James R. Lee, University of Washington Simons Institute Open Lectures simons.berkeley.edu/events/ope... Full title: The Unreasonable Effectiveness of Spectral Graph Theory: A Confluence of Algorithms, Geometry, and Physics
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@Onezero6758 жыл бұрын
great watch, thanks
@rbnn8 жыл бұрын
Great talk. I wish I'd seen that motivation when I was studying this.
what is the exact reason that the random walk was done on a torus and not on a square ?
@drewduncan57747 жыл бұрын
A square with opposite edges identified is a torus.
@MravojedNaTrotinetu5 жыл бұрын
Probably because square grid is topologicaly noncompact and that it requires boundary conditions to be specified while setup on torus is topologycaly compact and does not require boundary conditions (reason why it's more generic than finite square grid).
@augblog5 жыл бұрын
The grid on a torus is 4-regular.
@alfatti16034 жыл бұрын
Also note that the torus is topologically nontrivial ( genus-1 surface) which impacts the long term diffusion behaviour
@wayfinder1054 жыл бұрын
Torii have the easiest boundary conditions to program probably (just have to write every coordinate modulo, no need to write any special cases).