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AI for Autonomous Driving
Published in Josep Aulinas, Hanky Sjafrie, AI for Cars, 2021
On a global scale, the AVs “wants” to reach a destination from the known current position, which we can assume it is given by the combination of on-board global navigation satellite systems and sophisticated localization algorithms that are used to localize and associate static objects with previously mapped objects such as lane markings, poles and traffic signs. The best route is then calculated, given different parameters such as traffic rules, a priori traffic knowledge, current traffic conditions, distance etc. Traffic rules, street distances, and all other relevant information about the streets concerned are part of existing maps. Maps are typically represented in the form of graphs, while current traffic density and other real-time information are available through backend server communication including Vehicle-to-Vehicle (V2V) and Vehicle-to-Infrastructure (V2I). A graph consists of nodes and edges connecting these nodes; one can imagine a road intersection as a node and the roads reaching it as the edges. Each of the edges might be connected to another road intersection node at its other end. One can intuitively imagine each of these edges to be associated with a certain distance, maximum allowed speed, direction, current traffic information etc., which in graph theory is referred to as its weight.
Modeling the time-varying performance of electrical infrastructure during post disaster recovery using tensors
Published in Paolo Gardoni, Routledge Handbook of Sustainable and Resilient Infrastructure, 2018
Graph theory deals with the study of graphs, which are defined as mathematical structures or diagrams amounting from pairwise related objects. The objects that make the graph are called vertices (points or nodes) and the relation between a pair of nodes is called an edge (arc, line or link.) A graph can be written as , where is the set of nodes and is the set of links. A network is defined as a graph in which the nodes and links have attributes other than their topological identities (e.g., names, hierarchy, functions, and type.) Thus infrastructure can be represented as a collection of network layers. Each of the network layers have nodes and links with their respective state variables as attributes.
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Published in Eric J. Goethals, Telechelic Polymers: Synthesis and Applications, 2018
The formalism of the theory of branching processed is suited for treatment of weak cyclization. The procedure is called “spanning-tree” approximation. In the graph theory, a spanning tree is a tree-like graph obtained from graphs with cycles after cutting such edges so that all cycles can be eliminated and the connectivity of all nodes be retained. The main point is the following: for a newly formed bond, one distinguishes whether it is inter- or intramolecular, and labels by o the functional group engaged in cycles. The σ-functionalities are considered as reacted (they cannot react any more), but from the structure propagation point of view, they are considered as dead (Figure 4). The generation of structures occurs by combination of the intermolecularly reacted α-functionalities.
Exploring the Relative Effects of Body Position and Spatial Cognition on Presence When Playing Virtual Reality Games
Published in International Journal of Human–Computer Interaction, 2020
Aelee Kim, Min Woo Kim, Hayoung Bae, Kyoung-Min Lee
In graph theory, a graph is a collection of points called vertices (V), connected by lines called edges (E). The degree of a vertex (d(V)) is the number of edges incident to the vertex. In this research, it should be noted that we use the term route instead of edge when describing the formulas. In Appendix A, we explain the foundational concepts of the formulas. According to the formulas, when playing Bomb Hero, the number of routes that a player can select from a place (i.e., vertex) is no more than four, thus the DFN is finite. In contrast, for Moss, the number of routes a player can choose from a place (i.e., vertex) is not limited, meaning that the DFN is infinite. Through the formulas, we clearly understand that the DFN is much higher for Moss than Bomb Hero. Based on the more detailed explanation given in Appendix A, we constructed the two mathematical formulas presented in Table 1.
Degree centrality of combustion reaction networks for analysing and modelling combustion processes
Published in Combustion Theory and Modelling, 2020
Ahmad Saylam, Kamal Hadj Ali, Mustapha Fikri
The ideas of graph-theoretic methods were initiated by Leonhard Euler in 1730, studying the problem of the Seven Bridges of Köningsberg [11]. Graph theory is the study of graphs, which are mathematical representations used to model the relationships among objects. A graph is made up of vertices, nodes or points which are connected by edges, arcs, or lines. At present, graph theory is used as a modelling and analysing tool for many practical problems of biochemistry [12], electrical engineering [13], computer science [14] and human life [15]. A general overview on graph theory could be found in Harary’s graph theory [16] and Berge’s graphs and hypergraphs [17].
Computation of some important degree-based topological indices for γ- graphyne and Zigzag graphyne nanoribbon
Published in Molecular Physics, 2023
Abdul Hakeem, Asad Ullah, Shahid Zaman
Graph theory is an important branch of applied mathematics that deals with the study of graphs and their structures. In mathematics, the study of graphs is referred to as graph theory, and it is one of the main topics in discrete mathematics. A graph is essentially a collection of nodes or vertices, which are connected by edges or lines. These mathematical structures, known as graphs, are utilised for investigating pairwise relationships between things. If all the connections in a graph are unidirectional, it is referred to as a digraph or directed graph.