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A comparative analysis of structural and flow approaches to analysis of vulnerability of complex network systems (NS) from targeted attacks and non-target lesions of various types was carried out. Typical structural and functional scenarios of successive targeted attacks on the most important by certain characteristics system elements were considered, and scenarios of simultaneous group attacks on the most significant NS's components were proposed. The problem of system lesions scale from heterogeneous negative impacts was investigated and it was confirmed that the flow approach allows us to obtain a much more realistic picture of consequences of such lesions. It is shown that scenarios of group targeted attacks built on the basis of the NC flow model are more optimal from the point of view of choosing attack targets than structural ones., Comment: 11 pages, 4 figures, in Ukrainian

A flow approach to community detection in complex network and multilayer network systems is proposed. Two methods have been developed to search for communities in a network system (NS). The first of them is based on the calculation of flow influence parameters of NS's subsystems, selected according to the principle of nesting hierarchy. The second method uses the concept of flow core of network system. Two methods are also proposed for community detection in multilayer network system (MLNS). The first of them is based on the concept of MLNS aggregate-network and subsequent allocation of its flow core. The second method uses the concept of flow core of the process of intersystem interactions in general. All developed methods are based on the use of flow criterion that the selected group of nodes really forms a community. The results of application of developed approaches are illustrated by examples for which known methods are ineffective., Comment: 14 page, 8 figures, in Ukrainian

The approach to decomposition of multidimensional network systems on monoflow multilayer network systems (MLNS) is proposed, which significantly simplifies the analysis of intersystem interactions in multipurpose and multifunctional supersystem formations. A flow model of monoflow partially overlapped MLNS is built, which reflects the process of intersystem interactions between network systems that ensure the movement of flows of a certain type. The main local and global flow characteristics of MLNS elements are determined, which allow us more adequately from a functional point of view to establish the importance of nodes and edges of a multilayer system compared to their structural characteristics. The constructed model is proposed to be used for the development of methods of protecting complex network and multilayer network systems from targeted attacks and non-targeted lesions of various types and solving other practically important problems of system analysis., Comment: 18 pages, in Ukrainian language

On the basis of structural model of intersystem interactions, the main local and global structural characteristics of nodes of the multilayer network (MLN) are determined. The notions of weighted and binary aggregate-networks of MLN are introduced and integral indicators of the importance of nodes of the multilayer network are determined. The effectiveness of application of aggregate-networks for solving a number of practically important problems of the theory of complex networks is shown. To determine the most important components of intersystem interactions structure, the concepts of p-core of multilayer network and kag-core of its weighted aggregate-network are introduced. The effective scenarios of successive and simultaneous group attacks on the structure of multilayer network systems have been built based on the use of these cores. Indicators of the importance of separate layers of MLN are introduced and approaches to building scenarios of successive and simultaneous system-wide attacks on the structure of intersystem interactions are formulated., Comment: 19 pages, in Ukrainian language, 3 figures

The main types of negative internal and external influences on complex network systems (NS) and intersystem interactions in monoflow partially overlapped multilayer network systems (MLNS) are analyzed. Among such influences, targeted attacks on real complex systems and their non-targeted damages of various nature are primarily singled out. On the basis of structural and flow models of NS and MLNS, sequential and simultaneous local, group and system-wide damages to the structure and operation process of complex network systems and intersystem interactions are considered. The existing structural and functional scenarios of consecutive attacks on the most important components of the system and the need to neutralize the sources of such attacks as one of the means of system protection are analyzed. The peculiarities of application of such scenarios for the protection of NS and MLNS from system-wide non-target lesions are considered. Approaches to evaluation and overcoming the consequences of negative impacts on the structure and operation process of complex network systems and intersystem interactions are proposed., Comment: 18 pages, in Ukrainian language, 2 figures

Method of U-statistics is used to analyze the efficiency of functioning of the motor transport system of a large city as a complex network system with partially ordered traffic flows. Based on the results of continuous monitoring of movement of the ordered part of flows equipped with GPS-trackers, namely, public transport means, methods of interactive, forecasting and aggregated analysis of the state and operation process of motor transport system components of various hierarchy levels have been developed. The proposed technique can be easily automated and used for operational analysis and forecasting of the development of traffic situations on city highways and creation of effective tools to optimize the process of motor transport system functioning., Comment: 11 pages, 3 figures, in Ukrainian

The paper introduces a number of structural and functional features of classification of multilayer networks (MLN), by means of which distinguish monoflow partially overlapped MLN, that are quite common in the study of intersystem interactions of different nature. The concept of MLN's aggregate-network is defined, which in many cases significantly simplifies the study of intersystem interactions, and the properties of its k-cores are investigated. The notion of p-cores is introduced, with help of which the components of MLN that are directly involved in the implementation of intersystem interactions are distinguished. Methods of reducing the complexity of multilayer network models are investigated, which allow us to significantly decrease their dimensionality and better understand the processes that take place in complex network systems and intersystem interactions of different types. Using the introduced local and global structural characteristics of elements, effective scenarios of targeted attacks on monoflow partially overlapped multilayer networks have been developed, the main attention of which is focused on the transition points of MLN through which intersystem interactions are actually realized. It is shown that these scenarios can also be used to solve the inverse problem, namely, which elements of MLN should be blocked in the first place to prevent the acceleration of spread of epidemics of dangerous infectious diseases, etc., Comment: 18 pages, 7 figures

The problem of selection, storage, search and analysis of information about the state, functioning and interaction of elements of complex hierarchical network systems is considered. The principles of construction of information models of such systems and models of evaluation of their operation efficiency are proposed. These models are formed on the basis of results of regular planned studies of the system and continuous monitoring of the activities of its components at all levels of the hierarchy. The problem of novelty detection in the information model of system is investigated and it is shown how the application of evaluation theory methods allows to solve it. The proposed methods of complex analysis of the behavior of real complex systems and optimization of data processing makes it possible to significantly simplify and speed up the decision-making process for further action for such systems., Comment: 12 pages, 3 figures

The flow models of complex network system are developed and main flow characteristics of its elements are defined. Those characteristics are applied for determining actual structure of the system, analyzing its development on all lifecycle stages and finding alternative flow directions that bypass isolated areas of network. Influence and betweenness parameters of components of network systems are defined. Using those parameters, the conditions were studied under which system is resistant to negative internal and external influence. The notion of flow core of complex network systems is defined, that allows to distinguish the most important components of system structure in terms of operation to solve the problem of finding communities within the network. The notions of p-core and kernel of mono flow partially overlapped multilayered network are defined that allow to determine components of system structure that play the most important role in implementation of interactions between systems. The methodology is developed for complex evaluation of quality of complex hierarchical network systems. This methodology combines the interconnected methods of local, forecasting, interactive and aggregated analysis of system components behavior on all hierarchy levels. It is demonstrated that application of proposed complex evaluation methodology is efficient for solving problem of defining practically possible criteria of network system element quality, novelty detection, determining critical and optimal system operation modes and selecting optimal system of given class of systems., Comment: 29 pages, in Ukrainian

The problem of blocking certain areas of network systems and their boundary case, which is the granulation of network to a set of isolated zones, is investigated in the article. The losses that await the system due to blocking of its separate components are determined, and method for finding alternative ways of flow motion bypassing the isolated zone of network are proposed. The granulation process of the network system is reflected as a temporal network and the losses that await the system during the deployment of such processes are calculated., Comment: 6 pages, 2 figures

The paper investigates the problem of finding communities in complex network systems, the detection of which allows a better understanding of the laws of their functioning. To solve this problem, two approaches are proposed based on the use of flows characteristics of complex network. The first of these approaches consists in calculating the parameters of influence of separate subsystems of the network system, distinguished by the principles of ordering or subordination, and the second, in using the concept of its flow core. Based on the proposed approaches, reliable criteria for finding communities have been formulated and efficient algorithms for their detection in complex network systems have been developed. It is shown that the proposed approaches make it possible to single out communities in cases in which the existing numerical and visual methods turn out to be disabled., Comment: 5 pages, 1 figure

The orthogonality of Hilbert spaces whose elements can be represented as simple and double layer potentials is determined. Conditions of well-posed solvability of integral equations for the sum of simple and double layer potentials equivalent to double-sided Dirichlet, Neumann, and Dirichlet-Neumann boundary value problems for the Laplacian are established in the Hilbert space, elements of which as well as their normal derivatives have the jump through boundary surface. The properties of boundary operators that relate the double-sided boundary conditions of different types for the three-dimensional Laplace equation are investigated., Comment: 7 pages. arXiv admin note: substantial text overlap with arXiv:1910.01301

The conditions of well-posed solvability of searched function and its normal derivative three dimensional jump problem for the Laplacian and equivalent to them integral equation system for the sum of the simple and double layer potentials are determined in the Hilbert space, element of which as well as their normal derivatives have the jump through boundary surface., Comment: 6 pages

This paper provides the analysis for functional approaches of complex network systems research. In order to study the behavior of these systems the flow adjacency matrices were introduced. The concepts of strength, power, domain and diameter of influence of complex network nodes are analyzed for the purpose of determining their importance in the systems structure. The notions of measure, power, domain and diameter of betweenness of network nodes and edges are introduced to identify their significance in the operation process of network systems. These indicators quantitatively express the contribution of the corresponding element for the motion of flows in the system and determine the losses that are expected in the case of blocking this node or edge or targeted attack on it. Similar notions of influence and betweenness are introduced to determine the functional importance of separate subsystems of network system and the system as a whole. Examples of practical use of the obtained results during investigation of real complex network systems are given., Comment: 20 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1807.06044

This paper provides the analysis for structural and functional approaches of complex network systems research. In order to study the behavior of these systems the flow adjacency matrices were introduced, and local and global dynamic characteristics of system elements were defined. The notion of the flow core of network system was introduced and its advantages over the k-core of complex network were analyzed. The methods were proposed for identifying real structure of network system and reducing the dimensionality of its model., Comment: 12 pages, 5 figures

This article is dedicated to research of approximation properties of B-splines and Lagrangian finite elements in Hilbert spaces of functions defined on surfaces in three-dimensional space. Hereinafter the conditions are determined for convergence of Galerkin and collocation methods for solving Fredholm integral equations of the first kind for simple layer potential that is equivalent to Dirichlet problem for Laplace equation in R3. Estimation is determined for the error of approximate solution of this problem obtained using potential theory methods., Comment: 13 pages

Subject of research is complex networks and network systems. The network system is defined as a complex network in which flows are moved. Classification of flows in the network is carried out on the basis of ordering and continuity. It is shown that complex networks with different types of flows generate various network systems. Flow analogues of the basic concepts of the theory of complex networks are introduced and the main problems of this theory in terms of flow characteristics are formulated. Local and global flow characteristics of networks bring closer the theory of complex networks to the systems theory and systems analysis. Concept of flow core of network system is introduced and defined how it simplifies the process of its investigation. Concepts of kernel and flow core of multiplex are determined. Features of operation of multiplex type systems are analyzed., Comment: 22 pages, 9 figures

Region of the country is treated as an open megasystem that consists of many interconnected complex network systems. Classification of such systems on the basis of ordered motion of flows is performed. The main approaches to investigation of complex systems are described. Theory of evaluation is considered as a tool for analysis of network systems. Purpose and subject of evaluation of the systems are formulated. The main problems of evaluation are analyzed and the ways of further research are determined., Comment: 6 pages. arXiv admin note: text overlap with arXiv:1602.07548

The main approaches for the formation of generalized conclusions about operation quality of complex hierarchical network systems are analized. Advantages and drawbacks of the "weakest" element method and a weighted linear aggregation method are determined. Nonlinear aggregation method is proposed for evaluating the quality of the systems, which consist of elements of the same priority. Hybrid approaches to form generalized conclusions are developed based on the main aggregation methods. It is shown that they allow to obtain more reliable aggregation results., Comment: 7 pages, 3 figures. arXiv admin note: text overlap with arXiv:1602.07548

This article covers the problem of processing of Big Data that describe process of complex networks and network systems operation. It also introduces the notion of hierarchical network systems combination into associations and conglomerates alongside with complex networks combination into multiplexes. The analysis is provided for methods of global network structures study depending on the purpose of the research. Also the main types of information flows in complex hierarchical network systems being the basic components of associations and conglomerates are covered. Approaches are proposed for creation of efficient computing environments, distributed computations organization and information processing methods parallelization at different levels of system hierarchy., Comment: 7 pages, 2 figures

The methods are proposed for evaluation of complex dynamical systems, choice of their optimal operating modes, determination of optimal operating system from given class of equivalent systems, system's timeline behaviour analysis on the basis of versatile multicriteria and multilevel analysis of behaviour of system's elements., Comment: 6 pages, 1 figure

Methods of complex evaluation based on local, forecasting, aggregated, and interactive evaluation of the state, function quality, and interaction of complex system's objects on the all hierarchical levels is proposed. Examples of analysis of the structural elements of railway transport system are used for illustration of efficiency of proposed approach., Comment: 14 pages, 2 figures