The Projection Method for Reaching Consensus and the Regularized Power Limit of a Stochastic Matrix

In the coordination/consensus problem for multi-agent systems, a well-known condition of achieving consensus is the presence of a spanning arborescence in the communication digraph. The paper deals with the discrete consensus problem in the case where this condition is not satisfied. A characterization of the subspace $T_P$ of initial opinions (where $P$ is the influence matrix) that \emph{ensure} consensus in the DeGroot model is given. We propose a method of coordination that consists of: (1) the transformation of the vector of initial opinions into a vector belonging to $T_P$ by orthogonal projection and (2) subsequent iterations of the transformation $P.$ The properties of this method are studied. It is shown that for any non-periodic stochastic matrix $P,$ the resulting matrix of the orthogonal projection method can be treated as a regularized power limit of $P.$Comment: 19 pages, 2 figure

Functional regulation of movements in rehabilitation of patients with spinal cord injury

The new therapeutic method of functional regulation of movements (FRM) as a part of treatment course for children with cerebral paralysis was developed. It is an individual technique of consensual work of anatomically remote muscular groups. This approach provides the influence on mechanisms of pathological activity of central nervous system by means of including deep regulating processes representing ontogenetic programs of motor activity. This technique has the advantage of immediate formation of correct motor stereotype and highly individual approach that promotes increase of therapy effectivenes

Efficacy evaluation of functional motor regulation method with mathematical analysis of EEG

Effects of functional motor regulation method have been measured using the spectral and coherent EEG. Obtained results have fully confirmed the hypothesis that the clinical effectiveness of the method is associated with the formation of new regulatory links in the CNS with inclusion of such deep structures as the limbic and diencephalic system

Differentiated method of physiotherapy for patients with congenital hip dislocation in postoperative rehabilitation period

The aim of the research was to develop a new rehabilitation method for patients with congenital dislocation of hip in the late postoperative period. It is based on anatomical, physiological, pathogenetic, functional and ontogenetic foundations and prevents coxarthrosis development and progress. Materials. The data from examination and treatment of 71 patients are presented. The main group consisted of 48 children and the comparison group consisted of 23 children. Methods. Data processing was made by «Statistica 6,0» programme. Normalcy of distribution was estimated by the Shapiro-Wilktest. Hypothesis proof of two means equality was provided by the Wilcoxon signed-ranktest. Correlation analysis was made by definition of the Pearson correlation coefficient and the Spearman»s rank correlation coefficient. Rate difference was considered as a reliable rate if p<0,05. Results. According to the results, a proper short-term gait stereotype formation has been attained as opposed to the routine rehabilitation methods. Conclusion. Due to advantages of the new method, therapy efficiency is extended and reoperation risks are decrease