Vol 79, No 8 (2018)

We consider discrete-time switched systems with switching of linear time-invariant right-hand parts. The notion of a connected discrete switched system is introduced. For systems with the connectedness property, we propose necessary and sufficient frequency-domain conditions for the existence of a common quadratic Lyapunov function that provides the stability for a system under arbitrary switching. The set of connected switched systems contains discrete control systems with several time-varying nonlinearities from the finite sectors, considered in the theory of absolute stability. We consider the case of switching between three linear subsystems in more details and give an illustrative example.

We consider phase systems of order six, four, and three that admit chaotic attractors of various types. We apply a localization method that makes it possible to find regions in the phase space (localizing sets) that contain all attractors of the system. We obtain systems of inequalities that define localizing sets and represent estimates of the amplitudes of established oscillations and chaotic attractors.

We study nonsmooth convex stochastic optimization problems with a two-point zero-order oracle, i.e., at each iteration one can observe the values of the function’s realization at two selected points. These problems are first smoothed out with the well-known technique of double smoothing (B.T. Polyak) and then solved with the stochastic mirror descent method. We obtain conditions for the permissible noise level of a nonrandom nature exhibited in the computation of the function’s realization for which the estimate on the method’s rate of convergence is preserved.

We construct and investigate a mathematical model for joint servicing of real-time multiservice traffic in access networks with a hierarchical topology. The model takes into account how the arrival of claims in each flow depends on the number of users that form this flow of claims and that are being serviced. We define quality indicators for joint servicing of claims through the values of stationary probabilities in the model. We obtain relations between them that simplify their estimation. We develop an algorithm for calculating the characteristics of the model based on an implementation of the convolution algorithm. We propose a procedure for estimating the transmission rate of connecting lines in the access network needed to service incoming traffic with a given quality. We also give numerical examples that illustrate the characteristic features of implementing the developed computational procedures.

We consider the problems of defects arising in the production of continuously cast billets at continuous casting plants. We propose a model for predicting slab cracks based on the random forest machine learning algorithm. We determine the main technological parameters that influence the appearance of cracks and present the results of the model.

We consider the problem of model selection for deep learning models of suboptimal complexity. The complexity of a model is understood as the minimum description length of the combination of the sample and the classification or regression model. Suboptimal complexity is understood as an approximate estimate of the minimum description length, obtained with Bayesian inference and variational methods. We introduce probabilistic assumptions about the distribution of parameters. Based on Bayesian inference, we propose the likelihood function of the model. To obtain an estimate for the likelihood, we apply variational methods with gradient optimization algorithms. We perform a computational experiment on several samples.

This paper considers a voting problem in which the individual preferences of electors are defined by the ranked lists of candidates. For single-winner elections, we apply the criterion of weak positional dominance (WPD, PD), which is closely related to the positional scoring rules. Also we formulate the criterion of weak mutual majority (WMM), which is stronger than the majority criterion but weaker than the criterion of mutual majority (MM). Then we construct two modifications for the median voting rule that satisfy the Condorcet loser criterion. As shown below, WPD and WMM are satisfied for the first modification while PD and MM for the second modification. We prove that there is no rule satisfying WPD and MM simultaneously. Finally, we check a list of 37 criteria for the constructed rules.

This paper considers a modification of the multistage bidding model with continuous bids. Bidding takes place between two players for one unit of a risky asset (one stock). Player 1 knows the real price of the asset while Player 2 knows only the probabilities of high and low prices of the asset. At each stage of the bidding, players make real valued bids. The higher bid wins, and one unit of the risky asset is transacted to the winning player. The price of the transaction is a convex combination of the bids with a given coefficient. The optimal strategies of the players and the value of the n-stage game are found.