# Publications

Shortest path problems play important roles in computer science, communication networks, and transportation networks. In a shortest path improvement problem under unit Hamming distance, an edge-weighted graph with a set of source–terminal pairs is given. The objective is to modify the weights of the edges at a minimum cost under unit Hamming distance such that the modified distances of the shortest paths between some given sources and terminals are upper bounded by the given values. As the shortest path improvement problem is NP-hard, it is meaningful to analyze the complexity of the shortest path improvement problem defined on rooted trees with one common source. We first present a preprocessing algorithm to normalize the problem. We then present the proofs of some properties of the optimal solutions to the problem. A dynamic programming algorithm is proposed for the problem, and its time complexity is analyzed. A comparison of the computational experiments of the dynamic programming algorithm and MATLAB functions shows that the algorithm is efficient although its worst-case complexity is exponential time.

In this paper, we present fixed-parameter tractable algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems’ formulations are near square. The parameter is the maximum absolute value of the rank minors in the corresponding matrices. Additionally, we present fixed-parameter tractable algorithms with respect to the same parameter for the problems, when the matrices have no singular rank submatrices.

We discuss the video classification problem with the matching of feature vectors extracted using deep convolutional neural networks from each frame. We propose the novel recognition method based on representation of each frame as a sequence of fuzzy sets of reference classes whose degrees of membership are defined based on asymptotic distribution of the Kullback–Leibler information divergence and its relation with the maximum likelihood method. In order to increase the classification accuracy, we perform the fuzzy intersection (product triangular norms) of these sets. Experimental study with YTF (YouTube Faces) and IJB-A (IARPA Janus Benchmark A) video datasets and VGGFace, ResFace and LightCNN descriptors shows that the proposed approach allows us to increase the accuracy of recognition by 2–6% compering with the known classification methods.

This study based on the use of methods of corpus linguistics compares literary and “naive autobiographies” of men and women. The empirical material of this research is represented by texts of autobiographies of men from provincial Russia, the corpus of “naive” male autobiographies comprises 36 interviews (28 335 word usages). For the comparative analysis 46 female autobiographies have been used (the total corpus contains 48.530 word usages) dwelling in the countryside and provincial towns as well. The other group of materials includes 20 “literary autobiographies” of writers (the corpus of literary male autobiographies contains 27 241 word usages). It was found that the autobiographies of writers, as well as the autobiographies of “ordinary males”, are being constructed by the authors within the boundaries of the “male culture” rules regardless of abilities and literary experiences.

**Annotation**.

Background. The research in question is based on the gender schema theory by Sandra Bem.

Objective. The purpose of the research is to study male narrative features in the context of the norms of male socialization.

The aim of the research under consideration is a comparative analysis of male and female autobiographies features, which are not confined to male and female speech characteristics and reflect revision of gender socialization norms by the subject.

Design. With the help of biographical interview method autobiographies of women aged 31 to 72 (N= 34) and men aged from 23 to 69 (N= 36) living in provincial Russian towns were transcribed and contrasted. The autobiographies underwent categorial analysis procedure conducted by experts; the obtained categorial matrices were processed with the use of mathematical methods of statistics. Considerable attention was given to men’s life stories during the process of analysis. Quantitative data analysis allowed to reconstruct the structure of men’s and women’s autobiographies, which reflected gender socialization norms. Rules for creating male and female autobiographies were defined through correlation analysis. The ‘classification tree’ method was employed in order to identify the rules of text construction (with the use of ‘Information gain’ metric).

Results. The obtained algorithm, being geared towards the search for gender markers in the autobiographies, identified gender-specific markers in men’s texts whereas the female ones were retrieved owing to non-specific categories. This allowed to conclude that the modern Russian male socialization practices are more traditional.

Conclusion. According to the results of the research, the categorial structure of autobiographical texts in men and in women is similar in key events and specific to each gender group at the same time. As far as gender normativity is concerned, male stories are more frequent to contain the gender norms abidance markers. Female stories are more individualized and fall into different scenarios (gender-standardized and non-standard). It is concluded that the male culture of provincial Russian towns steadily preserves traditional traits. The results of the empirical research of the male and female autobiographies define the theoretical background regarding the social creativity of the female gender group, constituting women’s autobiographies in the tideway of changing traditional ‘cultural scripts’.

In this paper it is proved that every orientable surface admits an orientation-preserving Morse-Smale diffeomorphism with one saddle orbit. It is shown that these diffeomorphisms have exactly three node orbits. In addition, all possible types of periodic data for such diffeomorphisms are established.

In this paper we construct a smooth arc without bifurcation points connecting the sourse-sink diffeomrphisms on the two-dimensional sphere.

Research into the market graph is attracting increasing attention in stock market analysis. One of the important problems connected with the market graph is its identification from observations. The standard way of identifying the market graph is to use a simple procedure based on statistical estimations of Pearson correlations between pairs of stocks. Recently a new class of statistical procedures for market graph identification was introduced and the optimality of these procedures in the Pearson correlation Gaussian network was proved. However, the procedures obtained have a high reliability only for Gaussian multivariate distributions of stock attributes. One of the ways to correct this problem is to consider different networks generated by different measures of pairwise similarity of stocks. A new and promising model in this context is the sign similarity network. In this paper the market graph identification problem in the sign similarity network is reviewed. A new class of statistical procedures for the market graph identification is introduced and the optimality of these procedures is proved. Numerical experiments reveal an essential difference in the quality between optimal procedures in sign similarity and Pearson correlation networks. In particular, it is observed that the quality of the optimal identification procedure in the sign similarity network is not sensitive to the assumptions on the distribution of stock attributes.

In this paper we propose the two-stage approach of organizing information in video surveillance systems. At first, the faces are detected in each frame and a video stream is split into sequences of frames with face region of one person. Secondly, these sequences (tracks) that contain identical faces are grouped using face verification algorithms and hierarchical agglomerative clustering. Gender and age are estimated for each cluster (person) in order to facilitate the usage of the organized video collection. The particular attention is focused on the aggregation of features extracted from each frame with the deep convolutional neural networks. The experimental results of the proposed approach using YTF and IJB-A datasets demonstrated that the most accurate and fast solution is achieved for matching of normalized average of feature vectors of all frames in a trackI

We study damping of phase-mixed Alfvén waves propagating in non-reflective axisymmetric magnetic plasma configurations. We derive the general equation describing the attenuation of the Alfvén wave amplitude. Then we applied the general theory to a particular case with the exponentially divergent magnetic field lines. The condition that the configuration is non-reflective determines the variation of the plasma density along the magnetic field lines. The density profiles exponentially decreasing with the height are not among non-reflective density profiles. However, we managed to find non-reflective profiles that fairly well approximate exponentially decreasing density. We calculate the variation of the total wave energy flux with the height for various values of shear viscosity. We found that to have a substantial amount of wave energy dissipated at the lower corona, one needs to increase shear viscosity by seven orders of magnitude in comparison with the value given by the classical plasma theory. An important result that we obtained is that the efficiency of the wave damping strongly depends on the density variation with the height. The stronger the density decrease, the weaker the wave damping is. On the basis of this result, we suggested a physical explanation of the phenomenon of the enhanced wave damping in equilibrium configurations with exponentially diverging magnetic field lines.

A complex analysis of the social and economic consequences of China, Ukraine, and Russia’s accession to the WTO was used to identify recommendations for the most successful adaptation of Russia to WTO standards. Russia tries to adapt to the WTO standards. The study focuses on the Chinese experience. China’s membership in the WTO is extremely useful for Russia from due to China’s positive influence on the development of its economy , as there has been expansion in the industrial and production sectors of its economy and promotion of goods in world markets, as well as an opportunity to use the WTO’s legal instruments for national domestic market protection.

China’s positive experience as a WTO member somehow contrasts with the described experience of Ukraine. An assessment of Ukraine’s versatile policy and its association with the EU allowed concluded that it is impossible for Ukraine to follow two ways at once: that of Eurasian integration and that of European integration.

Recently, the aggravated trade, economic and political confrontations between Russia and its American and European partners spurred radical changes in Russia’s economic strategy. Areas of such transformations can be determined by understanding both the positive and negative experiences of Russia’s old trade partners, namely China and Ukraine as they joined the world economic environment.

The modern qualitative theory of dynamical systems is thoroughly intertwined with the fairly young science of topology. Many strange constructions of topology are found sooner or later in dynamics of discrete or continuous dynamical systems. In the present paper we show that the wild Fox-Artin arc emerges naturally in invariant sets of dynamical systems.

Numerous magnetic fragments in the interior of the Sun give rise to many interesting energy processes in the solar corona, for example solar flares and prominences. Magnetic charge topology explains these phenomena by appearance and disappearance of heteroclinic trajectories (separators) --- magnetic lines that belong to an intersection of stable and unstable invariant two-dimensional manifolds (fans) of different saddle singularities (nulls). Separators are the locations in the magnetic field configuration where the magnetic energy is transferred from one region (a connected component into which the fans divide the solar corona) to another. Many recent papers has gone into investigation of the configurations that arise in different concrete models. In the present paper we solve the problem of interrelation between existence of separators of any given magnetic field in the Solar corona and the type and the number of saddle singularities and charges. Following the classical definition we introduce the concept of equivalence of two magnetic fields and get a classification of such fields up to topological equivalence.

We show that, up to topological conjugation,} the equivalence class of a Morse-Smale diffeomorphism without heteroclinic curves on a $3$-manifold is completely defined by an embedding of two-dimensional stable and unstable heteroclinic laminations to a characteristic space.

Structurally stable (rough) flows on surfaces have only finitely many singularities and nitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads to Ω-stable flows on surfaces, which are not structurally stable. However, in the present paper we prove that a topological classication of such flows is also reduced to a combinatorial problem. Our complete topological invariant is a multigraph, and we present a polynomial-time algorithm for the distinction of such graphs up to an isomorphism. We also present a graph criterion for orientability of the ambient manifold and a graph-associated formula for its Euler characteristic. Additionally, we give polynomial-time algorithms for checking the orientability and calculating the characteristic.

The dynamics of two-component solitons is studied, analytically and numerically, in the framework of a system of coupled extended nonlinear Schrödinger equations, which incorporate the cross-phase modulation, pseudo-stimulated-Raman-scattering (pseudo-SRS), cross-pseudo-SRS, and spatially inhomogeneous second-order dispersion (SOD). The system models co-propagation of electromagnetic waves with orthogonal polarizations in plasmas. It is shown that the soliton's wavenumber downshift, caused by pseudo-SRS, may be compensated by an upshift, induced by the inhomogeneous SOD, to produce stable stationary two-component solitons. The corresponding approximate analytical solutions for stable solitons are found. Analytical results are well confirmed by their numerical counterparts. Further, the evolution of inputs composed of spatially even and odd components is investigated by means of systematic simulations, which reveal three different outcomes: formation of a breather which keeps opposite parities of the components; splitting into a pair of separating vector solitons; and spreading of the weak odd component into a small-amplitude pedestal with an embedded dark soliton.

The nonlinear Schrödinger (NLS) equation describing the propagation of inhomogeneous vertical wave packets in an infinitely deep fluid has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. It is shown that the modulation instability criteria of the considered weakly vortical waves and potential Stokes waves on deep water coincide. The effect of vorticity manifests itself in the shift of the wave number. A special case of Gerstner waves is noted, for which the coefficient of the nonlinear term in the NSE is zero.