Abstract: We present a brief overview of some notions of discrete curvatures for hypernetworks. In particular, we focus on the adaptation of the Forman-Ricci curvature to the hypernetworks setting, and its applications to genetic networks, more specifically to the understanding of dynamics pluripotent stem cells and cancer cells. We next concentrate on Ollivier-Ricci curvature based hypernetworks curvatures, and in particular on a newly proposed Ricci curvature for hypernetworks stemming from the generalized Wasserstein distance of Piccoli and Rossi and motivated, again, by biological networks.

Contact: Indika Rajapakse