Abstract

Street gangs are a continued problem not only to the greater Los Angeles area, but also in many urban areas of the United States. This talk highlights mathematical models used to describe two aspects of gang violence: gang rivalry networks and inferring affiliation for violent events. To further understand the generation of a gang rivalry network, an agent based model is presented. The movement dynamics of agents are coupled to an evolving network of gang rivalries, which is determined by previous interactions among agents in the system. To infer gang affiliation of violent events in the presence of incomplete data, the Estimate & Score algorithm will be presented. Even when gang activity is highly stochastic, localized excitations in parts of the known dataset can help identify gangs responsible for unsolved crimes. Assuming the data is a realization of a Hawkes process, this algorithm assigns weights to the inferred culpable gang as well as estimate the process parameters in the presence of incomplete data.