Thursday, July 26, 2012

Statistical Physics of Human Mobility: Paper

Statistical physics help understand relating the microscopic properties of atoms and molecules to the macroscopic properties of materials that can be observed in everyday life. As a result, it is able to explain thermodynamics as a natural result of statistics, classical mechanics, and quantum mechanics at the microscopic level. [1]

By looking into the GPS information, from vehicles (collected) in Italy, Gallotti et al have performed a study to apply ideas of statistical physics to describe the properties of human mobility.

The human mobility is an interesting research question. Understanding of human mobility can be useful in urban planning, and to understand spread of epidemic. In addition, the authors suggest that such studies may also be useful to discover possible "laws" that can be related to the dynamical cognitive features of individuals.

 The average speed variance (on the left), the distribution (on the right) can be decomposed as a mixture of Gaussian. Two Gaussians with mean speed of around 20 Km/hr and 45 Km/hr emerges. This indicates the distinct behavior of drivers. I find this to be an interesting decomposition.

 The left figure shows the statistical distribution of the activity time. The presence of straight line indicates Benford's law. Figure on the right shows "total activity time". With the help of the "down time" i.e. the period for which the GPS is turned off, the authors suggest that at least three distinct peaks for full-time (~9 hrs), part-time (~4 hrs) jobs and night rest (~13 hrs). However, there is also one more peak around 1hr downtime. I guess the down-time for one hour peak shows short-term activities such as shopping behavior.

In the paper, using the travel time as a cost function, the authors show that the distribution between successive trips are indeed driven by an underlying Benford's law. The ranking of the the distribution of the average visitaion frequency may also help to understand how people organize their daily agenda. An interesting feature comes out when the average speed distribution for the recorded trip is decomposed as a mixture of two Gaussians: one with ≤ 5km. I think such characteristics distribution indicate the local constraint on the movements. Obviously, the motion is not free of constraints. The mobility data is strictly constrained by the road structures.
It would be interesting to see if there are such statistical phenomena as "phase transition" in such statistical law of human mobility.
This is an interesting paper. See [2].

At last, Why do we move from one place to another?
If we assume some aggregate effect on social scale; are we different than the gas molecules contained in a box? Moreover, it seems someone has to drive an extra mile since the system demands it!

References:
(Special thanks to Prof. Armando Bazzani for allowing me to use the figures.)
[1] http://en.wikipedia.org/wiki/Statistical_physics
[2] Towards a Statistical Physics of Human Mobility
Riccardo Gallotti, Armando Bazzani, Sandro Rambaldi
http://arxiv.org/abs/1207.5698