More plots

Five plots this time. Here's the data in tabular form:

/tuning-math/files/MikeBattaglia/HE
Optimizations test 2/ent.xls
/tuning-math/files/MikeBattaglia/HE
Optimizations test 2/opt.xls
/tuning-math/files/MikeBattaglia/HE
Optimizations test 2/opt2.xls
/tuning-math/files/MikeBattaglia/HE
Optimizations test 2/opt3.xls
/tuning-math/files/MikeBattaglia/HE
Optimizations test 2/opt4.xls

Here's them all overlaid on top of one another:

/tuning-math/files/MikeBattaglia/HE
Optimizations test 2/HEoverlay.png

These are all mediant-mediant widths, NOT sqrt(n*d) widths. sqrt(n*d)
is harder to do in this case.

There shouldn't be any objections to these.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> There shouldn't be any objections to these.

I object to the fact that I can't seem to find them.

On Tue, Feb 1, 2011 at 3:51 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > There shouldn't be any objections to these.
>
> I object to the fact that I can't seem to find them.

I hate computers. Here's the folder where they all reside:

/tuning-math/files/MikeBattaglia/HE%20Optimizations%20test%202/

Here's with fixed links:

/tuning-math/files/MikeBattaglia/HE%20Optimizations%20test%202/ent.xls
/tuning-math/files/MikeBattaglia/HE%20Optimizations%20test%202/opt.xls
/tuning-math/files/MikeBattaglia/HE%20Optimizations%20test%202/opt2.xls
/tuning-math/files/MikeBattaglia/HE%20Optimizations%20test%202/opt3.xls
/tuning-math/files/MikeBattaglia/HE%20Optimizations%20test%202/opt4.xls

Here's them all overlaid on top of one another:

/tuning-math/files/MikeBattaglia/HE%20Optimizations%20test%202/HEoverlay.png

PS, Gene, there is apparently good precedent for what you were talking
about, in terms of each HE series implying a "measure," in this
extension of discrete entropy to the continuous case:

http://en.wikipedia.org/wiki/Limiting_density_of_discrete_points

It's supposed to be more well-behaved than just the naive, continuous
extension of discrete entropy that doesn't throw the invariant measure
in. I'm not sure if m(x) is supposed to be infinitesimally small, but
if so, then we're stuck with the interesting case of what happens as x
goes to 0 and log(x) goes to infinity. I don't understand how measures
work enough to know about that.

-Mike