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This study presents a methodology for assessing the functioning of complex systems, taking into account the type of distribution of indicators characterizing the functioning of structural elements of such a system operating under conditions of uncertainty. Unlike previous studies, the work integrates the identification of the type of indicator distribution with their Bayesian assessment, taking into account the norms characterizing the required results of the functioning of the structural elements of the system. The type of distribution and its characteristics provide more complete information about the properties of an object and their consideration affects the results of evaluating the functioning of elements of complex systems, especially in cases of the presence of “heavy” tails characteristic of a number of socio-economic processes and systems. It is shown that it is advisable to identify the type of distribution based on modified data due to the exclusion of the best trend in statistical characteristics. The determination of the best type of distribution is carried out according to the Kolmogorov – Smirnov agreement criterion, which showed the best (according to the available sample) statistical estimates compared to other criteria or a mixture of them. The obtained type of distribution is used in the probabilistic assessment of the results of the functioning of subsystem elements based on Bayesian intelligent technologies that successfully operate in conditions of uncertainty, and which make it possible to present such results on numerical and linguistic scales in a general hierarchical information model. The methodology was tested using the example of the object subsystem (G.B.Kleiner’s spatio-temporal classification) of the economic subsystem of the Tula region, considered as a complex system — a socio-ecological-economic system. The volume of gross domestic product by region in six sections of the all-Russian classifier of economic activities (sections A, B, C, D, E) was used as assessment indicators. In some cases, it is possible to reduce the level of uncertainty in the estimates of indicators.; to obtain estimates that are more stringent than the norm, which ultimately leads to the conclusion that the use of the distribution type in the formation of probabilistic estimates of indicators of structural elements of complex systems makes it possible to justify their correct application within the framework of the concept of evidence-based modeling.

The paper contains a mathematical model for the optimal location of enterprises producing fuel from renewable wood waste for the regional distributed heating supply system. Optimization is based on total cost minimization of the end product – the thermal energy from wood fuel. A method for solving the problem is based on genetic algorithm. The paper also shows the practical results of the model by example of Udmurt Republic.

The probabilistic topic model of a text document collection finds two matrices: a matrix of conditional probabilities of topics in documents and a matrix of conditional probabilities of words in topics. Each document is represented by a multiset of words also called the “bag of words”, thus assuming that the order of words is not important for revealing the latent topics of the document. Under this assumption, the problem is reduced to a low-rank non-negative matrix factorization governed by likelihood maximization. In general, this problem is ill-posed having an infinite set of solutions. In order to regularize the solution, a weighted sum of optimization criteria is added to the log-likelihood. When modeling large text collections, storing the first matrix seems to be impractical, since its size is proportional to the number of documents in the collection. At the same time, the topical vector representation (embedding) of documents is necessary for solving many text analysis tasks, such as information retrieval, clustering, classification, and summarization of texts. In practice, the topical embedding is calculated for a document “on-the-fly”, which may require dozens of iterations over all the words of the document. In this paper, we propose a way to calculate a topical embedding quickly, by one pass over document words. For this, an additional constraint is introduced into the model in the form of an equation, which calculates the first matrix from the second one in linear time. Although formally this constraint is not an optimization criterion, in fact it plays the role of a regularizer and can be used in combination with other regularizers within the additive regularization framework ARTM. Experiments on three text collections have shown that the proposed method improves the model in terms of sparseness, difference, logLift and coherence measures of topic quality. The open source libraries BigARTM and TopicNet were used for the experiments.

Laminar-turbulent transition is the subject of an active research related to improvement of economic efficiency of air vehicles, because in the turbulent boundary layer drag increases, which leads to higher fuel consumption. One of the directions of such research is the search for efficient methods, that can be used to find the position of the transition in space. Using this information about laminar-turbulent transition location when designing an aircraft, engineers can predict its performance and profitability at the initial stages of the project. Traditionally, $e^N$ method is applied to find the coordinates of a laminar-turbulent transition. It is a well known approach in industry. However, despite its widespread use, this method has a number of significant drawbacks, since it relies on parallel flow assumption, which limits the scenarios for its application, and also requires computationally expensive calculations in a wide range of frequencies and wave numbers. Alternatively, flow analysis can be done by using Dynamic Mode Decomposition, which allows one to analyze flow disturbances using flow data directly. Since Dynamic Mode Decomposition is a dimensionality reduction method, the number of computations can be dramatically reduced. Furthermore, usage of Dynamic Mode Decomposition expands the applicability of the whole method, due to the absence of assumptions about the parallel flow in its derivation.

The presented study proposes an approach to finding the location of a laminar-turbulent transition using the Dynamic Mode Decomposition method. The essence of this approach is to divide the boundary layer region into sets of subregions, for each of which the transition point is independently calculated, using Dynamic Mode Decomposition for flow analysis, after which the results are averaged to produce the final result. This approach is validated by laminar-turbulent transition predictions of subsonic and supersonic flows over a 2D flat plate with zero pressure gradient. The results demonstrate the fundamental applicability and high accuracy of the described method in a wide range of conditions. The study focuses on comparison with the $e^N$ method and proves the advantages of the proposed approach. It is shown that usage of Dynamic Mode Decomposition leads to significantly faster execution due to less intensive computations, while the accuracy is comparable to the such of the solution obtained with the $e^N$ method. This indicates the prospects for using the described approach in a real world applications.

This study proposes a methodology for anomaly detection in educational assessment data, demonstrated on the case of the 2023–2024 Basic State Exam (BSE) in mathematics in Russia. The relevance of the study is related to the absence of mandatory video surveillance during the examination period, which creates a risk of potential rule violations both by individual students and by entire educational institutions. By analyzing the distribution of primary scores, we identify a big spike in the area between grades 2 and 3 as a specific pattern in results that may indicate cases of cheating during the exam. To determine the most suspicious results, two anomaly criteria were constructed. The first criterion relies on comparing the magnitude of the spike in empirical distribution function in school’s results with the corresponding regional average level. This criterion made it possible to identify 47 educational institutions with abnormally high values of the spike. The second (general) criterion was derived from comparing students’ scores on the examination with their performance on a diagnostic mathematics test conducted in grade 8 under video surveillance. This comparison is appropriate because almost the same group of students took part in both assessments. This approach helps reduce the number of detected anomalies by distinguishing those more likely to reflect actual protocol violations from those arising due to the specific characteristics of a particular student population and their exam preparation within a given educational institution. The application of the oneclass support vector machine method enabled the identification of 12 schools with atypical anomalous results. The proposed methodology could be useful for the detection of potential cases of cheating during exams and the development of methods for preventing such behavior. In particular, it can be used to support targeted preventive work with specific schools in order to reduce the risk of exam rule violations.

This paper presents a model of replenishment of bank liquidity by additional income of banks. Given the methodological basis for the necessity for bank stabilization funds to cover losses during the economy crisis. An econometric derivation of the equations describing the behavior of the bank financial and operating activity performed. In accordance with the purpose of creating a stabilization fund introduces an optimality criterion used controls. Based on the equations of the behavior of the bank by the method of dynamic programming is derived a vector of optimal controls.