New ideas and technologies adopted by a small number of individuals occasionally spread globally through a complex web of social ties. Here, we present a simple and general approximation method, namely, a message-passing approach, that allows us to describe the diffusion processes on complex...

The question of how to stabilize financial systems has attracted considerable attention since the global financial crisis of 2007-2009. Recently, Beal et al. ("Individual versus systemic risk and the regulator's dilemma", Proc Natl Acad Sci USA 108: 12647-12652, 2011) demonstrated that higher...