# Computer Sciences

## Construction of All Nonisomorphic Minimal Vertex Extensions of the Graph by the Method of Canonical Representatives

In 1976 John P. Hayes proposed a graph model for investigating the fault tolerance of discrete systems. The technical system is mapped to a graph. The elements of the system correspond to the vertices of the graph, and links between the elements correspond to edges or arcs of the graph. Failure of a system element refers to the removal of the corresponding vertex from the system graph along with all its edges. Later together with Frank Harary the model was extended to links failures. The formalization of a fault-tolerant system implementation is the extension of the graph.

## On Optimization of Reconfiguration Procedure in Multiprocessor Systems

Some questions concerned to organization of programming procedure being optimized in accordance with a number of parameters for multiprocessor fault-tolerant system’s components in cosideration with compensation by properly functioned components of possible faults are reviewed in the paper. An algorithm to form a subsets of processor elements is developed and an anayitic expressions allow to reduce the time or hardware spendings in such systems are produced.

## Mathematical Models for Evaluation of the Higher Education System Functions with DEA Approach

The purpose of this research is to develop the Data Envelopment Analysis (DEA) methodology for modeling of the assessment of the regional higher education systems effectiveness. The importance and topicality of this study is based on the increasing role of universities in the economic development of regions and countries in recent decades as well as the need to develop approaches for assessing the university effectiveness, and using mathematical models and methods for these goals.

## Classification and Recognition of Structures of Genetic Sequences

For solving problems of determining the relationships between the properties of organisms and the properties of the corresponding genetic sequences, we proposed a classification of genetic sequences based on numerical indicators of recurrent and Z-recurrent shapes, which define the structure of functional relationships of elements in sequences. For numerical indicators of recurrent and Z-recurrent shapes, we introduce a method of classification of genetic sequences.

## A Method of Protected Distribution of Data Among Unreliable and Untrusted Nodes

We consider a model of protecting the confidentiality and recoverability of data in a distributed storage system. It is assumed that in- formational blocks are coded into the code blocks. Then the blocks are divided into parts and distributed among repositories of the distributed storage. A modification of the code noising method is con- structed which simultaneously provides computational resistance to coalition attacks on confidentiality of stored data. Moreover, the modification also provides protection from the failure of a part of the storage nodes.

## Fuzzy Linear Automata Testing

The article deals with the problem of synthesis of tests for fuzzy linear automata (FLA). Now several varieties of FLA are used as models of real fuzzy systems. The article introduces and investigates one particular type of FLA. The fuzziness of the behavior of the automaton is suggested to appear due to the use of elements of a special type in the characteristic matrices. Each such element is a certain set of elements of the field over which the FLA is given.

## Administration of Virtual Data Processing Center over OpenFlow

This paper researches the building principles and administration of virtual data processing centers based on hyper-converged systems over OpenFlow. We provide the implementation features of such virtual centers on the basis of software-defined networking that is managed by a dedicated controller (a server). We suggest the graph administration model of hyper-converged system resources compliant with required performance on the one hand and economic requirements on the other.

## The Use of a Genetic Algorithm in Modeling the Electrophysical Properties of a Layered Nanocomposite

The research proposes an approach to solving the problem of selecting layered nanocomposite components with given electrical properties. The known methods for modeling the nanocomposites electrical characteristics are based on a preliminary analysis of such characteristics as the dielectric constant and electrical conductivity of the materials that make up a nanocomposite. The study proposes an algorithm for the selection of components of a layered nanocomposite using a genetic algorithm.

## Estimation of Quality of Non-Stationary Systems on the Return Frequency Characteristic Plane

Direct quality parameters, such as time of regulation, overshoot, damping decrement are widely used for estimation of linear systems quality. Alongside with direct parameters indirect estimations of quality are used. One of such quality parameters for nonlinear systems is the degree of stability or response speed. A number of research studies show that properties of nonlinear systems investigation is reduced to the analysis of absolute stability of processes.

## Prevention of Accidental Combinations of Events in the Control of Human-Machine Systems

In the work the problem of accidental combinations of events is investigated. An accidental combination of events is a set of defects in equipment, software and human errors, relatively non-dangerous separately but leading to an accident when they occur in a certain order at a certain time interval. Modern warning tools can parry mainly individual adverse effects and to effectively prevent critical modes it is necessary to provide mathematical analysis of systems for accidental combinations of events at different time intervals.