  We study the dynamics of diffusion processes acting on directed multiplex
networks, i.e., coupled multilayer networks where at least one layer consists
of a directed graph. We reveal that directed multiplex networks may exhibit a
faster diffusion at an intermediate degree of coupling than when the two layers
are fully coupled. We use three simple multiplex examples and a real-world
topology to illustrate the characteristics of the directed dynamics that give
rise to a regime in which an optimal coupling exists. Given the ubiquity of
both directed and multilayer networks in nature, our results could have
important implications for the dynamics of multilevel complex systems towards
optimality.
