Closed mbudisic closed 9 years ago
jeanluct
commented
9 years ago Can you check what I refer it as in my 2005 and 2010 papers? The word 'braiding factor' comes from my 2005 papers, I think.
But on the other hand, I don't think it's a huge issue that complexity is slower than entropy('onestep')? It's a long Matlab tradition to have different ways to do things that have different efficiency, and the more intuitive one is not always the fastest.
mbudisic
commented
9 years ago In 2005 paper you call the analog of this quantity braiding exponent, while in 2010 paper you talk about entropy of a random braid. Braiding factor is indeed from 2005 paper, but it is directly the largest eigenvalue of the Burau matrix, of which you take a log and divide by time to get the braiding exponent.
I am not sure what to take away from your second comment. Are you suggesting then to use databraid.complexity for this new function (now called databraid.dilatation) even though we actually use braid.entropy to compute it by default?
mbudisic
commented
9 years ago I was half-joking about Finite Time Braiding Exponent, but it might not be a bad idea. It's the same "feel" of the calculation as FTLE, so I'm guessing that people would have a better intuition about it just by reading the name.
jeanluct
commented
9 years ago Ok, let's start by listing the things that are set in stone:
The latter two are not approprate to a databraid, since it is not closed. (In fact perhaps we should hide them?) Maybe we should say the same about complexity: it was defined for real closed braids, so it may not be appropriate to use it on a databraid. In that sense braiding factor/exponent might be more appropriate.
mbudisic
commented
9 years ago I agree, this was my line of thought exactly. If someone wants to force the use of braid methods, they can invoke superclass braid but these should not be allowed by default.
Between "factor" and "exponent", I would definitely go for the latter, as "factor" somehow carries the notion of multiplication in it, so I'd (loosely) say that factor = exp( exponent ) which is how you used it in 2005 paper.
mbudisic
commented
9 years ago So, FTBE it is?
jeanluct
commented
9 years ago Oh yes, the factor is definitely multiplicative. If we implement the braiding factor then there should be no log, but I don't think we should.
Let's go with fbte!
jeanluct
commented
9 years ago Closing, since no longer automatically closed (like BitBucket).
mbudisic
commented
9 years ago My semantics was wrong! :) https://help.github.com/articles/closing-issues-via-commit-messages/
jeanluct
commented
9 years ago I thought I tried this...
On Sun, Dec 7, 2014 at 7:58 AM, Marko Budisic notifications@github.com wrote:
My semantics was wrong! :) https://help.github.com/articles/closing-issues-via-commit-messages/
— Reply to this email directly or view it on GitHub https://github.com/jeanluct/braidlab/issues/84#issuecomment-65938103.
(Assigned to JLT but just so you see it sooner than later :) )
I am trying to give a proper name to "databraid complexity", the quantity that we called "braiding factor" in my APS presentation and the writeup.
Strictly speaking, the quantity that we are computing really is D-W complexity with two modifications: (a) we divide by the length of physical time which the braid spans, (b) we allow for length to be computed using alternative methods, e.g., minlength.
I would be perfectly happy to name this function "complexity" in braidlab and be done with it, but there are few hangups.
Alternative names: braiding factor, FTBE (Finite Time Braiding Exponent - cf. FTLE calculation, and similar interpretation), dilatation exponent, FTDE (same as above except Dilatation instead of Braiding - as that is what we are measuring anyway).
I am working on this at the moment (Tue afternoon), and I'll commit it as "dilatation", just so I am not hiding any braid. functions. But let's think and settle this before v2.2.