Reaction–diffusion type replicator systems are investigated for the case of a bimatrix. An approach proposed earlier for formalizing and analyzing distributed replicator systems with one matrix is applied to asymmetric conflicts. A game theory interpretation of the problem is described and the relation between dynamic properties of systems and their game characteristics is determined. The stability of a spatially homogeneous solution for a distributed system is considered and a theorem on maintaining stability is proved. The results are illustrated with two-dimensional examples in the case of distribution.

In this paper, we consider the problem of optimal resource allocation for the Gale problem of demand and supply in the presence of uncertain factors. Based on the Danzig-Wolfe decomposition method and the generalized potential method developed by the author earlier for the deterministic version of the problem, a numerical algorithm for solving the problem is constructed and justified

Integral equations emerging in a model of stationary biological communities such that their kernels have variable coefficients of excess (kurtosian kernels)are investigated. The dependence of the first and second spatial moment on the dimension of the environment is considered. A fastcomputation algorithm for the multi-dimensional nonlinear convolution is considered. The existence of a radial solution is proved.

A computational solution to the integral equation in the biological spatial model is found. The numerical techniques that are used (the Nystr{\"o}m and Neumann series methods, the latter being one of successive approximations) yield a reasonably accurate solution. An approach of moving from multidimensional equations to a one-dimensional equation for high-dimensional spaces is proposed. Explicit formulas for kernels when there are normal initial kernels are also proposed.

The problem of computing the width of simplices generated by the convex hull of their integer vertices is considered. An FPT algorithm, in which the parameter is the maximum absolute value of the rank minors of the matrix consisting from the simplex vertices, is presented.

The influence of ringing effect (which is based on the Gibbs phenomenon) on the mutual coherence in sparse representation approach is considered. It is shown that for random vectors, the ringing effect increases the average mutual coherence. Numerical results that demonstrate that the mutual coherence behaves identically for real images are given. It is also shown how the ringing effect affects the sparsity of representations (which is closely related to the mutual coherence).

The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ B n ± O(1), where τ B is a constant that depends only on the basis B, are obtained for the delay of a multiplexer function of order n. These bounds are used in the given model to obtain asymptotic bounds of the form τ B n±O(1) for the corresponding Shannon function, i.e., for the delay of the “worst” Boolean function of the given n variables.

The two-species model of self-structured stationary biological communities proposed by U. Dieckmann and R. Law is considered. A way of investigating the system of integro-differential equations describing the model equilibrium is developed, nontrivial stationary points are found, and constraints on the model parameter space resulting in similar stationary points are studied. The results are applied to a number of widely known biological scenarios

The two-species model of self-structured stationary biological communities proposed by U. Dieckmann and R. Law is considered. A way of investigating the system of integro-differential equations describing the model equilibrium is developed, nontrivial stationary points are found, and constraints on the model parameter space resulting in similar stationary points are studied. The results are applied to a number of widely known biological scenarios.

We study some simple models of confidential databases in cloud computing systems. In the framework of these models we introduce a concept of deductive security for queries to such databases, find necessary and sufficient conditions of deductive security, and describe some classes of queries which satisfy these requirements.

We study a formal model of cloud computing systems with auxiliary cryptoservers. Assuming an existence of a secure threshold somewhat homomorphic public key cryptosystem we show how to build a cloud computing system secure in this model.

It is established that for nonconstant Boolean function f(x1, …, xn), there is a testable gen eralized iterative switching circuit in which function f(x1, …, xn) is realized and the single fault detec tion test of constant length is assumed. Ke

A study is performed of the main approaches to investigating the stochastic process of population dynamics. Continuous time and space and immovable individuals are used to derive a denumerable system of integrodifferential equations corresponding to the dynamics of the spatial momentum of this process. A way to find an approximate solution using the momentum approach is described.

The problem of optimal distribution of resources dedicated to a certain complex of interrelated tasks according to the criterion of minimum execution time of all tasks is described