The article forms the task of hierarchical classification of texts, describes approaches to hierarchical classification and metrics for evaluating their work, examines in detail the local approach to hierarchical classification, describes different approaches to local hierarchical classification, conducts a series of experiments on training local hierarchical classifiers with various vectorization methods, compares the results of evaluating the work of trained classifiers.

Keywords: classification, hierarchical classification, local classification, hierarchical presicion, hierarchical recall, hierarchical F-measure, natural language processing, vectorization

Modern approaches to synthetic speech recognition are in most cases based on the analysis of specific acoustic, spectral, or linguistic patterns left behind by speech synthesis algorithms. An analysis of open sources has shown that the further development of methods and algorithms for synthetic speech recognition is crucial for providing protection against emerging threats and maintaining trust in existing biometric systems.
This paper proposes an algorithm for synthetic speech detection based on the calculation of audio signal entropy. The relevance of the work is driven by the increasing number of cases involving the malicious use of synthetic speech, which is becoming almost indistinguishable from genuine human speech. The results demonstrated that the entropy of synthetic speech is significantly higher, and the algorithm is robust to data losses. The advantages of the algorithm are its interpretability and low computational complexity. Experiments were conducted on the CMU ARCTIC dataset using the XTTS v.2 model. The proposed algorithm enables making a decision on the presence of synthetic speech without the need for complex spectral analysis or machine learning methods.

Keywords: synthetic speech, spoofing, Shannon entropy, speech recognition

The work is devoted to the application of a linear Kalman filter (KF) for estimating the roll angle of a quadcopter with structural asymmetry, under which the control input contains a nonzero constant component. This violates the standard assumption of zero mathematical expectation and reduces the efficiency of traditional KF implementations. A filter synthesis method is proposed based on the optimization of the covariance matrices ratio using a criterion that accounts for both the mean square error and the transient response time. The effectiveness of the approach is confirmed by simulation and experimental studies conducted on a setup with an IMU-6050 and an Arduino Nano. The obtained results demonstrated that the proposed Kalman filter provides improved accuracy in estimating the angle and angular velocity, thereby simplifying its tuning for asymmetric dynamic systems.

Keywords: Kalman filter, quadcopter with asymmetry, optimization of covariance matrices, functional with mean square error and process time, complementary filter, roll and pitch control

An algorithm has been developed and a program has been compiled in the Python programming language for calculating numerical values of the optimal lagged filtering operator for an L-Markov process with quasi-rational spectral density, which is a generalization of the Markov process with a rational spectrum. The construction of an optimal delayed filtering operator is based on the spectral theory of random processes. The calculation formula of the filtration operator was obtained using the theory of L-Markov processes, methods for calculating stochastic integrals, the theory of functions of a complex variable, and methods of trigonometric regression. An example of an L-Markov process (signal) with a quasi-rational spectrum is considered, which is interesting from the point of view of controlling complex stochastic systems. The trigonometric model was used as the basis for constructing a mathematical model of the optimal delayed filtration operator. It is shown that the values of the delayed filtering operator are represented by a linear combination of the values of the received signal at certain time points and the values of the sinusoidal and cosine functions at the same time points. It is established that the numerical values of the filtering operator significantly depend on the parameter β of the joint spectral density of the received and transmitted signals, and therefore three different tasks of signal transmission through different physical media were considered in the work. It is established that the absolute value of the real part of the filtration operator at all three intervals of the delay period change and in all three media exceeds the absolute value of the imaginary part by an average of two or more times. Graphs of the dependence of the real and imaginary parts of the filtration operator on the delay period t are constructed, as well as three-dimensional graphs of the dependence of the filtration operator itself with a delay on the delay period. The physical justification of the obtained results is given.

Keywords: random process, L-Markov process, noise, delayed filtering, spectral characteristic, filtering operator, trigonometric trend, standardized approximation error

The article explores the application of the residue number system in text information processing. The residue number system, based on the principles of modular arithmetic, represents numbers as sets of residues relative to pairwise coprime moduli. This approach enables parallel computation, potential data compression, and increased noise immunity. The study addresses issues such as character encoding, parallel information processing, error detection and correction, computational advantages in implementing polynomial hash functions, as well as practical limitations of the residue number system.

Keywords: residue number system, modular arithmetic, text processing, parallel computing, data compression, noise immunity, Chinese remainder theorem, polynomial hashing, error correction, computational linguistics

A mathematical model has been constructed, an algorithm has been developed, and a program has been written in the Python programming language for calculating the numerical values of the optimal filtering operator with a forecast for an L-Markov process with a quasi-rational spectrum. The probabilistic model of the filtering operator formula has been obtained based on the spectral analysis of L-Markov processes using methods for calculating stochastic integrals, the theory of analytical functions of a complex variable, and methods for correlation and regression analysis. Considered an example of L-Markov process, the values of the optimal filtering operator with a forecast for which it was possible to express in the form of a linear combination of the values of the process at some moments of time and the sum of numerical values of cosines and sines at the same moments. The basis for obtaining the numerical values of the filtering operator was the mathematical model of trigonometric regression with 16 harmonics, which best approximates the process under study and has a minimum

Keywords: random process, L-Markov process, prediction filtering, spectral characteristics, filtering operator

The article describes the process of developing a volumetric display for information and communication interaction in the Arctic, where traditional means of visualization and communication face the challenges of extreme climate, isolation and limited infrastructure. An analysis of the main areas of using volumetric in the Arctic zone is carried out. The main disadvantages of methods for creating a volumetric image in existing 3D displays are considered. Taking into account the main tasks to be solved - creating the illusion of a three-dimensional object for a group of people (more than 2 people) at a wide viewing angle - a description and analysis of two main developed configurations of the optical system is given, the latter of which meets the requirements, ensuring stable operation in Arctic conditions and opening up prospects for implementation in remote and hard-to-reach regions of the Far North.

Keywords: volume display, arctic zone, 3D image, system analysis, lens, optical system, computer modeling

Ontological modeling is a promising direction in the development of the scientific and methodological base for developing intelligent information systems in the power industry. The article proposes a new approach to using ontological models in creating artificial intelligence systems for forecasting time series in electrical engineering problems. Formal metrics are introduced: the ontological distance between a feature and a target variable, as well as the semantic relevance of a feature. Using examples of domain ontologies for wind energy and electricity consumption of an industrial enterprise, algorithms for calculating these metrics are demonstrated and it is shown how they allow ranking features, implementing an automated selection of the most significant features, and providing semantic regularization of training regression models of various types. Recommendations are given for choosing coefficients for calculating metrics, an analysis of the theoretical properties of metrics is carried out, and the applicability limits of the proposed approach are outlined. The results obtained form the basis for further integration of ontological information into mathematical and computer models for forecasting electricity generation and consumption in the development of industry intelligent systems.

Keywords: ontology, ontological distance, feature relevance, systems analysis, explainable artificial intelligence, power industry, generation forecasting, electricity consumption forecasting

In the modern world, when technology is developing at an incredible rate, computers have gained the ability to "see" and perceive the world around them like a human. This has led to a revolution in visual data analysis and processing. One of the key achievements was the use of computer vision to search for objects in photographs and videos. Thanks to these technologies, it is possible not only to find objects such as people, cars or animals, but also to accurately indicate their position using bounding boxes or masks for segmentation. This article discusses in detail modern models of deep neural networks used to detect humans in images and videos taken from a height and a long distance against a complex background. The architectures of the Faster Region-based Convolutional Neural Network (Faster R-CNN), Mask Region-based Convolutional Neural Network (Mask R-CNN), Single Shot Detector (SSD) and You Only Look Once (YOLO) are analyzed, their accuracy, speed and ability to effectively detect objects in conditions of a heterogeneous background are compared. Special attention is paid to studying the features of each model in specific practical situations, where both high-quality target object detection and image processing speed are important.

Keywords: machine learning, artificial intelligence, deep learning, convolutional neural networks, human detection, computer vision, object detection, image processing

The paper considers the synthesis of a non-stationary automatic control system for braking the wheels of a heavy vehicle using the generalized Galerkin method. The research method under consideration is used to solve the problem of synthesizing a non-stationary system whose desired program motion is specified at the output of a nonlinear element. The paper presents the results of studying the impact of non-stationarity on the parameters of the fixed part of the system (object) on the deterioration of the quality of the transient process. For critical operating conditions, the parameters of the controller were recalculated, and the results of accounting for non-stationarity and re-synthesis were evaluated.

Keywords: automatic control system, regulator, braking system, unsteadiness of parameters, generalized Galerkin method

This study analyzes the performance of Reed-Solomon codes (RS codes) using the MATLAB software environment. RS codes are selected as a class of error-correcting codes characterized by high performance under multiple burst errors, which makes them widely applicable in areas such as digital television, data storage (CD/DVD, flash memory) and wireless communication. The paper demonstrates and evaluates the performance of RS codes in practice through their simulation in MATLAB. The study covers the creation of simulation models for encoding, error insertion and decoding data using RS algorithms in MATLAB. The performance of the codes is evaluated by calculating the bit error rate (BER) and other relevant metrics. The influence of key parameters of RS codes (e.g., codeword length, number of check symbols) on their error-correcting ability is analyzed. The results of the study are intended to clearly show how RS codes cope with different types of errors and how their performance can be optimized by tuning the parameters. The work highlights the importance of MATLAB as a tool for developing, testing and optimizing coding systems, providing practical tools for researchers and engineers.

Keywords: Reed-Solomon codes, MATLAB, error correction, simulation, performance, error probability, communication systems, data storage

This article presents the development of a combined method for summarizing Russian-language texts, integrating extractive and abstractive approaches to overcome the limitations of existing methods. The proposed method is preceded by the following stages: text preprocessing, comprehensive linguistic analysis using RuBERT, and semantic similarity-based clustering. The method involves extractive summarization via the TextRank algorithm and abstractive refinement using the RuT5 neural network model. Experiments conducted on the Gazeta.Ru news corpus confirmed the method's superiority in terms of precision, recall, F-score, and ROUGE metrics. The results demonstrated the superiority of the combined approach over purely extractive methods (such as TF-IDF and statistical methods) and abstractive methods (such as RuT5 and mBART).

Keywords: combined method, summarization, Russian-language texts, TextRank, RuT5

The article considers the parameter identification issues of linear non-stationary dynamic systems adaptive models using the example of a linearized adjustable model of a DC motor with independent excitation. A new method for estimating the parameters of adjustable models from a small number of observations is developed based on projection identification and the apparatus of linear algebra and analytical geometry. To evaluate the developed identification method, a comparison of the transient processes of the adaptive model of a DC motor with independent excitation with the obtained parameter estimates with reference characteristics was carried out. The efficiency of the proposed identification method in problems of DC electric drive control is shown.

Keywords: DC motor, projection identification, dynamic system parameter estimation, adaptive model of non-stationary dynamic system

Modern computer systems for controlling chemical-technological processes make it possible to programmatically implement complex control algorithms, including using machine learning methods and elements of artificial intelligence. Such algorithms can be applied, among other things, to complex non-stationary multi-product and flexible discrete productions, which include such low-tonnage chemical processes as the production of polymeric materials. The article discusses the production of fluoroplastic in batch reactors. This process occurs under constantly changing parameters such as pressure and temperature. One of the important tasks of the control system is to stabilize the quality of the produced polymer, and for these purposes it is important to predict this quality during the production process before the release of fluoroplastic. The quality of the product, in turn, strongly depends on both the quality of the initial reagents and the actions of the operator. In non-stationary process conditions, typical virtual quality analyzers based on regression dependencies show poor results and are not applicable. The article proposes the architecture of a virtual quality analyzer based on mathematical forecasting methods using such algorithms as: random forest method, gradient boosting, etc.

Keywords: polymerization, multi-product manufacturing, low-tonnage chemistry, quality forecasting, machine learning

The article focuses on the development of a web portal for monitoring and forecasting atmospheric air quality in the Khabarovsk Territory. The study analyzes existing solutions in the field of environmental monitoring, identifying their key shortcomings, such as the lack of real-time data, limited functionality, and outdated interfaces. The authors propose a modern solution based on the Python/Django and PostgreSQL technology stack, which enables the collection, processing, and visualization of air quality sensor data. Special attention is given to the implementation of harmful gas concentration forecasting using a recurrent neural network, as well as the creation of an intuitive user interface with an interactive map based on OpenStreetMap. The article provides a detailed description of the system architecture, including the backend, database, and frontend implementation, along with the methods used to ensure performance and security. The result of this work is a functional web portal that provides up-to-date information on atmospheric air conditions, forecast data, and user-friendly visualization tools. The developed solution demonstrates high efficiency and can be scaled for use in other regions.

Keywords: environmental monitoring, air quality, web portal, forecasting, Django, Python, PostgreSQL, neural networks, OpenStreetMap

Analysis of a digital data transmission system through a noisy communication channel based on the Huffman compression method and encoding using cyclic Bose-Chowdhury-Hockingham codes This article examines the effectiveness of a digital data transmission system through a noisy communication channel using the Huffman compression method and cyclic BCH encoding (Bose-Chowdhury-Hockingham). Huffman compression reduces data redundancy, which increases the effective transmission rate, while BCH codes detect and correct errors caused by channel noise. The analysis likely includes evaluating parameters such as compression ratio, data transmission rate, error probability after decoding, and computational complexity of the algorithms. The results demonstrate the effectiveness of this combination of techniques in improving data transmission reliability in noisy environments.

Keywords: digital transmission system, cyclic coding, compression ratio, decoding, encoding

This article discusses the implementation features of named entity recognition models. In the course of the work, a number of experiments were conducted with both traditional models and well-known neural network architectures, a hybrid model, the features of the results, their comparison and possible explanations are considered. In particular, it is shown that a hybrid model with the addition of a bidirectional long short-term memory can give better results than the basic bidirectional representation model based on transformers. It is also shown that, improved by adding a thinning layer for regularization, a weighted loss function and a linear classifier on top of the outputs, a bidirectional representation model based on transformers can give high metric values. For clarity, the work provides graphs of model training and tables with metrics for comparison. In the process of work, conclusions and recommendations were formed.

Keywords: text analysis, artificial intelligence, named entity recognition, neural networks, deep learning, machine learning

To ensure the stable and reliable operation of isolated power systems, models based on rapid processing and analysis of non-Gaussian data are needed, which contributes to increased energy efficiency and improved energy management. Within the framework of the theory of optimal control of power consumption, based on a comprehensive ranking analysis procedure, a model of regime rationing was developed, which differs from the known ones in that for the first time an R-distribution device based on rank analysis was used, as well as a device and method of regime rationing, which automatically ensures the necessary stable power consumption of the regional electrical complex in conditions of resource constraints.

Keywords: Regime normalization, rank analysis, OLAP data cube, half division method, entropy, topological data, rank topological measure, resource constraints plan, approximation, regional electric complex, power consumption

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

This paper is devoted to the construction of a visual-inertial odometry system for an unmanned vehicle using both binocular cameras and inertial sensors as an information source, which would be able to simultaneously determine the vehicle's own position and the relative position of other road users. To ensure accurate and continuous localization, it is proposed to use an inertial navigation system and two types of image keypoints. Deep learning models are used to accurately and reliably track keypoints. To achieve efficient and reliable matching of objects between two frames, a multi-level data association mechanism is proposed that takes into account possible errors of various system components. The experimental results demonstrate the feasibility and application potential of the proposed system.

Keywords: multi-object visual-inertial odometry, localization, data association, tracking of 3D dynamic objects

The article is devoted to the description and mathematical justification of the U-shaped distribution of topic shares that arises in the latent Dirichlet allocation model with symmetric hyperparameters. It is shown that the bimodal shape is due to the reduction of the Dirichlet vector to a beta distribution, which makes traditional unimodal approximations incorrect. A composite probability model is proposed that combines beta, gamma, and Poisson components, as well as covariate accounting for semantic connectivity. The model parameters are determined by the differential evolution method using a criterion that includes the Wasserstein distance and the Jensen–Shannon and Kulbak–Leibler divergences. Based on the corpus of texts from the information field of the Rosatom State Corporation, it has been established that the new model is more accurate than lognormal, Pareto, exponential, and normal approximations, allowing for reliable characterization of thematic flows and supporting decisions in large text data monitoring tasks.

Keywords: system analysis, latent Dirichlet allocation, topic modeling, Dirichlet latent distribution, topic signal intensity, beta distribution, gamma distribution, Poisson process, Jensen–Shannon divergence, Wasserstein distance, Kulbak–Leibler divergence

This article proposes a new concept of production management of a chemical industry holding as the basis for mathematical support of an automated control system. The concept is based on the use of both traditional methods of proactive management (preventive and predictive) and new generation proactive management, which not only prevents the occurrence of undesirable events, but also ensures a decrease in the frequency of occurrence of such events in the future. A system of basic concepts and principles of proactive production management has been developed. The proposed concept will allow developing the existing mathematical support of an automated production control system and increasing its efficiency.

Keywords: production, automated production control system, mathematical support, concept, proactivity, strategies, proactive management

In this paper, methods for estimating one's own position from a video image are considered. A robust two-stage algorithm for reconstructing the scene structure from its observed video images is proposed. In the proposed algorithm, at the feature extraction and matching stage, a random sample based on the neighborhood graph cuts is used to select the most probable matching feature pairs. At the nonlinear optimization stage, an improved optimization algorithm with an adaptive attenuation coefficient and dynamic adjustment of the trust region is used. Compared with the classical Levenberg-Marquard (LM) algorithm, global and local convergence can be better balanced. To simplify the system's decisions, the Schur complement method is used at the group tuning stage, which allows for a significant reduction in the amount of computation. The experiments confirmed the operability and effectiveness of the proposed algorithm.

Keywords: 3D reconstruction, graph-cut, Structure-from-Motion (SfM)，RANSAC，Bundle Adjustment optimization，Levenberg-Marquardt algorithm，Robust feature matching

This paper presents the design and experimental validation of an external load-balancing mechanism for server clusters that support a distributed educational network. A hybrid strategy is proposed that merges classical policies (Round Robin, Least Connections) with an evolutionary search based on a genetic algorithm. At the modeling level the user-session assignment problem is formulated as a minimization of the maximum node load under latency constraints. The solution is implemented entirely on a domestic technology stack— “1C:Enterprise” server clusters, Docker containers, and the “1C:Bus” integration middleware. Experimental results show that the new scheduling logic improves system resilience under traffic fluctuations, lowers user response times, and utilizes spare resources more efficiently, while imposing no substantial overhead on the control nodes. The study confirms the practical viability of evolutionary approaches for real-time load balancing.

Keywords: load balancing, server clusters, genetic algorithm, simulation modeling, 1C:Bus middleware

The purpose of the article is to study the possibility of the influence of various factors affecting the process of eliminating a water pipeline accident based on its modeling using fuzzy logic methods. The article discusses various options for managing the process of eliminating a water pipeline accident and, during the analysis, determines a set of qualitative parameters that are used in the fuzzy inference model based on the Mamdani method. To build a mathematical model, 37 products were formulated with the help of a group of experts, so that the model can work with selected qualitative variables as with quantitative ones and track the changes that occur in the process. The result of the inference cycle is a clear value of the parameters describing the possible actions necessary to eliminate the accident. The resulting mathematical model allows you to analyze the input parameters at a qualitative level, gives a qualitative representation of the result at the output, which will increase the effectiveness of actions aimed at eliminating a water pipeline accident. The quality of functioning of the described model is verified by a group of experts.

Keywords: fuzzification, defazziification, Mamdani method, system analysis, fuzzy logic, qualitative parameters, water pipe accident, mathematical model