That way we can commit everything.

R

• http://www.inside-r.org/r-doc/utils/unzip
• http://stackoverflow.com/questions/12460938/r-reading-in-a-zip-data-file-without-unzipping-it

data <- read.table(unz("Sales.zip", "Sales.dat"), nrows=10, header=T, quote="\"", sep=",")

Python

• https://docs.python.org/2/library/zipfile.html#zipfile.ZipFile.open
• https://docs.python.org/2/library/zipfile.html#zipfile.ZipFile.read

There are too many issues with mapping observed tangles to those enumerated by the tangle submodule.

This one I'm definitely ready to conjecture about, and I think we can prove it as follows.

Say t_n = (n,(n-1,(n-2,....(1,2)))) and s_n = (1,(n,(n-1,(n-2,....(2,3))))). I conjecture that kappa(t_n, s_n) goes to zero as n goes to infinity.

This is of course saying that W_1(t_n, s_n) goes to 1 as n goes to infinity. The only way this could happen is that if a nonzero fraction of neighbors of t_n were also neighbors of s_n. But almost all SPR moves are independent of the move differentiating t_n and s_n, so that can't be true.

So far we are just considering trees of the same shape in the access time.

How are these coming? At the very least I would like to include the 7-taxa curvature distribution to prove that we did compute them and to show that curvatures can be negative.

I don't think 7-taxa access times are necessary.

I have just pushed SVGs to the repo. If you want tooltipped versions just run distribution.Rmd through RStudio (one click of a button).

4 taxa

5 taxa

6 taxa

• Will the smallest curvature for a given distance always be achieved by a tangle with a comb tree? Note that for 5 taxa, the smallest for distance 2 is achieved by a pair consisting of a comb and a tree of topology (,((,),(,))).
• As the number of leaves goes to infinity, do all curvatures go to zero?

Right now, I have used

lazy_unif
unif_prior_mh
equal
lazy-RW-vs-unif-MH

that's bad and it's all my fault.

After getting the FOCS paper submitted, I'd like to

• decide about case convention for GAP code

T_1 typically (always?) has the lower degree right? Then that matches our observation that the curvature decreases with large degree changes.

variable                     coefficient    p-value 
----------                   -------------  ---------
 $T_1$ degree                 12.15          2.7e-55 
 $T_2$ degree                 6.629          4.3e-21 
 $d_{\operatorname{rSPR}}$    41.19          1.1e-44 

Of course, for the time being we are interested in unrooted trees underlying things, but we don't necessarily have the technology to look at SPRs on unrooted trees.

Say we are interested in finding a rooting such that there is a one to one correspondence between uSPR and rSPR moves for a shortest path between two given trees. How far apart can those trees be? I think that you've said before that the answer is one.

then make it consistent.

@cwhidden -- can you point me to the code that generates matrix_7 and and matrix_nni_7, etc? Note that SAGE is happier with big adjacency lists than it is with big matrices, and I think you generated those for me before. If that's correct, can you point out how it's done?

All we actually need as input into the linear program to calculate the curvature between x and y are the pairwise distances of all trees in the k-neighborhoods around x and y. There will be many duplicates of these objects in terms of tangles. Thus, does it make sense to consider methods for calculating the k-neighborhood of tangles around a given tangle, where this is defined as the tangles coming from all pairs of trees in the two k-neighborhoods?

I wonder if this symmetry could be productively incorporated into the linear program itself, or if we would just have to have lots of identical entries.

The access times in https://github.com/matsengrp/curvature/blob/master/figs/short-time-kappa-access.pdf seem odd. How can there be a 0 access time? Is the access time axis off by 1?

Clearly the labeling doesn't matter as such, it only matters in terms of comparing one tree to another. Thus, for example, we can interchange labels that only label cherries on both trees.

I'd like to enumerate all equivalence classes of pairs of trees and determine their sizes. This seems like something that folks looking at SPR must have done, because it's useful in that setting for sure.