Articles

In the article, the asymptotics of the coefficients of the generating functions are found with a certain accuracy, which can be used to calculate the powers of layers of certain types of partially ordered sets, as well as to calculate the values of the sums of boundary functionals when estimating the number of antichains in such sets. In addition, applications of the obtained results are considered using examples.

The unification problem for parameterized finite state machines consists in finding for two given automata such values of their parameters that these automata will compute the same transduction relations. This presents a quadratic time algorithm for computing the most general unifiers of parameterized deterministic finite state machines. This algorithm is based on the Martelli–Montanari unification algorithm for terms and the equivalence checking algorithm for deterministic finite state machines

The efficiency of network services depends on how applications are distributed in the network. At the same time, these services are to be provided with a certain quality of services and experience for users, i.e.:

1) access to information “at any time anywhere”;

2) seemless integration of informational systems;

3) timely monitoring and analysis of different data sources;

4) migration from a centralized scheme “data download with cleaning followed by analysis and distribution” to the scheme “distributed placement and preprocessing of data and, if necessary, subsequent loading, analysis and distribution”.

One of the key preconditions to provide an acceptable level of services is forecasting the execution time of network services on a variety of virtualization platforms and physical equipment.

The work analyzes approaches to predicting temporal characteristics of network services. The methods are based on operational log data of services and physical equipment, take into account the current and predictable state of hardware and software resources. Among the solutions considered are machine learning models, including a random forest, multilayer perceptrons, and convolutional neural networks.

5G NR communication systems use antenna arrays for directional transmission and reception, which in turn contributes to increased communication performance and efficiency. For duplex systems with frequency division of channels, feedback about the channel status is important. The code page for the configuration of the base station’s antenna array and the antenna ports of the client device is selected through the exchange of reports. The essence of the work is to optimize the exchange procedure, apply and study data compression methods.

Using the technique of Boolean algebras, all 55 implicatively implicit extensions of systems of one-place functions of three-valued logic are defined. It is established that the specified extensions are defined by systems of one-place functions containing from one to three functions.

This paper shows that an arbitrary scale mixture of normal laws can be a stationary distribution of a stochastic difference equation (first-order autoregressive scheme) with random coefficients.

An example is given of what a (random) diffusion coefficient should look like for a particular mixture to be a stationary distribution.

Automated assessment of a group of autonomous agents’ spatial structure reduces development costs for group control systems and eliminates the human factor in analyzing group behavior. To construct a metric for the spatial regularity of an agent group, it is proposed to use a repeatability characteristic of the spatial structure based on autocorrelation methods. The paper examines various methods for calculating autocorrelation using a matrix of pairwise distances between agents, and their application to different types of spatial structures.

The paper considers an approach to solving the problem of noise removal in a large array of sparse data under weak dependence. The approach is based on the method of controlling the false discovery rate (FDR). For this approach, the rate of convergence of the mean–square risk estimator to the normal law is obtained.

The particle method is a numerical method for modeling large systems based on their Lagrangian description.

The discontinuous particle method is of the “particle–particle” type and consists of two main stages: predictor and corrector. At the predictor stage, a particle shift occurs. At the corrector stage, a partner for interaction is selected among the neighbors of the particle, most influencing the local dynamics of the system. The “discontinuity” of the method lies in the method of density correction only one of the interacting particles, due to which the restoration of the distribution density occurs in a minimal region defined by only two selected particles, which leads to smearing of the front by only one particle.

The novelty of the method presented in this article is that The density of the particles is put in the foreground, not their shape. The criterion for restructuring is the preservation of the projection of the mass onto the plane passing through the centers masses of interacting particles. The neighbor for density correction is selected using the “impact parameter”. The density is constructed using two selected interacting particles, which makes it possible to reduce a two-dimensional problem to a one-dimensional one.

The effectiveness of the method is presented using the Crowley test as an example. It is shown that the Runge–Kutta method at the predictor stage significantly increases the accuracy of the numerical solution.

Our Lagrangian approach to constructing the particle method contrasts with another frequently used particle-particle method, the smoothed particle method (SPH).

The inverse Sturm–Liouville problem consists in determining the coefficient (potential) in the stationary Schrцdinger equation on a segment based on a set of eigenvalues. The paper considers a numerical solution to the inverse problem based on a finite set of the first eigenvalues of two Sturm–Liouville problems. The remaining eigenvalues are set according to the classical asymptotics.

The method of solving the inverse spectral problem is based on a one-to-one correspondence between the inverse spectral problem and the nonstationary inverse problem for a telegraphic equation with a variable coefficient (potential). The reduction to a non-stationary problem is carried out analytically by inverting the Laplace transform according to the Mellin formula. An explicit formula for the reaction function in the inverse scattering problem is obtained.

The inverse scattering problem for the telegraphic equation is to determine an unknown coefficient from the reaction function. This problem is solved numerically by the inversion of a difference scheme. The paper presents the results of solving a series of inverse Sturm–Liouville problems. In conclusion, it is noted that the number of given frequencies corresponds to the number of harmonics in the expansion of a desired potential.

The author considers an inverse coefficient problem for a model of sorption dynamics. The inverse problem is reduced to a nonlinear operator equation for an unknown coefficient. The differentiability of the nonlinear operator is proved. The Newton–Kantorovich method and the modified Newton–Kantorovich method are constructed for the numerical solution of the inverse problem. The results of numerical calculations are presented.

When describing the group behavior of high-frequency traders, a boundary value problem arises based on the concept of mean field games. The system consists of two coupled partial differential equations: the Hamilton–Jacobi–Bellman equation, which describes the evolution of the average payoff function in backward time, and the Kolmogorov–Fokker–Planck equation, which describes the evolution of the probability density distribution of traders in forward time. The system is ill-conditioned due to the turnpike effect. Under certain assumptions, it is possible to reduce the system to a set of Riccati equations; however, the question of the well-posedness of the reduced problem remains open. This work investigates this question, specifically the conditions for the existence and uniqueness of the solution to the boundary value problem depending on the model parameters.

Statistical inference often assumes that the distribution being sampled is normal. As observed, following the normal distribution assumption blindly may affect the accuracy of inference and estimation procedures. For this reason, many tests for normality have been proposed in the literature. This paper deals with the problem of testing normality in the case when data consists of a number of small independent samples such that in each small sample observations are independent and identically distributed while from sample to sample they have different parameters but the same type of distribution (call this multi-sample data). In this case it is necessary to use test statistics which do not depent on the parameters. A natural way to exclude the nuisance location parameter is to replace the observations within each small group by diferences. We obtain some estimates of stability of such a decomposition and study and compare the power of eight selected normality tests in the case of multi-sample data. The following tests are considered: the Pearson chi-square test, the Kolmogorov–Smirnov, the Cramer–von Mises, the Anderson-Darling, the Shapiro–Wilk, the Shapiro–Francia, the Jarque–Bera, and the adjusted Jarque–Bera tests. Power comparisons of these eight tests were obtained via the Monte Carlo simulation of sample data generated from several alternative distributions.

This article presents a new algorithm for calculating singularity (boundary) type of ribbon surface of generalized pseudo-Anosov homeomorphism using the surface’s combinatorial description provided with the so-called configuration. As an additional output the fundamental group relators of the ribbon surface are calculated for its co-presentation associated with a given ribbon partition. In comparison to a known algorithm, the one which is presented in this article does not involve any auxiliary sets nor recurrent functions.

The creation of cryptographic systems based on lattice theory is a promising direction in the field of post-quantum cryptography. The aim of this work is to obtain new properties of lattices through related objects — dense packings of equal spheres. The article proposes a method for constructing lattice packings of equal spheres corresponding to the packing density of the “Lambda” series in dimensions 1–24, using a series of coefficients to the height of a fundamental parallelepiped of dimension (n−1): 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2, √−1, 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2, √−1, 1/2, 1/3, 1/2, 0, 1/2, 1/3, 1/2. The construction of lattice packings of equal spheres using this method was carried out up to dimension 11 inclusive.