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## Double Layer Interval Graph Model: The Universal Tool for Data Driven Market Analysis and Forecasting

This scientific work is dedicated to the development, improvement and application of double layer interval weighted graphs (DLIG) for non-stationary time series forecasting. This model appears to be the universal and easy-to-use tool for modeling the non-stationary time series and forecasting. We observe the double layer version of the model because it’s the most representative way in the sense of main idea though you can add several layers more for different purposes. The first layer of the graph is based on empirical fluctuations of system and displays the most potential fluctuations of the system at the time of system training. The second layer of the graph as a superstructure of the first layer displays the degree of modeling error and it’s connected with the first layer nodes by edges. The second layer is the way of supervised training implementation with the aim of error minimization.

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Devoted to use of analytically-digital method of Y.A.Bychkov in the solution of non-linear economical dynamics problems. The Lottki-Volterra Model with consequence action, being widely used in economics, biology and sociology, is considered. Through that model, the efficiency of Bichkov Method for the solution of economical dynamics problems is shown

Venture capital (VC) provides financial and managerial support for new innovative ideas at the initial stages of commercialization. It has helped to find the market for many radical innovations of 20th century, including personal computer, Internet and genetic engineering.

As a part of market economy venture business was not stable from the very beginning. The periods of rapid growth alternated with deep recessions. However each time VC revived anew as the Phoenix due to its very important function in modern knowledge-based economy.

This report presents an analysis of statistical data that prove the existence of several cycles in VC dynamics in the USA and the Great Britain. The main factors of these cycles formation are discussed. The author proposes two possible scenarios of development of VC market for the first 30 years of the new 21st century. A hypothesis is put forward about the relation between VC cycle's amplitude and a phase of Kondratieff's cycle.

The article analyzes the current state of the Russian statistics. It points to the progress achieved, namely, free access to statistical data and adjustment to the market economy. Unsolved problems of the statistical methodology, usability of statistical data, and gaps in statistics are discussed.

In this article we describe a system allowing companies to organize an efficient inventory management with 40 suppliers of different products. The system consists of four modules, each of which can be improved: demand planning, inventory management, procurement planning and KPI reporting. Described system was implemented in a real company, specializing on perishable products totaling over 600 SKUs. The system helped the company to increase its turnover by 7% while keeping the same level of services.

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.

It is well-known that the class of sets that can be computed by polynomial size circuits is equal to the class of sets that are polynomial time reducible to a sparse set. It is widely believed, but unfortunately up to now unproven, that there are sets in EXPNP, or even in EXP that are not computable by polynomial size circuits and hence are not reducible to a sparse set. In this paper we study this question in a more restricted setting: what is the computational complexity of sparse sets that are *selfreducible*? It follows from earlier work of Lozano and Torán (in: Mathematical systems theory, 1991) that EXPNP does not have sparse selfreducible hard sets. We define a natural version of selfreduction, tree-selfreducibility, and show that NEXP does not have sparse tree-selfreducible hard sets. We also construct an oracle relative to which all of EXP is reducible to a sparse tree-selfreducible set. These lower bounds are corollaries of more general results about the computational complexity of sparse sets that are selfreducible, and can be interpreted as super-polynomial circuit lower bounds for NEXP.