Alethea Barbaro February 17, 2010
Gangs are a problem in Los Angeles!
The Violence Data: 1998, 1999 and 2000
My Life of Crime: Criminology Meets Math Wanted: mathematical model to explore dynamics of gangs in Los Angeles! Eventual goal: better understand what causes gang violence Spatial information very important in this problem Need a model for movement of gang members REU students last summer: promising results
What We Know: Info from Criminology Community Each gang has a central gathering space, called a set space Gangs form dynamically evolving rivalries with one another After major gang violence, there is a period of low violence before retaliation Group size affects probability of fights Avoidance of certain established territories Most violence occurs outside own territory
Motivation for an agent-based model in particular Want to take a bottom-up approach More accessible to criminologists More flexible for exploring different behavioral rules Allows for implementation of heuristic rules and geographical information
Questions to Answer: Do we need behavior rules which incorporate information from criminologists and gang specialists? Or does a more simple model explain the dynamics? How are the rivalries among gangs created? Do we need to use this rivalry network in order to simulate violence among gangs?
Hollenbeck
Gang Territories and Numbers in Hollenbeck HOLLENBECK AREA GANG TERRITORY MAP (5294) ACTIVE GANG MEMBERS ~ AVENUES (673) EASTSIDE 18TH ST (341) HIGHLANDS (14)./ I CLOVER (170) LINCOLN HTS (135) EASTLAKE (88) HAPPY VALLEY (32) ROSE HILLS (37) ELSERENO LOCKE ST (379) LOWELL ST (27) /.,/ I-M-E-T-R-O-1-3-(4-5-) I PRIMERA FLATS (246) ~~~=~-J I HAZARD (336) I STATE ST (99) 1./ I/ CLARENCE ST (63). BREED ST (85) TINY BOYS (116) SENTINEL BOYS (83) VICKYSTOWN (107) L1L EASTSIDE (45) KRAZY ASS MEXICANS (245) MICHIGAN CRIMINAL FORCE (112) ELA-13 TINY DUKES (194) WHITE FENCE (598) EVERGREEN (76) THE MOB CREW (141) CUARTRO FLATS (134) BOYLE HGTS (20) Map prepared by Hollenbeck Crime Analysis Detail on 06/04/09. VARRIO NUEVO ESTRADA (419) 8TH ST (104) OPAL ST (54) INDIANA DUKES (76) For internal distribution only.
The Rivalry Network
The Rivalry Network Embedded in Space
Code architecture Making use of the object-oriented nature of C++ The City contains an array of gang members Each gang member can have many attributes, such as: Location Speed Aggressiveness Status in the gang Gang affiliation The City also has a rivalry matrix of intergang rivalry strengths The rivalry matrix is updated as gang violence occurs
A Control: Just Diffusion
What s Going Wrong?
Where to Go Next: Freeways Heading home Avoiding set spaces Decay on the edges of graph Coupling the rivalry network and avoidance strength Levy flights Von Mises distributions Geographic Threshold Graphs
Incorporating Freeways
Future work on crime Use dynamics for network creation and instead model violence Once the model reproduces rivalries: Analyze how rivalry networks influence dynamics by altering rivalries but not behavioral rules Couple probability of violence to rivalry strengths from network for dynamic evolution Consider continuum Fokker-Planck-type description of model