Entropy model of the investment portfolio

A stochastic model of the investment portfolio based on maximization of entropy was proposed. The model claims at simulating behavior of the investor at portfolio formation. Consideration was given to the computational methods adapted to the problems arising in these models.     

Analytical expression of the expected values of capital at voting in the stochastic environment

In the simplest variant of the model of collective decision making in the stochastic environment, the participants were segregated into egoists and a group of collectivists. “Proposal of the environment” is the stochastically generated vector of algebraic increments of capitals. The social dynamics was defined by the sequence of proposals accepted by threshold-majority voting. Analytical expressions of the expected values of the capitals of participants, collectivists and egoists were obtained. Distinctions of some principles of group voting were discussed.     

Strategies of voting in stochastic environment: Egoism and collectivism

Consideration was given to a model of social dynamics controlled by successive collective decisions based on the threshold majority procedures. The current system state is characterized by the vector of participants’ capitals (utilities). At each step, the voters can either retain their status quo or accept the proposal which is a vector of the algebraic increments in the capitals of the participants. In this version of the model, the vector is generated stochastically. Comparative utility of two social attitudes—egoism and collectivism—was analyzed. It was established that, except for some special cases, the collectivists have advantages, which makes realizable the following scenario: on the conditions of protecting the corporate interests, a group is created which is joined then by the egoists attracted by its achievements. At that, group egoism approaches altruism. Additionally, one of the considered variants of collectivism handicaps manipulation of voting by the organizers.     

Predictive non-iterative coordinations in hierarchical systems

Predictive and goal-oriented coordinations are primarily used in multilevel systems. In this paper, they are developed in non-iterative form. Proof for the predictive coordination strategy is given. Properties and disadvantages of real-time control for a two-level system are analyzed. For optimization problems, load and coordination rate are estimated in terms of the number of floating-point operations per second.     

Structure of equilibrium time-varying trajectories in the Lucas endogenous growth model

A family of time-varying equilibrium trajectories in the well-known Lucas endogenous economic growth model is studied. The equilibrium trajectories are shown to differ not only in level, but also in long-term growth rate under a certain combination of parameters.     

Optimal multilevel organizations for the power cost functions

The problem of maximizing the profit of an economic organization with simultaneous selection of its composition and structure was formulated. Consideration was given to a class of the power cost functions whose parameters reflect the organization environmental characteristics. The optimal organization was analytically established for this case, and the regularities of its variation vs. the environmental conditions were investigated.     

Model of community emergence in weighted social networks

Over the years network theory has proven to be rapidly expanding methodology to investigate various complex systems and it has turned out to give quite unparalleled insight to their structure, function, and response through data analysis, modeling, and simulation. For social systems in particular the network approach has empirically revealed a modular structure due to interplay between the network topology and link weights between network nodes or individuals. This inspired us to develop a simple network model that could catch some salient features of mesoscopic community and macroscopic topology formation during network evolution. Our model is based on two fundamental mechanisms of network sociology for individuals to find new friends, namely cyclic closure and focal closure, which are mimicked by local search-link-reinforcement and random global attachment mechanisms, respectively. In addition we included to the model a node deletion mechanism by removing all its links simultaneously, which corresponds for an individual to depart from the network. Here we describe in detail the implementation of our model algorithm, which was found to be computationally efficient and produce many empirically observed features of large-scale social networks. Thus this model opens a new perspective for studying such collective social phenomena as spreading, structure formation, and evolutionary processes.     

Control of single-sector economy over a finite time interval with allowance for employer consumption

The problem of optimal control of a single-sector economics over a finite time interval was studied for the class of the linear uniform production functions in terms of the criterion for maximum employer consumption under exponential growth of the manpower resources. Solution was obtained in the form of the “turnpike theorem.” Its properties were considered. The results obtained were specified for the case of the Cobb-Douglas production function.     

Peculiarities of equilibria in the forbidden-situation games

Continued was a previous study of the peculiarities of the forbidden-situation games that analyzed the guaranteed results for various sequences of the participants’ actions. Consideration now was given to the deformations of the Nash and Pareto equilibria by the mutual actions of the game participants on the set of permissible controls. The general constructions are illustrated by the analytical solutions for the Cournot model of competitive interaction of two manufacturing companies complemented by a constraint on the total raw-material resource.     

The cost of approximate controllability for semilinear heat equations

We consider the semilinear heat equation with globally Lipschitz non-linearity involving gradient terms in a bounded domain of R^n. In this paper, we obtain explicit bounds of the cost of approximate controllability, i.e., of the minimal norm of a control needed to control the system approximately. The methods we used combine global Carleman estimates, the variational approach to approximate controllability and Schauder＇s fixed point theorem.     

Development and application of the theory of parametric regulation of evolution of economic systems based on a neoclassical model of optimal growth

Presented were some results on roughness of the mathematical model of the neoclassical theory of optimal growth with and without parametric regulation, selection of the optimal law of parametric regulation, and the optimal law of parametric regulation vs. the uncontrollable parameters of this mathematical model based on the parametric regulation theory.     

Guaranteed results in games with forbidden situations

The best guaranteed results in games where “others’” control actions influence not only the utility function but also the admissibility set of each participant are analyzed and compared. The research is conducted without a formal reduction to classical games on direct products of rigid admissibility sets by means of penalized extension of the utility function. By the example of the generalized Cournot duopoly, it is shown that, for a chosen participant, his right to be the first to use common scarce resources might be more important than awareness of previous choices of his competitors. This means the possibility of violating the fundamental inequality of the classical game theory which states that the max-min of the utility function does not exceed its min-max, established for games on direct products of sets of admissible control actions.     

Entropy of hierarchical games

Numerical characteristics of complexity of decision making in the hierarchical game were introduced. Their properties, in particular coordination with the notion of information extension, were established. Examples enabling one to estimate the correspondence of the introduced notions to the intuitive concepts of game complexity were presented and used to demonstrate the techniques to determine the explicit numerical estimates.     

基于费用函数的测试性指标优化分配方法

测试性指标的优化分配关系到改进系统测试性水平所需的费用。建立了基于费用函数的测试性指标优化分配模型。根据费用函数需满足的基本要求,以费用最小为目标,设计了一种实用的非线性费用函数。分析了费用函数中各参数对费用的影响以及各参数的获取方法。针对该非线性规划问题,在给定的系统测试性指标下,采用遗传算法求解全局最优解。应用结果表明遗传算法能够获得合理的测试性分配值,费用函数可以用于系统测试性指标的优化分配。     

On controllability of the real shifted inverse power iteration

Controllability properties of the inverse power method on projective space are investigated. For complex eigenvalue shifts a simple characterization of the reachable sets in terms of invariant subspaces can be obtained. The real case is more complicated and is investigated in this paper. Necessary and sufficient conditions for complete controllability are obtained in terms of the solvability of a matrix equation. Partial results on conditions for the solvability of this matrix equation are given.     

A stabilized finite element method for modeling of gas discharges

An efficient stabilized finite element method for modeling of gas discharge plasmas is represented which provides wiggle-free solutions without introducing much artificial diffusion. The stabilization is achieved by modifying the standard Galerkin test functions by means of a weighted quadratic term that results in a consistent Petrov-Galerkin formulation of the charge carriers in the plasma. Using the example of a glow discharge plasma in argon, it is shown that this efficient method provides more accurate results on the same spatial grid than the widely used finite difference approach proposed by Scharfetter-Gummel if the weighting factor is determined in dependence on the local Péclet number and the modified test functions are consistently applied to all terms of the governing equations.     

Optimal maximum norm error estimates for some finite element methods for treating the Dirichlet problem

The goal of this paper is to establish optimalL ^∞ error estimates for a few different finite element type methods for the Dirichlet problem in a bounded domain. The methods are selected so as to avoid the necessity for imposing boundary conditions on the trial functions, usually difficult in practice. Three specific methods are treated. These are the method of interpolated boundary condition and two methods of Nitsche.     

Progress in the understanding of the fluctuating lattice Boltzmann equation

We give a brief account of the development of methods to include thermal fluctuations into lattice Boltzmann algorithms. Emphasis is put on our recent work [B. Dünweg, U.D. Schiller, A.J.C. Ladd, Phys. Rev. E 76 (2007) 036704] which provides a clear understanding in terms of statistical mechanics.     

Duality of the notions of controllability and observability for degenerate linear hybrid systems

Consideration was given to the linear system of equations in continuous and discrete time with constant matrices of coefficients which is not explicit in the derivative of the continuous component of the desired vector function. The notion of conjugate system was introduced, and an analog of the Kalman duality theorem relating the notions of total controllability and observability was proved.     

Optimal control problem of development of an electric power system

A problem is considered for the definition of long-term strategies of the placing in service and disassembly of electric powers of an electric power system, which is described with the aid of nonclassical Volterra integral equations of the 1st kind. A problem is stated of the search for optimal terms of service of generating powers that afford the prescribed requirement for electric energy at the minimum of total expenditures, for the placing in service (input) and operation of generating powers. Results are given of the calculation for the United electric power system of Russia.