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Mathematical Modeling to Find the Potential Number of Ways to Distribute Certain Things to Certain Places in Medical Field
Published in Jyoti Mishra, Ritu Agarwal, Abdon Atangana, Mathematical Modeling and Soft Computing in Epidemiology, 2020
G. Mahadevan, S. Anuthiya, M. Vimala Suganthi
The (m, n) tadpole graph, also called a dragon graph or kite graph, is the graph obtained by joining a cycle graph to a path with a bridge. The (m, n) lollipop graph is obtained by joining a complete graph to a path graph with a bridge. For n ≥ 3, a closed helm graph CHn is obtained from Hn by adding edges between the pendent vertices where supports in base wheel are adjacent. A uniform n-ply graph is a graph obtained from n distinct paths Pm, m ≥ 3 by merging all the initial vertices to a vertex u and all the terminal vertices to a vertex v. The uniform n-ply graph is denoted by Pn(u, v). Tn(K1,m) is obtained by pasting the root vertex of K(1, m) to the nth vertex of the path in the triangular snake graph T.
Spectrum Fragmentation Management Approaches Considering Non-defragmentation
Published in Bijoy Chand Chatterjee, Eiji Oki, Elastic Optical Networks: Fundamentals, Design, Control, and Management, 2020
Bijoy Chand Chatterjee, Eiji Oki
The details of the path graph transformation is presented in Algorithm 3. Step 1 initializes the graph, whereas step 2 generates vertices of the graph. A vertex corresponds to a path. Each vertex is assigned a value that corresponds to the traffic demand of the path. Step 3 generates the edges of the graph. It establishes an edge between two vertices that belong to the multiple paths of the same source-destination pairs. This guarantees that the multiple paths of the same source-destination pairs are not be assigned in the disjoint connection group together. It also establishes an edge between two vertices whose corresponding paths are not disjointed. This ensures that all the members of the disjoint connection group have disjoint paths from each other.
Multi-Aerial-Robot Planning
Published in Yasmina Bestaoui Sebbane, Multi-UAV Planning and Task Allocation, 2020
If n aerial robots communicate according to a time-invariant undirected communication graph G = (I, E) where I = {1,..., n}, E = {(i, j)∈ I × I|i and j communicate } and Ni = {j ∈ I|(i, j) ∈ E} is the set of neighbors of node I. A path graph is a graph in which there are only nodes of degree 2 except for two nodes of degree 1. The nodes of degree 1 are called external nodes and denoted 1 and n, while the others are called internal nodes [438]. A cycle graph is a graph in which all the nodes have degree 2. The aerial robots are modeled as single integrators running on a consensus algorithm based on a Laplacian control law [76]. The continuous time dynamics of the agents are given by x˙i(t)=-∑j∈Nixi(t)-xj(t)i∈(1,…,n)
Fastest random walk on a path
Published in International Journal of Systems Science, 2019
A path graph with n vertices is illustrated in Figure 1, where the vertices are numbered from 1 to n starting from the left and the transition probability from vertex i to vertex j is denoted by . Note that we have for and for each i. Mathematically, this can also be expressed as where is called the transition probability matrix of the Markov chain and is the vector of all ones. Throughout the paper, we describe Markov chains by their transition probability matrices.
Conceptual design synthesis based on series-parallel functional unit structure
Published in Journal of Engineering Design, 2018
As shown in Figure 22, we can concluded the work of constructing the appropriate SPFUSs for the FR into 5 points. Generate the decomposition path graph of the given number with the decomposition path graph generating algorithm.Find out all the binomial decompositions from the decomposition path graph.Find out all the hierarchical arrangements by considering the combinations of the component arranging orders in the binomial decomposition.Establish all the SPFUS structures from the hierarchical arrangements.Fill the SPFUS structures with the FUs in the given FU scope, and check the obtained SPFUSs if the operations of their FU-connectors and FR-connectors can actually work. The SPFUSs which can pass the check are the appropriate SPFUSs we want.
Moving object removal and surface mesh mapping for path planning on 3D terrain*
Published in Advanced Robotics, 2020
Yoshitaka Hara, Masahiro Tomono
Next, nodes and arcs of the surface mesh map are constructed from the point cloud map. This part is almost equivalent to the 3D polygon mesh reconstruction. Then, our method calculates the node costs and the arc costs. As a result, surface mesh mapping is completed. The inputs of path planning are the surface mesh map, start and goal positions. In path planning, a path graph is generated from the map, and a graph search is performed by considering the various costs.