[2] Universal Spatial Distribution of Mobile Agents

In a recent paper "Understanding individual human mobility patterns" published by Marta C. Gonzalez et al. in Nature, the authors tracked the coordinates of mobile phone users over an extended period.

In this study, space was divided into cells (the range of a single mobile phone antenna) and the actual raw data consisted of the sequence of cells in which each user was found. In most of the cells, the same user was found several times. In particular, there was a cell of maximum occupancy for each user.

For each individual, the spatial distribution pattern (formally equivalant to a mass distribution) was artificially centered around the origin. Next, it was rotated around its center of mass, so that the main axis of the inertia tensor became alligned along the x-axis. Next, the pattern was flipped, such that the cell of maximum occupancy was located at the right side. It was then scaled to a fixed standard deviation in both x- and y-directions. The centered, rotated, flipped and scaled distributions were finally averaged over all individual trajectories (CRFSA method) . The result was a "universal" and surprisingly non-trivial distribution pattern:



It seems worthwhile to apply a similar procedure to the trajectories of microbeads attached to the living cytoskeleton. I shall name this project "Universal PDF".