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The research is devoted to the estimation the structural complexity of programs. The algorithm of finding cyclomatic routes for program executions is described. By now, two directions of obtaining estimates for the complexity estimates in software modules have been defined: structural and statistical. Both directions connect the value of program complexity with the labor intensity related to their development. The structural complexity of program modules is determined by the number of interacting components, the number and complexity of links between them. The complexity of a program's behavior depends to a large extent on the set of routes through which it is executed. The complexity metric obtained from these positions allows us to determine estimates of the cost of designing the program as a whole, as well as to identify the modules that are likely to contain the most errors, especially the logical ones.

Relevance. The practical importance of the tasks of utility networks design, namely, the problems of optimizing the structure of the main pipeline according to given criteria, such as efficiency, reliability etc., under conditions of limitations, for example, the compatibility of various types of utilities. Since the main pipeline is laid on the ground with various physical and geological factors, natural and situational conditions, it is advisable to take the reliability of its operation as a global criterion. The task of network optimization is proposed in the form of displaying the main pipeline along the selected routes in three-dimensional space, which considers various existing communications and objects, as well as elevation marks of the area. The paper presents the problems of optimizing networks, both in the continuous case and in the discrete case, and also studies various indicators of the reliability of the operation of the main pipeline. Aim. To develop a model for laying the main pipeline in three-dimensional space, considering the reliability of the pipeline transport; to conduct a comparative analysis for various reliability indicators and topologies of the main pipeline. Objects. Utility communications and networks laid in three-dimensional space. Methods. Calculus of variations, discrete optimization methods, graph theory and hypernet theory methods, network reliability analysis methods. Results. The task of optimizing the main pipeline transport is given taking into account its nesting along the route in three-dimensional space with the choice of an optimization criterion (economic efficiency, reliability, etc.). The problem is presented in the form of continuous and discrete formulations, which is important for its development both within the theory of the calculus of variations and discrete optimization. In this work, the problem was studied within the framework of the theory of graphs and hypernets, which allow, firstly, taking into account the nesting of one structure (main pipeline) into another (a discrete analogue of three-dimensional space) and, secondly, clearly illustrating the results of numerical experiments. It is shown that under the conditions of a given variants for laying a secondary network along the primary channels, various optimal structures are obtained when considering various reliability indicators as a criterion, which can be used to implement a design solution for the construction and operation of pipeline transport for various purposes.

The report is aimed at improving the software systems of general-purpose graph editors for the needs of object search and administration of the metadata network of the electronic library. One of the trends in the development of electronic libraries is the enrichment and complication of metadata due to the content of electronic documents stored in the library. Metadata helps to make better use of library collections, as it reflects the relevant areas of knowledge in a structural form, describing the context, content and structure of an electronic document throughout its life cycle. The idea of analyzing the structure of scientific discourse in order to display it in metadata dates back to the last years of the twentieth century, when the theory of structural rhetoric appeared, which continued its development in the first decade of the new century. The idea of modeling scientific and technological progress based on a network of problems dates back to the same years. In such a system, the user sees on the computer screen a complex network consisting of a network of scientific and technical problems, a network of innovative cycles of technical products related to the problems shown, and a network of library documents. Problem networks are visualized by a representative of a special class of applied software systems – a graph editor that reads a network representation in text or binary format from a file. The graph editor builds network elements in its memory in the form of objects and shows them in its windows in two forms: in the form of a marked-up colored graph and in the form of a table displaying the attributes of objects. The urgency of the problem of choosing a basic software tool and its subsequent modification for working with metadata networks of electronic libraries is revealed. The main provisions of the modification of the editor interface are presented, which allow adapting the graph editor software system to work with the metadata network of the electronic library. The proposed concept of the editor interface allows you to use an extended instance of a special representative of a class of similar software systems for the needs of an electronic library.

Automata theory is one of the branches of mathematical cybernetics, that studies information transducers that arise in many applied problems. The major objective of automata theory is to develop methods by which one can describe and analyze the dynamic behavior of discrete systems. In this paper, we consider automata without output signals (called semiautomata). Depending on study tasks, semiautomata are considered, for which the set of states is equipped with additional mathematical structure preserved by the transition function of semiautomata. We investigate semiautomata over graphs and call them graphic semiautomata. For graphs $G$ a universal graphic semiautomaton $\rm{Atm}(G)$ is the universally attracted object in the category of graphic semiautomata, for which the set of states is equipped with the structure of the graph $G$. The input signal semigroup of the universal graphic semiautomaton is $S(G) = \rm{End}\ G$. It may be considered as a derived algebraic system of the mathematical object $\rm{Atm}(G)$. It is common knowledge that properties of the semigroup are closely interconnected with properties of the algebraic structure of the semiautomaton. This suggests that universal graphic semiautomata may be researched using their input signal semigroups. In this article, we investigate the concrete characterization problem of graphic semiautomata over quasi-acyclic reflexive graphs. The main result of our study states necessary and sufficient conditions for a semiautomaton to be a universal graphic semiautomaton over quasi-acyclic reflexive graphs.

Purpose of the work is to study the dynamics of the asymptotic behavior of trajectories of discrete Lotka–Volterra dynamical systems with homogeneous tournaments operating in an arbitrary (m − 1)-dimensional simplex. It is known that a dynamic system is an object or a process for which the concept of a state is uniquely defined as a set of certain quantities at a given time, and a law describing the evolution of initial state over time is given. Mainly in questions of population genetics, biology, ecology, epidemiology and economics, systems of nonlinear differential equations describing the evolution of the process under study often arise. Since the Lotka–Volterra equations often arise in life phenomena, the main purpose of the work is to study the trajectories of discrete dynamical Lotka–Volterra systems using elements of graph theory. Methods. In the paper cards of fixed points are constructed for quadratic Lotka–Volterra mappings, that allow describing the dynamics of the systems under consideration. Results. Using cards of fixed points of a discrete dynamical system, criteria for the existence of fixed points with odd nonzero coordinates are given in a particular case, and these results on the location of fixed points of Lotka–Volterra systems are generalized accordingly in the case of an arbitrary simplex. The main results are theorems 5–9, which allow us to describe the dynamics of these systems arising in a number of genetic, epidemiological and ecological models. Conclusion. The results obtained in the paper give a detailed description of the dynamics of the trajectories of Lotka–Volterra maps with homogeneous tournaments. The map of fixed points highlights a specific area in the simplex that is most important and interesting for studying the dynamics of these maps. The results obtained are applicable in environmental problems, for example, to describe and study the cycle of biogens.

The paper investigates the effectiveness of using radiomics methods to extract features from medical images when solving the problem of recognizing cerebral aneurysms using a graph neural network. The construction of a graph model of the vascular network based on the results of angiography of cerebral vessels allows you to move from the original image (an ordered sequence of voxel values) to a more structured representation of the original data, consisting of a set of local node descriptors and connections between them. This representation reflects the most significant features of the recognized objects and allows you to significantly reduce the amount of processed data. In this regard, one of the key aspects of successfully solving the problem of recognizing cerebral aneurysms based on a graph model of the vascular network is the formation of an informative feature description for graph nodes. In this paper, the characteristic description of graph nodes corresponds to image biomarkers – quantitative indicators characterizing various pathological changes – obtained using radiomics methods. A graph neural network is used as an algorithm for recognizing aneurysms. The paper considers the shape characteristics of the selected image areas, histogram and texture features, as well as some other characteristics. To identify the most informative features, a number of computational experiments were conducted using various sets of features. Based on the statistical analysis of the experimental results, it was concluded that the largest part of the information significant for the recognition of cerebral aneurysms is contained in the shape characteristics of the areas highlighted in the image, as well as in histogram features. However, the experimental results also showed that the constructed feature description is not sufficient for accurate recognition of cerebral aneurysms, and it requires expansion due to the introduction of new more complex indicators.

It is well known that the problem of algorithms for estimating the similarity of graphs rests on the complexity of their computation. Most proposed algorithms for estimating graph similarity are based on Ullman’s algorithm. The philosophy of Ullmann's algorithm is to work with adjacency matrices. Ulman’s algorithm has high computational complexity, and the application of parallel computations, including on video cards, leaves Ullman’s algorithm NP-complex. In addition, Ullmann’s algorithm just provides information on whether graphs are isomorphic or whether one of them is a subgraph of the other, and additional computations are needed to obtain a numerical estimate of similarity. The wireframe similarity estimation algorithm proposed in the article calls to move away from the philosophy of Ullmann’s algorithm, namely, work with adjacency matrices. The new algorithm is based on the construction and study of frameworks of compared graphs. The article provides a definition and an algorithm for constructing a graph framework, which, in turn, are built on the basis of a previously published iterative algorithm for finding all the shortest paths between two vertices. The wireframe algorithm has asymptotic complexity O(|V|2), it is able to detect graph homomorphism and quantify the similarity of two compared graphs.

In modern practice of diagnosing complex technical devices, along with developing built-in diagnostic systems, a wide niche is still occupied by troubleshooting based on logical patterns. Logical algorithms for troubleshooting are the basis for diagnostic maps of car power plants. They do not always have an optimal structure in terms of achieving the lowest cost and time indicators of the diagnostic process. Thus, the problem of structural optimization of logical diagnostic algorithms is relevant, as well as the formation of a simple and understandable standardized procedure for optimizing diagnostic algorithms. The paper substantiates the criterion for evaluating the effectiveness of a diagnostic algorithm and the structure of the initial data for calculating the criterion. Variants of visual formalization of a diagnostic map are proposed in order to increase visibility and carry out further actions to optimize its structure, as well as options for formalizing visual information in digital form for its processing by computing means. The procedure for optimizing the structure in the JavaScript programming language has been developed and implemented. The reverse transition from a digital form to graphic one is described, which will immediately introduce the results into the practice of car service organizations. An analysis of a sample of 22 diagnostic maps has shown that the proposed optimization method will reduce the average cost of diagnostics up to 17 %.

Objective. The aim of the study is to build emulators of the main sensors of a small spacecraft (SC).Method. The quality of recovery is determined by the standard deviation (RMS) of the data from the standards. The study is based on the application of the dynamic programming method.Result. A review of works in the field of application of stable characteristics - invariants, in the applied areas of pattern recognition and state control of complex technical systems is carried out. A method aimed at identifying failures and building small spacecraft sensor emulators based on the analysis of stable indicators: correlation and covariance coefficients is proposed and tested. The proposed approach makes it possible to increase the overall reliability of the information-measuring system of a small spacecraft (SC). In the future, to emulate a failed sensor, it is planned to use multiple correlation of time sequences.Conclusion. In the general case, recognition is reduced to comparing the graph structures of objects to the correct matching of hierarchical image models based on various invariants. Control of the states of complex systems is based on the use of stable characteristics that act as invariant or subinvariant descriptors. Invariants in various applications help to recognize the current situation with a sufficient degree of accuracy, usually reducing the dimension of the problem.

Обсуждается методика использования компьютера при изучении вузовских курсов «Дискретная математика» и «Теория графов». В работе показывается применение пакета символьных вычислений Maple для обнаружения свойств основных матриц графа и экспериментальной проверки этих свойств.

The paper introduces a new method for modeling a terminological field with its content and structure. The method is a foundation for a computer program able to evaluate students’ professional knowledge both in qualitative and quantitative aspects. The method includes several stages: processing the lexical content of a terminological field, revealing elements that structure this content, and graphical representation of the terminological field model. The list of methods included the thesaurus approach and the componential analysis of lexical meaning. The thesaurus approach detects the basic types of semantic relationships between lexical units within a terminological field. The componential analysis explicates elements that arrange these units. The model is represented as a tree graph structure, which is ideal for visualizing multi-level hierarchic structures. This graph consists of two types of elements: terms and structure units. The method is designed to be flexible and versatile so that it can be effectively applied to any terminological field. The method can be applied to a specific terminological field in order to build its model with particular regard to all characteristic features of its content and structure

Introduction. The paper deals with the problem of automated construction of a local area network using tools and methods for traffic analysis at the link layer of OSI model. The problem is caused by two factors. These are difficulties of the manual determination of the communication between equipment and the lack of physical access to communication lines of an already functioning network. The purpose of the work is to reduce the time spent on building a local network diagram through automating the process of determining the communication between the equipment.Materials and Methods. To solve the set tasks, a method for determining the relative location of devices is proposed. The network adapters of a specialized software and hardware complex, which are connected to a communication line break at different points of the network, are used in opposite directions. The method used is based on calculations of intersections of address sets received from these adapters. The structural schemes of the construction of such a software and hardware complex and the requirements for it are given. The methods of obtaining MAC addresses from transit packets are described. Examples of libraries of software components for performing this operation are given. The structure of a relational database is proposed for storing the received data. The format and content of the fields of its table are described.Results. Using the developed methods, a typical example of an Ethernet network shows a way to determine the relative location of end devices specified by their MAC addresses, as well as at least two switches located between them. The signs by which it is possible to judge the presence of switching equipment in a particular segment are determined. A method is proposed that enables through using a set of relational operations, to sequentially refine the network topology until the required accuracy is achieved.Discussion and Conclusions. The results obtained can be used under the administration of large local networks with an extensive structure. The proposed approach allows you to reduce the time required for building a scheme. This is possible due to the automation of the process of obtaining information about devices operating on the network and their mutual location.

There is a problem of finding the shortest paths between two vertices in an unweighted, undirected graph, which is aggravated by the fact that the available algorithms for finding all paths have a complexity of at least . The proposed new method for finding the shortest path in an unweighted undirected graph allows obtaining all shortest paths with acceptable complexity , and on average, . The existing algorithm for finding all paths, the Floyd-Warshall algorithm has complexity , Deikastra's algorithm, although it has complexity , but to find all the paths, you need to recalculate the paths to find all the paths between two vertices in the graph. This article describes a new iterative algorithm, justifies its asymptotic complexity, and compares the time and results of work with Deikasta's algorithm, thereby proving that the justification for asymptotic complexity is justified correctly, and the algorithm works much faster.

Logistics as a science and as an area of practical knowledge has recently aroused increasing interest, since its activities are multifaceted. Logistics includes the management of transport, warehousing, inventory, human resources, the organization of information systems, commercial activities and much more. At the same time, there is a novelty of the approach in logistics - the organic interconnection, the integration of the above areas into a single management of material flows. Transport logistics refers to the main sections of the logistics of the movement of resources. Transport logistics allows you to solve many different problems of varying complexity and scale on a scientific basis. The article deals with a mathematical model of a logistics problem with variable transportation tariffs. Numerical solutions of the mathematical model by a symmetric algorithm, based on the averaging of variable tariffs, are given. The ways of transportation cost reduction are considered. Automation of information flows accompanying cargo flows is one of the most essential technical components of logistics. The use of methods of logistics opens up new reserves for creation of competitive advantage of this or that firm on the basis of maximum satisfaction of clients’ demands. Purpose. Finding the minimum path by the symmetric algorithm method; investigate the efficiency of the warehouse location. Methodology in article use methods of solving the transportation problem, elements of graph theory, elements of the theory of fuzzy sets. Results. A study was conducted on the efficiency of the location of the warehouse, the method of symmetric algorithm was found the minimum path; estimated the cost of the input measures. Practical implications it is expedient to apply the received results in transportation management, resource flow management (warehouses).

In the article we consider graphs whose vertices or edges are colored in a given number of colors — vertex and edge colorings. The study of colorings of graphs began in the middle of the 19th century, but the main attention is paid to proper colorings, in which the restriction applies that the colors of adjacent vertices or edges must be different. This paper considers colorings of graphs without any restrictions. We study the problem of generating all non-isomorphic vertex and edge $k$-colorings of a given graph without direct checking for isomorphism. The problem of generating non-isomorphic edge $k$-colorings is reduced to the problem of constructing all vertex $k$-colorings of a graph. Methods for generating graphs without direct checking for isomorphism or isomorphism rejection are based on the method of canonical representatives. The idea of the method is that a method for encoding graphs is proposed and a certain rule is chosen according to which one of all isomorphic graphs is declared canonical. All codes are built and only the canonical ones are accepted. Often, the representative with the largest or smallest code is chosen as the canonical one. In practice, generating all codes requires large computational resources; therefore, various methods of enumeration optimization are used. The paper proposes two algorithms for solving the problem of generating vertex $k$-colorings with isomorphism rejection by McKay and Reed – Faradzhev methods. A comparison of the proposed algorithms for generating colorings on two classes of graphs — paths and cycles is made. Computational experiments show that the Reed – Faradzhev method is faster for paths and cycles.

The research focuses on the metrics that allow assessing the stability of a graph and centrality measures. Their calculation underlies the percolation of the key elements of the graph. The experiment involved methods for calculating the average path length of vertex connectivity, clustering coefficient, and graph efficiency based on graph theory. To determine the optimal network stability metric, the principal component method was used, based on the theoretical provisions of mathematical statistics. In this study, the authors solved two scientific tasks: the main and auxiliary ones. The latter was to review the existing network stability metrics, which allowed them to choose the optimal one. The choice of the metrics was carried out using the principal component method. As a result, the average path length proved to be optimal. The solution of the auxiliary problem enabled the authors to analyze the ways to reduce the network stability based on the sequential removal of key elements, which is the main scientific task of the study. The analysis revealed that the nodes whose importance is expressed based on the measurement of centrality by degree are best suited for reducing the network stability. To estimate the stability of networks, an original complex two-criterion coefficient was developed. The analysis of the ways to reduce the stability was carried out by measuring this coefficient in model and real networks. Thus, testing of the proposed methods confirmed their efficiency and enabled their application in various fields of science and technology, e.g., sociology, medicine, physics and radio engineering.

Disadvantages of the traditional description of a mechanical engineering product are shown, which are based on technological features oriented to single, typical and group operations of the technological process. It is proposed to represent the design of the product and its parts with a structured set of relevant technological modules, in the form of a graph of a hierarchical structure. The availability of a unified methodological base makes it possible to control the development of constructively complex products, minimize duplication in the creation of new designs and effectively develope resource-saving technologies for their manufacture. The choice of the method for assessing the manufacturability of the product design is substantiated by the labor intensity of the processes at the stages of its life cycle and the formation of a set of criteria that generalize the assessment of design and technological solutions by coefficients that take into account their degree of influence on the technical and economic indicators of the processes. On the basis of a technical and economic analysis, a method for the integral assessment of production manufacturability in the product life cycle has been formed. The method combines various coefficients of manufacturability, taking into account the degree of their influence on the labor intensity of production and maintenance, repair and disposal of the product structure. Based on the results of the feasibility study, it was proposed to understand the manufacturability of the product design at the stages of its production and disposal as production adaptability.

Due to the increasing complexity of radio electronic equipment, the problem of its reliability becomes much more acute. At the same time, the task of evaluating on-board equipment at the design and production stages becomes very urgent. An important issue is also the reliable determination of numerical values of its reliability indicators. Ground-based experimental testing of samples of on-board radio-electronic facilities, devices, assemblies and units facilitates the solution of this problem. Inthe course of this testing, various tests conducted. It been shown that the timeliest information about the quality and reliability of the equipment can be obtained from autonomous tests. In the article, the choice of an autonomous test facility has made. Amicroprocessor-based temperature controller chosen as an autonomous test object. The expert evaluation method used to select the object. Analysis of specifications carried out. The scope of autonomous tests was determined. An algorithm for autonomous testing of on-board radio electronic equipment of spacecraft was developed. It has properties of discreteness, determinacy, limb and mass. The development of the autonomous test algorithm takes more account of the specifics of the technology used to manufacture the product under test and the test sequence. One of the options for mathematical modelling of the process of selecting test equipment for autonomous tests been considered.

Graphs, for which the degree of a certain vertex is equal to (d + 1) and the degrees of all other vertices are at most d , d ≥ 3 , were considered. Properties were obtained to color vertices of these graphs in d colors.

The paper discusses a method of visual attention based on vertex ranking of graphs on the basis of image features. The aim of the research is to develop a method that allows high-precision detection of objects in images with low color contrast between the selected and background areas. The image is pre-segmented into regions to calculate the saliency map. The graph is based on regions. Each region is associated with related regions, as well as with areas adjacent to adjacent regions. The regions are vertices of the graph. The vertices of the graph are ranked according to the characteristics of the corresponding image areas. The scope is highlighted based on requests from background areas. The saliency map is determined based on background area queries. Regions adjacent to the edges of the image belong to the background areas. Color features of the image were used in the existing approach of visual attention based on the manifold ranking. Texture features and shape features are additionally used in the proposed method to improve accuracy. Gabor's energy function is used to calculate texture features. The distance between centers of the regions is calculated by analyzing the form. The proposed method has shown good results for detecting objects in images in which the background color and object color are in similar ranges. The experimental results are presented on test images. Precision-recall curves showing the advantage of the developed method are constructed.

processing systems is to identify authors of publications based on bibliographic data. This task is an important citation analysis system for publications. Information in such systems is automatically collected from various sources. It is necessary to automatically process the collected bibliographic data. Such a task is important for scientometric systems that analyze numerous types of scientific products (publications, dissertations, patents, lectures, etc.) too. The accuracy of the author's definition affects the quality of the results of scientometric assessment of the scientific activity of subjects. In addition, the accuracy of determining the author is important for protecting systems that use modern models of logical access control. The article describes an algorithm developed to solve this problem, which is currently used in the scientometric system IAS ISTINA. This system has been used since 2012 to collect data on scientific activities at Moscow State University. M.V. Lomonosov. The system processes data on scientific publications, pedagogical activity, research, dissertations, participation in various councils, obtaining scientific awards and many other indicators. Currently, IAS ISTINA is used in more than twenty organizations. The main feature of this algorithm is the use of a co-authorship graph to identify the author. It is built for publications and other results of scientific activity. In this article id described the structure of the bibliographic data analysis module, which is implemented in the IAS ISTINA system, and the algorithm for identifying authors based on bibliographic data of the publication. The results of testing of the algorithm are presented at the end of the article. It demonstrates the high accuracy of algorithm operation.

Subject of Research.Simulation is one of the most powerful tools among information security provision measures in the design process of communication systems. As compared to other methods, it considers large-capacity communication systems, improves the quality of network resource management solutions and predicts more accurately their consequences. In this case, random graphs are the basic mathematical models for the analyzed systems. They provide fundamental understanding of the analyzed network properties and serve as the basis for simulation. With regard to the processing power high development rate for computers and simulation environments, the study of the topological properties of random graphs becomes especially urgent. It involves analyzing the probabilistic dynamics of centrality measures. Method.In the experiment we used centrality calculation methods for vertices and the graph as a whole based on the scientific apparatus of the graph theory. Comparison method based on span diagrams was used in the study of probabilistic dynamics of graph mathematical models. Main Results. We have studied the dynamics of centrality measures in the Erdös-Renyi random graph model, the Watts-Strogatz small world model and the freely scalable Barabashi-Albert model. The centrality measures of these models have been compared with a real network. We have made it clear that the topological properties of a real network are described by the Barabashi-Albert model to the fullest extent possible. The analysis of centrality measures presented in the paper gives the possibility to trace interconnections between the parameters of various graph models, that, in turn, can be used in the analysis of real networks. Practical Relevance.The obtained results can be applied in modeling of physical and social systems presented in the form of graphs. The paper findings are of interest for professionals involved in the analysis of networks in various fields of science and technology: sociology, medicine, physics and radio engineering.

The article is devoted to the study of the statistical characteristics of the text, which are calculated on the basis of the graph model of the text from the linguistic corpus. The introduction describes the relevance of the statistical analysis of the texts and some of the tasks solved using such an analysis. The graph model of the text proposed in the article is constructed as a graph in the vertices of which the words of the text are located, and the edges of the graph reflect the fact that two words fall into any part of the text, for example, in — a sentence. For the vertices and edges of the graph, the article introduces the concept of weight as a value from some additive semigroup. Formulas for calculating a graph and its weights are proved for text concatenation. Based on the proposed model, calculations are implemented in the Python programming language. For an experimental study of statistical characteristics, 24 values are distinguished, which are expressed in terms of the weights of the vertices, edges of the graph, as well as other characteristics of the graph, for example, the degrees of its vertices. It should be noted that the purpose of numerical experiments is to squeak in the characteristics of the text, with which you can determine whether the text is man-made or randomly generated. The article proposes one of the possible such algorithms, which generates random text using some other text created by man as a template. In this case, the sequence of parts of speech in an auxiliary text alternation is preserved in the random text. It turns out that the required conditions are satisfied by the median value of the ratio of the text graph edge weight value to the number of sentences in the text.

Introduction. The amount of information offered for study in modern educational institutions is rapidly increasing. Overcoming the inconsistency of the obligation to master the increasing flow of educational information and achieving the necessary "level" of training in fulfilling the traditional requirement of pedagogy – withstanding an acceptable amount of visibility leads to the mass introduction of multimedia tools. The folding so-called clip thinking shades the problems of filling thesaurus learning information virtually uncontrollable content and quality.Materials and Methods. Theoretical and empirical methods of research were used in the course of the work: analysis, synthesis, generalization, comparison, comparison, scientific theorization.Results. Clip-thinking interferes with a clear understanding of the context, and therefore the clip leaves no trace in semantically related phenomena. The trend of radical change in the roles of teachers and students reveals the main reasons and conditions for the transition to visualized presentation of educational information. In addition to the apparent negative consequences of the current pedagogical situation, some advantages of the protective reactions developed by modern learners to the most powerful stream of educational information are revealed. Studies have confirmed the risks of over-visibility in the learning process. Objective differences in the purpose and effectiveness of the types of visibility considered are highlighted. The main points of the formation of visual images are reflected, the obligatory maintenance of the conditions of problems in the educational process is emphasized.Discussion and Conclusions. The studies that have been carried out present an argument for the recommendations for the proposed frame-graphic approach in the organization of the educational process. The orientation of the educational process for each allocated group is justified, which requires a rather different nature of the script. One solution is to use educational information visualization tools to ensure the sustainability of the creative thinking vector.

Objectives This paper sets out to provide a theoretical substantiation of the placement of external fire-prevention water supply sources when designing unique construction objects, for which standard requirements of fire safety cannot be applied. Problematic situations arising during the design of unique construction objects, which relate to the provision of the required level of fireextinguishing substances supply, are described.Method A model constructed on the basis of graph theory is presented for the preliminary calculation of the location of external fire-fighting water supply sources that takes the equipment of fire-rescue units into account. The utility of developing a universal mathematical model for the preliminary definition of arrangement parameters of sources of external fire-prevention water supply when designing construction objects is substantiated.Results Examples of preliminary calculation of the number of external fire-fighting water supply sources are given considering the shape of the building perimeter. Additional factors determining the distances from external fire-fighting water supply sources to the projected objects are given.Conclusion A conclusion regarding the adequacy of the proposed model is formulated and directions for future research indicated that allows the applicability of the model to be specified for the calculation of the projected objects, which differ in terms of dimensions given in the plan by above-normative characteristics.

A method has been developed for finding the shortest Hamiltonian path in an arbitrary graph based on the rank approach, which provides high efficiency and a significant reduction in the error in solving the problem of organizing the process of managing multiple transactions and queries when they are implemented in network databases. In many cases, existing solutions do not provide the necessary results in terms of access time and accuracy of the found solution. Using the developed method allows minimizing the idle time of computing devices, reducing the volume and time of data transfer from one device to another, increases overall scalability, minimizes data access time, etc. An important advantage of the proposed method is to reduce the number of elementary operations and the number of vectors being processed the queue of the operations of the request, which leads to a significant reduction in time to implement the procedures for the formation of echer di operations in the requests. Methods of graph theory were used in this paper. The effectiveness of the task solution was evaluated using a systems approach, system analysis and the theory of operations research. Processing of experimental data obtained during the work was carried out in accordance with the provisions of mathematical statistics.

The relevance of the research is caused by necessity to transport geo-resources from extraction sites to processing sites for further distribution of different resources among consumers. In this regard, the task of choosing the routes for laying a trunk pipeline to transport geo-resources from extraction sites to processing sites is relevant. At the same time, it is necessary to provide a minimum spending (capital investment and operating costs) and reliability of the trunk pipeline operation in conditions of unforeseen natural and technogenic impacts. The main aim of the research is to propose a new method for laying a trunk pipeline, taking into account the compatibility or incompatibility of different geological resources types for laying in the same technical corridor, as well as a reliability of a trunk pipeline. Object: trunk pipeline laying on a given area. Methods: methods of graph theory and theory of hypernets; methods of evolutionary synthesis; computer simulation of geo-resources transportation; discretization of the trunk pipeline location area. Results. The authors have proposed a new mathematical apparatus based on the hypernet theory, taking into account the hierarchy of the structure of a designed trunk pipeline. On the basis of the hypernet approach, a new method for laying a trunk pipeline is obtained, taking into account the incompatibility of different types of resources for laying in the same technical corridor. A two-stage method is developed for designing a trunk pipeline ensuring minimum capital investment and operating costs. In addition, the authors developed a modified ant colony algorithm which provides not only a cheap solution, but reliable enough with respect to a given threshold in assumption that failures occur in the primary (physical) network. As a measure of reliability we consider the minimum among all pair probabilities of connectivity between each processing point and the corresponding source. The numerical experiments show the applicability of the methods proposed.

The problem of finding the shortest paths on weighted graphs is considered. The variants of statement of the problem, known algorithms for it solving, areas of practical application and existing challenges, in particular, the challenge of scalability, are analyzed. The class of block-parallel algorithms, their advantages and disadvantages is investigated. A fast block-parallel threaded algorithm oriented to large-sized graphs is proposed. It differs by changing the order of block calculations, reducing the critical path and operating time on a multi-core system, decreasing the data exchanges among local caches of cores and between neighbor levels of hierarchical memory.

The article is devoted to the development of strategies for identifying the location of special programmable devices (sensors) in network nodes for collecting, processing, analyzing information about the flow function in order to evaluate arc flows in that part of the network that is not directly observed. One of the ways to solve this problem is to search through possible placements, based on heuristic considerations. In work as a model of a flow network with sensors, a sparse underdetermined system of linear algebraic equations is used. The conditions for the uniqueness of the solution of a special kind of system obtained as a result of the use of a priori information from sensors installed in the monitored nodes of the network are determined. However, checking these conditions with a full search can only be used for small networks. The estimations limiting the number of viewed configurations of nodes are obtained and the interval of changing the number of monitored nodes that guarantee the complete observability of the network is justified. These results make it possible to increase the dimensionality of the problems being solved. Methods are developed for finding suboptimal solutions to establish the complete observability of the network for a given intensity threshold. Numerical results of constructing suboptimal solutions for various values of the intensity threshold are obtained. The results of visualization of the sensory configuration of the observed nodes are presented, which guarantee complete observability of the network. Conditions for effective applicability of exact methods are obtained for problems of the investigated class.

Thematic search for information is an important problem now. The search for specialists can be called the most difficult direction for thematic search. This direction needs to be developed in many areas of activity. At the beginning of the article, a brief overview of existing approaches to solving this problem is given. The following is a list of existing information systems for finding specialists and experts. The paper describes an algorithm developed for solving this problem. Approbation of the algorithm is implemented on the data of the scientometric system IAS ISTINA, which has been used since 2012 to collect data on scientific activities at the Lomonosov Moscow State University. Thematic search uses data analysis of articles, reports and abstracts of conferences, monographs, dissertations, lectures and training courses. The following information about the objects of scientific activity is used: name of object; list of authors; keywords and annotations. The main features of the developed algorithm are: the search for specialists without their active participation in the search process, the ability to search in Russian and English; use all kind of scientific products for searching; additional definition of the authority of specialists in the co-authorship graph. The article describes the developed thematic search algorithm and the interface of its software implementation. This interface was created to test the algorithm on real data of the scientometric system ISTINA. In this interface, you can search by keywords with additional filtering by headings and view detailed information on the specialists found.

Approaching a hypothetical thermodynamically reversible process is one of the main directions of energy saving in distillation. In practice, this is achieved by the use of systems with coupled thermal and material flows (STMP). Such systems have long been used in the separation of zeotropic mixtures. As follows from the analysis of literature data, they save energy costs by up to 30%. Recently, it has been revealed that the use of such systems is possible, expedient and energetically advantageous for separating the close-boiling and azeotropic mixtures by extractive distillation (ED). The article considers the main approaches to the synthesis of distillation schemes, including systems with STMP: 1) a method based on the construction of a "superstructure"; 2) a method based on the concept of thermodynamically equivalent configurations; 3) an evolutionary algorithm; 4) a method based on the transformation of distillation scheme graphs. As the analysis of the literature has shown, the first three methods are sufficiently well developed only for the synthesis of distillation schemes with STMP to separate zeotropic mixtures. There are a relatively small number of publications that consider the generation of ED schemes with STMP based on the concept of thermodynamically equivalent configurations for distillation of specific binary mixtures. The only current system approach to the synthesis of ED schemes with coupled thermal and material flows for multicomponent mixtures is the method of graphs (algorithm 4). At present, the first step has been taken to implement it in the form of a computer program. Thus, the article presents the current state of the problem of synthesizing highly effective, energy-saving distillation technologies, including extractive distillation, based on the analysis of publications over the past 20-25 years.

The purpose of the article is to investigate the semantic structure of a text with the help of an experimental method. Text meaning and sense are supposed to be the components of the semantic structure. In the article the definitions of the terms “contents”, “meaning” and “sense” are given. The term “contents” is used differently from the terms “meaning” and “sense” when speaking about a text. Experimental research, described in the article, proves that there are mechanisms of text meaning formation and sense building which are not the same: preserving or change in the hierarchy of denotates in the contents structure of T2 in accordance with T1. We investigated a source text (T1) and produced texts (T2) and analyzed the mentioned above mechanisms. For the research we used such psycholinguistic methods as creating the denotational graph, pointing out themes, subthemes and analysis of denotational and connotational meanings of synonyms in the produced texts. These texts were produced in different ways: in an “active” and “passive” ones. As a result we proved the existence of mechanisms of text meaning formation and sense building as different phenomena and ascertained the necessity of the future research of the individual strategies of text perception by teenagers. The necessity of the further investigation of the individual strategies used in the process of understanding a text is explained.

One of the problems of computer corpus linguistics is an automatic determination of keywords inthe text. The solution is a statistical method based on calculation of various frequency characteristics of the text. In this case, the most commonly used model is a “bag of words”, which does not take into account the order of words in the text. In this paper, we propose a graph model of the text that allows us to calculate the frequency characteristics of words in the text not only within the framework of the “word bag” model, but with respect to location of pairs of owls in some common part of the text, for example, in one sentence. To work with such a model, a software model is constructed in the form of a database schema intended for storing various statistical text information. Taking into account such a data model, the article proposes an algorithm for determining the keywords of the text, the implementation of which is performed in the Python programming language. When analyzing a document d of linguistics corpus D, our algorithm creates a list of about 40 words with the largest measure tf-idf, and choise from them 20 words, which are more often used in the document d. We regard these words as vertices of some graph G, and the multiplicity of the edge, connecting the vertices t and t’ is equal to the number of sentences in document d, containing both these words. Approximately 10 vertices of the graph with the greatest degree are selected. The words corresponding to these vertices are taken for key words of document d.

The article deals with the main form of international payment - bank transfer and features when it is charging by banks correspondent fees for transit funds in their correspondent accounts. In order to optimize the cost of expenses for international money transfers there is a need to develop models and toolkit of automatic generation of the total amount of commissions in international interbank settlements. Accordingly, based on graph theory, approach to the construction of the model was developed.

One of the main problems of model-driven user interface development approach is the complexity of the development of tools that maintain this methodology at all stages of the software lifecycle. Applicability of graph theory to formalize the Web application model was analyzed. Graph theory provides a means for a formalized description of the model of interaction and ensure the provision of precise mathematical relationships between the components. A scheme for modeling Web applications was proposed.

In the article the method of automated sentiment analysisevaluation of social network users is represented. The advantage of suggested method consists in ability taking into accountuser’s authority as well as the fact of several messages from one user. As input data for the sentiment analysis with respect to a certain topic is its relevant messages. Automated analysisof these messages is obtained with application of fuzzy logicalgorithms. Particularly when in messages contains fuzzyhedges. The paper presents experimental data showing the steps of calculation of the resulting sentiment evaluation ofmessages on a certain topic.

Graph theory provides a means for a formalized description of the model of interaction and ensure the provision of precisemathematical relationships between thecomponents. A scheme for modeling Web applications was proposed. The system of evaluation models UI Web application. Taking into account such factors as understandability, predictability, learning. For each indicator matrix is constructed for assignment to class compliance.

The work objective is to study a critical traveling salesman problem which is NP complicated task of the discrete optimization. It is shown that only heuristics is appropriate in achieving this goal. The result of the ant colony algorithm (ACA) and genetic algorithm (GA) sharing is presented for the problem solution. The point is that the problem is solved using only mutations of various types (without crossover). The investigated GA is improved by the elitist strategy. The testing is done on graphs of the middle and large dimension. An “elite” sample obtained by the ACA is improved by a mean of 11%. It is shown that the efficiency of the genetic algorithm depends directly on the number of ants in the generation, and on the number of algorithm iterations. Target function values are improved more than twofold after the introduction of the elitist strategy. Increasing the number of ACA runs raises the efficiency of the algorithm by approximately 2%.

Equilibrium situations in a problem of patrolling on a graph were obtained using game theory methods. The solution of the game was found for a graph modeling the flux of information from data source to sink. It is assumed that there is a tracking camera in each graph vertex. Under this assumption, equilibrium was found in the game for an undirected connected tree and a directed tree.

The problem of finding the maximum flow in nets of a special form is considered. In such nets the arcs are related in such a way that the total flow passing through the related arcs does not exceed the minimum throughput of these arcs. It is shown that the theorem by Ford and Fulkerson, according to which the maximum flux value is equal to the throughput of a minimum cut, is not performed for such networks. The estimations of the maximum flow in a generalized net with bound arcs are proposed. And the algorithm for finding the maximum flow in such nets is developed.

The classes of graphs closed regarding the set-theoretical operations of union and intersection are considered. Some constructive descriptions of the closed graph classes are set by the element and operational generating basses. Such bases have been constructed for many classes of graphs. The backward problems (when the generating bases are given and it is necessary to define the characteristic properties of corresponding graphs) are solved in the paper. Subsets of element and operational bases of the closed class of all graphs are considered as generating bases.

This paper describes the software for graph storage, analysis and visualization. The article presents a comparative analysis of existing software for analysis and visualization of graphs, describes the overall architecture of application and basic principles of construction and operation of the main modules. Furthermore, a description of the developed graph storage oriented to storage and processing of large-scale graphs is presented. The developed algorithm for finding communities and implemented algorithms of autolayouts of graphs are the main functionality of the product. The main advantage of the developed software is high speed processing of large size networks (up to millions of nodes and links). Moreover, the proposed graph storage architecture is unique and has no analogues. The developed approaches and algorithms are optimized for operating with big graphs and have high productivity.

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The relevance of the discussed issue is caused by the need to develop a problem-oriented method of hierarchical multilevel (stratified) formalization which allows to overcome the difficulties of modeling multistate complex technological systems in studying the efficiency of their functioning, taking into account the impact of elements reliability. The main aim of the study: development of a problem-oriented stratified method of formalization of complex technological systems of a certain class with a large dimension of state space and its practical application in the development of a stratified model of technological system of ore grinding, with due consideration of the impact of equipment reliability on its functioning efficiency. The methods used in the study: concept of multilevel hierarchical description of complex systems, general theory of systems, theory of reliability, simulation method, algebra of logic, methods of applied statistics. The results. The authors proposed a problem-oriented method of stratified formalization which allows to overcome the difficulties of formalizing CTS of a certain class in the study of efficiency of their functioning taking into account the reliability of components by simulation modeling. By using the proposed method the authors developed a stratified computer model of ore grinding of Zangezur Copper Molybdenum Combine (Armenia), describing the process of its functioning under the influence of the random process of failures and recovery of failed equipment at three levels: at the level of grinding aggregates, at the level of grinding complexes and at the system level. Application of the proposed method of formalizing allowed to reduce the description of ore grinding technological system to the description of its parts and their conjugation, giving the possibility of analytical description of the system at the first and third levels. Thanks to this the construction of a simulation model of the overall system can be substantially simplified, the number of full-scale experiments is drastically reduced, which, in turn, has led to a significant reduction in time and complexity of building a computer model of the whole system.

Engineering infrastructure of modern cities represents a rather complex hierarchical system, which involves the structuring of the design process into separate subsystems taking into account the prospects of their development and reconstruction. While designing communications the technical and economic feasibility of their construction at the appropriate place should be considered, as it impacts the efficiency of future communication. In this regard, it is urgent to create specialized geographic information systems (GIS), allowing to estimate the projected cost of utilities prior to commencement of construction works, and to take into account the spatial location of the various utilities, their multi-level nature and interaction. The main aim of the study: development of creation concept of the specialized GIS based on model hyper networks, allowing the designer or user to consider the spatial location of the various utilities, their multi-level nature and interaction in the organization and management of engineering infrastructure of cities. The methods used in the study: grid method in the construction of terrain models in the form of a discrete analogue of the staging area; methods of graph theory to find the optimal routes for laying of engineering networks; methods of the theory of hyper networks to describe the multi-levelness of creation of engineering infrastructure of modern cities. The results. The authors introduced a hyper network technology of creation of the specialized geographic information systems, which is based on the hypernetwork models and structuring of the design process into separate subsystems. The proposed approach, unlike traditional methods of creation of GIS-technologies, allows organizing optimal spatial placement of engineering utilities for various purposes at the stage of their design taking into account their interrelation and interdependence. The conclusions: the proposed method of creation of the specialized GIS, which is based on the hypernetwork models, allows taking into account special features of the real terrain, the type and purpose of the designed communication.

Analysis of visualization techniques for various types of graphs is done. Conclusion about the relevance of method development for metagraph visualizing is made. The paper deals with issues that arise when solving the problem of metagraph visualization, such as: the placement of nodes that belong to metavertices and do not belong to them, figures intersection of metavertices. These problems are exemplified. Criteria are proposed for the final image to be considered coherent, understandable for users and corresponding to a predetermined metagraph. The problem of metagraph visualization is posed. The method based on the principles of force algorithms is proposed for the problem solving. The rules for forces between metagraph nodes are defined in the framework of the method. These forces depend on nodes type between which they are performed and the presence of edges between them. This method does not involve human intervention during the formation of the image, thus saving time at frequent changes that require rebuilding of the image. The resulting image gives the possibility to portray clearly the entities of the subject area and the links between them. Graphical analysis methods can be applied to the image. Areas for the future researches are identified. They are: minimization of the number of edges intersections and the area occupied by the resulting image. Results of the modified visualization method can improve the visual metagraph representation.

Mathematical model for the possible development of the primary explosion at the grain processing enterprise is created. It is proved that only instability is possible for the combustion process. This model enables to estimate possibility of the secondary explosion at any object of the enterprise and forms the base for mathematical support of the decision support system for explosion-proof. Such decision support system can be included in the control system of the processing enterprise.