INFORMATION DRIVEN SELF-ORGANIZATION OF AGENTS AND AGENT COLLECTIVES A thesis submitted in partial fulfilment of the requirements of the University of Hertfordshire of the degree of Doctor of Philosophy. Malte Harder May 2013 MalteHarder AnsbacherStr.69a 28215Bremen Germany [email protected] TypesetinCardov1.04andAdobeSourceSansProv1.038withConTEXt,TikZ,andPGFPlots. LayoutinspiredbyTheElementsofTypographicStylebyRobertBringhurst. Comicsfromhttp://www.xkcd.com(licensedunderCC-BY-NC2.5). TypesetonThursdayApril3,2014. ©2013–2014MalteHarder.AllRightsReserved. ABSTRACT Fromavisualstandpointitisofteneasytopointoutwhetherasystemisconsideredtobe self-organizingornot,thoughaquantitativeapproachwouldbemorehelpful.Information theory,asintroducedbyShannon,providestherighttoolsnotonlyquantifyself-organ- ization,butalsotoinvestigateitinrelationtotheinformationprocessingperformedby individualagentswithinacollective. Thisthesissetsouttointroducemethodstoquantifyspatialself-organizationincollective systems in the continuous domain as a means to investigate morphogenetic processes. In biology, morphogenesis denotes the development of shapes and form, for example embryos, organs or limbs. Here, I will introduce methods to quantitatively investigate shapeformationinstochasticparticlesystems. In living organisms, self-organization, like the development of an embryo, is a guided process,predeterminedbythegeneticcode,butexecutedinanautonomousdecentralized fashion. Information is processed by the individual agents (e.g. cells) engaged in this process.Hence,informationtheorycanbedeployedtostudysuchprocessesandconnect self-organization and information processing. The existing concepts of observer based self-organization and relevant information will be used to devise a framework for the investigationofguidedspatialself-organization. Furthermore,localinformationtransferplaysanimportantroleforprocessesofself-organ- ization. In this context, the concept of synergy has been getting a lot attention lately. Synergyisaformalizationoftheideathatforsomesystemsthewholeismorethanthesum ofitspartsanditisassumedthatitplaysanimportantroleinself-organization,learningand decisionmakingprocesses.Inthisthesis,anovelmeasureofsynergywillbeintroduced, thataddressessomeofthetheoreticalproblemsthatearlierapproachesposed. i ii »Themostexcitingphrasetohearinscience,theonethatheraldsnew discoveries,isnot‘Eureka!’(Ifoundit!)but‘That’sfunny...’« ISAACASIMOV,Unknown »Thedifferencebetweenlifeandnon-lifeisamatternotofsubstancebut ofinformation.« RICHARDDAWKINS,TheGreatestShowonEarth iii iv » To anyone who understands information theory and security and is in an infuri- ating argument with someone who does not (possibly involving mixed case), I sincerely apologize « XKCD, 936 v vi ACKNOWLEDGEMENTS I thank my principal supervisor Dr. Daniel Polani and my secondary supervisor Prof. ChrystopherNehanivformanyinspiringandinvaluablediscussionswhichinarguablyhad asignificantimpactonmyresearch.Iamalsothankingeverybodywhoprovidedfeedback tothisthesisandthearticlesthatIpublishedduringthisprogramme. Furthermore,IamgratefultomyformerhousematesfromGloucesterCourtforthemany cupsofteawehad,thatwereoftenaccompaniedbyscientificdiscussions,tomyfriendsfor offeringtheoccasionalescapefrominformationtheory,tomyfamilyforalwayssupporting me,especiallyduringthelastmonthsofwritingthisthesis.Specialthanksgotomybrother forkeepingmefromgoinginsaneonseveraloccasionsby‘showingmewherethatone semicolonwasmissing’. vii CONTENTS 1 INTRODUCTION 15 Motivation 15 Overview 17 Contribution 18 2 BACKGROUND 20 InformationTheory 20 RelatedWork 28 3 QUANTIFYINGSELF-ORGANIZATION 37 Introduction 37 Self-Organization&Complexity 37 StatisticalComplexity 41 Self-organizationviaObservers 46 ComparisonofSC-OrganizationandO-Organization 51 EstimationofMulti-information 53 Discussion 62 4 SELF-ORGANIZATIONOFPARTICLESYSTEMS 68 ParticleCollectives&Self-organisation 69 Methods 74 Examples 76 Results 79 Discussion 88 5 INFOGENESIS 90 Introduction 90 Information-theoreticControlTheory 91 RelevantInformation 93 Embodiment&Perception-actionLoops 96 Multi-AgentRelevantInformation 99 RelevantInformation&Self-Organization 102 EpisodicTasks&ShapesasGoals 103 SharedControlandSensorCoordination 106 Experiments 108 Discussion 111 6 REDUNDANTINFORMATION 114 WhatisRedundancy 114 MeasureCandidates 115 ConstructionofaNewMeasure 119 PartialInformationDecomposition 125 viii
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