Monday, July 11, 2016
Technische Universität Berlin
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin
room MA 041
Lecture - 14:00
Abstract:
Physarum is a slime mold. It was observed over the past 15 years that the mold is
able to solve shortest path problems and to construct nice
networks (Nakagaki-Yamada-Toth,Tero-Takagi-et al). In a nutshell, the
shortest path experiment is as follows: A maze is built and the
mold is made to cover the entire maze. Food is then provided at two positions
and the evolution of the slime is observed. Over time, the slime retracts to
the shortest path connecting the two food sources. A video showing the experiment is available at
http://people.mpi-inf.mpg.de/~mehlhorn/ftp/SlimeAusschnitt.webm
A mathematical model of
the slime's dynamic behavior was proposed by Tero-Kobayashi-Nakagaki.
Extensive computer simulations confirm the experimental
findings; the slime retracts to the shortest path. We (joint work with Vincenzo Bonifaci and Girish Varma) have
have proved convergence (Journal of Theoretical Biology, 2012, ICALP 2013) of the continuous model and its
discretization.
I will start with the video mentioned above. Then I review the mathematical model and
explain the computer simulation. Next, I will discuss how we formulated the right conjecture based on computer experiments. Finally, I will briefly discuss the convergence proof.
In the second part of the talk, I will discuss follow-up work by Straszak and Vishnoi (ITCS 2016) and the slime ability to construct networks. I will close with some open problem.
Colloquium - 16:00
- - - cancelled - - -