A Model of Directed Graph Cofiber

In the homotopy theory of spaces, the image of a continuous map is contractible to a point in its cofiber. This property does not apply when we discretize spaces and continuous maps to directed graphs and their morphisms. In this paper, we give a construction of a cofiber of a directed graph map whose image is contractible in the cofiber. Our work reveals that a category-theoretically correct construction in continuous setup is no longer correct when it is discretized and hence leads to look at canonical constructions in category theory in a different perspective.

Mathematical model and algorithm for calculating the cycles of the cells of the graph map

Выделенные свойства циклов DFS-базиса блока карты простого графа позволили составить математическую модель вычисления циклов ячеек карты графа. По данной модели предложен практический алгоритм вычисления циклов ячеек карты графа. Алгоритм имеет квадратическую сложность относительно числа вершин в графе. The selected properties of the cycles of the DFS-basis block of a simple graph map allowed us to create a mathematical model for calculating the cycles of the cells of the graph map. According to this model, a practical algorithm for calculating the cycles of the graph map cells is proposed. The algorithm has a quadratic complexity relative to the number of vertices in the graph.

An Intrusion Intention Analysis Algorithm Based on Attack Graph

The discovery of intrusion intention is one of the challenging tasks faced by network security managers. To detect intrusion detections, this paper presents a domain-device attack graph, and collects and analyzes the underlying data of the network topology. On this basis, the attack graph Map was quantified by the Bayesian theory. The minimum weight spanning tree (Min-WFS) algorithm was adopted to automatically recognize the calculation cost of key devices in the network topology, providing an important basis for network maintenance. Experimental results show that the intrusion intentions can be effectively identified with the aid of the quantified domain-device attack graph Map, and this identification method is easy to implement.

CARTOGRAPHIC MODELS OF PEST DIFFUSION PROCESSES IN NETWORK CYBERSPACE

Рассматривается весьма актуальная проблема моделирования процесса диффузии вредоносных кодов и деструктивных контентов в киберпространстве, которое в современных условиях носит все более выраженный сетевой характер. В отличии от ранее широко используемых аналоговых и даже развивающих их дискретных эпидемических моделей, в настоящей работе учитываются статический (накопленную информацию) и динамический (информационный трафик) ресурсы узлов и ветвей сети. Наряду с этим принимается во внимание дозировка вредоноса, внедряемого в сеть для нарушения её работоспособности. Все это позволяет осуществить сетевое картографирование эпидемического процесса, порождаемого в результате диффузии вредоносной инъекции. Предлагаемая модель открывает новую страницу в описании информационных эпидемий (и не только) во взвешенных сетях, где предлагаемая авторами формализация масштабирует изображаемые размеры узлов и ветвей модели в соответствии со значениями ресурсов или потенциалов её элементов. Фактически получается граф (карта) исследуемого сетевого ландшафта, в котором циркулирует информация. В случае внедрения вредоноса компоненты карты окрашиваются с учетом дозировки его присутствия в них, где топологической основой выступают “звезды” сети. Для этого авторами предлагаются соответствующие аналитические выражения. The article deals with a very relevant problem of modeling the process of diffusion of malicious codes and destructive content in cyberspace, which in modern conditions has an increasingly pronounced network character. In contrast to the previously widely used analog and even developing discrete epidemic models, this paper takes into account the static (accumulated information) and dynamic (information traffic) resources of nodes and branches of the network. Along with this, the dosage of the malware introduced into the network to disrupt its performance is taken into account. All this makes it possible to carry out network mapping of the epidemic process generated as a result of the diffusion of malicious injection. The proposed model opens a new page in the description of information epidemics (and not only) in weighted networks, where the formalization proposed by the authors scales the depicted sizes of nodes and branches of the model in accordance with the values of resources or potentials of its elements. In fact, a graph (map) of the network landscape under study is obtained, in which information circulates. In the case of the introduction of the malware, the map components are colored taking into account the dosage of its presence in them, where the topological basis is the “stars” of the network. For this purpose, the authors propose the corresponding analytical expressions.

Building Collaborative Ontologies

The chapter describes the research performed within the KOMET (Knowledge and cOntent structuring via METhods of collaborative ontology design) project, which was aimed at developing a new paradigm for knowledge structuring. By knowledge structure, the authors define the main domain concepts and relations between them in a form of graph, map, or diagram. The approach considers the specifics of individual cognitive style. Two stages of research have been completed: research into correlations between the expert's individual cognitive style and the peculiarities of expert's subject domain ontology development; and study of correlations between the expert's individual cognitive style and the group ontology design (including the design performed in groups consisting of experts either of similar or of different cognitive styles). The results of this work can be applied to organizing collaborative ontology design (especially for research and learning purposes), data structuring, and other group analytical work. Implications for practice are briefly delineated.