Articles

This paper is devoted to the problem of separation of mixtures of probability distributions. An optimization method is proposed as an alternative to the EM-algorithm (Expectation-Maximization) for statistical estimation of mixture parameters. The idea of approximating the distribution of increments (logarithms) of financial data by a mixture of normal laws is considered. The practical application of such an approximation to the problems of calculating and predicting volatility, as well as to the problem of calculating the risk measure (Value at Risk), is presented. The results obtained allow us to conclude that the application of mixtures of normal distributions to the description of financial data is adequate.

The article deals with localization methods of inverse magnetoencephalography tasks. Localization methods are important in real clinical practice. During neurosurgical interventions, various areas of the brain can be damaged, including non-recoverable areas. Since the location of functional areas in the human brain is individual, the doctor must be able to localize these areas in the preoperative period with high accuracy. The developed methods serve the solution of such an important problem.

Similarity transformations are the main part of matrix theory, which studies numerous classes of special matrices. Accordingly, there are many ways of describing such classes. In most cases, one can verify whether a matrix belongs to the required class by a rational calculation, that is, by a finite algorithm using only arithmetical operations.

The use of a large number of drones set us the tasks of correct, transparent, and high-performance modeling of their collective activity within the framework of swarm behavior. For this, an example of transitioning from the description of the control system of a single drone to the behavior of a swarm of identical drones based on Hadamard algebra (product) was developed and given. It was found that the use of such an approach increases the performance of the model by dozens of times and allows modeling of swarm systems with a very large number of agents.

We study the existence of an implicit function, defined by an equation G(x, σ) = 0, in a neighborhood of an abnormal point (x0, σ0). We prove that if some λ-truncation of the mapping F(x) = G(x, σ0) is regular in a certain direction, then the sought implicit function exists.

The paper considers the problem of feedback control for a group of several quadrocopters. The main goal is to transfer this group from a given initial position to a given target position for a fixed period of time, provided that at each intermediate time instant the quadrocopters must be in a small neighborhood of a fixed smooth curve in space. A centralized group control scheme is used. The main difficulty here is the complex, nonlinear mathematical model, describing the movement of each individual aircraft. It is necessary to develop computationally efficient algorithms for approximate search for feedback control, which allow to cope simultaneously with nonlinear dynamics, point-to-point constraints on control parameters, as well as state constraints arising in connection with group motion (in particular, due to the requirements of pairwise collision avoidance). Modifications of ellipsoidal calculus methods are used here to construct such algorithms.

It is considered the question about continuity of optimal time, as the function of initial state, for linear control objects. We obtained some generalization of the Theorems 21, 22 from the second Chapter of monograph E.B.Lee, L.Markus “Foundations of Optimal Control Theory,” J.Wiley and Sons, 1967, connected with continuity of optimal time, as the function of initial state, for linear controlled objects. In the article we broadly use the apparatus of support functions from Convex Analysis. Our results are obtained in more constructive form than another general results In this direction. In the first part we consider stationary case and in the second part it is considered non-stationary case.

Approximate bilinear algorithms for multiplication of 2 × 3 and 3 × 4 matrices (complexity 18), 2 × 4 and 4×4 matrices (complexity 24), 2×5 and 5×4 matrices (complexity 30) are presented, and approximate bilinear algorithms for multiplication of 2×n and n×4 matrices (complexity 6n) over field of characteristic zero gotten via them.

Dirichlet boundary value problem for the elliptic equation in a rectangle with a noninteger degeneration and analytic coefficients is considered. Applying the method of spectral isolation of singularities, the formal solution to the problem is constructed as a series which exhibits its non-analytic dependence with respect to y at the origin. Green’s function method verifies the convergence of the series to the classical solution of the considered problem.

The time optimal control problem with a state constraint investigates in the article. The object’s behavior is described by a system of second-order differential equations. The coefficient matrix for state variables has zero eigenvalues. The state constraint is linear. An admissible control is a piecewise continuous function that takes values from a given compact set. Sets of controllability to the origin are constructed for time intervals of various lengths.

It was proved earlier that product xy is a universal function for the class of linear functions depending on two arguments if k = 6l±1. In the paper we prove that there is no universal polynomials for the class of linear functions depending on two arguments for any even k.

Multiple structure protein alignments are essential to protein function analysis. Most methods of multiple protein structure alignment are based on pairwise alignment methods, where a resulting alignment is built up by merging pairwise alignments into the resulting alignment according to a guide tree. In this paper we propose the genetic algorithm for guide tree optimisation and provide the theoretical proof of convergence and experimental study of the proposed algorithm.

Is proposed the description of the implementation stabilizer construction algorithm for a switched linear system operating under parametric uncertainty in the Matlab package of applied mathematics is proposed.

In this paper asymptotic theorems are proved for estimates of the characteristic index, the scale parameter, and the shape and scale parameters for the remaining fixed parameters of the digamma distribution with a random sample size. Particular cases of limit distributions are given in the case when the sample size has a mixed Poisson distribution.

We discuss how to get a normal matrix from a binormal one and, conversely, how to get a binormal matrix from a normal one via the right multiplication on a suitable unitary matrix. Let N be a normal matrix badly conditioned with respect to inversion, that is, having a large condition number cond2N. We show that, among the binormal matrices B that can be obtained from N, there is a matrix whose eigenvalues have individual condition numbers of order (cond2N)1/2.