Fitting urban movements.

<p>Probability Density Functions (PDF) of human movements and corresponding fits with the rank-distance and gravity models in three cities (Houston, San Francisco and Singapore). In the rank-distance model the probability of transiting from a place to a place in a city, only depends on the rank value of with respect to . In the case of the gravity model, the deterrence affect of distance is co-integrated with a mass based attractiveness of a place . The associated mass, , has been defined according to the number of neighboring places. The parameters for the depicted fit of the gravity model are and meters. The places of a city employed for the simulation experiments where those observed in the Foursquare dataset, hence while the rank-based model is the same for all cities the underlying spatial distribution of places may vary. Excellent fits are observed for all cities analyzed. It is interesting to note that the model is able to reproduce even minor anomalies, such as the case of San Francisco where we have ‘jumps’ in the probability of a movement at 20 and 40 kilometers.