# Publications

The universal mechanism of modulation instability (MI) has been discovered first for the Nonlinear Schr¨odinger equation (NLS) and is well studied in the frame of the higher order NLS equations. Recent studies demonstrated by pure existence theorems that also the higher order Korteweg-de Vries (KdV) equations might possess the MI. In this Letter we present explicit form of the conditions for the MI to appear in the KdV-family of equations of the general form ut + sup ux + uxxx =0 where s = ±1 with p > 0 being an arbitrary integer.

A mathematically correct description is presented on the interrelations between the dynamics of divergence free vector fields on an oriented 3-dimensional manifold M and the dynamics of Hamiltonian systems. It is shown that for a given divergence free vector field Xwith a global cross-section there exist some 4-dimensional symplectic manifold M̃⊃M and a smooth Hamilton function H:M̃→R such that for some c∈R one gets M={H=c}and the Hamiltonian vector field XH restricted on this level coincides with X. For divergence free vector fields with singular points such an extension is impossible but the existence of local cross-section allows one to reduce the dynamics to the study of symplectic diffeomorphisms in some sub-domains of M. We also consider the case of a divergence free vector field X with a smooth integral having only finite number of critical levels. It is shown that such a noncritical level is always a 2-torus and restriction of X on it possesses a smooth invariant 2-form. The linearization of the flow on such a torus (i.e. the reduction to the constant vector field) is not always possible in contrast to the case of an integrable Hamiltonian system but in the analytic case (M and X are real analytic), due to the Kolmogorov theorem, such a linearization is possible for tori with Diophantine rotation numbers.

In this paper we find all possible periodic data for orientation preserving gradient-like diffeomorphisms of orientable surfaces with one saddle orbit. We also construct a system of this class for every admissible collection of periodic data.

Topological classification of even the simplest Morse-Smale diffeomorphisms on 3-manifolds does not fit into the concept of singling out a skeleton consisting of stable and unstable manifolds of periodic orbits. The reason for this lies primarily in the possible ``wild'' behaviour of separatrices of saddle points. Another difference between Morse-Smale diffeomorphisms in dimension 3 from their surface analogues lies in the variety of heteroclinic intersections: a connected component of such an intersection may be not only a point as in the two-dimensional case, but also a curve, compact or non-compact. The problem of a topological classification of Morse-Smale cascades on 3-manifolds either without heteroclinic points (gradient-like cascades) or without heteroclinic curves was solved in a series of papers from 2000 to 2006 by Ch. Bonatti, V. Grines, F. Laudenbach, V. Medvedev, E. Pecou, O. Pochinka. The present paper is devoted to a complete topological classification of the set $MS(M^3)$ of orientation preserving Morse-Smale diffeomorphisms $f$ given on smooth closed orientable 3-manifolds $M^3$. A complete topological invariant for a diffeomorphism $f\in MS(M^3)$ is an equivalent class of its scheme $S_f$, which contains an information on a periodic date and a topology of embedding of two-dimensional invariant manifolds of the saddle periodic points of $f$ into the ambient manifold.

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.

In the present paper axiom $A$ diffeomorphisms of closed 2-manifolds of genus $p \geq 2$ whose nonwandering set contains perfect spaciously situated one-dimensional attractor are considered. It is shown that such diffeomorphisms are topologically semiconjugate to pseudo-Anosov homeomorphism with the same induced automorphism of fundamental group. The main result of the paper is the following. Two diffeomorphisms from the given class are topologically conjugate on attractors if and only if corresponding pseudo-Anosov homeomorphisms are topologically conjugate by means of homeomorphism that maps a certain subset of one pseudo-Anosov map onto the certain subset of the other pseudo-Anosov map.

We provide a definition of a two-colored graph of a Morse-Smale diffeomorphism without heteroclinical intersection defined on the sphere $S^n$, $n\geq 4$ and prove that this graph is the complete topological invariant for such diffeomorphisms.

The article is devoted to the identification of key factors that influence the educational activity of working citizens and the establishment of the role of adults educational programs and vocational education and trainings (AE&VET) in the macroeconomic development of regions and territories. Based on the analysis of the statistical data there was established a correlation between the supplementary education attainment rate and the volume of **fixed capital investment **per capita in the regions of the Russian Federation, which indicates the leading role of regional investors in the education and training of personnel. In the regions, where the volume of investments is growing, the coverage of the population with the continuous education is also increasing, aiming at the implementation of new technologies at the enterprises being built, which, in its turn, boosts the investment appeal of the territory. The authors formulated and confirmed the hypothesis that due to the launch of the educational programs via investments the labor productivity increases, which, in turn, together with the high correlation coefficients, has a positive impact on the growth rates of wages and gross regional product as a whole. Thus, it was concluded that the differentiation of subjects of the Russian Federation on socio-economic indicators is directly related to the general indicators of the regional AE&VET systems. It was noted that for the effective development of AE&VET at the current stage in Russia, it is necessary to incentive an active participation of all the stakeholders: the worker himself, the employers, the investors, the regional authorities and the government. Considering the lack of the employers’ willingness to finance the workers’ education and training, the authors justify the need to introduce state programs stimulating additional education, including budget certificates. The main provisions and conclusions of the article can be used for the development of the regional AE&VET-systems in the interests of ensuring the economic growth as well as the investment appeal of the territory.

The Cell Formation Problem (CFP) is an important optimisation problem in manufacturing. It has been introduced in the Group Technology (GT) and its goal is to group machines and parts processed on them into production cells minimising the movement of parts to other cells for processing and maximising for each cell the loading of its machines with operations on its parts. We consider one of the computationally hardest formulations of this problem – the CFP with a variable number of cells and the grouping efficacy objective, which is a fractional function. The CFP literature contains many heuristic algorithms, but only a small number of exact approaches especially for this formulation. In the current paper, we present an exact branch-and-bound algorithm for the same hard CFP formulation. To linearise the fractional objective function, we apply the Dinkelbach approach. We have been able to solve 24 of the 35 instances from the well known GT benchmark. For the remaining 11 instances, the difference in the grouping efficacy with the best known solutions is less than 2.6%.

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.

Advance price announcements in the form of general rate increase (GRIs) by liner shipping companies have recently become the subject of investigations by competition authorities in different jurisdictions, including the European Union and Russia. The main goal of this paper is to answer the question whether GRIs predict price changes of competitors. Comparison of GRIs with actual price changes in particular routes, defined as antitrust markets in competition investigations in Russia, shows a limited anti-competitive effect of advance price announcements, albeit under specific market conditions. Regression analysis, undertaken in the context of the Russian investigation, rejects the hypothesis that the GRI of a particular company would be followed by price increases of its competitors. Moreover, the frequent changes in the market shares of liner companies support the hypothesis of competition vis à vis collusion. Remedies applied by competition authorities address content and timing of GRIs. The theory of tacit collusion suggests that remedies, which further specify the content of price announcements, may paradoxically enhance non-cooperative pricing, in contrast to remedies that restrict audience of GRIs by customers.

The Vehicle Routing Problem (VRP) is one of the most popular combinatorial optimization problems which is closely related to the real-life optimization challenges. Being developed for more than 60 years the problem has been considered in many different formulations. In real-life goods distribution such constraints as fleet size and mix, sitedependency constraints, hard and soft time windows, vehicle capacity constraints are very important. In this paper we consider Capacitated Vehicle Routing Problem with hard Time Windows. We propose a hybrid heuristic algorithm which contains elements of ant colony optimization strategy and tabu search technique. Our algorithm shows good performance and results for the well-known Solomon dataset.

The independent set problem for a given simple graph is to determine the size of a maximal set of its pairwise non-adjacent vertices. We propose a new way of graph reduction leading to a new proof of the NP-completeness of the independent set problem in the class of planar graphs and to the proof of NPcompleteness of this problem in the class of planar graphs having only triangular internal facets of maximal vertex degree 18

One of the approaches for the nearest neighbor search problem is to build a network which nodes correspond to the given set of indexed objects. In this case the search of the closest object can be thought as a search of a node in a network. A procedure in a network is called decentralized if it uses only local information about visited nodes and its neighbors. Networks, which structure allows efficient performing the nearest neighbor search by a decentralized search procedure started from any node, are of particular interest especially for pure distributed systems. Several algorithms that construct such networks have been proposed in literature. However, the following questions arise: “Are there network models in which decentralized search can be performed faster?”; “What are the optimal networks for the decentralized search?”; “What are their properties?”. In this paper we partially give answers to these questions. We propose a mathematical programming model for the problem of determining an optimal network structure for decentralized nearest neighbour search. We have found the exact solutions for a regular lattice of size 4x4 and heuristic solutions for sizes from 5x5 to 7x7. As a distance function we use L_1, L_2 and L_inf metrics. We hope that our results and the proposed model will initiate study of optimal network structures for decentralized nearest neighbour search.

Studying the dynamics of a flow on surfaces by partitioning the phase space into cells with the same limit behaviour of trajectories within a cell goes back to the classical papers of Andronov, Pontryagin, Leontovich and Maier. The types of cells (the number of which is finite) and how the cells adjoin one another completely determine the topological equivalence class of a flow with finitely many special trajectories. If one trajectory is chosen in every cell of a rough flow without periodic orbits, then the cells are partitioned into so-called triangular regions of the same type. A combinatorial description of such a partition gives rise to the three-colour Oshemkov-Sharko graph, the vertices of which correspond to the triangular regions, and the edges to separatrices connecting them. Oshemkov and Sharko proved that such flows are topologically equivalent if and only if the three-colour graphs of the flows are isomorphic, and described an algorithm of distinguishing three-colour graphs. But their algorithm is not efficient with respect to graph theory. In the present paper, we describe the dynamics of Ω-stable flows without periodic trajectories on surfaces in the language of four-colour graphs, present an efficient algorithm for distinguishing such graphs, and develop a realization of a flow from some abstract graph.

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 study, we investigated how scientific collaboration represented by co-authorship is related to citation indicators of a scientist. We use co-authorship network to explore the structure of scientific collaboration. For network construction, the profiles of scientists from various countries and scientific fields in Google Scholar were used. We ran the count data regression model for a sample of more than 30 thousand authors with the first citation after 2007 to analyze the correlation between co-authorship network parameters of scientists and their citation characteristics. We identify that there is a positive correlation between citation of scientist and number of his co-authors, between citation and the author’s closeness centrality, and between scholar’s citation and the average citation of his co-authors. Also, we reveal that h-index and i10-index are correlated significantly with the number of co-authors and average citation of co-authors. Based on these results, we can conclude that scientists who maintain more contacts and more active than others have better bibliometric indicators on an average.

This book constitutes the proceedings of the 6th International Conference on Analysis of Images, Social Networks and Texts, AIST 2017, held in Moscow, Russia, in July 2017.

The 29 full papers and 8 short papers were carefully reviewed and selected from 127 submissions. The papers are organized in topical sections on natural language processing; general topics of data analysis; analysis of images and video; optimization problems on graphs and network structures; analysis of dynamic behavior through event data; social network analysis.

The Cell Formation Problem has been studied as an optimization problem in manufacturing for more than 90 years. It consists of grouping machines and parts into manufacturing cells in order to maximize loading of cells and minimize movement of parts from one cell to another. Many heuristic algorithms have been proposed which are doing well even for large-sized instances. However, only a few authors have aimed to develop exact methods and most of these methods have some major restrictions such as a fixed number of production cells for example. In this paper we suggest a new mixed-integer linear programming model for solving the cell formation problem with a variable number of manufacturing cells. The popular grouping efficacy measure is used as an objective function. To deal with its fractional nature we apply the Dinkelbach approach. Our computational experiments are performed on two testsets: the first consists of 35 well-known instances from the literature and the second contains 32 instances less popular. We solve these instances using CPLEX software. Optimal solutions have been found for 63 of the 67 considered problem instances and several new solutions unknown before have been obtained. The computational times are greatly decreased comparing to the state-of-art approaches

A beam pulsed amplifier mechanism responsible for effective amplification of short very low frequency (VLF) electromagnetic pulses is proposed. Effective amplification near the magnetic equator outside the plasmasphere is considered. A conditional growth rate of short electromagnetic pulses is calculated. Obtained results can explain some important features of the oblique electromagnetic chorus emissions without hiss-like radiation background.

The heterogeneity of interconnected devices and communication technologies in the Internet of Things (IoT) domain courses the problem of impossibility to synchronize several different objects in one scheme of the smart space effectively and automatically. Such diversity of technologies results in the need to have special skills in order to reach once created behavior for the smart space. In addition, there are many platforms, which allows to interconnect different devices, but only if they fulfill their protocols. All these lead to the idea, that a new, unified approach to the smart devices representation is needed, which allows to represent objects in a compact form by a platform-independent way. In this article we propose an object-oriented model for representation of the smart devices and demonstrate its efficiency by the simple case of smart space scenes adaptation.