Multiscale entropy rate analysis of complex mobile agents

Abstract

Accurate prediction of the motion of objects is a central scientific goal. For deterministic or stochastic processes, models exist which characterize motion with a high degree of reliability. For complex systems, or those where objects have a degree of agency, characterizing motion is far more challenging. The information entropy rate of motion through a discrete space can place a limit on the predictability of even the most complex or history-dependent actor, but the variability in measured encountered locations is inexorably tied to the spatial and temporal resolutions of those measurements. This relation depends on the path of the actor in ways that can be used to derive a general law in closed form relating the mobility entropy rate to different spatial and temporal resolutions, and the path properties within each cell along the path. Correcting for spatial and temporal effects through regression yields the path properties and a measure of mobility entropy rate robust to changes in dimension, allowing comparison of mobility entropy rates between datasets. Employing this measure on empirical datasets yields novel findings, from the similarity of taxicabs to drifters, to the predictable motions of undergraduates, to the browsing habits of Canadian moose.