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On Hamiltonian Property of Cayley Digraphs

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 547-556页

作者： Fang DUAN Qiong-xiang HUANG school of mathematics science Xinjiang Normal UniversityUrumqi 830017China College of mathematics and systems science Xinjiang UniversityUrumqi 830017China

Let G be a finite group generated by S and C(G,S) the Cayley digraphs of G with connection set *** this paper,we give some sufficient conditions for the existence of hamiltonian circuit in C(G,S),where G=Zm×H is a semiproduct of Zmby a subgroup H of *** particular,if m is a prime,then the Cayley digraph of G has a hamiltonian circuit unless G=Zm×*** addition,we introduce a new digraph operation,called φ-semiproduct of Γ1by Γ2and denoted by Γ1×Γ_φΓ2,in terms of mapping φ:V(Γ2)→{1,-1}.Furthermore we prove that C(Zm,{a})×_φ C(H,S) is also a Cayley digraph if φ is a homomorphism from H to{1,-1} ≤ Zm~*,which produces some classes of Cayley digraphs that have hamiltonian circuits.

关键词： Cayley digraphs hamiltonian circuit external semidirect product

On limit fractional Volterra hierarchies

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Communications in Theoretical Physics 2024年第1期76卷 7-16页

作者： Lixiang Zhang Chuanzhong Li school of mathematics and Statistics Ningbo UniversityNingbo315211China College of mathematics and systems science Shandong University of Science and TechnologyQingdao266590China

For the limit fractional Volterra(LFV)hierarchy,we construct the n-fold Darboux transformation and the soliton ***,we extend the LFV hierarchy to the noncommutative LFV(NCLFV)hierarchy,and construct the Darboux transformation expressed by quasi determinant of the noncommutative ***,we establish the relationship between new and old solutions of the NCLFV ***,the quasi determinant solutions of the NCLFV hierarchy are obtained.

关键词： limit fractional Volterra hierarchy noncommutative limit fractional Volterra hierarchy Darboux transformation soliton solution quasi determinant solution

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

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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 New Method for Solving Nonlinear Partial Differential Equations Based on Liquid Time-Constant Networks

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Journal of systems science & Complexity 2024年第2期37卷 480-493页

作者： SUN Jiuyun DONG Huanhe FANG Yong College of mathematics and systems science Shandong University of Science and TechnologyQingdao 266590China

In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation *** addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling *** this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical ***,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the *** the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.

关键词： Nonlinear partial differential equations numerical solutions physics-informed liquid networks physics-informed neural networks

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Quantum control based on three forms of Lyapunov functions

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Chinese Physics B 2024年第4期33卷 216-222页

作者：俞国慧杨洪礼 College of mathematics and systems science Shandong University of Science and TechnologyQingdao 266590China

This paper introduces the quantum control of Lyapunov functions based on the state distance, the mean of imaginary quantities and state *** this paper, the specific control laws under the three forms are *** is analyzed by the La Salle invariance principle and the numerical simulation is carried out in a 2D test *** calculation process for the Lyapunov function is based on a combination of the average of virtual mechanical quantities, the particle swarm algorithm and a simulated annealing ***, a unified form of the control laws under the three forms is given.

关键词： quantum system Lyapunov function particle swarm optimization simulated annealing algorithms quantum control

Partial Linear Model Averaging Prediction for Longitudinal Data

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Journal of systems science & Complexity 2024年第2期37卷 863-885页

作者： LI Na FEI Yu ZHANG Xinyu Faculty of science Kunming University of Science and TechnologyKunming 650500China school of Statistics and mathematics Yunnan University of Finance and EconomicsKunming 650221China Academy of mathematics and systems science Chinese Academy of SciencesBeijing 100190China

Prediction plays an important role in data *** averaging method generally provides better prediction than using any of its *** though model averaging has been extensively investigated under independent errors,few authors have considered model averaging for semiparametric models with correlated *** this paper,the authors offer an optimal model averaging method to improve the prediction in partially linear model for longitudinal *** model averaging weights are obtained by minimizing criterion,which is an unbiased estimator of the expected in-sample squared error loss plus a *** properties,including asymptotic optimality and consistency of averaging weights,are established under two scenarios:(i)All candidate models are misspecified;(ii)Correct models are available in the candidate *** studies and an empirical example show that the promise of the proposed procedure over other competitive methods.

关键词： Asymptotic optimality longitudinal data model averaging estimator partially linear model prediction

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Prescribed-time stabilization and inverse optimal control of stochastic high-order nonlinear systems

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science China(Information sciences) 2024年第2期67卷 144-156页

作者： Ran LIU Hui WANG Wuquan LI school of mathematics and Statistics science Ludong University

This paper investigates the prescribed-time state-feedback stabilization and prescribed-time inverse optimality problems for stochastic high-order nonlinear systems. First, a time-varying controller is designed by developing scaled quartic Lyapunov functions, which can guarantee that the system has a unique strong solution almost surely on the prescribed interval for any system initial conditions and that the states and the control converge to the origin in a mean-square form within the prescribed time. Then, the controller is redesigned to address the problem of prescribed-time inverse optimal mean-square stabilization. Finally,a concrete example is provided to confirm the efficiency of the proposed design schemes.

关键词： stochastic high-order nonlinear systems prescribed-time stabilization the scaled design inverse optimality

Deciphering and integrating invariants for neural operator learning with various physical mechanisms

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National science Review 2024年第4期11卷 111-122页

作者： Rui Zhang Qi Meng Zhi-Ming Ma Academy of mathematics and systems science Chinese Academy of Sciences(CAS) Microsoft Research

Neural operators have been explored as surrogate models for simulating physical systems to overcome the limitations of traditional partial differential equation(PDE) solvers. However, most existing operator learning methods assume that the data originate from a single physical mechanism, limiting their applicability and performance in more realistic scenarios. To this end, we propose the physical invariant attention neural operator(PIANO) to decipher and integrate the physical invariants for operator learning from the PDE series with various physical mechanisms. PIANO employs self-supervised learning to extract physical knowledge and attention mechanisms to integrate them into dynamic convolutional *** to existing techniques, PIANO can reduce the relative error by 13.6%–82.2% on PDE forecasting tasks across varying coefficients, forces or boundary conditions. Additionally, varied downstream tasks reveal that the PI embeddings deciphered by PIANO align well with the underlying invariants in the PDE systems, verifying the physical significance of PIANO.

关键词： neural operator PDE solver contrastive learning physical invariants