All issues

At the middle of the 2000-th, scientists studying the functioning of insect communities identified four basic patterns of the organizational structure of such communities. (i) Cooperation is more developed in groups with strong kinship. (ii) Cooperation in species with large colony sizes is often more developed than in species with small colony sizes. And small-sized colonies often exhibit greater internal reproductive conflict and less morphological and behavioral specialization. (iii) Within a single species, brood size (i. e., in a sense, efficiency) per capita usually decreases as colony size increases. (iv) Advanced cooperation tends to occur when resources are limited and intergroup competition is fierce. Thinking of the functioning of a group of organisms as a two-level competitive market in which individuals face the problem of allocating their energy between investment in intergroup competition and investment in intragroup competition, i. e., an internal struggle for the share of resources obtained through intergroup competition, we can compare such a biological situation with the economic phenomenon of “coopetition” — the cooperation of competing agents with the goal of later competitively dividing the resources won in consequence In the framework of economic researches the effects similar to (ii) — in the framework of large and small group competition the optimal strategy of large group would be complete squeezing out of the second group and monopolization of the market (i. e. large groups tend to act cooperatively) and (iii) — there are conditions, in which the size of the group has a negative impact on productivity of each of its individuals (this effect is called the paradox of group size or Ringelman effect). The general idea of modeling such effects is the idea of proportionality — each individual (an individual/rational agent) decides what share of his forces to invest in intergroup competition and what share to invest in intragroup competition. The group’s gain must be proportional to its total investment in competition, while the individual’s gain is proportional to its contribution to intra-group competition. Despite the prevalence of empirical observations, no gametheoretic model has yet been introduced in which the empirically observed effects can be confirmed. This paper proposes a model that eliminates the problems of previously existing ones and the simulation of Nash equilibrium states within the proposed model allows the above effects to be observed in numerical experiments.

The main aim, formulated in the first part of article, is to carry out detailed numerical studies of the chemical, ionization, optical, and temperature characteristics of the lower ionosphere perturbed by powerful radio emission. The brief review of the main experimental and theoretical researches of physical phenomena occurring in the ionosphere when it is heated by high-power high-frequency radio waves from heating facilities is given. The decisive role of the $D$-region of the ionosphere in the absorption of radio beam energy is shown. A detailed analysis of kinetic processes in the disturbed $D$-region, which is the most complex in kinetic terms, has been performed. It is shown that for a complete description of the ionization-chemical and optical characteristics of the disturbed region, it is necessary to take into account more than 70 components, which, according to their main physical content, can be conveniently divided into five groups. A kinetic model is presented to describe changes in the concentrations of components interacting (the total number of reactions is 259). The system of kinetic equations was solved using a semi-implicit numerical method specially adapted to such problems. Based on the proposed structure, a software package was developed in which the algorithm scheme allowed changing both the content of individual program blocks and their number, which made it possible to conduct detailed numerical studies of individual processes in the behavior of the parameters of the perturbed region. The complete numerical algorithm is based on the two-temperature approximation, in which the main attention was paid to the calculation of the electron temperature, since its behavior is determined by inelastic kinetic processes involving electrons. The formulation of the problem is of a rather general nature and makes it possible to calculate the parameters of the disturbed ionosphere in a wide range of powers and frequencies of radio emission. Based on the developed numerical technique, it is possible to study a wide range of phenomena both in the natural and disturbed ionosphere.

The paper is a study of the mathematical model and kinematics of a parallel spherical manipulator. This type of manipulator was proposed back in the 80s of the last century and has since found application in exoskeletons and rehabilitation robots due to its structure, which allows imitating natural joint movements of the human body.

The Parallel Spherical Manipulator is a robot with three legs and two platforms, a base platform and a mobile platform. Its legs consist of two support links that are arc-shaped. Mathematically, the manipulator can be described using two virtual pyramids that are placed on top of each other.

The paper considers two types of manipulator configurations: classical and asymmetric, and solves basic kinematic problems for each. The study shows that the asymmetric design of the manipulator has the maximum workspace, especially when the motors are mounted at the joints of the manipulator’s links inside legs.

To optimize the parameters of the parallel spherical manipulator, we introduced a metric of usable workspace volume. This metric represents the volume of the sector of the sphere in which the robot does not experience internal collisions or singular states. There are three types of singular states possible within a parallel spherical manipulator — serial, parallel, and mixed singularity. We used all three types of singularities to calculate the useful volume. In our research work, we solved the problem related to maximizing the usable volume of the workspace.

Through our research work, we found that the asymmetric configuration of the spherical manipulator maximizes the workspace when the motors are located at the articulation point of the robot leg support arms. At the same time, the parameter $\beta_1$ must be zero degrees to maximize the workspace. This allowed us to create a prototype robot in which we eliminated the use of lower links in legs in favor of a radiused rail along which the motors run. This allowed us to reduce the linear dimensions of the robot itself and gain on the stiffness of the structure.

The results obtained can be used to optimize the parameters of the parallel spherical manipulator in various industrial and scientific applications, as well as for further research of other types of parallel robots and manipulators.

In this paper, we consider two variants of the concept of sharp minimum for mathematical programming problems with quasiconvex objective function and inequality constraints. It investigated the problem of describing a variant of a simple subgradient method with switching along productive and non-productive steps, for which, on a class of problems with Lipschitz functions, it would be possible to guarantee convergence with the rate of geometric progression to the set of exact solutions or its vicinity. It is important that to implement the proposed method there is no need to know the sharp minimum parameter, which is usually difficult to estimate in practice. To overcome this problem, the authors propose to use a step adjustment procedure similar to that previously proposed by B. T. Polyak. However, in this case, in comparison with the class of problems without constraints, it arises the problem of knowing the exact minimal value of the objective function. The paper describes the conditions for the inexactness of this information, which make it possible to preserve convergence with the rate of geometric progression in the vicinity of the set of minimum points of the problem. Two analogs of the concept of a sharp minimum for problems with inequality constraints are considered. In the first one, the problem of approximation to the exact solution arises only to a pre-selected level of accuracy, for this, it is considered the case when the minimal value of the objective function is unknown; instead, it is given some approximation of this value. We describe conditions on the inexact minimal value of the objective function, under which convergence to the vicinity of the desired set of points with a rate of geometric progression is still preserved. The second considered variant of the sharp minimum does not depend on the desired accuracy of the problem. For this, we propose a slightly different way of checking whether the step is productive, which allows us to guarantee the convergence of the method to the exact solution with the rate of geometric progression in the case of exact information. Convergence estimates are proved under conditions of weak convexity of the constraints and some restrictions on the choice of the initial point, and a corollary is formulated for the convex case when the need for an additional assumption on the choice of the initial point disappears. For both approaches, it has been proven that the distance from the current point to the set of solutions decreases with increasing number of iterations. This, in particular, makes it possible to limit the requirements for the properties of the used functions (Lipschitz-continuous, sharp minimum) only for a bounded set. Some computational experiments are performed, including for the truss topology design problem.

The article deals with the nonlinear boundary-value problem of hydrogen permeability corresponding to the following experiment. A membrane made of the target structural material heated to a sufficiently high temperature serves as the partition in the vacuum chamber. Degassing is performed in advance. A constant pressure of gaseous (molecular) hydrogen is built up at the inlet side. The penetrating flux is determined by mass-spectrometry in the vacuum maintained at the outlet side.

A linear model of dependence on concentration is adopted for the coefficient of dissolved atomic hydrogen diffusion in the bulk. The temperature dependence conforms to the Arrhenius law. The surface processes of dissolution and sorptiondesorption are taken into account in the form of nonlinear dynamic boundary conditions (differential equations for the dynamics of surface concentrations of atomic hydrogen). The characteristic mathematical feature of the boundary-value problem is that concentration time derivatives are included both in the diffusion equation and in the boundary conditions with quadratic nonlinearity. In terms of the general theory of functional differential equations, this leads to the so-called neutral type equations and requires a more complex mathematical apparatus. An iterative computational algorithm of second-(higher- )order accuracy is suggested for solving the corresponding nonlinear boundary-value problem based on explicit-implicit difference schemes. To avoid solving the nonlinear system of equations at every time step, we apply the explicit component of difference scheme to slower sub-processes.

The results of numerical modeling are presented to confirm the fitness of the model to experimental data. The degrees of impact of variations in hydrogen permeability parameters (“derivatives”) on the penetrating flux and the concentration distribution of H atoms through the sample thickness are determined. This knowledge is important, in particular, when designing protective structures against hydrogen embrittlement or membrane technologies for producing high-purity hydrogen. The computational algorithm enables using the model in the analysis of extreme regimes for structural materials (pressure drops, high temperatures, unsteady heating), identifying the limiting factors under specific operating conditions, and saving on costly experiments (especially in deuterium-tritium investigations).

The advent of laser scanning technologies has revolutionized forestry. Their use made it possible to switch from studying woodlands using manual measurements to computer analysis of stereo point images called point clouds.

Automatic calculation of some tree parameters (such as trunk diameter) using a point cloud requires the removal of foliage points. To perform this operation, a preliminary segmentation of the stereo image into the “foliage” and “trunk” classes is required. The solution to this problem often involves the use of machine learning methods.

One of the most popular classifiers used for segmentation of stereo images of trees is a random forest. This classifier is quite demanding on the amount of memory. At the same time, the size of the machine learning model can be critical if it needs to be sent by wire, which is required, for example, when performing distributed learning. In this paper, the goal is to find a classifier that would be less demanding in terms of memory, but at the same time would have comparable segmentation accuracy. The search is performed among classifiers such as logistic regression, naive Bayes classifier, and decision tree. In addition, a method for segmentation refinement performed by a decision tree using logistic regression is being investigated.

The experiments were conducted on data from the collection of the University of Heidelberg. The collection contains hand-marked stereo images of trees of various species, both coniferous and deciduous, typical of the forests of Central Europe.

It has been shown that classification using a decision tree, adjusted using logistic regression, is able to produce a result that is only slightly inferior to the result of a random forest in accuracy, while spending less time and RAM. The difference in balanced accuracy is no more than one percent on all the clouds considered, while the total size and inference time of the decision tree and logistic regression classifiers is an order of magnitude smaller than of the random forest classifier.

The study of elastic waves in porous media is relevant for mineral exploration, the use of porous screens for shock wave damping, and the study of the structure of the earth’s crust. The elastic properties of a porous medium, which can be judged by the propagation velocity of various types of waves, depend on the degree of consolidation of the porous medium. For example, bulk media (sand, glass beads, granular materials) have a low sound velocity (about 100 m/s); compaction of such media is accompanied by a slight increase in velocity, while their consolidation (sandstone, gas hydrate cementation) leads to a multiple increase in the acoustic wave velocity, on the order of 2000–3000 m/s. This paper theoretically investigates the dynamics of a wave pulse in a shock tube containing a layer of a bulk medium. Numerical modeling was performed under experimental conditions. A description of a shock tube experimental setup is provided. The setup consists of a high-pressure volume (HPV), a low-pressure volume (LPV), and a bulk medium section. A shock wave pulse (SWP) is generated by the rupture of a diaphragm between the HPV and LPV. The SWP dynamics are recorded by piezoelectric sensors located flush on the inside of the tube. In the shock tube, equipped with a bulk medium section, the wave experiences multiple reflections from the surface of the porous medium under study and the upper end of the tube. The reflected signals are used as probe pulses to study changes in the porous medium caused by repeated passages of the shock wave pulse, with a period of approximately 10 ms. A mathematical model is used that includes the equations of conservation of mass, momentum, and energy for the gas phase and solid particles with closure relations. The process is described for one-dimensional planar motion of the gas and dispersed phases. The numerical solution utilizes an approximation of the equations based on the control volume method. Numerical results have shown that the proposed model accurately describes, qualitatively and quantitatively, the occurrence of a sharp, short-term increase in the total voltage (peak) during repeated pulse passage through a layer of bulk material, as observed in experiments.

Aberrant alternative splicing of the CD44 gene drives colorectal cancer progression and facilitates the emergence of cancer stem cells. Although biomedical research recognizes this transmembrane glycoprotein as a major catalyst of malignancy, deciphering its multi-isoform regulatory networks remains a complex analytical challenge. To address this knowledge gap, this study presents a machine learning framework designed to decode these biological mechanisms. The author constructed a neural network regressor based on beta regression to model bounded isoform proportions. This computational architecture jointly estimates both the mean and the precision parameters of the underlying probability distribution. Furthermore, the system employs elastic net regularization to perform quantitative feature selection from highdimensional molecular expression data.

The investigation evaluates the proposed framework using gene expression profiles from colorectal cancer patients. The primary objective involves identifying specific ribonucleic acid-binding proteins acting as regulatory splicing factors. The experimental design contrasts two distinct mathematical modeling strategies. The first configuration incorporates an independent ”one-vs-all” approach that treats each transcript variant as an isolated regression target. The second formulation utilizes a structured ”isoform tree” method that directly mirrors hierarchical exon inclusion relationships. Validation experiments on synthetically generated datasets confirmed the mathematical integrity of the network. The model recovered true distribution parameters with precision and exhibited no systematic bias. Comprehensive empirical comparisons subsequently demonstrated that the independent ”one-vs-all” layout consistently outperforms the hierarchical tree configuration in predictive stability and accuracy.

The computational analysis maps the regulatory landscape of the CD44 gene. The framework validates several established splicing factors while uncovering new candidate proteins, including ACO1, NUDT21, and AGO2. Based on these statistical associations, the paper introduces a biological hypothesis. This concept functionally connects intracellular iron metabolism via the ACO1 protein with the shifting balance of CD44 variants. These discoveries provide deeper insights into oncogenic splicing regulation. Ultimately, they highlight molecular targets for future therapeutic interventions aimed at suppressing the cancer stem cell phenotype.

This paper discusses the modeling of the deformation of polymer nanocomposites containing "hard" and "soft" inclusions, using cellular automata and parallel computing. The paper describes an algorithm based on the model, a comparison with experimental data is shown, software for the numerical experiment is described.

High-purity hydrogen is required for clean energy and a variety of chemical technology processes. A considerable part of hydrogen is to be obtained by methane conversion. Different alloys, which may be wellsuited for use in gas-separation plants, were investigated by measuring specific hydrogen permeability. One had to estimate the parameters of diffusion and sorption to numerically model the different scenarios and experimental conditions of the material usage (including extreme ones), and identify the limiting factors. This paper presents a nonlinear model of hydrogen permeability in accordance with the specifics of the experiment, the numerical method for solving the boundary-value problem, and the results of parametric identification for the alloy V₈₅Ni₁₅.