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Equilibrium Arrivals to Preemptive Queueing System with Fixed and Random Population Size

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Journal of the Operations research Society of China 2024年第1期12卷 77-92页

作者： Julia Chirkova Vladimir Mazalov Institute of Applied Mathematical research Karelian Research Centre of RASPetrozavodsk185910Russia School of Mathematics and statistics Qingdao UniversityQingdao266071ShandongChina

A single-server queueing system with preemptive access is *** customer has one attempt to enter the system at its working interval[0,T].As soon as the customer request enters the system,the server immediately starts the *** when the next request arrives in the system,the previous one leaves the system even he has not finished his service *** study a non-cooperative game in which the customers wish to maximize their probability of obtaining service within a certain period of *** characterize the Nash equilibrium and the price of anarchy,which is defined as the ratio between the optimal and equilibrium social *** models are *** the first model the number of players is fixed,while in the second it is random and obeys the Poisson *** demonstrate that there exists a unique symmetric equilibrium for both ***,we calculate the price of anarchy for both models and show that the price of anarchy is not monotone with respect to the number of customers.

关键词： Service system Preemptive priorities Strategic users Random number of players Optimal arrivals Kolmogorov backward equations Nash equilibrium Price of anarchy

A New Class of Strong Orthogonal Arrays of Strength Three

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Journal of Systems Science & Complexity 2024年第3期37卷 1233-1250页

作者： WANG Chunyan LIU Min-Qian YANG Jinyu Center for Applied statistics and School of statistics Renmin University of ChinaBeijing 100872China School of statistics and Data Science LPMC&KLMDASRNankai UniversityTianjin 300071China

Strong orthogonal arrays(SOAs) were recently introduced and studied as a class of spacefilling designs for computer experiments. To surely realize better space-filling properties, SOAs of strength three or higher are desirable. In addition, orthogonality is also an important property for designs of computer experiments, because it guarantees that the estimates of the main effects are uncorrelated. This paper first provides a systematic study on the construction of(nearly) orthogonal strength-three SOAs with better space-filling properties. The newly proposed strength-three SOAs enjoy almost the same space-filling properties of strength-four SOAs, and can accommodate much more columns than the latter. Moreover, they are(nearly) orthogonal and flexible in run sizes. The construction methods are straightforward to implement, and their theoretical supports are well established. In addition to the theoretical results, many designs are tabulated for practical needs.

关键词： Computer experiment orthogonality space-filling property strong orthogonal array

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

Preface: The Special Issue on Dynamic and Networking Games

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Journal of the Operations research Society of China 2024年第1期12卷 1-3页

作者： Hong-Wei Gao Vladimir Mazalov School of Mathematics and statistics Qingdao University266071QingdaoShandongChina Institute of Applied Mathematical research Karelian Research Centre of RAS185910PetrozavodskRussia

Numerous game theory-based techniques to characterize agent behavior haveemerged in response to the swift advancements in technology,communications,indus-trial organization,economic integration,and international *** is a huge varietyof mathematical techniques used in game *** application of dynamic and net-working game techniques is the main topic of this special *** strategicinteractions between many decision-makers with dynamic and varied connections isthe focus of research in the game theory discipline of dynamic and networking *** field of study examines how agents or people make choices in dynamic circum-stances and how those choices impact their overall outcomes and payoffs.

关键词： agent strategic advancement

Equilibrium Reinsurance Strategy and Mean Residual Life Function

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 758-777页

作者： Dan-ping LI Lv CHEN Lin-yi QIAN Wei WANG School of statistics Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOEEast China Normal UniversityShanghai 200062China Academy of statistics and Interdisciplinary Sciences Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOEEast China Normal UniversityShanghai 200062China School of Mathematics and statistics Ningbo UniversityNingbo 315211China

In this paper,we analyze the relationship between the equilibrium reinsurance strategy and the tail of the distribution of the *** Mean Residual Life(MRL)has a close relationship with the tail of the distribution,we consider two classes of risk distributions,Decreasing Mean Residual Life(DMRL)and Increasing Mean Residual Life(IMRL)distributions,which can be used to classify light-tailed and heavy-tailed distributions,*** assume that the underlying risk process is modelled by the classical CramérLundberg model *** the mean-variance criterion,by solving the extended Hamilton-Jacobi-Bellman equation,we derive the equilibrium reinsurance strategy for the insurer and the reinsurer under DMRL and IMRL,***,we analyze how to choose the reinsurance premium to make the insurer and the reinsurer agree with the same reinsurance *** find that under the case of DMRL,if the distribution and the risk aversions satisfy certain conditions,the insurer and the reinsurer can adopt a reinsurance premium to agree on a reinsurance strategy,and under the case of IMRL,the insurer and the reinsurer can only agree with each other that the insurer do not purchase the reinsurance.

关键词： mean residual life excess-of-loss reinsurance insurer reinsurer stochastic control

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Character Sheaves for Classical Graded Lie Algebras

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Acta Mathematica Sinica,English Series 2024年第3期40卷 870-884页

作者： Ting XUE School of Mathematics and statistics University of MelbourneVIC 3010Australia Department of Mathematics and statistics University of HelsinkiHelsinki 00014Finland

In this note we study character sheaves for graded Lie algebras arising from inner automorphisms of special linear groups and Vinberg’s type Ⅱ classical graded Lie algebras.

关键词： Graded Lie algebras character sheaves Fourier transform nilpotent orbits

Optimal confrontation position selecting games model and its application to one-on-one air combat

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Defence Technology（防务技术） 2024年第1期31卷 417-428页

作者： Zekun Duan Genjiu Xu Xin Liu Jiayuan Ma Liying Wang School of Mathematics and statistics Northwestern Polytechnical UniversityXi'an 710072China International Joint research Center on Operations research Optimization and Artificial IntelligenceXi'an 710129China AVIC Xi’an Aeronautics Computing Technique research Institute Xi'an 710065China Unmanned System research Institute Northwestern Polytechnical UniversityXi'an 710072China

In the air combat process,confrontation position is the critical factor to determine the confrontation situation,attack effect and escape probability of ***,selecting the optimal confrontation position becomes the primary goal of maneuver *** taking the position as the UAV’s maneuver strategy,this paper constructs the optimal confrontation position selecting games(OCPSGs)*** the OCPSGs model,the payoff function of each UAV is defined by the difference between the comprehensive advantages of both sides,and the strategy space of each UAV at every step is defined by its accessible space determined by the *** we design the limit approximation of mixed strategy Nash equilibrium(LAMSNQ)algorithm,which provides a method to determine the optimal probability distribution of positions in the strategy *** the simulation phase,we assume the motions on three directions are independent and the strategy space is a cuboid to simplify the *** simulations are performed to verify the feasibility,effectiveness and stability of the algorithm.

关键词： Unmanned aerial vehicles(UAVs) Air combat Continuous strategy space Mixed strategy Nash equilibrium

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

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