dimensionless and coordinate-free?

A lot of talk about Buckingham pi in my world. This is a theorem that says that any dimensional equation in physics with k dimensional inputs can be re-written as a dimensionless equation with fewer than k dimensionless inputs. But this is useless when we think about geometric equations—and many equations in physics are geometric.

Consider, for example, the coordinate-free equation F=ma. This equation has two dimensional vector terms. If we apply Buckingham pi, we get three coupled equations with non-scalar, non-coordinate-free dimensionless ratios. That's terrible, and useless! Can we replace Buckingham pi with something that makes equations that are both dimensionless and coordinate-free?


non-convolutional neural networks

Here's a quotation from an email I sent to Schölkopf (MPI-IS) and Villar (JHU) today:

First, I believe (am I wrong?) that a CNN works by repeating the precisely identical weights for every pixel. So if, in a CNN layer, there are k channels of 3x3 filters, there are only 9k weights that set all the k responses of every pixel in the layer to the 3x3 pixels centered on that pixel in the layer below. The sparsity comes not just from the fact that each pixel in one layer connects to only the 9 pixels below it, but also from the fact that the 9k weights are the same for every pixel (except maybe at edges). That enforces a kind of translation symmetry.

Okay, now, we could make a non-convolutional neural net (NCNN) layer as follows: Each pixel is connected, like in the CNN, to just the 3x3 pixels in the layer below, centered on that pixel. And again, there will be k channels and only 9k weights for the whole layer. The only difference is that at each pixel, a rotation (of 0, 90, 180, or 270 degrees) gets applied and a flip (by the identity or across the x direction) gets applied to the weight maps. That is, every pixel has the same k filters applied but at each pixel, there has been one of the 8 rotation-reflection transformations assigned to the 9k-element 3x3 weight map. This NCNN layer would, like the CNN layer, have 9k weights in the layer, and it would be just as local and sparse as the matching CNN layer.

My conjecture is that the NCNN will perform far worse on image-recognition tasks than the CNN. It is also (fairly) easy (I believe) to build a NCNN from a light modification of a CNN code. Comparison is clean and straightforward. I am ready to bet substantial cash on this one.


First Science Results from JWST, day two

Today was day two of the First Science Results from JWST meeting at STScI. Once again, it was a blast of results from all different fields. Some things I'll think about more going forward include: Something like 3 percent of white dwarf stars show an infrared excess that is consistent with them having a Saturn-like ring system? How did I not know this previously? It makes me want to find a WD with a transiting exoplanet to map the rings and maybe even ring gaps! There is a huge class of red luminous outbursts that appear to be the result of mergers of binary stars (maybe often when one of the binary pair starts to go off the main sequence and engulf its partner). Some of these, for energetic and other reasons, look like they are created not by binary-star systems but instead by star–planet systems. I wonder if the populations can be connected to the population of stars with weird lithium and refractory abundances?


First Science Results from JWST, day one

Today was day one of the First Science Results from JWST meeting at STScI. Today (like all days, I expect) was a barrage of information on different topics, filled with exciting results and systematic errors! I love meetings like this, because it is fun to see people struggling with data they don't quite understand yet. And I can see lots of opportunities for my interests in spectrographs and imagers to be useful in this community. My favorite talks today (unfairly!) were the talks on the instruments and their status. There are some beautiful lens-flare-like artifacts in the NIRISS instrument; that would be a fun problem (for example!). There are insane “snowball” cosmic-ray hits in the NIRSpec data, the likes of which I've never seen before. One nice thing about contemporary NASA: The plan is to make all the calibration pipelines completely open and user-operable, so it is easy to intervene on these data.


towards flexible dynamical models

There are many conversations going on right now in the Flatiron dynamics community about making flexible models for galaxy dynamics. For example, there is work on replacing parametric models with non-parametric basis expansions in various bases. For another, Price-Whelan and I have been trying to think about how one might just image the orbital tori directly with the stellar element-abundance maps. We brought two of these conversations together today, in which Ben Cassese (Columbia) and Danny Horta-Darrington (Flatiron) showed that they are using near-identical forms for data-driven orbit forms in the vertical dynamics of the disk. We also spent a lot of time talking about what constitutes a sensible likelihood function for torus imaging and distribution-function-fitting projects.


can you see the orientation of a star?

Stars don't have uniform surfaces, and they rotate. Can you see the orientation of the star in a single spectrum? Of course the answer is no: You don't have a coordinate system! But if you have some previous spectra of the star, can you establish a rotation period and define an angular coordinate system, and then follow that by taking a new spectrum and saying where the star is in its rotational phase? It looks like the answer to this question might be yes, based on experiments that Lily Zhao (Flatiron) is doing. Of course we don't really care about the stellar orientation. What we care about is capturing or correcting the artificial radial-velocity signals introduces to the data from the rotating, non-uniform surface.


phase and frequency variations

If a star has a (relatively) coherent oscillation mode, and you can monitor it over a long period of time, then orbital motion of the star can be seen as either phase or frequency variations of that mode. I've been working on this in different collaborations, with Dan Hey, with Simon J Murphy, with Abby Shaum (CUNY), and recently with Nora Eisner (Flatiron). Right now, Shaum, Eisner, and I are looking at signal-processing approaches that look like demodulators. What I'm interested in—at least in terms of me learning about signal processing—is how can we make a demodulator that demodulates both phase and frequency simultaneously. There must be hybrid and combined approaches. I'm also interested in what we can measure from incoherent oscillators.


new LIGO events

Today Mathias Zaldarriaga (IAS) gave the NYU Astro Seminar. He told us about work he has been doing to increase the sensitivity of the LIGO data to inspiral events, and how that is impacting beliefs about populations of black holes.


the stability of the vacuum

The research highlight of my day today was our weekly lunchtime blackboard talk, as it often is on Mondays. TOday it was Isabel Garcia Garcia (NYU), talking about the stability of the vacuum. She was specifically talking about the stability of a false vacuum, and specifically when there are large extra dimensions. The weird thing is, in all string-like models for the fundamental particle physics model there are both large extra dimensions and an exceedingly low probability that we live in the true vacuum state. That means a decay to a different state is possible (inevitable?). Why has this vacuum lived so long?


the discussion section of a paper

I spent the afternoon writing the discussion section of my nascent paper with Andy Casey (Monash), about spectrum combinations. My philosophy of the discussion section is: Return to each of the most important assumptions you made (and, hopefully, stated explicitly in some early section), and say what you would do, what you would get, and what you would pay, if you wanted to relax that assumption. I spent a lot of time speaking about spectral variability, which can come not just from the source itself, but from the hardware, from backgrounds, or from data processing issues.


simulating data for phase and frequency modulation

Abby Shaum (CUNY) and I have been working on phase demodulation for binary detection and characterization, using coherent oscillation modes in stellar light curves. We are taking a pure signal-processing approach, which is lightweight and fast, such that we could automatically apply it to everything in Kepler or TESS. We also want to do frequency modulation for incoherent modes (which somehow our people think won't work; won't it?).

Today we discussed how to build fake data to fully test our systems. In the coherent case, this is easy! In the incoherent case this is harder. We discussed simulating it by drawing from a Gaussian Process. And we discussed simulating it by forward modeling a stochastically forced, damped harmonic oscillator.


geometric convolutional networks

Today I had a great meeting with Wilson Gregory (JHU), Drummond Fielding (Flatiron), and Soledad Villar (JHU) about a project to learn partial differential equations from simulation data. This is a toy problem from our perspective, but it is a baby step towards big, real computational problems in physics. Fielding produces training data, Gregory produces geometric convolution networks, Villar proves things, and I cheer from the sidelines.

Our approach is to replace convolutional neural networks with geometric operators that are generalizations of convolutions that know more about geometric forms like vectors, tensors, pseudovectors, and so on. By building methods that use geometric objects responsibly, we automatically enforce coordinate freedom and other deep symmetries.


degeneracies and optimization

With Emily Griffith (Colorado) I have been working on a purely data-driven nucleosynthetic model, trained on the abundances measured in stars by the APOGEE surveys. This model looks a lot like a non-negative matrix factorization, so it is a kind of model I've worked with many times in my life. We've figured out an optimization scheme and made it (exceedingly) fast with jax. Nonetheless, we have been having troubles with the optimization, getting stuck in bad local minima or even pathological locations in parameter space.

Today I discussed this model with Soledad Villar (JHU) who warned me that the model has potential pathologies, and strong degeneracies. I thought I was breaking these degeneracies with regularizations, but in fact the degeneracies are bigger than I thought. Villar's advice (which aligns with the machine learning zeitgeist) was to leave the degeneracies free and then rotate or transform the model to where I want it to be at the end. She also had useful advice about optimizing non-convex functions.


Iron Snail (tm)

My day started (at 07:00) with a call with Neige Frankel (CITA) and Scott Tremaine (IAS) about our project to understand the phase-space spiral in the vertical kinematics of the disk in terms of metallicity, element abundances, stellar ages, and so on. Indeed, we have a general argument that any non-equilibrium perturbation of the Galaxy, winding up into a spiral, will show a metallicity (or other stellar-label) effect, provided that there were gradients in the metallicity (or other label) with respect to stellar density, or phase-space density, or orbital actions. The argument is exceedingly general; I want to write a paper with wide scope. Tremaine is careful with his conclusions; he wants to write a paper with narrow scope. We argued. The data (compiled and visualized very cleverly by Frankel) are beautiful.


halo mass assembly

On Fridays, Kate Storey-Fisher (NYU) organizes a small meeting to discuss her projects on dark-matter halos using equivariant scalar objects constructed from n-body simulation outputs. Today we included Yongseok Jo (Flatiron), who has worked on building tools to paint galaxies onto dark-matter-only n-body simulations. We discussed joint projects, and conceptual issues about mass-assembly histories. In particular, I am interested in how we can predict formation histories of dark-matter halos from the galaxy contents alone, or infer the dark matter distribution in phase space from the stellar distribution in phase space. I love these projects, because they combine growth of structure, gravitational dynamics, galaxy formation, and machine learning.


non-parametric model of the density of the Milky Way disk?

Danny Horta-Darrington (Flatiron) has been working with Adrian Price-Whelan (Flatiron) to measure things about abundances and dynamics of stars in the Milky Way disk. Horta is finding that there are way better abundance gradients, in way more directions in phase space, than previously have been (usefully) visualized. But along the way, he stumbled upon a plot that clearly shows the variation of the Milky Way thin disk density with radius. We discussed today how to make the simplest possible measurement of this, with a variation of Orbital Torus Imaging, or really a simplification of it. We realized today that there is enough data to just make this measurement in patches all over the (nearby) disk. The scale length looks short!


parameters and nuisance parameters

Long ago, Adrian Price-Whelan (Flatiron) and I and others built The Joker, which is a Monte Carlo method (but not a MCMC method) for dealing with the Kepler problem. It exploits the fact that some parameters are linear, and some are nonlinear. This week, Lawrence Peirson (Stanford) is visiting Flatiron to generalize this point. Peirson's point is that the trick we use for linear parameters can be used for any parameters that have smooth, unimodal-ish posteriors. We just have to add some linearization and some optimization. So we are working on writing that down. And coding it up.

Along the way, Peirson found another linear parameter in The Joker, so we can now make it way, way faster. That's awesome!


dust and star formation

Julianne Dalcanton (Flatiron) gave a great talk at NYU today about star formation, interstellar medium, stellar ages, and dust in Local Group galaxies. She showed that the standard star-formation indicators from infrared emission from dust are way wrong. But she also showed lots of interesting detail in the interstellar medium and star-formation history in M33 and M31. M31 really does seem to have a ring which is not just over-dense in star formation; it's actually over-dense in stars. That's odd, and interesting.


Ising model and gauge

I understood cool things about gauge freedom today, during a beautiful blackboard talk by Himanshu Khanchandani (NYU), who was talking about the 2-d Ising model and how it relates to the continuum limit (which is a field theory, interestingly!). He showed that if you introduce certain kinds of linear defects into the lattice, the change to the Hamiltonian depends only on the locations of the endpoints of the line of linear defects. This is because there is a gauge freedom, which is that you can change the signs of the spin-spin interactions at a point, and also change the labeling of what constitutes the positive and negative local state. This leads to topological properties of defects. It's gorgeous! And maybe related to the problems we want to solve in machine learning with images and geometry.



Today Andy Casey (Monash) joined a regular meeting I have with Megan Bedell (Flatiron) and Lily Zhao (Flatiron) about things related to precision spectroscopy. We discussed projects we can do with surface spectra of the Sun, one from the quiet part, and one from a spot. Casey is involved in the Korg project led by Adam Wheeler (OSU); we discussed fitting both spectra with Korg, and learning about the physical differences between the quiet and active regions in the Sun. We also discussed Zhao's projects to empirically correct for stellar activity in time-domain spectroscopy looking for planets.


JWST and open science

Today I hosted Sarah Kendrew (STScI) at NYU. She gave the Physics Colloquium, about NASA JWST launch, commissioning, and early science. She has been the lead of a JWST instrument mode for something like 14 years; now she has data! She talked about how JWST works and showed some beautiful exoplanet results. One of the great things about her talk is that she explained a point on which they made some mistakes, and how interactions with the user community helped them to fix those mistakes. It was a great endorsement of the open model for science.


what is the scope of our image models?

There is a bit of a disagreement between Soledad Villar (JHU) and me on the scope of the methods that we are building to operate on images of scalars, vectors, and tensors. Soledad's view is that they apply to physics problems, like fluids. Mine is that they apply to absolutely every image of every kind ever taken, like vacation snapshots. Today we had a meeting with Drummond Fielding (Flatiron) and Wilson Gregory (JHU) about making some training data from a small 2D fluids simulation. (That is, we were adopting, for today, Villar's position on our scope.) Apparently 2D fluids is a standard problem in machine learning these days? I can't imagine why. But anyway, on the call, Fielding promised to make us some toy data. And, tonight, he did. Awesome!


bi-linear-ish models

Before my day got ruined by a deadly SDSS-V Advisory Council meeting, I worked with Emily Griffith (Colorado) on a data-driven 2-process model for nucleosynthesis. This model is amplitudes (2 per star) times process yield vectors (2 per element). In this sense it is like a matrix factorization. But it involves a log-sum-exp (rather than just a matrix multiply), so it is mildly nonlinear. It can still be optimized the same way and it is well behaved. In some sense, I realized, it is very like The Cannon in form. But different! We failed to fully implement before I turned into a (very unhappy) technocrat.


SDSS-V Science Festival, day 2

On day two of the Collaboration meeting, I talked to Emily Griffith (Colorado) about data-driven models of nucleosynthetic processes. We were inspired by this paper, on which Griffith is an author. The paper builds an empirical two-process enrichment model based on the observed morphology of the [Fe/Mg] vs [Mg/H] plane. We discussed how to make this model into a full (but constrained) latent-variable model. I am interested in moving it towards causal inference, but we could also look at third processes, anomalous stars, anomalous elements, calibration issues, and so on. We wrote down math and started to write code.


SDSS-V Science Festival, day 1

Today was the first day of the SDSS-V Collaboration Meeting in Toronto. We talked about the state of the survey and the survey mission, shared values, and operating principles. This was great; it is the first full in-person meeting since survey start. Much of the day was open working and break-out time.

Late in the day, Adam Wheeler (OSU) made a great plot comparing SDSS-IV velocities (Doppler shifts) to ESA Gaia velocities, as a function of APOGEE fiber. It looks like there are substantial differences, and systematic with fiber. If this is real, fixing it will have a big impact on work I've done on spectroscopic binaries in the sample.



I had a great visit to UCLA Astronomy today. I learned a ton. I gave a messy, disorganized talk about machine learning. I learned, as I often do, that it is not a good idea to try to tweak an old talk into a new talk. The best move is to start from scratch and make new slides. It's fresher. And better! And more aligned with the new me. But I at least started some conversation (it is an engaged audience there). Giving talks is hard.


Jim Peebles

Today was a celebration in Princeton for Jim Peebles (Princeton) and his 2019 Nobel Prize. As my loyal reader knows, I hate the Nobel Prize, and I say so in the slides from my talk. But I love Jim Peebles, who has been incredibly important to my career and life. I spoke about epistemology and large-scale structure.

In the other presentations during the day, Suzanne Staggs (Princeton) gave a deep and hilarious picture of the early days of CMB cosmology. Would she be upset to hear me call her early career the “early days” of CMB? Vicky Kaspi (McGill) showed an amazing result from the study of fast radio bursts: The rotation measures to the bursts increase with redshift in exactly the way you would expect from the cosmological baryon density and the world model in LCDM. That's incredible! Frans Pretorius (Princeton) gave a great talk about numerical relativity, in which he showed almost no numerical relativity computations! He talked about what might happen in the fully relativistic version of the black-hole-black-hole merger problem, in which the incoming black holes have their mass energies overwhelmed by the center-of-mass kinetic energies. He came up with many possible outcomes and explained why the answers aren't known. The answers involve incredibly qualitatively different outcomes!


code and words on Standard Practice (tm)

I worked today on the code and text on my project with Andy Casey (Monash) on combining spectra. What I did today was code up and describe what I call Standard Practice (tm), which is to shift (interpolate) and coadd (average) your data.


abundance gradients in the Milky Way

I had an absolutely great meeting this morning with Danny Horta-Darrington (Flatiron) and Adrian Price-Whelan (Flatiron), in which Horta showed us plots of various stellar surface abundances as a function of dynamical quasi-invariants in the Milky Way. That is, abundance gradients! But abundance gradients get stronger and more informative when they are plotted in terms of dynamical invariants than when they are plotted versus position (say), because positions of stars change with time. There is so much information for us to use here!

One thing we discussed is what units or transformations of the dynamical invariants we should plot. We're leaning towards the transformations that have units of length, which are guiding radius, z-max, and radial span.



I find it hard to admit to myself that I (and collaborators) are considering submitting a manuscript to Nature Communications, which is part of the evil publishing empire (though at least it is Open Access). I have been pretty morally pure on this point for many years. But! It is hard to find publishing venues that are truly interdisciplinary. And many of those venues are bad (pirates even, and I don't mean that in a good way).

If we are going to publish in Nature Communications then we need an infographic or good visuals. Today, Soledad Villar (JHU) and I worked through possible visuals and design ideas for a good infographic. I have to say that I benefitted enormously from the extremely informative and compact visualization that Lily Zhao (Flatiron) made for Excalibur (Figure 1 of this paper).


don't interpolate your data!

I found a place to hide and write code this afternoon. I built the code to make fake data and do experiments in my new project with Andy Casey (Monash) which is about combining multi-epoch spectroscopy. The goal is to replace the shift-and-average things that most projects do with something that never interpolates or shifts the data; it only interpolates or shifts a data-driven model of the combined spectrum. I wrote a full set of code (it is only a few lines), and it works! Now to figure out if it is better than, or the same as, standard practices. I sure hope it's better!


latent-variable models

Trevor David (Flatiron) convened a group to talk about latent-variable models and the myriad decisions they require. He is trying to model the ages and the abundances of stars, with the hope of getting a new age indicator. Nora Eisner (Flatiron) is building a very similar model but for the classifications by participants in a big citizen-science project. We discussed the relationships between number of latents, model complexity, regularization, and predictions. We also discussed testing, interpretation, and trustworthiness. It's a big space.


models for images; talking about stuff in progress

As my loyal reader knows, I have been working on new machine-learning methods for imaging, based on scalars, vectors, and tensors, and group-theoretic invariants. Today I had a long conversation with Kaze Wong (Flatiron) about these things, with ideas about implementation and model structure. With Soledad Villar (JHU) I have been thinking about convolutional layers, and nonlinearities, but Wong wanted to talk about full-network architecture. It's hard! So we discussed, and realized that we need to do some serious work if we are going to find a way to implement something general and useful and computationally tractable.

Before that, in Astronomical Data Group meeting, I got tons of great feedback about my project with Andy Casey (Monash) to combine shifted spectra into a rest-frame average spectrum. I described the project in the words I like to use, and the audience heard something totally different! So I know what I have to be emphasizing in the writing. I can't say enough how important it is to talk to people about your science in progress!


orbital torus imaging: What's next?

Today so many cool things happened research-wise, it is hard to choose what to highlight here. For example, Kate Daniel (Arizona) brought her students to Flatiron Galactic Dynamics meeting and we heard about many interesting projects across a range of subjects and modalities. In that same meeting, Danny Horta-Darrington (Flatiron) showed really rich plots of mean abundances (as measured by SDSS-IV APOGEE and ESA Gaia) of stars as a function of positions, velocities, actions, energies, and so on. He's gearing up to take the next step in orbital torus imaging, which is a method to find the acceleration field of the Galaxy using relationships between kinematics and stellar surface abundances (or other invariants). Horta's plots show tons of structure and I believe (not everyone agreed maybe?) that they show the outlines of orbital 3-tori in phase space! Anyway, now's the time to specify a well-defined, achievable project. One thing I said in the meeting, that was surprising to some (and maybe worth a paper?), is that there are strong abundance gradients in the Milky Way disk with respect to all three actions!


time dependences in ultra-short-period planets

I had a great conversation with Noah Sodickson (high schooler) about ultra-short planets in the NASA Kepler data. He has been filtering the light curves, running astronomers'-favorite “box least squares” and plotting the folded light curves. When he does this in quarters (meaning, cutting the data into 90-day chunks), he can see small variations in the transit shapes. These have been attributed to various things. My goal is to figure out a way to model these variations without averaging the data. Binning is sinning, after all. Sodickson can see that everything we see is a strong function of how we filter the light curves, so we have to think pretty hard about that.


writing in various

I keep saying that if I only wrote one paragraph per day, I'd write many papers (or one book) every year! And that just makes me realize that I don't really write one paragraph per day in anything, at least not in the mean. Bernhard Schölkopf (MPI-IS) helpfully (?) mentioned to me that this means that I write more in my blog than in all my scientific papers, combined. Whoops? Anyway, I caught up today and wrote many paragraphs, some in my paper about coordinate freedom and other symmetries, and some in my paper about not stacking your data.


infrared-excess stars

My day started with a call with Gaby Contardo (SISSA) and Trevor David (Flatiron) about Contardo's project to find stars in ESA Gaia and NASA WISE that have infrared excesses. These stars should be young or dust-enveloped or host aliens! We are trying to phrase this problem as a prediction problem: How well can we predict infrared brightness from Gaia (visible) information, and are there stars with significant excess infrared? The answer seems to be yes: The histogram of differences between predicted and observed skews nicely to infrared-excess. Now: Are any of these known objects? And can we rediscover (say) star-forming regions?


writing an interpolator in jax

Today I pair-coded with Matt Daunt (NYU) a general kernel-based interpolator in jax. Actually, I am not certain that what we wrote can be handled by jax gracefully, because I don't understand the functional programming model. But I learned that interpolation is harder than I thought: If your interpolator is higher-order than linear, the interpolation involves solving an inverse problem. The fast interpolators (like spline) have such solutions coded with clever iteration schemes that require only one pass through the data, like the fast GPs we love. But if you want to write something general, you might have to suck up some (sparse) linear algebra. Daunt and I discussed strategies for our spectroscopic model, given these realities.


never shift-and-coadd your data!

I had a great (weekly) call with Andy Casey (Monash) today. We discussed many things, including a hilarious idea for April Fools' that Matt Daunt (NYU) and I conceived. But one of my action items out of the meeting is to start a short note on how to avoid ever shifting and stacking your data (think spectra taken at different times of year, so at different Doppler shifts relative to the Earth). How can you combine data without doing any interpolation of the data? The answer is simple: You forward-model your data with a model that (by optimization) becomes the average of those data. (And the optimization is often closed-form.) Then you only ever shift the model, and you don't have to deal with shifting noise arrays or mask arrays, or anything else. I'll try to write a stub this weekend.


can a (say) 5-sigma result be interpreted as a p-value?

In preparing for class today (I am teaching NYU #data4physics), I worked through the relationship between a p-value (like what's used in medical research) and a physicist's n-sigma measurement. They are related in some very special cases, like in particular when the value being measured is a linear parameter (like an amplitude) and the noise is Gaussian. But those cases are special. And also: Converting n-sigma to p-value depends very critically on the noise model. So I don't like thinking of it as a p-value. That said, maybe there is no difference?


patches of imaging

I am discussing with Sean Ku (NYU) and Victor Kuang (NYU) the NASA Cassini imaging of Saturn. We want to make (from the data) a high-quality face-on picture of the rings. This is a problem (from my perspective) in computer vision, so we need a camera model (and a lot of other things). One thing I hypothesized about this problem today is the following (am I right?):

Any sufficiently small patch of a camera image can be modeled with a pinhole-camera-like camera model, provided that we give the camera model the freedom to make the image plane not perpendicular to the line from the pinhole to the patch of the image plane. Is this correct? We are about to find out, the hard way.


writing for deadline

I don't like the way computer science works, with conferences and deadlines. I could complain about it for hours. Journals are a thing, people! But anyway, at Dagstuhl last week, Villar, Schölkopf, and I decided to sprint out a paper for the physics-and-ML workshop at NeurIPS this year. Deadline is in two days. Guess what I did with all my research time today?


Dagstuhl, day 4

Today was day 4 of Machine Learning for Science: Bridging Data-driven and Mechanistic Modeling at Schloss Dagstuhl.

I spoke today, about passive symmetries and the constraints on machine-learning models they imply. My talk was totally new for me, and based on conversations between Villar, Schölkopf, and me during the meeting. That was fun. So now I have a new way of talking about all this stuff, and the three of us are trying to write a short paper about it.

Among the talks today, one idea I really liked is the idea, from Carl Henrik Ek, that trust and interpretability might be strongly related. Indeed, when I talk about interpretability, it is often in the same context that I am talking about models that make sense to a physicist, which are, in turn, models that I would trust. And that is also very related to what I myself talked about today: If models look more like physical law, then they are much more trustworthy. And maybe also more interptetable.


Dagstuhl, day 3

Today was day 3 of Machine Learning for Science: Bridging Data-driven and Mechanistic Modeling at Schloss Dagstuhl.

We had an open discussion about goals for ML in science today. The idea of explainability came up. I liked the comment that explainability (or what counts as explainability) might depend incredibly strongly on field or context. Like it is different in medicine and in astronomy. And, related, the idea of how models are communicated is very context dependent. And maybe very dependent on history. For example, in the future, models might be communicated through APIs rather than scientific papers maybe?

Causation and causal inference was a big theme of the day with Bernhard Schölkopf, Jonas Peters, Bubacar Bah, and Niki Kilbertus all talking about overlapping ideas in causal inference, mechanism inference, differential equation inference, and symbolic regression. Is causation the new framework for machine learning? Many in the room think so.


Dagstuhl, day 2

Today was day 2 of Machine Learning for Science: Bridging Data-driven and Mechanistic Modeling at Schloss Dagstuhl. Many great things happened. Here are two highlights:

Bernhard Schölkopf (MPI-IS), in a discussion session, asked what the key questions were for machine learning as a field. I love this question! Astronomy and physics do, I think, have key questions, which guide research and contextualize choices. Machine learning does not really, or if it does, the questions are implicit. I want to work on this.

Philipp Hennig (Tübingen) gave an energizing talk about the relationship between simulations of the world and observations of (or data about) the world. He argued (convincingly!) that we should not think of these as totally different things, and that learning from data and simulating a process could or even should always be integrated and done together. He demonstrated this with a simple model of infectious disease, but the point is extremely general.


Dagstuhl, day 1

Today was day 1 of Machine Learning for Science: Bridging Data-driven and Mechanistic Modeling at Schloss Dagstuhl. The first day was mainly about applications of machine learning, in Earth science, livestock management, astrophysics (dark matter), cells, and mechanical engineering. I had many thoughts and realizations. Here are a few random ones:

The problems that appear in Earth science, and the data types, are very similar to those that appear in astrophysics! But in Earth science, biology is a big driver of global processes, and there is no good mechanistic model for (say) how plants grow and take up carbon. The world is filled with mobile phones, with good cameras, and the methods we could could be employing to be doing science in a distributed way are way, way under-used. Cells are incredibly complicated. The mechanistic model involves literally thousands of individual processes. Like our model for the cell is as complicated as our model for the entire Earth system (which, by the way, depends on cells!), or even more complicated.

In the areas of the cell and the Earth, a theme was that the investigators want to preserve the causal structure we believe, and just use the machine learning to replace one tiny piece, with a data-driven model. Related: You can think of the machine learning as an effective theory for something (a sub-part of the problem) that doesn't work well from first principles. That's a good idea!


signal processing vs forward modeling

Abby Shaum (CUNY) and I are trying to write up a paper about our work treating oscillating stars as something like FM radios: We use the oscillation modes as carrier frequencies and find any orbital companions through phase or frequency variations of that carrier signal. Today we discussed the difference between doing that and forward modeling the signal. The former is signal processing. The latter is a generative model. Very different! And in many senses forward modeling is more principled. But I still think (and hope) that signal processing has a place in astronomy.


the chevron

A research highlight today was the Flatiron Galactic dynamics internal group meeting. We discussed kinematic features in the Milky Way halo that have appeared in ESA Gaia DR3 in maybe this paper. We looked at data and (toy) simulations. I'm interested in whether the features appear in metallicity or abundances. The arguments that Neige Frankel (CITA) and I worked out this summer for The Snail looks like they maybe work for all phase-space overdensities caused by perturbations?


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!


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.



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.


yet another version of The Cannon?

I started to write an implementation of The Cannon today. Probably a mistake! But I don't love any of the implementations out there, even my own. I was inspired because I want to train a model of the ESA Gaia RVS DR3 spectra using the SDSS-IV APOGEE labels for training. I want to write the implementation well so it's robust, easy to maintain, simple, and consistent with astropy. Is this a mistake?


metallicity and spiral arms

In Milky Way Group Meeting at MPIA today we discussed this paper on spiral structure as observed by Gaia. The paper shows that the spiral arms appear not just in the density of young stars but in their metallicities (at very low amplitude). What does this mean? I think maybe it's just the response of a smoother disk population to a perturbation: If you have a smooth disk with a metallicity gradient in it, and you perturb it, you wind up a spiral in the disk and that spiral appears as a low-amplitude abundance feature, because the spiral involves synchronizing the radial oscillations of stars at different guiding radii (and hence, given the gradient, different abundances). It is easy to work out quantitatively though. Maybe I should do that? Reminds me of what I have been working on with Neige Frankel (CITA), but in the vertical (rather than azimuthal) dynamics.


how many equivariant linear functions are there?

O. M. G. As my loyal reader knows, Soledad Villar (JHU) and I are trying to build a replacement for convolutional neural networks that can handle geometric objects (scalars, vectors, pseudovectors, tensors of any order, so on) and that can create functions that exactly (or approximately if you like) obey the symmetries of classical physics (rotation, translation, parity, boost, maybe even gauge). Our method produces polynomial functions of images (functions where both the input and the output are images), making use of convolutions, outer products, index contractions, index permutations, cross-products, pooling, and so on.

Meanwhile, Ben Blum-Smith (NYU, JHU) has been doing (scary to me) group theory stuff in which he has been computing the number of unique polynomial functions of images of fixed polynomial degree that are possible, given image inputs and outputs (of some tensor orders), when those polynomial functions obey the symmetries of classical physics. And he has results! He can tell us how many unique linear and quadratic, say, functions there are of vector images (say) that output vector images. It's a formula that depends on the image size and the degree of the polynomial.

Today Villar and I had a breakthrough: We used our geometric generalization of convolutions to produce all possible linear functions of small images, deduplicated the results using a singular value decomposition, and (thereby) counted all linearly independent group-equivariant linear functions there are that go from vector images to vector images. And our results agree with Blum-Smith's formula. So we may actually have a complete basis for all image functions that could ever exist in the context of classical physics?


spherical-harmonic transforms of point sets

On the weekend I computed the spherical-harmonic transform of Kate Storey-Fisher's quasar sample made from ESA Gaia data. I also computed the spherical-harmonic transform of the random catalog we use to map the selection function. The two transforms are extremely similar in their complex amplitudes! Since the random catalog is made assuming perfect homogeneity and isotropy, this similarity directly translates into a measurement of the isotropy of the Universe.


is the time just a housekeeping datum?

I had a lunch conversation with Melissa Hobson (MPIA) about finding Earth-like planets in long-term radial-velocity surveys. We discussed instrument calibration, and how one interpolates the calibration data from the arcs or LFCs onto the science exposures. I think we should be doing this not in time (or not only in time) but in other housekeeping quantities like instrument temperature state. That is, the most relevant calibration exposure might not be the closest in time, it might be the closest in instrument temperature. From my perspective, the time is just another piece of housekeeping data, and its value for calibration is to be determined empirically.


jackknife practice and intuitions

Last week I gave a colloquium at MPIA in which I advocated the use of jackknife and bootstrap resampling to obtain empirical uncertainty estimates in a complex data analysis. Today I actually implemented jackknife in my project on cosmic homogeneity (and isotropy). I jackknifed by sky position: I split the sky into 12 nearly-equal regions for 12-fold leave-one-out. I have intuitions about when it is a good idea to jackknife on a quantity (like sky position) and when it is a good idea to jackknife on a quantity that is completely random, but I don't know exactly where my intuition comes from. In general it must be the case that jackknifing on different things answers different questions about your noise.


direct planet spectroscopy

I had a great conversation over lunch today with Lorenzo Pino (Arcetri), who is measuring exoplanet direct spectra in systems with large, hot planets. He makes a data-driven model for the star spectrum (and its variations) in a time-domain spectroscopic campaign, and then stacks the residuals in the (computed) rest frame of the planet to get the planet spectrum. We discussed the next-order correction to this method that approximates simultaneous fitting of planet and star.


Hekker group visit

Today I visited the group of Saskia Hekker (HITS). We discussed many things asteroseismological! We discussed:

  • the ESA Plato observing strategy
  • is the asteroseismic signal a Gaussian process to any degree of accuracy?
  • using asteroseismic information to improve and inform open-cluster membership
  • synchronization of orbital periods with primary-star rotation periods
  • are two distributions different?
and much, much more. I had a lovely day at HITS.


do the stars make up a coordinate system?

Long, long ago, when I worked with Sam Roweis (deceased) and Dustin Lang (Perimeter) on locating images on the sky, we used to discuss coordinate systems: You don't actually need a long-lat or theta-phi coordinate system to describe the locations of things on the sky, right? You can just use angular relationships among sources to locate everything precisely and unambiguously! And with that approach, you don't need to make as many choices and standards and lines of code about reference frames. But, alas, this point of view is not in the ascendent.

Not being deterred, I put the bright stars on my maps (from this weekend) of Kate Storey-Fisher's ESA Gaia quasar sample. Can you find the big dipper and Orion? And Sirius?


Lambert's projection

At the Heidelberg Tiergarten Schwimmbad I worked out the mathematics for an equal-area projection of the sphere, centered on the poles. It turns out that I reinvented Lambert's projection from the 1770s. Here's a plot of the Gaia DR3 quasar sample (censored by some dust cuts) in my new projection:


flexible models and interpolation

I gave the Königstuhl Colloquium today, which was fun. I spoke about this paper and related matters. I got great questions. One was about when to fit a very flexible model vs just doing simple interpolation. I gave some kind of minimal answer in my talk but then I thought about it a lot more later. The key difference between fitting a very flexible model and interpolation is that the former can be made part of a bigger probabilistic model whereas the latter (without serious modifications) cannot. That's a big deal when (say) you are trying to find planet transits in the face of stellar and spacecraft variability.


start a paper on homogeneity

After making (yesterday) all the plots that demonstrate the uniformity and large-scale homogeneity of Kate Storey-Fisher's Gaia quasar catalog (which she is writing up now), I decided (tentatively) to write a paper on cosmic homogeneity with these data: When a catalog shows beautiful homogeneity, that is both a statement about the catalog and a statement about the Universe. I wrote a title and abstract and some figure captions today.


the fractal dimension of the Universe is 3

Back around 2004 I promised myself I would never compute a fractal dimension ever again! But I did today, using Kate Storey-Fisher's (NYU) new quasar catalog from the ESA Gaia data. And it turns out that it is 3. Good! Actual measurement with uncertainty coming soon.


visualizing a tensor field

I am working with Soledad Villar (JHU) and others on making generalizations of convolutional operators (and image-based non-linear functions based on those convolutions) that can deal (correctly) with input data that contain vectors and tensors. That is, tensor convolutions of tensor images. Anyway, one of the problems is: How do you visualize a tensor field or an image of tensors? I implemented a possible solution, pictured below: You make a figure that has no symmetry, and you take that figure through the tensor! That only works for 2-tensors of course. 3- and 4-tensors? I'm at a loss.


new paper scope

We had a great meeting today with Kate Storey-Fisher (NYU), Hans-Walter Rix (MPIA), Christina Eilers (MIT), and me to discuss KSF's progress on the ESA Gaia quasar sample. We looked at her large-scale structure results and her jackknifes and discussed paper scope. Options range from a quasar-catalog paper to a selection-function paper to a full cosmological parameter-estimation paper. Of course we decided to do all three! But importantly we decided that this week we would focus on writing a quasar-catalog paper. That's good, and achievable.


jackknife the sky?

On the weekend, Kate Storey-Fisher (NYU) and I implemented jackknife uncertainty estimation for KSF's cosmology-with-Gaia-quasars project. We jackknifed by cutting the sky into RA slices. This is standard practice but I don't love it! It assumes that you know that your main source of error is calibration or sample consistency over the sky. It might be something way more insidious. In principle I guess you should jackknife over many things, and also randomly.


uncertainty propagation for a neural network

Today Matthias Samland (Stockholm) gave a nice Königstuhl Colloquium at MPIA about direct imaging of exoplanets with high-contrast imaging. He showed some beautiful results from ESO Gravity and from NASA JWST. One of his main take-away points is that the situation is changing fast, and we might achieve very much higher contrast ratios in the near future than we've ever had, and thus get many more planets.

I spent some time late in the day looking at uncertainty propagation for neural networks: Given that you can optimize a NN, and given that it makes good predictions for held-out data, and given that you can take all derivatives of everything with respect to everything, does that mean you can propagate errors or noise from the data to the results? I think the answer is yes in a limited sense: You can see how the output depends on the input at the training step. But what you can't do—and probably will never be able to do—is propagate the uncertainties that come from your training set (the uncertainties in your weights, as it were). And these uncertainties can be very large, especially since the models tend to be enormously over-parameterized, and also contain combinatorially large exact and near-exact degeneracies. (I think maybe the near-exact degeneracies are worse than the exact ones.) I vaguely recall Tom Charnock making strong statements about all these things at Ringberg.


do we have the baryon acoustic feature?

Today I posted this tweet (below), which I think explains what happened today! I also gave a talk at MPIA Galaxy Coffee, with Adrian Price-Whelan (Flatiron), about the appearance of stellar parameters in the ESA Gaia XP spectral coefficients.


definition of the pseudoscalar, pseudovector, and pseudotensor

I am fully obsessed with geometry these days. In particular, I am obsessed with the point that scalars aren't just numbers, but rather numbers that don't depend on your choice of coordinate system. Similarly, vectors aren't just things with a magnitude and a direction: They are things with a magnitude and a direction which are coordinate free, or which have a stable direction and magnitude no matter what coordinate system you choose. Thus, for example, the unit vectors defining the x, y, and z directions of your coordinate system are not really vectors at all. But the acceleration due to gravity right here is a vector.

But there are pseudo- quantities. For example, the angular momentum isn't exactly a vector; it is a pseudo-vector: It's magnitude and direction doesn't depend on the orientation (or translation) of the coordinate system, but its direction does depend on the handedness of the coordinate system. Thus there are pseudoscalar, pseudovector, and pseudotensors in addition to scalars, vectors, and tensors. Today Soledad Villar (JHU) wrote definitions for these in the paper we are drafting. It isn't trivial, because we want a notation that is agnostic about the group operator and the thing it is operating on.


quasars and stellar density

Kate Storey-Fisher (NYU) has made really nice random catalogs that look very very similar, in sky coordinates, to the quasars we have. However, there is obviously more exclusion of quasars from the Galactic plane region than we can explain with any reasonable model of how dust is affecting things. It's the stellar density of course: ESA Gaia selection is very sensitive to stellar density, especially (as now) when you are using the XP spectra. Today she included the stellar density in the random-catalog regression and boom: Excellent random! Our model is not mechanistic, it is effective and data-driven.


writing in the discussion section

I spent time in an undisclosed location on the weekend writing in the discussion section of my draft with Megan Bedell (Flatiron) on information theory and extreme precision radial-velocity measurement. I think my language is a bit loose when I write on vacation!


non-separable and generative random catalogs

Standard practice in large-scale structure is to make large-scale structure and cross-correlation measurements using a catalog of tracers (quasars in our case now) with random catalogs taking the role of tracking the selection function. In most cases this random catalog is made by sampling from a model for the angular selection function and, separately, for each object, sampling from a model for the radial selection function (redshift distribution in our case now). But of course the redshift distribution depends, in detail, on the angular selection function (because, for example, some of the angular selection is set by dust extinction). Kate Storey-Fisher (NYU) and I discussed now to capture these issues in the random we are building for the ESA Gaia quasar sample we are using. One idea is to give the randoms quasar-like luminosities and building the random catalog using our causal ideas about how things make it into the catalog


reverse-engineering the quasar sample

Kate Storey-Fisher (NYU) (with some consulting by me and others) has been trying to model the selection function (in the form of an accurate random catalog) for the ESA Gaia DR3 quasar sample (or a cleaned-up version of it). We currently believe that the selection function should depend most on the Gaia scan history, the local stellar crowding, and the interstellar dust. We are finding that scan history is a very subtle (maybe ignorable) effect, and that dust is big. But when we apply the dust correction, the random-catalog features don't look quite like the features in the real data. Today KSF showed (anti-) correlations between the observed quasar density and the stellar density on the sky. Will correcting for this fix our issues? I sure hope so.


refactoring geometry code

I spent the day refactoring the code I wrote (months ago) on geometric (scalar, vector, and tensor) convolution filters for convolutions on geometric (scalar, vector, and tensor) images. I refactored so that all kinds of geometric objects can be operated on transparently. The good thing is that we have provable tests that test our code for correctness (yay properties of groups!), but the bad thing is that the operations aren't trivial to implement correctly for arbitrary dimensions. I learned a lot about numpy.einsum().


scope for a paper on convolutional functions

Today Soledad Villar (JHU) and I met to discuss the status of our project generalizing convolutional neural networks to images (or lattices) that contain vectors and tensors, respecting group-action properties. We realized that we have absolutely everything in place and we are only writing (and figure-making) away from having a paper on this. Our big issue is that we don't have an implemented application (we have lots of applications, none implemented). We decided that we would put the idea on the arXiv and then see who wants to implement!


latent-variable model

On the weekend Adrian Price-Whelan and I decided that we have to implement the linear latent-variable model (our name!), which is a generative model for both features and labels, if we are going to do well labeling stars with ESA Gaia XP spectra at low signal-to-noise (faint magnitudes). The reason is: The latent-variable model generates the data, so it deals naturally with the different noise in stars of different brightnesses (or different signal-to-noise). We think this is important! We'll see this coming week.


generative model for XP

Adrian Price-Whelan (Flatiron) and I worked out a form for a possible generative model for the ESA Gaia XP spectra and stellar parameters. The idea of going generative is that it should degrade at low signal-to-noise ratios more sensibly than discriminative models degrade. Discriminative models, as a reminder, find a function of the features that predict the labels. Generative models find a function of latents that predict both the features and the labels; labeling becomes an inverse or inference problem.


distances from proper motions

Long, long ago, people used “reduced proper motion” to separate (for example) white dwarfs from main-sequence stars. Good! Now, in the age of ESA GAia, it is time to do better. Today in Milky Way Group Meeting at MPIA, both Coryn Bailer Jones (MPIA) and Eleonora Zari (MPIA) told us about projects to use the proper motions (and velocity structure models for the Milky Way) to infer distances. Bailer-Jones is trying to do something very general. Zari is doing something very specific: She cares about OB stars, which are primarily a thin-disk population, so she has a very specific kinematic model for their velocity distribution. She gets really nice results (see Appendix B).


so much Gaia; #renameJWST

I spent the day working on ESA Gaia data, parallel to Kate Storey-Fisher (NYU). She was working on the quasar catalog and the correlation with the CMB convergence maps; I was working on estimating stellar luminosities from low-resolution spectral coefficients. We are too much in the thick of it to report how it's going yet. But stellar luminosities are hard to predict from spectra!

Late in the day I sent this letter to NASA:

I served on the US Astronomy and Astrophysics Advisory Committee (AAAC) for several years; I served on the NASA Spitzer Space Telescope Oversight Committee for many years; I served on the NASA Extragalactic Database User Committee for several years; and my research has been funded by NASA for my entire career (since I was a PhD student in the 1990s). I currently do research with HST, Kepler, TESS, 2MASS, WISE, and WMAP data, and now I'm getting ready for JWST and SPHEREx.

I am writing to say that I think it would serve NASA's interests, and the interests of NASA science especially, to rename JWST. There have been plenty of discussions of the name; it is clear that many scientists (and especially those who are part of the LBGT community or who have concerns for the LBGT community) feel disrespected by the name. I also personally think that the evidence is clear that some of the career activities of James Webb did direct harm to patriotic Americans who were gay.

I want to emphasize, however, that I think the important argument about the name goes beyond the question of any individual historical facts: The LBGT communities are of great importance to all of us. These voices must be heard, and the legitimate concerns must be addressed.

Because NASA is a forward-looking agency, and working towards a more equitable, better world, especially for people working in science and engineering in the US, I think it is time that the spacecraft be renamed. I think this could be done easily and without any trouble; many spacecraft have either officially or effectively changed names at or around first light, two examples that come immediately to mind are WMAP and Spitzer.


Gaia quasar redshift distributions

Today I worked with Kate Storey-Fisher on the ESA Gaia quasar sample. We looked at the redshift distribution as a function of magnitude and as a function of color cuts or selection. Right now we are getting an odd angular correlation function for the sample, which we think is because our random catalog (or completeness model) is wrong in important but subtle ways. Interestingly, there are probably terms coming from both the dust map (extinction) and from the Gaia internal completeness (scanning law) and maybe both contribute enough to change the answer? But it sure looks like dust dominates.


Doppler shifts and radial velocities

I am a big believer that there is a difference between a Doppler shift and a radial velocity. For one, they have different units! For another, the former is measurable (sometimes) and the latter is not (or rarely). But today I agreed with Megan Bedell (Flatiron) that we should write our paper on the subject in terms of the words “radial velocity” and not “Doppler shift”. After all, we are talking to a community with a common language! I spent some time on the train from Vienna to Heidelberg editing the figures for our paper on this subject.


is it ever scientifically conservative to use machine learning?

I gave a talk Is machine learning good or bad for science? in Vienna today (slides here). I spent a lot of time on the ontology and epistemology of it all. One thing that led to some debate afterwards is my claim (at the end of the talk) that using extremely flexible machine learning methods can be extremely conservative in some cases: If you are modeling a nuisance that possibly interferes with your signal of interest, and you used a very flexible model, you have a strong argument that you tried as hard as you could (in some sense) to dilute your signal of interest with that nuisance. My talk was followed by interesting discussion with many, and a lovely dinner with Viennese (not just Austrian, but Viennese) wine.


Dr Ratzenböck

It was my pleasure to be a part of the PhD committee for Sebastian Ratzenböck (Vienna), who wrote a dissertation in computer science but as applied to astrophysics. He had three advisors, in statistics, in computer science, and in astronomy, and he beautifully bridged the three worlds. His research was on finding members of stellar clusters, and on finding new stellar clusters. He showed (pretty convincingly, I think) that star-forming regions break up into many individual star-forming events with different ages and different kinematics. One of his conclusions is that all star formation happens in clusters or groups! He also made a nice technical advance, which was to build a tool to select clustering hyper-parameters in the space of physical quantities one cares about, instead of in the space of arbitrarily-defined clustering-method parameters. It was a great thesis, a beautiful defense, and a fun time drinking afterwards. Congratulations Dr Ratzenböck!


is machine learning good or bad for science?

I took the train to Vienna today, for a PhD defense and to give a talk about machine learning. My talk is interdisciplinary so I looked at how to generalize my arguments about astrophysics to all of the natural sciences. It turns out that this isn't as easy as I'd like, since it is hard to be specific outside of astrophysics! I'm going to learn a lot getting this talk ready.


Gaia quasar redshifts

Today Kate Storey-Fisher (NYU) arrived in Heidelberg and we worked on improving the ESA Gaia DR3 quasar redshifts, using NASA WISE and IRAS information. We were trying to reproduce experiments performed by Hans-Walter Rix (MPIA) last week. It looks like we can get clean-ish samples, where more than 90 percent of the redshifts are correct (as compared to ground-based spectroscopic surveys), provided that we stick to bright quasars. The question is: Is this good enough for our cosmological goals? We discussed how to empirically evaluate the selection function, which is our next task.


bouncing ball

I worked on the weekend on making a toy problem for testing physics-related machine-learning methods: A ball bouncing off an elastic surface, under gravity. Both the surface and the gravity vector break the symmetry; this problem is not at all invariant with respect to rotation, translation, or boost. And yet the laws of physics can be written in a coordinate-free form. I am trying to figure out whether we can make this distinction usefully in the literature: The distinction between coordinate-free and equivariant. I think they are different concepts, even though the mathematics of them are identical.


local linear regressions

For some reason, even though I dislike deep learning, I love local linear regressions. My friends tell me that RELU networks are locally linear, so I am really just a hypocrite. Anyway, today Adrian Price-Whelan and I built a regression in which we find nearest neighbors (among the training-set objects) in the space of ESA Gaia DR3 Bp/Rp spectral coefficients and, among those neighbors, we fit a locally linear model to predict the parallax of the test object. Technically we use a clever trick called the ”schmag“ but which should probably be called the reduced parallax, in which we correct the parallax into the inverse of the square root of the luminosity. Why? It's so we can use the parallax errors fairly, and include training-set objects with negative parallaxes.

Hill I will die on: If you cut your sample to high SNR parallaxes or positive parallaxes, you will bias any regressions you do to predict parallaxes or distances or distance moduli!


Gaia Hike, day 5

Today was day 5 of the Gaia Hike. Jason Hunt and I looked at a file of kinematic information prepared by Adrian Price-Whelan (Flatiron) to look at the possibility that the Milky Way has a low-amplitude counter-rotating disk of stars. We found nothing. This was in contrast to what Claudia Bielecki and Federico Sestito were finding—with a similar file created by George Kordopatis. By the time I had to leave the meeting, we hadn't resolved the discrepancy. It's interesting either way!


Gaia Hike, day 4

On day 4 of the Gaia Hike, Neige Frankel (CITA) and I tried to look for the signature of the Snail (the vertical phase spiral in the Milky Way stellar kinematics) in metallicity. It's visible in the Gaia Collaboration chemical cartography paper. But it's not trivial to find it. We got a tiny hint of it using RVS metallicities, and we resolved to try some more tomorrow. We also figured out that it should be there even if the Snail is a late production of a late interaction: Abundance gradients FTW.


Gaia Hike, day 3

Today was the literal hike day of the Gaia Hike. I couldn't go, for uninteresting technical reasons. So instead I spent my time preparing hack projects for those who are looking for straightforward hack ideas and want to learn. I got stuck many times and Adrian Price-Whelan (Flatiron) helped me un-stick. I guess straightforward isn't straightforward! Anyway, I produced this document which contains hack ideas. It is just a start, just a stub, but maybe it will be useful?


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.


radio reboot

[Somehow this blog keeps failing. I will try to get back into it, but no promises! I apologize to my loyal reader.]

Today I met with Abby Shaum (IPAC) who worked with me a few years ago making a phase demodulator to find stellar companions. The idea is that if a star is broadcasting a coherent (or even incoherent) asteroseismic or pulsation mode, and if the star is orbiting a companion, the kinematics of the orbit will be imprinted on phase and frequency modulations of the carrier frequency. Like a radio! Indeed we built a signal-processing method that looks just like a radio demodulator. Today we discussed how to reboot this project and write a paper for the refereed literature.



I gave a seminar at lunch today (black-board talk) about how sailboats work. I got lots of great comments and questions, especially about sailing down wind faster than the wind. I vowed to add a paragraph to my paper on sailing (with Matt Kleban) about how to sail this way. I think it is extremely hard to do, technically. So much so that some of the books on sailing say that it is impossible! It isn't, in principle.


extragalactic stellar stream

Sarah Pearson (NYU) is working on modeling a stellar stream (disrupted satellite galaxy) around an external galaxy. The goal is to figure out what observables are most critical, and what properties of the host galaxy are most strongly constrained by a good model. That is, information theory. Pearson showed beautiful results today to Adrian Price-Whelan (Flatiron) and me: She can show that the mass of the galaxy's dark-matter halo is covariant with velocity gradients along the stream. Those would be hard to measure but not impossible. One high-level objective is to understand what would be the scientific merit of a big program with new imaging data and follow-up spectroscopy.


simulating BpRp spectra

I had an early meeting with Maddie Lucey (UT Austin) and Adrian Price-Whelan (Flatiron) about simulating ESA Gaia BpRp spectra. Lucey has this technology and can simulate stars with any parameters. We discussed making a fake-data set that we can use to test ideas and methods we would like to use after Gaia DR3 in June. We ended with a plan to simulate matched BpRp spectra, one for each APOGEE DR17 spectrum. Lucey is on the case. Let us know if you are interested in doing preparatory science with such a data set!


how do clustering results scale with survey size?

I spoke with Abby Williams (NYU) and Kate Storey-Fisher (NYU) today about Williams's forecasts for measuring cosmological-scale gradients in the large-scale structure. We came up (many moons ago) with approximate scalings with survey volume, the number of tracers, and the amplitude of the clustering. Some of these are obeyed by Williams's results and some aren't! What gives? We think it might have to do with the occupation number of the modes. If the number density of tracers is high, the clustering precision depends on volume, not galaxy number density.


distributions of dimensionless quantities

In finishing up our paper on dimensional analysis for machine learning, Soledad Villar and I have been discussing how to talk about out-of-distribution generalization of machine-learning methods. The space of dimensionless quantities is smaller in many ways, but I couldn't figure out how to argue that it is easier to match the test data to the training data in the dimensionless quantities than in the original, dimensional inputs. Villar pointed out that one way to see it is that many different distributions in the dimensional quantities map to the same distribution in the dimensionless quantities. For example, if you multiply all the masses by five, you haven't changed the distribution in the mass ratios, even though your mass distributions will no longer overlap. That's a good argument, and what we ended up arguing in the paper.


GPRV, day 4

Today was day 4 and the last day of GPRV in Oxford. The day ended with a discussion led by Heather Cegla (Warwick) and Jennifer Burt (JPL) about EPRV and national priorities. Exoplanet science is obviously extremely important to the 2021 Decadal Survey, but in detail, the first seven chapters of that Survey (the chapters to which NASA and NSF must respond) do not actually mention radial velocity! The conversation in the room today was extremely wide-ranging; it covered hardware, software, science goals, and community-building goals. But it also covered months, years, and decade-long time-scales.

The highest level recommendation of the Decadal Survey was that we need to do preparatory work to design and assess feasibility of a large IR–visible–UV telescope that will discover habitable worlds. There is no doubt (I think it's uncontroversial) that this preparatory work will require lots and lots of EPRV science and observations. Of course the fact that this is obvious is separated somewhat from the question of whether there will be abundant funding!

It will come as no surprise to my loyal reader that I was a proponent, in this discussion, of building open-science communities around open data, open-source software, and open science collaborations. I think we have so much evidence now that open-science communities science way better. What I loved is that there were absolutely no objections in the room to this idea. The only controversies were about exactly how open data should be managed and released in that utopian future. I'm optimistic about this business!

And I thank Suzanne Aigrain (Oxford) and her OC for a great meeting!


GPRV, day 3

Day 3 of GPRV continued great! There were a few talks and discussions of very young stars that got everyone in the room quite excited, from Di Maio (INAF), Suárez Mascareño (IAC), and Nielsen (Oxford). The activity signals are huge, but the planets are extremely interesting, so how do we approach this? Tons of of observing time? Cleverness? Give up? Of course I think it is so important to understand how planetary systems form and evolve, I would be willing to spend the telescope time.

In the morning, Luger (Flatiron) gave a seminar and then a tutorial about modeling stellar surfaces and predicting spectroscopic quantities. The tutorial was fun; his code Starry does everything an astronomer could want, and beautifully (and, of course, blazingly fast). We had fun playing with it in a group hacking session.


GPRV, day 2

Today was day two of GPRV. It was a delight! Here's another highly unfair summary of the day:

Hara (Geneva) kicked it off with a discussion of a Bayesian-decision-theory-like method for deciding on the reality and correctness of exoplanet discoveries. He made clever choices to deliver really strong probabilistic results. I was about to object to all this but then he disarmed me at the end of the talk by noting that everything is extremely sensitive to noise models and that is the biggest issue. He gave some chilling examples.

Shahaf (Tel Aviv) showed some very nice results in old-school statistics that generalize the periodogram to a correlation between phase differences and distances between pairs of any quantities you like, as a function of period. This can be used to perform causal inferences for periods seen in naive periodograms. He uses a very interesting phase variable for these phase differences; this is extremely relevant to things I have been discussing with Zhao and Bedell.

Mortier (Cambridge) mesmerized the room with her work with six (yes 6) years of solar data from HARPS-N (maybe). She can show amazing relationships between pipeline RVs, activity indicators, and spectral shape measures. But she showed that often the correlations are not at zero-time-lag. Often the correlations are strongest with delays of 1/9 to 1/8 of a rotation period. When she sub-samples the data to typical kinds of long-term monitoring campaigns we are going to do on distant stars, it is a bit scary. That led to a lot of discussion over lunch and dinner.

Zhao (Flatiron), Bucchave (DTU), and Dumusque (Geneva) led discussions on community-building, hardware, instrument calibration, and other things. The meeting is set up for lots of discussion and is itself an extremely good example of a community-building activity, around the hard challenges of EPRV. I opined in one of these sessions that EPRV now looks like cosmology around 2000, when everything was just about to go open and the world community started working together. This meeting is part of this change that we want to see.

Finally, a theme of the day was representations for spectral signals. Dumusque (inadvertently, I think) made a strong case that we should be working in the 2-d spectrograph images directly! That's music to my heart. He also emphasized that the stellar surface is a complex physical place. I agree! And Cretignier (Geneva) showed a beautiful representation of the spectral residuals to disentangle Doppler and spectral-variability variations. I think his work and Shahaf's could be combined in interesting ways; I am excited to get back to the lab.