Abstract|The problem of reaching consensus in multiagent second-order systems without a spanning outgoing tree in the dependency digraph is considered. A theorem stating that the asymptotic behavior of the system is uniquely determined by the eigenprojector of the Laplacian matrix of the dependency digraph is proved. The earlier results established by the author and by Ren and Atkins in their papers are further generalized. For the case in which the dependency digraph contains no spanning outgoing tree, a regularization method is proposed.

The analysis of subjective time scales of the subjects with perspective human-computer interfaces was carried out: neurocomputer (brain-computer), electromyographic, oculografic. It is shown that for all of them it is typical to underestimate the maximum time spent for the execution of one team. In this case, for the electromyographic and oculografic, this feature is also preserved for the indicators of the average time for executing the commands. The results of the assessment demonstrate a unified approach of users to the formation of subjective time when working with various interfaces: the user estimates both the averaged and the best (minimum) with the worst (maximum) time for executing commands on a single scale. Subjects who switched worse from generating one command for the interface to another subjectively rated the interface as slower. The HRV data showed the LF-band relationship with a subjective estimate of the time spent working with the interface. Analysis of the relationship (true time-subjective) / true time has shown that subjective time scales when working with the neurocomputer and oculographic interfaces demonstrate a high correlation with each other as opposed to electromyographic.

Sparse large matrices with a block-staircase and block-treelike structure are studied. They are called quasi-block matrices and consist of independent blocks that are connected to each other pairwise or in a more general fashion. The interdependence of parameters of such matrices, such as the number of nonzero elements, the number of blocks, and the matrix size, is determined. Integer programming problems with large quasi-block matrices are described. For the efficient solution of these problems, a local elimination algorithm is used. This is an iterative algorithm in which certain variables are eliminated at each step. The issues concerning the optimal elimination order are studied. This problem turns out to be exponentially complex, which is proved using a graph interpretation of the concepts of block-treelike and block-staircase structures. The complexity of the local elimination algorithm is considered. This is important for deciding which methods are better in different situations. The numerical results are presented; in particular, efficient procedures for determining the optimal elimination order are described. Special attention is given to the parallelization of particular quasi-block Boolean programming problems on a computer GRID if these problems cannot be solved on a single processor due to their large size.

A way of creating analytical models that describe the distribution of vortex magnetization in a two-dimensional Bloch domain wall (DW) is proporsed, based on a system of equations for the line of transition. The structure and energy of Bloch DWs in thin magnetic permalloy-type films are studied at a film thickness of 100 nm. The results from calculation are cpmpared to those of other authors.