|
|
 Выпуск 99
- Breer V. Game-theoretical models of binary collective behavior
The article deals with game-theoretic models of threshold binary collective behavior that characterize social interaction between agents. For binary models, the function that characterizes the preferences of the players, equivalent to the utility function (UF) is the choice indicator. The sign of the choice indicator, and not the maximization of the UF, here characterizes the rational behavior of the agent. Using the choice indicator, we introduce a rational behavior operator that is an automorphism on the set of situations, and we prove the assertion that its fixed point is a Nash equilibrium (NE). It is also proved that any binary game-theoretic model is equivalent to some threshold model. Examples from the works of T. Schelling (two groups of agents) and M. Granovetter (one group of agents) are generalized to a collective consisting of an arbitrary number of groups, and for this model, statements about finding the NE through the agent threshold distribution function are proved. The existence conditions and the number (as well as the maximum possible number) of NE, as well as their structure, are investigated. Pareto-effective equilibria are found. Models of indicator behavior are studied and the convergence of its recurrent procedure to one of the NEs is proved.
- Yurchenkov A. Sensor network adjacency matrix set up based on anisotropic criterion
In this paper, the linear discrete time-varying system of sensors network is considered. Each sensor has appropriate dropout probability with Bernoulli distribution. The dropout occurs if measurement output contains only noise term. The external disturbance belongs to sequences of random vectors with bounded anisotropy of extended vector. The estimation model of the system is given, for the model an adjacency matrix set up is suggested based on anisotropic criterion. The input-to-estimation error system is derived, it has the multiplicative noise system form. The estimation problem is reduced to convex optimization one. The suggested method of optimization is based on applying bounded real lemma with anisotropic norm boundedness sufficient condition. The solution of considered problem allows to decrease anisotropic norm of the input-to-estimation error system, it yields to better performance in estimation problem.
- Selezneva I., Klochkov V., Egoshin S. Mathematical model of intersectoral coordination of development strategies (on the example of healthcare and aircraft industry)
The article examines the expediency of joint coordination of different industries policies to create products, including public goods. The article also assesses losses due to imperfect coordination. For this purpose, the paper proposes a model of choosing strategies of the interacting industries development (on the example of healthcare and aircraft industry, in the part of sanitary aviation development) with varying degrees of their coordination with each other and with national interests. Egoistic strategies of industries are studied, when each industry has its own private utility function that does not coincide with the public utility function, and strategies of industries with co-directed interests, when the private utility functions of industries are co-directed with the public utility function, but there is no information interaction between industries. The costs of industries and the total costs of the state are calculated depending on the degree of policy coordination between them, the rules of interaction in the creation of public goods and the policy of their financing by the state. The public welfare losses from imperfect coordination of development strategies are estimated. Based on realistic initial data on the parameters of industries, a strategy, that leads to the worst consequences for public welfare, has been determined. The consequences criticality of the presence of costly industries incentives and information barriers is compared. The necessary conditions of effective, from the point of the national economy view, interaction between industries are determined, such as the formation of cost-effective mechanisms (incentives) for industries and the availability of mathematical models that allow all parties to clearly see their possible costs and benefits, and calculate optimal solutions.
- Maryasin O., Lukashov A., Smirnov N. Market electricity prices and peak load hours forecasting for a region of the russian federation
The article considers the use of a digital model of an electricity consumer for the analysis and forecasting of market electricity prices and peak load hours for the Yaroslavl region of the Russian Federation. To build a digital model of an electricity consumer, the apparatus of artificial neural networks was used. This apparatus has a wide range of forecasting capabilities and allows researchers to obtain the required forecasting accuracy hourly values of market electricity prices. The results of numerical experiments on forecasting market electricity prices using the application developed by the authors are presented. In the course of numerical experiments, the quality of the forecast was studied depending on the type of artificial neural network and its structure. To forecast peak load hours, we used an indirect method based on forecasting of the total electricity consumption of the region. The results of numerical experiments on forecasting the total energy consumption of the region and peak load hours for the month ahead are presented. The article shows how the data obtained from the analysis of peak load hours for previous years can be used to improve the reliability of the forecasts made. Forecasting market electricity prices and peak load hours creates opportunities for solving problems of optimal energy scheduling.
- Pechnikov A., Bogdanov N. Two approaches for detecting pneumonia in x-ray images: description, implementation and comparison
The paper investigates two approaches for classification of x-ray images for presence of pneumonia. The first, widely used approach relies on neural networks (NN). The second approach utilises the theoretical concept of Kolmogorov complexity. The latter approach further enables the use of normalised compression distance (NCD) which defines a distance measure for arbitrary data objects, including images. Both ap-proaches and their underlying algorithms are described in described in detail and implemented programmatically. The X-rays for this work are taken from the database of the Kaggle social network for data processing and machine learning. Optimal model parameters are found empirically. Experimental results show high accuracies for both approaches. This is a clear indication of reliability and applicability of either method for identifying the presence of pneumonia in x-ray images. The NN approach performs well when ample training data is available. The NCD method is turn appli-cable when training data is limited and the NN approach fails. These results provide a solid foundation for developing precise and reliable diagnostics of pneumonia, using a combination of the two approaches.
- Morozov N., Grishin E., Pravdivets N., Korovkin D., Tiulenev I. Optimization of transshipment points seaport – railway
Due to the growth volumes of multimodal transportation, Russian Railways requires a more efficient use of available resources. Because of the large international cargo turnover, today the most popular type of international delivery is sea transport, followed by transshipment onto the railroad for delivery to the destination on the mainland. This article proposes a complex mathematical model that includes two subtasks: the berth assignment problem (BAP) and the task of forming trains. The joint solution of these interrelated tasks allows us to take into account all the constraints in the solution process and find a solution that is optimal both from the point of view of optimizing the seaport and the technical features of the railway. The proposed model makes it possible to obtain effective solutions for the combined task of a transshipment point. The Gurobi optimizer was used to carry out computational experiments. The choice of the Gurobi optimizer is due to the fact that it allows obtaining a better-quality solution compared to heuristic algorithms, although it works longer on average. The increase in the efficiency of the port, associated with a better-built schedule, is in priority over a longer computation time. For the experiments, pseudo-real data were generated corresponding to the infrastructure of the Far Eastern Railway, with dimensions of up to 15 berths and 12 ships. Calculations were carried out with a time limit of 60 minutes, in which for some of test examples it was possible to find the optimal solution, and for the rest of test examples, the error estimate of the obtained value of the objective function is less than 10%.
- Grebenuk G., Lubkov N. Reliability approach to the analysis of the stability of engineering infrastructure
Issues of safety and sustainability of critical infrastructure are of particular importance for the life of the population of any state. This is caused by a large number of threats of internal and external nature, to which the critical infrastructure and its most important component - engineering are subject. The variety of engineering systems included in the critical infrastructure and their features and mutual dependence have led to the emergence of various definitions of the concept of sustainability of engineering infrastructure, the development of various mathematical models for their study. Based on the evaluation of existing models and concepts, it is shown that the analysis of the stability of engineering infrastructure can be performed within the framework of reliability analysis with the involvement of data on the characteristics of destructive factors, their intensity and geographical area of action. These factors affect the failure rate of equipment, vulnerability and stability of the system. The importance of solving the direct problem of assessing the stability of engineering infrastructure and the inverse problem of finding critical sections is shown. To solve the inverse problem, a topological model of the system and a method of probabilistic modeling are used in the search for cross sections. The proposed results have methodological and practical components that are important for improving infrastructure security at the stages of system design and operation.
|
|
