Before revision:  To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega and \omega ) .
After revision:  To provide analytical insight, we characterize stationary distributions for when there is timescale separation between transitions within and between layers (i. e., \omega and \omega employ spectral perturbation theory to characterize the stationary distribution for the limits of small and large \omega, and we show that MMCs inherently exhibit optimality for intermediate \omega in terms of their convergence rate and the extent of convection. As an application, we conduct an MMC-based analysis of brain-activity data, finding MMCs to differ between healthy persons and those with Alzheimer's disease. Overall, our work suggests MMCs and convection as two important new directions for network-related research .