# 2022 year, volume 26, issue 2 (PDF)

Goal. To discuss the cognitive level and substantiate the basic principle of artificial intelligence of smart systems, human-centricity - subordination and service to a person (master). Methods. The central role of the radical (redundant) model of the theater of operations of a smart system as the core of artificial intelligence is emphasized. The stages of creating an ultrasystem to ensure the information and system security of a smart system, its intelligent planning of actions and situational behavior management in the theater of its actions, including the development of the system itself and the reasonable transformation of the theater of its actions, are discussed. Results. There are five main levels of artificial intelligence development. The features of the first and second signaling systems (primary and language sensoriums) are studied. The information and system irregularities of a smart system are highlighted as points of growth of its intellectual development based on machine learning. The collective artificial intelligence of a group of smart systems is being investigated within the framework of their unified theater of action and subordination to the human master of the grouping. The principle of human-centric goal-setting of any technical intelligent system, determined by its unconditional subordination to its human owner, is substantiated. The corresponding requirements for the ultrasystem and its language operating system of intelligent planning and situational management of the behavior of a separate smart system or a team of smart systems are discussed. The problems of the development of a separate smart system, the reengineering of a collective of such systems and the problem of reasonable transformation of the theater of actions of such a collective are considered.

**Keywords:** cognitiveness of natural intelligence, automated smart
system, collective artificial intelligence, radical, language, Internet of
Things, interface, information system security, tactical and operational
planning of smart system actions.

This article discusses the problem of predicting sports results using data analysis and machine learning methods and determining the quality of such a forecast. Also giving a comparison of the constructed model with the model used by bookmakers.

**Keywords:** machine learning, sports performance prediction, data
analysis, classification.

The adverse clinical outcome risk assessing model is considering. It is proposed the unsupervised learning method application for a binary classification problem with a single answer training set. A truncated set is a dataset with a small examples number of one of the classes (favorable or unfavorable). A truncated set is also the data obtained after original table clearing. Some results of this model application are presented in a research [1] conducted by the scientists of the National Research Center for Therapy and Preventive Medicine of the Ministry of Health of the Russian Federation and the scientists of the Faculty of Mechanics and Mathematics of the Lomonosov Moscow State University. It is proposed the general method for such problems.

**Keywords:** neural networks, unsupervised learning, Auto-associative
neural networks, autoencoder, adverse clinical outcome.

This work considers the question of discovering an upper-bound estimation of parameters quantity of neural network architecture well-approximating particle-linear dependances. The main result of this article consists of the theorem asserting that any particle-linear function can be approximated with any degree of precision on the big part of space by neural network with sigmoidal activation functions. This theorem has a constructive proof, i.e. neural network architecture with mentioned features building explicitly.

**Keywords:** schemes of functional elements, neural networks,
architecture, approximation, upper-bound estimation, particle-linear
functions.

New mathematical concepts are often introduced with some quantifier definitions. If we have a sufficiently large stock of such notions, it can allow to reformulate the new quantifier definitions in a quantifier-free form. This makes the problem of finding basic concepts, which make further quantifiable definition redundant, worth considering. Creating computer programs that automatically introduce such bases is also worth considering. The present paper considers the quantifier expressibility in 4 algebraic systems. This paper provides bases of quantifier expressibility of small depth.

**Keywords:** predicate logic, quantifier expressibility, algebraic
system

In this paper, a new mathematical model of cryptographic protocols is presented, and examples of the application of this model for solving problems of verification of cryptographic protocols are given. Cryptographic protocols are distributed algorithms designed to enable the transmission of confidential information in an insecure environment. They are used, for example, in electronic payments, electronic voting procedures, systems for accessing confidential data, etc. Errors in cryptographic protocols can lead to great damage, therefore it is necessary to use mathematical methods to substantiate the various properties of correctness and security of cryptographic protocols. The paper outlines new methods for formal verification of cryptographic protocols.

**Keywords:** cryptographic protocols, sequential processes,
distributed processes, verification.

For a finite system of piecewise parallel functions implemented by schemes of linear elements and Heaviside functions, the criterion for the expressiveness of piecewise constant functions is obtained, supplemented by all single linear functions. Thus, the criterion of expressiveness of the binary classifier implemented by the McCulloch-Pitts neural scheme is obtained.

**Keywords:** Piecewise constant function, piecewise parallel function,
completeness problem, expressibility problem, McCulloch-Pitts neural
circuits.