Pattern formation in physical, biological, and sociological systems has been studied for many years. Despite the fact that these subject areas are completely diverse, the mathematics that describes underlying patterns in these systems can be surprisingly similar. Mathematical tools can be used to study such systems and predict their patterns.
One area where the study of pattern formation has been of growing interest is in crime modeling. It has been observed that criminal activity tends to cluster in space and time in urban settings. Analyzing spatio-temporal patterns of urban crime using mathematical modeling can reveal hidden patterns in the process of criminal activity, and potentially help establish methods for prevention.
The authors of a paper published this month in the SIAM Journal on Mathematical Analysis analyzed pattern formation as a model to predict burglaries. The rate of burglaries tends to be higher for houses that have been burglarized before or are close neighbors of those that have been burglarized. This leads to the creation of burglary hotspots. Authors Steve Cantrell, Chris Cosner, and Raúl Manásevich propose a model to generate patterns that would describe the specific location of such hotspots.
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