The article examines the influence of the data processing direction on the results of the discrete cosine transform (DCT). Based on the theory of groups, the symmetries of the basic functions of the DCT are considered, and the changes that occur when the direction of signal processing is changed are analyzed. It is shown that the antisymmetric components of the basis change sign in the reverse order of counts, while the symmetric ones remain unchanged. Modified expressions for block PREP are proposed, taking into account the change in the processing direction. The invariance of the frequency composition of the transform to the data processing direction has been experimentally confirmed. The results demonstrate the possibility of applying the proposed approach to the analysis of arbitrary signals, including image processing and data compression.

Keywords: discrete transforms, basic functions, invariance, symmetry, processing direction, matrix representation, correlation

Modern engineering equipment operation necessitates solving optimal control problems based on measurement data from numerous physical and technological process parameters. The analysis of multidimensional data arrays for their approximation with analytical dependencies represents both current and practically significant challenges. Existing software solutions demonstrate limitations when working with multidimensional data or provide only fixed sets of basis functions.
Objectives. The aim of this study is to develop software for multidimensional regression based on the least squares method and a library of constructible basis functions, enabling users to create and utilize diverse basis functions for approximating multidimensional data.
Methods. The development employs a generalized least squares method model with loss function minimization in the form of a multidimensional elliptical paraboloid. LASSO (L1), ridge regression (L2), and Elastic Net regularization mechanisms enhance model generalization and numerical stability. A precomputation strategy reduces asymptotic complexity from O(b²·N·f·log₂(p)) to O(b·N·(b+f·log₂(p))). The software architecture includes recursive algorithms for basis function generation, WebAssembly for computationally intensive operations, and modern web technologies including Vue3, TypeScript, and visualization libraries.
Results. The developed web application provides efficient approximation of multidimensional data with 2D and 3D visualization capabilities. Quality assessment employs MSE, R², and AIC metrics. The software supports XLSX data loading and intuitive basis function construction through a user-friendly interface.
Conclusion. The practical value lies in creating a publicly accessible tool at https://datapprox.com for analyzing and modeling complex multidimensional dependencies without requiring additional software installation.

Keywords: approximation, least squares method, basic functions, multidimensional regression, L1/L2 regularization, web application, multidimensional elliptical paraboloid

The study addresses the problem of short-term forecasting of ice temperature in engineering systems with high sensitivity to thermal loads. A transformer-based architecture is proposed, enhanced with a physics-informed loss function derived from the heat balance equation. This approach accounts for the inertial properties of the system and aligns the predicted temperature dynamics with the supplied power and external conditions. The model is tested on data from an ice rink, sampled at one-minute intervals. A comparative analysis is conducted against baseline architectures including LSTM, GRU, and Transformer using MSE, MAE, and MAPE metrics. The results demonstrate a significant improvement in accuracy during transitional regimes, as well as robustness to sharp temperature fluctuations—particularly following ice resurfacing. The proposed method can be integrated into intelligent control loops for engineering systems, providing not only high predictive accuracy but also physical interpretability. The study confirms the effectiveness of incorporating physical knowledge into neural forecasting models.

Keywords: short-term forecasting, time series analysis, transformer architecture, machine learning, physics-informed modeling, predictive control

This paper is devoted to the theoretical analysis of the methods used in verifying the dynamics of a signature obtained from a graphic tablet. A classification of three fundamental approaches to solving this problem is carried out: matching with a standard; stochastic modeling and discriminative classification. Each approach in this paper is considered using a specific method as an example: dynamic transformation of the time scale; hidden Markov models; support vector machine. For each method, the theoretical foundations are disclosed, the mathematical apparatus is presented, the main advantages and disadvantages are identified. The results of the comparative analysis can be used as the necessary theoretical basis for developing modern signature dynamics verification systems.

Keywords: verification, biometric authentication, signature dynamics, graphic tablet, classification of methods, matching with a standard, stochastic modeling, discriminative classification, hidden Markov models, dynamic transformation of the time scale

The characteristics of a submersible induction motor are described with sufficient reliability for practice by the theory of multi-motor electric drive. In this case, the classical circuit of a submersible induction motor is a coupled system of several equivalent-T circuits. In turn, this significantly increases its computational complexity and reduces the speed of ACS. It is proposed to construct a mathematical model of the submersible electric motor in the form of polynomials with significantly higher speed using the methods of experiment planning. In the area of applicability, the differences in the estimation of energy performance do not exceed 1.1%, between the proposed models and classical equivalent-T circuits.

Keywords: automated control system, mathematical model, polynomial, mean absolute percentage error, computational complexity, design of experiment, scatter diagram, modal interval, submersible electrical motor, rotor package

The article is devoted to the study of the possibilities of automatic transcription and analysis of audio recordings of telephone conversations of sales department employees with clients. The relevance of the study is associated with the growth of the volume of voice data and the need for their rapid processing in organizations whose activities are closely related to the sale of their products or services to clients. Automatic processing of audio recordings will allow checking the quality of work of call center employees, identifying violations in the scripts of conversations with clients. The proposed software solution is based on the use of the Whisper model for speech recognition, the pyannote.audio library for speaker diarization, and the RapidFuzz library for organizing fuzzy search when analyzing strings. In the course of an experimental study conducted on the basis of the developed software solution, it was confirmed that the use of modern language models and algorithms allows achieving a high degree of automation of audio recordings processing and can be used as a preliminary control tool without the participation of a specialist. The results confirm the practical applicability of the approach used by the authors for solving quality control problems in sales departments or call centers.

Keywords: call center, audio file, speech recognition, transcription, speaker diarization, replica classification, audio recording processing, Whisper, pyannote.audio, RapidFuzz

The article presents a mathematical model that formalizes the process of managing the scientific activities of an organization. The model based on the theory of queuing. The principle of death - reproduction used in the construction. For a special case, a graph of states and a system of Kolmogorov differential equations are given. The intensity of the input and output streams are time-dependent non-stationary streams. The model allows us to consider various structures and schemes of interaction between scientific departments and various sce-narios for setting scientific tasks and the intensity of their solution by employees of the organization. A software package for decision-making has developed for the model for optimal management of the scientific activities of the department. The article presents one of the results of an experimental and model study of the influence of the motivational component and the level of competence of employees. Graphs of the system states given for the resulting solution. The research can used for comprehensive evaluation of results, planning, resource allocation and management of scientific activities.

Keywords: scientific activity, mathematical model, queuing system, death-reproduction principle, graph of states, system of differential equations

The article discusses the structure and principle of operation of an improved centrifugal unit for mixing bulk materials. A special feature of which is the ability to control mixing modes. Due to its design, the selection of a rational position of the bump makes it possible to provide such conditions for the impact interaction of particle flows, in which a high-quality homogeneous mixture of components is formed, the particles of which have different sizes, shapes and other parameters. To characterize the resulting mixture, the coefficient of heterogeneity was used, the conclusion of which is based on a probabilistic approach. A computational scheme of the rarefied flow formation process is given. An expression is derived for calculating the coefficient of heterogeneity when mixing bulk media, the particles of which have different sizes, shapes and other parameters. The research conducted in the article allows not only to predict the quality of the resulting mixture, but also to identify the factors that have the greatest impact on achieving the required uniformity.

Keywords: aggregate, bulk media, mixing, coefficient of heterogeneity, concentration, design scheme, particle size

The article presents a novel approach for adaptive control of genetic algorithm parameters using reinforcement learning methods. The use of the Q-learning algorithm enables dynamic adjustment of mutation and crossover probabilities based on the current population state and the evolutionary process progress. Experimental results demonstrate that this method offers a more efficient solution for optimization problems compared to the classical genetic algorithm and previously developed approaches employing artificial neural networks. Tests conducted on the Rastrigin and Shaffer functions confirm the advantages of the new method in problems characterized by a large number of local extrema and high dimensionality. The article details the theoretical foundations, describes the implementation of the proposed hybrid model, and thoroughly analyzes experimental results. Conclusions highlight the method's adaptability, efficiency, and potential for application in complex optimization scenarios.

Keywords: genetic algorithm, reinforcement learning, adaptive control, Q-learning, global optimization, Rastrigin function, Shaffer function

The article discusses a software module developed by the authors for automatic generation of program code based on UML diagrams. The relevance of developing this module is due to the limitations of existing foreign code generation tools related to functionality, ease of use, support for modern technologies, as well as their unavailability in Russian Federation. The module analyzes JSON files obtained by exporting UML diagrams from the draw.io online service and converts them into code in a selected programming language (Python, C++, Java) or DDL scripts for DBMS (PostgreSQL, Oracle, MySQL). The Python language and the Jinja2 template engine were used as the main development tools. The operation of the software module is demonstrated using the example of a small project "Library Management System". During the study, a series of tests were conducted on automatic code generation based on the architectures of software information systems developed by students of the Software Engineering bachelor's degree program in the discipline "Design and Architecture of Software Systems". The test results showed that the code generated using the developed module fully complies with the original UML diagrams, including the structure of classes, relationships between them, as well as the configuration of the database and infrastructure (Docker Compose). The practical significance of the investigation is that the proposed concept of generating program code based on visual models of UML diagrams built in the popular online editor draw.io significantly simplifies the development of software information systems, and can be used for educational purposes.

Keywords: code generation, automation, python, jinja2, uml diagram, json, template engine, parsing, class diagram, database, deployment diagram

Traditional marketing methods of promoting goods and services are aimed at a wide audience and do not take into account the individual characteristics of consumers, which can lead to a small percentage of positive responses and even to negative responses (loss of customers). Wide audience coverage leads to an increase in the cost of marketing interactions and does not guarantee the achievement of the goals of marketing campaigns. In such a situation, the task is to minimize excess costs through a more rational organization of marketing interactions aimed at obtaining maximum profit from each target client. To implement such a strategy, tools are needed that can identify customer segments, marketing interaction with which will lead to a positive response. One of the technologies for building such tools is uplift modeling, which is a section of machine learning and is considered a promising direction in data-driven marketing. In this article, based on the open data X5 RetailHero Uplift Modeling Dataset, provided by X5 Retail Group, a comparative analysis of the effectiveness of various uplift modeling approaches is conducted to identify the segment of customers who are most susceptible to target impact. Various uplift metrics and visual technologies are used to conduct the comparative analysis.

Keywords: effective marketing communications with customers, customer segmentation, machine learning methods, uplift modeling, uplift quality metrics

The article studies possibilities for analyzing geopolitical processes within the framework of situational analysis methodology using cognitive modeling. Situational analysis description is given, and scenario for developing events is presented where two stages are distinguished: a preparatory stage (a pre-scenario stage) which is essential for performing descriptive and explanatory functions of predictive research, and a scenario stage intended for substantive and formal research as well as for description of predicted processes, construction of system models and preparation of all significant information for scenario synthesis. Furthermore, a method for applying situational analysis is proposed to be used within the framework of the cognitive modeling toolkit of a “future scenario” option and its analysis with account of new “main” factors, relationships, feedbacks and dynamics of their alterations. When forming a scenario for a specific geopolitical situation within the framework of cognitive modeling, this method can be presented by causal (functional) and logical-semantic relation between the elements/agents of actions and counteractions. By interpreting the logical-semantic as structural, and the causal as dynamic, we obtain a structural-dynamic systemic description of geopolitical confrontation using the language of cognitive graphs, i.e. presenting a graphical expression of causal relationships between the concepts (factors) that characterize a particular geopolitical process. Thus, within the framework of a scenario stage the following procedures are conducted: analyzing the initial geopolitical situation, namely: determining key factors that build up the scheme of internal connections and external relationships, and their structuring; defining factors that make an impact; determining impact directions and force (positive and negative effect); choosing basic stereotypes or generalized models of interactions that correspond to the initial situation; constructing cognitive models of the current state of a situation; studying trends for the situation’s development and its dynamics analysis; transferring a scenario onto a practical basis. 

Keywords: geopolitical processes, situational analysis, cognitive modeling, and forecasting scenario

Changes in external conditions, parameters of object functioning, relationships between system elements and system connections with the supersystem lead to a decrease in the accuracy of the artificial intelligence models results, which is called model degradation. Reducing the risk of model degradation is relevant for electric power engineering tasks, the peculiarity of which is multifactor dependencies in complex technical systems and the influence of meteorological parameters. Therefore, automatic updating of models over time is a necessary condition for building user confidence in forecasting systems in  power engineering tasks and industry implementations of such systems. There are various methods used to prevent degradation, including an algorithm for detecting data drift, an algorithm for updating models, their retraining, additional training, and fine-tuning. This article presents the results of a study of drift types, their systematization and classification by various features. The solution options that developers need to make when creating intelligent forecasting systems to determine a strategy for updating forecast models are formalized, including update trigger criteria, model selection, hyperparameter optimization, and the choice of an update method and data set formation. An algorithm for forming a strategy for automatic updating of artificial intelligence models is proposed and practical recommendations are given for developers of models in problems of forecasting time series in the  power industry, such as forecasting electricity consumption, forecasting the output of solar, wind and hydroelectric power plants.

Keywords: time series forecasting, artificial intelligence, machine learning, trusted AI system, model degradation, data drift, concept drift

This paper provides a survey of metrics used to assess the quality of images generated by generative models. Specialized metrics are required to objectively evaluate image quality. A comparative analysis showed that a combination of different metrics is necessary for a comprehensive evaluation of generation quality. Perceptual metrics are effective for assessing image quality from the perspective of machine systems, while metrics evaluating structure and details are useful for analyzing human perception. Text-based metrics allow for the assessment of image-text alignment but cannot replace metrics focused on visual or structural evaluation. The results of this study will be beneficial for specialists in machine learning and computer vision, as well as contribute to the improvement of generative algorithms and the expansion of diffusion model applications.

Keywords: deep learning, metric, generative model, image quality, image

The article presents and analyzes the algorithm for calculating bending reinforced concrete structures by normal section based on a nonlinear deformation model recommended in the standards for the design of reinforced concrete structures SP 63.13330.2018. Calculation of reinforced concrete structures based on a nonlinear deformation model is a priority, since it expands the set of controlled parameters, which leads to a more accurate description of the operation of building structures. The features of performing the calculation using this algorithm, as well as other approaches to calculating bending reinforced concrete structures by a normal section based on deformation and other models, are considered. The sequence of calculations using computer technologies is shown using the example of calculations in the engineering nonlinearity1 system of the LIRA-SAPR software package. The results of calculating a rod element of the calculation scheme are given: changes of the bending moment, stiffness, and deformation modulus for finite elements along the rod length. In this case, the calculation in the engineering nonlinearity1 system is performed with subsequent adjustment of the stiffness characteristics of the finite elements, carried out during the iterative calculation, with clarification of the stress-strain state, deflection of the element and its reinforcement. Additional capabilities of performing calculations using the engineering nonlinearity2 system are described: expanded the possibilities of assigning various laws of material deformation, describing the loading of the calculation scheme, reinforcement of structures, and the possibility of using a step processor.

Keywords: bending reinforced concrete structures, nonlinear deformation model, calculation scheme, calculation algorithm, PC LIRA-SAPR, engineering nonlinearity, system

The article is devoted to the application of modern methods of generative image compression using variational autoencoders and neural network architectures. Special attention is paid to the analysis of existing approaches to image generation and restoration, as well as a comparative assessment of compression quality in terms of visual perception and metric indicators. The aim of the study is to systematize deep image compression methods and identify the most effective solutions based on the variational Bayesian approach. The paper considers various architectures, including conditional autoencoders and hypernetwork models, as well as methods for evaluating the quality of the data obtained. The main research methods used were the analysis of scientific literature, a comparative experiment on the architectures of generative models and a computational estimation of compression based on metrics. The results of the study showed that the use of variational autoencoders in combination with recurrent and convolutional layers makes it possible to achieve high-quality image recovery with a significant reduction in data volume. The conclusion is made about the prospects of using conditional variational autoencoders in image compression tasks, especially in the presence of additional information (for example, metadata). The presented approaches can be useful for developing efficient systems for storing and transmitting visual data.

Keywords: variational autoencoders, generative models, image compression, deep learning, neural network architectures, data recovery, conditional models

The article focuses on developing data clustering algorithms using asymmetric similarity measures, which are relevant in tasks involving directed interactions. Two algorithms are proposed: stepwise cluster formation and a modified version with iterative center refinement. Experiments were conducted, including a comparison with the k-medoids method. The results showed that the fixed-center algorithm is efficient for small datasets, while the center-recalculation algorithm provides more accurate clustering. The choice of algorithm depends on the requirements for speed and quality.

Keywords: clustering, asymmetric similarity measures, clustering algorithms, iterative refinement, k-medoids, directed interactions, adaptive methods

This paper considers the modeling of user work with a multi-server database developed on the basis of microservice architecture. The subject area was analyzed, the main entities of the system were described, and the mechanisms of data transfer and service interaction using Docker and Apache Kafka were implemented. It was revealed that the development of a multi-server database allowed to achieve high scalability and fault tolerance of the system. The implementation of replication and sharding mechanisms provided even load distribution, and the use of Kafka message broker facilitated efficient data exchange between services. The testing confirmed the system's reliability under high load, as well as revealed its strengths and potential improvements.

Keywords: modeling, load balancing, Docker, Apache Kafka, microservice architecture, distributed systems, query optimization

The article is devoted to the method of calculating the effective frequency of the load impulse FWD, which allows establishing a correspondence between the laboratory-determined viscoelastic characteristics of asphalt concrete layers included in the road pavement and the modulus of elasticity calculated by backcalculation based on the deflection  bowl determined in field tests using FWD. The article proposes an algorithm for finding this frequency, presents the results of its calculations, and compares the elastic moduli obtained in the laboratory and by the results of the backcalculation. The conducted numerical experiment confirms that for the deflection cups generated within the viscoelastic calculation model, the difference in modules does not exceed 8%. At the end of the work, ways are proposed for the practical application of the calculated parameter and further improvement of the method on real deflection  bowl obtained on  road pavements.

Keywords: dynamic loading system, road surface, deflection bowl, asphalt concrete, elastic modulus, relaxation modulus, AMPT test, master curve, backcalculation, effective pulse frequency

The article presents numerical modeling of flow dividers (separators) with different hole diameters (3.5 mm, 7.0 mm, 14.0 mm) to prevent cavitation damage. The hole diameters, number, and rows in the separators have equivalent significance, as they determine the distribution of local velocities and pressures in the flow. This minimizes the risk of vapor bubble formation and subsequent collapse, which can lead to erosion of metal surfaces. For clarity, the simulation results are presented in the form of pictures of the distribution of pressure and velocities in each of the separators with different diameters. In order to prevent cavitation, the authors have presented a design of a "short-stroke" valve in which it is allowed to use flow dividers with enlarged holes.

Keywords: valve, cavitation, distribution pattern, separator, holes, rotation, simulation, flow divider

An ensemble of models for predicting the position of a mobile robot moving in an unstructured environment is presented. An architecture has been developed that integrates a kinematic motion model with trainable models utilizing elevation map data and semantic segmentation. The principles for constructing a spatial feature map are described, incorporating geometric characteristics such as the terrain roughness index and a fuzzy traversability index. A modular structure of the following blocks is proposed: data preprocessing, geometric property computation, segmentation, and decision-making. Test results demonstrate the advantage of combining kinematic and sensor-based models for autonomous navigation in complex environments.

Keywords: traversability model, elevation map, point cloud, kinematic model, segmentation, machine learning, feature map

The article is devoted to assessing the influence of possible inhomogeneities in the layers of road pavements on the results of backcalculation of elastic moduli based on testing data of falling weight deflectometres (FWD). The article discusses the influence of different locations of theoretically specified inhomogeneities of structural layers within the roadway. Additionally, the influence of the location of the edge of the pavement on the results of calculating elastic moduli by backcalculation is considered. The conducted numerical experiment confirms that possible inhomogeneities of the road pavement can significantly influence the results of reverse calculations, and as a consequence, the decision-making on the appointment of repair measures. The boundaries are also determined at which the presence of a shoulder with a pavement design that differs from the roadway significantly distorts the results obtained. At the end of the work, ways to practically take into account inhomogeneities and further improve the method of inverse calculation of the elastic moduli of non-rigid road pavements are proposed.

Keywords: dynamic loading system, road pavement,structural layers, deflection bowl, asphalt concrete, elastic modulus, backcalculation, heterogeneity of layers, roadway, roadside

The calculation of wind loads on curtain facades and their fastening elements for high-rise buildings and structures using engineering methods and various numerical techniques remains an important task to this day. The corner sections of the building, where the greatest negative wind pressure occurs, are of particular interest. Incorrect calculation of wind suction can lead to the separation of panels during strong winds. The article calculates the peak wind load using a numerical method for a rectangular building with an aspect ratio of 0.6. Numerical calculations of the two-dimensional flow around the building profile in the ANSYS Fluent program using the k-e Realizable turbulence model were used to obtain the coefficients of drag, lateral force, and the distribution of the pressure coefficient at maximum lateral force. The calculations showed that the wind suction at the edge of the building exceeds the standard value by approximately 30%. The results obtained in the article should be taken into account when designing the facade.

Keywords: peak wind load, wind suction, rectangular buildings, peak negative aerodynamic pressure coefficient

The article examines a functional-dynamic model of implementing intelligent digital platforms and solutions, whose governing role in the development of a macroeconomic system is taken into account using a feedback mechanism. The relevance of the study is demonstrated in the context of active digital transformation of industries. The mathematical form of the model under consideration is a system of nonlinear differential equations of an evolutionary type, similar to dynamic models of the development of biological communities. An analysis of a macrosystem influenced by innovative technologies is carried out. As such a system, a two-sector macrostructure is considered, simulating the impact through the implementation and use of intelligent digital platforms (IDP) of two related industries, which are the transport and logistics and manufacturing sectors. The objective of the work is to study the stable states of such a structure. The model allows for taking into account the influence of investments in IDPs based on the principle of their proportionality to the growth rates of return on assets in these industries. In the work, quantitative estimates of the parameters of the original model are adjusted. An analysis of the macrosystem is carried out under conditions of different development rates of the interacting industries. The stability of the system according to Lyapunov is studied. An asymptotic approximation ‒ a solution to the problem ‒ was constructed using A.B. Vasil’eva's boundary layer decomposition method. The results describe the process of self-organization in a stable model of interaction between two related industries, supported by integrated digital platforms.

Keywords: functional-dynamic model, intelligent digital platforms, two-sector macrostructure, transport and logistics industry, production, sustainability, inter-industry interaction, asymptotic analysis, boundary layer function method

Verification and debugging of algorithms and related software that implements the search for such dangerous phenomena for aircraft flights as wind gusts and turbulence areas can be implemented in radar signal simulators, including using the concept of accessing databases storing test wind fields by coordinate components. The practical value of this approach is to minimize the number of expensive flight tests in difficult weather conditions. After implementing database data interpolation, continuous fields can be obtained, including predicted radar parameters, the processing of which, depending on the changing parameters of the locator: beam width, probe pulse duration, leads to different estimates, including the measured parameters of the movement of air masses. This article describes an approach to simulation modeling that makes it possible, by generating radio signals, the primary source of which are continuous interpolated functions of air mass motion parameters, to obtain either averaged radial velocity values in resolution elements or its standard deviation.  As a result, it allows us to test signal processing algorithms for detecting wind shifts or turbulence in weather navigation radars. The results of verification of the procedure for processing radio signals generated using the proposed approach are presented, confirming the correctness of the formation and detection of simulated fields of turbulent regions.

Keywords: on-board radar, meteorological navigation, simulation, algorithms, parameter estimation