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

Computational Modeling and Simulation ofSpatiotemporal Characteristics of Crime in

Urban Environments

Uwe GlässerSoftware Technology Lab

School of Computing ScienceSimon Fraser University

[email protected]

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

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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)


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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


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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

VerificationEnvironment Graphical UI

TestingEnvironment

AbstractStorage

Interpreter

Scheduler

Parser

Control API

CoreASM Engine

Problem…

CoreASM

AsmL, XASM, …

Implementation

Ground model

Detailed ground model

Code

Ref

inem

ent

Design

Construction

Coding

Abstract Software Model


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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?

A notorious problem


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Sequential ASMs

Parallel ASMs (synchronous)Distributed ASMs (asynchronous)

Can any algorithm, 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.

Yuri Gurevich


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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 methodnot demanding any insight or ingenuity

An algorithm can be given a precise meaning by a Turing machine.

Can one generalize Turing machines so that any algorithm, never mind how abstract, can be modeled by a generalized machine very closely and faithfully?


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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)

… ?


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Abstract state machineAn 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 x in S: (x) R(x)

…


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Computation

X0 X1 X2 … Xi Xi1 …1 2

i 1

(,Xi)

Evolution of the state

Initial state


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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.


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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


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Mastermind

Crime patterns in urban environmentsP. 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


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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 a

social system one composed of criminals, victims and targets

─ interacting with one another


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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


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Challenges and needs

Approach Common semantic framework Abstract State Machines:

common core for linkingmulti-disciplinary aspects

Semantic foundation Discrete mathematics Computational logic

ASM

KnowledgeRepresent.

KnowledgeRepresent.

Neural Nets

Neural Nets

DecisionMaking

DecisionMaking

LearningLearning

Multi-AgentSystems

SystemDynamics

Navigation

Criminology

Environment Planning

ExperimentalValidation

AI/ALife

``Computational thinking’’


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Mental Maps

“Every inhabitant of Amsterdam has an invisible map ofthe city in his head. The way he moves about the city

and the choices made in this process are determined bythis mental map. Amsterdam Real Time attempts tovisualize these mental maps through examining the

mobile behavior of the city's users.” Amsterdam Real Time

Mental maps


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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

Geographic Environment

Perception

Awareness Space

Activity Space

ObjectiveEnvironment

SubjectiveEnvironment


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Abstract mathematical data structure

Max Speed30 mi/h

ConstructionZone

1.2 mi

Trafficdensity

49 21’ 06”123 15’ 04”Attributed Directed Graph


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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

{e E density(a,e) thresholdactivity}a


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Agent Architecture: BDI-based Model

En

viro

nm

ent

Space Evolution Module

Perception

AwarenessSpace

ActivitySpace

Agent DecisionModule

Cognition Rules

Working Memory

Action Rules

Communication FROM Environment

Communication TO Environment

Target Selection ModuleProfile

MotivationsIntentionsIntentions

Beliefs

Desires

Intentions

Deliberation

Means-End

Reasoning

Cognition Rules

Working Memory

Action Rules


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Distributed ASM model

Space Evolution Module (SEM) Agents move within their environment Evolving spatial characteristics

Awareness space Activity space Crime occurrence space

Master Agent(PERSON agent)

SEMagent

TSMagent

ADMagent

Computationalagents

A

S

C

B

DPath planning

e


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Simulation: Activity Space


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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?


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Simulation Model: Architecture

Simulation Engine

Map(Graph)

AgentProfiles

Visualization

Graphical User

Interface

GIS2Graph

GIS Map

Text Files


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Safeguard

Aviation securityU. 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.

Idle

ScreeningPassed

False

True

True

secContrl Ensured

Initialize-Screening InProgress Perform-Screening

Passed

Failed

Prepare-for-Additional-Screening

Additional ScreenReq

?

secContrlPassed := True

False

secContrlPassed := True

Done

True

False

secContrlPassed := False


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Large area surveillance

Distributed information fusion and dynamic resources management for decision support

UAV

UAV

UAV

Platforms Swarm

Shared informatio

n

Control Stations

CP140 MHP

CP140 MHP


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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


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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)

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

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