Gaia Hike, day 2

Today was day two of the Gaia Hike at UBC. The results of yesterday's discussions and hacking were discussed in the morning and then we moved to tutorials about how to use the ESA Gaia data responsibly. From my own personal perspective, the highlight was a big tutorial from George Seabroke (UCL) on the high-resolution RVS spectra. His presentation went through all the properties and issues with the data, including things like overlapping spectra on the focal plane. It was really impressive, incredibly useful, extremely detailed, and an amazing representation of how complex and challenging a mission like Gaia is. Congratulations to the entire DPAC for pulling this off!


Gaia Hike, day 1

Today was the first day of the Gaia Hike hosted at UBC and led by Neige Frankel (CITA). The day started with business cards (short intro talks from everyone), followed by an attempt to find common themes across participants. Once the themes were identified, we split into groups to talk about what we might do this week with the ESA Gaia DR3 data. I ended up in a mapping and visualization group, which was fun, and (of course!) we closed out the day hacking on a piece of the data on stellar parameters, trying to figure out why the stellar parameters don't look exactly as we expect.


coordinate freedom?

I spent the weekend recovering from the Gaia Fete. During my recovery day, I worked on very long-term projects. For example, I spent some time working on how to express the following issue in my work (with Villar) on exact symmetries:

The mathematics and computer-science communities call these exact symmetries “equivariances” and they are imagining that the data or the laws of physics are precisely equivariant in the sense that if you (say) rotate all the inputs, you get a rotated output. But this is not the main reason that we write the laws of physics in terms of exact symmetries! We write the laws of physics in terms of invariants because we want our laws of physics to be coordinate free. This is required even when the laws aren't equivariant! But I have trouble making this distinction clearly, since the mathematical implementations of the two symmetries are identical. There's some cool philosophy here: Does coordinate freedom enforce symmetries? What would it even look like for the laws of physics to be asymmetric but coordinate free?


Dr Tomer Yavetz

Today Tomer Yavetz (Columbia) defended his PhD, which was in part about the dynamics of stellar streams, and in part about macroscopically quantum-mechanical dark matter. The dissertation was great. The stellar-stream part was about stream morphologies induced by dynamical separatrices in phase space: If the stars on a stream are on orbits that span a separatrix, all heck breaks loose. The part of the thesis on this was very pedagogical and insightful about theoretical dynamics. The dark-matter part was about fast computation of steady-states using orbitals and the WKB approximation. Beautiful physics and math! But my favorite part of the thesis was the introduction, in which Yavetz discusses the point that dynamics—even though we can't see stellar orbits—does have directly observable consequences, like the aforementioned streams and their morphologies (and also Saturn's rings and the gaps in the asteroid belt and the velocity substructure in the Milky Way disk). After the defense we talked about re-framing dynamics around this idea of observability. Congratulations, and it has been a pleasure!


discretized vector calculus

On Friday, Will Farr (Flatiron) suggested to me that the work I have been doing (with Soledad Villar) on image-convolution operators with good geometric and group-theoretic properties might be related somehow to discretized differential geometry. It does! I tried to read some impenetrable papers but my main take-away is that I have to understand this field.


discovering quantum physics, automatically?

I have been working on making machine-learning methods dimensionless (in the sense of units). In this context, a question arises: Is it possible to learn that there is a missing dimensional input to a physics problem, using machine learning? Soledad Villar (JHU) and I ignored some of our required work today and wrote some code to explore this problem, using as a toy example the Planck Law example we explained in this paper. We found that maybe you can discover a missing dimensional constant? We have lots more to do to decide what we really have.


making a mock Gaia quasar sample

I had conversations today with both Hans-Walter Rix (MPIA) and Kate Storey-Fisher (NYU) about the upcoming ESA Gaia quasar sample. We are trying to make somewhat realistic mocks to test the size of the sample, the computational complexity of things we want to do, the expected signal-to-noise of various cosmological signals, and the expected amplitude and spatial structure of the Gaia selection function. We have strategies that involve making clean samples with a lognormal mock, and making realistic samples (but which have no clustering) using the Gaia EDR3 photometric sample (matched to NASA WISE).


making Fourier fitting super fast

At the request of Conor Sayres (UW), I have been looking at distortion patterns in the SDSS-V Focal Viewing Camera (FVC), which is the part of the system that looks at whether the focal-plane fiber robots are where they need to be. The distortions are extremely bad; they are large in amplitude and vary on extremely small scales on the focal plane. So I have to fit an extremely flexible model. Here are my comments:

First, you should use mixtures of sines and cosines for problems like this. Not polynomials! Why? Because sines and cosines do not blow up at the edges.

Second, you should punk fast Fourier transform (FFT) codes to speed up your regressions. I wrote code to do this, which wraps the finufft best-in-class non-uniform FFT code in scipy.sparse linear-algebra code. This wrapping makes the FFT operators into linear-algebra operators and permits me to do solve() operations. That move (wrapping FFT in linear algebra) sped up my code by factors of many!


coordinate freedom vs equivariance, again

With Soledad Villar (JHU) and others I have been discussing making generalizations (or restrictions?) of image convolution operators to make machine learning respect more symmetries. One kind of generalization is going to 3-d images, and another is making the weights in the convolution filters geometric objects, like vectors, pseudovectors, and tensors. Then we developed a group-averaging technique to make these geometric filters equivariant. And now we are considering products and contractions of these geometric objects to make universally approximating function spaces. I don't love the word “equivariant” here: In my view the symmetries are coordinate freedoms, not relations between inputs and outputs. But the machine-learning world has spoken.


accretion and mathematical physics

In the CCPP brown-bag today, Andrei Gruzinov (NYU) went through the full mathematical-physics argument of Bondi (from the 1950s) that leads to the Bondi formula for accretion from a stationary, thermal gas onto a point mass. He also talked about a generalization of the Bondi argument that he developed this year (permitting the gas to be moving relative to the point mass) and also a bevy of reasons, both theoretical and observational, that the Bondi solution never actually applies ever in practice! Haha, but beautiful stuff.


generalized flat-relative extraction

I asked, in the Astronomical Data Group meeting at Flatiron, about the method of spectral 2D-to-1D extraction known as flat-relative optimal extraction. It's genius, and simple, but it makes strong assumptions about the spectrograph. I asked how we might improve it. And I think I maybe have a plan. The idea (which was thrown out by Megan Bedell) is to make the spectral representation something continuous, and evaluate it individually at every pixel, not just once per column of the detector. This should improve extraction. And it is relevant to the NASA proposal I am writing with Matt Daunt.


wacky shape scalars

Kate Storey-Fisher (NYU) showed me today the results of her work predicting stellar contents of dark-matter halos in hydrodynamic n-body simulations. She is building her shape scalars from geometric properties (scalars, vectors, and tensors) of the position-space and velocity-space distributions of the n-body particles. She did a very principled feature-importance study, including one feature at a time, combinatorically, and seeing how each feature helps, differentially. The most important features are... strange! Why? Because most of the regression work is done by very simple features (halo mass, halo size, halo velocity) so the (dimensionless) shape scalars we have made are fixing up non-trivial problems. Time to write the paper!


Dr Yucheng Zhang

Today Yucheng Zhang (NYU) defended his PhD. He used SDSS eBOSS large-scale structure samples to test gravity on large scales, and also made forecasts for measuring the non-Gaussiany parameter fnl and other very-large-scale-structure measurements in upcoming surveys. Beautiful work and a very nice defense. In the question period, Kate Storey-Fisher (NYU) asked Zhang about his possible forecasts for the upcoming ESA Gaia sample of 6.4 million quasars. Zhang has not considered this sample yet (almost no cosmologists have!) but he said that he does have the technology to make predictions for it. His intuition is that it would be great for measuring baryon acoustic feature and fnl. We plan to take Zhang out to lunch to discuss in the near future!


information loss

I wrote words today about how information is being lost in radial-velocity-spectrograph data-analysis pipelines at the stage of going from 2D spectra to 1D spectra. I am proposing to NASA (with Matt Daunt, NYU) to fix these problems! This is important, in my opinion, but I have to admit that it is not currently considered the tall pole in EPRV.


exoplanet roadmaps, plans, and surveys

Inspired by research by Matt Daunt (NYU), I looked at the various reports, presentations, and papers that have been written by NASA panels, committees, and projects about the tall poles and engineering gaps in the exoplanet research ecosystem. Why? Writing a proposal, of course! Daunt and I are proposing to work very close to the metal in radial-velocity work, so we are looking at the critical infrastructure that's close to the metal.