Saturday, February 20, 2010

Gangs and Statistical Mechanics?

   The Los Angeles Police Department may have a new ally who, while not as all-knowing as Charlie Epps from Numb3rs, will help reduce crime by predicting where and when it might occur.   This morning, Professor Andrea Bertozzi  spoke about models that she and her team of post-docs at UCLA are developing to model gang violence.  Using statistical mechanics, bifurcation theory, and partial differential equations, she aims to predict where and when hot-spots of gang-related activity will emerge.  These tools have a long history in the physical and biological sciences, and are similar to those tools used to study the behavior of swarms of insects, which is the subject of some of her past research.
Dr. Bertozzi's newest paper on modeling gang activity will soon be published in the Proceedings of National Academy of Sciences.
   In order to model crime occurrence, Dr. Bertozzi consults the LAPD as well as Anthropologist Jeff Brantingham , whose research shows that criminals tend to commit their crimes near their own homes in areas with which they are familiar.  The model is designed with this in mind, and consists of a grid with a "house" situated at each vertex, freely moving "burglars", and an "attractiveness" function that depends on both space and time.  Different factors determine the attractiveness of a house to a burglar -- these include how close the house is to the burglar's home, whether the house was recently burgled, whether any of its neighbors have been victimized recently, and constants like the presence of graffiti or the type of housing prevalent in the area.  Two behaviors emerge from the simulations:  one in which a police presence would simply displace the criminal activity and one in which a police presence would actually eliminate the problem.  The model compares favorably to data collected over the period of a year in a particular LA neighborhood, and Dr. Bertozzi sees this as a first step in applying mathematical modeling to other social science issues.
    Where are the gangs?  Gang-related violence modeling is done by post-doc Alethea Barbaro , who studies gang networks, patterns in tagging, and how rivalries arise and dissipate.  In response to a question concerning how this work might inform decisions concerning the balance between hiring more policemen and "cleaning up the streets" to reduce the "attractiveness", Dr. Bertozzi responded "Sounds like a good research proposal!  These questions are excellent and hopefully will employ people like us for years to come."


  1. Why are the people who have been presenting these at the conferences the past have not been mentioned? Is this completely different from whats been circulating at all the mathematics conferences?

  2. Because this is a blog about all the math I can find at the 2010 AAAS conference, I am focusing on current research. This research is new, and you can read more about it at
    or you can read the article scheduled to be published in the Proceeding of National Academy of Sciences, which would not have published this if it were old. While mathematical methods may have been used in the past to analyze data about crimes, these methods are different.

  3. Yes this is an active area of research. We held a conference at UCLA a few years ago
    that brought together mathematicians, social scientists, and law enforcement personnel.
    While researchers in the past have used agent based models for social science problems, there is very little in the literature that is able to analytically understand or solve those models. Here we show how this can be done for a particular model on crime hotspots. By going to a mean field partial differential equations model we can use bifurcation theory to analyze the nonlinear dynamics of the system. This allows us to make predictions for the agent based simulation without having to actually run the simulation. The analysis also explains why some hotspots can be permanently suppressed whereas others can not.