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Registration Number

0223U003883, 0118U000648 , R & D reports

Title

Discrete analysis and control of random processes

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Head

Oliynyk Bogdana V., Доктор фізико-математичних наук

Registration Date

18-07-2023

Organization

National University of Kyiv-Mohyla Academy

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The object of research is discrete structures: graphs, permutation groups, discrete metric spaces, random processes, resource extraction game with an arbitrary number of participants, in which the utility functions of agents are power-law, and the stochastic law of transition between states is a geometric random walk relative to the joint investment of the players . The subject of the research is the constructive characterization of discrete objects, algorithms for the application of discrete objects in the theory of coding and cryptography, the problems of existence (Stationary) Markov perfect equilibrium for symmetric and asymmetric game models outlined by the object of research, as well as the existence of equilibria between stable coalitions of symmetric players and the properties of the found equilibria. The purpose of the work is constructive characterization of discrete objects, management of random processes, filling gaps in existing scientific research on the existence of Markov perfect equilibrium in stochastic models of resource extraction game, in particular in the context of unlimited utility functions of players, unlimited space of states and distribution of transitions between states, which is the stochastic kernel with respect to the agents' joint investment. As a result of the work, the methods and methods of studying the metric dimension of graphs and metric spaces were improved, fast algorithm for finding the Hamming distance between substitutions was described, and estimates for codes over Sylow p-subgroups of symmetric groups were obtained. In the project we obtained some results about metric dimension of unicyclic graphs, the metric dimension of ultrametric spaces is fully characterized, an algorithm for calculating such a dimension is given, and a fast algorithm for finding the Hamming distance between permutations using the representation of permutations by root trees is described.

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2023-07-18