: ( ): : 2019 : : Novikov D.A. Regularities of Iterative Learning. 2nd ed., revised. Moscow: Institute of Control Sciences of the Russian Academy of Sciences, 2019. 67 p. : The research is devoted to the study of common for systems of animate and inanimate nature a person, a group of people, animals, artificial systems of the quantitative laws of iterative learning (understood as repeated repetition of actions, trials, attempts, etc., by a trained system to achieve fixed goal under constant external conditions). The main research method is mathematical modeling.
The book (which is a translation from first edition, published in 1998 in Russian) is aimed at specialists in pedagogy, psychology and physiology of humans and animals, control theory, as well as undergraduate and graduate students of relevant specialties.
: : 2021 : .. : Discrete applied mathematics () : 305 : Goubko M., Veremyev A. Bilinear matrix equation characterizes Laplacian and distance matrices of weighted trees // Discrete Applied Mathematics, Volume 305, 31 December 2021, P. 1-9 : It is known from algebraic graph theory that if L is the Laplacian matrix of some tree G with a vertex degree sequence d=(\delta_1,..., \delpa_n)^T and D is its distance matrix, then LD+2I=(2*\vec{1}-d)1^T, where \vec{1} is an all-ones column vector. We prove the converse proposition: if this identity holds for the Laplacian matrix of some graph G with a degree sequence d and for some matrix D, then G is essentially a tree, and D is its distance matrix. This result immediately generalizes to weighted graphs. Therefore, the above bilinear matrix equation in L, D, and d characterizes trees in terms of their Laplacian and distance matrices, so it can be used as a constraint in mixed-integer formulations of distance-related tree topology design problems (e.g., optimum communication spanning tree or hop-constrained minimum spanning tree problems). If the matrix D is symmetric, the lower triangular part of this matrix identity is redundant and can be omitted, which halves the number of constraints in an optimization problem. Applications to the extremal graph theory (especially, to topological index optimization and to optimal tree problems) and to road topology design are discussed.
: : 2020 : : MLSD : Novikov D. RESEARCH PRINCIPLES OF MATHEMATICAL THEORY
OF SOCIO-TECHNICAL SYSTEMS CONTROL / IEEE Proceedings of 13-th International Conference Management of Large-scale System Development (MLSD). 2020. DOI 10.1109/MLSD49919.2020.9247699 : The general research principles of mathematical theory of socio-technical systems (STS) control are considered. These principles - rationality, coordination and decomposition reflect the specifics of STS as control objects with a complex structure (logical, cause-and-effect, process, etc.), requiring coordination of the life cycles of their elements and including subjects demonstrating active behavior.