Geographical influences of an emerging network of gang rivalries

We propose an agent-based model to simulate the creation of street gang rivalries. 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. Basic gang data, geographic information, and behavioral dynamics suggested by the criminology literature are integrated into the model. The major highways, rivers, and the locations of gangs’ centers of activity influence the agents’ motion. We use a policing division of the Los Angeles Police Department as a case study to test our model. We apply common metrics from graph theory to analyze our model, comparing networks produced by our simulations and an instance of a Geographical Threshold Graph to the existing network from the criminology literature.

[1]  M. Short,et al.  Cooperation and punishment in an adversarial game: how defectors pave the way to a peaceful society. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Frederic M. Thrasher,et al.  The gang : a study of 1,313 gangs in Chicago. , 1936 .

[3]  Mirta B. Gordon,et al.  A random walk in the literature on criminality: A partial and critical view on some statistical analyses and modelling approaches , 2010, European Journal of Applied Mathematics.

[4]  A. Bertozzi,et al.  Self-propelled particles with soft-core interactions: patterns, stability, and collapse. , 2006, Physical review letters.

[5]  M. Macy,et al.  FROM FACTORS TO ACTORS: Computational Sociology and Agent-Based Modeling , 2002 .

[6]  S. R. Jammalamadaka,et al.  Topics in Circular Statistics , 2001 .

[7]  Kyunghan Lee,et al.  On the Levy-Walk Nature of Human Mobility , 2008, IEEE INFOCOM 2008 - The 27th Conference on Computer Communications.

[8]  Elizabeth R. Groff,et al.  ‘Situating’ Simulation to Model Human Spatio‐Temporal Interactions: An Example Using Crime Events , 2007, Trans. GIS.

[9]  H. Herrmann,et al.  Agent-based model for friendship in social networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Scott H. Decker,et al.  Life in the Gang: Family, Friends, and Violence , 1996 .

[11]  Marco Tomassini,et al.  Mutual trust and cooperation in the evolutionary hawks-doves game , 2009, Biosyst..

[12]  Frank M. Weerman,et al.  Street Gang Violence in Europe , 2006 .

[13]  Jasmine Novak,et al.  Geographic routing in social networks , 2005, Proc. Natl. Acad. Sci. USA.

[14]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[15]  P. Brantingham,et al.  Offender Mobility and Crime Pattern Formation from First Principles , 2008 .

[16]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[17]  C. Hemelrijk,et al.  Density distribution and size sorting in fish schools: an individual-based model , 2005 .

[18]  Clifford A. Grammich,et al.  Reducing Gun Violence: Results from an Intervention in East Los Angeles , 2003 .

[19]  S. R. Jammalamadaka,et al.  Directional Statistics, I , 2011 .

[20]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Colin Flint,et al.  Spatializing Social Networks: Using Social Network Analysis to Investigate Geographies of Gang Rivalry, Territoriality, and Violence in Los Angeles , 2010 .

[22]  M. W. Klein,et al.  The Eurogang Paradox - Street Gangs and Youth Groups in the U.S. and Europe , 2000 .

[23]  L. Freeman Centrality in social networks conceptual clarification , 1978 .

[24]  M. Newman,et al.  Random graphs with arbitrary degree distributions and their applications. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  Frank Schweitzer,et al.  Brownian Agents and Active Particles: Collective Dynamics in the Natural and Social Sciences , 2003 .

[26]  Alethea Barbaro,et al.  Modelling and simulations of the migration of pelagic fish , 2009 .

[27]  N. Fisher,et al.  Efficient Simulation of the von Mises Distribution , 1979 .

[28]  Claudio Agostinelli,et al.  circular: Circular Statistics, from "Topics in circular Statistics" (2001) S. Rao Jammalamadaka and A. SenGupta, World Scientific. , 2004 .

[29]  George E. Tita,et al.  An ecological study of the location of gang set space , 2005 .

[30]  Aric A. Hagberg,et al.  The Structure of Geographical Threshold Graphs , 2008, Internet Math..

[31]  Fabrizio Sebastiani,et al.  Machine learning in automated text categorization , 2001, CSUR.

[32]  Yiming Yang,et al.  A re-examination of text categorization methods , 1999, SIGIR '99.

[33]  I. Good Nonparametric roughness penalties for probability densities , 1971 .

[34]  R. Berk How you can tell if the simulations in computational criminology are any good , 2008 .

[35]  Pierre Baldi,et al.  Assessing the accuracy of prediction algorithms for classification: an overview , 2000, Bioinform..

[36]  C. D. Kemp,et al.  Density Estimation for Statistics and Data Analysis , 1987 .

[37]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[38]  Jos'e A. Carrillo,et al.  A well-posedness theory in measures for some kinetic models of collective motion , 2009, 0907.3901.

[39]  M. Newman,et al.  Scientific collaboration networks. II. Shortest paths, weighted networks, and centrality. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Albert-László Barabási,et al.  Understanding individual human mobility patterns , 2008, Nature.

[41]  T. Geisel,et al.  The scaling laws of human travel , 2006, Nature.

[42]  Barry Wellman,et al.  Are personal communities local? A Dumptarian reconsideration☆ , 1996 .

[43]  George E. Tita,et al.  Making Space for Theory: The Challenges of Theorizing Space and Place for Spatial Analysis in Criminology , 2010 .

[44]  Erik A. Lewis,et al.  Statistical Modeling of Gang Violence in Los Angeles , 2009 .

[45]  B. Matthews Comparison of the predicted and observed secondary structure of T4 phage lysozyme. , 1975, Biochimica et biophysica acta.

[46]  Bin Jiang,et al.  Characterizing the human mobility pattern in a large street network. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  Frank Schweitzer,et al.  Self-assembling of networks in an agent-based model. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Garry Robins,et al.  A spatial model for social networks , 2006 .

[49]  L. Tesfatsion Agent-based computational economics : A constructive approach to economic theory , 2006 .

[50]  Andrea L Bertozzi,et al.  Dissipation and displacement of hotspots in reaction-diffusion models of crime , 2010, Proceedings of the National Academy of Sciences.

[51]  Jie-Jun Tseng,et al.  Statistical properties of agent-based models in markets with continuous double auction mechanism , 2010, 1002.0917.

[52]  Elijah Anderson Code of the Street: Decency, Violence, and the Moral Life of the Inner City , 1999 .

[53]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[54]  J. Neuman,et al.  Statistical and Stochastic Modeling of Gang Rivalries in Los Angeles , 2010 .

[55]  R. A. Gaskins,et al.  Nonparametric roughness penalties for probability densities , 2022 .

[56]  N. Konno,et al.  Geographical threshold graphs with small-world and scale-free properties. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  S. Osher,et al.  Fast TV Regularization for 2D Maximum Penalized Likelihood Estimation , 2011 .

[58]  A. Papachristos Murder by Structure: Dominance Relations and the Social Structure of Gang Homicide in Chicago , 2007, AJS; American journal of sociology.

[59]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[60]  P. Eggermont,et al.  Maximum penalized likelihood estimation , 2001 .

[61]  Ashley B. Pitcher Adding police to a mathematical model of burglary , 2010, European Journal of Applied Mathematics.

[62]  D. Foley,et al.  The economy needs agent-based modelling , 2009, Nature.

[63]  G. G. Stokes "J." , 1890, The New Yale Book of Quotations.

[64]  D. Ley,et al.  URBAN GRAFFITI AS TERRITORIAL MARKERS , 1974 .

[65]  Andrea L. Bertozzi,et al.  Improving Density Estimation by Incorporating Spatial Information , 2010, EURASIP J. Adv. Signal Process..

[66]  John E. Eck,et al.  Contrasting simulated and empirical experiments in crime prevention , 2008 .

[67]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[68]  P. Torrens Geography and computational social science , 2010 .

[69]  Andrea L. Bertozzi,et al.  Collaborative Searching Through Swarming , 2010 .

[70]  Michael T. Gastner,et al.  The spatial structure of networks , 2006 .

[71]  Mike O'Leary,et al.  The mathematics of geographic profiling , 2009 .

[72]  Scott H. Decker,et al.  Life in the Gang: Family, Friends, and Violence , 1996 .

[73]  A. Wilhite Economic Activity on Fixed Networks , 2006 .

[74]  Robert Garcia,et al.  Residence and Territoriality in Chicano Gangs , 1983 .

[75]  Andrea L. Bertozzi,et al.  c ○ World Scientific Publishing Company A STATISTICAL MODEL OF CRIMINAL BEHAVIOR , 2008 .

[76]  Aric A. Hagberg,et al.  Giant Component and Connectivity in Geographical Threshold Graphs , 2007, WAW.

[77]  P. Jones STATISTICAL MODELS OF CRIMINAL BEHAVIOR: THE EFFECTS OF LAW ENFORCEMENT ACTIONS , 2010 .

[78]  Phillip D. Stroud,et al.  EpiSimS simulation of a multi-component strategy for pandemic influenza , 2008, SpringSim '08.

[79]  Z. Toroczkai,et al.  Proximity networks and epidemics , 2007 .