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Modeling Small Network Dynamics Whitman Richards M. I. T. Computer Science and Artificial Intelligence Laboratory MURI: Computational Models for Belief Revision, Group Decisions and Cultural Shifts QuickTime™ and a TIFF (LZW) decompressor are needed to see this picture. 28 Feb 07 Sageman & Chen, 2005 A Complex Network Structure Clumps Central Staff Core Arab Southeast Asian Maghreb Arab Node Size Leader Lieutenant Other people Fate Dead Captured Militant Core => a small social network Leaders < 3 Soldiers < 12 +/- Supporters 10 - 50+ Itza Church Start-up Street Gang Sports Team Activist Group Mafia Militia Terrorist Cell Three Aspects of Small Groups Goals, beliefs: sacred vs secular values Model for Core (i.e leader-soldier relations): a network Model for Recruitment: conformity vs consistency Part I: Recruitment Conformity - Consistency Model (Page et al.) Conformity: want to be like “one of the BIG guys” Consistency: want your beliefs to be in harmony A Surprise: Time to Equilibrium (mean field) * * * * * Sacred Beliefs: 1 Consanguineous Marriages (Bittles et al.) Part II Small Network Models Leaders < 3 Soldiers < 12 +/- Small Graphs Supporters 10 - 50+ 1. Impossibility “Theorem”: think small ! 2. New Representation: leader dominance vs bonding 2004 Australian Bombing (Militant Minority) [Atran, Magourik et al] Ring Banten Group An-Nur Group Kompak Group Accommodations Group Core Bombing Group = Lukmanul Group = Ngruki Ties = an-Nur Group = Ring Banten Group = Kompak Group = Afghan Ties = Misc Other + = Dead = Arrest Descriptive Parameters: graphs: {# nodes, #edges} Model Abstraction: Dominance of Leader vs Coherence of Network Two Measures of Social Network Structure Leadership Dominance: {max. vtx. deg,} Coherence: {cluster coeff.} (Freeman, 1978) Watts & Strogatz (1998), Newman(2004) 2004 Australian Bombing (Militant Minority) [Atran et al] Ring Banten Group Max. Vtx. Deg = 3 An-Nur Group # Triangles = 1 n=4 Kompak Group Coherence, C: Leadership, L: Accommodations Group = Lukmanul Group #triangles / nC3 = Ngruki Ties = an-Nur Group = Ring Banten Group ∑(MaxDeg - VtxDeg.)/(n-1)*(n-2) = Kompak Group Core Bombing Group = Afghan Ties = Misc Other + = Dead = Arrest Key observation: as bonding increases, dominance of leader decreases Lacunae: Data lacking on….. • Street Gang Evolution Hmong, Haitian, Yakusa, Somali… • Street Gang Recruitment What’s sacred? Why join? Buddy vs friend of friend Roles of contact, video, email • Mergers: from Small to Global More Lacunae Mergers: Physical vs Virtual links; given 2 gangs, which member of each is most likely to build bridge? Web networking: friends of friends (myspace, etc.); likely candidates for militant acts (eg High School) How to evaluate trust in a network? Disenchantment (return to earlier beliefs) Email analysis: text style -> tag for hidden content (analog to voice analysis.) Violent vs non-violent spectrum: what are key parameters? Long term supporters (requires different model.) Extent of strategizing; at what level? Emotional factors. Y-factor: propaganda, secular vs sacred. MURI Scope Network Complexity WWII Society Community Jihad Itza Street Gang Contextual Complexity Football Family chess Individual Morra, Chicken Colored Trails Strategic Complexity The Team Belief Structures: Scott Atran, Univ. of Michigan & John Jay, CUNY, Anthropology Doug Medin, Northwestern University, Psychology Ken Forbus, Northwestern Univ., Computer Science and Education Mark Finlayson & P. H. Winston, MIT, Computer Science and AI Network Structure & Evolution Joshua Tenenbaum, MIT, Computation and Cognitive Science Jenna Bednar, Univ. of Michigan, Political Science & Public Policy Scott Page, University of Michigan, Political Science & Complexity Whitman Richards, MIT, Cognition and Artificial Intelligence Decision-Making & Strategic Planning: Brian Stankiewicz, Univ. of Texas, Austin, Expt’l Psychology Avi Pfeffer, Harvard, Computer Science Consultants: Robert Axelrod, University of Michigan, Political Science Marc Sageman, University of Penna., M.D., PhD.