# Computer Sciences

## Zero-Knowledge Proof Authentication Protocols

The paper presented the comparative analysis of the authentication Shnorr’s protocol and the authentication protocol based on the task of finding a Hamilton cycle in the graph. It is shown that with the use of CUDA technology the productivity of protocols on graphs is a shighas Shnorr’s protocol productivity. Theim portance of such research is that protocols on graphs (the authentication protocol on the basis of the proof of graph isomorphism, the authentication protocol based on the task of finding a Hamilton cycle in the graph, etc.) have the property of zero-know ledge proof.

## Multiple Hedging on Energy Market

The article is devoted to the calculation of the dynamic hedge ratio based on three different types of volatility models, among which S-BEKK-GARCH model takes into account cross-sectional dependence. The hedging strategy is built for eight stock-futures pairs on energy market in Russia.

## Hybrid Automation Extended Model

An extended model of hybrid automata for dynamic systems is considered, where, along with a discrete control subsystem and control objects with lumped parameters, there are control objects with distributed parameters (linear and stationary from the point of view of automatic control theory). The possibility of software implementation of an extended model of hybrid automata on embedded computing systems is shown.

## Learning Neural Network Controllers for Stabilizing Hybrid Dynamic Systems

Control modules based on artiﬁcial neural networks (NN) are often used for controlling objects with lumped parameters. Controled objects in such systems have ﬁnite set of natural oscillation frequencies.

## On a Goodman–Hedetniemi Sufﬁcient Condition for the Graph Hamiltonicity

In 1859 the Irish mathematician Sir William Rowan Hamilt onpropose daga mein which it was required to ﬁnd a dodeca hedron bypass around its edges with a return to the starting point. In his honor, the corresponding path in the graph was later called the Hamiltonian cycle: it is the spanning cycle in the graph, that is, the cycle passing through all the vertices of the graph. A graph containing a Hamiltonian cycle is said to be Hamiltonian.

## Empirical Analysis of Algorithms for Solving the Index Tracking Problem

Index tracking is a passive financial strategy that tries to replicate the performance of a given index or benchmark. The aim of investor is to find the weights of assets in her/his portfolio that minimize the tracking error, i.e. difference between the performance of the index and the portfolio. The paper considers the index tracking problem with cardinality constraint, i.e. the limit on the number of assets in the portfolio with non-zero weights.

## Convergent and Hyperconvergent Computing Systems

In the work the questions of construction of hyperconvergent computer systems and their functioning on the basis of a program-configurable network are considered. The features of the OpenFlow protocol and technological solutions that transfer control of the software-configurable network to a dedicated controller (server) are presented. A graph model of resource management of a hyperconvergent computer system is proposed that meets the requirements of a given quality of service on the one hand and economic requirements on the other.

## Development of Speech Recognition Systems Based on Hidden Markov Models of Individual Words

The results of the development of software modules implementing the speech recognition system based on the hidden Markov models of individual words and the use of linear prediction in the coding of signs of an audio signal are presented. The structure of the speech recognition system is based on the hidden Markov models of individual words, consisting of four modules: a module for extracting words from the sound stream, a module for analyzing the features of a word, a module for learning the hidden Markov models, and a word recognition module.