Identifying Persistent Social Groups

1. Identifying Persistent Social Groups Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) Who’s Company? and University of Illinois at Chicago Tanya Berger-Wolf

2. Zebras Dan Rubenstein, Siva Sandaresan, Ilya Fischhoff (Princeton) Movie credit: “Champions of the Wild”, Omni-Film Productions.

3. Ants Stephen Pratt (Princeton)

4. People – Hidden Groups Baumes et al. (RPI)

5. What’s a group? • Zebras – harems, herds, physically close collection of individuals • Ants – ants being carried by a scout • People – families, friends, collection of individuals with a common goal, sexual contacts, individuals at the same location

6. file 4 1 3 9 1

7. 4 4 4 4 9 8 8 4 1 9 4 4 3 3 4 2 9 2 1 1 2 1 2 t=2 t=3 t=4 t=1

8. Theseus’s Paradox • During a twelve month period 95% of all the atoms that make up your 50 trillion cells are replaced • FAA regulations: airplane = left rudder number • Ship of Theseus"The ship wherein Theseus and the youth of Athens returned [from Crete] had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same."

9. What is persistence? A group is persistent (stable) if it is there all the time A group is persistent if some (big) fraction β of it exists some (big) fraction α of time (recurs regularly?)

10. 4/5 4/5 4/5 4/5 4/5 2/3 1/3 4/7 4/7 1/2 2/3 2/3

11. 2/13 16/17 16/17 1 1 1 1 1 4 4 4 4 4 1 8 8 9 4 9 2/5 1/5 1 6/7 2/3 2/3 1 1 1 3 4 3 4 1/5 2/3 9 2 1 2 1 2 2 1 β=.5 β=.9 t=4 t=2 t=3 t=1

12. 10 5 3 4 9 2 7 8 1 6 Time step = 4 seconds 9 10 1 2 7 8 9 10 4 5 6 7 1 2 3 4 2 3 4 5 3 4 5 6 5 6 7 8 1 2 3 4 3 4 5 6 5 6 7 8 3/4 3/4 3/4 3/4 0 0 0 0 Time step = 1 second

13. How do we get the groups? • Zebra – photos, sensor collars (ZebraNet)physical proximity • Ants – video markingphysical proximity • People: • Report of personal contacts (epidemiology) • Cell phone communication • Computer communication • Intelligence information (database queries) • Simulations

14. Zebras (Ants, People) - Clustering Objects within a cluster are closer to eachother than to objects in other clusters

15. Clustering Joachim M. Buhmann, Department of Computer Science ETH Zurich

16. People – Connected Components Baumes et al.(RPI) and Washington Post PentagonPennsylvaniaWTC NorthWTC South Jan-Dec 2000 Jan-Apr 2001 May-Jul 2001 Aug-Sep 2001

17. easy hard Great! But… There are millions of people, groups change constantly – finding groups is COMPUTATIONALLY EXPENSIVE • Given a group – is it persistent? • To what persistent groups does a given individual belong? • I know persistent groups are no bigger than 100. Find them? • I know there is exactly one persistent group. Can you find it?

18. Credits: Dan Rubenstein Siva Sundaresan Ilya Fischhoff Jared Saia Simon Levin S. Muthu Muthukrishana Martin Pal