I just read Sean B Carrol's "Endless Forms Most Beautiful" on evolutionary development which covered genetic switches in detail and I was left wondering how concentration gradients could lead to such precise patterning and design.... well now I know. Sort of. Thanks for this great series.
Thanks Eric, for the kudos and for watching! I have several mathematical biological examples in here, but they're somewhat buried. Your comment got me thinking that I should probably put all the example clips in a separate playlist to make them easier to find.
Is the ghost theory (bottle-neck regions) developed for 1-dimensional systems change or different for two-dimensional system or greater? For example, time delay theory in 2-dimensions. Any feedback or references on this topic would be appreciated.
You might want to email me (my address is easy to find), but in brief, I don't know about the ghost / bottleneck theory for time delay systems, or if there is one. I have done some work on studying these regions/phenomena in two and higher dimensional dynamical systems from mechanics. There are tools for identifying regions of "high residence time", or in chemistry, "transition states" between large regions of phase space where trajectories can spend an arbitrary amount of time. I have some slides for a talk on understanding fluid flow where these topics came up: chaotician.com/talks/Pitt-2016-post-red.pdf
