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

SAMSINovember 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

Nodes (Agents)

iA

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SOCIAL NETWORK MODEL

– observed characteristics )(tCi

MATHEMATICAL MODEL

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Essentially Deterministic

Noise Enriched

Noise Enlarged

Noise Dominated

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CHARACTERIZE MODEL BEHAVIOR:

FANTASY OR REALITY?

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

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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

0165.0b

NOISE ENRICHED SAMPLES

Agent 2 Agent 7

MORE NOISE ENRICHED SAMPLES

Agent 6 Agent 10

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

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