Unexpectedly Intriguing!
February 18, 2009

When it comes to mobility, people are creatures of habit. Most people spend about 40% of their time in just two places with much of their remaining time spent visiting anywhere from 5 to 50 other places, which they visit with diminishing regularity. What's more, we can predict the likelihood that an individual is a certain distance away from their preferred two places.

We know this because the typical daily travel of a large sample of people was tracked and analyzed by Marta C. González, César A. Hidalgo and Albert-László Barabási, who studied the trajectory of 100,000 anonymous mobile phone users over a six-month period of time and found that when it comes to mobility patterns, the distance humans travel is remarkably predictable. Their findings are presented in the June 2008 paper Understanding Individual Human Mobility Patterns.

Using the geographic data provided by the observed sample's mobile phone use, which allowed the researchers to determine the location of the tracked individuals with respect to the cell phone towers through which their calls were processed, González, Hidalgo and Barabási observed that human mobility was not random, but rather best described by a kind of probability distribution called a Truncated Lévy Flight (TLF). This kind of probability distribution was first introduced in 1996 by Rosario N. Mantegna and H. Eugene Stanley and is a special "bounded" case of a "fat-tailed" probability distribution first described by French mathematician Paul Pierre Lévy and known as a Lévy flight.

Here, the distance traveled by an individual follows a power-law distribution. Most distances people travel are short, but there is a significant probability that individuals will travel a long distance, more so than would be predicted using the well-established statistical math given by a normal probability distribution. Since the distance an individual can travel is not infinite, the probability distribution given by Mantegna and Stanley's truncated Lévy flight works best to describe the likelihood that an individual has traveled a certain distance.

We thought it might be fun to build a tool using the results of Gonzalez, Hidalgo and Barabasi's study to find the probability that an individual has traveled a given distance that the authors have referenced with respect to a typical "radius of gyration," which we'll describe as being the distance typically traveled between "home" and "work", or in the authors' terminology, an individual's "preferred locations."

Distance Traveled
Input Data Values
Distance Traveled by Individual [miles]

Probability of Individual Traveling Entered Distance
Calculated Results Values
Probability of Traveling Specific Distance

We'll conclude that this kind of information might be really useful is in fighting communicable diseases, where knowing how mobile people are can help better focus epidemic prevention efforts. For our interests, the kind of math described by this research is very similar to that which can best describe how stock prices change over time.

Update: Brainstorm! Why not use this mathematical model of human mobility to put a Predator on a certain well-known terrorist with whom we have issues? If the wild animal model of mobility can put the guy within three possible locations, this one might be able to take it down to just one. If it works, don't thank us, just send us a video of the creep's final moments....

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