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A Mean-Field Game for a Forward-Backward Stochastic System With Partial Observation and Common Noise

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IEEE/CAA Journal of Automatica Sinica 2024年第3期11卷 746-759页

作者： Pengyan Huang Guangchen Wang Shujun Wang Hua Xiao the school of Control Science and Engineering Shandong University the school of statistics and mathematics Shandong University of Finance and Economics IEEE the school of Management Shandong University the school of mathematics and statistics Shandong University

This paper considers a linear-quadratic(LQ) meanfield game governed by a forward-backward stochastic system with partial observation and common noise,where a coupling structure enters state equations,cost functionals and observation ***,to reduce the complexity of solving the meanfield game,a limiting control problem is *** virtue of the decomposition approach,an admissible control set is *** a filter technique and dimensional-expansion technique,a decentralized control strategy and a consistency condition system are derived,and the related solvability is also ***,we discuss an approximate Nash equilibrium property of the decentralized control ***,we work out a financial problem with some numerical simulations.

关键词： Decentralized control strategy ϵ-Nash equilibrium forward-backward stochastic system mean-field game partial observation

Strategies for mitigating detrimental effects in cyber-physical multiplex networks

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Science China(Information Sciences) 2024年第6期67卷 453-454页

作者： Yudong GONG Shenghai YANG Sanyang LIU Pei WANG Yiguang BAI school of mathematics and statistics Xidian University

Detrimental effects,such as widespread epidemics or rumors,can inflict significant damage on society in a remarkably short time[1].Various studies have focused on mitigating these effects independently within single-l... 详细信息

关键词： Cost effectiveness

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Adversarial data splitting for domain generalization

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Science China(Information Sciences) 2024年第5期67卷 28-42页

作者： Xiang GU Jian SUN Zongben XU school of mathematics and statistics Xi'an Jiaotong University

Domain generalization aims to learn a model that is generalizable to an unseen target domain,which is a fundamental and challenging task in machine learning for out-of-distribution generalization. This paper proposes a novel domain generalization approach that enforces the learned model to be able to generalize well over the train/val subset splitting of the training dataset. This idea is modeled herein as an adversarial data splitting framework, formulated as a min-max optimization problem inspired by the metalearning approach. The min-max optimization problem is solved by iteratively splitting the training dataset into the training and val subsets to maximize the domain shift measured by the objective function and updating the model parameters to enable the model to generalize well from the training subset to the val subset by minimizing the objective function. This adversarial training approach does not assume the known domain labels of the training data; instead, it automatically investigates the “hard” splitting of the train/val subsets to learn the generalizable model. Extensive experimental results using three benchmark datasets demonstrate the superiority of this approach. In addition, we derive a generalization error bound for the theoretical understanding of our proposed approach.

关键词： domain generalization adversarial learning data splitting meta-learning out of distribution

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Evolutionary game dynamics of combining two different aspiration-driven update rules in structured populations

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Chinese Physics B 2024年第5期33卷 182-191页

作者：杨智昊杨彦龙 mathematics and statistics school Guizhou UniversityGuiyang 550025China

In evolutionary games,most studies on finite populations have focused on a single updating ***,given the differences in individual cognition,individuals may change their strategies according to different updating *** this reason,we consider two different aspiration-driven updating mechanisms in structured populations:satisfied-stay unsatisfied shift(SSUS)and satisfied-cooperate unsatisfied defect(SCUD).To simulate the game player’s learning process,this paper improves the particle swarm optimization algorithm,which will be used to simulate the game player’s strategy selection,i.e.,population particle swarm optimization(PPSO)*** find that in the prisoner’s dilemma,the conditions that SSUS facilitates the evolution of cooperation do not enable cooperation to *** contrast,SCUD conditions that promote the evolution of cooperation enable cooperation to *** addition,the invasion of SCUD individuals helps promote cooperation among SSUS *** by the PPSO algorithm,the theoretical approximation results are found to be consistent with the trend of change in the simulation results.

关键词： evolutionary game dynamics aspiration-driven update structured populations

Non-interactive SM2 threshold signature scheme with identifiable abort

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Frontiers of Computer Science 2024年第1期18卷 171-185页

作者： Huiqiang LIANG Jianhua CHEN school of mathematics and statistics Wuhan UniversityWuhan 430072China

A threshold signature is a special digital signature in which the N-signer share the private key x and can construct a valid signature for any subset of the included t-signer,but less than t-signer cannot obtain any *** the breakthrough achievements of threshold ECDSA signature and threshold Schnorr signature,the existing threshold SM2 signature is still limited to two parties or based on the honest majority setting,there is no more effective solution for the multiparty *** make the SM2 signature have more flexible application scenarios,promote the application of the SM2 signature scheme in the blockchain system and secure cryptocurrency *** paper designs a non-interactive threshold SM2signature schemebasedon partially homomorphic encryption and zero-knowledge *** the last round requires the message input,so make our scheme non-interactive,and the pre-signing process takes 2 rounds of communication to complete after the key *** allow arbitrary threshold t

关键词： SM2 signature secure multi-party computation threshold signature UC-secure dishonest majority

BANDED M-MATRIX SPLITTING PRECONDITIONER FOR RIESZ SPACE FRACTIONAL REACTION-DISPERSION EQUATION

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Journal of Computational mathematics 2024年第2期42卷 372-389页

作者： Shiping Tang Aili Yang Yujiang Wu school of mathematics and statistics Lanzhou UniversityLanzhou 730000China school of mathematics and statistics Hainan Normal UniversityHaikou 570000China

Based on the Crank-Nicolson and the weighted and shifted Grunwald operators,we present an implicit difference scheme for the Riesz space fractional reaction-dispersion equations and also analyze the stability and the convergence of this implicit difference ***,after estimating the condition number of the coefficient matrix of the discretized scheme,we find that this coefficient matrix is ill-conditioned when the spatial mesh-size is sufficiently *** overcome this deficiency,we further develop an effective banded M-matrix splitting preconditioner for the coefficient *** properties of this preconditioner together with its preconditioning effect are ***,Numerical examples are employed to test the robustness and the effectiveness of the proposed preconditioner.

关键词： Riesz space fractional equations Toeplitz matrix conjugate gradient method Incomplete Cholesky decomposition Banded M-matrix splitting

THE SMOOTHING EFFECT IN SHARP GEVREY SPACE FOR THE SPATIALLY HOMOGENEOUS NON-CUTOFF BOLTZMANN EQUATIONS WITH A HARDPOTENTIAL

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Acta Mathematica Scientia 2024年第2期44卷 455-473页

作者：刘吕桥曾娟 school of mathematics and statistics Anhui Normal UniversityWuhu241002China school of mathematics and statistics Wuhan UniversityWuhan430072China

In this article, we study the smoothing effect of the Cauchy problem for the spatially homogeneous non-cutoff Boltzmann equation for hard potentials. It has long been suspected that the non-cutoff Boltzmann equation enjoys similar regularity properties as to whose of the fractional heat equation. We prove that any solution with mild regularity will become smooth in Gevrey class at positive time, with a sharp Gevrey index, depending on the angular singularity. Our proof relies on the elementary L^(2) weighted estimates.

关键词： Boltzmann equation Gevrey regularity non-cutoff hard potential

High-dimensional robust inference for censored linear models

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Science China mathematics 2024年第4期67卷 891-918页

作者： Jiayu Huang Yuanshan Wu school of mathematics and statistics Wuhan UniversityWuhan 430072China school of statistics and mathematics Zhongnan University of Economics and LawWuhan 430073China

Due to the direct statistical interpretation,censored linear regression offers a valuable complement to the Cox proportional hazards regression in survival *** propose a rank-based high-dimensional inference for censored linear regression without imposing any moment condition on the model *** develop a theory of the high-dimensional U-statistic,circumvent challenges stemming from the non-smoothness of the loss function,and establish the convergence rate of the regularized estimator and the asymptotic normality of the resulting de-biased estimator as well as the consistency of the asymptotic variance *** censoring can be viewed as a way of trimming,it strengthens the robustness of the rank-based high-dimensional inference,particularly for the heavy-tailed model error or the outlier in the presence of the *** evaluate the finite-sample performance of the proposed method via extensive simulation studies and demonstrate its utility by applying it to a subcohort study from The Cancer Genome Atlas(TCGA).

关键词： censoring mechanism heavy-tailed distribution non-smooth loss function outlier rank regression

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On self-affine tiles that are homeomorphic to a ball

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Science China mathematics 2024年第1期67卷 45-76页

作者： Jorg M.Thuswaldner Shu-Qin Zhang mathematics and statistics University of LeobenLeoben 8700Austria school of mathematics and statistics Zhengzhou UniversityZhengzhou 450001China

Let M be a 3×3 integer matrix which is expanding in the sense that each of its eigenvalues is greater than 1 in modulus and let D?Z^(3)be a digit set containing|det M|*** the unique nonempty compact set T=T(M,D)defined by the set equation MT=T+D is called an integral self-affine tile if its interior is *** D is of the form D={0,v,...,(|det M|-1)v},we say that T has a collinear digit *** present paper is devoted to the topology of integral self-affine tiles with collinear digit *** particular,we prove that a large class of these tiles is homeomorphic to a closed 3-dimensional ***,we show that in this case,T carries a natural CW complex structure that is defined in terms of the intersections of T with its neighbors in the lattice tiling{T+z:z∈Z^(3)}induced by *** CW complex structure is isomorphic to the CW complex defined by the truncated octahedron.

关键词： self-afine sets tiles and tilings low-dimensional topology truncated octahedron