APPLIED MATHEMATICS
AND CONTROL SCIENCES

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.

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.

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.

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.

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.