stellar noise as a physical process

Today I was privileged to be part of a great and productive meeting between Jesse Cisewski (Wisconsin), Megan Bedell (Flatiron), and Lily Zhao (Flatiron) about noise sources in extreme-precision radial-velocity measurements. The conversation was inspired by the realization (obvious, really) that any physical effect on the surface of stars (spots, plages, convection pattern, p-modes, flares) that affect the radial-velocity measurement must (unless the Universe is truly adversarial) leave other imprints on the spectrum at the same signal-to-noise or even higher signal-to-noise. This means that any claim that RV measurements are affected by spots (say) should be backed up by an observation in the spectrum that is orthogonal to the RV signal that supports the claim. We discussed relevant research and decided to jointly read this paper before our next meeting!

nada

The beginning of the semester is brutal!

simulating a patch of a spectrograph

In preparation for writing something (or proposing something, maybe?) about new methods for extracting spectra from spectrograph data, I wrote a tiny simulation code that makes fake spectroscopy data. The issue is that (except in rare circumstances) the spectral trace is not aligned perfectly with a CCD row (or column) and (except in rare circumstances) the cross-wavelength direction directions of constant wavelength) are not aligned perfectly with a CCD column (or row). How to adjust current methods to address this? I think I know! And I think it doesn't require a full instrument model.

the symmetries of the observed universe are different from the symmetries of the latent universe

Kate Storey-Fisher and I spent a long time today talking about how to build a project that is about cosmological observables, built from the concepts in her projects on applying coordinate-free geometric forms to theoretical objects in cosmology. The idea could be: Find geometric scalars that exist in the theoretical (or latent) universe, find geometric scalars that exist in any observational survey of the observable universe, and learn the relationships between these; construct cosmological tests and tests of the dark-matter model. The big issue (from my perspective) is that the symmetries that apply to the 6-dimensional phase space of the Universe are different from the symmetries that apply to the observed 3-dimensional redshift-and-angle-space of the (galaxy or quasar, say) observations. Some might say that there are no symmetries in this observational space, since there are window functions and selection functions, but this is not correct: Coordinate symmetries still exist there, it is just that these other functions must also be tracked, in the same space. Anyway, it's a nice research program to figure all this out.

regularities of dark-matter halos

There is a regular dynamics meeting (maybe Galactic dynamics meeting?) at Flatiron. I went today and I learned a lot, from Ivana Escala (Princeton) and Danny Horta-Darrington (Flatiron). I briefly presented Kate Storey-Fisher's project of describing dark-matter halos with coordinate-free nonlinear geometric scalars, which isn't really a dynamics project but it could be, because these scalars could be part of a canonical transformation of the dark sector. Anyway, the crowd had interesting things to say. In particular, the idea came up that the subspace in which the dark-matter halos live (subspace of the space of these scalars) is likely to be very compact (or low-dimensional, or both) and that the susbspace probably depends on the dark-matter model. That's a great idea, and suggests that maybe we can construct new tests of gravity.

nothing

The start of the academic year took out the day!

continuous representations of stellar spectra

Matt Daunt (NYU) and I had lunch today and discussed various things. One is the idea that we need (for technical reasons of data analysis) to make and use continuous representations of spectra. That is, we need to represent our spectra of stars such that they can be exactly and losslessly interpolated to any (sufficiently fine) grid of points. The ESA Gaia Mission XP spectra have this property: They are represented as polynomial basis functions, which confuse and surprise everyone. They are hard! But there are many other choices. For example, if the spectra are represented with b-spline basis coefficients, the coefficients “look like” just a set of flux values at wavelengths (so traditionalists are happy), but in fact they are the parameters of a continuous model that can be interpolated losslessly to any grid.

argh new writing projects?

Oh no! I spent the weekend accidentally starting new writing projects. What's wrong with me? One of the things that's wrong with me is that I am about to start teaching a new PhD-level class Statistics and Data Science for Physics and I find that I don't have good reading materials for the students. Here's a lack: A good, sensible discussion of when to take a frequentist approach in your data analysis, and when to take a Bayesian approach, divorced from (or not emphasizing) the philosophical differences.

a gallery of tensor images

I spent some time working on a possible introduction figure for the paper I am writing with Soledad Villar on images and grids and lattices of geometric objects (like scalars, vectors, and tensors). This introduction figure would give a set of examples of different kinds of data that come up in natural-science contexts. This is all a great idea! But then I need to understand (and explain!) exactly what each image in the gallery shows, and also get permissions to republish. Worth it (I hope).

a reference implementation of The Cannon

I had a great conversation with Andy Casey (Monash) today about many things. Hopefully it is the start of a regular. We discussed making a reference version of The Cannon, which would make use of jax, which I love, and which could be an affiliated package for astropy. I want this because (a) there is no completely simple, completely robust implementation out there, and (b) I want to transfer labels to all of the ESA Gaia RVS spectra from the SDSS-IV APOGEE data.

applying the SVD to nontrivial objects

Singular value decomposition (SVD) is a method for finding the equivalent of eigenvalues and eigenvectors for a rectangular matrix. It is what we use when we want to know the rank of a rectangular matrix, or make a low-rank matrix factorization (indeed, it is precisely what is used in principal components analysis or PCA).

The cool thing is: The method is exceedingly general; it can find the rank or a low-rank approximation to any space; it doesn't have to be a vector space exactly. It just has to obey certain algebra rules. So in my work with Soledad Villar (JHU) we use it to find a basis to represent all the linearly independent geometric images (grids of tensors) possible subject to constraints (like symmetries). I wrote words about using the SVD in this context in our nascent paper. Here is some example output of my SVDs in eye-candy form:

introduction for our geometric-convolution paper

My loyal reader knows that Soledad Villar (JHU) and I are working on a replacement for convolutional neural networks, that preserves convolutional structure, but enforces important physical symmetries (most importantly coordinate-freedom, or what I call coordinate-freedom). Today I deleted the introduction to our paper and re-wrote it from scratch.

When we last wrote the introduction, we thought we were writing code for cosmology. Now we think we are doing something way more general. In writing this, I realized that we need a figure that shows some kind of gallery or set of examples of the kinds of data we are talking about, which are images or grids of scalars, vectors, and tensors.

getting ready for the job market

I had a great conversation with Kate Storey-Fisher (NYU) today about her preparations for the academic job market. We talked about places, applications, proposals, and so on. In particular, we spent time talking about the structure of a good job proposal, which I think involves lots of scales from very very big picture down to very specific ideas for particular shovel-ready projects. We also talked about what makes Storey-Fisher unique on the market and how to talk about that uniqueness in the application. I think an odd thing about applications is that you have to narrate your work—which usually is a set of random and contingent projects—like it is a scientific program with coherence. This is odd, but not really irrelevant, since the ability to narrate it well shows an ability to make connections and see themes.

what to say for Jim Peebles

I have been honored by an invitation to speak at a meeting in honor of Jim Peebles (Princeton) and his 2019 Nobel Prize in Physics. I spent the day working on things I want to say at this event. Obviously I have to be very critical of the Nobel Prize and all prizes! Haha. But I want to talk about large-scale structure and also the problem that we only ever get to observe one Universe. What does that mean for inductive reasoning and epistemology?

continuum normalization of spectra

How do you continuum-normalize a spectrum in a low-resolution spectrograph? You can't really, unless you have exceedingly good models for stars (which you could use to fit the normalization); but of course if you had extremely good models for stars you probably wouldn't have to normalize!

I had an interesting conversation about this with Alex Dimoff (MPIA). He is continuum-normalizing spectra in a high-resolution echelle spectrograph. He has a good measurement of the “blaze function” so I suggested that he just add some polynomial or sine-and-cosine adjustments to that in each order. My main advice about continuum normalization is to avoid things that are very sensitive to signal-to-noise: As you degrade the signal-to-noise, your continuum estimate should not systematically deviate low. Most methods in play right now have this problem, and bad. Think: Fit to pixels that are “consisten” with being continuum pixels. That's going to depend very strongly on signal-to-noise.