Most viewed papers

191. Silaev D.A., Korotaev D.O.
     Solving of boundary tasks by using S-spline
     Computer Research and Modeling, 2009, v. 1, no. 2, pp. 161-171

     This article is dedicated to use of S-spline theory for solving equations in partial derivatives. For example, we consider solution of the Poisson equation. S-spline — is a piecewise-polynomial function. Its coefficients are defined by two states. The first part of coefficients are defined by smoothness of the spline. The second coefficients are determined by least-squares method. According to order of considered polynomial and number of conditions of first and second type we get S-splines with different properties. At this moment we have investigated order 3 S-splines of class C¹ and order 5 S-splines of class C² (they meet conditions of smoothness of order 1 and 2 respectively). We will consider how the order 3 S-splines of class C¹ can be applied for solving equation of Poisson on circle and other areas.

     Keywords: S-spline theory, Poisson equation, differential equations solving.
     Views (last year): 8. Citations: 8 (RSCI).
192. Vrazhnov D.A., Shapovalov A.V., Nikolaev V.V.
     Symmetries of differential equations in computer vision applications
     Computer Research and Modeling, 2010, v. 2, no. 4, pp. 369-376

     In our work we present generalization of well-known approach for construction of invariant feature vectors of images in computer vision applications. Basic feature of the suggested algorithm is replacement of commonly used Gaussian filter by convolution of image function with Green’s function of evolution operator, which inherits symmetries of this operator. The use of general filtration allows to obtain additional characteristics of invariant feature vectors.

     Keywords: computer vision, pattern recognition, filtering, symmetries of differential equations, Green Function.
     Views (last year): 8. Citations: 4 (RSCI).
193. Aponin Yu.M., Aponina E.A.
     The invariance principle of La-Salle and mathematical models for the evolution of microbial populations
     Computer Research and Modeling, 2011, v. 3, no. 2, pp. 177-190

     A mathematical model for the evolution of microbial populations during prolonged cultivation in a chemostat has been constructed. This model generalizes the sequence of the well-known mathematical models of the evolution, in which such factors of the genetic variability were taken into account as chromosomal mutations, mutations in plasmid genes, the horizontal gene transfer, the plasmid loss due to cellular division and others. Liapunov’s function for the generic model of evolution is constructed. The existence proof of bounded, positive invariant and globally attracting set in the state space of the generic mathematical model for the evolution is presented because of the application of La-Salle’s theorem. The analytic description of this set is given. Numerical methods for estimate of the number of limit sets, its location and following investigation in the mathematical models for evolution are discussed.

     Keywords: evolution of microbial populations, mathematical modeling, Liapunov’s function, bounded globally attracting set.
     Views (last year): 8. Citations: 3 (RSCI).
194. Moskalev P.V.
     The structure of site percolation models on three-dimensional square lattices
     Computer Research and Modeling, 2013, v. 5, no. 4, pp. 607-622

     In this paper we consider the structure of site percolation models on three-dimensional square lattices with various shapes of (1,π)-neighborhood. For these models, are proposed iso- and anisotropic modifications of the invasion percolation algorithm with (1,0)- and (1,π)-neighborhoods. All the above algorithms are special cases of the anisotropic invasion percolation algorithm on the n-dimensional lattice with a (1,π)-neighborhood. This algorithm is the basis for the package SPSL, released under GNU GPL-3 using the free programming language R.

     Keywords: site percolation, n-dimensional square lattice, non-metric Minkowski distance, R programming language, SPSL package.
     Views (last year): 8. Citations: 5 (RSCI).
195. Zenyuk D.A., Malinetsky G.G., Faller D.S.
     Simulation of corruption in hierarchical systems
     Computer Research and Modeling, 2014, v. 6, no. 2, pp. 321-329

     Simulation model of corruption in hierarchical systems which takes into account individual strategies of elements and collective behavior of large groups is proposed. Evolution of various characteristics like level of corruption or ratio of corrupted elements and their dependence on external parameters are discussed. The effectiveness of various anticorruptional strategies is examined by means of numeric analysis.

     Keywords: corruption, stochastic simulation, corporation management, graph theory, self-organization, social systems.
     Views (last year): 8. Citations: 11 (RSCI).
196. Dähmlow P., Luengviria C., Müller S.C.
     Electric field effects in chemical patterns
     Computer Research and Modeling, 2014, v. 6, no. 5, pp. 705-718

     Excitation waves are a prototype of self-organized dynamic patterns in non-equilibrium systems. They develop their own intrinsic dynamics resulting in travelling waves of various forms and shapes. Prominent examples are rotating spirals and scroll waves. It is an interesting and challenging task to find ways to control their behavior by applying external signals, upon which these propagating waves react. We apply external electric fields to such waves in the excitable Belousov–Zhabotinsky (BZ) reaction. Remarkable effects include the change of wave speed, reversal of propagation direction, annihilation of counter-rotating spiral waves and reorientation of scroll wave filaments. These effects can be explained in numerical simulations, where the negatively charged inhibitor bromide plays an essential role. Electric field effects have also been investigated in biological excitable media such as the social amoebae Dictyostelium discoideum. Quite recently we have started to investigate electric field effect in the BZ reaction dissolved in an Aerosol OT water-in-oil microemulsion. A drift of complex patterns can be observed, and also the viscosity and electric conductivity change. We discuss the assumption that this system can act as a model for long range communication between neurons.

     Keywords: autowaves, chemical patterns, electric field effects.
     Views (last year): 8.
197. Okhapkina E.P., Okhapkin V.P.
     Approaches to a social network groups clustering
     Computer Research and Modeling, 2015, v. 7, no. 5, pp. 1127-1139

     The research is devoted to the problem of the use of social networks as a tool of the illegal activity and as a source of information that could be dangerous to society. The article presents the structure of the multiagent system with which a social network groups could be clustered according to the criteria uniquely defines a group as a destructive. The agents’ of the system clustering algorithm is described.

     Keywords: multi-agent system, cluster analysis, system interaction, security.
     Views (last year): 8. Citations: 2 (RSCI).
198. Gavrilov S.V., Matyushkin I.V.
     Statistical analysis of Margolus’s block-rotating mechanism cellular automation modeling the diffusion in a medium with discrete singularities
     Computer Research and Modeling, 2015, v. 7, no. 6, pp. 1155-1175

     The generalization of Margolus’s block cellular automaton on a hexagonal grid is formulated. Statistical analysis of the results of probabilistic cellular automation for vast variety of this scheme solving the test task of diffusion is done. It is shown that the choice of the hexagon blocks is 25% more efficient than Y-blocks. It is shown that the algorithms have polynomial complexity, and the polynom degree lies within 0.6÷0.8 for parallel computer, and in the range 1.5÷1.7 for serial computer. The effects of embedded into automaton’s field defective cells on the rate of convergence are studied also.

     Keywords: diffusion, method of modeling, discrete singularities, block cellular automata, Margolus neighborhood, hexagonal grid.
     Views (last year): 8. Citations: 4 (RSCI).
199. Khosaeva Z.K.
     The mathematics model of protests
     Computer Research and Modeling, 2015, v. 7, no. 6, pp. 1331-1341

     A mathematical model that reflects the main features of the protests is constructed in this paper. An analytical solution was found with assuming that only excited part of the population involved in protests. The numerical value of the model coefficients was estimated from the real data for the cascade of protests that took place in Leipzig in 1989. The changes of the participants number in the protest action with influence the model coefficients was analysed.

     Keywords: protests mathematical modelling, analytical solution, coefficients estimation.
     Views (last year): 8. Citations: 2 (RSCI).
200. Stepantsov M.Y.
     A discreet ‘power–society–economics’ model based on cellular automaton
     Computer Research and Modeling, 2016, v. 8, no. 3, pp. 561-572

     In this paper we consider a new modification of the discrete version of Mikhailov’s ‘power–society’ model, previously proposed by the author. This modification includes social-economical dynamics and corruption of the system similarly to continuous ‘power–society–economics–corruption’ model but is based on a stochastic cellular automaton describing the dynamics of power distribution in a hierarchy. This new version is founded on previously proposed ‘power–society’ system modeling cellular automaton, its cell state space enriched with variables corresponding to population, economic production, production assets volume and corruption level. The social-economical structure of the model is inherited from Solow and deterministic continuous ‘power–society–economics–corruption’ models. At the same time the new model is flexible, allowing to consider regional differentiation in all social and economical dynamics parameters, to use various production and demography models and to account for goods transit between the regions. A simulation system was built, including three power hierarchy levels, five regions and 100 municipalities. and a number of numerical experiments were carried out. This research yielded results showing specific changes of the dynamics in power distribution in hierarchy when corruption level increases. While corruption is zero (similar to the previous version of the model) the power distribution in hierarchy asymptotically tends to one of stationary states. If the corruption level increases substantially, volume of power in the system is subjected to irregular oscillations, and only much later tends to a stationary value. The meaning of these results can be interpreted as the fact that the stability of power hierarchy decreases when corruption level goes up.

     Keywords: ‘power–society’ system, cellular automata, numerical experiment, simulation, economics, corruption.
     Views (last year): 8. Citations: 1 (RSCI).

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