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. 4 9 3 1 1 file

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

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."Ship of Theseus

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 4/7 2/3 4/7 1/3 2/3 1/2

11. 1/5 2/5 2/13 1 4 9 3 1 1 t=1 4 8 3 2 2 1 t=2 9 4 4 4 9 1 t=4 4 4 4 8 2 2 t=3 111 16/17 1 1 1 1 1 6/7 2/3 β=.5β=.9

12. 12345678910 Time step = 1 second 12341234 23452345 3/4 34563456 45674567 56785678 Time step = 4 seconds 12341234 56785678 0 9 10 1 2 0 34563456 0 7 8 9 10 0

13. How do we get the groups? Zebra – photos, sensor collars (ZebraNet) physical proximity (ZebraNet) Ants – video marking physical 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 each other 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 PostWashington Post Pentagon Pennsylvania WTC North WTC South Jan-Dec 2000 Jan-Apr 2001May-Jul 2001Aug-Sep 2001

17. 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? easy hard

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