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SENSITIVITY TO NOISE VARIANCE IN A SOCIAL NETWORK DYNAMICS MODEL

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.

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SENSITIVITY TO NOISE VARIANCE IN A SOCIAL NETWORK DYNAMICS MODEL

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  1. 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.

  2. TALK OVERVIEW • Mathematical Model • An Example • Numerical Results • Conclusions and Future work

  3. SOCIAL NETWORK MODEL Nodes (Agents) • observed characteristics

  4. MATHEMATICAL MODEL where • : number of elements in • : degree of influence that exert on

  5. CHARACTERIZE MODEL BEHAVIOR: FANTASY OR REALITY? Noise Dominated ?? ?? Noise Enriched Noise Enlarged ?? Essentially Deterministic

  6. 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

  7. TWO CLUSTER SENARIO

  8. THREE CLUSTER SCENARIO

  9. ONE CLUSTER SCENARIO

  10. 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

  11. NOISE ENRICHED SAMPLES Agent 2 Agent 7

  12. MORE NOISE ENRICHED SAMPLES Agent 6 Agent 10

  13. CONCLUSIONS AND FUTURE WORK • is more sensitive to the regime than • Noise Enlarged regime does not exist • Model richness and flexibility (e.g., ) • Sensitivity Analysis • Model Generalizations • Links that are born and die • Overlaid network (multi-dimensional links)

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