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 paper considers a method of stabilized hard thresholding in the problem of inverting linear homogeneous operators using wavelet decomposition. In a data model with additive Gaussian noise, an analysis of the unbiased estimate of the mean square risk of this method is carried out. Under the assumption of a long-term dependence between noise coefficients, conditions are given under which the unbiased risk estimate is strongly consistent and asymptotically normal.

The problem of Hausdorff approximation by finite sets of the solution and the value of a multicriteria mixed strategy bimatrix game using a representation based on linear scalarization is considered. For the case of 2×2 matrices, explicit formulas are obtained for constructing nodes of a δ-net on the product of simplices of scalarization parameters. It is proved that the set of the equilibrium values obtained for the net converges in the Hausdorff metric to the solution of the initial game at δ →0. Possibile appearance of degenerate bimatrix games in scalarization is taken account. Examples are given for two-criteria 2×2×2 games.

In this paper, the definitions of generalized Student’s distributions are extended to a wider set of parameters of these distributions and multiplication theorems are given that allow the generalized Student’s and Lomax’s distributions to be represented as scale mixtures of the same distributions but with larger parameters. A similar result is obtained for beta distributions. Analogs of multiplication theorems are obtained for the classical Student’s and Lomax’s distributions as corollaries; in particular, it is shown that the Student’s distribution can be represented as a scale mixture of the Student’s distribution with a large number of degrees of freedom. A representation of strictly stable distributions concentrated on the positive semiaxis is also obtained as scale mixtures of a special distribution that is not stable. This alternative representation complements the multiplication theorem for such strictly stable laws.

We present an efficient algorithm for checking language equivalence of states in top-down deterministic finite tree automata (DFTAs). Unlike string automata, tree automata operate over hierarchical structures, posing unique challenges for algorithmic analysis. Our approach reduces the equivalence checking problem to that of checking the solvability of a system of language-theoretic equations which specify the behavior of a DFTA. By constructing such a system of equations and systematically manipulating with it through substitution and conflict detection rules, we develop a decision procedure that determines whether two states accept the same tree language. We formally prove the correctness and termination of the algorithm and establish its worst-case time complexity as O(n²) under the RAM (Random Access Machine) model of computation augmented with pointers.

The aim of equivalence testing is to verify that two parameters are sufficiently close or, alternatively, that the parameter of interest lies within two pre-specified limits. The two one-sided tests procedure is arguably the most widely known approach for assessing equivalence in the pharmaceutical field. Using a model that accounts for missing data, it is shown analytically that the type I error rate may exceed the nominal significance level. A refined estimate of this error is also obtained. For the standard 2x2 crossover design, a method is proposed that enables control of the type I error in the presence of missing data.

This study presents a modified vector autoregression (VAR) method for forecasting the quality metrics of overlay channels. The modification involves the introduction of weighted coefficients for time series quantiles, with two distinct approaches proposed for calculating these weights: exponential weighting (EVAR) and linear weighting (LVAR). Experimental results demonstrate that the proposed method improves prediction accuracy by 2.6% to 25.2% compared to classical AR and VAR methods, albeit at the expense of higher computational complexity.

It was proved earlier that product xy is a universal function for the class of linear functions depending on two arguments if k=6l±1. Then the criterion of existence of a universal polinomial was obtained for any number of arguments and any k. In this paper we show that product xy is universal for any class of linear functions over Galua field GF(p^m), where p is any prime and m is natural, m⩾2.

A detailed description of the implementation of an algorithm for constructing a variable-structure stabilizing controller for a switched interval linear system with slow switches inaccessible to observation is proposed. It is proposed to use a neural network as an observer of the active modes of a closed system. The simulation results of the constructed stabilization system are presented.

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.