# Publications

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%.

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, site-dependency 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.

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

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.

We present a general method of solving the Cauchy problem for a linear parabolic partial differential equation of evolution type with variable coefficients and demonstrate it on the equation with derivatives of orders two, one and zero. The method is based on the Chernoff approximation procedure applied to a specially constructed shift operator. It is proven that approximations converge uniformly to the exact solution.

In this paper we are going to review both theoretical studies in the field of intellectual capital measurement and empirical research, devoted to analyses of intellectual capital influence on companies’ value and financial performance. As a result, potential areas for further investigations in this field were revealed.

Considering groups of intellectual capital measurement methods, we identified that direct intellectual capital methods and scorecard methods are the most appropriate for the purpose of IC components measurement. To obtain objective results of measurement it seems reasonable to develop system of proxy indicators for all intellectual capital components (human, structural and relational capitals) and subcomponents (process and innovation, client and network capitals). Basing on existing literature, we make an attempt to identify and systemize indicators, associated with intellectual capital and reveal that network capital metrics remain under-researched and deserve closer examination. It was also found that investigators should develop the system of intellectual capital indicators, taking into account industry specificity.

As for empirical studies, in order to investigate the influence of intellectual capital on corporate value and financial performance, it seems reasonable to elaborate models, which include factors, associated with all intellectual capital components and subcomponents and, what is just as important, their interrelations. Furthermore, it is vital to investigate the relationships between the values of IC components for companies. The models should be adopted for both developed and developing countries. It is also important to analyze the influence of intellectual capital in various industries separately, taking into consideration phase of economic cycle.

In this paper a branch-and-bound algorithm for the Symmetric Travelling Salesman Problem (STSP) is presented. The algorithm is based on the 1-tree Lagrangian relaxation. A new branching strategy is suggested in which the algorithm branches on the 1-tree edge belonging to the vertex with maximum degree in the 1-tree and having the maximum tolerance. This strategy is compared with} branching on the shortest edge and the so-called strong branching, which is the branching on the edge with maximum tolerance also applied by Held & Karp (1971). The computational experiments show that {proposed} branching strategy provides better results on TSPlib benchmark instances

In this paper, we propose the approach of structuring information in video surveillance systems by grouping the videos, which contain identical faces. First, the faces are detected in each frame and features of each facial region are extracted at the output of preliminarily trained deep convolution neural networks. Second, the tracks that contain identical faces are grouped using face verification algorithms and hierarchical agglomerative clustering. In the experimental study with the YTF dataset, we examined several ways to aggregate features of individual frame in order to obtain descriptor of the whole video track. It was demonstrated that the most accurate and fast algorithm is the matching of normalized average feature vectors.

Graphical models are used in a variety of problems to uncover hidden structures. There is an important number of different identification procedures to recover graphical model from observations. In this paper, undirected Gaussian graphical models are considered. Some Gaussian graphical model identification statistical procedures are compared using different measures, such as Type I and Type II errors, ROC AUC.

Contributions in this volume focus on computationally efficient algorithms and rigorous mathematical theories for analyzing large-scale networks. Researchers and students in mathematics, economics, statistics, computer science and engineering will find this collection a valuable resource filled with the latest research in network analysis. Computational aspects and applications of large-scale networks in market models, neural networks, social networks, power transmission grids, maximum clique problem, telecommunication networks, and complexity graphs are included with new tools for efficient network analysis of large-scale networks.

This proceeding is a result of the 7th International Conference in Network Analysis, held at the Higher School of Economics, Nizhny Novgorod in June 2017. The conference brought together scientists, engineers, and researchers from academia, industry, and government.

The article discusses an empirical study that was conducted by the authors, in which they surveyed focus groups of young innovative entrepreneurs who are at different stages of creating their own projects. The authors devote particular attention to how training programs for the founders and staff should be implemented as the startup develops from its early phases into a sustainable-growth business.

The article discusses the problems and prospects for using the methodology of Digital Humanities in the historical psychological studies. The authors present the results of the search and analysis of the mentions found for the name of the outstanding psychophysiologist, psychoneurolo-gist, and psychologist Vladimir M. Bekhterev (1857-1927) in the body of texts in the Google Books system in Russian and English languages. Hypotheses are advanced regarding the high or low frequency of references. The dissemination of the scientist’s ideas in various scientific fields is analyzed in both Russian and English. The results of the mentioning frequency study on the names of Vladimir Bekhterev and Lev Vygotsky are compared to define the factors that determine the use of the name and these scientists’ ideas. The advantages and disadvantages of qualitative and quantitative analysis and interpretation of texts within the framework of digital humanities are shown.

We suggest a new model of the fast nondissipative kinematic dynamo which describes the phenomenon of exponential growth of the magnetic eld caused by the motion of the conducting medium. This phenomenon is known to occur in the evolution of magnetic elds of astrophysical bodies. In the 1970s A.D. Sakharov and Ya.B. Zeldovich proposed a \rope" scheme of this process which in terms of the modern theory of dynamical systems can be described as Smale solenoid. The main disadvantage of this scheme is that it is non-conservative. Our model is a modication of the Sakharov-Zeldovich's model. We apply methods of the theory of dynamical systems to prove that it is free of this fault in the neighborhood of the nonwandering set.