detecting shifts with cross-correlations

Lily Zhao (Flatiron) has been looking at the variability of the SDSS-IV BOSS spectrograph calibration frames, in the thought that if we can understand them well enough, we might be able to substantially reduce the observing overheads for the robotic phase of SDSS-V. To start, we are doing simple cross-correlations between calibration images. After all, the dominant calibration changes from exposure to exposure appear to be shifts. But these cross-correlations have weird features in them that I don't understand: In general if you are cross-correlating two images that are very similar, the cross-correlation function should look very symmetric, I think? But Zhao's cross-correlation functions look asymmetric in weird ways. We ended our session puzzled.

other people's code

I spent much of the day understanding Other People's Code (tm). One piece of code is legacy code from Aaron Dotter (Harvard) that computes magnitudes from flux densities. I was looking at it to confirm my frantic writing of yesterday. Another piece of code is the code by Weichi Yao (NYU) that implemented our group-equivariant machine learning. I was looking at it to see if we can modify it to impose units equivariance (dimensional scaling symmetries). I think we can, and I confirmed that it Just Works (tm).

magnitudes are (logarithmic) ratios of signals

A couple of weeks ago I had intense arguments with Belokurov (Cambridge) and Farr (Stony Brook) about the definition of a photometric bandpass and a photometric magnitude. And a few months ago I had long conversations with Breivik (Flatiron) about the bolometric correction. For some reason these things took over my mind today and I couldn't stop myself from starting a short pedagogical note about how magnitudes are related to spectral energy distributions. It's not trivial! Indeed, the integral isn't the integral you naively think it might be, because most photometric systems count photons (they don't integrate energy). People often say that a magnitude is negative-2.5 times the log of a flux. But that's not right! It is negative-2.5 times the log of a ratio of signals measured in two experiments.

building dimensionless monomials

I got stuck today on a problem that seems trivial but is in fact not at all trivial: Given N inputs, how to make all possible dimensionless monomials of those N inputs, at (or less than) degree d. For our purposes (which are the units-equivariant machine-learning projects I have with Soledad Villar, JHU), a dimensionless monomial of degree d is a product of integer powers of the inputs, in which those powers can be positive or negative, such that the dimensions cancel out completely, and for which the the max (or sum or some norm) of the absolute values of the powers is ≤d. We have a complete basis of dimensionless monomials, such that any valid dimensionless monomial can be expressed as a monomial of the basis monomials. Because of this, the dimensionless monomials can be seen as the vertices of a Bravais lattice, technically. The problem is just to traverse the entire lattice within some kind of ball. Why is this hard? Or am I just dull? I feel like there are fill algorithms that should do this correctly.

refereeing can be very valuable

Christina Eilers (MIT) and I discussed our referee report today, on our paper on re-calibrating abundance ratios as measured by APOGEE to remove log-g-dependent systematics. The referee report came quickly! And it was very useful: The referee found an assumption that we are making that we had not explicitly stated in the paper. And this is important: As my loyal reader knows, I believe that a data-analysis paper is correct only insofar as it is consistent with its explicitly stated (and hopefully tested and justified) assumptions. So if a paper is missing an assumption, it is wrong!

what is academic freedom?

In response to feedback from current and former members of the Center for Cosmology and Particle Physics, Mike Blanton (NYU) organized a career panel on careers outside of physics today. It was great! Three of my former collaborators—Andreas Berlind (NSF), Morad Masjedi (Brevan Howard), and Adi Zolotov (BCG)—were on the panel. They said so many interesting things I can't summarize it all here. But here are a few examples:

Zolotov said that one of the ways in which she used her physics training in her current work (which is consulting for government agencies and companies) is that she was (right from the outset) comfortable preparing and giving talks to smart, skeptical (even hostile) audiences. That's interesting! They all had interesting things to say about preparing to move out of physics; what homework should you do? The panelists were asked about writing, because Masjedi said that one of the proximal reasons for going from physics to finance was that he didn't love writing! Interestingly, Masjedi followed up by saying that he has spent his entire career without ever having to do a lot of writing. That surprises me! Berlind generalized this by commenting that the fundamental reason to leave academia is that you can find other jobs that are a better match to your interests and capabilities.

That's an interesting thought, in the context of academic freedom. As you my loyal reader knows, I love and respect academic freedom immensely. But for all my freedom to work on what I want, the modes in which I work (publishing in scientific literatures, writing grant proposals) are very constrained; almost fixed. If you are an academic, you get academic freedom. But in the real world you get the freedom to pursue and find the position and career path that matches your interests. Definitely things to think about.

One take-away though is how damned successful they all are. Zolotov spoke about building a new 20-person group within a consulting company (prior to BCG), and advising people at the highest levels of government. Masjedi spoke of analyzing and buying bonds and bond-like securities for huge clients, including even the Federal Reserve (prior to being at Brevan Howard). Berlind came straight into a Program Director position at NSF, one of the highest ranks in the agency. My loyal reader also knows that, in my view, the most important thing about this job is the people. I'm really proud of them and everything they've done.

optimization is terrible

I had a great conversation this morning with Kiyan Tavangar (Chicago) and Adrian Price-Whelan (Flatiron) about finding a dynamical model for the GD-1 stellar stream and the (purported) compact mass perturber that distorted the stream. They are building a likelihood function and trying to optimize in the kinematic parameters of the perturber. But it's hard! Because every model involves a full forward model for the stream, and how do you compare a particle simulation to a set of observed stars? We've worked on problems like this for years, and we don't have extremely satisfying answers. But the question we talked about today is: Even once you have a good likelihood function implementation: How to initialize the optimization? My position is that optimization needs to be principled, but initialization of that optimization can be arbitrarily nasty. We discussed nasty options. My experiene is that optimization is the hardest part of many of the projects I've done in my life.

maximum-likelihood estimates are often optima of cross-correlations

I've been writing like mad in a paper about measuring radial velocities. The standard practice involves cross correlations. The information-theoretic results suggest maximum-likelihood estimates. What gives? It turns out that, provided that your models are normalized in a certain way, maximizing a cross-correlation between data and a template can be equivalent to minimizing a chi-squared or maximizing a log likelihood. I wrote words about all this in my de-novo re-write of my paper with Bedell (Flatiron) on how you measure a radial velocity.

re-start a paper on EPRV

I promised Megan Bedell (Flatiron) that, in January, I would finish our paper on how you measure a radial velocity. I looked at this today. Once a draft of a paper is a few years (!) old, the only option is to re-start from scratch. There's no salvaging that shih. So I re-started from scratch today. Here's to finishing this, this month.

a phase diagram for sailboats

Matt Kleban (NYU) and I are finishing up a paper on the theoretical basis for sailing (yes sailing). One of our conclusions is that (large) sailboats are described by three dimensionless ratios: The sail-to-keel ratio, the ratio of the sail working force to the air drag force, and the ratio of the keel working force to the water drag force. We imagined today a phase diagram that shows the space of dimensionless ratios that permit, for example, upwind sailing. And sailing downwind faster than the wind. And sailing cross-wind faster than the wind. And so on.

other kinds of sailing

In finishing up the first draft (yay!) of my paper on sailing, I thought about other kinds of sailing (for the discussion). One is solar sails: In principle if a spacecraft has a sufficiently large solar sail, of which it can change the size and shape, the spacecraft can navigate in arbitrary directions and perform arbitrary three-axis attitude adjustments, by working on a combination of radiation pressure and gravity. It's really very flexible. It makes me want to design a spacecraft!

I also thought about ice boats. An ice boat is like a sailboat with an extremely large keel and almost no water drag. That is, it sails like a sailboat in the limit that the keel gets large but the water drag gets small. This should make ice boats extremely fast at upwind sailing. Maybe I'll try to find an opportunity to sail on ice this winter?

emulators

Right now, in cosmology, emulators are all the rage: Cosmological simulations are slow and expensive, and we need to speed them up! But I'm concerned: What if we use emulators in all our Euclid and LSST pipelines, and then we find something very surprising? What then? Do we check it all using full-blown simulations? But then, if so, why not do full-blown from the outset? Or do our standards of care depend on our results? They aren't supposed to, but maybe they do?

Worried about all this, I have been thinking about how to make emulators better, and give them provably better properties. It's why I've been working on building methods that exactly obey symmetries. But from an epistemological perspective, emulators might be the Worst Idea Ever^TM.

In detail, I'm working out how we might build emulators that are trained on one simulation suite but can be tested on another, made with a different cosmology and at a different mass resolution. I think work I've been doing with Villar (JHU) on the exact symmetries imposed by geometry and units might make this possible. I'm trying to figure out the scope of an achievable paper on this.

sailing upwind; lift ratios; sail-to-keel ratio

In writing up a description of some of my physics-of-sailing results, I realized some things about sailboat design. For deep reasons you want the ratio of the area of the sail to the area of the keel to be roughly the ratio of the density of water to the density of air, or 700. That flows from the point that the sail and the keel have symmetric roles in sailing. But if you set this ratio to 700, you can only sail upwind if the sail lift ratio (the ratio of useful sail force to drag force) is very high. Since it is hard to make this lift ratio high on a commercial boat, the alternative is to make the sail smaller (relative to the keel). Looking at the data I can find on real sailboats, most have okay lift ratios but small sail-to-keel ratios (smaller than 700 anyway), so that they can sail quickly upwind. The cost of these design choices is that you can't go downwind faster than the wind. If you want to be able to sail both downwind faster than the wind—and also upwind—you have to have amazing sail and keel lift ratios.

steerable machine learning

Inspired by the hope of mashing up our paper on scalars and vectors in machine learning with work like this on steerable neural networks, I worked with Soledad Villar (JHU) today on writing down all possible linear convolutional kernels in a 3x3x3 block of a 3-d image that satisfy the geometric symmetries of scalar, vector, and second-order tensor forms. I feel like recent work on machine-learning in cosmology like this could be vastly improved by these geometric methods.

modeling arid ecologies?

[This blog died for a few months. I apologize. I am back now, and hope to continue.]

Today I worked with Soledad Villar (JHU) on our project to execute regressions (and other machine-learning methods) that are constrained to be exactly symmetric (or equivariant) with respect to units and dimensions. Our target problem is a regression involving ecologies of arid regions. There are differential-equation models for this, and all the inputs to the equations have interesting units (such as water volume per area, and grams of vegitation, and so on). It was fun to do some real coding again, after days of grading final exams!