cross-discipline concepts and methodologies to extract the behavior characteristics of players in the empirical case study.About the individual behavior patterns,the authors find that human players prefer short-term periods to AI in decision-making.The interaction relationship analysis reveals a dynamic relationship between possible short-term co-movement and nearly counter-movement in the long run.The authors apply principal component analysis to descriptive indicators and discover a regular decision hierarchy.The main behavior pattern of players in the game of Go is switching between careful and daring behaviors.The differences in the decision hierarchies imply a discrepancy of patience between humans and AI.

关键词： Coherence analysis decision hierarchy machine behaviour multitaper spectral analysis

Forward to the Special Topic on“Solving Differential Equations with Deep Learning”

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Journal of systems Science & Complexity 2024年第2期37卷 389-390页

作者： YAN Zhenya academy of mathematics and systems Science Chinese Academy of SciencesBeijing 100190China

The concept of artificial intelligence(AI)was first presented at the Dartmouth SummerResearch Project on AI hosted by McCarthy and Minsky in 1956.After that,the developmentof AI has experienced ups and downs due to some limited conditions including intelligentcomputing techniques,computer and hardware and software^([1,2]).In particular,with the rapidof deep artificial neural networks,machine learning(ML)and deep learning(DL)techniques^([3,4])have been applied in many fields of science and engineering,including machine translation,image recognition,genomics,scientific computing and atmospheric science,etc^([5]).

关键词： has artificial hardware

Distributed Least Squares Algorithm of Continuous-Time Stochastic Regression Model Based on Sampled Data

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Journal of systems Science & Complexity 2024年第2期37卷 609-628页

作者： ZHU Xinghua GAN Die LIU Zhixin The Key Laboratory of systems and Control Academy of Mathematics and Systems ScienceChinese Academy of Sciencesand School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijing 100190China Zhongguancun Laboratory Beijing 100094China

In this paper,the authors consider the distributed adaptive identification problem over sensor networks using sampled data,where the dynamics of each sensor is described by a stochastic differential equation.By minimizing a local objective function at sampling time instants,the authors propose an online distributed least squares algorithm based on sampled data.A cooperative non-persistent excitation condition is introduced,under which the convergence results of the proposed algorithm are established by properly choosing the sampling time interval.The upper bound on the accumulative regret of the adaptive predictor can also be provided.Finally,the authors demonstrate the cooperative effect of multiple sensors in the estimation of unknown parameters by computer simulations.

关键词： Cooperative excitation condition distributed least squares regret sampled data stochastic differential equation

On the convergence of tracking differentiator with multiple stochastic disturbances

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Science China(Information sciences) 2024年第2期67卷 157-169页

作者： Zehao WU Huacheng ZHOU Baozhu GUO Feiqi DENG School of mathematics and Big Data Foshan University School of mathematics and Statistics Central South University academy of mathematics and systems Science Chinese Academy of Sciences systems Engineering Institute South China University of Technology

This paper investigates the convergence, noise-tolerance, and filtering performance of a tracking differentiator in the presence of multiple stochastic disturbances for the first time. We consider a general case wherein the input signal is corrupted by additive colored noise, and the tracking differentiator is disturbed by additive colored noise and white noise. The tracking differentiator is shown to track the input signal and its generalized derivatives in the mean square sense. Further, the almost sure convergence can be achieved when the stochastic noise affecting the input signal is vanishing. Herein, numerical simulations are performed to validate the theoretical results.

关键词： tracking differentiator convergence noise-tolerance filtering performance multiple stochastic disturbances