Analysis of vehicle formations using the eigenprojection of the Laplacian matrix

AbstractContact networks provide insights on disease spread due to the duration of close proximity interactions. For systems governed by consensus dynamics, network structure is key to optimising the spread of information. For disease spread over contact networks, the structure would be expected to be similarly influential. However, metrics that are essentially agnostic to the network’s structure, such as weighted degree (strength) centrality and its variants, perform near-optimally in selecting effective spreaders. These degree-based metrics outperform eigenvector centrality, despite disease spread over a network being a random walk process. This paper improves eigenvector-based spreader selection by introducing the non-linear relationship between contact time and the probability of disease transmission into the assessment of network dynamics. This approximation of disease spread dynamics is achieved by altering the Laplacian matrix, which in turn highlights why nodes with a high degree are such influential disease spreaders. From this approach, a trichotomy emerges on the definition of an effective spreader where, for susceptible-infected simulations, eigenvector-based selections can either optimise the initial rate of infection, the average rate of infection, or produce the fastest time to full infection of the network. Simulated and real-world human contact networks are examined, with insights also drawn on the effective adaptation of ant colony contact networks to reduce pathogen spread and protect the queen ant.

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Direct 3D model extraction method for color volume images

Technology and Health Care ◽

10.3233/thc-218014 ◽

2021 ◽

Vol 29 ◽

pp. 133-140

Author(s):

Bin Liu ◽

Shujun Liu ◽

Guanning Shang ◽

Yanjie Chen ◽

Qifeng Wang ◽

...

Keyword(s):

3D Model ◽

Clinical Medicine ◽

Three Dimensional ◽

Laplacian Matrix ◽

Segmentation Method ◽

Human Organs ◽

Model Segmentation ◽

Treatment Objective ◽

Organ Models ◽

Different Parts

BACKGROUND: There is a great demand for the extraction of organ models from three-dimensional (3D) medical images in clinical medicine diagnosis and treatment. OBJECTIVE: We aimed to aid doctors in seeing the real shape of human organs more clearly and vividly. METHODS: The method uses the minimum eigenvectors of Laplacian matrix to automatically calculate a group of basic matting components that can properly define the volume image. These matting components can then be used to build foreground images with the help of a few user marks. RESULTS: We propose a direct 3D model segmentation method for volume images. This is a process of extracting foreground objects from volume images and estimating the opacity of the voxels covered by the objects. CONCLUSIONS: The results of segmentation experiments on different parts of human body prove the applicability of this method.

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Matrix Completion Using Graph Total Variation Based on Directed Laplacian Matrix

Circuits Systems and Signal Processing ◽

10.1007/s00034-020-01613-5 ◽

2021 ◽

Author(s):

Alireza Ahmadi ◽

Sina Majidian ◽

Mohammad Hossein Kahaei

Keyword(s):

Total Variation ◽

Matrix Completion ◽

Laplacian Matrix

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The normalized distance Laplacian

Special Matrices ◽

10.1515/spma-2020-0114 ◽

2021 ◽

Vol 9 (1) ◽

pp. 1-18

Author(s):

Carolyn Reinhart

Keyword(s):

Spectral Radius ◽

Characteristic Polynomial ◽

Adjacency Matrix ◽

Connected Graph ◽

Distance Matrix ◽

Laplacian Matrix ◽

Diagonal Matrix ◽

The Matrix

Abstract The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of transmissions of the vertices of the graph. The normalized distance Laplacian, 𝒟𝒧(G) = I−T(G)−1/2 𝒟(G)T(G)−1/2, is introduced. This is analogous to the normalized Laplacian matrix, 𝒧(G) = I − D(G)−1/2 A(G)D(G)−1/2, where D(G) is the diagonal matrix of degrees of the vertices of the graph and A(G) is the adjacency matrix. Bounds on the spectral radius of 𝒟 𝒧 and connections with the normalized Laplacian matrix are presented. Twin vertices are used to determine eigenvalues of the normalized distance Laplacian. The distance generalized characteristic polynomial is defined and its properties established. Finally, 𝒟𝒧-cospectrality and lack thereof are determined for all graphs on 10 and fewer vertices, providing evidence that the normalized distance Laplacian has fewer cospectral pairs than other matrices.

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On minimum algebraic connectivity of graphs whose complements are bicyclic

Open Mathematics ◽

10.1515/math-2019-0119 ◽

2019 ◽

Vol 17 (1) ◽

pp. 1490-1502 ◽

Cited By ~ 1

Author(s):

Jia-Bao Liu ◽

Muhammad Javaid ◽

Mohsin Raza ◽

Naeem Saleem

Keyword(s):

Connected Graph ◽

Diffusion Processes ◽

Laplacian Matrix ◽

Group Differences ◽

Algebraic Connectivity ◽

Connected Graphs ◽

Bicyclic Graph ◽

Smallest Eigenvalue ◽

Unique Graph ◽

The Stability

Abstract The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (networks). A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, firstly the unique graph with a minimum algebraic connectivity is characterized in the class of connected graphs whose complements are bicyclic with exactly three cycles. Then, we find the unique graph of minimum algebraic connectivity in the class of connected graphs $\begin{array}{} {\it\Omega}^c_{n}={\it\Omega}^c_{1,n}\cup{\it\Omega}^c_{2,n}, \end{array}$ where $\begin{array}{} {\it\Omega}^c_{1,n} \end{array}$ and $\begin{array}{} {\it\Omega}^c_{2,n} \end{array}$ are classes of the connected graphs in which the complement of each graph of order n is a bicyclic graph with exactly two and three cycles, respectively.

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Community Detection Based on Graph Representation Learning in Evolutionary Networks

Applied Sciences ◽

10.3390/app11104497 ◽

2021 ◽

Vol 11 (10) ◽

pp. 4497

Author(s):

Dongming Chen ◽

Mingshuo Nie ◽

Jie Wang ◽

Yun Kong ◽

Dongqi Wang ◽

...

Keyword(s):

Community Detection ◽

Network Structure ◽

Clustering Algorithm ◽

Laplacian Matrix ◽

Representation Learning ◽

Detection Algorithm ◽

Graph Representation ◽

Time Slice ◽

Current Time ◽

Evolutionary Networks

Aiming at analyzing the temporal structures in evolutionary networks, we propose a community detection algorithm based on graph representation learning. The proposed algorithm employs a Laplacian matrix to obtain the node relationship information of the directly connected edges of the network structure at the previous time slice, the deep sparse autoencoder learns to represent the network structure under the current time slice, and the K-means clustering algorithm is used to partition the low-dimensional feature matrix of the network structure under the current time slice into communities. Experiments on three real datasets show that the proposed algorithm outperformed the baselines regarding effectiveness and feasibility.

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