Publications

We study necessary conditions for stability of a Numerov-type compact higher-order finite-difference scheme for the 1D homogeneous wave equation in the case of non-uniform spatial meshes. We first show that the uniform in time stability cannot be valid in any spatial norm provided that the complex eigenvalues appear in the associated mesh eigenvalue problem. Moreover, we prove that then the solution norm grows exponentially in time making the scheme strongly non-dissipative and therefore impractical. Numerical results confirm this conclusion. In addition, for some sequences of refining spatial meshes, an excessively strong condition between steps in time and space is necessary (even for the non-uniform in time stability) which is familiar for explicit schemes in the parabolic case.

We construct a new spatial finite-difference discretization for a regularized 3D Navier--Stokes--Cahn--Hilliard system of equations. The system {can be attributed to phase field type models} and describes flows of a viscous compressible isothermal two-component two-phase fluid with surface effects; the potential body force is also taken into account. In the discretization, the main sought functions are defined on one and the same mesh, and an original approximation of the solid wall boundary conditions (homogene\-ous with the discretization of equations) is suggested. The discretization has an important property of the total energy dissipativity allowing one to eliminate completely the so-called spurious currents. The discrete total mass and component mass conservation laws hold as well, and the discretization is also well-balanced for the equilibrium solutions. To ensure that the concentration $C$ remains within a physical\-ly meaningful interval $(0,1)$, the non-convex part of the Helmholtz free energy is taken in a special logarithmic form (the Flory--Huggins potential). The speed of sound can depend on $C$ that leads to different equilibrium mass densities of the ``pure'' phases. The results of numerical 3D simulations are also presented including those with a gravitational-type force. The positive role of the relaxation parameter is discussed too.

This work is devoted to the methodology for identifying structurally close objects of the type “country_year” based on a system of indicators characterizing the state capacity 1996–2015. A comparison of clustering methods (including hierarchical clustering) with methods of analyzing patterns based on a pairwise comparison of indicators, ordinal-fixed and ordinal-invariant pattern clustering, is proposed. The possibility of sharing the methods of clustering and pattern analysis to obtain interpretable results from the point of view of political science is demonstrated. Groups of countries with similar development paths by reference years on the basis of a dynamic analysis of patterns are identified. The dynamic change in state capacity (from the point of view of the selected indicator system) of 166 countries of the world is determined.

none

The global economy is in recession due to the pandemic of the coronavirus infection COVID-19. According to available estimates, Russia's GDP in 2020 will fall by 2–8%, so that in its consequences the current crisis may be tougher than the crises of 1998 and 2008. In the coming years, the Russian economy will have to recover and enter a new long-term growth path. At what expense and in which industries will this happen?

The report based on the experience of previous crises using industry accounts of economic growth and Russia KLEMS data, examined possible sources of recovery of the Russian economy after the crisis of 2020. By analogy with the recovery after 2008, it is likely to be associated with increased demand for raw materials on world markets and the reaction of the Russian oil and gas complex. Stagnation after 2008 is due to a decrease in production efficiency, especially in the expanded mining complex, as well as the cessation of technological make-up. Growth stimulation measures should include finding ways to increase the efficiency of the expanded mining complex, stimulating the adaptation of advanced technologies, and preserving existing adaptation channels in times of crisis - for example, successful export-oriented industries integrated into global value chains.

We study necessary conditions for stability of a Numerov-type compact higher-order finite-diffe\-rence scheme for the 1D homogeneous wave equation in the case of non-uniform spatial meshes. We first show that the uniform in time stability cannot be valid in any spatial norm provided that the complex eigenvalues appear in the associated mesh eigenvalue problem. Moreover, we prove that then the solution norm grows exponentially in time making the scheme strongly non-dissipative and therefore impractical. Numerical results confirm this conclusion. In addition, for some sequences of refining spatial meshes, an excessively strong condition between steps in time and space is necessary (even for the non-uniform in time stability) which is familiar for explicit schemes in the parabolic case.

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.

Regional authorities consider the expediency of developing a new cargo transportation hub in the region in which it would provide transshipment services. It is considered that each transportation operator working in the region will use these services only if they are competitive with the currently existing ones. This competitiveness for a particular cargo means that the total transportation tariff for moving this cargo does not exceed (substantially or in principle) the (minimal) currently existing one as a result of including a transshipment via the hub in the transportation scheme for the cargo. A verifiable sufficient condition for the transshipment service competitiveness is proposed. Its verification consists of establishing the solvability of a system of linear inequalities being part of the system of constraints in the problem of finding optimal competitive transshipment tariffs for a set of cargoes expected to be moved via the hub. The latter problem is formulated as a quadratic programming one.

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.