CrimeUsing math to track, predict criminals’ next move
One way to study criminal behavior and predict a criminal’s next move is by analyzing his or her movement. Several mathematical models have addressed this in detail, in particular, the UCLA “burglary hotspot” model. Mathematicians now propose a mathematical model that analyzes criminal movement in terms of a Lévy flight, a pattern in which criminals tend to move locally as well as in large leaps to other areas. This closely replicates daily human commute in big cities.
One way to study criminal behavior and predict a criminal’s next move is by analyzing his or her movement. Several mathematical models have addressed this in detail, in particular, the UCLA “burglary hotspot” model, also the topic of a previous Nugget published by the Society for Industrial and Applied Mathematics (SIAM).
A SIAM release reports that in a paper published last month in the SIAM Journal on Applied Mathematics, authors Sorathan Chaturapruek, Jonah Breslau, Daniel Yazdi, Theodore Kolokolnikov, and Scott McCalla propose a mathematical model that analyzes criminal movement in terms of a Lévy flight, a pattern in which criminals tend to move locally as well as in large leaps to other areas. This closely replicates daily human commute in big cities.
“The main goal of this study is to elucidate how various movement strategies of criminals affect the crime rate,” authors Theodore Kolokolnikov and Scott McCalla wrote in an e-mail.
“With our model, we can infer criminal movement patterns from burglary data, and thus gain information on how burglars explore possible targets.”
The UCLA model studied the formation of hotspots of criminal activity based on the broken window effect, which proposes that localized regions of high crime activity can occur as a result of previous crimes in an area. For a brief period after a home is burgled it becomes a target for another burglary, as do other houses in the vicinity. This is observed in burglary data; previous crimes make homes more attractive to burglars for a variety of reasons, such as knowledge of how to break in, information about the valuables in a home, ability to navigate the neighborhood, and greater confidence in getting away with the crime.
The UCLA model, which uses a random walk with a bias toward attractive burglary sites to analyze criminal movement, can however, be restrictive. “The pioneering UCLA hotspot model assumed that criminals move locally, following Brownian (or random) motion. The model assumed that criminals only had access to information about burglary targets in their immediate vicinity, and that they were unlikely to travel large distances to access different neighborhoods with better targets,” say Kolokolnikov and McCalla. “A much more realistic model of human locomotion allows for occasional ‘big jumps’. This is typically modeled using Lévy flights.”
The release notes that Lévy flights are a modified form of the standard random walk; the latter uses random step lengths as well as a random direction.
