Goal of research
Study of models of decision-making and data analysis, in particular, models of competitive cooperation, optimal allocation of objects, scheduling theory, specialization in abstract systems, preferences in social choice theory, ranking of options and rules for choosing optimal alternatives, solutions for non-numerical estimation of preferences and uncertainties, analysis of network structures, analysis and interpretation of complex structure of data, application of the belief function theory to data analysis, regulation of the banking sector, etc.
Methods and models
Theory of multi-criteria decision making, theory of social and individual choice, belief function theory, cluster and network data analysis, optimization methods, machine learning methods, system analysis, probability theory, etc.
Empirical base of research
Online surveys data, results of parliamentary elections and roll-call votes, S&P500 stock index data, data on international food trade, data on migrant flows, bank data for assessing credit risk, a collection of scientific publications, etc.
Results of research
‒ the study of manipulability of social choice rules is continued in two directions: computations of the probability of individual manipulation with counterthreats, and theoretical study of the safety of coalitional manipulation under scoring rules; it is proven that scoring rules with only one jump of scores are always manipulable; it is proven that for Borda rule unsafely manipulable profile exists when the number of voters or the number of alternatives being greater or equal to 5;
‒ methods for analyzing decisions under uncertainty are considered based on the theory of qualitative importance of criteria without the use of utility functions and quantitative probabilities;
‒ axiomatic analysis of methods for choosing optimal options and constructing a rating of alternatives is performed;
‒ in the study of preference profiles, the following results have been obtained: the exact formula for the number of group-separable preference profiles; recursive formula for the number of narcissistic group-separable preference profiles;
‒ as part of the study of stable matching, a new extension of the sequential preference condition is developed, which leads to unique stable matching in all subpopulations, obtained by consistent restrictions of marriage matching problem; under the new conditions, the Gale-Shapley algorithm is stable, consistent, strategy-proof, Pareto optimal for men and Pareto optimal for women;
‒ a method for assessing the impact in multiplex network structures has been developed; the proposed model is applied to networks of international food trade and arms trade;
‒ a number of measures for assessing the importance of edges in network structures are proposed and investigated;
‒ network analysis of international migration from 1970 to 2014 based on data on migration flows between countries has been conducted; ratings of influential countries in the process of international migration are determined using centrality indices, both classical and new indices developed in our team taking into account group as well as indirect interactions;
‒ a network analysis of international trade has been carried out taking into account direct and indirect interaction between countries;
‒ a novel method is proposed for finding a most specific generalization of a query set represented by a fuzzy set of topics assigned to leaves of the rooted tree of a taxonomy in the framework of text analysis methods study; this algorithm is applied to the structural analysis and description of a collection of abstracts of research papers published in Springer journals related to Data Science and taxonomy of Data Science is extracted from the Association for Computing Machinery Computing Classification System 2012;
‒ as part of the development of pattern analysis methods, an algorithm for detecting symmetric patterns on large and very noisy data has been proposed; it is shown that the symmetry of patterns is preserved in any order of their formation;
‒ the concept of the SATA loop was introduced on the basis of results of educational and research filed course in the framework of the Society and Advanced Technology in the Arctic (SATA) project;
‒ a mathematical model is proposed for assessing the necessary investment in the development of a regional cargo transportation infrastructure; the proposed model is tested on model examples of freight transport systems; some recommendations for using this model are formulated;
‒ classes of systemic problems associated with the formation of public-private partnerships (for example, energy systems) are identified and described;
‒ mathematical models on the basis of which the problems of estimating the amount of investment required to locate the chain of charging stations of electric vehicles on the highway are reformulated and investigated;
‒ the possibility of applying the methods of the theory of non-additive measures and the belief function theory to solve a number of problems of political science analysis is shown; in particular, the following problems have been solved on the basis of an analysis of data online polls of parties in Germany before the Bundestag elections in 2013, and the results of these elections: finding the most relevant groups of questions for voting, assessing the political heterogeneity of society, the significance of the positions of individual parties for voting, the conflicting positions of parties on significant issues;
‒ the basic models and methods for evaluating polarization and political influence are analyzed, including models that take into account preferences for coalition formation;
‒ in the framework of the analysis of models in the banking sector, the influence of model risk on the accuracy of estimates of the value of risk weighted assets obtained using the internal ratings -based approach is analyzed; measures to take into account such influence in the problem of increasing the comparability of credit risk assessments are proposed;
‒ as part of the study of structural complexity of graphs, a new modification of the graph complexity index based on the construction of a family of graph dichotomies has been developed; graphs for stock market data S&P-500 for the period 1991-2019 analyzed using the proposed approach in order to predict special periods in the behavior of the stock market;
‒ an explicit two-level symmetric in space finite-difference scheme for the one-dimensional gas dynamics system of equations with quasi-gasdynamic regularization linearized at a constant solution (with arbitrary velocity) has been studied;
‒ the optimization problem of the emergence of specialization in an abstract multicellular system based on maximizing the effectiveness of the functioning of this system is formulated and studied.
Level of implementation, recommendations on implementation or outcomes of the implementation of the results
Both fundamental and applied results have been obtained. Most applicable results have an analytical and a recommendation character.