Curvature Analysis of Estrogen Receptor Positive Breast Cancer Under PI3K Inhibition

Abstract

In this note, we re-examine the work of Bosch et al. from a network point of view. In particular, we employ an extended defintion of Ollivier-Ricci curvature that allows us to study graphs with both positive and negative weights. This is done by utilizing a dual formulation of the Wasserstein 1-metric, allowing us to extend the Earth Movers Distance to signed measures. The resulting curvature may be applied study the robustness properties of general networks modelled as weighted graphs. In this note, we apply the theory to elucidate the robustness and therefore possible mechanisms of resistance of estrogen receptor positive breast cancer under PI3K inhibition.