### Article

## Robust identification in random variables networks

A class of distribution free multiple decision statistical procedures is proposed for threshold graph identification in correlation networks. The decision procedures are based on simultaneous application of sign statistics. It is proved that single step, step down Holm and step up Hochberg statistical procedures for threshold graph identification are distribution free in sign similarity network in the class of elliptically contoured distributions. Moreover it is shown that these procedures can be adapted for distribution free threshold graph identification in Pearson correlation network.

Network model of stock market based on correlation matrix is considered. In the model vector of stock returns is supposed to hve multivariate normal distribution with given correlation matrix. Statistical uncertainty of some popular market network structures is analyzed by numerical simulation for network models of stock makets for different countries. For each market statistical uncertainty of different structures is compared. It is observed that despite of diversity the results of comparison are nearly the same for different markets. This leads to conjecture that there is some unknown common feature in different market network.

Financial market can be modeled as network represented by a complete weighted graph. Differet characteristics of this graph (minimum spanning tree, market graph ad others) give an impotant information on the network. In the pesent paper it is studied how the choice of measure of similarity between stocks influences the statistical errors in the calculation of network characteristics. It is shown tat sign correlation is a robust measure of similarity in contrast with Person correlation widely used in market network analysis. This gives a possibility to get more precise information on stock market from observations.

Using network models to investigate the interconnectivity in modern economic systems allows researchers to better understand and explain some economic phenomena. This volume presents contributions by known experts and active researchers in economic and financial network modeling. Readers are provided with an understanding of the latest advances in network analysis as applied to economics, finance, corporate governance, and investments. Moreover, recent advances in market network analysis that focus on influential techniques for market graph analysis are also examined. Young researchers will find this volume particularly useful in facilitating their introduction to this new and fascinating field. Professionals in economics, financial management, various technologies, and network analysis, will find the network models presented in this book beneficial in analyzing the interconnectivity in modern economic systems.

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.

Full texts of third international conference on data analytics are presented.

The main goal of the present paper is the development of general approach to network analysis of statistical data sets. First a general method of market network construction is proposed on the base of idea of measures of association. It is noted that many existing network models can be obtained as a particular case of this method. Next it is shown that statistical multiple decision theory is an appropriate theoretical basis for market network analysis of statistical data sets. Finally conditional risk for multiple decision statistical procedures is introduced as a natural measure of quality in market network analysis. Some illustrative examples are given.

Market graph is known to be a useful tool for market network analysis. Cliques and independent sets of the market graph give an information about con- centrated dependent sets of stocks and distributed independent sets of stocks on the market. In the present paper the connections between market graph and classical Markowitz portfolio theory are studied. In particular, efﬁcient frontiers of cliques and independent sets of the market graph are compared with the efﬁcient frontier of the market. The main result is: efﬁcient frontier of the market can be well ap- proximated by the efﬁcient frontier of the maximum independent set of the market graph constructed on the sets of stocks with the highest Sharp ratio. This allows to reduce the number of stocks for portfolio optimization without the loss of quality of obtained portfolios. In addition it is shown that cliques of the market graphs are not suitable for portfolio optimization.

Among the negative predictors of sexual freedom, cultural complexity has been always mentioned as most important. However, regression analysis revealed the existence of a reverse trend within the interval between 11 and 22 points of Murdock's cumulative scale of cultural complexity. This suggests that it is senseless to try to find a general set of regularities regarding the correlation between cultural complexity and sexual freedom. One would expect to find different sets of regularities for simple, medium-complexity, complex and supercomplex cultures. In this paper we begin with a summary analysis of research conducted on simple societies, suggesting a model of relationships between cultural complexity and female premarital sexual freedom among foragers. We suggest that the underlying variable in this model is foraging intensification. This intensification appears to be one of the most important preconditions for the significant growth of cultural complexity among the foragers. As shown in the ethnographic record, this intensification mostly occurs through the development of hunting and/or fishing practices (i.e. in most cases predominantly male activities). This tends to lead to a decline in female contribution to subsistence which, in turn, appears to lead to the societal decline of female status. This, the general argument goes, contributes to the decrease of the female premarital sexual freedom. On the other hand, we argue that this is not the only mechanism explaining the negative correlation between cultural complexity and female premarital sexual freedom among foragers. The intensification of a foraging economy tends to lead to the rise of the wealth accumulation, and the growth of cultural complexity components such as the development of a medium of exchange and social stratification. This situation seems to “entice” the development of modes of marriage that involve the transfer of valuables/ services. The growth of social stratification appears to have an independent influence on the decline of female premarital sexual freedom among foragers. The growth of similar components of cultural complexity seems to lead to the development of slavery and polygyny, whereas the combined action of these factors appears to entice what we call "bride commodification" which against the background of declining female status appears, naturally, to lead to the restriction of the female premarital sexual freedom. The growth of such components of cultural complexity as political integration, fixity of settlement and community size seems to contribute to the decline of female premarital sexual freedom through the growth of social control (against the background of declining female status).

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.

Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.