Discrete and Continuous Models and Applied Computational Science

The use of generative artificial intelligence (GenAI) in scientific publications requires strict guidelines to ensure transparency, credibility, and ethics of research.

We propose a construction method for network structure based algorithms (NS-algorithms), aimed at solving the correlation clustering problem (CCP) specifically for signed networks. Our model assumes an undirected, unweighted simple signed graph. This problem is considered in optimization form with the error functional as a linear combination of inter-cluster and intra-cluster errors. It is known that this formulation of the problem is NP-hard. The technique of NS-algorithms constructing is grounded on the system approach presented in the form of a general scheme. The proposed scheme comprises six interconnected blocks, each corresponding to a stage in addressing the CCP solution. The main idea of the technique is to combine modules representing each block of the scheme. The proposed approach has been realized as a software package. The paper presents a model NS-algorithm constructed using the proposed technique. To evaluate its performance, computational experiments utilizing synthetic datasets are conducted, comparing the new algorithm against existing methods.

The increasing complexity of university admissions requires efficient, standardized processes to manage large volumes of applications and changing regulatory requirements. To address this, the paper applies the TM Forum’s Business Process Framework (eTOM) from the telecommunications industry, a standard for modeling and optimizing academic admissions workflows. Using RUDN University as a case study, the entire admissions process is formalized into a hierarchical model that aligns with the eTOM level 2 processes. The approach integrates discrete-event simulation (DES) and queueing network analysis, providing detailed process modeling and analytical solutions for assessing the average execution time. DES replicates the dynamic interactions between applicants and staff. Queueing analysis provides mathematical model to analyze the average execution times for each step in the process. Together, these techniques help optimize the admissions process and ensure efficient management of large volumes of applications. Through this approach, we aim to streamline processes, increase transparency, and support digital transformation efforts within universities.

The paper discusses the application of the adaptive interpolation algorithm to problems of chemical kinetics and gas dynamics with interval uncertainties in reaction rate constants. The values of the functions describing the reaction rate may differ considerably if they have been obtained by different researchers. The difference may reach tens or hundreds of times. Interval uncertainties are proposed to account for these differences in models. Such problems with interval parameters are solved using the previously developed adaptive interpolation algorithm. On the example of modelling the combustion of a hydrogen-oxygen mixture, the effect of uncertainties on the reaction process is demonstrated. One-dimensional nonequilibrium flow in a rocket engine nozzle with different nozzle shapes, including a nozzle with two constrictions, in which a standing detonation wave can arise, is simulated. A numerical study of the effect of uncertainties on the structure of the detonation wave, as well as on steadyystate flow parameters, such as the ignition delay time and the concentration of harmful substances at the nozzle exit, is performed.

The article studies the effectiveness of implementation of multi-agent systems based on large language models in various spheres of human activity, analyses their advantages, problems and challenges. The results of the research have shown that multi-agent systems based on large language models have significant potential and wide opportunities in modelling various environments and solving various tasks.