Recommender systems make it easier to search with a large amount of content, supplementing or replacing the classic search output with recommendations. In P2P networks, their use can have additional benefits. Because of indexing and search problems, previously added files may not be available to P2P network users. If the user cannot find the file he is looking for, one can provide him with a list of recommendations based on his preferences and search query. The object of research is the process of creating recommendations for users of decentralized P2P networks to facilitate data search. The urgent task of increasing the accuracy of mathematical modeling of recommender systems by taking into account the requirements for reliability and data security during changes in the structure of a decentralized P2P network is solved. An analytical model of the recommender system of a decentralized P2P network has been developed, the main feature of which is taking into account the requirements of reliability and security of recommendation messages. This was done by introducing the following indicators into the general model of the decentralized recommender system – the probability of reliable packet transmission and the probability of safe packet transmission. The developed analytical model makes it possible to conduct a comparative analysis of different methods of operation of recommender systems and to set acceptable parameters under which the degree of relevance does not fall below a certain threshold. The developed mathematical model of the system based on the GERT scheme differs from the known ones by taking into account the reliability and security requirements during changes in the structure of the decentralized P2P network. This has made it possible to improve the accuracy of simulation results up to 5 %. The proposed mathematical model could be used for prototyping recommender systems in various fields of activity

The subject of this study is the process of anomaly detection in high-load complex computer systems (HLCCSs). The task addressed in the paper is the lack of real-time anomaly detection models in HLCCS with a specified accuracy. A set of mathematical models for real-time anomaly detection has been built and investigated. This set includes a mathematical model for detecting anomalous connections between components of computer system (DACCCSs) and a mathematical model for assessing current state of computer system (CSACS). The results of models tests showed the following efficiency metrics. For a DACCCS model: accuracy – 84 %, positive predictive value – 87 %, recall – 74 %, and weighted average accuracy (WAA) – 78 %. For a CSACS model: accuracy – 91 %, positive predictive value – 82 %, recall – 68 %, and WAA – 67 %. The positive results of the study can be attributed to the following factors. A DACCCS model uses projection matrices and orthogonal vector functions to analyze anomalies. This enables the creation of spatial decompositions that reveal complex interrelationships between system components using only eigenvalues and eigenvectors. A CSACS model applies the singular value decomposition method, which implies solving a system of scalar equations to determine the current state of the system. This approach minimizes computational costs compared to methods requiring the solution of complex matrix equations. Thus, the model could be applied for real-time data analysis and anomaly detection under conditions of limited resources and high system load. The practical application scope includes HLCCS, such as banking transaction servers and cloud platforms, in which it is essential to enable stable operation under high request amount and to minimize the risk of data loss or service failure

The goal of this work is to research and comparative analysis of methods and data structures for storing information of a recommendation system in order to compare the effectiveness of their use in terms of time and memory costs. The choice of the method for presenting the data used by the recommendation system is important since an effective way of building a database for the operation of such a system can reduce the amount of resources required and increase the number of available algorithms for generating lists of recommendations, and is also important from the point of view of the quality of its work, speed, scalability, and ease of performing basic operations with data to generate recommendations. The presence of a large number of different methods for implementing databases and presenting information that can be used to build recommendation systems necessitates a comparative analysis and selection of the optimal method and data structure for storing information in them. In the work, research was carried out of various data structures that can be used to store information of the recommender system. In particular, such as linked list, unrolled linked list, hash table, B-tree, B+-tree and binary decision diagram. To carry out experiments comparing the effectiveness of using various data structures in terms of time and memory costs, a computer model of a simplified recommendation system was developed, in which three main entities were distinguished - an agent, a session, and an object. The best results were obtained with data storing methods using unrolled and inverted unrolled linked lists. Therefore, it was decided to also conduct an additional series of experiments with these data structures for different sizes of the list bl ock. The unrolled list showed the best results in terms of memory used and session generation time. The inverted unrolled list showed an advantage in the generation of recommendations. Метою даної роботи є дослідження та порівняльний аналіз методів і структур даних для зберігання інформації рекомендаційної системи, щоб порівняти ефективність їх використання за затратами часу та пам’яті. Вибір методу представлення даних, якими оперує рекомендаційна система, має важливе значення, оскільки ефективний спосіб побудови бази даних для роботи такої системи може зменшити кількість потрібних ресурсів та збільшити кількість доступних алгоритмів для формування списків рекомендацій, а також є важливим з точки зору якості її роботи, швидкості, можливостей масштабування та зручності виконання основних операцій з даними для формування рекомендацій. Наявність великої кількості різних методів реалізації баз даних та представлення інформації, що можна використати при побудові рекомендаційних систем, викликає необхідність порівняльного аналізу та вибору оптимального методу і структури даних для зберігання інформації в них. У роботі було проведено дослідження різних структур даних, які можна використати для зберігання інформації рекомендаційної системи. Зокрема, таких як зв’язний список, розгорнутий зв’язний список, хеш-таблиця, B-дерево, В+-дерево та бінарна діаграма рішень. Для проведення експериментів з порівняння ефективності застосування різних структур даних за затратами часу та пам’яті було розроблено програмну модель спрощеної рекомендаційної системи, в якій було виділено три основні сутності – агент, сесія та предмет. Найкращі результати показали методи зберігання даних з використанням розгорнутого та інвертованого розгорнутого з’язних списків. Тому було вирішено також провести додаткову серію експериментів з цими структурами даних для різного розміру блоку списку. Розгорнутий список показав кращі результати за використовуваною пам’яттю та за часом генерації сесій. Інвертований розгорнутий список показав перевагу за часом генерації рекомендацій

Poisoning and shilling attacks remain a serious threat to recommender systems, especially as attackers increasingly mimic plausible profile statistics. This paper proposes an architecture-independent behavioral detection layer that models user interactions as short-window phase-dynamic trajectories rather than static aggregates. Interaction logs are transformed into temporal signals, reconstructed in phase space by delay embedding, and summarized by a compact 15-dimensional portrait combining recurrence-based, entropy-based, spectral, and stabilizing statistical descriptors. In a controlled targeted injection protocol evaluated over 10 independent runs, the statistical baseline achieved PR-AUC = 0.723 ± 0.037 and TPR@1%FPR = 0.029 ± 0.006, the dynamic block achieved PR-AUC = 0.831 ± 0.011 and TPR@1%FPR = 0.220 ± 0.050, and the full portrait achieved PR-AUC = 0.872 ± 0.017 and TPR@1%FPR = 0.291 ± 0.043. Sensitivity analysis showed that recurrence-only descriptors were parameter-sensitive, whereas the extended dynamic block formed a stable high-performance region across a broad range of embedding settings. An IQR-normalized aggregated risk score further demonstrated clear post-window regime separation during injection periods. The results indicate that poisoning attacks primarily deform the temporal organization of behavior rather than only first-order statistics. The proposed phase-dynamic portrait is therefore best interpreted as a complementary behavioral risk-scoring layer for auditing, filtering, and monitoring rather than as a standalone defense.

Yelyzaveta Meleshko, Professor, Doctor in Technics (Doctor of Technic Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine, e-mail: elismeleshko@gmail.com, ORCID ID: 0000-0001-8791-0063 Mykola Yakymenko, Associate Professor, PhD in TPhysical and Mathematicals (Candidate of Physical and Mathematical Sciences), Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine, e-mail: m.yakymenko@gmail.com, ORCID ID: 0000-0003-3290-6088 Volodymyr Mikhav, Doctor of Philosophy, Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine, e-mail: mihaw.wolodymyr@gmail.com, ORCID ID: 0000-0003-4816-4680 Yaroslav Shulika, post-graduate, Central Ukraіnian National Technical University, Kropyvnytskyi, Ukraine, e-mail: yar.shulika@gmail.com, ORCID ID: 0000-0002-6713-7269 The object of the research is the process of detecting anomalies in high-load complex computer systems (HLCSS). The practical application area includes HLCSS such as banking transaction servers and cloud platforms, where stable operation must be ensured under heavy request loads. The problem addressed in the research is the lack of real-time anomaly detection models in HLCSS with a specified accuracy under resource constraints. Anomalies may signal system malfunctions, process mismatches, or potential cyberattacks. High-load systems are particularly sensitive to even minor disruptions, as they can cause significant delays or complete service unavailability for many users simultaneously, leading to financial losses and loss of customer trust. Modern web services face issues such as attempts of DDoS attacks, significant fluctuations in user requests, database connection problems, memory leaks, and the impact of unexpected changes in network or hardware configuration. Therefore, ensuring timely anomaly detection is a critical aspect of high-load system security. Automating the analysis process and promptly identifying potential problems in real time help reduce risks and minimize downtime. Developing a mathematical model for anomaly detection in high-load web services aims not only to improve detection accuracy but also to ensure a timely response to potential threats under resource constraints. This helps avoid significant financial losses and enhances user trust in such services. The paper creates and investigates a mathematical model for detecting anomalous connections between components of a complex computer system (HLCSS). The testing results of the model showed the following performance metrics: accuracy – 84%, precision – 87%, recall – 74%, F1-Score – 78%. The positive results of the study are explained by the following prerequisites: the HLCSS model uses projection matrices and orthogonal vector functions for anomaly analysis. This allows for the creation of spatial decompositions that reveal complex interconnections between components of a complex computer system using only eigenvalues and vectors. Thus, the model can be applied for operational data analysis and anomaly detection in resource-constrained environments.