Applied Mathematics and Control Sciences

Applied Mathematics and Control Sciences is an open-access periodical scientific peer-reviewed journal.

Full Journal Title: Applied Mathematics and Control Sciences

Abbreviation: Appl. Math. Control Sci.

Publisher: Perm National Research Polytechnic University, Perm, Russian Federation

DOI: 10.15593/2499-9873

Languages: Russian, English

Editor-in-Chief: Professor, Dr. Sci. Valerii Yu. Stolbov

Executive Editor: C.Sci. Aleksandr O. Alekseev

Editorial Contact: 

Address: Editorial Board "Applied Mathematics and Control Sciences", Russian Federation, Perm, 614990, Komsomolsky ave., 29
Phone: +7 (342) 219-85-87; + 7 (909) 1000-150

Frequency: Quarterly

Applied Mathematics and Control Sciences has no article processing and/or article submission charges.

All Journal's Content, including articles,  is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0). Editorial of the Journal allows readers to read, download, copy, distribute, print, search, or link to the full texts of its articles and allows readers to use them for any other lawful purpose in accordance with Budapest Open Access Initiative's definition of Open Access.

Journal intended for researchers specializing in the field of applied mathematics, mathematical modeling, differential equations, dynamical systems, optimal control, organizational behavior control, automation, senior students of natural areas.

Since 2019 the journal included in the List of peer-reviewed scientific journals, formed by the Higher Attestation Commission under the Ministry of Science and Higher Education of the Russian Federation.

In 2022 the journal is categorized as category K1 (included in 25% leading Russian peer-reviewed scientific journals).

The years 2022-2031 have been declared the Decade of Science and Technology by decree of the president of the Russian Federation

Current Issue

No 4 (2023)

Review of methods and systems for generation of synthetic training data
Rabchevsky A.N.


It is impossible to imagine the advancement of modern artificial intelligence systems without neural network technologies. During the design process researchers are often faced with the fact that there is not enough data to train modern neural network models, these data may be unbalanced or highly sparse. Often it happens that real data simply does not exist, as the research field is still emerging. A relevant problem is ensuring the confidentiality of real personal or patient medical data, which is used in the exchange between researchers or in the testing of various neural network systems. In many subject areas, the cost of collecting and marking up real data can be very high. Synthetic data is increasingly being used to solve these problems. The purpose of this publication is to introduce readers to advances in the generation and use of synthetic data. The paper presents a description of various methods, systems and software tools used to generate synthetic data, which can help to improve neural network models. Since an entire industry for synthetic data production has already formed, the leading data synthesis technology platforms are presented. The paper is of an overview nature, so it contains an extensive bibliography. The value of the article lies in the fact that this review will help readers broaden their understanding of the use of synthetic data in solving a wide range of neural network problems, as well as to become more familiar with the methods and tools for their generation.
Applied Mathematics and Control Sciences. 2023;(4):6-45
Comparison of features elimination methods for geomagnetic data classification
Gainetdinova A.A., Vorobev A.V.


The main stages of processing and feature selection methods for their further use in machine learning algorithms for building models that are designed to predict auroras are considered. The aim of this work is to compare the methods of feature selection when constructing a model for diagnosing the presence of auroras based on the intellectual analysis of geomagnetic data. Data from the Lovozero Observatory (LOZ) for nine years (2012–2020) were used as data for processing. A distinctive feature of the data is their heterogeneity: the set contains both categorical (binary and non-binary) and quantitative data. We consider such feature selection methods as principal component analysis, support vector machines, recursive feature elimination, and the Extra-Trees algorithm. The results of the study showed that the use of selected features based on the analysis in the projection of the principal components will overcome the curse of dimensionality, eliminate noise and reduce model overfitting.
Applied Mathematics and Control Sciences. 2023;(4):46-55
Multicriteria ranking and selection in rank gradations of objects measured in different types of scales
Korneenko V.P.


To solve multi-criteria applied problems related to the construction of ratings of organizations, the choice of effective objects (alternatives, solutions), the initial data of which are presented in different types (quantitative, ordinal) measurement scales, the use of a generalized criterion in the form of an additive convolution of particular criteria is incorrect. In this regard, methods for narrowing the initial set of objects, as well as methods for constructing the resulting ranking (Kemeny-Snell medians), have become widespread. However, if the initial estimates of objects are transformed into the resulting homogeneous scale i.e., if there is a scale with the same scope of criteria, then the use of an additive aggregation mechanism in this case will be correct. An ordinal rank scale can serve as such a resultant scale. The paper substantiates a method in which the results of the transformation of quantitative (point) estimates of objects in the gradation of the rank scale when solving multi-criteria problems will be invariant for any quantitative transformations of the original scales. The preservation of the ordering of objects according to generalized estimates in the form of the sum of ranks according to equally important criteria is proved. At the same time, object orderings based on relationships with the k-th order of strict preference are also preserved. Illustrative examples are given.
Applied Mathematics and Control Sciences. 2023;(4):55-69
Stochastic model of the smart power grid section functioning
Sidorov S.M., Obzherin Y.E.


A feature of large systems, in particular electric power systems, is that the entire system physical state of the is affected by a large number of interacting elements that are randomly in different states. The work relevance is caused by to the fact that construction of mathematical models taking into account the structure and features of the power grid functioning allows us to solve important problems of the energy intellectualization. The goal of the study is due to the desire to show the advantages that arise when using the apparatus of the hidden Markov models theory to semi-Markov models of intelligent electrical systems. To do this, we build a semi-Markov model of a section of a distribution power grid (intelligent electrical grid). Using the theory of semi-Markov processes with a common phase space of states, it is possible to determine the temporal characteristics of the system reliability and obtain a more adequate model. However, territorial dispersion, inaccessibility of some sections of electrical networks and the widespread introduction of automation tools give rise to new problems. For a timely response to various factors, it becomes necessary to as-sess and forecast the states of the system (sections of the system) depending on the signals received in the course of its operation. This can be achieved by applying the hidden Markov models theory. Reliability characteristics are determined and, using the algorithm of stationary phase enlargement, an enlarged semi-Markov model of the section of the intelligent distribution grid is built, which allows passing to the finite state space of the model. Using the merged model, the parameters are determined and a hidden Markov model is developed, for which the most probable states corresponding to a given signal vector are found, the elements subsequent states of the modeled system and signals are predicted. The final part of the article provides an example of finding the reliability characteristics of the system and solving a number of problems in hidden Markov models theory.
Applied Mathematics and Control Sciences. 2023;(4):70-82
Autonomous collision avoidance system for unmanned vessels: algorithms and software.
Barakat L.A., Kvyatkovskaya I.Y.


Ship collision is one of the most substantial concerns in the global maritime transportation industry. Hence, navigation safety is considerably cited topic in maritime literature. Recently, Unmanned Navigation (UN) technology is gradually becoming more widely used across in the field of marine robotics. The paper investigates the problem of navigation safety in the movement control of Unmanned Vessels (UVs). The object of the study is the process of avoiding collisions of UVs. The subject of the research is the algorithms of the autonomous decision-making system and software for preventing vessel collisions during UN. The intent of this article is to improve the safety of UN by developing new Decision-Making algorithms for autonomous collision prevention of UVs in real time, taking into account the International Rules for the Prevention of Collisions at Sea, 1972 (COLREGs-72) and the recommendations of the Federal agency for sea and inland water transport of the Russian Federation (Rosmorrechflot).In this article, the fundamental concept and the key functions set of the Autonomous Collision Avoidance System (ACAS) are carried out for UVs which are marine transport vehicles capable of sensing its environment and operating without human involvement. Along this line of research, this work focuses on the development of a software algorithm for determining the most dangerous obstacle located within a radius of 12 miles (recommendations of Rosmorrechflot) around an UV based on the principle of vessels collision avoidance geometry, collision risk assessment and the characteristics of obstacles. Moreover, the proposed algorithms can prevent the collision and address the issues of real-time collision avoidance for UVs. The simulation results also demonstrate the promising application of the proposed algorithms in studying the UN safety. Nonetheless, this study provides a way forward to conduct a new information decision-making system design for UVs collision avoidance. This is currently under development, and will be proposed later.
Applied Mathematics and Control Sciences. 2023;(4):83-93
Application of computer vision to identify reference points for assessing postural disorders
Shitoev I.D., Nikitin V.N., Ivanova M.D., Kloyan G.Z., Muravev S.V.


The use of computer vision to determine reference points on the human back is a relatively new approach in medicine. The relevance of this study is due not only to the need to develop new methods and approaches in determining postural disorders, but also to the growing interest in the development and application of artificial intelligence in medicine. This study is devoted to the creation and training of a neural network to find reference points of the back when diagnosing postural disorders. In this study, we use a set of ready-made neural network tools that are freely available. Training was carried out on models of photographed volunteers to determine the reference points of the back. The results of the study indicate that, as part of the study, a search was made for alternative (reference points) that determine the geometry of the back using developed neural network algorithms. It was shown that the accuracy of point detection by a neural network trained on more than 2400 grouped photographs reaches 85%, which indicates a good determination of object boundaries and their classification. The use of computer vision to identify reference points for assessing postural abnormalities can bring significant benefits to medical practice. This tool may be more accurate and efficient than traditional diagnostic methods, as well as more accessible and convenient for the patient. In addition, the use of neural networks can speed up the diagnostic process and reduce research costs.
Applied Mathematics and Control Sciences. 2023;(4):94-106
Features of competent models’ development in the field of information security
Kotsyuba I.Y., Shestakov A.V.


The article is devoted to the study of procedures for the formation of assessment tools in the training of departmental specialists implementing the functions of planning, implementation and control of organizational systems of higher and additional education, aimed at improving the mechanisms for forming information security policies and assessing the effectiveness of systems, tools and measures taken for informatization objects devoted to various levels of the hierarchy . The problematic issues being studied are related to the development of the theoretical foundations of management in organizational systems, methods and algorithms for solving management problems, including information and software. The results of scientific research, applied scientific research and qualification work for forming educational and methodological support for educational organizations and funds of assessment tools in the field of information security are analyzed, taking into account the features of competency models for the training of departmental specialists. The mechanisms and detailed procedures for the formation of assessment tools, focused on promising technologies for ensuring compliance of knowledge, motivational attitudes and skills with the competencies of a specialist in the field of information security, are generalized. Conceptual models of the competency modeling in object-oriented programming paradigms, new mathematical models for managing individual educational trajectories and designing competency-oriented tasks for assessing the development of competencies are proposed.
Applied Mathematics and Control Sciences. 2023;(4):107-125
Optimization algorithm of interacting countries and its application for solving problems of pharmacokinetics
Krasheninnikov R.S., Mitrichev I.I.


With the increasing complexity of optimization problems in the scientific environment, evolutionary algorithms inspired by certain processes in the world are becoming increasingly popular. This paper proposes a new evolutionary algorithm for interacting countries, which is mostly inspired by classical genetic algorithm, island algorithm and migration algorithm. Next, in the article, we study the performance of the algorithm on classical test functions. The results of the algorithm demonstrate its suitability for solving optimization problems and the prospects for its further study. In conclusion, the application of this algorithm to the search for pharmacokinetic constants of the two-compartment model is considered.
Applied Mathematics and Control Sciences. 2023;(4):126-135
Dual-channel call center model with exchange of requests and repeat calls
Barkalov S.A., Serebryakova E.A.


Computer simulation of stationary distribution of states in a call center for a two-channel RQ system with exchange of requests is presented. Such systems are becoming increasingly relevant due to the parallel use of both human dispatchers and voice intelligent bots for servicing calls. The simulation is based on solving the system of stationary Chapman-Kolmogorov equations for the Markov process describing the RQ-system. The system of equations proposed in the work differs from previous models by the presence of an exchange of requests between service channels in accordance with customer preferences. It takes into account the possibility of random repeated calls within a given average time. Service time in channels and delay time of requests in orbits have exponential distribution laws. Requests in orbit have the property of impatience, i.e. leave the system after some random time. To find the stationary distribution of states in orbits, the iterative numerical Gauss-Seidel method is used, which ensures fast convergence of calculations. Each channel has its own orbit of requests. The accuracy of the solution is controlled by increasing the maximum number of requests in orbit until the result stabilizes. The model demonstrates the sensitivity of system performance to the asymmetry of customer preferences when changing channels. Numerical simulation was carried out for the call center of the housing management company "StroyTekhnika" in the city of Voronezh. Application flows and repeat call parameters were calculated based on data from the company website and social network analysis. Accounting for repeat calls reduces system throughput compared to the option of completely impatient customers who do not use repeat calls. The case of completely impatient customers describes the limit state of a service system. At the same time, redistributing calls in favor of a more productive channel improves the overall performance of the system. The results obtained show the feasibility of using high-performance multi-channel voice bots while simultaneously stimulating a shift in customer preferences in favor of intelligent automata.
Applied Mathematics and Control Sciences. 2023;(4):136-145
Mathematical modeling of the regional budget formation procedure
Shalanov N.V., Zlobina S.L., Shalanova O.N., Peshkova M.N., Yakovleva A.A.


The regional budget is a key element of the regional financial system. According to budget legislation, the formation of the budget of the subject of the Russian Federation is carried out by state authorities of the constituent entity of the Russian Federation in accordance with the requirements established by the Budget Code of the Russian Federation, as well as the laws of the subject of the Russian Federation and other regulatory documents adopted in accordance with it. The procedure for forming a regional budget is quite well regulated, but poorly formalized. It should be noted that budget planning tactics and strategy differ significantly, since long-term goals are set on the basis of the development of strategic plans. The purpose of this study is to implement an approach to the formation of the regional budget according to the optimal structure. The uniqueness of the concept lies in the development of the target vector and positioning of budget planning as a Bayesian process. The criterion of optimality is the location of a multidimensional point expressing the composition of the budget on a straight line reflecting the target vector. Such an approach in relation to the procedure for the formation of the regional budget has not been considered before. The solution to this problem involves the formation of a target vector for both its revenue and expenditure parts. The methodological tools used in the work are classical methods of analytical geometry and an algorithm for forming a regional budget. To increase the adequacy of the results when modeling the regional budget, it is advisable to add the condition that the random process belongs to the Bayesian type, then, in addition to the obtained values, the share of the item in the regional budget is also taken into account. The Bayesian process takes into account conditional probabilities. In this work, the relative measure of achievement of each budget item of the target state in the base period acts as conditional probabilities. The article uses an illustrative example to show the use of the proposed methodological approach for the formation of an optimal regional budget within the framework of revenue and expenditure parts for items approved by Russian legislation. The construction and analysis of a regional budget allows us to take a new approach to solving this problem, and most importantly, to create an optimal budget while saving intellectual and time costs for participants in the budget process. The results of mathematical modeling of the regional budget are presented in the form of an algorithm, which makes it possible to consolidate the relevant procedures for calculating the revenue and expenditure parts of the budget in regulatory documents (at the federal and/or regional level) for their further use in the budget process.
Applied Mathematics and Control Sciences. 2023;(4):146-156

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