Linear feedback shift registers (LFSR) and the pseudo-random sequences of maximum length (m-sequences) generated by them have become widely used in solving problems of mathematical modeling, cryptography, radar and communications. The wide distribution is due to their special properties, such as correlation. An interesting, but rarely discussed in the scientific literature of recent years, property of these sequences is the possibility of forming quasi-orthogonal matrices on their basis.In this paper, was conducted a study of methods for generating quasi-orthogonal matrices based on pseudo-random sequences of maximum length (m-sequences). An analysis of the existing method based on the cyclic shift of the m-sequence and the addition of a border to the resulting cyclic matrix is carried out. Proposed an alternative method based on the relationship between pseudo-random sequences of maximum length and quasi-orthogonal Mersenne and Hadamard matrices, which allows generating cyclic quasi-orthogonal matrices of symmetric structure without a border. A comparative analysis of the correlation properties of the matrices obtained by both methods and the original m-sequences is performed. It is shown that the proposed method inherits the correlation properties of m-sequences, provides more efficient storage, and is potentially better suited for privacy problems.

Keywords: orthogonal matrices, quasi-orthogonal matrices, Hadamard matrices, m-sequences

The article considers the options for visual programming of information support means for software and information complexes for UAV operators training. The main criterion indicators for systematically organizing the set of components for reusing program code are identified. An example of an unmanned payload carrier in various representative forms of visualization is given. A comparison of the labor intensity of developing the specified software and information implementations for the same unmanned robotics object with their normative labor intensity is shown. The variants of content filling during the development of the same material part of the considered device for various aspects of training specialists in the management and operation of UAV are considered. The principle of systematization of components by means of ordering the complexity of presentation and softwarе implementation is shown.

Keywords: risk forecasting, information support, training of unmanned aircraft systems operators, labor intensity assessment

The paper presents a method for quantitative assessment of zigzag trajectories of vehicles, which allows to identify potentially dangerous behavior of drivers. The algorithm analyzes changes in direction between trajectory segments and includes data preprocessing steps: merging of closely spaced points and trajectory simplification using a modified Ramer-Douglas-Pecker algorithm. Experiments on a balanced data set (20 trajectories) confirmed the effectiveness of the method: accuracy - 0.8, completeness - 1.0, F1-measure - 0.833. The developed approach can be applied in traffic monitoring, accident prevention and hazardous driving detection systems. Further research is aimed at improving the accuracy and adapting the method to real-world conditions.

Keywords: trajectory, trajectory analysis, zigzag, trajectory simplification, Ramer-Douglas-Pecker algorithm, yolo, object detection

The article deals with the principles of creating software used as part of sensing systems for restoring the visibility of the gas smoke protection service link in a smoke-filled environment during rescue operations. The architectural part of the device and the description of algorithms of the device operation are described. Attention is paid to the methods of forming a digital model of obstacle heights and visualization of the spatial situation. Approaches to filtering of erroneous sensor values and selection of significant contours of objects, processing of data from ultrasonic grating, infrared sensors, as well as temperature and humidity sensors are given. The role of the device in providing accurate navigation, reducing the time to search for the fire center and improving the overall safety of the gas smoke protection service unit when working in a smoky environment is emphasized.

Keywords: smoke protection service, smoke-filled environment, sensing device, algorithms, software, firefighting, reconnaissance, modeling, navigation, sensor data

The article explores the implementation of digital and mathematical technologies in decision support systems (DSS) aimed at enhancing the efficiency of livestock enterprises. In the context of digital transformation and increasing uncertainty in agriculture, the authors emphasize the importance of intelligent DSS capable of processing large datasets and supporting rapid, evidence-based decision-making. The purpose of the study is to identify effective technological and methodological approaches for optimizing livestock management, particularly in the area of animal feeding. Methods include the use of mathematical models, predictive algorithms, automated control systems, and big data analytics. The proposed DSS architecture enables real-time monitoring, adaptive ration formulation, and integration of physiological, environmental, and economic data. The paper provides practical examples of successful DSS applications, such as automated milking systems and health monitoring technologies, and analyzes their impact on productivity and cost reduction. A set of methodological recommendations is formulated to enhance management efficiency, including modular system design, staff training, and integration of IoT and AI technologies. The article concludes that intelligent DSS not only reduce feeding costs but also improve animal health, optimize resource use, and support sustainable agricultural practices. The results are of practical significance for researchers, developers, and farm managers aiming to implement data-driven solutions in livestock production.

Keywords: diversification of management, production diversification, financial and economic purposes of a diversification, technological purposes of ensuring flexibility of production

A class of mathematical methods for code channel division has been developed based on the use of pairs of orthogonal encoding and decoding matrices, the components of which are polynomials and integers. The principles of constructing schemes for implementing code channel combining on the transmitting side and arithmetic code channel division on the receiving side of the communication system and examples of such schemes are presented. The proposed approach will significantly simplify the design of encoding and decoding devices used in space and satellite communication systems.

Keywords: telecommunications systems, telecommunications devices, multiplexing, code division of channels, matrix analysis, encoding matrices, synthesis method, orthogonal matrices, integers

The article discusses a mathematical model of the production application distribution process on an aggregator platform. A formal approach based on a finite state machine and Petri nets is proposed to describe the states of orders, their transitions and constraints. A comprehensive model has been developed that takes into account the criteria for selecting a contractor, selecting equipment, and analyzing the production process, taking into account time, cost, and resource availability. The presented approaches ensure accuracy and efficiency in order management on digital production platforms.

Keywords: mathematical modeling, finite state machine, Petri net, digital production, service aggregator, choice of contractor

The article discusses approaches to the systematic analysis of historical data collected from water treatment facilities. By using tools from mathematical statistics, machine learning methods, and visual analysis techniques, the article proposes a formalized approach to assessing the efficiency of water treatment equipment. This approach makes it possible to identify hidden patterns in the data, build robust models of interdependencies, and develop recommendations for optimizing the technological process.

Keywords: water treatment, telemetry data, time series analysis, machine learning, equipment efficiency

This work is devoted to describing the development and integration of two key subsystems of an insect-like six-legged robot: a gait control module and a computer vision system for autonomous navigation. It examines architectural solutions, algorithmic foundations, and the practical implementation of components that ensure stable movement and intelligent interaction of the robot with its surroundings.

Keywords: insect-like robot, gait control module, computer vision, autonomous navigation, ROS2, SLAM, RTABMap, NAV2, OctoMap, tripod gait, Raspberry Pi, LiDAR

The article discusses a methodology for predicting global horizontal radiation for the day ahead, based on the concept of characteristic days – typical daily profiles of global horizontal insolation. The method is aimed at use in the absence of operational meteorological information and is intended as an alternative (backup) method of short-term forecasting in autonomous energy systems. As a test case, data from the Murino station (Khanty-Mansiysk Autonomous Okrug), obtained from the PVGIS service based on ERA5 reanalysis, was used. The average and median characteristic days for each month are constructed and the accuracy of forecasts using the RMSE, MAE, MdAE and R2 metrics is compared. It is shown that median profiles provide more stable results in conditions of increased weather variability. The method can be used for approximate planning of photovoltaic installations in remote and northern regions with limited access to meteorological data.

Keywords: solar radiation, global horizontal insolation, ERA5, statistical forecasting methods, forecasting in energy systems, forecasting horizon, forecasting for the day ahead, methods for constructing characteristic days, average and median profiles

In this paper, a star sensor tracking method without a star library based on the angular distance chain algorithm is proposed to solve the problem that traditional star sensors rely on a fixed star library and need to be configured to work with multiple units in the tracking mode. This method achieves star map matching by dynamically generating angular distance chains, avoiding the dependence on the global star library. Experiments show that the recognition time of the algorithm in the tracking mode is reduced to milliseconds, and the maximum pose determination error is no more than 0.035°, which proves its effectiveness and reliability. The study provides key technical support for the development of low-cost and lightweight star sensors that are suitable for scenarios such as deep space exploration and near-Earth satellite clusters.

Keywords: angular distance chain algorithm, star sensor without star library, star map recognition, tracking mode, orientation, dynamic matching, deep space exploration

A method is proposed for cascading connection of encoding and decoding devices to implement code division of channels. It is shown that by increasing the number of cascading levels, their implementation is significantly simplified and the number of operations performed is reduced. In this case, as many pairs of subscribers can simultaneously exchange information, what is the minimum order of the encoding and decoding devices in the system. The proposed approach will significantly simplify the design of encoding and decoding devices used in space and satellite communication systems.

Keywords: telecommunications systems, telecommunications devices, multiplexing, code division of channels, orthogonal matrices, integers, cascaded connection

Regression analysis based on the use of statistical data and their processing by special methods is an effective method of researching and forecasting the number of employees of structural units. In this paper, based on statistical information on 81 regional offices of the Social Fund of Russia, a regression analysis of the staffing of individual information protection divisions was carried out taking into account the total area and population of the regions. It is shown that a number of subjects are understaffed and some of them, on the contrary, are overstaffed.

Keywords: information protection, regression model, adequacy criteria, forecasting, staffing analysis, information protection units

The paper develops an algorithm for constructing an optimal lagged filtration operator for an L-Markov process. The explicit formula of the filtration operator is obtained on the basis of methods for calculating stochastic integrals and the theory of analytical functions of a complex variable using spectral analysis and the theory of L-Markov processes. An interesting example of an optimal lagged filtration operator for an L-Markov process is considered, which can be used for modeling and controlling complex stochastic systems. It is shown that this operator is represented as a linear combination of the values of the received signal and an integral with an exponentially decaying function.

Keywords: random process, L-Markov process, noise, lag filtering, spectral characteristic, filtering operator

The effectiveness of advanced pavement defect detection algorithms is considered depending on the data collection devices used, such as cameras, GPR, LiDAR and IMU sensors installed in smartphones. Rational use of these hardware and software tools will allow utilities to identify and eliminate road surface defects in a timely manner, thereby improving road safety.

Keywords: transportation sector, pavement defects, mobile road laboratories, neural network algorithms, computer vision

The article considers the issues of developing a database of wooden architecture objects in Karelia. The database includes 1009 attributed photographs obtained as part of the comprehensive expedition of the Ministry of Culture of Karelia in 1979-1980 and the comprehensive expedition to Syamozerye in 2000-2001. The expedition research was carried out by specialists and students of Petrozavodsk State University under the supervision of Academician Vyacheslav Petrovich Orfinsky. The database was developed in the MySQL database management system. The database scheme is provided, the tables are described, and an example of a photograph with attributes is presented. The database allows storing and editing materials from historical and architectural expeditions and research by employees of Petrozavodsk State University, as well as searching for photographs of wooden architecture objects in Karelia by various criteria, including date, location, type of object, and author.

Keywords: wooden architecture, database, expeditions, MySQL DBMS, photographs of wooden architecture objects

The article studies the application of neural networks with long short-term memory (LSTM) for forecasting the precipitation of asphalt-resin-paraffin deposits (ARPD) during oil pumping through main oil pipelines. The authors of the article outline the relevance of the problem of ARPD formation in main oil transportation and consider modern approaches to mathematical modeling of forecasting the precipitation of deposits. The aim of the study was to develop a neural network model that allows constructing a graph of the distribution of ARPD along the length of the model pipeline over time. Taking into account the features of various types of neural networks and the available input data, a corresponding neural network model based on LSTM was developed. The key parameters of the "oil - pipeline - soil" system were determined, which should be taken into account as initial data. The developed model demonstrates a sufficient degree of forecasting accuracy and at the same time has prospects for its improvement. The results obtained can be applied by operators of main oil transportation for more accurate forecasting and determining the most cost-effective period for cleaning the pipeline.

Keywords: recurrent neural network, asphalt-resin-paraffin deposits, neural networks, forecasting, short-term long-term memory networks, oil trunk pipeline, oil transportation

A Simulink model is considered that allows calculating transient processes of objects described using a transient function for any type of input action. An algorithm for the operation of the S-function that performs calculations using the Duhamel integral is described. It is shown that due to the features of the S-function, it can store the values of the previous step of the Simulink model calculation. This allows the input signal to be decomposed into step components and the time of occurrence of each step and its value to be stored. For each step of the input signal increment, the S-function calculates the response by scaling the transient response. Then, at each step of the calculation, the sum of such reactions is found. The S-function provides a procedure for freeing memory when the end point of the transient response is reached at each step. Thus, the amount of memory required for the calculation does not increase above a certain limit, and, in general, does not depend on the length of the model time. For calculations, the S-function uses matrix operations and does not use cycles. Due to this, the speed of model calculation is quite high. The article presents the results of calculations. Recommendations are given for setting the parameters of the model. A conclusion is formulated on the possibility of using the model for calculating dynamic modes.

Keywords: simulation modeling, Simulink, step response, step function, S-function, Duhamel integral.

The development, research and construction of devices that speed up the process of interaction between various modules (for example, telemetry and remote control systems), and in general, hybrid communication systems of a digital city that include a variety of systems used in an Intelligent Building is an urgent problem. One of these devices presented in the article is the optimal multi–frequency modem developed. In addition to the developed modem, the article presents examples of the development of similar types of devices and systems by both Russian and foreign researchers. At the same time, the authors proved that the use of the proposed modem provides a gain in spectral and energy efficiency in comparison with analogues. The proposed approach can be used to organize high-speed data transmission over frequency-limited communication channels based on new wired technologies of the digital subscriber line standard, as well as wireless systems.

Keywords: telemetry and remote control system, intelligent building, digital city hybrid communications system, modem, multi-frequency modulation, digital subscriber line, optimal finite signal, modulator, demodulator, wireless communication system

This study describes approaches to automating full-text keyword search in the field of patent information. Automating the search by keywords (n-grams) is a significantly more difficult task than searching by individual words, in addition, it requires morphological and syntactic analysis of the text. To achieve this goal, the following tasks were solved: (a) the full-text search systems were analyzed: Apache Solr, ElasticSearch and ClickHouse; (b) a comparison of the architectures and basic capabilities of each system was carried out; (c) search results in Apache Solr, ElasticSearch and ClickHouse were obtained on the same dataset. The following conclusions were drawn: (a) all the systems considered perform full-text keyword search; (b) Apache Solr is the system with the highest performance, it also has very convenient functions; (b) ElasticSearch has a fast and powerful architecture; (c) ClickHouse has a high data processing speed.

Keywords: search, keyphrases, patent, Apache Solr, Elasticsearch, ClickHouse

The article presents a comprehensive analysis of a systematic approach to the implementation and development of innovative information technologies aimed at preventing offenses committed by foreign citizens. The introduction provides an overview of the growing importance of employing advanced technological solutions in law enforcement, particularly in addressing challenges associated with foreign nationals. The main objectives of the study are to explore how the integration of technologies such as big data processing, artificial intelligence, and geographic information systems can enhance the efficiency of preventive measures. The article details the use of data analysis techniques, machine learning models, and system integration to create a unified information platform. This platform enables the consolidation of data from diverse sources, thereby improving the coordination between different law enforcement units and facilitating faster and more informed decision-making processes. The integration of these technologies also supports process standardization, reducing data inconsistencies and ensuring more reliable operations across various departments. The results highlight the benefits of utilizing big data analytics to process vast amounts of information that would be otherwise impossible to handle efficiently. Artificial intelligence, through predictive models and risk assessment tools, plays a crucial role in identifying potential threats and allocating resources effectively. Geographic information systems contribute by mapping crime hotspots and providing spatial analysis, which aids in targeted intervention strategies. The discussion emphasizes the importance of a unified approach to technology implementation, focusing on the creation of an integrated information system that can adapt to ongoing changes in the social and legal environment. The adaptability of the system is critical for maintaining its effectiveness in the face of new challenges and evolving regulatory requirements. The development of standardized data collection and processing protocols further enhances the system's resilience and operational efficiency. In conclusion, the article underscores that a systematic and integrated use of innovative information technologies significantly improves the effectiveness of crime prevention efforts and the overall efficiency of law enforcement agencies. The proposed approach not only facilitates proactive measures but also ensures a high level of responsiveness to emerging security threats, thereby strengthening public safety.

Keywords: systemic approach, innovative information technologies, crime prevention, foreign citizens, big data, artificial intelligence, geoinformation systems, information platform, standardization, law enforcement agencies, efficiency management, data integration

Abstract. It is revealed that specific forms of a simulation game combined with some peculiarities of training sessions in organizational systems could result in developing adaptable simulation models of a business situation. It is recommended to use a cognitive model in problem analysis of organizational systems, which allows switching from cognitive to simulation models naturally still being in visual topological descriptions. The AnyLogic software platform was chosen for developing a model which provides ample opportunities for creating an innovative educational environment with the elements of game simulations and AI. Cognitive analysis of a game learning process has revealed that the latter should have one cycle of a business game with two interactive nodes to introduce a host and a player into the game. It is noted that business games focused on developing management styles in a conflict are mostly in demand. Therefore, a simulation model has been developed to train executives to counteract an organizational conflict within the variability of authoritarian, democratic and liberal management styles. The model uses a paradigm of systems dynamics and is implemented in the AnyLogic software platform notation. To set the rules, the game host in the initial state or when starting the next game cycle sets the dynamics characteristics of a process while managing the organizational structure, as well as changes characteristics values of a pre-conflict situation. In response to conflict development the player performs management using auxiliary services available to him. In fact, the model is not limited by a list of the game’s tasks or possible options for a player’s decision.

Keywords: management diversification, production diversification, financial and economic diversification goals, production and technical goals to ensure production flexibility

The relevance of the problem of pattern recognition lies not only in the quality of recognition - classification of images, but also in the possibility of their rapid restoration in noisy conditions. Such solutions are useful, for example, for automatic access control systems to a protected area in the case of recognition of license plates or an on-board computer when recognizing license plates in real time. It is shown that a recurrent neural network with the Hopfield architecture copes well with the recognition of simple monochrome images of small size in conditions of their noisiness. The architecture of the Hopfield neural network is given, the peculiarity of which is a small amount of memory, which determines the scope of application of the neural network of this architecture. The algorithm for training the Hopfield neural network is given. Examples and results of recognition of noisy monochrome images are demonstrated using the example of road signs. The results of the experiment on noisy images demonstrate the possibility of image restoration with less than 40% of distorted bits.

Keywords: pattern recognition, recurrent neural network, noisy monochrome image, reference sample, training

The architecture of a multi-agent system defines the basic principles of its formation and operation, including the format of the organizational structure representing a graph in which agents act as vertices, and the links between them are designated by edges. A common drawback of existing approaches to representing the architectures of multi-agent systems is the support of no more than two types of organizational structures, among which the optimal one for the given environmental parameters may be absent. This paper proposes a method for representing the architecture of a multi-agent system, implemented by borrowing the mechanisms of living nature, namely the principles of organizing animal communities. The proposed approach allows modeling organizational structures of the following types: "coalition", "team", "hierarchical structure", "federation", "congregation". To determine the optimal architecture of a multi-agent system, optimal for specific environmental conditions, it is possible to use a "genetic algorithm".

Keywords: multi-agent system, architecture, agent, organizational structure, optimization

The relationship between "old" and "new" concepts/metrics for quality assensing of statistical detection criteria and binary events classification is considered. Independence and consistency assessments of analyzed metrics relative to initial input data volume/composition are provided. Recommendations for the use of "new" metrics for assessing the quality of detection and binary classification events are clarified.

Keywords: Type I and Type II errors, accuracy, recall, specificity, F-score, ROC curve, AUC integral metric