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Transcript of SENSITIVITY TO NOISE VARIANCE IN A SOCIAL NETWORK DYNAMICS MODEL Hoan K. Nguyen Center for Research...
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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
SAMSINovember 10-11, 2005
Collaborators: H.T Banks, A.F. Karr, and J.R. Samuels, Jr.
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TALK OVERVIEW
• Mathematical Model
• An Example
• Numerical Results
• Conclusions and Future work
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Nodes (Agents)
iA
jA
),,( tije),,( tjie
SOCIAL NETWORK MODEL
– observed characteristics )(tCi
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MATHEMATICAL MODEL
ejiji
tNj
Ciji
i
ii
dWdttCtCftjide
WddttCtCN
tCdi
,
2
)(
)()( ),,(
)()()(
0b,12)( bef
)( };0),,(|{)( tNtjiejtN ii
where
• : number of elements in
• : degree of influence that exert on
)(tN i
)(tNA ij 0i iA
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Essentially Deterministic
Noise Enriched
Noise Enlarged
Noise Dominated
??
??
??
CHARACTERIZE MODEL BEHAVIOR:
FANTASY OR REALITY?
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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
outiC
1i
)5,5()0(7 C
sqiC
);10,10()0(2 C
),10,10()0( iC
;7,2i
0)0,,( jie
0b
)033.0,0(b ]105.0,033.0[b),105.0( b
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TWO CLUSTER SENARIO
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THREE CLUSTER SCENARIO
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ONE CLUSTER SCENARIO
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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
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NOISE ENRICHED SAMPLES
Agent 2 Agent 7
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MORE NOISE ENRICHED SAMPLES
Agent 6 Agent 10
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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)
j
Ciji
j
ii dWdttCtCtjie
tjietCd
)()(),,(),,(
)(
im
iibb ;;
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