Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to de...Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network.展开更多
The existence of the genome population in condition of radiation environment has been considered. The differences between the laws of the allele frequencies for autosomal genes and genes linked to sex are described. R...The existence of the genome population in condition of radiation environment has been considered. The differences between the laws of the allele frequencies for autosomal genes and genes linked to sex are described. Radiation conditions were found at maintenance of the balance of the Hardy-Weinberg genotype in the population, as well as conditions of complete elimination of the targeted allele by ionizing radiation. Conclusions about the nature of radiation resistance of the population are drawn.展开更多
Potential games are noncooperative games for which there exist auxiliary functions, called potentials,such that the maximizers of the potential are also Nash equilibria of the corresponding game. Some properties of Na...Potential games are noncooperative games for which there exist auxiliary functions, called potentials,such that the maximizers of the potential are also Nash equilibria of the corresponding game. Some properties of Nash equilibria, such as existence or stability, can be derived from the potential, whenever it exists. We survey different classes of potential games in the static and dynamic cases, with a finite number of players, as well as in population games where a continuum of players is allowed. Likewise, theoretical concepts and applications are discussed by means of illustrative examples.展开更多
We present in this article an epidemic model with saturated in metapopulation setting. We develop the mathematical modelling of HIV transmission among adults in Metapopulation setting. We discussed the positivity of t...We present in this article an epidemic model with saturated in metapopulation setting. We develop the mathematical modelling of HIV transmission among adults in Metapopulation setting. We discussed the positivity of the system. We calculated the reproduction number, If ?for , then each infectious individual in Sub-Population j infects on average less than one other person and the disease is likely to die out. Otherwise, if ?for , then each infectious individual in Sub-Population j infects on average more than one other person;the infection could therefore establish itself in the population and become endemic. An epidemic model, where the presence or absence of an epidemic wave is characterized by the value of ?both ideas of the inner equilibrium point of stability properties are discussed.展开更多
The response of ecosystems to perturbations is considered from a thermodynamic perspective by acknowl-edging that, as for all macroscopic systems and processes, the dynamics and stability of ecosystems is sub-ject to ...The response of ecosystems to perturbations is considered from a thermodynamic perspective by acknowl-edging that, as for all macroscopic systems and processes, the dynamics and stability of ecosystems is sub-ject to definite thermodynamic law. For open ecosystems, exchanging energy, work, and mass with the en-vironment, the thermodynamic criteria come from non-equilibrium or irreversible thermodynamics. For ecosystems during periods in which the boundary conditions may be considered as being constant, it is shown that criteria from irreversible thermodynamic theory are sufficient to permit a quantitative prediction of ecosystem response to perturbation. This framework is shown to provide a new perspective on the popula-tion dynamics of real ecosystems.展开更多
In this paper, we study a stochastic epidemic model in Meta-population setting. The stochastic model is obtained from the deterministic model by set up random perturbations about the endemic equilibrium state. The out...In this paper, we study a stochastic epidemic model in Meta-population setting. The stochastic model is obtained from the deterministic model by set up random perturbations about the endemic equilibrium state. The outcome of random perturbations on the stability actions of endemic equilibrium is discussed. Stability of the two equilibriums is studied using the Lyapunov function.展开更多
This paper studies the backward-forward linear-quadratic-Gaussian(LQG)games with major and minor agents(players).The state of major agent follows a linear backward stochastic differential equation(BSDE)and the states ...This paper studies the backward-forward linear-quadratic-Gaussian(LQG)games with major and minor agents(players).The state of major agent follows a linear backward stochastic differential equation(BSDE)and the states of minor agents are governed by linear forward stochastic differential equations(SDEs).The major agent is dominating as its state enters those of minor agents.On the other hand,all minor agents are individually negligible but their state-average affects the cost functional of major agent.The mean-field game in such backward-major and forward-minor setup is formulated to analyze the decentralized strategies.We first derive the consistency condition via an auxiliary mean-field SDEs and a 3×2 mixed backward-forward stochastic differential equation(BFSDE)system.Next,we discuss the wellposedness of such BFSDE system by virtue of the monotonicity method.Consequently,we obtain the decentralized strategies for major and minor agents which are proved to satisfy the-Nash equilibrium property.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11275017 and 11173028
文摘Based on the infectious disease model with disease latency, this paper proposes a new model for the rumor spreading process in online social network. In this paper what we establish an SEIR rumor spreading model to describe the online social network with varying total number of users and user deactivation rate. We calculate the exact equilibrium points and reproduction number for this model. Furthermore, we perform the rumor spreading process in the online social network with increasing population size based on the original real world Facebook network. The simulation results indicate that the SEIR model of rumor spreading in online social network with changing total number of users can accurately reveal the inherent characteristics of rumor spreading process in online social network.
文摘The existence of the genome population in condition of radiation environment has been considered. The differences between the laws of the allele frequencies for autosomal genes and genes linked to sex are described. Radiation conditions were found at maintenance of the balance of the Hardy-Weinberg genotype in the population, as well as conditions of complete elimination of the targeted allele by ionizing radiation. Conclusions about the nature of radiation resistance of the population are drawn.
基金supported by Consejo Nacional de Ciencia y Tecnología of Mexico (Grant No. 221291)
文摘Potential games are noncooperative games for which there exist auxiliary functions, called potentials,such that the maximizers of the potential are also Nash equilibria of the corresponding game. Some properties of Nash equilibria, such as existence or stability, can be derived from the potential, whenever it exists. We survey different classes of potential games in the static and dynamic cases, with a finite number of players, as well as in population games where a continuum of players is allowed. Likewise, theoretical concepts and applications are discussed by means of illustrative examples.
文摘We present in this article an epidemic model with saturated in metapopulation setting. We develop the mathematical modelling of HIV transmission among adults in Metapopulation setting. We discussed the positivity of the system. We calculated the reproduction number, If ?for , then each infectious individual in Sub-Population j infects on average less than one other person and the disease is likely to die out. Otherwise, if ?for , then each infectious individual in Sub-Population j infects on average more than one other person;the infection could therefore establish itself in the population and become endemic. An epidemic model, where the presence or absence of an epidemic wave is characterized by the value of ?both ideas of the inner equilibrium point of stability properties are discussed.
文摘The response of ecosystems to perturbations is considered from a thermodynamic perspective by acknowl-edging that, as for all macroscopic systems and processes, the dynamics and stability of ecosystems is sub-ject to definite thermodynamic law. For open ecosystems, exchanging energy, work, and mass with the en-vironment, the thermodynamic criteria come from non-equilibrium or irreversible thermodynamics. For ecosystems during periods in which the boundary conditions may be considered as being constant, it is shown that criteria from irreversible thermodynamic theory are sufficient to permit a quantitative prediction of ecosystem response to perturbation. This framework is shown to provide a new perspective on the popula-tion dynamics of real ecosystems.
文摘In this paper, we study a stochastic epidemic model in Meta-population setting. The stochastic model is obtained from the deterministic model by set up random perturbations about the endemic equilibrium state. The outcome of random perturbations on the stability actions of endemic equilibrium is discussed. Stability of the two equilibriums is studied using the Lyapunov function.
基金support partly by RGC Grant 502412,15300514,G-YL04.ZWu acknowledges the Natural Science Foundation of China(61573217),111 project(B12023)the National High-level personnel of special support program and the Chang Jiang Scholar Program of Chinese Education Ministry.
文摘This paper studies the backward-forward linear-quadratic-Gaussian(LQG)games with major and minor agents(players).The state of major agent follows a linear backward stochastic differential equation(BSDE)and the states of minor agents are governed by linear forward stochastic differential equations(SDEs).The major agent is dominating as its state enters those of minor agents.On the other hand,all minor agents are individually negligible but their state-average affects the cost functional of major agent.The mean-field game in such backward-major and forward-minor setup is formulated to analyze the decentralized strategies.We first derive the consistency condition via an auxiliary mean-field SDEs and a 3×2 mixed backward-forward stochastic differential equation(BFSDE)system.Next,we discuss the wellposedness of such BFSDE system by virtue of the monotonicity method.Consequently,we obtain the decentralized strategies for major and minor agents which are proved to satisfy the-Nash equilibrium property.
