Condensing on metric spaces [Elektronische Ressource] : modeling, analysis and simulation / von Mostafa Zahri

CONDENSING ON METRIC SPACESMODELING, ANALYSIS AND SIMULATIONDissertationzur Erlangung des Doktorgradesder NaturwissenschaftenDr. phil. nat.vorgelegt beim Fachbereich Informatik und Mathematikder Johann Wolfgang Goethe Universitätin Frankfurt am Mainvon1Dipl. Math./B.Sc. Stat. Mostafa Zahri(Geb. in Taourirt, Marokko)Frankfurt am MainMärz 20091Corresponding author: zahri@gmx.netAbstractIn this work, we extend the Hegselmann and Krause (HK) model, presented in [16]to an arbitrary metric space. We also present some theoretical analysis and somenumerical results of the condensing of particles in finite and continuous metricspaces. For simulations in a finite metric space, we introduce the notion "randommetric" using the split metrics studies by Dress and al. [2, 11, 12].KeywordsCondensing, forming a group, multi agents system, discrete dynamical system, col lective intelligence, manifold and geodesic, random metric, metric spaces.1ContentsABSTRACT AND KEYWORDS 1LIST OF FIGURES 2INTRODUCTION 41 CONDENSING ON FINITE METRIC SPACE 71.1 Condensing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2 Convergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.3 Random metric on finite metric space . . . . . . . . . . . . . . . . 121.3.1 Extremal pseudometrics . . . . . . . . . . . . . . . . . . . 121.3.2 Algorithms for the construction of random metrics . . . . . 151.3.3 Numerical simulations of random metrics . . . . . . . . . .