Hubs-biased advection-diffusion on undirected graphs.

Abstract:

In certain real-world scenarios it is important to account for the influence of nearest neighbors on the diffusion of a particle located at a node of an undirected graph. To capture this influence the so-called hubs-biased Laplacians were proposed. We investigated the self-adjoint of these operators and discovered that they correspond to operators describing advective processes, where a degree-based drift pulls the diffusive particle from/towards the hubs. Advection operators were previously defined only for digraphs, where the direction of the edges ruled the drift, but the new operators that we present here act on undirected graphs. In this talk, we will explain how this new advective operators in undirected graphs are constructed, which properties do they have and which is its final configuration. Moreover, we will construct an advection-diffusion equation in which both processes “compete” in a graph. showing the analytic expression of the steady state of these processes. Finally, we will study how advection-diffusion shapes movement of the species L. catta when the foraging occurs in a patched landscape network in Southern Madagascar.