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In this paper, we present an effective method for analyzing patterns in the Russia–Ukraine war based on the Lanchester model. Due to the limited availability of information on combat powers of engaging forces, we utilize the loss of armored equipment as the primary data source. To capture the intricate dynamics of modern warfare, we partition the combat loss data into disjoint subsets by examining their geometric properties. Separate systems of ordinary differential equations for these subsets are then identified using the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm under a generalized formulation of the historical Lanchester model. We provide simulations of our method to demonstrate its effectiveness and performance in analyzing contemporary warfare dynamics. [ABSTRACT FROM AUTHOR]

In the spring of 2022, a new round of epidemic broke out in Shanghai, causing a shock to the Shanghai carbon trading market. Against this background, this paper studied the impact of the new epidemic on the price of Shanghai carbon emission rights and tried to explore the prediction model under the unexpected event. First, because a model based on point value data cannot capture the information hidden in inter-day price fluctuation, based on the interval price of Shanghai carbon emission rights (SHEA) and its influencing factors, an autoregressive conditional interval model with jumping and exogenous variables (ACIXJ) was established to explore the influence of the Russian–Ukrainian conflict and COVID-19 on the interval price of SHEA, respectively. The empirical results show that the conflict between Russia and Ukraine has no obvious influence on the price of SHEA, but COVID-19 led to a decline in the price trend of SHEA over four days before the city was closed, and the volatility changed significantly on the day before the city was closed. The price fluctuation was the strongest within 3 days after the city was closed; In addition, in order to accurately predict the interval data of SHEA against the background of COVID-19, based on the interval data decomposition algorithm (BEMD), a hybrid forecasting model of NDGM-ACIXJ/CNN-LSTM was constructed, in which the discrete gray model of approximate nonhomogeneous exponential series (NDGM) combined with the ACIXJ model is used to predict the high-frequency sub-interval, and the convolution neural network long-term and short-term memory model (CNN-LSTM) is used to predict the low-frequency sub-interval. The empirical results show that the prediction model proposed in this article has higher prediction precision than the reference models (ACIX, ACIXJ, NDGM-ACIXJ, BEMD-ACIX/CNN-LSTM, BEMD-ACIXJ/CNN-LSTM). [ABSTRACT FROM AUTHOR]

The urgent need of society for creative and critical thinkers dictates the need to manage and develop the project-based and research activities of schoolchildren. Neural networks, as effective tools for solving complex, multi-component, multifunctional problems, have created an opportunity to develop tools for the content and quality assessment of project-based, research activities and personal achievements of each student with a dynamic and stratified sampling of complex knowledge, to identify individual educational paths, tools and instructions for research and creative activity reflected on the layers of an artificial neural network. The purpose of this study is to define and develop the concept of supporting a hybrid intelligent system of project-based and research activities in a comprehensive information and educational environment to create an applied intellectual technology that supports project-based and research activities and classifies the growth of schoolchildren's scientific potential. The paper considers the development of technologies for the pedagogical, algorithmic and information organization of ontological engineering and support models for project-based and research activities, as well as the growth of scientific student training based on the construction of an artificial neural network with a teacher and an array of training samples using expert systems and decision theory. It also defines the selection criteria, hierarchies and content of the generalized constructs of complex knowledge (modern achievements in science) by modeling creative activities while further predicting the growth of a student's scientific potential based on the layers of the neural network. The original technology of training samples used for constructing hybrid neural networks was determined using expert systems, the psychological method of parallel slices and clustering of the personal characteristics of schoolchildren. An innovative intellectual environment is being introduced into the practice of mathematical education in high schools in Russia. The study made it possible to create applied intelligent technology to support and display the dynamic profiles of the project-based and research activities of schoolchildren and act as a growth classifier of their scientific potential. In terms of concept implementation, the phased growth technology to analyze students' scientific potential was developed during the study of the generalized construct of complex knowledge. Individual educational workshops for school students to master project-based and research activities and display their dynamic profiles during the implementation of a hybrid intellectual environment for support and decision-making will allow school students to develop their personal potential, increase their educational motivation and allow researchers and educators to realize the potential of adapting modern achievements in science to school mathematics and create conditions for the modernization of educational programs in a developing digital environment. [ABSTRACT FROM AUTHOR]

Ensuring the rational use of limited space is a key function of government bodies at any level of power. Spatial development of the economy is modeled in the presented paper based on the concept of economic complexity. In addition to the innovative application of the economic complexity concept to the analysis of territorial systems in the form of macroregions, this study used an improved methodology for calculating the index of economic complexity in relation to the processes of interregional cooperation. The methodology of constructing a model of the spatial organization of the economy included determining the composition of the system of equations and their structure, formulating the prerequisites and limitations of the model, and determining an objective function of the model. The minimum level of heterogeneity of spatial development and the maximum of macroregion economic complexity indexes were chosen as the criterion of optimality. As a result of testing the model on real statistical data of the regions in Russia, a grid of macroregions was formed, providing an increase in the diversification of the types of production activities within the macroregion and a decrease in the differentiation of the development of the territories included in it. A computer program was developed during the course of the study that allows simulation experiments to be carried out in order to find the optimal variant of spatial organization of the economy. In addition, in the example of the aerospace industry, the management algorithm of the regional sectoral branching process was tested. [ABSTRACT FROM AUTHOR]

Ticks and tick-borne diseases present a well-known threat to the health of people in many parts of the globe. The scientific literature devoted both to field observations and to modeling the propagation of ticks continues to grow. To date, the majority of the mathematical studies have been devoted to models based on ordinary differential equations, where spatial variability was taken into account by a discrete parameter. Only a few papers use spatially nontrivial diffusion models, and they are devoted mostly to spatially homogeneous equilibria. Here we develop diffusion models for the propagation of ticks stressing spatial heterogeneity. This allows us to assess the sizes of control zones that can be created (using various available techniques) to produce a patchy territory, on which ticks will be eventually eradicated. Using averaged parameters taken from various field observations we apply our theoretical results to the concrete cases of the lone star ticks of North America and of the taiga ticks of Russia. From the mathematical point of view, we give criteria for global stability of the vanishing solution to certain spatially heterogeneous birth and death processes with diffusion. [ABSTRACT FROM AUTHOR]

The effect of the COVID-19 pandemic on crude oil prices just faded; at this moment, the Russia–Ukraine war brought a new crisis. In this paper, a new application is developed that predicts the change in crude oil prices by incorporating these two global effects. Unlike most existing studies, this work uses a dataset that involves data collected over twenty-two years and contains seven different features, such as crude oil opening, closing, intraday highest value, and intraday lowest value. This work applies cross-validation to predict the crude oil prices by using machine learning algorithms (support vector machine, linear regression, and rain forest) and deep learning algorithms (long short-term memory and bidirectional long short-term memory). The results obtained by machine learning and deep learning algorithms are compared. Lastly, the high-performance estimation can be achieved in this work with the average mean absolute error value over 0.3786. [ABSTRACT FROM AUTHOR]

The consideration of infectious diseases from a mathematical point of view can reveal possible options for epidemic control and fighting the spread of infection. However, predicting and modeling the spread of a new, previously unexplored virus is still difficult. The present paper examines the possibility of using a new approach to predicting the statistical indicators of the epidemic of a new type of virus based on the example of COVID-19. The important result of the study is the description of the principle of dynamic balance of epidemiological processes, which has not been previously used by other researchers for epidemic modeling. The new approach is also based on solving the problem of predicting the future dynamics of precisely random values of model parameters, which is used for defining the future values of the total number of: cases (C); recovered and dead (R); and active cases (I). Intelligent heuristic algorithms are proposed for calculating the future trajectories of stochastic parameters, which are called the percentage increase in the total number of confirmed cases of the disease and the dynamic characteristics of epidemiological processes. Examples are given of the application of the proposed approach for making forecasts of the considered indicators of the COVID-19 epidemic, in Russia and European countries, during the first wave of the epidemic. [ABSTRACT FROM AUTHOR]

Policymakers and researchers worldwide are interested in measuring the subjective well-being (SWB) of populations. In recent years, new approaches to measuring SWB have begun to appear, using digital traces as the main source of information, and show potential to overcome the shortcomings of traditional survey-based methods. In this paper, we propose the formal model for calculation of observable subjective well-being (OSWB) indicator based on posts from a social network, which utilizes demographic information and post-stratification techniques to make the data sample representative by selected characteristics of the general population. We applied the model on the data from Odnoklassniki, one of the largest social networks in Russia, and obtained an OSWB indicator representative of the population of Russia by age and gender. For sentiment analysis, we fine-tuned several language models on RuSentiment and achieved state-of-the-art results. The calculated OSWB indicator demonstrated moderate to strong Pearson's ( r = 0.733 , p = 0.007 , n = 12 ) correlation and strong Spearman's ( r s = 0.825 , p = 0.001 , n = 12 ) correlation with a traditional survey-based Happiness Index reported by Russia Public Opinion Research Center, confirming the validity of the proposed approach. Additionally, we explored circadian (24 h) and circaseptan (7 day) patterns, and report several interesting findings for the population of Russia. Firstly, daily variations were clearly observed: the morning had the lowest level of happiness, and the late evening had the highest. Secondly, weekly patterns were clearly observed as well, with weekends being happier than weekdays. The lowest level of happiness occurs in the first three weekdays, and starting on Thursday, it rises and peaks during the weekend. Lastly, demographic groups showed different levels of happiness on a daily, weekly, and monthly basis, which confirms the importance of post-stratification by age group and gender in OSWB studies based on digital traces. [ABSTRACT FROM AUTHOR]

In this paper, we assess sentiment and emotion regarding green energy through employing a social listening analysis on Twitter. Knowing the sentiment and attitude of the population is important because it will help to promote policies and actions that favor the development of green or renewable energies. We chose to study a crucial period that coincides with the onset of the 2022 Ukrainian–Russo conflict, which has undoubtedly affected global energy policies worldwide. We searched for messages containing the term "green energy" during the days before and after the conflict started. We then performed a semantic analysis of the most frequent words, a comparative analysis of sentiments and emotions in both periods, a dimensionality reduction analysis, and an analysis of the variance of tweets versus retweets. The results of the analysis show that the conflict has changed society's sentiments about an energy transition to green energy. In addition, we found that negative feelings and emotions emerged in green energy tweeters once the conflict started. However, the emotion of confidence also increased as the conflict, intimately linked to energy, has driven all countries to promote a rapid transition to greener energy sources. Finally, we observed that of the two latent variables identified for social opinion, one of them, pessimism, was maintained while the other, optimism, was subdivided into optimism and expectation. [ABSTRACT FROM AUTHOR]

The paper describes a method of gravity data inversion, which is based on parallel algorithms. The choice of the density model of the initial approximation and the set on which the solution is sought guarantees the stability of the algorithms. We offer a new upward and downward continuation algorithm for separating the effects of shallow and deep sources. Using separated field of layers, the density distribution is restored in a form of 3D grid. We use the iterative parallel algorithms for the downward continuation and restoration of the density values (by solving the inverse linear gravity problem). The algorithms are based on the ideas of local minimization; they do not require a nonlinear minimization; they are easier to implement and have better stability. We also suggest an optimization of the gravity field calculation, which speeds up the inversion. A practical example of interpretation is presented for the gravity data of the Urals region, Russia. [ABSTRACT FROM AUTHOR]

In this survey paper, we analyze the development of Fractional Calculus in Russia at the end of the XIX century, in particular, the results by A. V. Letnikov, N. Ya. Sonine, and P. A. Nekrasov. Some of the discussed results are either unknown or inaccessible. [ABSTRACT FROM AUTHOR]

The paper addresses the application of Volterra integral equations of the first kind for modeling dynamic power systems. We study the problem of forecasting the commissioning of capacities of the electric power system, taking into account various hypotheses about the dynamics of equipment aging, and the known prehistory. The numerical results of the application of two models to the problem of the development of a large electric power system using the example of the Unified Energy System of Russia are presented. Theoretical results were formulated for a two-dimensional Volterra integral equation of the first kind with variable limits of integration. This class of equations arises when solving the actual problem of identifying variable characteristics of a nonlinear dynamic system of the "input-output" type. [ABSTRACT FROM AUTHOR]