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The model of market pricing in duopoly describing the prices dynamics as a two-dimensional map is presented. It is shown that the fixed point of the map coincides with the local Nash-equilibrium price in duopoly game. There have been numerically identified a bifurcation of the fixed point, shown the scheme of transition from periodic to chaotic mode through a doubling period. To ensure the sustainability of local Nashequilibrium price the controlling chaos mechanism has been proposed. This mechanism allows to harmonize the economic interests of the firms and to form the balanced pricing policy.

Our purpose is to study the spatio-temporal population wave behavior observed in the predator-prey system. It is assumed that predators move both directionally and randomly, and prey spread only diffusely. The model does not take into account demographic processes in the predator population; it’s total number is constant and is a parameter. The variables of the model are the prey and predator densities and the predator speed, which are connected by a system of three reaction – diffusion – advection equations. The system is considered on an annular range, that is the periodic conditions are set at the boundaries of the interval. We have studied the bifurcations of wave modes arising in the system when two parameters are changed — the total number of predators and their taxis acceleration coefficient.

The main research method is a numerical analysis. The spatial approximation of the problem in partial derivatives is performed by the finite difference method. Integration of the obtained system of ordinary differential equations in time is carried out by the Runge –Kutta method. The construction of the Poincare map, calculation of Lyapunov exponents, and Fourier analysis are used for a qualitative analysis of dynamic regimes.

It is shown that, population waves can arise as a result of existence of directional movement of predators. The population dynamics in the system changes qualitatively as the total predator number increases. А stationary homogeneous regime is stable at low value of parameter, then it is replaced by self-oscillations in the form of traveling waves. The waveform becomes more complicated as the bifurcation parameter increases; its complexity occurs due to an increase in the number of temporal vibrational modes. A large taxis acceleration coefficient leads to the possibility of a transition from multi-frequency to chaotic and hyperchaotic population waves. A stationary regime without preys becomes stable with a large number of predators.

State-of-the-art localization and mapping approaches for augmented (AR) and mixed (MR) reality devices are based on the extraction of local features from the camera. Along with this, modern AR/MR devices allow you to build a three-dimensional mesh of the surrounding space. However, the existing methods do not solve the problem of global device co-localization due to the use of different methods for extracting computer vision features. Using a space map from a 3D mesh, we can solve the problem of collaborative global localization of AR/MR devices. This approach is independent of the type of feature descriptors and localisation and mapping algorithms used onboard the AR/MR device. The mesh can be reduced to a point cloud, which consists of only the vertices of the mesh. We propose an approach for collaborative localization of AR/MR devices using point clouds that are independent of algorithms onboard the device. We have analyzed various point cloud registration algorithms and discussed their limitations for the problem of global co-localization of AR/MR devices indoors.

Predicting novel drug properties is fundamental to polypharmacology, repositioning, and the study of biologically active substances during the preclinical phase. The use of machine learning, including deep learning methods, for the identification of drug – target interactions has gained increasing popularity in recent years.

The objective of this study was to develop a method for recognizing psychotropic effects and drug mechanisms of action (drug – target interactions) based on an analysis of the bioelectrical activity of the brain using artificial intelligence technologies.

Intracranial electroencephalographic (EEG) signals from rats were recorded (4 channels at a sampling frequency of 500 Hz) after the administration of psychotropic drugs (gabapentin, diazepam, carbamazepine, pregabalin, eslicarbazepine, phenazepam, arecoline, pentylenetetrazole, picrotoxin, pilocarpine, chloral hydrate). The signals were divided into 2-second epochs, then converted into $2000\times 4$ images and input into an autoencoder. The output of the bottleneck layer was subjected to classification and clustering using t-SNE, and then the distances between resulting clusters were calculated. As an alternative, an approach based on feature extraction with dimensionality reduction using principal component analysis and kernel support vector machine (kSVM) classification was used. Models were validated using 5-fold cross-validation.

The classification accuracy obtained for 11 drugs during cross-validation was $0.580 \pm 0.021$, which is significantly higher than the accuracy of the random classifier $(0.091 \pm 0.045, p < 0.0001)$ and the kSVM $(0.441 \pm 0.035, p < 0.05)$. t-SNE maps were generated from the bottleneck parameters of intracranial EEG signals. The relative proximity of the signal clusters in the parametric space was assessed.

The present study introduces an original method for biopotential-mediated prediction of effects and mechanism of action (drug – target interaction). This method employs convolutional neural networks in conjunction with a modified selective parameter reduction algorithm. Post-treatment EEGs were compressed into a unified parameter space. Using a neural network classifier and clustering, we were able to recognize the patterns of neuronal response to the administration of various psychotropic drugs.

The problem is constructing the differences that arise on ${\mathrm{\LaTeX}}$ documents editing. Each document is represented as a parse tree whose nodes are called tokens. The smallest possible text representation of the document that does not change the syntax tree is constructed. All of the text is splitted into fragments whose boundaries correspond to tokens. A map of the initial text fragment sequence to the similar sequence of the edited document corresponding to the minimum distance is built with Hirschberg algorithm A map of text characters corresponding to the text fragment sequences map is cunstructed. Tokens, that chars are all deleted, or all inserted, or all not changed, are selected in the parse trees. The map for the trees formed with other tokens is built using Zhang–Shasha algorithm.

The article covered results of three-dimensional modeling of ecologic situation of shallow water on the example of the Azov Sea with using schemes of increased order of accuracy on multiprocessor computer system of Southern Federal University. Discrete analogs of convective and diffusive transfer operators of the fourth order of accuracy in the case of partial occupancy of cells were constructed and studied. The developed scheme of the high (fourth) order of accuracy were used for solving problems of aquatic ecology and modeling spatial distribution of polluting nutrients, which caused growth of phytoplankton, many species of which are toxic and harmful. The use of schemes of the high order of accuracy are improved the quality of input data and decreased the error in solutions of model tasks of aquatic ecology. Numerical experiments were conducted for the problem of transportation of substances on the basis of the schemes of the second and fourth orders of accuracy. They’re showed that the accuracy was increased in 48.7 times for diffusion-convection problem. The mathematical algorithm was proposed and numerically implemented, which designed to restore the bottom topography of shallow water on the basis of hydrographic data (water depth at individual points or contour level). The map of bottom relief of the Azov Sea was generated with using this algorithm. It’s used to build fields of currents calculated on the basis of hydrodynamic model. The fields of water flow currents were used as input data of the aquatic ecology models. The library of double-layered iterative methods was developed for solving of nine-diagonal difference equations. It occurs in discretization of model tasks of challenges of pollutants concentration, plankton and fish on multiprocessor computer system. It improved the precision of the calculated data and gave the possibility to obtain operational forecasts of changes in ecologic situation of shallow water in short time intervals.

The fast-paced environment of DevSecOps requires integrating security at every stage of software development to ensure secure, compliant applications. Traditional methods of security testing, often performed late in the development cycle, are insufficient to address the unique challenges of continuous integration and continuous deployment (CI/CD) pipelines, particularly in complex, high-stakes sectors such as industrial automation. In this paper, we propose an approach that automates the analysis and testing of security requirements by embedding requirements verification into the CI/CD pipeline. Our method employs the ARQAN tool to map high-level security requirements to Security Technical Implementation Guides (STIGs) using semantic search, and RQCODE to formalize these requirements as code, providing testable and enforceable security guidelines.We implemented ARQAN and RQCODE within a CI/CD framework, integrating them with GitHub Actions for realtime security checks and automated compliance verification. Our approach supports established security standards like IEC 62443 and automates security assessment starting from the planning phase, enhancing the traceability and consistency of security practices throughout the pipeline. Evaluation of this approach in collaboration with an industrial automation company shows that it effectively covers critical security requirements, achieving automated compliance for 66.15% of STIG guidelines relevant to the Windows 10 platform. Feedback from industry practitioners further underscores its practicality, as 85% of security requirements mapped to concrete STIG recommendations, with 62% of these requirements having matching testable implementations in RQCODE. This evaluation highlights the approach’s potential to shift security validation earlier in the development process, contributing to a more resilient and secure DevSecOps lifecycle.

In general, solving the information explosion problem can be delegated to systems for automatic processing of digital data. These systems are intended for recognizing, sorting, meaningfully processing and presenting data in formats readable and interpretable by humans. The creation of intelligent knowledge extraction systems that handle unstructured data would be a natural solution in this area. At the same time, the evident progress in these tasks for structured data contrasts with the limited success of unstructured data processing, and, in particular, document processing. Currently, this research area is undergoing active development and investigation. The present paper is a systematic survey on both Russian and international publications that are dedicated to the leading trend in automatic text data processing: Text Mining (TM). We cover the main tasks and notions of TM, as well as its place in the current AI landscape. Furthermore, we analyze the complications that arise during the processing of texts written in natural language (NLP) which are weakly structured and often provide ambiguous linguistic information. We describe the stages of text data preparation, cleaning, and selecting features which, alongside the data obtained via morphological, syntactic, and semantic analysis, constitute the input for the TM process. This process can be represented as mapping a set of text documents to «knowledge». Using the case of stock trading, we demonstrate the formalization of the problem of making a trade decision based on a set of analytical recommendations. Examples of such mappings are methods of Information Retrieval (IR), text summarization, sentiment analysis, document classification and clustering, etc. The common point of all tasks and techniques of TM is the selection of word forms and their derivatives used to recognize content in NL symbol sequences. Considering IR as an example, we examine classic types of search, such as searching for word forms, phrases, patterns and concepts. Additionally, we consider the augmentation of patterns with syntactic and semantic information. Next, we provide a general description of all NLP instruments: morphological, syntactic, semantic and pragmatic analysis. Finally, we end the paper with a comparative analysis of modern TM tools which can be helpful for selecting a suitable TM platform based on the user’s needs and skills.

The paper investigates the dynamics of a finite-dimensional model describing the interaction of three populations: prey $x(t)$, its consuming predator $y(t)$, and a superpredator $z(t)$ that feeds on both species. Mathematically, the problem is formulated as a system of nonlinear first-order differential equations with the following right-hand side: $[x(1-x)-(y+z)g;\,\eta_1^{}yg-d_1^{}f-\mu_1^{}y;\,\eta_2^{}zg+d_2^{}f-\mu_2^{}z]$, where $\eta_j^{}$, $d_j^{}$, $\mu_j^{}$ ($j=1,\,2$) are positive coefficients. The considered model belongs to the class of cosymmetric dynamical systems under the Lotka\,--\,Volterra functional response $g=x$, $f=yz$, and two parameter constraints: $\mu_2^{}=d_2^{}\left(1+\frac{\mu_1^{}}{d_1^{}}\right)$, $\eta_2^{}=d_2^{}\left(1+\frac{\eta_1^{}}{d_1^{}}\right)$. In this case, a family of equilibria is being of a straight line in phase space. We have analyzed the stability of the equilibria from the family and isolated equilibria. Maps of stationary solutions and limit cycles have been constructed. The breakdown of the family is studied by violating the cosymmetry conditions and using the Holling model $g(x)=\frac x{1+b_1^{}x}$ and the Beddington–DeAngelis model $f(y,\,z)=\frac{yz}{1+b_2^{}y+b_3^{}z}$. To achieve this, the apparatus of Yudovich's theory of cosymmetry is applied, including the computation of cosymmetric defects and selective functions. Through numerical experimentation, invasive scenarios have been analyzed, encompassing the introduction of a superpredator into the predator-prey system, the elimination of the predator, or the superpredator.

We consider strongly-convex-strongly-concave saddle-point problems with general non-bilinear objective and different condition numbers with respect to the primal and dual variables. First, we consider such problems with smooth composite terms, one of which has finite-sum structure. For this setting we propose a variance reduction algorithm with complexity estimates superior to the existing bounds in the literature. Second, we consider finite-sum saddle-point problems with composite terms and propose several algorithms depending on the properties of the composite terms. When the composite terms are smooth we obtain better complexity bounds than the ones in the literature, including the bounds of a recently proposed nearly-optimal algorithms which do not consider the composite structure of the problem. If the composite terms are prox-friendly, we propose a variance reduction algorithm that, on the one hand, is accelerated compared to existing variance reduction algorithms and, on the other hand, provides in the composite setting similar complexity bounds to the nearly-optimal algorithm which is designed for noncomposite setting. Besides, our algorithms allow one to separate the complexity bounds, i. e. estimate, for each part of the objective separately, the number of oracle calls that is sufficient to achieve a given accuracy. This is important since different parts can have different arithmetic complexity of the oracle, and it is desired to call expensive oracles less often than cheap oracles. The key thing to all these results is our general framework for saddle-point problems, which may be of independent interest. This framework, in turn is based on our proposed Accelerated Meta-Algorithm for composite optimization with probabilistic inexact oracles and probabilistic inexactness in the proximal mapping, which may be of independent interest as well.