|
|
 Âûïóñê 111
- Iskakov M., Iskakov A. The meta-theorem for the existence of equilibrium in secure strategies
The paper is a continuation of the cycle of papers in 2018-2023 devoted to the theoretical justification of equilibrium in secure strategies (EinSS) as a concept of solving non-cooperative games in pure strategies.A method for constructing EinSS existence theorems from known Nash equilibrium (NE) existence theorems is presented. In particular, theorems for the existence of Nash equilibria are formulated in a standard form and are inserted as a condition into the meta-theorem for the existence of EinSS. According to this method, two theorems for the existence of EinSS are derived and proven based on the theorem of Reny (1999) on the existence of Nash equilibria. The general scheme of deriving existence theorems is as follows. Section 2 summarizes the theorems published in the author's previous papers. Section 3 presents two original theorems from Reny's paper. Section 4 gives a detailed interpretation of the conditions of Reni's theorems, compared to the conditions of Debre's theorem. Section 5 gives a detailed analysis of Reni's theorem. Using a number of examples, the condition of the theorem is interpreted as the condition that there are no jump points or points that guarantee the best answer. Section 6 constructs formally, by the method of meta-theorem, two existence criteria for EinSS that use the original NE existence theorems. In Sections 7 and 8, two theorems are formulated and proved, which are specifically refined for solving applied problems (Hotelling's spatial competition, Tullock's rent competition, Bertrand – Edgeworth oligopoly). All considered theorems are summarized in a final table.
- Sedykh I., Makarov K. Identification of quadratic complex-valued dynamic neighborhood models on clustereddata and with outclustering
Neighborhood models and their modifications used to model various distributed systems and processes. The study considers a quadratic complex-valued dynamic neighborhood model in which the parameters, inputs and states are complex numbers, and its definition is given. The model functions in discrete time. An example of a complex-valued dynamic neighborhood model consisting of three nodes shown, for which the graph of the structure and the functions of the intersection of states given in general form. A special case of recalculation functions for a quadratic model is also considered. An algorithm for identifying a complex-valued dynamic neighborhood model whose parameters are determined by the least squares method given. A general view of the matrices of a system of linear equations for finding the parameters of a quadratic model shown. Matrices are given and identification performed for the considered example of a neighborhood model. The root-mean-square and average reduced identification errors are found. The paper also considers the identification of a complex-valued dynamic neighborhood model on clustered data. Clustering performed using complex data sets by the k-means method. The proposed identification algorithms implemented in the form of a program in the Mathcad package, with the help of which the results of identification of a quadratic complex-valued dynamic neighborhood model on clustered data and without clustering are compared.
- Egorkin A. PageRank centrality, accounting for the weights of links
The work is devoted to finding the centrality of nodes of weighted graphs. The relevance of this task is due to the fact that ignoring the weights of the arcs of the graph when finding the centrality of its nodes is unacceptable for a number of applied tasks, primarily related to tasks from the financial sphere. In the classical formulation of the PageRank algorithm, part of the information about the weights of connections is lost when forming a matrix of transient probabilities from the adjacency matrix. This effect has been demonstrated in this article. A method for determining the centrality of network nodes is proposed, based on the PageRank algorithm, which allows taking into account all the weights of the links. The graph of financial transactions was considered as an example. The nodes of the graph are the clients of a commercial bank, including the bank itself, and the arcs are money transfers between nodes. The ranking quality was determined by comparing various centrality measures with an external node parameter unrelated to the network characteristics of the transaction graph. According to the results of the study, it was shown that the proposed centrality measure ranks the most important nodes of the graph in the best way compared to other centrality measures. The convergence of the proposed algorithm was also demonstrated.
- Rey A., Shiroky A. Complex information risks assessment. II: Algorithm for identifying the structure of the tree of integrated information risk assessment
When assessing information security risks, it is essential to take into account the various types of uncertainties that are inherent in information systems. Current methods and algorithms for risk assessment may not account for all of these uncertainties, which can lead to inaccurate risk estimates. Therefore, it becomes necessary to develop a new or adapt an existing method for risk assessment that considers all types of uncertainty specific to the class of system under consideration. In this paper, we build on our previous idea of using an integrated assessment method to evaluate information risks. This method aggregates assessments of information systems based on standard information security criteria such as confidentiality, integrity, and availability. By incorporating these criteria, we aim to obtain more accurate and reliable risk estimates that take into account all relevant uncertainties. In the first part of the work, we demonstrated that this method, with appropriate modifications, allows for taking into account all necessary types of uncertainty. We propose an algorithm for identifying the structure of an integrated assessment tree based on the principle of combining related criteria. We demonstrate the efficiency of the algorithm by building risk assessment trees for confidentiality, integrity, and accessibility in SMART systems based on the Internet of Things using this approach.
- Krygin A., Tarasova S. Reduction the dimensionality of the task of finding critical nodes in the network
One of the classes of problems solved in the assessment of the stability of an engineering network is the problem of finding critical nodes. In many formulations, this problem is posed as finding a subset of nodes of a given cardinality (critical nodes) such that the failure of which would cause maximum damage to the entire network. And the most common way to assess the damage in such a formulation is to determine the number of connected node pairs in the network with excluded critical nodes. For such nodes that correspond to the minimum number of connected pairs, additional measures are required to increase reliability and safety. Several methods of solving the problem of finding critical nodes use reducing it to an equivalent linear programming problem. The main problem of this approach is the large size of the problem, and consequently, the high computational complexity of its solution. The work conducts research on various characteristics of vertices of a graph model of a network, the analysis of the values of which will allow determining in advance the fact of belonging to the subset of critical or, conversely, to the subset of non-critical nodes. Thanks to this, it is possible to form additional constraints that reduce the dimensionality of the linear programming problem and its computational complexity, which will allow finding critical nodes in engineering networks with a large number of objects in an acceptable time. During the research, a large number of different subproblems were solved, so the work describes only the first, preparatory part of it.
- Avdeeva Z., Kovriga S. Fuzzy-cognitive-maps analysis and modelling in the state strategic planning system
One of the main tasks of scientific and methodological support of the state strategic planning is the development of methodology of indicative planning and monitoring of the implementation of strategic planning documents. Indicative planning is a tool for assessing the achievement of the goals of socio-economic development and security, it is based on a system of indicators. Indicators make it possible to measure, monitor, assess the achievability of the set development goals and, in case of deviations, to ensure the correction of public policy in the right direction of sustainable socio-economic development. The problems of system inconsistency of strategic planning documents, the lack of mechanisms (1) to check the consistency of goals, objectives and measures provided for in these documents, the provision of goals and objectives with sets of target indicators and indicators, (2) to trace the structure of links between parameters (goals – objectives – indicators) have been identified. Based on the identified problems, a model of systematisation of goals – objectives – indicators using the model of fuzzy cognitive maps is proposed. Analytical bases of tracking and implementation of the basic task of monitoring the parameters of this model on the basis of analysing its structural properties are presented. The workability of the proposed scientific-methodological and information-analytical toolkit is demonstrated using a number of strategic planning documents of the Russian Federation. Some directions for further research are outlined in terms of (1) expanding the task of monitoring the achievability of development goals with the inclusion of a model of the external environment to track the impact of external signals on the goals in the current situation, (2) the development of methods of composition and analysis of a multilevel network of goals-tasks-activities, formed by a cross-section of given strategic goals on the system of strategic planning documents.
- Vladova A. Developing group and individual performance paths based on e-learning platform data
Maintaining a high level of education is a key task in university management. Despite continuous monitoring of student performance, educational institution management fails to adequately utilize performance forecasting methods when shaping student learning paths. The proposed approach differs from existing ones in several aspects. Firstly, it analyzes features containing grades for various assignments completed by students on the e-learning platform, expanding the feature space by normalizing grades on a single scale and creating new features: an index and changes in performance for different types of assignments. Secondly, it identifies students at academic risk. Thirdly, it predicts exam scores for each student using a linear regression model. Fourthly, it groups students with similar learning trajectories for personalized consultations. The approach to predicting exam results for individual students demonstrates a commitment to providing comprehensive support beyond simple assessment. Through analysis, modeling, and personalized consultations, the research aims to proactively enhance academic performance in university settings.
- Klochkov V., Yegoshin S. Organizational mechanizm for the introduction of aviation technologies to ensure an acceptable level of flight safety and the total cost of ownership of new aircraft products
In modern conditions, the study of large-scale systems can significantly improve the efficiency of industry management. The approach considered makes it possible, using the example of the aviation industry, to develop a justification for an organizational mechanism that differs from traditional business models of aviation application by the ability to achieve maximum economic effect, taking into account compliance with modern requirements for aviation operations and services in terms of flight safety. The mechanism is based on the a priori acceptance by the aircraft manufacturer of responsibility for all failures that occur during the operation of a new aircraft technology at the initial stage of its lifetime. The research methodology is based on mathematical modeling and methods of system analysis. As an example, the industry of promising application of unmanned aircraft systems "last mile delivery" is considered. The proposed approach makes it possible to carry out more effective development planning and development of management decisions when introducing new aviation equipment with the potential for wide application, including in the formation of state programs of the Russian Federation, strategies for the development of industrial organizations in the aircraft industry.
- Vandilovskaya P., Krygin A., Lukinova O., Roschin A. Method for finding cuts for engineering infrastructure management tasks
The goal of the functioning of engineering networks is to ensure the delivery of a particular resource to a consumer, ideally with uninterrupted supply which directly depends on the integrity of the network infrastructure. However, various factors such as attacks by malicious actors, natural disasters, and technological accidents can lead to the disconnection of certain parts of the network, resulting in the disruption of resource delivery. This necessitates the task of identifying the most vulnerable parts of the engineering network in terms of potential damage, which allows appropriate measures to be taken to protect the network from negative factors and ensure maximum uninterrupted resource delivery. Engineering networks are commonly modeled as graph structures, therefore one method of solving this task is to find the cuts of the network graph. While such methods exist, they all have certain limitations. This study proposes a new method for finding all cuts of a directed graph of arbitrary dimension, which eliminates these limitations, describes the algorithm for this method, and provides theoretical justification. The concept of the method is based on constructing graph cuts (multicuts) in such a way that all cuts are identified, and can be done in a reasonable amount of time. Examples of engineering networks where this method can be used as a tool for making rational decisions in operating network objects include power grids, transportation networks, water supply and sewerage networks, as well as communication and telecommunications networks.
- Tyrsin A., Kashcheev S. Well interaction modeling to analyze flooding systems efficiency on small data samples
At the final stage of oil field development, an urgent problem is to maintain acceptable levels of oil production through operational flooding management. The complexity is compounded by the increasing number of wells operating in the field and the variability of the process of their interaction. This requires new approaches that consider these trends in oil production. A popular approach for analyzing the effectiveness of oilfield flooding systems in recent years has been the use of proxy models of the CRM family (capacitance-resistive models), which are mathematical models of material balance. At the same time, the inverse problem is solved to determine the model parameters. However, the small size of the data samples and the large number of functioning wells in the flooding system limits the effective practical application of this approach. The purpose of the article is to increase the efficiency of monitoring water flooding systems by reducing the size of the training data sample and expanding the scale of the analyzed systems from several tens to hundreds of wells. Two algorithms focused on large dimensions and small data samples are proposed. They were tested on model data in which there were 60 injection and 160 production wells, and 17 observations and random errors were present. The injectivity of injection wells is actual data from a real water flooding system. The flow rates of production wells are model values, taking into account random errors present in practice. These algorithms have demonstrated acceptable characteristics both in terms of accuracy and speed, and if possible, their application for forecasting.
- Martynova L., Pavlov A. Method choosing an energy economical way to bypass a complex obstacle by autonomous
A method based on bathymetric and physical maps of the World Ocean has been developed to select a bypass path around a complex obstacle. It has been proposed to use the Kriging algorithm to go from mesorelief to minirelief. It has been proposed to consider a depth grid in the form of an oriented weighted graph to determine the most energy-efficient bypass path around complex obstacles. The conditions for the shortest path on the graph to be the most energy efficient way have been determined. An algorithm for enumerating bypass path options with pruning has been developed, based on the "depth-first graph search" algorithm. The advantage of using the proposed method for selecting a bypass option over the traditionally proposed bypasses from above or from the side of the obstacle has been shown in an example of bypassing a complex obstacle. The results of the conducted numerical experiments confirmed the correctness of the proposed solution: the reduction of the path for the considered variant of the obstacle was 15-20%, which makes it possible to implement the proposed method of selecting an energy-efficient spatial path to bypass a complex obstacle in the control system of an autonomous underwater vehicle.
- Bazhenov S., Veresnikov G., Golev A., Goncharenko V., Erofeev E., Lazurin G., Skryabin A., Timofeeva A., Fedenyuk V. Development of a methods and instruments for conducting life tests to build an early diagnostics system for uav electromechanical actuator
The work is devoted to the creation of a technology for obtaining and accumulating experimental data during electromechanical actuator (EMA) life tests, necessary for the intelligent analysis algorithms development that provide EMA early diagnostics for aircraft condition-based maintenance. A life tests program and methodology have been developed that make it possible to accelerate EMA components wear processes and obtain data on functioning when reproducing loading cyclograms corresponding to ground testing during pre-flight preparation («active experiment») and during the flight of the aircraft («passive experiment»). An early diagnostics system prototype has been created, which includes a bench installation that provides elastic or weight mechanical loading of the unmanned aerial vehicle (UAV) EMA, and a software and hardware data collection complex that provides measurement and registration of physical quantities associated with the EMA work processes in various operating conditions and various technical conditions caused by wear. It is proposed to use physical quantities of electrical, mechanical, thermal and vibroacoustic nature as diagnostic signals. The results of UAV EMA life tests samples are presented, which made it possible to clarify the test program in terms of existing loads.
- Zverkina G., Koshelev A. On the modeling the behaviour of one Markov process using the method of modeling random variables using intensities
In the past, the authors proposed a method for modeling of random variable using intensity which is one of the characteristics of the distribution function. The results of testing this method to simulate the behaviour of a stochastic model, specifically a model of a pair of recoverable dependent elements, are presented. The model under study’s behavior can be studied analytically by selecting the characteristics of periods of failure-free operation and recovery periods. Simulation modeling using both the ``classical’’ method and the method of modeling random variables by intensity yielded results. The availability factor behaviour of the model under study was compared to an analytical solution based on these results. The analytical solution was compared to numerical experiments to arrive at the following conclusion: the classical modeling method does not outperform the accuracy of modeling the behaviour of a random process using the method of modeling random variables using intensities.
|
|
