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The paper addresses the problem of modeling the formation and propagation of panic states in social groups with relatively stable structures of interpersonal interactions. Panic is interpreted as a nonlinear process of emotional contagion arising from the interaction between individual psychological characteristics and collective effects within a social environment. In contrast to models focused on the spatial dynamics of moving crowds, the proposed approach concentrates on quasi-stationary interaction networks that reflect informational and emotional contacts among individuals.

The developed discrete network dynamical system integrates individual temperament parameters (sanguine, choleric, phlegmatic, melancholic), the structure of social connections, and nonlinear mechanisms of collective behavior. The individual dynamics of panic are described using an S-shaped growth function, which ensures boundedness of the emotional arousal level and captures the stages of its formation and saturation. Social influence is modeled on a graph of interpersonal interactions (an Erdos –Renyi random network) through local contacts between individuals.

Additionally, the model incorporates the effects of collective contagion and avalanche-like amplification driven by the average panic level in the group, as well as a baseline stress factor depending on group size. Numerical simulation is implemented in a discrete iterative form, allowing for the analysis of both individual and group panic trajectories. A quantitative indicator of the panic propagation rate is introduced, defined by the time required for the group to reach a state close to full panic.

A comparative analysis of heterogeneous and homogeneous groups is conducted, demonstrating that group heterogeneity significantly accelerates panic propagation due to inter-temperament interactions: highly excitable individuals act as initiators of emotional contagion, while more stable individuals partially dampen its dynamics. The evaluation of the model quality using the coefficient of determination shows a high degree of consistency within the simulation data.

The practical significance of the work lies in the potential application of the model for analyzing the resilience of social groups to panic states, assessing risks at mass events, and developing intelligent systems for monitoring collective behavior. Future research directions include extending the model to account for directed and dynamic networks, as well as its calibration based on empirical data.

Non-smooth optimization often arises in many applied problems. The issues of developing efficient computational procedures for such problems in high-dimensional spaces are very topical. First-order methods (subgradient methods) are well applicable here, but in fairly general situations they lead to low speed guarantees for large-scale problems. One of the approaches to this type of problem can be to identify a subclass of non-smooth problems that allow relatively optimistic results on the rate of convergence. For example, one of the options for additional assumptions can be the condition of a sharp minimum, proposed in the late 1960s by B. T. Polyak. In the case of the availability of information about the minimal value of the function for Lipschitz-continuous problems with a sharp minimum, it turned out to be possible to propose a subgradient method with a Polyak step-size, which guarantees a linear rate of convergence in the argument. This approach made it possible to cover a number of important applied problems (for example, the problem of projecting onto a convex compact set). However, both the condition of the availability of the minimal value of the function and the condition of a sharp minimum itself look rather restrictive. In this regard, in this paper, we propose a generalized condition for a sharp minimum, somewhat similar to the inexact oracle proposed recently by Devolder – Glineur – Nesterov. The proposed approach makes it possible to extend the class of applicability of subgradient methods with the Polyak step-size, to the situation of inexact information about the value of the minimum, as well as the unknown Lipschitz constant of the objective function. Moreover, the use of local analogs of the global characteristics of the objective function makes it possible to apply the results of this type to wider classes of problems. We show the possibility of applying the proposed approach to strongly convex nonsmooth problems, also, we make an experimental comparison with the known optimal subgradient method for such a class of problems. Moreover, there were obtained some results connected to the applicability of the proposed technique to some types of problems with convexity relaxations: the recently proposed notion of weak $\beta$-quasi-convexity and ordinary quasiconvexity. Also in the paper, we study a generalization of the described technique to the situation with the assumption that the $\delta$-subgradient of the objective function is available instead of the usual subgradient. For one of the considered methods, conditions are found under which, in practice, it is possible to escape the projection of the considered iterative sequence onto the feasible set of the problem.

Accurate tree identification is essential for ecological monitoring, biodiversity assessment, and forest management. Traditional manual survey methods are labor-intensive and ineffective over large areas. Advances in remote sensing technologies including lidar and hyperspectral imaging improve automated, exact detection in many fields.

Nevertheless, these technologies typically require extensive labeled data and manual feature engineering, which restrict scalability. This research proposes a new method of Self-Supervised Learning (SSL) with the SimCLR framework to enhance the classification of tree species using unlabelled data. SSL model automatically discovers strong features by merging the spectral data from hyperspectral data with the structural data from LiDAR, eliminating the need for manual intervention.

We evaluate the performance of the SSL model against traditional classifiers, including Random Forest (RF), Support Vector Machines (SVM), and Supervised Learning methods, using a dataset from the ECODSE competition, which comprises both labeled and unlabeled samples of tree species in Florida’s Ordway-Swisher Biological Station. The SSL method has been demonstrated to be significantly more effective than traditional methods, with a validation accuracy of 97.5% compared to 95.56% for Semi-SSL and 95.03% for CNN in Supervised Learning.

Subsampling experiments showed that the SSL technique is still effective with less labeled data, with the model achieving good accuracy even with only 20% labeled data points. This conclusion demonstrates SSL’s practical applications in circumstances with insufficient labeled data, such as large-scale forest monitoring.

The purpose of this study is to develop a methodology for change points detection in time series, including financial data. The theoretical basis of the study is based on the pieces of research devoted to the analysis of structural changes in financial markets, description of the proposed algorithms for detecting change points and peculiarities of building classical and deep machine learning models for solving this type of problems. The development of such tools is of interest to investors and other stakeholders, providing them with additional approaches to the effective analysis of financial markets and interpretation of available data.

To address the research objective, a neural network was trained. In the course of the study several ways of training sample formation were considered, differing in the nature of statistical parameters. In order to improve the quality of training and obtain more accurate results, a methodology for feature generation was developed for the formation of features that serve as input data for the neural network. These features, in turn, were derived from an analysis of mathematical expectations and standard deviations of time series data over specific intervals. The potential for combining these features to achieve more stable results is also under investigation.

The results of model experiments were analyzed to compare the effectiveness of the proposed model with other existing changepoint detection algorithms that have gained widespread usage in practical applications. A specially generated dataset, developed using proprietary methods, was utilized as both training and testing data. Furthermore, the model, trained on various features, was tested on daily data from the S&P 500 index to assess its effectiveness in a real financial context.

As the principles of the model’s operation are described, possibilities for its further improvement are considered, including the modernization of the proposed model’s structure, optimization of training data generation, and feature formation. Additionally, the authors are tasked with advancing existing concepts for real-time changepoint detection.

A new approach to the identification of hardly perceptible diagnostically significant changes in electrocardiograms is suggested. The approach is based on the analysis of topological transformations in wavelet spectra associated with electrocardiograms. Possible practical application of the approach developed is discussed.

Variational inequalities constitute a broad class of problems with applications in a number of fields, including game theory, economics, and machine learning. Today’s practical applications of VIs are becoming increasingly computationally demanding. It is therefore necessary to employ distributed computations to solve such problems in a reasonable time. In this context, workers have to exchange data with each other, which creates a communication bottleneck. There are three main techniques to reduce the cost and the number of communications: the similarity of local operators, the compression of messages and the use of local steps on devices. There is an algorithm that uses all of these techniques to solve the VI problem and outperforms all previous methods in terms of communication complexity. However, this algorithm is limited to unbiased compression. Meanwhile, biased (contractive) compression leads to better results in practice, but it requires additional modifications within an algorithm and more effort to prove the convergence. In this work, we develop a new algorithm that solves distributed VI problems using data similarity, contractive compression and local steps on devices, derive the theoretical convergence of such an algorithm, and perform some experiments to show the applicability of the method.

We propose a family of Gauss –Newton methods for solving optimization problems and systems of nonlinear equations based on the ideas of using the upper estimate of the norm of the residual of the system of nonlinear equations and quadratic regularization. The paper presents a development of the «Three Squares Method» scheme with the addition of a momentum term to the update rule of the sought parameters in the problem to be solved. The resulting scheme has several remarkable properties. First, the paper algorithmically describes a whole parametric family of methods that minimize functionals of a special kind: compositions of the residual of a nonlinear equation and an unimodal functional. Such a functional, entirely consistent with the «gray box» paradigm in the problem description, combines a large number of solvable problems related to applications in machine learning, with the regression problems. Secondly, the obtained family of methods is described as a generalization of several forms of the Levenberg –Marquardt algorithm, allowing implementation in non-Euclidean spaces as well. The algorithm describing the parametric family of Gauss –Newton methods uses an iterative procedure that performs an inexact parametrized proximal mapping and shift using a momentum term. The paper contains a detailed analysis of the efficiency of the proposed family of Gauss – Newton methods; the derived estimates take into account the number of external iterations of the algorithm for solving the main problem, the accuracy and computational complexity of the local model representation and oracle computation. Sublinear and linear convergence conditions based on the Polak – Lojasiewicz inequality are derived for the family of methods. In both observed convergence regimes, the Lipschitz property of the residual of the nonlinear system of equations is locally assumed. In addition to the theoretical analysis of the scheme, the paper studies the issues of its practical implementation. In particular, in the experiments conducted for the suboptimal step, the schemes of effective calculation of the approximation of the best step are given, which makes it possible to improve the convergence of the method in practice in comparison with the original «Three Square Method». The proposed scheme combines several existing and frequently used in practice modifications of the Gauss –Newton method, in addition, the paper proposes a monotone momentum modification of the family of developed methods, which does not slow down the search for a solution in the worst case and demonstrates in practice an improvement in the convergence of the method.