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jeanluct / braidlab

Matlab package for analyzing data using braids
GNU General Public License v3.0
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Asymptotic entropy for one large braid? #45

Closed jeanluct closed 9 years ago

jeanluct commented 9 years ago

Given a braid of n strands, obtained from a smooth dynamical system, can we predict the asymptotic entropy by sampling substrands? That is, there are nchoosek braids of size k, which is a huge number for most k. If we randomly pick and average the entropy, can we get a plot like Marko's and predict the asymptote, or does the fact that we're working from a single braid kill us?

mbudisic commented 9 years ago

From what I saw in calculations, it looks like this can be done in the fashion you suggest. In other words, that sampling substrands is somehow still "independent" information from the entropy of the full braid. I'll produce an example in coming days.

jeanluct commented 9 years ago

I think we've conclude in the FTBE paper that this works great.

mbudisic commented 9 years ago

Well, we know that subsampling k-out-of-N braids is as good as determining the mean of FTBE(k) as is random seeding of groups of k initial conditions. However, we still don't know how to extrapolate to FTBE(N).

jeanluct commented 9 years ago

Yes, I don't know how I thought this would help with the asymptote. Keeping this closed.