M3C 2017 Final Project Solution

Part 1 Solution

Part 2 Solution

Part 3 solution

M3C 2017 topics

A little background information on some of the homework problems.

1) Random network generation: this is a form of a process called “Diffusion-limited aggregation” which you can read more about here:

2) Bracket-descent: This algorithm is a crude version of the Nelder-Mead derivative-free optimization scheme which is provided in the scipy optimize package. The idea of several triangles “shifting” towards a global minimum is borrowed from a method called particle swarm optimization which is a much more recently-developed derivative-free global optimization scheme (and which is also available in scipy)

3) Pedestrian motion: You were asked to simulate the Viscek model for collective motion which you can read more about here:

4) Waves on complex networks: Transport processes on complex networks have received a great deal of attention in recent years though the focus has tended to be on diffusive rather than wave-like dynamics. For more information, see the chapter on “spreading phenomena” in Network Science by Barabasi which is freely available online at barabasi.com