Sensitivity to noise variance in a social network dynamics model
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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

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
TALK OVERVIEW

  • Mathematical Model

  • An Example

  • Numerical Results

  • Conclusions and Future work


SOCIAL NETWORK MODEL

Nodes (Agents)

  • observed characteristics


Mathematical model
MATHEMATICAL MODEL

where

  • : number of elements in

  • : degree of influence that exert on


CHARACTERIZE MODEL BEHAVIOR:

FANTASY OR REALITY?

Noise Dominated

??

??

Noise Enriched

Noise Enlarged

??

Essentially Deterministic


An example
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





Regime definition
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
NOISE ENRICHED SAMPLES

Agent 2

Agent 7


More noise enriched samples
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

    • Overlaid network (multi-dimensional links)


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