and Computational Methods

Rubric: "2.3.1. System analysis, management and information processing (technical sciences)"

doi: 10.18698/2309-3684-2022-4-114125

The work is devoted to methods for detecting long-term memory in financial time series. Using the method of analysis with the help of the original program code, a number of values of the real financial index S & P500 were studied, estimates of the Hurst index were obtained, and persistence was demonstrated. To solve the problem of predicting the future values of a series, the ARFIMA model is proposed, which is a generalization of the standard ARIMA model and involves the use of a fractional differentiation opera-tor. A two-stage algorithm for constructing a forecast for a series of logarithmic profits is presented and implemented. It is shown that the use of the ARFIMA model improves the quality of the forecast in comparison with ARIMA for all standard metrics.

Облакова Т.В., Касупович Э. Численное исследование персистентных временных рядов на основе модели ARFIMA. Математическое моделирование и численные методы, 2022, № 4, с. 114–125.

doi: 10.18698/2309-3684-2022-1-129140

The article discusses the method of finding optimal solutions in the presence of a model of a complex technical system in the optimal design problem. The method is based on the use of nondominable, lambda optimal solutions and is a generalization of the method of Krasnoshchekov P.S., Morozov V.V., Fedorov V.V. [1]. The method allows in many cases (for lambda monotone objective functions) to reduce the number of calculations and reduce the dimension of the original problem. A numerical method for constructing lambda optimal solutions has been developed. A numerical example is given in which it is shown that the number of lambda optimal solutions consists of a single point, and the set of Pareto–optimal solutions is a curve on which it is necessary to build an ε–network to find the optimal solution.

Киселев В.В. Метод нахождения недоминируемых решений в задачах декомпозиции моделей сложных систем. Математическое моделирование и численные методы, 2022, № 1, с. 129–140.

doi: 10.18698/2309-3684-2021-3-88104

This work is devoted to the study and application of methods of intellectual analysis for the implementation of the scheme of the nowcasting of dangerous phenomena. In the course of the work, data sets were formed with differ in the methods of information processing for their preparation. For each set, a number of mathematical models were constructed for classifying cloud cells according to the degree of danger of tornadoes forming from them. The Python programming language has been chosen as the main development language. The work is of great practical importance in the field of forecasting weather events. Its novelty lies in the use of modern machine learning methodology, instead of the traditional approach to data extrapolation, widely used in various schemes of nowcasting.

Шершакова А.О., Пархоменко В.П. Методы интеллектуального анализа данных в модели наукастинга опасных явлений. Математическое моделирование и численные методы, 2021, № 3, с. 88–104.

doi: 10.18698/2309-3684-2021-2-8695

On the basis of the theory of continuous Markov processes, a model of a two–way battle of two similar combat units of side X against two different types of enemy units is developed. Calculation formulas are obtained for calculating the current and final states for various tactics of fighting by the X–side. The developed model of two–way combat can be used to assess the combat effectiveness of multi-purpose weapons systems.

Чуев В.Ю., Дубограй И.В. Стохастическая модель боевых действий однотипных боевых единиц против разнотипных. Математическое моделирование и численные методы, 2021, № 2, с. 86–95.

doi: 10.18698/2309-3684-2021-2-96116

The problems of estimating the similarity index of inhomogeneous scientific publications containing equations and formulas are discussed for the first time. It is shown that the presence of equations and formulas (as well as figures, drawings, and tables) is a complicating factor that significantly complicates the study of such texts. It has been proved that the method for determining the similarity index of publications, based on taking into account individual mathematical symbols and parts of equations and formulas, is ineffective and can lead to erroneous and even completely absurd conclusions. Possibilities of the most popular analytical systems Antiplagiat and iThenticate, currently used in scientific journals, are investigated for detecting plagiarism and self–plagiarism. The results of processing by the iThenticate system of specific examples and specific test problems containing equations and formulas are presented. It has been established that this analytical system, when analyzing heterogeneous texts, is often unable to distinguish self– plagiarism from pseudo-self-plagiarism, seeming real (but false and imaginary) self– plagiarism. A model complex situation is considered, in which the identification of self–plagiarism requires the involvement of highly qualified specialists of a narrow profile. Various ways to improve the work of analytical systems for comparing inhomogeneous texts are proposed. This article will be useful to researchers and university teachers in physics, mathematics, and engineering, programmers dealing with problems in image recognition and research topics of digital image processing, as well as a wide range of readers who are interested in issues of plagiarism and self–plagiarism.

Полянин А.Д., Шингарева И.К. Индекс подобия математических и других научных публикаций с уравнениями и формулами и проблема идентификации самоплагиата. Математическое моделирование и численные методы, 2021, № 2, с. 96–116.

doi: 10.18698/2309-3684-2023-1-112123

The study's aim is to predict main trends and create scenarios for the economic development of BRICS countries (Brazil, India, China, Russia, South Africa) and the USA. Regression autonomous macro models were built, as well as a model of trade between them. The autonomous submodels use Population, Fixed Capital, Gross Domestic Product and Gross Capital Formation as key indicators. Autoregressive equations describe the dynamics of these variables. The resulting system of equations allowed us to describe the historical dynamics of demographic and macroeconomic indicators from 1990 to 2015 and to do a forecast until 2030. In the trade submodel bilateral trade flows link with gross domestic products of the economies. The relationship is described by the power dependence of the export flow on the gross domestic product of both trading partners. Unlike gravity-type models, the regression equation parameters are assumed to be constant for each pair of trading partners over the entire predicted time interval. The calculations showed that the models satisfactorily describe the dynamics of monotonically changing indicators and therefore can be used as a simple tool for forecasting the national and regional economy.

Малинецкий Г.Г., Махов С.А. Динамика макроэкономических показателей и взаимной торговли стран БРИКС и США. Математическое моделирование и численные методы, 2023, No 1, с. 112–123.

doi: 10.18698/2309-3684-2023-3-125133

With the help of probabilistic methods, a model of the conflict of two interacting systems consisting of numerous structural units is proposed, taking into account the effect of delaying information about the mutual state: about the structure, number and parameters of each other's structural units. A study was made of the influence of insufficient information at a particular point in time on the outcome of the process of conflict development. It is shown that the availability of information about the state of the structural units of the opposite side can significantly increase the probability of successful development of the conflict, and with an increase in the number of units of structural units, the difference in the probability of successful development of the conflict scenario increases significantly

Чуев В.Ю., Дубограй И.В. Моделирование конфликта взаимодействующих систем с учетом эффекта получения информации о взаимном состоянии. Математическое моделирование и численные методы, 2023, № 3, с. 125–133

doi: 10.18698/2309-3684-2022-2-6377

The paper presents a mathematical statement and presents the results of calculations in the problem of determining the temperature field during deformation of a strip made of aluminum alloy AD0 on a vertical-type casting and forging module of a new modification. The design of the casting and forging module assumes that one of the four walls of the mold is stationary, the second performs a rotational movement on eccentric shafts, the other two move in a vertical plane, ensuring that the deformed billet is fed down. When solving the problem, a proven numerical method is used. For a moving medium, the heat equation is written in finite difference form in a curvilinear orthogonal coordinate system. The solution of the problem is carried out by the iterative method. When calculating the initial temperature field and its further change, the heat removal on the contact surfaces of the metal with the deformation tools is taken into account. The result of the solution is the temperature field in the spatial domain for discrete times corresponding to the steps of the numerical calculation. At each step, the boundary of the liquid and solidified metal is determined

Дмитриев Э.А., Потянихин Д.А., Одиноков В.И., Евстигнеев А.И., Квашин А.Е. Моделирование поля температур при получении металлоизделий на литейно-ковочном модуле с односторонним воздействием бокового бойка и неподвижной плитой. Математическое моделирование и численные методы, 2022, № 2, с. 65–79

doi: 10.18698/2309-3684-2021-4-103120

The article deals with the problem of classifying pixels of the radar image (RI). A locally homogeneous radar image model was used, in which the readings of each small area (local area) were considered to belong to only one class. The classification results of several real radar images by local areas are compared using the statistical criteria for the maximum a posteriori probability, Kolmogorov and Cramer-Mises-Smirnov. At the same time, in the case when the listed criteria made it difficult to classify a local area — when it hit the interface of the underlying surfaces, it was considered to be assigned to a special, boundary class, and its readings were processed using the grid method for separating mixtures of probability distributions. For each criterion, the classification accuracy was evaluated as the proportion of correctly classified pixels within the selected homogeneous areas. It has been established that in the case of significant interclass differences, the best classification accuracy is ensured by the use of the least powerful Kolmogorov criterion among nonparametric criteria. Also, using a real image as an example, it is shown that when the differences in the characteristics of objects of the same class are comparable to interclass differences, the highest classification accuracy is achieved when using the maximum a posteriori probability criterion. Such cases are typical for a wide class of classification problems, including those not related to image processing.

Достовалова А.М. Моделирование локально-однородных радиолокационных изображений при использовании различных статистических критериев. Математическое моделирование и численные методы, 2021, № 4, с. 103–120.