On an approach to constructing static ball models in general relativity

An approach to construction of static models is demonstrated for a fluid ball. Five examples are considered. Two of them are exact solutions of the Einstein equations; the other three are connected with the Airy special functions, the hypergeometric functions and the Heun functions.     

基于CCEA和改进郭涛算法的函数优化问题求解

在合作式协同演化(CCEA)的基础上,引入了使用高斯变异算子的郭涛算法,设计了一种求解函数优化问题的高效混合演化算法.通过求解复杂高维的函数优化问题的多个实例,并将该算法和CCEA与基本郭涛算法结合的方法--CCGT进行了对比.实验结果表明,新算法是高效的,其结果优于现存文献中的其它模型,但不及CCGT优秀.证明在该算法中引入的高斯变异算子的作用不大.     

On a class of linear stochastic differential games

The solution for a class of stochastic pursuit-evasion differential games between two linear dynamic systems is given. This class includes the classical interception game in Euclidean space. The performance index which is optimized is quadratic, and one of the two players has imperfect (noisy) knowledge of the states of the two systems. The "certainty-equivalence principle' or, equivalently, the technique of separating the estimator and the controller which characterizes the standard stochastic control problem is shown to be applicable to this class of differential games.     

Fuzzy restrictions and an application to cooperative games with restricted cooperation

The concept of restriction, which is an extension of that of interior operator, was introduced to model limited cooperation in cooperative game theory. In this paper, a fuzzy version of restrictions is presented. We show that these new operators, called fuzzy restrictions, can be characterized by the transitivity of the fuzzy dependence relations that they induce. As an application, we introduce cooperative games with fuzzy restriction, which are used to model cooperative situations in which each player in a coalition has a level of cooperation within the coalition. A value for these games is defined and characterized.     

On one approach to constructing timetables of freight trains in a railroad network

We consider scheduling problems for routing freight trains through a railroad network. To solve these problems, we propose models and methods that use ideas and principles previously applied to construct part processing job schedules in industrial shops. The proposed approaches have been implemented in software, and our computational experiments have shown their efficiency.     

Dynamic competition in IT security: A differential games approach

Hackers evaluate potential targets to identify poorly defended firms to attack, creating competition in IT security between firms that possess similar information assets. We utilize a differential game framework to analyze the continuous time IT security investment decisions of firms in such a target group. We derive the steady state equilibrium of the duopolistic differential game, show how implicit competition induces overspending in IT defense, and then demonstrate how such overinvestment can be combated by innovatively managing the otherwise misaligned incentives for coordination. We show that in order to achieve cooperation, the firm with the higher asset value must take the lead and provide appropriate incentives to elicit participation of the other firm. Our analysis indicates that IT security planning should not remain an internal, firm-level decision, but also incorporate the actions of those firms that hackers consider as alternative targets.     

On bang-bang solutions of stochastic differential games

We consider two classes of scalar stochastic differential games with hard constraints on controls. The solutions are found to be bang-bang, by extending a technique developed earlier for stochastic optimal control problems.     

An approach for community detection in social networks based on cooperative games theory

Detecting communities is of great importance in social network analysis. However it is an issue that has not yet been satisfactorily solved, despite the efforts made by interdisciplinary research communities over the past few years, because of the nature of complexity in deciding how community structures should be recognized. In this paper we propose an approach based on cooperative game theory for community detection in social networks. We regard individuals as players, and regard communities as coalitions formed by players, and model community detection problem as the formation and optimization of coalitions. Furthermore, we define coalition profile for players to indicate coalitions that players joined, the order of a coalition profile is defined as the number of coalitions in a coalition profile, and we introduce a utility function to measure preference of coalition profiles. Accordingly, we propose an algorithm to detect a coalition profile with maximal utility function values. We have implemented the algorithms developed in this study and experimental results demonstrate the effectiveness of our approaches.     

一般和博弈中的合作多agent学习

理性和收敛是多agent学习研究所追求的目标,在理性合作的多agent系统中提出利用Pareto占优解代替非合作的Nash平衡解进行学习,使agent更具理性,另一方面引入社会公约来启动和约束agent的推理,统一系统中所有agent的决策,从而保证学习的收敛性．利用2人栅格游戏对多种算法进行验证,成功率的比较说明了所提算法具有较好的学习性能．     

Fuzzy differential games for nonlinear stochastic systems:suboptimal approach

A fuzzy differential game theory is proposed to solve the n-person (or n-player) nonlinear differential noncooperative game and cooperative game (team) problems, which are not easily tackled by the conventional methods. In the paper, both noncooperative and cooperative quadratic differential games are considered. First, the nonlinear stochastic system is approximated by a fuzzy model. Based on the fuzzy model, a fuzzy controller is proposed to deal with the noncooperative differential game in the sense of Nash equilibrium strategies or with the cooperative game in the sense of Pareto-optimal strategies. Using a suboptimal approach, the outcomes of the fuzzy differential games for both the noncooperative and the cooperative cases are parameterized in terms of an eigenvalue problem. Since the state variables are usually unavailable, a suboptimal fuzzy observer is also proposed in this study to estimate the states for these differential game problems. Finally, simulation examples are given to illustrate the design procedures and to indicate the performance of the proposed methods     

On the expressiveness of the approach to constructing PLC-programs by LTL-specification

The article is devoted to an approach to constructing and verification of discrete PLC-programs by LTL-specification. This approach provides a possibility of analysing the correctness of PLCprograms by using the model checking method. The linear temporal logic LTL is used as a language of specification of the program behavior. The correctness analysis of LTL-specification is automatically performed by the symbolic model checking tool Cadence SMV. The article demonstrates the consistency of the approach to constructing and verification of PLC programs by LTL-specification from the point of view of Turing power. It is proved that in accordance with this approach for any Minsky counter machine an LTL-specification can be built, which is used for machine implementation in any PLC programming language of standard IEC 61131-3. Minsky machines are equipollent to Turing machines, and the considered approach also has the Turing power. The proof focuses on representation of a counter machine behavior in the form of a set of LTL-formulas and matching these formulas to constructions of ST and SFC languages. SFC is interesting as a specific graphical language. ST is considered as a basic language because the implementation of a counter machine on IL, FBD/CFC and LD languages is reduced to rewriting blocks of an ST-program. The idea of the proof is demonstrated by an example of a Minsky 3-counter machine, which implements a function of squaring.     

Duality on combinatorial structures. An application to cooperative games

This paper deals with cooperative games in which only certain coalitions are feasible. Several combinatorial structures have been used to represent feasible coalition systems for different situations: poset of ideals, connected sets in graphs, convex geometries or antimatroids. Augmenting systems are combinatorial structures generalizing antimatroids defined in the framework of the game theory. In this paper, we introduced decreasing systems as dual structures of the augmenting systems. We connect the classical concept of dual game with the duality between these structures. The Shapley and the Banzhaf values are studied and compared for augmenting and decreasing systems.     

On the theory of differential pursuit games in distributed parameter systems

This paper is devoted to a study of controlled pursuit-evading games in systems of parabolic type. The corresponding differential equations have variable coefficients and do not contain mixed derivatives. Our main technical tool is the finite difference method. Sufficient conditions for successful pursuit completion are obtained.     

A fuzzy approach to strategic games

A game is a decision-making situation with many players, each having objectives that conflict with each other. The players involved in the game usually make their decisions under conditions of risk or uncertainty. In the paper, a fuzzy approach is proposed to solve the strategic game problem in which the pure strategy set for each player is already defined. Based on the concepts of fuzzy set theory, the approach uses a multicriteria decision-making method to obtain the optimal strategy in the game, a method which shows more advantages than the classical game methods. Moreover, with this approach, some useful conclusions are reached concerning the famous “prisoner's dilemma” problem in game theory     

On numerical solution of positional differential games with nonterminal payoff

We propose a numerical method for an approximate construction of the game value and optimal control laws in a linear-convex positional differential game with a quality index that evaluates the collection of deviations of the motion trajectory at given time moments from given targets. We show the algorithmic complexity of this method, details of software implementation, and results of numerical experiments.     

Learning to play games using a PSO-based competitive learning approach

A new competitive approach is developed for learning agents to play two-agent games. This approach uses particle swarm optimizers (PSO) to train neural networks to predict the desirability of states in the leaf nodes of a game tree. The new approach is applied to the TicTacToe game, and compared with the performance of an evolutionary approach. A performance criterion is defined to quantify performance against that of players making random moves. The results show that the new PSO-based approach performs well as compared with the evolutionary approach.