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Locating Criminals with Geo-Profiling

Geoprofiling is a technique that has been used to locate criminals (with small success) or shark attacks, created by Kim Rossmo. It is based on two assumptions: the criminal does not commit crimes in a "buffer zone" close to his home, and he does not travel too far to find a new victim. Locators show the locations of crimes or shark attacks and the regions in red are the regions where the criminal's or shark's home is most likely to be.

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The formula used to find the probability of the criminal's residence is
,
where the sum is over crime locations and
.
Here is a point in the grid and is the distance to a crime location with a choosen metric, either the Manhattan or Euclidean distance. The "buffer zone" is the area where the criminal does not commit crimes; is its radius. The powers and affect the decay of the curve.
[1] J. Kun. "Hunting Serial Killers." (Jul 20, 2011) jeremykun.com/2011/07/20/serial-killers.
[2] R. A. Martin, D. K. Rossmo, and N. Hammerschlag, "Hunting Patterns and Geographic Profiling of White Shark Predation," Journal of Zoology, 279(2), 2009 pp. 111–118. doi: 10.1111/j.1469-7998.2009.00586.x
[3] SuperJustimagine. Geo-profiling on Numb3rs [Video]. (Aug 15, 2010) www.youtube.com/watch?v=AUub-ch_ULM.
[4] "The Math behind Numb3rs: Pilot Episode." (2007) numb3rs.wolfram.com/season1.html.
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