Happenings – 2011 Jun 25

My schedule has been topsy-turvy recently. It’s 3:30 PM and I’m just beginning to draft this week’s diary post.

Happenings – 2011 Jun 18

Well, this past week’s color post certainly wasn’t advanced mathematics – but it was fun.

I’ve made a little progress on a few things.

I’ve looked through Kippenhahn & Weigert’s “Stellar Structure and Evolution” – from where I sit, it looks pretty comprehensive for modeling the interiors of stars. That’s why I ordered a while ago.

And that book I ordered specifically about stresses in thin shells… it doesn’t look hard, but there’s an awful lot of it. Of course, that’s what I was hoping for.

I think I’ve worked just about all the examples of dimensional analysis that I think I need… so I should write it up sometime.

There’s a lot of things I should write up sometime…

Color – Using PieChart, and the artists’ color wheel

getting the computer color wheel via pie charts

I found the following example in the Mathematica® (v 7) help file. I thought it had promise.

Happenings – 2011 Jun 11

I feel like I’ve been stirring pots, instead of actually cooking. I’m messing around with a lot of things, but finishing none.

Mostly, I’ve continued playing with color. Mathematica®’s PieChart command is extremely convenient for displaying a palette of colors. Even better, it’s extremely convenient for displaying the two color wheels (the artist’s color wheel with green opposite red, and the other color wheel with cyan opposite red). At least it took a little mathematics to get a translation from one to the other.

Best of all, I can feed it a palette of colors and have it display them on a color wheel. (Yes, I had to write that myself.) I expect to discuss all this in more detail, but let me at least show it to you.

Here’s a palette out of Cabarga’s “Global Color Combinations”, p.25 (bibliography):

Here are those colors mapped to the artist’s color wheel (hue angle only, taking no account of tint-tone-shade):

The point of the second screenshot is that I clearly see that I have two sets of what are called analogous colors, and one complementary color.

Regression 1 – Multicollinearity in the Hald Data 3 (subsets)

Introduction

edit: two links. I first looked at subsets of data in this post; I decided that the matrix product X.v was worth computing in this post. Both links were for linear dependence rather than for multicollinearity, but these are where I first explained what I was doing with subsets and X.v .

For most purposes, what we have already done with the Hald data might be sufficient. We have identified the multicollinearity only in the regressions of interest, i.e. in the closest fits using 2 or 3 variables, and in the regression using all 4 variables. In particular, we never explicitly looked at the relationship between X1 and X3 (not beyond what the correlation matrix told us, anyway), because X1 and X3 did not occur together except for the regression on all variables. And for that regression, all four variables were multicollinear.

Maybe I should remind us that we’re pretty sure the Hald data has 3 multicollinearities:

1. all four variables sum to approximately 98.5;
2. X2 and X4 are multicollinear, but not as severely as all four;
3. X1 and X3 are multicollinear, but not as severely as X2 and X4.

On the other hand, there may be times when we want to investigate all of the multicollinearity, not just some of it. Then I, at least, would look at all subsets of the variables. (In this case, we didn’t look very closely at subsets which dropped the constant, because the singular values were relatively large.)

Let me do that.

Happenings – 2011 Jun 4

First off, let me point out that my prediction of an earthquake of magnitude 5 or greater every day in June somewhere on earth is doing just fine.

There were six on June 1, including one of magnitude 6.4 off the coast of Chile… three on June 2… four on June 3… and there has already been one today. As I said, this is not very useful prediction. The point is, it’s very easy to make useless predictions about earthquakes.

As far as I can tell, the USGS won’t let me build a map showing just the quakes so far this month – but I should be able to do it easily in Mathematica. Just not this morning.

Second, Roger Federer is in the final of the French Open… so I expect to be watching that tomorrow morning, instead of doing mathematics.

Third, I have understood the Buckingham Pi theorem in dimensional analysis (finding dimensionless numbers like the Reynolds number)… it is apparently nothing more than the rank–nullity theorem in linear algebra, that the rank of a matrix plus the dimension of its nullspace is equal to the number of columns.