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The Bulletin of the Adyghe State University, the series “Natural-Mathematical and Technical Sciences” |
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#1 / 2025MathematicsAydamir Kh. Stash, Rufina R. ShefrukovaOn the control of continuum spectra of oscillation indices of linear homogeneous differential systems
In this paper, we study the spectra of fluctuations of signs (strict and non-strict), zeros, roots and hyper roots of linear homogeneous differential systems with coefficients continuous on the positive semi-axis. For any n≥2 the existence of an n-dimensional differential system with continuous spectra of fluctuation indices is established, and the spectra of all fluctuation indices fill one and the same segment of the numerical axis with predetermined arbitrary positive incommensurable ends.
Investigation of a polynomial vector field of the n-th order having invariant straight-lines
For a dynamical system in the plane with a polynomial righthand side of nth degree, we con-sider sets that consist of s and only s parallel invariant lines with angular coefficient k. The affine transformation allows the original system to be reduced to a form more convenient for qualitative analysis based on the behaviour of such introduced sets. Thanks to these sets, the number of invariant lines and their mutual arrangement on the phase plane are established for certain classes of polynomial vector fields. The efficiency of application of the notions of nodal and extra-nodal points of a polynomial system having invariant lines is shown. With their help it is proved that in the class of systems under consideration the maximum number of invariant lines is possible only at n=5.
Technical SciencesYuriy V. Dubenko, Sergey A. Podgorny, Evgeniy E. Dyshkant, Vladislav A. DemidovAlgorithm for determining the optimal architecture multi-agent system
This paper considers an algorithm for determining the optimal architecture of a multi-agent system (MAS), which has several key characteristics that distinguish it from its analogues, namely: the ability to learn, dynamic adaptation of the architecture and organisational structure of the multi-agent system, the number of supported types of architectures equal to four. To determine the optimal architecture of the multi-agent system, a “genetic algorithm” is used, which is trained on a virtual model of the environment. This allows to find the most effective configurations of basic rules that define the principles of formation and functioning of the multi-agent system. The proposed algorithm allows to simulate different architectures of multi-agent systems, such as “coalition”, “team”, “federation” and “congregation”. Each of these architectures has its own peculiarities and can be applied depending on the specific task. Experimental evaluation has shown that the developed algorithm significantly improves the efficiency of the task performance. In particular, the algorithm showed better results in terms of “time of the system's task execution” compared to its analogues. The advantage of the proposed algorithm in comparison lies in its ability to automatically adapt the architecture of the multi-agent system in the process of problem solving. This allows the system to respond more efficiently to changes and consequently improves its overall performance and efficiency. The developed algorithm can be used in the control of MAS applied in such areas as monitoring the condition of infrastructure facilities, warehouse logistics and cargo delivery, agricultural work (harvesting, fertilisation, pest treatment of crops).
Software platforms for evaluating and protecting neural network models from adversarial attacks. A review of existing solutions
Software platforms for evaluating and protecting neural network models from adversarial at-tacks are considered. The main principles of adversarial attacks and their impact on the security and reliability of neural network systems are described. An overview of existing foreign and domestic solutions aimed at training models for resilience to such attacks, identifying potential threats, and assessing the likelihood of successful attacks is provided. Methods and algorithms used in various platforms for detecting and preventing adversarial influences are examined in detail. A comparative analysis of the presented solutions highlights their advantages and disadvantages. The relevance of the research is justified in the context of the rapid development of artificial intelligence methods and the increasing need to ensure their security. Based on the re-view, conclusions are drawn about the most effective approaches to protecting neural network models and directions for further research in this field.
Information systems of digital twins of patients for complex representation and processing of medical data
In the article possible methods for creating a digital double of a patient are considered. As technology advances and the volume of medical data increases, the need for efficient systems to process and analyse information is becoming more relevant. One of the promising directions in this field is the creation of digital patient twins, which are virtual models that reflect the health status and individual’s medical history. These systems allow not only to store and process data, but also to analyze it, which can significantly improve the quality of medical care. The patient's digital twin is created as a result of the transfer of the patient's physical characteristics and changes in his body into the digital environment. This technology offers innovative and definitive solutions for the correct diagnosis and adherence to patient-appropriate treatment processes, which is one of the most important principles of medicine. It is noted that the use of such technologies is observed in research in the field of personalized medicine and the pharmaceutical industry. Given the impressive potential of digital twin technology in the healthcare field, special attention is being paid to qualified studies that will serve as a guideline for future research.
Technological challenges of implementing artificial intelligence and machine learning in security: balancing innovation and responsibility
Important issues such as data privacy, continuous training of AI models, manipulation risks and ethical concerns are reviewed. A balanced approach that utilises technological innovation alongside rigorous ethical standards and robust security practices is also examined. The rapid evolution of the security landscape is driven by the integration of ever-improving artificial intelligence (AI) and machine learning (ML) technologies. This review demonstrates the critical role of AI and ML in enhancing security defences against increasingly complex threats, and high-lights the new vulnerabilities these technologies introduce. Through a comprehensive analysis incorporating historical trends, technological assessments, and predictive modelling, the dual nature of AI and ML in security is examined.
Methods for detecting bots in social networks: choosing an effective approach
The article examines the problem of automated accounts (bots) in social networks, their impact on public opinion and risks for users. Special attention is paid to the methods of detecting bots, which are divided into three main categories: structural discovery, data crowdsourcing, and machine learning applications. Structural detection includes SybilLimit, SybilInfer, and SybilRank algorithms that evaluate the integrity of nodes and rank them according to their degree of suspicion. Crowdsourcing uses data from users to instantly identify suspicious accounts. Machine learning is used for data analysis and includes supervised, semi-supervised, and unsupervised learning. The article describes in detail the algorithms of linear and logistic regression, decision trees, clustering and associative rules. The findings highlight the effectiveness of supervised machine learning, especially logistic regression and decision trees, to accurately identify bots in a dynamically changing data environment.
Information and communication technologies in social networking: a conceptual approach to enhancing the effectiveness of educational processes
The article discusses the concept of a student social network as an innovative tool designed to stimulate interaction between students and teachers, aimed at minimizing distractions and increasing the effectiveness of the educational process. The study analyzes existing social platforms and proposes a concept of a new network that includes the integration of educational tools. The main focus is on defining the goals, objectives and benefits of introducing such a network into the academic environment. The need to improve communication, create a platform for knowledge sharing, form communities of interest and support students' career guidance is described. In addition, it is emphasized how a student social network can help strengthen ties between students and teachers, create an innovative educational environment and develop interpersonal communication skills. In conclusion, it is argued that this concept has significant potential for improving the quality of the educational process and forming an active and responsible student community.
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