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The most important principle of military science and border security is the principle of concentrating the main efforts on the main directions and tasks. At the tactical level, there are many mathematical models for computing the optimal resource allocation by directions and objects, whereas at the state level there are no corresponding models. Using the statistical data on the results of the protection of the US border, an exponential type border production function parameter is calculated that reflects the organizational and technological capabilities of the border guard. The production function determines the dependence of the probability of detaining offenders from the density of border guards per kilometer of the border. Financial indicators in the production function are not taken into account, as the border maintenance budget and border equipment correlate with the number of border agents. The objective function of the border guards is defined — the total prevented damage from detained violators taking into account their expected danger for the state and society, which is to be maximized. Using Slater's condition, the solution of the problem was found — optimal density of border guard was calculated for the regions of the state. Having a model of resource allocation, the example of the three border regions of the United States has also solved the reverse problem — threats in the regions have been assessed based on the known allocation of resources. The expected danger from an individual offender on the US-Canada border is 2–5 times higher than from an offender on the US-Mexican border. The results of the calculations are consistent with the views of US security experts: illegal migrants are mostly detained on the US-Mexican border, while potential terrorists prefer to use other channels of penetration into the US (including the US-Canadian border), where the risks of being detained are minimal. Also, the results of the calculations are consistent with the established practice of border protection: in 2013 the number of border guards outside the checkpoints on the US-Mexican border increased by 2 times compared with 2001, while on the American-Canadian border — 4 times. The practice of border protection and the views of specialists give grounds for approval of the verification of the model.

Hemostasis system is one of the key body’s defense systems, which is presented in all the liquid tissues and especially important in blood. Hemostatic response is triggered as a result of the vessel injury. The interaction between specialized cells and humoral systems leads to the formation of the initial hemostatic clot, which stops bleeding. After that the slow process of clot dissolution occurs. The formation of hemostatic plug is a unique physiological process, because during several minutes the hemostatic system generates complex structures on a scale ranging from microns for microvessel injury or damaged endothelial cell-cell contacts, to centimeters for damaged systemic arteries. Hemostatic response depends on the numerous coordinated processes, which include platelet adhesion and aggregation, granule secretion, platelet shape change, modification of the chemical composition of the lipid bilayer, clot contraction, and formation of the fibrin mesh due to activation of blood coagulation cascade. Computer modeling is a powerful tool, which is used to study this complex system at different levels of organization. This includes study of intracellular signaling in platelets, modelling humoral systems of blood coagulation and fibrinolysis, and development of the multiscale models of thrombus growth. There are two key issues of the computer modeling in biology: absence of the adequate physico-mathematical description of the existing experimental data due to the complexity of the biological processes, and high computational complexity of the models, which doesn’t allow to use them to test physiologically relevant scenarios. Here we discuss some key unresolved problems in the field, as well as the current progress in experimental research of hemostasis and thrombosis. New findings lead to reevaluation of the existing concepts and development of the novel computer models. We focus on the arterial thrombosis, venous thrombosis, thrombosis in microcirculation and the problems of fibrinolysis and thrombolysis. We also briefly discuss basic types of the existing mathematical models, their computational complexity, and principal issues in simulation of thrombus growth in arteries.

Epidemics severely destabilize economies by reducing productivity, weakening consumer spending, and overwhelming public infrastructure, often culminating in economic recessions. The COVID-19 pandemic underscored the critical role of nonpharmaceutical interventions, such as lockdowns, in containing infectious disease transmission. This study investigates how the progression of epidemics and the implementation of lockdown policies shape the economic well-being of populations. By integrating compartmental ordinary differential equation (ODE) models, the research analyzes the interplay between epidemic dynamics and economic outcomes, particularly focusing on how varying lockdown intensities influence both disease spread and population wealth. Findings reveal that epidemics inflict significant economic damage, but timely and stringent lockdowns can mitigate healthcare system overload by sharply reducing infection peaks and delaying the epidemic’s trajectory. However, carefully timed lockdown relaxation is equally vital to prevent resurgent outbreaks. The study identifies key epidemiological thresholds—such as transmission rates, recovery rates, and the basic reproduction number $(\mathfrak{R}0)$ — that determine the effectiveness of lockdowns. Analytically, it pinpoints the optimal proportion of isolated individuals required to minimize total infections in scenarios where permanent immunity is assumed. Economically, the analysis quantifies lockdown impacts by tracking population wealth, demonstrating that economic outcomes depend heavily on the fraction of isolated individuals who remain economically productive. Higher proportions of productive individuals during lockdowns correlate with better wealth retention, even under fixed epidemic conditions. These insights equip policymakers with actionable frameworks to design balanced lockdown strategies that curb disease spread while safeguarding economic stability during future health crises.

An effective regional policy in order to stabilize production is impossible without an analysis of the dynamics of economic processes taking place. This article focuses on developing a mathematical model reflecting the interaction of several economic agents with regard to their interests. Developing such a model and its study can be considered as an important step in solving theoretical and practical problems of managing growth.

A hybrid cluster implies the use of computational devices with radically different architectures. Usually, these are conventional CPU architecture (e.g. x86_64) and GPU architecture (e. g. NVIDIA CUDA). Creating and exploiting such a cluster requires some experience: in order to harness all computational power of the described system and get substantial speedup for computational tasks many factors should be taken into account. These factors consist of hardware characteristics (e.g. network infrastructure, a type of data storage, GPU architecture) as well as software stack (e.g. MPI implementation, GPGPU libraries). So, in order to run scientific applications GPU capabilities, software features, task size and other factors should be considered.

This report discusses opportunities and problems of hybrid computations. Some statistics from tests programs and applications runs will be demonstrated. The main focus of interest is open source applications (e. g. OpenFOAM) that support GPGPU (with some parts rewritten to use GPGPU directly or by replacing libraries).

There are several approaches to organize heterogeneous computations for different GPU architectures out of which CUDA library and OpenCL framework are compared. CUDA library is becoming quite typical for hybrid systems with NVIDIA cards, but OpenCL offers portability opportunities which can be a determinant factor when choosing framework for development. We also put emphasis on multi-GPU systems that are often used to build hybrid clusters. Calculations were performed on a hybrid cluster of SPbU computing center.

The paper uses methods of mathematical modeling to estimate a zooplankton influence on the dynamics of phytoplankton abundance. We propose a three-component model of the “phytoplankton–zooplankton” community with discrete time, considering a heterogeneity of zooplankton according to the developmental stage and type of feeding; the model takes into account cannibalism in zooplankton community, during which mature individuals of some of its species consume juvenile ones. Survival rates at the early stages of zooplankton life cycle depend explicitly on the interaction between zooplankton and phytoplankton. Loss of phytoplankton biomass because of zooplankton consumption is explicitly considered. We use the Holling functional response of type II to describe saturation during biomass consumption. The dynamics of the phytoplankton community is represented by the Ricker model, which allows to take into account the restriction of phytoplankton biomass growth by the availability of external resources (mineral nutrition, oxygen, light, etc.) implicitly.

The study analyzed scenarios of the transition from stationary dynamics to fluctuations in the size of phytoand zooplankton for various values of intrapopulation parameters determining the nature of the dynamics of the species constituting the community, and the parameters of their interaction. The focus is on exploring the complex modes of community dynamics. In the framework of the model used for describing dynamics of phytoplankton in the absence of interspecific interaction, phytoplankton dynamics undergoes a series of perioddoubling bifurcations. At the same time, with zooplankton appearance, the cascade of period-doubling bifurcations in phytoplankton and the community as a whole is realized earlier (at lower reproduction rates of phytoplankton cells) than in the case when phytoplankton develops in isolation. Furthermore, the variation in the cannibalism level in zooplankton can significantly change both the existing dynamics in the community and its bifurcation; e.g., with a certain structure of zooplankton food relationships the realization of Neimark–Sacker bifurcation scenario in the community is possible. Considering the cannibalism level in zooplankton can change due to the natural maturation processes and achievement of the carnivorous stage by some individuals, one can expect pronounced changes in the dynamic mode of the community, i.e. abrupt transitions from regular to quasiperiodic dynamics (according to Neimark–Sacker scenario) and further cycles with a short period (the implementation of period halving bifurcation).

The article is devoted to the application of various methods of mathematical analysis, search for patterns and studying the composition of nucleotides in DNA sequences at the genomic level. New methods of mathematical biology that made it possible to detect and visualize the hidden ordering of genetic nucleotide sequences located in the chromosomes of cells of living organisms described. The research was based on the work on algebraic biology of the doctor of physical and mathematical sciences S. V. Petukhov, who first introduced and justified new algebras and hypercomplex numerical systems describing genetic phenomena. This paper describes a new phase in the development of matrix methods in genetics for studying the properties of nucleotide sequences (and their physicochemical parameters), built on the principles of finite geometry. The aim of the study is to demonstrate the capabilities of new algorithms and discuss the discovered properties of genetic DNA and RNA molecules. The study includes three stages: parameterization, scaling, and visualization. Parametrization is the determination of the parameters taken into account, which are based on the structural and physicochemical properties of nucleotides as elementary components of the genome. Scaling plays the role of “focusing” and allows you to explore genetic structures at various scales. Visualization includes the selection of the axes of the coordinate system and the method of visual display. The algorithms presented in this work are put forward as a new toolkit for the development of research software for the analysis of long nucleotide sequences with the ability to display genomes in parametric spaces of various dimensions. One of the significant results of the study is that new criteria were obtained for the classification of the genomes of various living organisms to identify interspecific relationships. The new concept allows visually and numerically assessing the variability of the physicochemical parameters of nucleotide sequences. This concept also allows one to substantiate the relationship between the parameters of DNA and RNA molecules with fractal geometric mosaics, reveals the ordering and symmetry of polynucleotides, as well as their noise immunity. The results obtained justified the introduction of new terms: “genometry” as a methodology of computational strategies and “genometrica” as specific parameters of a particular genome or nucleotide sequence. In connection with the results obtained, biosemiotics and hierarchical levels of organization of living matter are raised.

In our research, we focus on the problem of classification for silent speech recognition to develop a brain– computer interface (BCI) based on electroencephalographic (EEG) data, which will be capable of assisting people with mental and physical disabilities and expanding human capabilities in everyday life. Our previous research has shown that the silent pronouncing of some words results in almost identical distributions of electroencephalographic signal data. Such a phenomenon has a suppressive impact on the quality of neural network model behavior. This paper proposes a data processing technique that distinguishes between statistically remote and inseparable classes in the dataset. Applying the proposed approach helps us reach the goal of maximizing the semantic load of the dictionary used in BCI.

Furthermore, we propose the existence of a statistical predictive criterion for the accuracy of binary classification of the words in a dictionary. Such a criterion aims to estimate the lower and the upper bounds of classifiers’ behavior only by measuring quantitative statistical properties of the data (in particular, using the Kolmogorov – Smirnov method). We show that higher levels of classification accuracy can be achieved by means of applying the proposed predictive criterion, making it possible to form an optimized dictionary in terms of semantic load for the EEG-based BCIs. Furthermore, using such a dictionary as a training dataset for classification problems grants the statistical remoteness of the classes by taking into account the semantic and phonetic properties of the corresponding words and improves the classification behavior of silent speech recognition models.

This article presents a model of a fully automated warehouse with deep storage racks designed for boxed goods storage. The study focuses on optimizing warehouse operations through discrete multiagent simulation of shuttle movements for pallet loading and unloading tasks. The authors investigate various product placement strategies, including the Nearest Channel Positioning Algorithm (NCPA), Most Empty Channel Group Placement (MECGP), andMost Filled Channel Group Placement (MFCGP), while analyzing optimal routing schemes for the given warehouse topology.

A key contribution is determining the optimal number of shuttles to maximize warehouse throughput. Simulation results demonstrate that increasing the number of robots beyond 15 does not significantly improve efficiency due to increased route collisions. The study also examines 24-hour warehouse occupancy dynamics, revealing optimal storage utilization levels.

The developed model enables performance evaluation and optimization of task distribution among robots to minimize order processing time. Future research directions include implementing machine learning techniques to further enhance warehouse management systems.

In this paper, we test the performance of some modern stochastic optimization methods and practices with respect to the digital pre-distortion problem, which is a valuable part of processing signal on base stations providing wireless communication. In the first part of our study, we focus on the search for the best performing method and its proper modifications. In the second part, we propose the new, quasi-online, testing framework that allows us to fit our modeling results with the behavior of real-life DPD prototype, retest some selected of practices considered in the previous section and approve the advantages of the method appearing to be the best under real-life conditions. For the used model, the maximum achieved improvement in depth is 7% in the standard regime and 5% in the online regime (metric itself is of logarithmic scale). We also achieve a halving of the working time preserving 3% and 6% improvement in depth for the standard and online regime, respectively. All comparisons are made to the Adam method, which was highlighted as the best stochastic method for DPD problem in [Pasechnyuk et al., 2021], and to the Adamax method, which is the best in the proposed online regime.