Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the...Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the evolution.However,although there has been a lot of work on stochastic epidemic models,most of them focus mainly on qualitative properties,which makes us somewhat ignore the original meaning of the parameter value.In this paper we extend the classic susceptible-infectious-removed(SIR)epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with epidemic.Finally,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.展开更多
The Thresholding Bandit(TB)problem is a popular sequential decision-making problem,which aims at identifying the systems whose means are greater than a threshold.Instead of working on the upper bound of a loss functio...The Thresholding Bandit(TB)problem is a popular sequential decision-making problem,which aims at identifying the systems whose means are greater than a threshold.Instead of working on the upper bound of a loss function,our approach stands out from conventional practices by directly minimizing the loss itself.Leveraging the large deviation theory,we firstly provide an asymptotically optimal allocation rule for the TB problem,and then propose a parameter-free Large Deviation(LD)algorithm to make the allocation rule implementable.Central limit theorem-based Large Deviation(CLD)algorithm is further proposed as a supplement to improve the computation efficiency using normal approximation.Extensive experiments are conducted to validate the superiority of our algorithms compared to existing methods,and demonstrate their broader applications to more general distributions and various kinds of loss functions.展开更多
The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the d...The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments.From these, the time-consistent cooperative agreement can be strategically supported by ε-Nash or strong ε-Nash equilibria. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibria can be constructed.展开更多
基金supported by the National Natural Science Foundation of China(No.12172167)。
文摘Nonlinearity and randomness are both the essential attributes for the real world,and the case is the same for the models of infectious diseases,for which the deterministic models can not give a complete picture of the evolution.However,although there has been a lot of work on stochastic epidemic models,most of them focus mainly on qualitative properties,which makes us somewhat ignore the original meaning of the parameter value.In this paper we extend the classic susceptible-infectious-removed(SIR)epidemic model by adding a white noise excitation and then we utilize the large deviation theory to quantitatively study the long-term coexistence exit problem with epidemic.Finally,in order to extend the meaning of parameters in the corresponding deterministic system,we tentatively introduce two new thresholds which then prove rational.
基金supported by the Natural Science Foundation of Guangdong Province(No.2023A1515011667)the Science and Technology Major Project of Shenzhen(No.KJZD20230923114809020)+3 种基金the Key Basic Research Foundation of Shenzhen(No.JCYJ20220818100205012)the Guangdong Basic and Applied Basic Research Foundation(No.2023B1515120020)the Shenzhen Science and Technology Program(No.RCBS20221008093331068)the Hetao Shenzhen-Hong Kong Science and Technology Innovation Cooperation Zone Project(No.HZQSWS-KCCYB-2024016).
文摘The Thresholding Bandit(TB)problem is a popular sequential decision-making problem,which aims at identifying the systems whose means are greater than a threshold.Instead of working on the upper bound of a loss function,our approach stands out from conventional practices by directly minimizing the loss itself.Leveraging the large deviation theory,we firstly provide an asymptotically optimal allocation rule for the TB problem,and then propose a parameter-free Large Deviation(LD)algorithm to make the allocation rule implementable.Central limit theorem-based Large Deviation(CLD)algorithm is further proposed as a supplement to improve the computation efficiency using normal approximation.Extensive experiments are conducted to validate the superiority of our algorithms compared to existing methods,and demonstrate their broader applications to more general distributions and various kinds of loss functions.
基金supported by National Natural Science Foundation of China(Grant Nos.7117112071373262 and 71571108)+3 种基金Projects of International(Regional)Cooperation and Exchanges of National Natural Science Foundation of China(Grant No.71411130215)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20133706110002)Natural Science Foundation of Shandong Province of China(Grant No.ZR2015GZ007)Saint Petersburg State University(Grant No.9.38.245.2014)
文摘The problem of strategic stability of long-range cooperative agreements in dynamic games with coalition structures is investigated. Based on imputation distribution procedures, a general theoretical framework of the differential game with a coalition structure is proposed. A few assumptions about the deviation instant for a coalition are made concerning the behavior of a group of many individuals in certain dynamic environments.From these, the time-consistent cooperative agreement can be strategically supported by ε-Nash or strong ε-Nash equilibria. While in games in the extensive form with perfect information, it is somewhat surprising that without the assumptions of deviation instant for a coalition, Nash or strong Nash equilibria can be constructed.
