Approach to the inverse problem of superdiffusion on finite systems based on time-dependent long-range navigation.

This work addresses the superdiffusive motion of a random walker on a discrete finite-size substrate. It is shown that, with the inclusion of suitably tuned time-dependent probability of large distance jumps over the substrate, the mean square displacement (MSD) of the walker has a power-law dependence on time with a previously chosen exponent γ>1. The developed framework provides an exact solution to the inverse problem, i.

Relaxation time of the global order parameter on multiplex networks: The role of interlayer coupling in Kuramoto oscillators.

This work considers the time scales associated with the global order parameter and the interlayer synchronization of coupled Kuramoto oscillators on multiplexes. For two-layer multiplexes with an initially high degree of synchronization in each layer, the difference between the average phases in each layer is analyzed from two different perspectives: the spectral analysis and the nonlinear Kuramoto model. Both viewpoints confirm that the prior time scales are inversely proportional to the interlayer coupling strength.