### Book chapter

## Исследование асимптотического поведения энтропии русского и старославянского языков

The work is devoted to the estimation of the entropy of sources, generating messages from the letters of the Russian alphabet of 33 symbols (32 letters without "ё" and a space are taken into account) and the Old Church Slavonic alphabet of 45 symbols (44 letters of the Cyrillic alphabet and a special numeric character with the value 1000).

The problem of assessing the dynamics of development and comparing the characteristics of the Russian language of different eras is solved (XVIII - XXI centuries).

### In book

In this paper we propose a new machine learning concept called randomized machine learning, in which model parameters are assumed random and data are assumed to contain random errors. Distinction of this approach from "classical" machine learning is that optimal estimation deals with the probability density functions of random parameters and the "worst" probability density of random data errors. As the optimality criterion of estimation, randomized machine learning employs the generalized information entropy maximized on a set described by the system of empirical balances. We apply this approach to text classification and dynamic regression problems. The results illustrate capabilities of the approach.

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet. An effective algorithm for calculating the entropy of an invariant Erdos measure is proposed. It is shown that, for certain values of the Bernulli parameter, the algorithm gives the Hausdorff dimension of an Erdos measure to 15 decimal places.

Properties of Erdos measure and the invariant Erdos measure for the golden ratio and all values of the Bernoulli parameter are studies. It is proved that a shift on the two-sided Fibonacci compact set with invariant Erdos measure is isomorphic to the integral automorphism for a Bernoulli shift with countable alphabet.

*Proceedings* (ISSN 2504-3900) publishes publications resulting from conferences, workshops and similar events.

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.

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.

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.

The formula for calculating the entropy and the Hausdorff dimension of an invariant Erdos measure for the pseudogolden ratio and all values Bernoulli parameter is obtained. This formula make possible calculating the entropy and the Hausdorff dimension with high accuracy.