### Book

## Models, Algorithms and Technologies for Network Analysis, Springer Proceedings in Mathematics & Statistics

The contributions in this volume cover a broad range of topics including maximum cliques, graph coloring, data mining, brain networks, Steiner forest, logistic and supply chain networks. Network algorithms and their applications to market graphs, manufacturing problems, internet networks and social networks are highlighted. The "Fourth International Conference in Network Analysis," held at the Higher School of Economics, Nizhny Novgorod in May 2014, initiated joint research between scientists, engineers and researchers from academia, industry and government; the major results of conference participants have been reviewed and collected in this Work. 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.

We characterize the graphs whose induced subgraphs all have the following property: The maximum number of induced 4-paths is equal to the minimum cardinality of the set of vertices such that every induced 4-path contains at least one of them. In this chapter we describe all such graphs obtained from simple cycles by replacing some vertices with cographs.

We consider a game equilibrium in a network in each node of which an economy is described by the simple two-period model of endogenous growth with production and knowledge externalities. Each node of the network obtains an externality produced by the sum of knowledge in neighbor nodes. Uniqueness of the inner equilibrium is proved. Three ways of behavior of each agent are distinguished: active, passive, and hyperactive. Behavior of agents in dependence on received externalities is studied. It is shown that the equilibrium depends on the network structure. We study the role of passive agents and, in particular, possibilities of connection of components of active agents through components of passive agents. Changes of the equilibrium under changes in the network structure are studied. It is shown that appearance of a new link, as a rule, leads to decrease of knowledge in all nodes, but sometimes knowledge in some nodes increases. A notion of type of node is introduced and classification of networks based on this notion is provided. It is shown that the inner equilibrium depends not on the size of network but on its structure in terms of the types of nodes, and in similar networks of different size agents of the same type behave in similar way.

Random matrix theory (RMT) is applied to investigate the cross-correlation matrix of a financial time series in four different stock markets: Russian, American, German, and Chinese. The deviations of distribution of eigenvalues of market correlation matrix from RMT global regime are investigated. Specific properties of each market are observed and discussed.

The cell formation problem (CFP) is an NP-hard optimization problem considered for cell manufacturing systems. Because of its high computational complexity several heuristics have been developed for solving this problem. In this paper we present a branch and bound algorithm which provides exact solutions of the CFP. This algorithm finds optimal solutions for 13 problems of the 35 popular benchmark instances from the literature.

Methods of network analysis are used in this paper for mapping the local academic community of St. Petersburg sociologists. The survey data on relations between individual scholars serve as a guide in reconstruction of the communitys network history as well as a system of independent variables in accounting for differences between its various natural zones. In this manner, the paper explores the points of convergence between Chicago school social ecology and modern social network analysis.

This volume contains two types of papers—a selection of contributions from the “Second International Conference in Network Analysis” held in Nizhny Novgorod on May 7–9, 2012, and papers submitted to an "open call for papers" reflecting the activities of LATNA at the Higher School for Economics.

This volume contains many new results in modeling and powerful algorithmic solutions applied to problems in

- vehicle routing

- single machine scheduling

- modern financial markets

- cell formation in group technology

- brain activities of left- and right-handers

- speeding up algorithms for the maximum clique problem

- analysis and applications of different measures in clustering

The broad range of applications that can be described and analyzed by means of a network brings together researchers, practitioners, and other scientific communities from numerous fields such as Operations Research, Computer Science, Bioinformatics, Medicine, Transportation, Energy, Social Sciences, and more. The contributions not only come from different fields, but also cover a broad range of topics relevant to the theory and practice of network analysis. Researchers, students, and engineers from various disciplines will benefit from the state-of-the-art in models, algorithms, technologies, and techniques including new research directions and open questions.

This volume contains proceedings of the fourth conference on Analysis of Images, Social Networks and Texts (AIST’2015)1 . The first three conferences in 2012–2014 attracted a significant number of students, researchers, academics and engineers working on interdisciplinary data analysis of images, texts, and social networks. The broad scope of AIST makes it an event where researchers from different domains, such as image and text processing, exploiting various data analysis techniques, can meet and exchange ideas. We strongly believe that this may lead to crossfertilisation of ideas between researchers relying on modern data analysis machinery. Therefore, AIST brings together all kinds of applications of data mining and machine learning techniques. The conference allows specialists from different fields to meet each other, present their work, and discuss both theoretical and practical aspects of their data analysis problems. Another important aim of the conference is to stimulate scientists and people from the industry to benefit from the knowledge exchange and identify possible grounds for fruitful collaboration. The conference was held during April 9–11, 2015. Following an already established tradition, the conference was organised in Yekaterinburg, a cross-roads between European and Asian parts of Russia, the capital of Urals region.The key topics of AIST are analysis of images and videos; natural language processing and computational linguistics; social network analysis; pattern recognition, machine learning and data mining; recommender systems and collaborative technologies; semantic web, ontologies and their applications. The Program Committee and the reviewers of the conference included wellknown experts in data mining and machine learning, natural language processing, image processing, social network analysis, and related areas from leading institutions of 22 countries including Australia, Bangladesh, Belgium, Brazil, Cyprus, Egypt, Finland, France, Germany, Greece, India, Ireland, Italy, Luxembourg, Poland, Qatar, Russia, Spain, The Netherlands, UK, USA and Ukraine.

The article introduces a historical-sociological research project reconstructing intellectual and institutional transformations of post-soviet social sciences in the last 25 years. The projects ambition was to achieve this aim via applying classical community study research strategy and various methods derived from social science history to the case of St. Petersburg sociologists. We identified 622 individuals as St. Petersburg sociologists and traced records of their institutional trajectories, appearance in print, citing behaviour, social networks, political attitudes, sources of income, professional authorities, and attention spaces through 25 years.

This volume contains a selection of contributions from the "First International Conference in Network Analysis," held at the University of Florida, Gainesville, on December 14-16, 2011. The remarkable diversity of fields that take advantage of Network Analysis makes the endeavor of gathering up-to-date material in a single compilation a useful, yet very difficult, task. The purpose of this volume is to overcome this difficulty by collecting the major results found by the participants and combining them in one easily accessible compilation.

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.

The current paper aims to present the Scan-4-Light study, which was conducted for the systematic scanning and analysis of the Searchlight newsletters as a rapidly growing collection of articles on trends and topics in development and poverty. Built upon the concept of the systemic foresight methodology, the Scan-4-Light approach involves the integrated use of horizon scanning, network analysis and evolutionary scenarios combined with expert consultations and workshops. The study identified the emerging trends, issues, weak signals and wild cards; created high-value visualisations to emphasize the results and findings; and produced narratives to increase the impact and awareness of the development issues. The Scan-4-Light project has resulted in a large number of specific outputs, providing the views of the Searchlight newsletters' contents at various levels of granularity. It has set out to show how the tools used here can be applied to illustrate the relationships among issues, and how these vary across countries and regions over time, and are linked to various stakeholders and possible solutions to problems. Scan-4-Light demonstrates how foresight tools and techniques can be used for the analysis of complex and uncertain issues, such as development and poverty, in a systemic way. The Scan-4-Light approach can be applied in a number of areas for scanning and identifying emerging trends and issues, and understanding the relationships between systems and solutions. The paper gives evidence that most of the issues, if not all, related to development are not isolated, but interlinked and interconnected. They require more holistic understanding and intervention with an effective collaboration between stakeholders.

Semantic network reduction is considered in application to visual analytics of relational data. Merging structurally equivalent nodes it is straightforward to construct a reduced semantic network that completely species the initial structure of relations between nodes. This paper presents the analysis of such reduction applied to the communication network from Stanford Large Network Dataset Collection. It is shown how the reduction based on structural equivalence can help in visualization of large semantic networks.

We consider certain spaces of functions on the circle, which naturally appear in harmonic analysis, and superposition operators on these spaces. We study the following question: which functions have the property that each their superposition with a homeomorphism of the circle belongs to a given space? We also study the multidimensional case.

We consider the spaces of functions on the m-dimensional torus, whose Fourier transform is p -summable. We obtain estimates for the norms of the exponential functions deformed by a C1 -smooth phase. The results generalize to the multidimensional case the one-dimensional results obtained by the author earlier in “Quantitative estimates in the Beurling—Helson theorem”, Sbornik: Mathematics, 201:12 (2010), 1811 – 1836.

We consider the spaces of function on the circle whose Fourier transform is p-summable. We obtain estimates for the norms of exponential functions deformed by a C1 -smooth phase.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.