Articles

Physical education is the foundation of a healthy lifestyle. The effectiveness and correctness of physical exercises can't be ensured without the supervision of an expert. The article proposes a system architecture based on hybrid intelligence, in particular, methods for human pose estimation and fuzzy logical inference, which makes it possible to determine the indicators necessary to evaluate exercise performance and form personal recommendations with adjustments to achieve correct performance.

The paper examines a multispecies model of population dynamics of biological communities proposed by U. Dieckmann and R. Law in a space of arbitrary dimension. A system of nonlinear integral equations, arising in the problem of finding the equilibrium state after the three-parameter power-2 closure of the third spatial moments, is investigated. After preliminary transformations, this system is represented as a single operator equation in a Banach space of functional matrices of a special form, which allows describing the equilibrium state as the fixed point of a certain operator. Conditions are formulated that are sufficient to ensure that small changes in the closure parameters lead to small changes in the fixed points set of the operator, in terms of the distance induced by the norm of the Banach space.

A detailed description of the implementation of an algorithm for constructing a variable-structure stabilizing controller for a switched linear discrete system whose operating modes can have different dynamic orders is presented. A neural network is proposed as an observer of the closed-loop system's active modes. Simulation results of the constructed stabilization system are presented.

This work considers the problem of numerical solution of the multicomponent Smoluchowski coagulation equation using a low-rank representation in the tensor train (TT) format. An adaptive time-stepping approach based on a second-order Runge–Kutta method with local error control is proposed and tested. Numerical experiments are carried out for ballistic and generalized Brownian kernels in the two-dimensional case. The use of adaptive time stepping significantly reduces computational time compared to constant step size maintaining low relative error. The advantages of adaptive time stepping are most pronounced in the numerical solution of the problem of finding a steady-state solution of the two-component coagulation equation with a particle source. The results demonstrate the efficiency of adaptive methods for the multicomponent coagulation problems in combination with tensor decompositions.

Universal Boolean functions, determing any linear function by part of their values, were considered earlier. In this paper we studied the problem of constructing functions, determing by part of their values any arbitrary pair of linear functions, that are not negation of each other and differ by the value in zero. We obtained a sequence of such functions with the domain O(n^2) depending on n ⩾ 7 variables.

Each finite binary chain of zeros and ones will be assigned a number, which will be called a measure of the randomness of this chain. The larger this measure, the more "random" the chain will be. A method for constructing chains with the largest measure is proposed.

The paper finds optimal control strategies for energy storages with low efficiency of energy exchange with the electricity network and estimates investment returns for several types of hydrogen energy storages. A method for computation of the optimal storage volume is obtained. The paper shows a high investment attractiveness of hydrogen energy storages in the medium term.

This paper demonstrates the process of deriving macroscopic equations of gas dynamics from a stochastic microscopic model describing the behavior of gases from hard spheres. As the Knudsen number decreases, the resulting equations acquire a form similar to quasi-gasdynamic (QGD) equations with regularizing components that differ from the classical Navier–Stokes system.

A classic example of a simple discrete problem of the motion of a gas consisting of absolutely elastic spheres is considered. This example illustrates the key stages of constructing mathematical models for large systems using stochastic differential equations (SDE) and their computer implementation.

Ludwig Boltzmann derived his fundamental equation based on the balance of the distribution function describing the gas as a continuous medium in the phase space of coordinates and velocities, that is, using the Eulerian approach. We consider a gas as a set of individual particles, the dynamics of which is described by the SDE system, which means the Lagrange formalism.

The proposed model is self-sufficient and does not require setting additional equations of state or configurable parameters.

The article describes the process of forming a feature space for a system that allows monitoring the performance of physical exercises and developing personal recommendations for correcting their performance based on the rules used by an expert trainer. Human Pose Estimation (HPE) methods are used to digitally represent exercise performance. The feature space should represent HPE data (coordinates of human body parts) as a set of feature values for making recommendations (for example, exercise intensity, user endurance). The feature space plays a central role in the development of such systems: the richer it is, the better the recommendations can be implemented.

For a linear-quadratic tracking problem with a target trajectory described by a linear dynamics, convergence of reinforcement learning using policy iteration method is investigated. A proof of convergence is given, and convergence rate is analyzed. Namely, it is proven that the policy iteration method converges and has a quadratic convergence rate under relaxed constraints on the initial control.

In this paper, we propose a compact textual representation of scanned 3D objects. This representation can be obtained from the original point cloud by extracting geometric primitives, forming a topological graph depicting the relative positions of the primitives in the object, and then converting the graph into a string of characters. Our experiments show that many objects can be described quite accurately as a set of geometric primitives. Furthermore, the proposed representation significantly reduces the memory footprint compared to the original point cloud. The object recognition problem can be solved by searching the database for the object whose textual representation is closest in terms of the Levenshtein distance to the textual representation of the object being recognized. Computational experiments show that the proposed representation enables achieving a fairly high recognition accuracy.

It is shown that any scaled mixture of multivariate normal distributions can be a stationary distribution in the multivariate stochastic difference equation (SDE) scheme—a first-order multivariate autoregression with random coefficients. A correspondence is established between the resulting mixture and the behavior of the coefficients generating the stationary distribution.

In this paper, we study the spectral problem for the Sturm-Liouville equation. One of the boundary conditions is a homogeneous Dirichlet condition, and the other is a condition of the third kind, and contains the square of the spectral parameter. A biorthogonal system to the system of eigenfunctions of the task is constructed. The problems of the basis property and the Riesz basis property of system of eigenfunctions are investigated.

In this paper, we consider a numerical solution of the Cauchy problem for a second-order differential equation calculated using the interpolation (implicit) multistep Stormer method. A guaranteed error estimate is found using ellipsoids that contain exact and numerical solutions. The use of ellipsoids avoids the wrapping effect that occurs when using interval analysis methods. It is proposed to modernize the method of obtaining a more accurate estimate of small terms in the recalculation of ellipsoids, which was previously proposed for solving linear differential equations, to the case of nonlinear equations. Formulas for recalculating ellipsoids have been obtained to obtain a guaranteed estimate of the error of the Stormer interpolation multistep method. The results of estimating the error in the numerical solution of nonlinear second-order differential equations on large intervals are presented, demonstrating the effectiveness of the proposed method.

We consider universal functions for subclasses of linear Boolean functions. For classes of linear functions, keeping a constant, using universal functions of small number of variables, we obtained lower and upper bounds on the size of range of definition. For the classes of linear self-dual and linear self-dual, keeping constants, we constructed universal functions with minimal power of range o definition for an arbitrary number of variables.