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- Lapatin I., Lizyura O., Moiseev A., Nazarov A., Paul S., Salimzyanov R., Salimzyanova D., Fedorova E. Mathematical modeling of cloud node using queueing system with service rate degradation
This paper considers a cloud node operating model as an open infinite-server Markovian queueing system, taking into account various phases of the virtual machine lifecycle and the dependence of their performance on the number of virtual machines running in the node. We assume that each virtual machine can be in active and passive phases during operation, corresponding to different operating modes and resource requirements. This dependence arise because the node performance decreases due to competition between different virtual machines for its shared resources. In the proposed model, we take into account the decrease in performance using a service rate degradation function. Cloud node operation is described by a two-dimensional Markov process, which determines the number of machines in the active and passive phases. To study this random process, we apply asymptotic analysis, which allows us to derive formulas for approximating the probability distribution of this two-dimensional process. Using the obtained formulas and various performance criteria, we present examples of solving the node load optimization problem for fixed operating parameters.
- Lubenets Y. Inversion coefficient of concordance
The presence of high consistency of experts' opinions during a survey indicates the reliability of the results. Kendall’s coefficient of concordance is mostly often used for this purpose; this is fairly easy to calculate this measure, but it has some drawbacks. To eliminate some of them, there were introduced other coefficients evaluating the consistency of expert opinions, in particular, the alternative coefficient of concordance. The article defines the inversion coefficient of concordance for the case of no tied ranks, which generalizes the Kendall rank correlation coefficient for surveys of three or more experts. The defined coefficient does not use the squares of rank deviations, as Kendall’s coefficient of concordance, but it’s based on the difference in expert opinions during pairwise comparison of alternatives. There is estimated the number of different values that the inversion coefficient of concordance can take with a different number of experts and alternatives. A comparison of the distributions of the inversion coefficient of concordance and Kendall’s coefficient of concordance for a certain number of experts and alternatives is made. A formula for the average value of the inversion coefficient of concordance for different numbers of experts is proved. The equality of the average values for an even number of experts and the next odd number of experts is shown. The defined inversion coefficient of concordance can be used to assess the consistency of expert opinions, as well as Kendall’s coefficient of concordance. For two experts, the application of these coefficients of concordance is similar to Kendall’s rank correlation coefficient and Spearman’s rank correlation coefficient, respectively.
- Bishuk A., Nikitina M., Bakhteev O. Spectral characteristics of autoencoder parameters as a vector representation of~data
This paper examines the relationship between the parameters of autoencoder models and the statistical properties of the data on which they are trained. Autoencoders are defined as models with an encoder-decoder architecture, trained to reconstruct input data through a compressed latent representation. It is proposed that the model parameters can be viewed as a dense vector representation of the corresponding sample. To test this hypothesis, a theoretical and experimental study is conducted in which a vector representation is formed based on the spectral characteristics of the autoencoder parameter matrices. Theoretical analysis shows that the singular values of the model parameter matrices are related to the eigenvalues of the covariance matrix of the training data, ensuring the transfer of information between the data space and the parameter space. Experimental results on the CIFAR-10 and FashionMNIST datasets confirm that the resulting vector representations allow for a high degree of accuracy in distinguishing between models trained on different data subsets, without resorting to complex vector generation algorithms or using the original samples. These results suggest that the parameters of trained autoencoders can be viewed as sample representations.
- Nikolskii M. Asymptotic tracking of given parametric curve
In Automatic theory are considered different tracking problems of given curve with the help of trajectory ( or its projection) of controlled object. These problems are essential for modern Control theory. In practice not always the desirable parametrtc curve can be realized by trajectory (or its projection) of controlled object. Therefore it is useful realize the desirable curve in approximate form with the help of given control object. Offen for solution of tracking problems it is used Stability theory. For example well-known theory of controlled stabilization, developed by N.N.Krasovsky and others authors, can be used for solution of a number of tracking problems. Also V.I.Zubov developed his approach for solution some tracking problems using Stability theory. In the paper we consider one problem of asymptotic tracking of given parametric curve. We consider some nonlinear controlled object. The dynamics of this object contains linear and nonlinear items. These nonlinear items play role of nonlinear disturbances of the linear control object. In the paper under sufficiently wide assumptions about nonlinear controlled object, some set of smooth parametric curves was builded. For curve from this set it is possible efficiently construct control function which realize asymptotic tracking for this curve. Notice that for constructing of tracking control function, we use compensation control, which compensates some nonlinear items. Notice that ideas of compensation of some nonlinear members were widely used in works of A.A.Kolesnikov, P.D. Krutko and others authors. One illustrative example was considered. In our paper we used Linear Control Theory and the Set-valued Analysis.
- Kataev D., Shevlyakov A. Benchmarking optimization methods applied to selective damping regulator synthesis based on gramian spectral decomposition
This paper studies convergence of a few global numerical optimization methods applied to the previously proposed problem of selective damping regulator synthesis based on observability Gramian spectral decomposition. Damping or stabilizing regulators and control in general are used in many applied domains, such as robot actuator control, construction of earthquake and wind resistant buildings and bridges, designing suspension and vibroisolation in transport vehicles. Synthesizing a stabilizing regulator is also of some fundamental theoretical significance in itself. Detailed descriptions of these algorithms are provided. We consider generalized pattern search, particle swarm, genetic algorithm and surrogate optimization. The regulator synthesized is of immediate interest for large scale systems of medium to high order. Therefore, the speed of convergence is important for choosing the optimization method. This study presents the synthesis problem statement, brief descriptions of studied optimization methods, their efficiency analysis for the chosen synthesis problem, and provides practical recommendations for choosing a method depending on the problem.
- Krasnov D. Synthesis of mixed variable observer-differentiators for tracking systems with linear local feedback
The paper examines the principles of constructing tracking systems for one class of nonlinear objects with the same number of inputs and outputs, operating under conditions of external uncontrolled disturbances and incomplete measurements. The main idea of the proposed approach is the transition to a canonical input-output form in a coordinate basis of mixed variables, which serves as a unified foundation for the synthesis of a combined control and observer for mixed variables and generalized disturbances. Mixed variables are functions of state variables, external influences, and their derivatives and are subject to comprehensive evaluation. This approach simplifies the controller structure and reduces the dynamic order of the closed-loop system compared to standard solutions that use external influence generators and identifiers of uncertain parameters. The advantages of block-based tracking system synthesis compared to the classical approach to modal control synthesis within the output feedback linearization method are presented. The main results of this work are the design principle and synthesis method for an observer-differentiator of mixed variables and generalized disturbances, constructed using a block-level input-output form with linear local constraints. The use of piecewise linear corrective actions with saturation allows for the reconstruction of generalized disturbances without constructing a dynamic model. Unlike a similar observer with a standard structure, whose setup requires the development of cumbersome expressions for estimating the dynamics of estimation errors, the proposed observer-differentiator has a simple setup with independent selection of the gain factors for the corrective actions in each block.
- Shatov D. Fragility analysis of PI controllers via breaking by parameter method
Due to their simplicity and efficiency, PI controllers are widely used to solve a wide range of practical problems. Many modern controllers synthesis methods involve the numerical solution of optimization problems. Therefore, analyzing the fragility of the resulting PI controllers is particularly important. This article examines a control system with a second-order linear plant under a stabilizing PI controller. In this context, a new approach for analyzing the fragility of the PI controller is proposed. Fragility refers to the property of maintaining closed-loop system stability under static variations in controller parameters. The proposed approach is based on a well-known frequency-domain method for studying system robustness – the "breaking by parameter" technique. The essence of the method lies in transforming the closed "plant-controller" system into a form where the studied parameter is extracted from the closed loop and treated as a separate scalar block (static controller). The remaining part of the system is treated as a fictitious control plant. Using the Nyquist criterion, the stability region (not necessarily connected) is found for the parameter under study, which is equivalent to constructing a one-dimensional D-decomposition. The resulting stability region is identical to that of the original "plant-controller" system. In the considered problem of PI controller fragility analysis, the parameters under study are its coefficients. A numerical example demonstrates the application of the proposed approach to PI controller fragility analysis for a widely used linearized model of a first-order plant with time delay.
- Gadzhiev D., Makarenko A. Robustness in deep learning model at estimation keypoints coordinates on images with additive gaussian noise
This paper presents a qualitative and quantitative robustness analysis of the YOLOv8 model under additive Gaussian noise on a dataset of cattle images for animal pose estimation. The choice of this noise type is justified by a structural analysis of inter-ference components in modern semiconductor photosensors, which demonstrates the dominant character of the selected noise. Euclidean deviations and the number of missed keypoints were measured across 34 noise levels. The estimation error was decomposed into systematic and random components, and the robustness of 19 ana-tomical keypoints was analyzed, revealing distinct clusters with different stability patterns. The clusters correspond to anatomically and functionally related groups of keypoints with comparable sensitivity to noise intensity. Quantitative thresholds were established for the transitions from a robust pose estimation regime to pro-gressive degradation and then to systematic failure. The statistical significance of these transitions was confirmed using Tukey's test. Training on noisy data improved model accuracy by approximately a factor of three at a critical noise level, shifting the failure threshold toward significantly higher noise intensities. These findings provide deeper insight into error mechanisms and outline practical directions for enhancing the reliability and operational robustness of pose estimation systems in industrial environments.
- Podvesovskii A., Filonov A., Zakharova A., Tevyashov G., Romanova M. Representation and processing of fuzzy preference information in the reconfiguration of heterogeneous groups of cyber-physical system entities
This paper presents a continuation of research in the field of applying two-sided matching algorithms for optimal resource allocation in a heterogeneous group of interacting objects within a cyber-physical system. The study considers the problem of reconfiguration of a two-level group of unmanned aerial vehicles constructed according to the leader–follower scheme. The paper examines the situation where equivalence arises in the preferences of leader actors regarding subordinate ones and proposes an approach to its resolution based on the concept of a proportional fuzzy quantifier. An approach to constructing a decision-making model under conditions of equivalence among candidate actors is proposed. The core of the approach lies in a method of representing additional preference information under equivalence conditions using fuzzy quantifiers. The results of an experimental study of the proposed approach are discussed, and examples of proportional resource allocation among candidates with equal degrees of preference are presented. In conclusion, a general characterization of possible directions for further development of the proposed approach to constructing a decision-making model for the reconfiguration problem is provided.
- Eremenko A., Ignatova V. Methods for community detection in multiplex and temporal networks
The aim of this work is a comprehensive analysis and practical adaptation of the existing Louvain algorithm for detecting communities in multiplex and temporal scientific networks. The research systematized key concepts and reviewed contemporary methods for clustering network structures. Extensive data on authors, publications, and research topics was collected from the OpenAlex open bibliometric platform for conducting experiments. Using Python programming tools, these data were transformed and prepared for constructing specialized network models. The key result of the work was the application of modifications of the Louvain algorithm designed for multiplex and temporal networks. In the multiplex network, the developed modified Louvain algorithm was compared with the ABACUS and Flattening algorithms. For clustering temporal networks, the Smoothed Graph, Iterative Match, and Smoothed Louvain algorithms—all based on the classical Louvain algorithm — were reviewed and tested. The adapted algorithms demonstrated high performance in the following metrics: modularity, normalized mutual information, and the Jaccard coefficient. This confirms the effectiveness of the modified methods and their potential for use as foundational tools in future research.
- Krygin A., Grebenuk G. The evaluation of the computational complexity of the algorithm for finding critical nodes in a transportation network
One of the important stages in developing an algorithm to solve a given problem is assessing its computational complexity. The computational complexity of an algorithm is usually evaluated as the dependence of the growth rate of its running time on the size of the input data. Such an assessment makes it possible to compare the performance of algorithms that solve the same problem, regardless of the hardware and software platform. This work examines several algorithms designed to solve problems for engineering networks modeled as graphs. In studies dedicated to these algorithms, their computational complexity is not provided. It is generally accepted that the input size of graph algorithms is evaluated based on the number of vertices and edges. What the considered algorithms have in common is that their computational complexity depends not only on the number of vertices and edges, but also on the path length and the number of paths between two vertices. The study provides estimates for the dependence of the average number of paths and the average path length between two vertices in engineering network graphs. Using these estimates, an analysis was performed for one of the investigated algorithms, which addresses the problem of identifying critical nodes in a transportation network. The principle of operation of this algorithm is to reduce the problem to an equivalent integer linear programming problem. Estimates were obtained for how the number of variables and constraints depends on the number of nodes in the transportation network.
- Sergeev V., Chkhartishvili A. Large language model (LLM) as a player and as an advisor in the Ultimatum game
A study of the behavioral presets of large language models (LLMs) with varying numbers of parameters was conducted using the professional characteristics of a participant in the two-player Ultimatum game as an example. The authors compare the behavior of LLMs in two roles: that of the direct player (Player A, proposing a division) and that of an advisor to a human player. The ISCO-08 classification of professions is used to assign roles. Experiments were conducted on four modern LLMs (Phi-3.5-MoE-instruct, GPT-120b-oss, Qwen2.5-14b-Instruct, and Qwen3-235B-A22B-Instruct). It is shown that there is a difference between the profession to which an LLM assigns its opponent by default and the profession whose holder it acts as when playing as a player. It was found that, as a player, LLMs tend to perceive themselves as managers or experts and their opponent as a representative of a less qualified profession. When transitioning to the advisor role, models typically recommend a lower share of the split than they themselves would offer, and their behavior becomes less differentiated across occupations. These results are important for understanding the hidden biases of LLMs and for taking them into account when using LLMs as autonomous agents and advisors in decision-making problems.
- Belyakov B. Dynamic investor risk profiling based on behavioral finance: integration of required return, financial capacity, and psychological tolerance
This study presents a three-axis framework for dynamic investor risk profiling, integrating three independent dimensions: psychological risk tolerance, financial capacity to absorb losses, and the required rate of return as a goal-driven return threshold. Each dimension is assessed independently; where they diverge, the most restrictive constraint prevails while behavioral factors are explicitly incorporated. The framework rests on behavioral economics theory and conforms to prevailing regulatory standards, including MiFID~II, ESMA suitability requirements, and Bank of Russia guidelines. Profile updates are based on directly observed investment behavior rather than periodic self-reported questionnaire responses, reducing the response bias of static instruments. To measure behavioral reactions to market stress, the methodology employs simulation under heavy-tailed return distributions and structural regime changes, enabling robust calibration. Validation on a pilot sample of 100 real investors demonstrates that psychological risk tolerance constitutes the binding constraint under adverse market conditions, whereas financial capacity determines the outer limit of permissible risk exposure. The resulting instrument is reproducible, independently verifiable, and applicable in financial advisory services, automated advisers, and regulatory compliance contexts. It reduces reliance on subjective questionnaires and improves the accuracy of investor risk classification.
- Dranko O., Rezchikov A., Kushnikov V., Bogomolov A., Aseev N., Stepanovskaya I. Management of the aviation transport system according to the criterion of operational safety
The article presents the formulation and methodology for solving the problem of managing an aviation transport system according to the criterion of functional safety. We developed a new mathematical model of system dynamics that makes it possible to predict changes in the main safety characteristics over a given time interval. We also proposed a method for verifying the correctness of the model used in predicting the number of aviation disasters per year; the discrepancy functions demonstrate differences between experimental and calculated values of the safety characteristics of the aviation transport system. We presented the procedure for solving the problem of aviation transport system management, which makes it possible to select an optimal plan of organizational and technical measures that minimize the objective function of the problem being solved. Created software allows for the support of management solutions in the management of the aviation transport system according to the criterion of operational safety. We formed an information-logical scheme that characterizes the development in time and space of the aviation transport system management process. A model example confirms the possibility of using the created mathematical software in existing control systems. We proposed a methodology for implementing the developed software as well as the structure of a typical complex of technical means used in the management of an aviation transport system according to the criterion of operational safety is determined.
- Kulida E., Lebedev V. Development of solutions to prevent conflicts between two aircraft based on reinforcement learning
This paper briefly examines two main formulations of the aircraft conflict avoidance problem based on reinforcement learning: autonomous multi-aircraft conflict resolution using multi-agent deep reinforcement learning and conflict avoidance solution generation for air traffic controller decision support systems. The second formulation is particularly relevant for modern air traffic control, as the implementation of fully automated methods faces significant challenges in certifying machine-learning methods in civil aviation, where safety is crucial. This paper considers the problem of generating a horizontal maneuver to avoid a conflict between two aircraft using reinforcement learning. Unlike studies solving this problem in a continuous action space, this paper proposes learning an agent to act in a discrete space, which better aligns with the actions of air traffic controllers in centralized conflict avoidance. A formalization of the problem as a Markov decision process is presented. The reinforcement learning algorithms "dual deep Q-networks" and "proximal policy optimization" chosen to solve the problem are briefly described. The results of training and testing the agent in the developed simulation environment using the implemented algorithms are presented, and their effectiveness is compared.
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