In the present work, we study the properties of biological networks by applying analogous
notions of fundamental concepts in Riemannian geometry and optimal mass transport to …

The characterization of complex networks with tools originating in geometry, for instance
through the statistics of so-called Ricci curvatures, is a well established tool of network …

In the present work, we apply a geometric network approach to study common biological
features of anticancer drug response. We use for this purpose the panel of 60 human cell …

In this paper, we discuss the implementation of a curvature flow on weighted graphs based
on the Bakry–Émery calculus. This flow can be adapted to preserve the Markovian property …

In this sequence of two papers, we introduce a curvature flow on (mixed) weighted graphs
which is based on the Bakry-\'Emery calculus. The flow is described via a time-continuous …

Ollivier–Ricci curvature is a method for measuring the robustness of connections in a
network. In this work, we use curvature to measure changes in robustness of brain networks …

We introduce a notion of doubly warped product of weighted graphs that is consistent with
the doubly warped product in the Riemannian setting. We establish various discrete Bakry …

We propose a discrete curvature based approach to the intelligence and classification of
textures in images, with special emphasis on natural ones. We make appeal to a number of …

Fast improvements of technologies for the acquirement of large genomic data through single
cell RNA-sequencing have led to a need for new mathematical methods for the analysis of …

In this study, we adopted a discrete analogous notion of Ricci curvature in a Riemannian
manifold to infer certain robustness properties of networks of interest. We explored three …