Related papers: Spectral Analysis of Virus Spreading in Random Geo…
This Master's thesis examines the properties of large degree vertices in random recursive directed acyclic graphs (RRDAGs), a generalization of the well-studied random recursive tree (RRT) model. Using a novel adaptation of Kingman's…
When an infection spreads in a community, an individual's probability of becoming infected depends on both her susceptibility and exposure to the contagion through contact with others. While one often has knowledge regarding an individual's…
Consider a random regular graph of fixed degree $d$ with $n$ vertices. We study spectral properties of the adjacency matrix and of random Schr\"odinger operators on such a graph as $n$ tends to infinity. We prove that the integrated density…
We study eigenvalue distribution of the adjacency matrix $A^{(N,p,q)}$ of weighted random uniform $q$-hypergraphs $\Gamma= \Gamma_{N,p,q}$. We assume that the graphs have $N$ vertices and the average number of hyperedges attached to one…
There has been an increasing recognition of the utility of models of the spatial dynamics of viral spread within tissues. Multicellular models, where cells are represented as discrete regions of space coupled to a virus density surface, are…
We develop a theory to measure the variance and covariance of probability distributions defined on the nodes of a graph, which takes into account the distance between nodes. Our approach generalizes the usual (co)variance to the setting of…
In this paper, we give an analytic solution for graphs with n nodes and E edges for which the probability of obtaining a given graph G is specified in terms of the degree sequence of G. We describe how this model naturally appears in the…
Many natural and social systems develop complex networks, that are usually modelled as random graphs. The eigenvalue spectrum of these graphs provides information about their structural properties. While the semi-circle law is known to…
In the present work the spread of epidemic is studied over complex networks which are characterized by power law degree distribution of links and heterogeneous rate of disease transmission. The random allocation of epidemic transmission…
A summary is given of the mechanical characteristics of virus contaminants and the transmission via droplets and aerosols. The ordinary and partial differential equations describing the physics of these processes with high fidelity are…
A random geometric graph $G(\mathcal{X}_n, r_n)$ is formed by taking a binomial process $\mathcal{X}_n$ as the set of vertices and joining any two distinct points with an edge if they lie within distance $r_n$ of each other. We investigate…
I study the spreading of infectious diseases on heterogeneous populations. I represent the population structure by a contact-graph where vertices represent agents and edges represent disease transmission channels among them. The population…
We investigate gene interaction networks in various cancer cells by spectral analysis of the adjacency matrices. We observe localization of the networks on hub genes which have extraordinarily many links. The eigenvector centralities take…
In complex networks the degrees of adjacent nodes may often appear dependent -- which presents a modelling challenge. We present a working framework for studying networks with an arbitrary joint distribution for the degrees of adjacent…
Soft Random Geometric Graphs (SRGGs) have been widely applied to various models including those of wireless sensor, communication, social and neural networks. SRGGs are constructed by randomly placing nodes in some space and making pairwise…
Graph is an abstract representation commonly used to model networked systems and structure. In problems across various fields, including computer vision and pattern recognition, and neuroscience, graphs are often brought into comparison (a…
Exploring the internal mechanism of information spreading is critical for understanding and controlling the process. Traditional spreading models often assume individuals play the same role in the spreading process. In reality, however,…
This paper concerns the free boundary problem of an epidemic model. The spatial movements of the infectious agents and the infective humans are approximated by nonlocal diffusion operators. Especially, both the growth rate of the agents and…
In an attempt to characterize the structure of eigenvectors of random regular graphs, we investigate the correlations between the components of the eigenvectors associated to different vertices. In addition, we provide numerical…
Suppose that a cascade (e.g., an epidemic) spreads on an unknown graph, and only the infection times of vertices are observed. What can be learned about the graph from the infection times caused by multiple distinct cascades? Most of the…