# 2023 year, volume 27, issue 3 (PDF)the

In this article, for the ﬁrst time in the Russian-language literature, the neurobiological version of Karl Friston’s theory is presented. For the ﬁrst time, this theory is presented holistically, in detail and logically built within the framework of one article and, as far as possible, adapted for understanding by neuroscientists and neurophysiologists. How Friston applies this theory in practice is discussed. A critical analysis of internal problems and contradictions in Friston’s theory is carried out.

**Keywords:** free energy principle, Bayesian brain hypothesis, predictive coding, prediction error, observed states, unobserved states.

We consider the problem of the optimal radio resource management in MU-MIMO 5G cellular networks in Full Buﬀer traﬃc model. Unlike in the networks of the previous generation, in 5G users can share the same frequency resource with a small loss of quality, which leads to a more complicated problem statement. We study properties of the proportionally fair scheduler that meets the problem of maximizing the sum of logarithms of users’ average rates. We propose a computationally simple algorithm based on the studied properties that improves the proportional fairness in comparison with other well-known algorithms. The algorithms were compared using realistic data generated by the Sionna library.

**Keywords:** convex optimization, Karush–Kuhn–Tucker conditions, radio resource management, scheduler, 5G cellular networks, MU-MIMO, full buﬀer, proportional fairness, Sionna.

This article is devoted to ﬁnding the distance between pairs of words in a general ﬁnite alphabet under the action of the operation of replacing one letter into two (adjacent) and calculating the corresponding shortest chain of substitutions (if it exists). Initially, the problem was posed in a more general formulation for a pair of regular languages, but later the formulation of the problem was clariﬁed. At the same time, two possibilities are considered - with the permission to replace letters that were previously absent in the original word or with the prohibition of such operations. This direction is relevant and can be used, for example, in the theory of noise-resistant coding. In particular, it is worth mentioning the Levenstein metric, which inspires similar research on a new type of letter substitution operations.

**Keywords:** text recognition, Levenshtein distance, metric, optimal algorithm.

In this work the computability of one-place partial functions of countable-valued logic by collectives of automata is explored. The class of functions computable by two-automata collectives is found. These are periodic functions and the simplest linear functions, which, starting from some value of the argument x behave like \[ f(x) = x + C \] function. It is shown that the class of one-place partial functions of countable-valued logic computable by three-automata collectives is wider.

**Keywords:** computability, automaton, collectives of automata, periodic functions.