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Information about store traffic is of great value to businesses. It allows you to evaluate the effectiveness of marketing campaigns and optimize staff work schedules. Moreover, data on the number of visitors can be indirectly used to analyze the competitive environment. Despite the existence of various technological approaches to solving the problem of counting visitors, each of them has a number of significant disadvantages. The purpose of the research is to develop a software system for counting visitors based on the application of machine vision technologies to a video stream. To do this, it was proposed to split the counting task into two subtasks: detection and tracking of visitors’ movements in the frame, each of which was solved using convolutional neural networks. Training and validation of neural networks were carried out on data collected in real conditions exclusively from cameras of the system customer. Together with the advanced counting algorithm, the system became capable of: a) excluding from the count employees of the retail chain wearing a corporate uniform; b) correctly handles complex and unpredictable trajectories of visitors in a video surveillance scene; c) without compromising the calculation accuracy, correctly handle video stream decoding errors, which result in dropped frames. Testing of the quality of the system’s operation was carried out on 504 test videos, in which a total of 739 visitors entered and left the outlet. When processing each frame, the final calculation error was 3%. And in the course of a number of experiments, it was found that when processing only every 4 frames (the load on the system in this case was reduced by 4 times), the calculation error increased by only 1%.

The structure of the control model of a multi-link robot manipulator is proposed, the distinctive feature of which is the inclusion of blocks for solving problems of direct and inverse dynamics using the fuzzy interval method. The relevance of the research topic is characterized by the need to develop and implement robotic systems to replace human labor in hazardous and harmful industries, as well as to improve the algorithmic support of robot control systems in conditions of environmental uncertainty. Algorithms for solving direct and inverse problems of the dynamics of multi-link robot manipulators have been developed, based on a description of the motion of MLRM links in the form of a system of equations that take into account the uncertainties of the external environment, modeled by fuzzy logic methods. The object of the study was the process zones in the immediate vicinity of small-ore pelletizing units and ore heating furnaces of mining and processing plants, where there are uncertainty factors of the external environment of two main groups: the first includes factors that complicate the determination of the coordinates of the target object of the MLRM capture (for example, as a result of the dustiness of the environment), the second – factors affecting the movement of the moving parts of the MLRM (for example, caused by wear or heating of parts of the mechanisms). Testing of the proposed algorithms was carried out in a model experiment in the MatLab environment using the Simscape physical modeling tools, as well as the Robotics System Toolbox for designing, modeling and testing robotic applications. The experiment showed that the accuracy of positioning the end effector of the MRM in the case of using the proposed interval method, although it is not a fraction, but several percent of the specified terminal position, but exceeds the solutions obtained using the standard Robotics System Toolbox tools, which are not adapted to work in conditions of environmental uncertainty.

At present, it is an urgent task to describe macroeconomic phenomena through the construction of qualitative mathematical models. In the current economic landscape, the interaction among economic factors is of significant importance. Therefore, it is necessary to understand the relationships between key indicators that significantly contribute to economic growth. In particular, the interactions between these indicators can be investigated using vector autoregressive models, in which they are treated as endogenous variables. The strength of the relationship between variables can be determined through the use of impulse response functions, which provide an accurate economic estimation only when a vector autoregressive model is converted into a structural vector autoregressive model. In this study, we selected several indicators as objects of research, including the volume of food and non-food retail sales and the average wage level in the Volga Federal District of Russia. An econometric model was constructed using vector autoregression to analyze the relationships between these variables, and the model was verified and tested for its forecasting ability, confirming its high quality. Impulse response functions were also used to assess the mutual influence of these indicators, which were derived from the vector autoregression model after it was converted into a structural vector autoregression model. Finally, we analyzed the mathematical findings and provided them with economic interpretation.

Unmanned aerial vehicles have found wide application in various fields of monitoring, reconnaissance, remote control. To successfully fulfil these tasks, UAVs are equipped with mobile computer vision systems and computers. Visible images obtained by them may be of insufficient quality due to weather conditions or low illumination. Thus infrared spectrum imagery is the preferred output. This paper presents a neural network model for detecting small objects in infrared spectrum images acquired by UAVs. The model architecture is based on the YOLO5 deep learning model and consists of a basic block and an intermediate block and also includes a prediction block. The basic block is based on the CSPDarknet-53 neural network model and is designed to extract feature maps from the images as input to the model. To describe the intermediate module, it is proposed to use a Bi-FPN neural network that forms a pyramid of feature maps of input images. It was proposed to include coordinate attention modules in the architecture of the Bi-FPN network, which allowed to increase the recognition accuracy while maintaining the computational requirements for mobile machine vision systems. Numerical experiments were conducted on a set of HIT-UAV infrared images, showing the superiority of the proposed model over models such as SSD, Faster RCNN, Retinanet, and YOLO5. Computer experiments showed that the model is able to recognise objects with an accuracy of more than 81.57%.

A significant portion of modern production and telecommunication systems include asynchronous lines for the transmission of material and information flows. In this case, to increase the system reliability storage units are installed between the equipment units, performing various functions. Thus, in information systems, storage units are used to store information, in energy systems – to accumulate energy, in production systems – to create an interpretational stock of blanks, etc. Mathematical modeling of asynchronous lines allows us to evaluate the predicted characteristics of their reliability and operational efficiency at the design stage, which helps to minimize subsequent operating costs. In this connection, the urgent task of developing mathematical models of asynchronous lines, taking into account their application features and structure, as well as the parameters of the interpretational storage device, arises. To solve this problem, it is advisable to use the methods of semi-Markov processes theory with general state space. This allows to soften the known restrictions on the distribution laws of random variables characterizing the system stay in certain states and transitions from one state to another. The article presents the developed semi-Markov models with discrete-continuous phase space states for the analysis of the functioning of a two-phase asynchronous line. We consider two modes of its operation: only via storage device and only by direct transmission. Based on the use of the semi-Markov model and the asymptotic phase merging algorithm, we obtain approximate expressions for finding the reliability stationary characteristics of the functioning of the systems under consideration. The indicated dependencies are described in mathematical expectation terms and are applicable to arbitrary distribution laws of random variables characterizing the system. Someone can quite easily implement proposed models using common mathematical packages. It is shown that semi-Markov models of two-phase asynchronous lines make it possible to determine the main reliability indicators with acceptable accuracy, taking into account the dependence of these indicators on the capacity of the interpretational storage device and its operating mode. This makes it possible to conduct a comparative analysis of the operating modes under consideration, to solve optimization problems when determining the structure and control parameters of the modeled system both during its design and during operation.

The article presents a software model of complex processes of small-scale ore raw material processing based on a trainable tree of fuzzy logical inference systems. Processing of such raw materials not only provides a valuable end product, such as yellow phosphorus, but also helps to solve the problem of ore waste disposal, the fine fractions of which create significant environmental damage to the territories adjacent to mining and processing plants. The technological system of small-scale ore raw material processing consists of energy-intensive units, so even a slight relative reduction in resource and energy costs leads to large savings in absolute figures. Such a reduction can be achieved by optimizing the control of units, the synthesis of which requires the availability of process models, so improving the methods and tools for modeling is an urgent research task. A feature of the proposed model is that its inputs are not only variables describing resource transformations, but also variables reflecting the energy costs of individual technological units. This allows using the model to calculate the energy and resource efficiency of small-scale ore raw material processing. The hierarchical structure of the fuzzy-logical tree is capable of reflecting the interrelationship of processes of various natures accompanying the processing of small-scale raw materials, and also contributes to increasing the efficiency of its training by dividing the feature space of large dimension into several groups on which individual tree nodes are trained. The program developed in the MatLab environment and implementing the proposed model showed high regression accuracy on a synthetic set of input data, which may indicate the feasibility of using the proposed model in problems of optimizing control systems for processing small-scale raw materials according to the criterion of energy and resource efficiency.

Analysis of epidemic processes is one of the oldest tasks for the application of modeling methods in the field of studying the state of society. Despite the availability of many approaches to the development of epidemic models, experts were unable to timely obtain an acceptable forecast for the ongoing spread of coronavirus in the winter of 2024. With new waves, the updated virus has returned once again after victory over the infection was declared. The possibilities and problems of office structures based on modifications of SIR models for a modern epidemic stage of a virus that continues to mutate are determined. The global dynamics of infections changed the oscillation mode twice: after the peak in the spring of 2022 and in the winter of 2024. After the global Omicron wave, local epidemics acquired an asynchronous character based on the formation and attenuation of a series of waves. The frequency of occurrence of individual infection peaks varied significantly across regions already in 2020. In some countries, frequent short waves of large amplitude developed. We classified the scenarios according to the characteristic features of their nonlinear dynamics. We proposed a method for modeling the sharp development of spread of the virus based on equations with threshold regulation functions that describe variants of the formation of outbreaks of infections and situational damping functions that determine the form of oscillating attenuation for the number of infections. The fading trend after primary wave in the model is interrupted by a mass infection event, which induces an outbreak of infections and then a new regime of fluctuation attenuation follows. Our computational experiment simulates the development of an extreme peak after the stage of attenuation of waves of a local epidemic as a bifurcation scenario for the reactivation of waves of the SARS-CoV-2 coronavirus activity, which is due to effect of a crowded disease.

All steganographic methods are focused on a specific container file format. Text documents with markup are the most difficult object for steganography methods. The article suggests a model for embedding structured text documents in control tags. The model uses the document tree structure and embeds into free leaf nodes. This approach adds hidden data that does not affect the display of the document. Two steganographic methods are implemented based on this model. The first method embeds hidden data into html document tags. The embedding method adds underplayed tags and style classes to free leaf nodes. The hidden data extraction method uses the embedding identifier. This role is played by the name of the new class. The name generation algorithm is based on the embedding key and hash function. The format of the identifiers matches the format of the source document names. This naming method allows the hidden message blocks to be randomly allocated to free leaf nodes. The second method embeds steganographic inserts into xml documents. Hidden data is added to the free leaf node attributes. The method requires two new attributes to execute. The optional structure describes both attributes. The format of this structure is indistinguishable from the structures present in the document. The embedding identifier is also based on the embedding key and the embedded block number. The data view uses an encryption algorithm with an additional key. Both methods use embedded data masking to counteract source code steganalysis. Steganalysis of such methods has exponential algorithmic complexity, so both methods are only applicable to large files.