Speaker: Prof. Piet Van Mieghem, Delft University of Technology (https://www.nas.ewi.tudelft.nl/people/Piet)
Title: Linear Processes on Networks
Abstract: From a network science point of view, we will discuss linear processes on a graph, which are the easiest, but also the most elegant processes. We start with the Laplacian matrix of a graph and concentrate on a flow problem in networks. From the spectral decomposition of the Laplacian, we will introduce the simplex of an undirected, possibly weighted graph. The simplex geometry of a graph is, besides the topology domain and the spectral domain, the third equivalent description of a graph. Continuous-time Markov processes are described by the Chapman-Kolmogorov (linear) equations, in which the appearing infinitesimal generator is, in fact, a weighted Laplacian of the Markov graph. We will discuss Markovian epidemics on a fixed graph, show limitations of the linear theory on graphs and introduce a mean-field approximation, a powerful method from physics, that results into non-linear governing equations. We will end with recent work on non-Markovian epidemics on a fixed graph.
Bio available here: https://www.nas.ewi.tudelft.nl/people/Piet/