1. Inferring effective forces in collective motion Yael Katz, Christos Ioannou, Kolbjørn Tunstrøm and Iain Couzin Dept. of Ecology & Evolutionary Biology Princeton University Cristián Huepe Unaffiliated NSF Grantee Cristian Huepe Labs Inc. - Chicago IL This work was supported by the National Science Foundation under Grants No. DMS-0507745 & PHY-0848755

3. – Background

4.  Current efforts  Quantitative experiments  Distinguishing generic and specific behaviors  Challenges in modeling  Different models produce similar dynamics  We can be prejudiced by familiar interactions  The inverse problem:  Deducing the interaction rules from collective dynamics – Challenges

5. Intuitive flocking algorithm (Craig Reynolds – Sony) Generic rules (from computer graphics) –Flocks, Herds, and Schools: A Distributed Behavioral Model Computer Graphics, 21(4), pp. 25-34, 1987 –Defined Boids and simple interaction rules: ▪ Separation ▪ Alignment ▪ Cohesion

6. – The Vicsek model

7. The “zones” model – A more biological model Journal of Theoretical Biology (2002) 218, 1-11 I. D. Couzin, J. Krause, R. James, G. D. Ruxton & N. R. Franks - “Insect-like” swarm: - Torus, “milling”: - Migration, flocking:

8.  Different algorithms yield similar collective motion  What interactions are animal swarms actually using?  Are we making underlying assumptions?  In other words: Can we properly address the inverse problem?  Can we properly address the inverse problem? - Challenge: The inverse problem

10.  Experimental System Work with: Prof Iain Couzin, Dr Yael Katz, Dr Kolbjørn Tunstrøm Dr Christos Ioannou Other collaborators: Dr Andrey Sokolov Andrew Hartnett, Etc. Princeton University

11.  1000 fish dynamics

14.  The two-fish system

15.  Position-dependent forces Zero force  Zero force  high density ||v||>0.5 BL/s ||v||>0.5 BL/s F||(y), F  =(x) F||(y), F  =(x)

16.  Velocity-dependent forces Higher speed  Higher speed  larger forces & larger forces & preferred y-distance preferred y-distance Aligned  Higher F|| Aligned  Higher F|| Misaligned  Higher F  Misaligned  Higher F 

17.  Temporal correlation Orientation information  Front to back Speed information  Both ways

18.  The three-body problem

19.  Intrinsic 3-body interaction Best match: Residual 3-body interaction: “Non-negligible”“Negligible” Best match: Residual 3-body interaction:

20. … Fin