# Computer Sciences

## 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. Based on

## 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

## Implementation, Efficiency Analysis and Quality Evaluation of Clustering Algorithms for Graph Models of Social Networks

The article deals with the community detection problem (the clustering problem) for undirected graphs. The clustering (grouping together of similar objects) is one of the fundamental

tasks in the data analysis. This task is applied in a wide range of areas: image segmentation, marketing, anti-fraud, forecasting, text analysis and much more. At the moment, there is no universal

## On the Convergence of a Greedy Algorithm for the Solution of the Problem for the Construction of Monotone Regression

The paper presents greedy algorithms that use the Frank-Woolf-type approach for finding a sparse monotonic regression. The problem of finding monotonic regression arises in

smoothing an empirical data, in problems of dynamic programming, mathematical statistics and in many other applied problems. The problem is to find a non-decreasing sequence of points with the

lowest error of approximation to the given set of points on the plane. The problem of constructing monotonic regression can be formulated as a convex programming problem with linear constraints

## Genetic Algorithm for Placing Control Points in a Digital Device

The article considers the problem of placing control points in a digital device in order to increase its controlability. The previously known methods for solving this problem were based on a preliminary analysis of the device topology (structure) for the estimation of such parameters as controllability, observability and testability. The corresponding indicators in many well-known systems for analyzing compliance were calculated using software tools. Carrying out such an analysis is a rather laborious process.

## Inaccesible States in Dynamic Systems Associated with Paths and Cycles

Formulas are derived for calculation of the number of inaccesible states in dynamic systems formed by binary vectors encoding orientations of paths and cycles.

## On Lower Bound of Edge Number of Minimal Edge 1-Extension of Starlike Tree

For a given graph G with n nodes, we say that graph G∗ is its 1-edge extension if for each edge e of G∗ the subgraph G∗ −e contains graph G up to isomorphism. Graph G∗ is minimal 1-edge extension of graph G if G∗ has n nodes and there is no 1-edge extension with n nodes of graph G having fewer edges than G. A tree is called starlike if it has exactly one node of degree greater than two. We give a lower bound of edge number of minimal edge 1-extension of starlike tree and provide family on which this bound is achieved.

## Indices in Dynamical System (B, δ) of Binary Vectors

An algorithm is proposed for computation of indices of states in dynamical system (B, δ), whose states are binary vectors and evolutional function δ transforms vectors according to the following rules: the initial component 0 (if exists) is replaced by 1, every digram 10 by 01, and the final 1 (if exists) by 0. Correctness of the algorithm is proven..

## The Continuous Schedule with Two-Element Instructions

For two-element instructions conditions of existence of the continuous schedule of service are found.