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Computational Modeling and Simulation of Spatiotemporal Characteristics of Crime in Urban Environments

Computational Modeling and Simulation of Spatiotemporal Characteristics of Crime in Urban Environments. Uwe Glässer Software Technology Lab School of Computing Science Simon Fraser University glaesser@cs.sfu.ca. Specification technology. Abstract State Machines

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Computational Modeling and Simulation of Spatiotemporal Characteristics of Crime in Urban Environments

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  1. Computational Modeling and Simulation ofSpatiotemporal Characteristics of Crime in Urban Environments Uwe Glässer Software Technology Lab School of Computing Science Simon Fraser University glaesser@cs.sfu.ca

  2. Specification technology Abstract State Machines • Rigorous modeling and analysis of complex computational systems • Constructive approach for • Requirements analysis • Design specification • Experimental validation • Formal verification • ASM Research Center(www.asmcenter.org) Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  3. Applications • Semantic foundations • Modeling complex distributed systems • Communications software • Web service architectures • System design languages • Software technology for Intelligent Systems • Computational criminology • Aviation security • Computational methods and tools • Abstract executable specifications Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  4. Problem Verification Environment Graphical UI Testing Environment Abstract Software Model Control API Parser CoreASM Engine Ground model Design Abstract Storage Interpreter Refinement Detailed ground model Construction Scheduler Coding Code CoreASM • Executable specifications R. Farahbod, V. Gervasi and U. Glässer. CoreASM: An Extensible ASM Execution Engine. To appear in Fundamenta Informatica 77 (1-2), pp. 71-103 Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  5. Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  6. A notorious problem How can one cope with the notorious problem of establishing the correctness and completeness of abstract functional requirements in the design of discrete dynamic systems prior to actually building a system? Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  7. Can anyalgorithm, never mind how abstract, be modeled by a generalized machine very closely and faithfully? ... If we stick to one abstract level (abstracting from low-level details and being oblivious to a possible higher-level picture) and if the states of the algorithm reflect all the pertinent information, then a particular small instruction set suffices in all cases. Sequential ASMs Parallel ASMs (synchronous) Distributed ASMs (asynchronous) Yuri Gurevich Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  8. Can one generalize Turing machines so that any algorithm, never mind how abstract, can be modeled by a generalized machine very closely and faithfully? Church-Turing thesis Every computable function is Turing computable.(1936) Any algorithm can be simulated by a Turing machinewith only polynomial slowdown. … can be calculated by an effective or mechanical method not demanding any insight or ingenuity An algorithm can be given a precise meaning by a Turing machine. Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  9. The ASM thesis The ASM thesis is that any algorithm can be modeled at its natural abstraction level by an appropriate ASM.(Gurevich, 1985) Sequential thesis: Sequential ASMs capture sequential algorithms.(Gurevich, 2000) Parallel thesis: ASMs capture parallel algorithms.(Blass/Gurevich, 2003) … ? Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  10. Abstract state machine An ASM is a virtual machine with abstract states, combining two fundamental abstraction principles:first-order structures + state transition systems. Vocabulary Initial states Program f(t1,t2,…,tn): t0 if C then R1 else R2 do-in-parallel R1 Rk forall x in S R(x) choose xin S: (x) R(x) … Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  11. Computation i 1 1 2 X0  X1  X2 …  Xi  Xi1 … (,Xi) Initial state Evolution of the state Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  12. Sequential ASM Formalization of the notion of sequential algorithm Three postulates: Sequential time Abstract state Bounded exploration Syntax We assume informally that any algorithm A can be given by a finite text that explains the algorithm without presupposing any special knowledge. Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  13. Distributed ASM Asynchronous computation model (Gurevich, 1995) Computational agents Globally shared states Concurrent moves Semantic model resolves potential conflicts according to the definition of partially ordered runs Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  14. Mastermind • Crime patterns in urban environments P. L. Brantingham, U. Glässer, B. Kinney, K. Singh and M. Vajihollah. A Computational Model for Simulating Spatial Aspects of Crime in Urban Environments. In Proc. IEEE International Conference on Systems, Man and Cybernetics, Oct. 2005 Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  15. Crime is not random • Criminal events relate to people’s movement in the course of everyday lifes  Offenders commit offenses near places they spend most of their time  Victims are victimized near places where they spend most of their time • Patterns/ rules that govern the working of asocial system • one composed of criminals, victims and targets─ interacting with one another Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  16. Modeling and simulation Motivation • Crime analysis and prevention • Integration of established theories • Reasoning about likely scenarios Scope • Agents living in a virtual city • Commuting between home, work and recreation Goals Coherent and consistent semantic framework • Computational models for discrete event simulation • Integration and validation of patterns/ theories Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  17. Multi-Agent Systems Criminology System Dynamics Environment Planning ASM Navigation Experimental Validation AI/ALife Knowledge Represent. Decision Making Neural Nets Learning Challenges and needs Approach • Common semantic framework • Abstract State Machines: • common core for linkingmulti-disciplinary aspects • Semantic foundation • Discrete mathematics • Computational logic ``Computational thinking’’ Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  18. Mental Maps “Every inhabitant of Amsterdam has an invisible map of the city in his head. The way he moves about the city and the choices made in this process are determined by this mental map. Amsterdam Real Time attempts to visualize these mental maps through examining the mobile behavior of the city's users.”  Amsterdam Real Time Mental maps Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  19. Objective Environment Geographic Environment Perception Awareness Space Subjective Environment Activity Space Urban Environment(1) • Objective Environment • Physical reality • Subjective Environment • Subjective reality • Agent’s perception • Awareness Space • Part of perception • Activity Space • Subset of awareness space • Frequently visited Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  20. Urban Environment(2) Abstract mathematical data structure 49 21’ 06” 123 15’ 04” Attributed Directed Graph Max Speed 30 mi/h 1.2 mi  Traffic density Construction Zone Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  21. {e E density(a,e) thresholdactivity}a Urban Environment(3) • Directed graph H  (V,E) topological aspects • Attributed directed graph GGeoEnv (H,) attribution scheme (objective view) • Attributed directed graph with colored attributes GEnv (GGeoEnv ,) subjective view (perception)  Awareness space, activity space, crime occurrence space Goals: robustness, scalability, uniformity Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  22. Agent Architecture: BDI-based Model Communication FROM Environment Beliefs Profile Desires Space Evolution Module Target Selection Module Cognition Rules Cognition Rules Agent Decision Module Intentions Intentions Intentions Motivations Working Memory Working Memory Environment Deliberation Perception Action Rules Action Rules Means-End Reasoning Awareness Space Activity Space Communication TO Environment Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  23. Master Agent (PERSON agent) Path planning D A e S B C ADM agent SEM agent TSM agent Distributed ASM model Space Evolution Module (SEM) • Agents move within their environment • Evolving spatial characteristics • Awareness space • Activity space • Crime occurrence space Computational agents Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  24. Simulation: Activity Space Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  25. Simulation: Activity Space Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  26. Simulation: Activity Space Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  27. Fitness of the model Checking the validity • Role of modeling & simulation  Descriptive rather than prescriptive • Extracting behavior characteristics from response patterns • Generating and testing hypothesis • Identifying the system boundaries • Understanding the effect of changes (causality) • Providing evidence for the validity of a model has a different meaning than in prescriptive modeling • Compositional validation? Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  28. Simulation Model: Architecture GIS Map Text Files GIS2Graph Graphical User Interface Map (Graph) Agent Profiles Visualization Simulation Engine Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  29. InProgress Idle False secContrl Ensured Perform-Screening Initialize-Screening True Failed False ScreeningPassed secContrlPassed := True secContrlPassed := False True Done Passed Additional ScreenReq? False secContrlPassed := True True Prepare-for-Additional-Screening Safeguard • Aviation security U. Glässer, S. Rastkar and M. Vajihollahi. Computational Modeling and Experimental Validation of Aviation Security Procedures. In Proc. IEEE International Conference on Intelligence and Security Informatics, volume 3975 of LNCS, pp. 420-431, Springer-Verlag, 2006. Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  30. Large area surveillance • Distributed information fusion and dynamic resources management for decision support Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  31. Summary • A novel approach to Computational Criminology • Modeling and simulation of crime patterns/ theories • Tools for experimental research/ evidence based policy making • Well defined and robust semantic framework • Multi-agent system modeling • ASM computation model • Results • Theoretical • Abstract behavior model of person agents (agent architecture) • Abstract data structure of the environment • Practical • Mastermind model as platform for experimental development of discrete event simulation models Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

  32. Final remarks • Abstract state machines provide • an intuitive formalization of the notion of algorithm in a fairly broad sense, • a practical instrument for analyzing and reasoning about semantic properties of discrete dynamic systems, • abstract specifications that are executable in principle, • a corner stone in computer science education. • Interdisciplinary research @ SFU • ICURS: Computational Criminology (www.sfu.ca/icurs/) • IRMACS (www.irmacs.ca) Crime Hot Spots: Behavioral, Computational and Mathematical Models, IPAM, UCLA, Jan 29 - Feb 2, 2007

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