islands of stability; regression

[I was out sick for a few days]

In the weekly Dynamics meeting at Flatiron, Tomer Yavetz (Columbia) gave a very nice explanation for why stellar streams (from, say, disrupting globular clusters) in certain parts of phase space don't appear thin, which is an empirical result from simulations found by Pearson and Price-Whelan a few years ago. He shows that, near resonances in a non-integrable potential, stars that are just inside the resonant islands have average frequencies (beacause they orbit the resonance, in some sense) that more-or-less match the resonant frequencies, but stars just outside the separatrix-bordered island have average frequencies that are quite different. So a tiny change in phase space leads to a large change in mean frequencies and the stream doesn't appear coherent after even a very short time. That's a really nice use of theoretical ideas in dynamics to explain some observational phenomena.

I also gave the first of my computational data-analysis classes. I talked about fitting and regression and information and geometry. I had a realization (yes, whenever I teach I learn something), which is that fitting and regression look very similar, but they are in fact very different: When you are fitting, you want to know the parameters of the model. When you are regressing, you want to predict new data in the data space. So using a Gaussian Process (say) to de-trend light curves is regression, but when you add in a transit model, you are fitting.