### Book

## Дискретная математика. Модулярная алгебра, криптография, кодирование.

The textbook contains necessary information about universal and classical algebras, systems of axioms for the basic algebraic structures (groupoid, monoid, semi-groups, groups, partial orders, rings, fields). The basic cryptographic algorithms are described. Error-correcting codes - linear, cyclic, BCH are considered. Algorithms for designing of such codes are given. Many examples are shown. It is put in a basis of the book long-term experience of teaching by authors the discipline «Discrete mathematics» at the business informatics faculty, at the computer science faculty of National research university Higher school of economics, and at the automatics and computer technique faculty of National research university Moscow power engineering institute. The book is intended for the students of a bachelor degree, trained at the computer science faculties in the directions 09.03.01 Informatics and computational technique, 09.03.02 Informational systems and technologies, 09.03.03 Applied informatics, 09.03.04 Software Engineering, and also for IT experts and developers of software products.

An invariant subcode of a linear block code under the permutation is introduced. The concept of invariant subcode has two types of applications. The first type is decoding of linear block codes given the group of symmetry. The second type is the attack the McEliece cryptosystem based on codes correcting errors. Several examples illustrating the concept are presented.

Fast algorithms for decoding of linear block codes.

Using Stepanov’s method, we obtain an upper bound for the cardinality of the intersection of additive shifts of several multiplicative subgroups of a finite field. The resulting inequality is applied to a question dealing with the additive decomposability of subgroups.

This article describes the application of currently most promising methods of (1) network (graph) theory, (2) content analysis and (3) subject-oriented approach to business process modelling for creating and automation of innovative process and therefore for maximization of ROI (return on investments) in intellectual and social capital of enterprises.

Described approach delivers opportunities for unstructured information utilization in order to increase efficiency of innovation activity in organizations. As a result, virtual community with a multiple content centers is created presenting a prototype of intellectual neural network with distributed association nodes.

In a course of development, instant full-text indexation takes place and taxonomic picture of different branches for such community is formed. In due course system gathers the statistics and builds-up maps of intercommunication with priority allocation of most discussed topics. A group of predetermined experts begins discussion on development prospects of this or that subject afterwards. The strategic map of investments into innovative development that can be offered to group of investors for competitive investments eventually turns out. In this process all steps except final (gathering of experts) are human non-dependant, what increase efficiency of this process in general.

This article describes the application of currently most promising methods of (1) network (graph) theory, (2) content analysis and (3) subject-oriented approach to business process modeling for creating and automation of innovative process and therefore for maximization of ROI (return on investments) in intellectual and social capital of enterprises. Described approach delivers opportunities for unstructured information utilization in order to increase efficiency of innovation activity in organizations. As a result, virtual community with a multiple content centers is created presenting a prototype of intellectual neural network with distributed association nodes. In a course of development, instant full-text indexation takes place and taxonomic picture of different branches for such community is formed. In due course system gathers the statistics and builds-up maps of intercommunication with priority allocation of most discussed topics. A group of predetermined experts begins discussion on development prospects of this or that subject afterwards. The strategic map of investments into innovative development that can be offered to group of investors for competitive investments eventually turns out. In this process all steps except final (gathering of experts) are human nondependant, what increase efficiency of this process in general.

Legal, economic and organizational principles to use the logistics technologies in the customs sphere are investigated in the article. Speсific composition and characteristic features of the application of the customs logistic technologies within the framework of Comon Economic Space of EurAsEC are considered.

This book constitutes the refereed proceedings of the First International Conference on Data Compression, Communications and Processing held in Palinuro, Italy, in June 2011.

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.

Many electronic devices operate in a cyclic mode. This should be considered when forecastingreliability indicators at the design stage.The accuracy of the prediction and the planning for the event to ensure reliability depends on correctness of valuation and accounting greatest possiblenumber of factors. That in turn will affect the overall progress of the design and, in the end,result in the quality and competitiveness of products

Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables