SENSITIVITY TO NOISE VARIANCE IN A SOCIAL - SAMSI在一个社会samsi噪声方差的敏感性.ppt

SENSITIVITY TO NOISE VARIANCE IN A SOCIAL NETWORK DYNAMICS MODEL Hoan K. Nguyen Center for Research in Scientific Computation North Carolina State University LVSS Transition Workshop SAMSI November 10-11, 2005 Collaborators: H.T Banks, A.F. Karr, and J.R. Samuels, Jr. TALK OVERVIEW Mathematical Model An Example Numerical Results Conclusions and Future work MATHEMATICAL MODEL AN EXAMPLE 10 agents (A1, A2,…,AN) Each agent has 2 observable characteristics Sociability quotient ( ) : -10 (loners) 10 (people lovers) Outlook on life ( ) : -10 (negative outlook) 10 (positive outlook) determine different clustering scenarios : 1 cluster; : 2 clusters; : 3 clusters TWO CLUSTER SENARIO THREE CLUSTER SCENARIO ONE CLUSTER SCENARIO REGIME DEFINITION Fix to have single cluster scenario Essentially Deterministic: Both fate and path are as in the deterministic case Noise Enriched: Fate is the same as the deterministic case, but the set of paths is bigger Noise Enlarged: If fate is either a two cluster or a three cluster scenario described above Noise Dominated: No structured behavior at all NOISE ENRICHED SAMPLES MORE NOISE ENRICHED SAMPLES * Nodes (Agents) SOCIAL NETWORK MODEL observed characteristics where : number of elements in : degree of influence that exert on Essentially Deterministic Noise Enriched Noise Enlarged Noise Dominated ?? ?? ?? CHARACTERIZE MODEL BEHAVIOR: FANTASY OR REALITY? Agent 2 Agent 7 Agent 6 Agent 10 *