Graph Theory Approach to the Vulnerability of Transportation Networks

Exploring the Role of Indirect Coupling in Complex Networks: The Emergence of Chaos and Entropy in Fractional Discrete Nodes

Understanding the dynamics of complex systems defined in the sense of Caputo, such as fractional differences, is crucial for predicting their behavior and improving their functionality. In this paper, the emergence of chaos in complex dynamical networks with indirect coupling and discrete systems, both utilizing fractional order, is presented. The study employs indirect coupling to produce complex dynamics in the network, where the connection between the nodes occurs through intermediate fractional order nodes. The temporal series, phase planes, bifurcation diagrams, and Lyapunov exponent are considered to analyze the inherent dynamics of the network. Analyzing the spectral entropy of the chaotic series generated, the complexity of the network is quantified. As a final step, we demonstrate the feasibility of implementing the complex network. It is implemented on a field-programmable gate array (FPGA), which confirms its hardware realizability.

Fractal Nature Bridge between Neural Networks and Graph Theory Approach within Material Structure Characterization

Many recently published research papers examine the representation of nanostructures and biomimetic materials, especially using mathematical methods. For this purpose, it is important that the mathematical method is simple and powerful. Theory of fractals, artificial neural networks and graph theory are most commonly used in such papers. These methods are useful tools for applying mathematics in nanostructures, especially given the diversity of the methods, as well as their compatibility and complementarity. The purpose of this paper is to provide an overview of existing results in the field of electrochemical and magnetic nanostructures parameter modeling by applying the three methods that are “easy to use”: theory of fractals, artificial neural networks and graph theory. We also give some new conclusions about applicability, advantages and disadvantages in various different circumstances.

Semi-Local Integration Measure of Node Importance

Numerous centrality measures have been introduced as tools to determine the importance of nodes in complex networks, reflecting various network properties, including connectivity, survivability, and robustness. In this paper, we introduce Semi-Local Integration (SLI), a node centrality measure for undirected and weighted graphs that takes into account the coherence of the locally connected subnetwork and evaluates the integration of nodes within their neighbourhood. We illustrate SLI node importance differentiation among nodes in lexical networks and demonstrate its potential in natural language processing (NLP). In the NLP task of sense identification and sense structure analysis, the SLI centrality measure evaluates node integration and provides the necessary local resolution by differentiating the importance of nodes to a greater extent than standard centrality measures. This provides the relevant topological information about different subnetworks based on relatively local information, revealing the more complex sense structure. In addition, we show how the SLI measure can improve the results of sentiment analysis. The SLI measure has the potential to be used in various types of complex networks in different research areas.

The Impact of Carsharing on Transport in the City. Case Study of Tri-City in Poland

The work on the impact of innovative solutions in urban transport on the inhabitants’ quality of life was discussed. This paper presents the characteristics of the use of shared vehicles in the agglomeration, based on the example of the Tri-City. An analysis of vehicles’ use in given periods of time was performed, indicating the growing interest in using this type of transport in the city. The work was divided into four chapters. The first part concerns the history of travel and urban development. The second discusses all currently available communication solutions in cities. The third chapter contains the research part. It focuses on presenting changes in vehicle availability over a more extended period. The fourth chapter describes the functioning of cars “for minutes” and the operation and use of dedicated mobile applications. The work ended with a summary of theoretical and cognitive content. A significant contribution is a brief analysis of the shared car market in the Tri-City. The available options are characterized. Also, the degree of use has been analyzed. The study concluded with theses about the further rapid development of this industry in northern Poland.