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The article deals with the development of a methodological approach to forecasting and modeling the socioeconomic consequences of viral epidemics in conditions of heterogeneous economic development of territorial systems. The relevance of the research stems from the need for rapid mechanisms of public management and stabilization of adverse epidemiological situation, taking into account the spatial heterogeneity of the spread of COVID-19, accompanied by a concentration of infection in large metropolitan areas and territories with high economic activity. The aim of the work is to substantiate a methodology to assess the spatial heterogeneity of the spread of coronavirus infection, find poles of its growth, emerging spatial clusters and zones of their influence with the assessment of inter-territorial relationships, as well as simulate the effects of worsening epidemiological situation on the dynamics of economic development of regional systems. The peculiarity of the developed approach is the spatial clustering of regional systems by the level of COVID-19 incidence, conducted using global and local spatial autocorrelation indices, various spatial weight matrices, and L.Anselin mutual influence matrix based on the statistical information of the Russian Federal State Statistics Service. The study revealed a spatial cluster characterized by high levels of infection with COVID-19 with a strong zone of influence and stable interregional relationships with surrounding regions, as well as formed growth poles which are potential poles of further spread of coronavirus infection. Regression analysis using panel data not only confirmed the impact of COVID-19 incidence on the average number of employees in enterprises, the level of average monthly nominal wages, but also allowed to form a model for scenario prediction of the consequences of the spread of coronavirus infection. The results of this study can be used to form mechanisms to contain the coronavirus infection and stabilize socio-economic at macroeconomic and regional level and restore the economy of territorial systems, depending on the depth of the spread of infection and the level of economic damage caused.

An effective regional policy in order to stabilize production is impossible without an analysis of the dynamics of economic processes taking place. This article focuses on developing a mathematical model reflecting the interaction of several economic agents with regard to their interests. Developing such a model and its study can be considered as an important step in solving theoretical and practical problems of managing growth.

Simulation model of corruption in hierarchical systems which takes into account individual strategies of elements and collective behavior of large groups is proposed. Evolution of various characteristics like level of corruption or ratio of corrupted elements and their dependence on external parameters are discussed. The effectiveness of various anticorruptional strategies is examined by means of numeric analysis.

In this paper we consider mathematical model to control water quality. We study a system with two-level hierarchy: one environmental organization (supervisor) at the top level and a few industrial enterprises (agents) at the lower level. The main goal of the supervisor is to keep water pollution level below certain value, while enterprises pollute water, as a side effect of the manufacturing process. Supervisor achieves its goal by charging a penalty for enterprises. On the other hand, enterprises choose how much to purify their wastewater to maximize their income.The fee increases the budget of the supervisor. Moreover, effulent fees are charged for the quantity and/or quality of the discharged pollution. Unfortunately, in practice, such charges are ineffective due to the insufficient tax size. The article solves the problem of determining the optimal size of the charge for pollution discharge, which allows maintaining the quality of river water in the rear range.

We describe system members goals with target functionals, and describe water pollution level and enterprises state as system of ordinary differential equations. We consider the problem from both supervisor and enterprises sides. From agents’ point a normal-form game arises, where we search for Nash equilibrium and for the supervisor, we search for Stackelberg equilibrium. We propose numerical algorithms for finding both Nash and Stackelberg equilibrium. When we construct Nash equilibrium, we solve optimal control problem using Pontryagin’s maximum principle. We construct Hamilton’s function and solve corresponding system of partial differential equations with shooting method and finite difference method. Numerical calculations show that the low penalty for enterprises results in increasing pollution level, when relatively high penalty can result in enterprises bankruptcy. This leads to the problem of choosing optimal penalty, which requires considering problem from the supervisor point. In that case we use the method of qualitatively representative scenarios for supervisor and Pontryagin’s maximum principle for agents to find optimal control for the system. At last, we compute system consistency ratio and test algorithms for different data. The results show that a hierarchical control is required to provide system stability.

Modeling combat operations is an urgent scientific and practical task aimed at providing commanders and staffs with quantitative grounds for making decisions. The authors proposed the function of victory in combat and military operations, based on the function of the conflict by G. Tullock and taking into account the scale of combat (military) operations. On a sufficient volume of military statistics, the scale parameter was assessed and its values were found for the tactical, operational and strategic levels. The game-theoretic models «offensive – defense», in which the sides solve the immediate and subsequent tasks, having the formation of troops in one or several echelons, have been investigated. At the first stage of modeling, the solution of the immediate task is found — the breakthrough (holding) of defense points, at the second — the solution of the subsequent task — the defeat of the enemy in the depth of the defense (counterattack and restoration of defense). For the tactical level, using the Nash equilibrium, solutions were found for the closest problem (distribution of the forces of the sides by points of defense) in an antagonistic game according to three criteria: a) breakthrough of the weakest point, b) breakthrough of at least one point, and c) weighted average probability. It is shown that it is advisable for the attacking side to use the criterion of «breaking through at least one point», in which, all other things being equal, the maximum probability of breaking through the points of defense is ensured. At the second stage of modeling for a particular case (the sides are guided by the criterion of breaking through the weakest point when breaking through and holding defense points), the problem of distributing forces and facilities between tactical tasks (echelons) was solved according to two criteria: a) maximizing the probability of breaking through the defense point and the probability of defeating the enemy in depth defense, b) maximizing the minimum value of the named probabilities (the criterion of the guaranteed result). Awareness is an important aspect of combat operations. Several examples of reflexive games (games characterized by complex mutual awareness) and information management are considered. It is shown under what conditions information control increases the player’s payoff, and the optimal information control is found.

The problem of harvest optimization remains a central challenge in mathematical biology. The concept of Maximum Sustainable Yield (MSY), widely used in optimal exploitation theory, proposes maintaining target populations at levels ensuring maximum reproduction, theoretically balancing economic benefits with resource conservation. While MSYbased management promotes population stability and system resilience, it faces significant limitations due to complex intrapopulation structures and nonlinear dynamics in exploited species. Of particular concern are the evolutionary consequences of harvesting, as artificial selection may drive changes divergent from natural selection pressures. Empirical evidence confirms that selective harvesting alters behavioral traits, reduces offspring quality, and modifies population gene pools. In contrast, the genetic impacts of non-selective harvesting remain poorly understood and require further investigation.

This study examines how non-selective harvesting with constant removal rates affects evolution in genetically heterogeneous populations. We model genetic diversity controlled by a single diallelic locus, where different genotypes dominate at high/low densities: r-strategists (high fecundity) versus K-strategists (resource-limited resilience). The classical ecological and genetic model with discrete time is considered. The model assumes that the fitness of each genotype linearly depends on the population size. By including the harvesting withdrawal coefficient, the model allows for linking the problem of optimizing harvest with the that of predicting genotype selection.

Analytical results demonstrate that under MSY harvesting the equilibrium genetic composition remains unchanged while population size halves. The type of genetic equilibrium may shift, as optimal harvest rates differ between equilibria. Natural K-strategist dominance may reverse toward r-strategists, whose high reproduction compensates for harvest losses. Critical harvesting thresholds triggering strategy shifts were identified.

These findings explain why exploited populations show slow recovery after harvesting cessation: exploitation reinforces adaptations beneficial under removal pressure but maladaptive in natural conditions. For instance, captive arctic foxes select for high-productivity genotypes, whereas wild populations favor lower-fecundity/higher-survival phenotypes. This underscores the necessity of incorporating genetic dynamics into sustainable harvesting management strategies, as MSY policies may inadvertently alter evolutionary trajectories through density-dependent selection processes. Recovery periods must account for genetic adaptation timescales in management frameworks.

Analysis of regional economic indicators plays a crucial role in management and development planning, with Gross Regional Product (GRP) serving as one of the key indicators of economic activity. The application of artificial intelligence, including neural network technologies, enables significant improvements in the accuracy and reliability of forecasts of economic processes. This study compares three neural network algorithm models for predicting the GRP of a typical region of the Russian Federation — the Udmurt Republic — based on time series data from 2000 to 2023. The selected models include a neural network with the Bat Algorithm (BA-LSTM), a neural network model based on backpropagation error optimized with a Genetic Algorithm (GA-BPNN), and a neural network model of Elman optimized using the Particle Swarm Optimization algorithm (PSO-Elman). The research involved stages of neural network modeling such as data preprocessing, training model, and comparative analysis based on accuracy and forecast quality metrics. This approach allows for evaluating the advantages and limitations of each model in the context of GRP forecasting, as well as identifying the most promising directions for further research. The utilization of modern neural network methods opens new opportunities for automating regional economic analysis and improving the quality of forecast assessments, which is especially relevant when data are limited and for rapid decision-making. The study uses factors such as the amount of production capital, the average annual number of labor resources, the share of high-tech and knowledge-intensive industries in GRP, and an inflation indicator as input data for predicting GRP. The high accuracy of the predictions achieved by including these factors in the neural network models confirms the strong correlation between these factors and GRP. The results demonstrate the exceptional accuracy of the BA-LSTM neural network model on validation data: the coefficient of determination was 0.82, and the mean absolute percentage error was 4.19%. The high performance and reliability of this model confirm its capacity to predict effectively the dynamics of the GRP. During the forecast period up to 2030, the Udmurt Republic is expected to experience an annual increase in Gross Regional Product (GRP) of +4.6% in current prices or +2.5% in comparable 2023 prices. By 2030, the GRP is projected to reach 1264.5 billion rubles.

A crucial component of distributed computing systems is network infrastructure. While networking forms the backbone of such systems, it is often the invisible partner to storage and computing resources. We propose to integrate Network Elements directly into distributed systems through the workload management layer. There are many reasons for this approach. As the complexity and demand for distributed systems grow, it is important to use existing infrastructure efficiently. For example, one could use network performance measurements in the decision making mechanisms of workload management systems. New advanced technologies allow one to programmatically define network configuration, for example SDN — Software Defined Networks. We will describe how these methods are being used within the PanDA workload management system of the ATLAS collaboration.

One of the important direction of cloud technologies development nowadays is a creation of methods for integration of various cloud infrastructures. An actuality of such direction in academic field is caused by a frequent lack of own computing resources and a necessity to attract additional ones. This article is dedicated to existing approaches to cloud infrastructures integration with each other: federations and so called ‘cloud bursting’. A ‘federation’ in terms of OpenNebula cloud platform is built on a ‘one master zone and several slave ones’ schema. A term ‘zone’ means a separate cloud infrastructure in the federation. All zones in such kind of integration have a common database of users and the whole federation is managed via master zone only. Such approach is most suitable for a case when cloud infrastructures of geographically distributed branches of a single organization need to be integrated. But due to its high centralization it's not appropriate when one needs to join cloud infrastructures of different organizations. Moreover it's not acceptable at all in case of clouds based on different software platforms. A model of federative integration implemented in EGI Federated Cloud allows to connect clouds based on different software platforms but it requires a deployment of sufficient amount of additional services which are specific for EGI Federated Cloud only. It makes such approach is one-purpose and uncommon one. A ‘cloud bursting’ model has no limitations listed above but in case of OpenNebula platform what the Laboratory of Information Technologies of Joint Institute for Nuclear Research (LIT JINR) cloud infrastructure is based on such model was implemented for an integration with a certain set of commercial cloud resources providers. Taking into account an article authors’ experience in joining clouds of organizations they represent as well as with EGI Federation Cloud a ‘cloud bursting’ driver was developed by LIT JINR cloud team for OpenNebula-based clouds integration with each other as well as with OpenStack-based ones. The driver's architecture, technologies and protocols it relies on and an experience of its usage are described in the article.

Optimal management of fuel supply system boils down to choosing an energy development strategy which provides consumers with the most efficient and reliable fuel and energy supply. As a part of the program on switching the heat supply distributed management system of the Udmurt Republic to renewable energy sources, an “Information-analytical system of regional alternative fuel supply management” was developed. The paper presents the mathematical model of optimal management of fuel supply logistic system consisting of three interconnected levels: raw material accumulation points, fuel preparation points and fuel consumption points, which are heat sources. In order to increase effective the performance of regional fuel supply system a modification of information-analytical system and extension of its set of functions using the methods of quick responding when emergency occurs are required. Emergencies which occur on any one of these levels demand the management of the whole system to reconfigure. The paper demonstrates models and algorithms of optimal management in case of emergency involving break down of such production links of logistic system as raw material accumulation points and fuel preparation points. In mathematical models, the target criterion is minimization of costs associated with the functioning of logistic system in case of emergency. The implementation of the developed algorithms is based on the usage of genetic optimization algorithms, which made it possible to obtain a more accurate solution in less time. The developed models and algorithms are integrated into the information-analytical system that enables to provide effective management of alternative fuel supply of the Udmurt Republic in case of emergency.