Goal of research: development and analysis of new data analysis and decision-making methods with applications to socio-economic problems. Specific properties of the areas of possible applications dictate the need to work with large volumes of complex structured data, taking into account the “human factor” (using game-theoretic models, taking into account preferences and influences, etc.), uncertainty and/or inaccuracy of conditions and data, multi-criteria decisions etc.
Methodology: game theory and multi-criteria decision-making theory, individual and social choice theory, belief function theory, intelligent and network data analysis, optimization methods, methods of probability theory, clustering methods, etc.
Empirical base of research: ratings of economic journals, results of a survey of Russian economists, S&P500 stock index data, data on international food trade, data on migrant flows, data on bank failures, data on terrorist communities, data on oil spills and weather data at the spill site, etc.
Results of research:
- the problems of estimating the return of the required investments in the construction of a transport hub at a specific point in the region and on estimating the payback period of these investments are set mathematically; it is shown that both problems that are formulated as problems of finding the maximum of the maximin function, are reduced to the problem of quadratic programming, while finding the most unfavorable scenario of formation of market transport tariffs for transportation of goods is reduced to linear programming problems that form a dual pair;
- verifiable sufficient conditions of competitiveness of tariffs for the services of a transport hub in market conditions, which are used in the formulation of systems of constraints in both problems, are formulated and proved;
- generalized knockout tournament seedings for an arbitrary number of participants in one match are designed; several properties of knockout tournament seedings are investigated; enumeration results for knockout tournament seedings with different properties are obtained; several new generalized knockout tournaments seedings are proposed and justified by a set of properties;
- the first version of conceptual framework that allows investigating problems and possibilities for cooperation in the development of Arctic is proposed;
- an approach to sensitivity analysis of undominated alternatives to changes in the bounds of intervals of value tradeoffs, where the alternatives are selected based on interval data of criteria tradeoffs is proposed; methods of evaluation the sensitivity of individual undominated alternatives and the set of such alternatives as a whole are developed;
- an empirical study of the stability of aggregated ratings constructed using ordinal methods based on pair comparisons according to the majority rule has been performed within the framework of the analysis of the methods for choosing the best options and procedures for ranking alternatives;
- conflict measures induced by conjunctive and disjunctive combining rules of evidence were studied within the framework of the belief function theory; the matching conditions of the combining rules with the conflict measures are considered;
- within the framework of the belief function theory it is shown that metric and entropy components can be distinguished in conjunctive conflict measures; properties of changes to these components when combining evidence were investigated;
- a model of individual and coalitional manipulability of the aggregation schemes of preferences for a one-dimensional model is proposed; evaluation of manipulability for the majoritarian rules for 3 alternatives are performed;
- application of the model of the binomial test of correlated random binary variables for the problem of checking the accuracy of the prediction of the number of defaults has been considered within the framework of an analysis in the banking sector;
- an assessment of the impact of fraud on the vulnerability of the entire financial system has been carried out; agent-based approach to modeling critical levels of fraudulent activity is proposed; this approach has been applied to investigate such types of frauds as a pyramid scheme and hidden risk;
- an efficient algorithm for calculating short-range interaction centrality (SRIC) and long-range interaction centrality (LRIC) was proposed on the basis of previously developed models of influence in networks; the computational complexity of this algorithm is estimated;
- relations between countries at various levels of interaction are analyzed using network models, namely for: a) international migration from 1970 to 2014, based on data on migration flows between countries; b) food trade; c) terrorist communities;
- the heterogeneity of the community of Russian economists is analyzed by the results of the survey; several methods for compiling ratings of scientific journals in economics are proposed taking into account the heterogeneity of the community of Russian economists;
- properties of the ordinal-invariant pattern clustering are formulated and proved in the framework of the study of patterns; these properties show that for the practical implementation of the order-invariant and diffusion-invariant pattern clustering fast data sorting algorithms can be used;
- new computationally powerful version of the frequency algorithm for constructing a family of dichotomies of an arbitrary graph has been proposed in the study of the structural complexity of the graph; this allows calculating such an indicator of graph complexity as entanglement; this algorithm is applied to the S&P-500 stock market data to analyze the consistency of its operation;
- experimental comparison of clustering algorithms based on the affinity propagation method with other clustering algorithms has been carried out analyzing the correctness of determining the number of clusters and assessing the quality of the resulting partition compared to the true partitioning; numerical experiments have been performed on data with varying degrees of cluster mixing; the hierarchy of the quality of clustering algorithms based on the affine propagation method is defined for different types of data;
- a computer system that allows modeling the process of oil distribution on the surface of the Barents Sea based on the agent-network approach has been developed;
- explicit two-level finite-difference schemes for solving one-dimensional equations of barotropic gas dynamics are investigated; the schemes on a constant solution are linearized and the necessary condition of von Neumann type and the CFL type criterion for weak conservatism in for the corresponding problem on the whole line are derived;
- a new fitness optimization model describing the influence of environmental factors on the possibility of reproductive-somatic specialization in cell colonies has been proposed 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.