Publications

As a result of the global warming, the situation in the Barents Sea leads to several important consequences. Firstly, oil and gas drilling becomes much easier than before. Therefore, it may raise the level of discussions on disputed shelf zones where the deposits are located, especially near to Norway-Russia sea border. Secondly, oil and gas excavation leads to potential threats to fishing by changing natural habitats, which in turn can create serious damage to the economies.

We construct a model, which helps to highlight potential disputed territories and analyze preferences of the countries interested in fossil fuels and fish resources. We also compare different scenarios of resource allocation with allocation by current agreement.

Recently appeared online courses rapidly gained their popularity due to the great opportunities. Absolutely different people can study any discipline for various purposes. Online courses can be useful both to children in preparing for lessons, and to adults in advanced training. Gradually, courses are becoming not only part of the additional curriculum at the university, but part of the mandatory program, too. However, not everyone supports the new way of education. Therefore, the goal of this work was to identify students' attitudes towards online education, the reasons for their preferences on online format of education and the willingness to replace traditional lectures into an online format. The study was carried out on the basis of a survey of more than 6,000 students as part of the Student Life Survey conducted every year at the HSE. The analysis was made by using various clustering methods, such as hierarchical clustering, clustering using the K-means method and analysis of latent classes, as well as analysis of variance. The students were divided into 6 clusters based on the different attitude towards the replacement of all lectures to the online format: devotees of HSE, amateurs of online courses, disciplined, social, learners for the grades, a mixed cluster.

We consider the initial-boundary value problem for the 3D regularized compressible isothermal Navier-Stokes-Cahn-Hilliard equations describing flows of a two-component two-phase mixture taking into account capillary effects. We construct a new numerical semi-discrete finite-difference method using staggered meshes for the main unknown functions. The method allows one to improve qualitatively the computational flow dynamics by eliminating the so-called parasitic currents and keeping the component concentration inside the physically reasonable range (0,1)$. This is achieved, first, by discretizing the non-divergent potential form of terms responsible for the capillary effects and establishing the dissipativity of the discrete full energy. Second, a logarithmic (or the Flory-Huggins potential) form for the non-convex bulk free energy is used. The regularization of equations is accomplished to increase essentially the time step of the explicit discretization in time. We include 3D numerical results for two typical problems that confirm the theoretical predictions.

We consider the regularized 3D Navier-Stokes-Cahn-Hilliard equations describing isothermal flows of viscous compressible two-component fluids with interphase effects. We construct for them a new energy dissipative finite-difference discretization in space, i.e., with the non-increasing total energy in time. This property is preserved in the absence of a regularization. In addition, the discretization is well-balanced for equilibrium flows and the potential body force. The sought total density, mixture velocity and concentration of one of the components are defined at nodes of one and the same grid. The results of computer simulation of several 2D test problems are presented. They demonstrate advantages of the constructed discretization including the absence of the so-called parasitic currents.

In this article, we consider the problem of planning maintenance operations at a locomotive maintenance depot. There are three types of tracks at the depot: buffer tracks, access tracks and service tracks. A depot consists of up to one buffer track and a number of access tracks, each of them ending with one service track. Each of these tracks has a limited capacity measured in locomotive sections. We present a constraint programming model and a greedy algorithm for solving the problem of planning maintenance operations. Using lifelike data based on the operation of several locomotive maintenance depots in Eastern polygon of Russian Railways, we carry out numerical experiments to compare the presented approaches.

We apply Dempster-Shafer theory in order to reveal important elements in undirected weighted networks. We estimate cooperation of each node with different groups of vertices that surround it via construction of belief functions. The obtained intensities of cooperation are further redistributed over all elements of a particular group of nodes that results in pignistic probabilities of node-to-node interactions. Finally, pairwise interactions can be aggregated into the centrality vector that ranks nodes with respect to derived values. We also adapt the proposed model to multiplex networks. In this type of networks nodes can be differently connected with each other on several levels of interaction. Various combination rules help to analyze such systems as a single entity, that has many advantages in the study of complex systems. In particular, Dempster rule takes into account the inconsistency in initial data that has an impact on the final centrality ranking. We also provide a numerical example that illustrates the distinctive features of the proposed model. Additionally, we establish analytical relations between a proposed measure and classical centrality measures for particular graph configurations.

It is an important feature of a monotone measure that it is not additive in general. In the paper, we propose the mathematical tool, based on canonical sequences of monotone measures, for analyzing additivity of monotone measures on subalgebras and give a way of generating such monotone measures. It turns out that the generating rule can be considered as an effect of a linear operator defined on the set of monotone measures. We also investigate in what cases the sequence of such operators behaves commutatively and preserve continuity properties from the generating monotone measure.

Over the past years, there is a deep interest in the analysis of different communities and complex networks. Identification of the most important elements in such networks is one of the main areas of research. However, the heterogeneity of real networks makes the problem both important and problematic. The application of SRIC and LRIC indices can be used to solve the problem since they take into account the individual properties of nodes, the possibility of their group influence, and topological structure of the whole network. However, the computational complexity of such indices needs further consideration. Our main focus is on the performance of SRIC and LRIC indices. We propose several modes on how to decrease the computational complexity of these indices. The runtime comparison of the sequential and parallel computation of the proposed models is also given.

Tornado prediction variables are analyzed using machine learning and decision analysis techniques.  A model based on several choice procedures and the superposition principle is applied for different methods of data analysis. The constructed model has been tested on a database of tornadic events. It is shown that the tornado prediction model developed herein is more efficient than a previous set of machine learning models, opening the way to more accurate decisions.

Usually DEA methods are used for the assessment of the regions disaster vulnerability. However, most of these methods work with precise values of all the characteristics of the regions. At the same time, in real life, quite often most of the data consists of expert estimates or approximate values. In this regard, we propose to use modified DEA methods, which will take into account inaccuracy of the data. We apply these methods to the evaluation of wildfire preventive measures in regions of the Russian Federation.

The concept of conflict is one of the central in the belief functions theory. There are differences between external and internal conflicts. A new method for estimating the internal conflict is proposed and studied in this paper. This method assumes that the original body of evidence was derived from simpler evidence using some combining rule. Therefore, an internal conflict can be considered as an external conflict of decomposition of the original body of evidence. This approach is specified in the article for decomposition by the Dempster rule and decomposition by the disjunctive consensus rule. The possible limits of change of the internal conflict are found in the case of these two combining rules for single-focal (categorical) and two-focal bodies of evidence. The decomposition method is discussed in detail for the case of a universal set with two alternatives. 

Local perturbations of an infinitely long rod travel to infinity. On the contrary, in the case of a finite length of the rod, the perturbations reach its boundary and are reflected. The boundary conditions constructed here for the implicit difference scheme imitate the Cauchy problem and provide almost no reflection. These boundary conditions are non- local with respect to time, and their practical implementation requires additional calcu- lations at every time step. To minimise them, a special rational approximation, similar to the Hermite - Padé approximation is used. Numerical experiments confirm the high “transparency”of these boundary conditions and determine the conditional stability regions for finite-difference scheme.

We consider the problem of individual manipulation under incomplete information, when voters do not know a full preference profile. Instead, voters know the result of an opinion poll (the outcome of a poll information function π, e.g. a list of scores or a set of winners). In this case, a voter has an incentive to misrepresent her preferences (π-manipulate) if she knows that she will not become worse off and there is a chance of becoming better off. We consider six voting rules and eight types of poll information functions differing in their informativeness. To compare manipulability, first we calculate the probability that there is a voter which has an incentive to π-manipulate and show that this measure is not illustrative in the case of incomplete information. Then, we suggest considering two other measures: the probability of a successful manipulation and an aggregate stimulus of voters to manipulate, which demonstrate more intuitive behavior. We provide results of computational experiments as well as analytical proofs of some effects observed.

We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor products finite element method (FEM) based on the tensor products of the 1D high-order FEM spaces on multi-dimensional rectangular parallelepipeds for solving the $N$-dimensional Poisson type equation $-\Delta u+\alpha u=f$ ($N\geq 2$) with the Dirichlet boundary conditions. They are based on the well-known Fourier approaches. The key new points are a detailed description for the eigenpairs of the 1D eigenvalue problems for the high order FEM as well as the fast direct and inverse algorithms for expansion in the respective eigenvectors utilizing simultaneously several versions of the FFT (fast Fourier transform). Results of numerical experiments in 2D and 3D cases are presented. The algorithms can serve for numerous applications, in particular, to implement the tensor product high order finite element methods for various time-dependent partial differential equations (PDEs) including the multidimensional heat, wave and Schrödinger ones. %

We consider an application of long-range interaction centrality (LRIC) to the problem of the influence assessment in the global retail food network. Firstly, we reconstruct an initial graph into the graph of directed intensities based on individual node’s characteristics and possibility of the group influence. Secondly, we apply different models of the indirect influence estimation based on simple paths and random walks. This approach can help us to estimate node-to-node influence in networks. Finally, we aggregate node-to-node influence into the influence index. The model is applied to the food trade network based on the World International Trade Solution database. The results obtained for the global trade by different product commodities are compared with classical centrality measures.

Using the SIPRI Arms Transfers Database covering all trade in military equipment over the period 1950–2018, we examine the relationship between countries from a novel empirical perspective. We consider the arms transfers network as a multiplex network where each layer corresponds to a particular armament category. First, we analyze how different layers overlap and elucidate main ties between countries. Second, we consider different patterns of trade in order to identify countries specializing on particular armament categories and analyze how they change their export structure in dynamic. We also examine how countries influence each other at different layers of multiplex network. Finally, we analyze the influence of countries in the whole network.

The paper describes the assessment of data on the innovation development of individual countries and regions, taking into account a large number of different indicators. An overview of international and national approaches to the assessment of innovative development is presented: Global Innovation Index (Cornell University, INSEAD, and the World Intellectual Property Organization); Portfolio Innovation Index (USA). The mathematical apparatus for calculating each of them is given. The generalized groups of indicators included in each index are described. Designations and methods of calculation are given to a uniform form of presentation. A methodology for assessing the heterogeneity of the innovative development of countries/economic regions of innovation systems based on the use of clustering methods is proposed. The methodology of the compilation of three indices is given, taking into account the results of clustering and evaluating the qualitative proximity of the studied territorial entities.

We propose a novel method to estimate the level of interconnectedness of a financial institution or system, as the measures currently suggested in the literature do not fully take into consideration an important aspect of interconnectedness — group interactions of agents. Our approach is based on the power index and centrality analysis and is employed to find a key borrower in a loan market. It has three distinctive features: it considers long-range interactions among agents, agents’ attributes and a possibility of an agent to be affected by a group of other agents. This approach allows us to identify systemically important elements which cannot be detected by classical centrality measures or other indices. The proposed method is employed to analyze the banking foreign claims as of 1Q 2015. Using our approach, we detect two types of key borrowers (a) major players with high ratings and positive credit history; (b) intermediary players, which have a great scale of financial activities through the organization of favorable investment conditions and positive business climate.

We obtain criteria for the L2-dissipativity of finite-difference schemes based on regularizations of 1D barotropic and full gas dynamics systems of equations that are linearized at a constant solution. Bibliography: 8 titles.

We study an explicit in time and symmetric in space finite-difference scheme with a kinetic regularization for the 2D and 3D gas dynamics system of equations linearized at a constant solution (with any velocity). We derive both necessary and sufficient conditions for $L^2$-dissipativity of the Cauchy problem for the scheme by the spectral method. The Courant number is uniformly bounded with respect to the Mach number in them.

Generalized Pauli’s theorem, proved by D. S. Shirokov for two sets of anticommuting elements of a real or complexified Clifford algebra of dimension 2n, is extended to the case, where both sets of elements depend smoothly on points of Euclidean space of dimension r. We prove that in the case of even n there exists a smooth function such that two sets of Clifford algebra elements are connected by a similarity transformation. All cases of connection between two sets are considered in the case of odd n. Using the equation for the spin connection of general form, it is shown that the problem of the local Pauli’s theorem is equivalent to the problem of existence of a solution of some special system of partial differential equations. The special cases n = 2, r ≥ 1 and n ≥ 2, r = 1 with simpler solution of the problem are considered in detail.