## Mathematical Structures and Modeling ¹4(52)

 Mathematical Structures and Modeling. - Omsk : OmSU, 2019. ¹4(52), 144 p. ISSN (print): 2222-8772 ISSN (online): 2222-8799 For researchers, post-graduate students and senior students. Journal issue in one file

The Fundamental Mathematics and Physics

The paper gives conditions on the class of functions and the condition of weak dependence, that ensure the fulfillment of the conditions obtained earlier by the author for the applicability of the central limit theorem for symmetric functions of the dependent variables.
Keywords: symmetric functions, uniformly strong mixing condition, central limit theorem

The theoretical analysis of the "metaprogram"\ of substantiation of mathematics, which is in the basis of the modern conceptions of the mathematics development, is made in this paper with the help of the system principle. The biggest instrumental value of mathematics in the development of investigation is that the inner organization and structure of different natural scientific theories is expressed in the abstract language of mathematics.
Keywords: metaprogram, substantiation of mathematics, mathematical thinking, system approach, synthesis of directions of justification

Griselda Acosta, Eric D. Smith, Vladik Kreinovich
Dunning-Kruger Effect: A Simple System-Based Explanation

In their 1999 paper, psychologists David Dunning and Justin Kruger showed that, in general, experts not only provide better estimates of different situations, but they also provide a better estimates of the accuracy of their estimates. While this phenomenon has been confirmed by many follow-up experiments, it remains largely unexplained. In this paper, we provide a simple system-based qualitative explanation for the Dunning-Kruger effect.
Keywords: Dunning-Kruger effect, systems approach, expert estimates, estimation accuracy

Applied Mathematics and Modeling

A.V. Eremeev, Yu.V. Kovalenko
Applying Principles of Memetics to Solving the Traveling Salesman Problem

We consider a population-based algorithm for the asymmetric travelling salesman problem, based on the principles of the memetics. The initial population of tentative solutions is built by means of greedy constructive heuristics. The 3-opt local search is used to improve the initial and the final populations. A balance between the intensity of population-based search and the intensity of the local search methods is chosen by the means of adaptive restart rules. The results of computational experiment on the benchmark instances indicate the viability and effectiveness of the proposed algorithm.
Keywords: memes, genetic algorithm, local optimization, computational experiment

L.A. Volodchenkova, A.K. Guts
The Succession of the Spruce Forest in the Framework of the Moreno-Voit Mathematical Model

In the framework of the Moreno-Voit mathematical model we describe the succession of the spruce forest. Spruce forest forces out aspen/birch. Special attention we make to the fact that spruce evolution can go in different ways depending on the initial values of the phytomass of seeds (and soot), herbs, shrubs and aspen/birch.
Keywords: succession, forest ecosystem, phytomass, spruce forest

The paper considers two-dimensional isentropic flows of polytropic gas, arising after the instantaneous destruction of the impermeable wall in the initial point in time separating a non-uniform resting gas from the vacuum. As a mathematical model, the system of equations of gas dynamics taking into account gravity is used. Using the initial data, the background flow and the sound characteristic propagating along it are built. In the system of equations of gas dynamics, a self-similar singularity is introduced into the independent variable $$x$$ and the Cauchy problem with data on a sound characteristic is posed for the resulting system. From the necessary solvability conditions, the initial conditions are found. Next, the solution of the initial-boundary value problem is constructed in the form of a power series. The coefficients of the series are found when integrating ordinary differential equations.
Keywords: polytropic gas, vacuum, force of gravity, the gas dynamics equations, gas-vacuum boundary, initial-boundary value problem, Riemann problem, centered wave

Considering the set cover problem, by modifying the approach that gives a logarithmic approximation guarantee for the greedy algorithm, we obtain an estimation of the greedy algorithm's accuracy for a particular input. We compare the presented estimation to another estimations of this type. We give such examples of the set cover problem instances that the presented estimation sagnificantly improves over linear programming relaxation based estimation.
Keywords: set cover problem, greedy algorithm

L.U. Urazayeva, N.V. Manyukova, R.E. Mamedli
Mathematical Modeling of Migration Processes

The paper considers different approaches to mathematical modeling of migration processes. The necessity of structural modeling of migration processes is substantiated. Computer simulation of migration process using real data is carried out.
Keywords: mathematical modeling, migration process, population aging, labor demand, migration of skilled workers, migrants preferences

Why The Obvious Necessary Condition is (Often) Also Sufficient (TONCAS): An Explanation of the Phenomenon

In many graph-related problems, an obvious necessary condition is often also sufficient. This phenomenon is so ubiquitous that it was even named TONCAS, after the first letters of the phrase describing this phenomenon. In this paper, we provide a possible explanation for this phenomenon.
Keywords: graph theory, TONCAS phenomenon, typical (not abnormal) objects

Computer Science

N.M. Lychenko, A.V. Sorokovaja
Comparison of Effectiveness of Word Representations Methods in Vector Space for the Text Sentiment Analysis

The word representations in vector space is used for various tasks of automated processing of a natural language. There are many methods of vector representation of words, including neural network methods Word2Vec and GloVe, and the classical method of latent-sematic analysis LSA. This work is devoted to the study of the effectiveness of the application of vector representation of words in the neural network classifier for sentiment analysis of Russian and English texts based on the LSTM network. The features of word representations methods in vector space (LSA, Word2Vec, GloVe) are described, the architecture of a neural network classifier for sentiment analysis of text based on the LSTM network and the considered methods of vector representation of words are presented, the results of computational experiments and their discussion are presented. It is shown that the LSA model is the best model for the vector representation of words from the standpoint of learning speed, less corpus of words for learning, better accuracy and learning speed of the neural network classifier.
Keywords: word representations in vector space, LSA-method, Word2Vec and GloVe Methods, sentiment analysis, neural network classifier, LSTM network, classification accuracy, learning speed

D.N. Lavrov, A.P. Lapin
Code Obfuscation in Web-Presentation of Dialect Corpus of Folk Speech

The paper proposes an algorithm for obfuscation of thematic marking of the dialect corps, which allows to protect the work of researchers from illegal copying of data. The proposed approach is based on replacing real topic names with randomly generated identifiers. The substitution table is stored on the server and each time you access the body text, it is created for this text again with the generation of new identifiers. This work was supported by the Russian Foundation for Basic Research as part of a scientific project No. 18 - 012 - 00519.
Keywords: code obfuscation, thematic markup, dialect case

Education

N.V. Manyukova, L.Yu. Urazayeva, R.E. Mamedli
Mathematical Modeling in Information Technology Teaching

The paper discusses the technology of using methods of mathematical modeling in the teaching of information technology. The technique of choosing the types of tasks that can be solved using methods of mathematical modeling and decision making is presented.
Keywords: mathematical modeling, simulation, decision making, information technology, model

Julio C. Urenda, Olga Kosheleva, Vladik Kreinovich
Why Derivative: Invariance-Based Explanation

To many students, the notion of a derivative seems unrelated to any previous mathematics - and is, thus, difficult to study and to understand. In this paper, we show that this notion can be naturally derived from a more intuitive notion of invariance.
Keywords: derivative, invariance, teaching calculus