MURI Continuing Review @ MIT 17 Dec 07 (Location: Stata Center; 32 Vassar St. (Bldg 32-4th floor) Room 32D-463)
8:30 – 9:00 assemble; coffee & pastries
9:00 W. Richards & T. Lyons: Introductions & Objectives
Experimental & Network Analysis Results
9:15 M. Sageman: Militant Networks studies (with S. Atran)
9:45 comment by R. Axelrod: Reframing Sacred Values
10:00 D. Medin: Sacred & Secular results
10:30 Coffee & Soda break
Model Development and Applications
11:00 J. Tenenbaum: Infinite Block Model for Beliefs Categories
11:30 K. Forbus: Causal Models
12:00 comment by P. Winston on Story Workbench
12:15 Lunch: 4th Floor of Stata (a bargain for $6.00 !!!)
1:30 W. Richards: Small Group Network Evolution
2:00 A, Pfeffer: Multi-agent Models & Patterns of Reasoning
2:30 S. Page: Belief Revision Models
3:00 Coffee & Soda Break
3:30 General discussion & Future directions
4:00 T. Lyons (closed session)
5:30 Adjourn
Small Group Evolution
Whitman Richards
Scott Atran et al, Marc Sageman
Rajesh Kasturirangan, Kobi Gal
AFOSR MURI Review 17 Dec 07
The Problem
Typical Group Representation:
Number of Graphical Forms:
n=6: 110
n=8: 850
n=10: 10 million
n=12: 150 billion
A Picture is NOT worth 1000 words !!
Leadership:
Bonding:
Diversity:
L = 1.0
B = 1.0
D = 0.92
Proposed Solution: Three subgraphs that capture key properties of group formation
L ~ normalized sum of diff in vertex degrees
B ~ avg. number of among vertex & neighbors
D ~ num. K2 separated by at least two edge steps (Non-adjacent clusters of Kn increase diversity.)
L, B, D parameters are not independent
Leadership:
Bonding:
Diversity:
L = 0.67 (1.0)
B = 0.875 (1.0)
D = 0.33 (0.92)
Question
Can only three parameters (L,B,D) adequately describe a group during its evolution (i.e, is this compression of pictorial information sufficient) ?
Ans: Yes ! but …….
modeling the evolutionary dynamics will require the application of theories for strategic play….
An Example of Group Formation & Evolution
(to illustrate strategic aspects and model form)
Note: adding a cluster reduces overall bonding
Equilibrium? What’s Next?
Small Group Evolution: example
CASE STUDIES
1. Start-up Company
2. Madrid Militant Group
Start-up Evolution
Madrid Group Evolution
Summary
1. L, B, D parameters describe Small Group evolution(pictures are not always worth 1000 words)
2. Evolution entails strategic play (game theoretic)
Future
3. Is there an optimal evolutionary path ? (e.g. context, internal vs external forces on group, objectives )
=> analysis of patterns of strategic reasoning
= Lukmanul Group
= Kompak Group = Afghan Ties
= Ngruki Ties
+ = Dead = Arrest
= Misc Other
= an-Nur Group = Ring Banten Group
An-Nur Group
Accommodations Group
Ring Banten Group
Kompak Group
Core Bombing Group
(Non-adjacent clusters of Kn which increase diversity.)
Definitions
n = number of vertices; di = degree of vertex vi
L = (dmax −di ) / ((n−1)(n−2))i=1
n∑
B=3* #Δ 's / #connected_ triples_of _v's
D=#disjoin_dipoles(K2* ) / #K2
* for _Rn
Disjoint dipoles are separated by at least two edge steps K2*