The "New" Zodiac and the Earth's Spin

The latest rage in popular astronomy seems to be the realization that the Sun may now move through 13 constellations instead of 12. I haven't personally checked this, so I'm going to take their word for it. What's bothering me is something else that's being repeated in connection--that this is "due to shifts in the earth's rotation and orbit", or more flagrantly, that "since the zodiac periods were established millennia ago, the moon's gravitational pull has made the Earth 'wobble' around its axis in a process called precession".
Someone (I guess, me) needs to make it clear that any shift in the apparent path of the Sun through the background constellations can only be caused by a change in the inclination of the Earth's orbit (possibly as a result of the precession of the Earth's slightly inclined orbit around the Sun), not the precession of the Earth's axis of spin.

The reason the Sun appears to move through background constellations is because we're moving around the Sun (see figure to left). From the perspective of Earth (blue dots), the Sun (orange) appears in front of a different set of stars at different times of year, when the Earth is at different positions in its orbit. The project of the Sun from the perspective of the Earth is shown with dashed lines.

Now the thing is, that dashed line from the Earth through the Sun doesn't depend at all on the Earth's spin. To see this, imagine you remove the Earth from one of those locations and instead place yourself floating in space. You could turn any which way you want--upside-down, rightside-up, twisted alley-oop--the Sun is going to be in the same place relative to the stars behind. Similarly, the Earth's spin (and any precession in that spin axis) can change the orientation of the Earth, but makes no difference in what stars the Sun appears in front of.

What actually can change where the Sun appears relative to background stars is the physical location of the Earth.
This is a change in the Earth's orbit, not spin. One way to change where the Sun appears relative to background constellations is to move the Earth to different places in its elliptical orbit. This will move the Sun through the standard set of zodiacal constellations. In order to move the Sun out of the normal zodiacal progression, you need to move the Earth up or down. The way this can happen is if the plane of the Earth's orbit precesses around another axis, so that the "high" point in the orbit moves slowly around the Sun.

So to clarify, if the Sun appears to move through a new constellation, it is because the Earth's orbit around the Sun has changed, not because the Earth's spin has changed.

Distribution of Actual Births Around Estimated Due Date

Given that we're now in overtime here for our second child, I have become very interested in the question of what our "due date" meant in the first place.

The plotted on the left are data from a study of Canadian births, 1972-1986 (Arbuckle & Sherman 1989). I then started trying to aggregate some data for my own plots.

The first thing I noticed required a little attention was the "fence post" problem relating to recording gestational age. If a study A records births in the 39th week, where exactly is that on the x axis? Well, if we assume that they started counting with 1, then the 39th week is actually 38.5 +/- 0.5 weeks (they are counting fence). But if study B records births from week 39-40, the implication is that they started at 0 (they are counting fence posts), so 39-40 is 39.5 +/- 0.5. That was a little tricky.

Then we have studies that bin over different time intervals. If another study C records births at 37-41 weeks, how do we relate that to A and B? The intelligent way to plot this would be to use the probability density of going into labor, which divides out by the length of time over which the observation was made. So we should be careful to do that.

And then there's just the general problem that a lot of studies list percentages for births in each time bin, but don't list total populations or error bars, so we don't know what the errors in their measurements were. Ugh. So I crossed my fingers and hoped they followed good practices with their significant figures: I assigned an error equal to the last significant digit they list.


I got most of my data from this semi-thorough compilation of census data and going to some of the original sources. The data aren't great, but they are adequate (see plot to left). I fit to the data an increasing exponential tail to the left, plus a normal distribution. The fit isn't great (despite some claims in the literature of it being normally distributed), but it captures enough of the overall distribution.


The width of the normal distribution was 1.5 weeks, centered at 39.5 weeks. This seems consistent with several sources that suggest ~10% of pregnancies would go into the 42nd week if they were allowed to. It also suggests that the "due date" means the mean of the normal portion of the distribution. Yet fully 1/2 of pregnancies will go beyond the expected due date, and 1/6th will go past 41 weeks, according to this coarse fit.

Of course, none of this accounts for biases that we know exist. The growing prevalence of inductions and C-sections move births earlier artificially. Although the statistical significance may questionable owing to systematic biases (self-selection for uncomplicated pregnancies, etc.), it appears that the recorded midwife births go later than the aggregate (presumably hospital-dominated) births at the 2-sigma level. This may potentially indicate that without intervention biases, the distribution of birth dates around the expected due date could be broader and weighted toward later dates.

Listening to the Astro2010 Decadal Survey

Here are some streaming comments as I'm listening to results of the 2010 Decadal Survey. A shortlink to the report is here.

11:10 am EDT: Excellent placement of "what were the first luminous objects, and when did they form" second from the top of "Major questions to address this decade".

11:20 am EDT: Ooh, even better. "Cosmic Dawn" is the first of the 3 over-arching fields. Good fielding for EoR as a top science priority in the next decade!

11:23 am EDT: Now we're starting into descriptions of the panels. I was involved in several of the RMS (Radio, Millimeter, and Submillimeter) submissions, and am looking for HERA (the Hydrogen Epoch of Reionization Array). I'm also rooting for the Allen Telescope Array's Radio Sky Surveys Project. Finally, I'm hoping for some mention in the TEC (Technology development) program of prioritizing the development of shared solutions to digital signal processing hardware and libraries, which was the recommendation of a white paper I drafted with the help of the CASPER community.

11:45 am EDT: Mention of SKA as a priority for Radio Astronomy, unsurprisingly.

11:47 am EDT: Looks like Roger's wrapping up here. Turning to Q&A.

Meanwhile, I'm reading through the report. I see radio instrumentation is listed as a funding priority on ES-4, linking to 7-39. A good sign.

A painful line on 1-18: "U.S. participation in projects such as the Square Kilometer Array is possible only if there is either a significant increase in NSF-AST funding or continuing closure of additional unique and highly productive facilities." Ouch.

But on 2-12, my own sky map (well, with "permissions pending" for now). Now that's something!

12:01 pm EDT: An interesting question. "Why such a priority on habitable planets in the decadal review?" Sounds like the answer is that it's particularly primed to make big breakthroughs. I think I agree with that. I wasn't surprised that it was on there. There's some rumors going around that Kepler has found earth-like planets in earth-like orbits.

12:02 pm EDT: What about the surplus of post-docs relative to faculty positions? Answer: there are a wide range of careers and positions available to astronomers, so it's not unreasonable to have a larger number of post-doc positions where budding astronomers get training. I'm not sure that answer fully appreciates the scale of the problem.

Continuing with reading, on page 3-13, "The HERA program, a project that was highly ranked by the RMS-PPP and included by the committee in its list of compelling cases for a competed mid-scale program at NSF, provides a development pathway for the SKA-low facility. Progress on development of the SKA-mid pathfinder instruments, the Allen Telescope Array in the U.S., the MeerKAT in South Africa and the ASKAP in Australia, and in new instruments and new observing modes on the existing facilities ... will provide crucial insight into the optimal path towards a full SKA-mid." That's good to see mentioned. Sounds like it lays the groundwork for a strong future proposal to get funded. It's not a promise of funding, though. Not that such a promise was expected.

12:11 pm EDT: Second use of "tripwires" for projects. A very colorful phrase.

Interesting plot on 4-15: papers in all astronomy fields are increasing. Instrumentation papers seem to be low in number, but holding their own against other fields (same percentage contribution to total paper number).

On 5-14 for Data Reduction and Analysis Software: "Flexibility, openness, and platform independence, modularity, and public dissemination are essential to this effort. Focused investment in a series of small-scale initiatives for common tool development ... may be the most cost-effective approach, although there are undoubtedly synergies with the pipeline development needed for the large-scale projects." Sounds helpful for some of my projects like AIPY, SPEAD, and CASPER.

12:18 pm EDT: Comments on the SKA? Answer: SKA is the future, but the US can't pay for the construction on the proposed time scale (but slower might be ok). Technology development should be prioritized though. Low-frequency SKA, though, targets EoR, and we're interested in projects targeting that. Yes!

On 5-21 for Technology Development: "The committee received community input in the form of white papers on the funding needs for technology development in areas such as ... high speed, large N correlators. In these areas and others, researchers ... had come together to plan a coherent strategy for the decade. The OIR and RMS panels made a convincing case that the current level of ATI funding needs to be augmented in order to successfully pursue these highly-ranked technology development programs and roadmaps." Looks like my white paper fell on receptive ears.

12:28 pm EDT: Neil Tyson is closing down Q&A. He is one cool dude. I'm glad he was on the panel.

On 7-7 for Science Objectives for the Decade: "Find and explore the epoch of reionization using hydrogen line observations starting with the HERA telescopes that are already under construction." Wham. And in Table 7.1 on 7-32, Priority 2, Projects thought compelling: HERA.

On B-2 for Program Priorization, in Table B.1, I see both ATA and HERA. I'd say ATA didn't necessarily win big in the review, but at least they're there.

And finally, in appendix D-1: "Hydrogen Epoch of Reionization Array ... is a multi- stage project in radio astronomy to understand how hydrogen is ionized after the first stars start to shine. The first phase (HERA I) is under way and will demonstrate the feasibility of the technical approach. The second phase (HERA II) would serve as a pathfinder for an eventual world-wide effort in the following decade to construct a facility with a total collecting area of a square kilometer and the power to make detailed maps of this critical epoch in the history of the universe. Proceeding with HERA II should be subject to HERA I meeting stringent performance requirements in its ability to achieve system calibration and the removal of cosmic foreground emission." We've got our work cut out for us!

Don Backer

Sadly, the world and I lost Don Backer on July 25, 2010. In addition to being an inspiring scientist, instrumentalist, and educator, Don was my graduate and post-doctoral advisor, and my close friend. He and I worked closely together from 2004 until last Sunday, when he died suddenly of an apparent heart attack.



Don was well known for discovering the first millisecond pulsar early in his career. More recently, he and I had been working on the Precision Array for Probing the Epoch of Reionization--and experiment for detecting the first stars and galaxies that formed in the universe. We recently had a made a lot of exciting progress with this experiment, and it is especially tragic to lose him at such a pivotal time.

Don was a very warm yet reserved man. He was always extremely busy, and I envied his ability to juggle a huge number of tasks at once. Yet every time I walked into his office, gave me a big welcoming smile, saying "Hi Aaron! Come on in." In that instant between when he looked up and when recognized me, I would sometimes see a hint of displeasure at being interrupted (a lot of people in the department walked into Don's office to hassle him about any of the many projects that he was involved in), but it was always gone the instant he recognized me, and I took pride in being someone from whom Don welcomed interruptions.

Don was always a model to me of how to be and instrumentalist and a scientist. I've long been interested in both building and using scientific instruments, and Don was a shining example of how to do both. I learned a lot from Don that helped guide me professionally, and I owe him a lot for his advice and generosity. It is sobering to consider that my next steps will have to be without Don's quiet support and encouragement. In many respects, though, Don's generosity has already helped pave the next steps for me. I'm sure I will continue to incur debt to him for years to come.

One of my favorite qualities of Don was his grand sense of adventure. Our foray into the Karoo desert to deploy PAPER in South Africa could not have happened without Don's enthusiasm for traveling, roughing it, and flying by the seat of the pants. I loved going on deployment expeditions with Don. He was always bright-eyed and smiling, summoning such energy at 66 years that I, at 29, struggled to keep up. It was not hard to see the Don of the black-and-white photographs, the same wiry energy and wry grin that stood in front of me.

Don was never very forthcoming with advice--he advised me more by example. I'm pretty sure this was a result of a very ingrained sense of humility. Don never said "you're wrong", or "you should". I think he didn't feel it was his place to pass judgment on people. Despite this humility, or probably because of it, Don was an effective leader. Without badgering people or using heavy-handed methods, Don brought people into consensus and helped move projects forward. Unfortunately, his effectiveness, coupled with his self-described "responsibility gene", meant that he was often called upon to bail out troubled projects, and he had a hard time refusing them. I often wished Don spent more time on PAPER. I think he did, too.

Don and I were a great team. I'm not a good multi-tasker. Don insulated me from a lot of project management, logistics, and distractions, carving out a space for me to work effectively toward our goal. Soon, some of the important products of our partnership will bear fruit, and I'm sad that Don won't be there to see it. But he knew it was in the works before he left, and for that I am thankful.

I'm sad to have lost a good friend and mentor. Things are hard now as we try to pick up the pieces of all the many things Don was managing. I'm sad that he's not here to help. He was always good at bailing us out.

Who Dominates Health Care Costs?

There's nothing like a little bout with MRSA to make one pay a little more attention to the state of health care legislation. Two nights in the ER are definitely making me thankful for health insurance. Knowing that it wasn't going to cost me an arm and a leg to get antibiotics through an IV (in fact, it probably saved me the leg) definitely helped me to seek care early, rather than waiting for the infection to get truly life-threatening. And that probably saved in health care costs in the long run.

I've heard it argued many times by the other side that universal health care will drive up the cost of health care for everyone, because so-called "healthy people" will be paying, through their premiums, for the bills of the "unhealthy". Ignoring that:

1. the above is a tautological statement about what insurance is
2. people routinely go from the "healthy" group to the "unhealthy" group and back again
3. we should maybe feel a moral obligation to care for the unhealthy

Yeah, ignoring that, I wanted to know if the underlying assumption was, in fact, true. Who dominates health care costs? Is it the small number of extremely sick people? Or is it the larger number of moderately sick people?

To answer that question, I went searching for the population distribution of health care costs. I found the following publication: Variations in Lifetime Healthcare Costs across a Population (Forget et al. 2008). To the left are reproduced Figs. 4 and 5.

Given all the hype, I was somewhat underwhelmed to see that these curves depict (with the exception of an excess at the lowest cost bin) a gamma distribution. This isn't surprising, because a gamma distribution is supposed to represent the sum of a bunch of exponentially-distributed random variables.

To find the contribution of people in each cost bin to the total health care cost of the population, we simply need to multiply the population of that bin (drawn from a gamma function) by the mean health care cost of that bin (a linearly increasing function). Setting the mode of the gamma distributon to $90k for females, and tweaking the k and theta parameters (I'll chi-by-eye it at k=4.5, theta=1.0) we get the following distributions of fractional population (black) and fractional total health care cost (red), as a function of lifetime healthcare cost:

So who dominates health care costs? Those just slightly above the mode, which is to say, the large number of people who are just a little sicker than most. And that really could be any of us, folks.

AstroBaki on MediaWiki

I just started up a new wiki called AstroBaki. The main reason I did this was that my MoinMoin AIPY wiki was clunky to use and was getting spammed lots. I switched to the MediaWiki engine, which has better automated control over these kinds of things. As an added bonus, MediaWiki has support for latex math. This got me thinking...

When I started grad school, I had a hard time transitioning from feeling like I was producing and contributing (I was working as a development engineer for SETI) to just absorbing knowledge. To make myself feel better and more invested in learning, I started doing something for which I became moderately famous around the department: latexing lecture notes on-the-fly. For full disclosure, I should mention that I copycatted the idea of latexing on-the-fly from my friend Phil.

The key to success is to use lots of "defs", and to recognize when you need to def a sequence of commands. When the same sequence of symbols started popping up, I would pretend that I had already def'd the command and start using it, and when there was a pause in the derivation, I would remember to scribble down what that command should mean. In my later years, I also started drawing figures in paint for inclusion in latex.

Anyway, I now have about 4 or 5 latex'd class notes that I have put on my website. From what I hear, they are still regularly used in UCB classes, and I occasionally get happy emails from grad students thanking me for the effort. Meanwhile, I've been reading a book about Nicolas Bourbaki, a famous pseudonym for a group of (mostly French) mathematicians who collaboratively re-wrote mathematics from 1935 to the 70s. Nicolas Bourbaki was a wiki, ahead of its time.

"Now wouldn't it be cool," I thought to myself, "if students using these lecture notes could fix them when they are wrong (after all, they were written on-the-fly), and re-organize them to make more sense?" Could these notes become a sort of open-source textbook for astronomy? So AstroBaki was born.

The difficulty, I am finding, is in translating latex (especially latex heavy in defs) into mediawiki. The best tool I've found so far has been pandoc, which didn't do the defs, but did everything else pretty well. I'm loath to do things by hand, so I'll see what can be automated, and I'll keep you posted.

Hands-On Cosmology Education

Yesterday I spent the morning giving a gosh-wow talk about cosmology to a physics class at Athenian High School taught by my housemate Dave Otten. It was a lot of fun, and the students were all very enthusiastic. It was almost entirely driven by their questions, and they loved being pitched curveballs (time is reference-frame dependent, the universe is expanding, spiral arms are standing waves, etc). The hour-and-a-half lecture was over before we knew it.

Afterward, Dave mentioned that it would be really cool if there were a way to talk about galactic-scale astronomy and cosmology that was in keeping with the philosophy of their school, which emphasizes lab-based, hands-on learning. He mentioned that PhET is a free resource he uses for providing interactive simulations that make hands-on labs out of subjects that otherwise would be too slow, small, big, fast, or dangerous to perform live in a classroom. He also lamented that there aren't any galactic- or cosmological-scale simulators there that could help to understand how systems on this scale behave, and that could perhaps illustrate exactly where the problems of dark matter and dark energy are encountered. Has anyone seen something like this?

The Need for SPEAD

I've been absent for a good while now as a result of participating in a (successful) deployment of our PAPER experiment in South Africa. The Karoo desert in SA, where we were stationed, was very reminiscent of Rangely, CO where I grew up, except for the occasional baboon or kudu in the road. Though it came at a price of a lot of work piled up for me when I got back, and an awfully long time away from J, the isolation from all but our experiment helped ferment some ideas I'd been having about migrating the AIPY toolkit I've been developing to use a streaming data format that would avoid unnecessary disk accesses, would allow AIPY to be integrated directly with the correlators developed by our CASPER project, and would help our experiment develop a real-time analysis pipeline for compensating for ionospheric distortion in our data.

After chatting with a lot of guys working on the Karoo Array Telescope in Cape Town, we came up with a concrete protocol build on something already being used for CASPER correlator output. I just got done writing my first grant proposal to the NSF, funding a graduate student to work on this protocol--the Streaming Protocol for Exchanging Astronomical Data (SPEAD, pronounced "speed"). The process of writing a grant myself was a learning process, and helped me understand where a lot of the questions I got asked by my previous advisors were coming from.

A lesson I got to take away from SA was this: the reason we were in SA (as opposed to Australia) for PAPER was because we had been working with the KAT team, sharing correlator development. The reason we were working with the KAT team was because CASPER and KAT started up a collaboration a few years before. And that collaboration was started up because Dan Werthimer went down to visit SA some years ago to help advise them in a review of the design of their telescope electronics. Dan was invited there because he struck up a fast friendship with Alan Langman (the KAT director) at an earlier conference. The moral of this chain of causes and effects being that sometimes large projects go in new directions because of personal friendships, and sometimes those friendships end up making the difference in the success of a project.

Graph-SLAM

After a trying, but ultimately successful month spent extracting the family from Puerto Rico and re-embedding us in Berkeley, I'm just starting to get back on top of things enough to think about posting...

I had lunch yesterday with a good friend of mine, Pierre, who co-founded a company that specializes in sensory and mapping systems such as those that are used to create Google's "Street View". I was impressed to learn about their system for combining data from GPS, LIDAR, car odometers, and IMUs to create a consistent picture of how a vehicle is located and oriented in space as a function of time. They've spent a lot of time calibrating their systems, and use some sophisticated MCMC post-processing methods for deriving the actual trajectory of a vehicle.

Although the antennas in the PAPER array (that's the low-frequency interferometer I'm working on), are much less mobile than a car, there was considerable overlap between the problem Pierre has been working to solve and the calibration problem I am facing the requires positioning antennas and celesital sources as a function of time in the face of ionospheric distortion, variable gains, etc. Pierre pointed me to Graph-SLAM as a formal description of the problem that we are trying to solve, and suggested that Kalman Filtering with RTS Smoothing was a powerful technique for converging to the optimal solution (with covariance information) in linear time.

Ida y Vuelta: a Tail?

It was all over the news and the net yesterday: the missing link has been found! Darwin has finally been proven right!

Hold on a minute. There's no "missing link"--we have example after example of the evolutionary forebearers of Homo sapiens. Evolution was not in question--we already knew Darwin was right. Ida (the name of the fossil found) is not a direct ancestor of humans--the fossil represents a transitional form between lemurs and other apes.

I do not mean to denigrate what is obviously a very important and exceptionally well-preserved fossil that may provide important insights into primate evolution. My objection is to the media frenzy that gives the impression that this is the final resolution to a scientific debate about evolution that a) never existed and b) would not have been resolved by the fossil in question if it did exist.

We have Neanderthals, Homo erectus, Homo habilis, Australopithecus afarensis, and more. Why is Ida, who isn't even our evolutionary forebearer, the "missing link"? I have a theory: it's about the tail. I think that somehow, through all the monkey-human-common-ancestor debate, through the discovery of early hominids, through all of the discussion about increasing cranial capacity and tool usage, everyone has really been wondering "what about the tail? What happened to the tail?" The media was holding out for something it could tout as a human ancestor (or something close enough) with a tail to finally declare the "missing link" found and the evolution debate settled.

You might say that this is all for the best--that the false debate, however belatedly, is finally being put to rest with one last hurrah. But here's a scenario that makes be cringe just to think about it: suppose it turns out that this fossil, which was recovered from a private collection, turns out to be something other than the specimen that the scientist in question thinks it is. Scientists makes mistakes--that's what peer review is for. Then suddenly we've breathed new life into a misconception about evolution that has been hanging around for way too long already.

Golomb Rulers/Squares/Rectangles

Yesterday I came across an interesting example of the isolation of academic fields from one another.

A common design parameter for antenna arrays is to try to obtain uniform coverage of the aperture plane to get as many independent measurements as possible. Interferometers sample the aperture plane at locations that correspond to the difference vectors between antenna elements. For example, in one dimension, if I put four antennas at locations (0,1,4,6), then that array would sample the difference set of those positions: (1,2,3,4,5,6). However, if I put antennas at (0,1,2,3), the difference set would only include (1,2,3) with 1 occuring 3 times and 2 occuring twice. For the purpose of uniformly sampling an aperture, redundant spacings are lost measurements. We're looking for a minimum-redundancy array.
There have been a few papers in radio astronomy on minimum-redundancy arrays for the more useful 2-dimensional case, including Golay (1971), Klemperer (1974), and Cornwell (1988).

Thinking that this might be a mathematical problem of interest, I ran it by a good friend of mine: Phil Matchett Wood--a mathematician at Princeton. He quickly uncovered the equivalent problem as formulated in math literature: Golomb rulers in 1-D and Golomb rectangles in 2-D. Some relevant papers on the subject are Shearer (1995), Meyer & Jaumard (2005), Robinson (1985), and Robinson (1997). These papers are on the exact problem and describe applications to "radar and sonar signal detection", obviously referring to the need for independent aperture samples in radar and sonar interferometers. Somehow, the differing nomenclature between these fields was never quite bridged, and so there has not been and cross-referencing between these two formulations of the same underlying problem. People like to talk about the possibility that relevant research in one field goes unnoticed by other fields. This is the first time I've across it myself, though.

Compressed Sensing and Wiener Filtering

Today I'm trying to expand my understanding of how we can best remove contaminant signals from the data we take with the Precision Array for Probing the Epoch of Reionization (PAPER). There is a specific problem I want to make sure we can solve for PAPER. Foregrounds to our signal, particularly synchrotron radiation, are expected to be very smooth with frequency. The idea put forth by the MWA and LOFAR groups is that by observing the same spatial harmonics at multiple frequencies, we should be able to remove such smooth components to suppress them relative to the cosmic reionization signal we are looking for. However, generating overlapping coverage of spatial harmonics as a function of frequency is expensive. My intuition is that since foregrounds do not have a spatial structure that changes dramatically with frequency, we shouldn't need to sample a given spatial harmonic very finely in frequency to get the suppression we want. This would allow us to spread our antennas out a little more and get measurements of the sky at a variety of spatial modes.

In many ways, our problem is analogous to what was done with the Cosmic Microwave Background (CMB). For foreground removal in CMB work, Tegmark and Efstathiou (1996) begin with an assumption that foregrounds can be described as the product of a spatial term and a spectral frequency term. This allows them to construct Wiener filters that use the internal degrees of freedom of their data, together with a model of their foreground and a weighting factor based on the noisiness of their data, to construct a filter for removing that foreground. For the most part, this is standard Wiener filtering, except they have to be careful about what they do to their power spectrum, so they apply a normalization factor to correct for a deficiency in Wiener filters. Tegmark (1998) goes on to generalize this technique for foregrounds that vary slowly with frequency. I'm in the process of wading through these papers, but they seem to be directly applicable to what we are doing, and seem to confirm my suspicions that synchrotron emission should be well-enough behaved to require only sparse frequency coverage of a wavemode in order to be suppressed.

Another tactic that I am investigating is that of compressed sensing which I was alerted to in talks by Scaife and Schwardt at the SKA Imaging Workshop in Socorro this last April. The landmark paper on this principle seems to be Donoho (2006), where it is shown that the compressibility of a signal (being sparse for some choice of coordinates) is a sufficient regularization criterion to faithfully reconstruct signals using a small number of samples. In a way, this technique has an element of Occam's Razor in it--it tries to find a solution, in some optimal basis, that needs the fewest non-zero numbers to agree with the measured data. At least, that's my take on it without having finished the paper.

The relevance of compressed sensing to image deconvolution is explored in Wiaux et al (2009), and it seems to be powerful. I'm excited by this deconvolution approach because it meshes well with the intuitive approach I've been taking to deconvolution, which was to use wavelets and a Markov Chain Monte Carlo optimizer to find the model with the fewest number of components that reproduces our data to within the noise. Compressed sensing seems to be exactly this idea, but is agnostic about the basis chosen, instead of mandating one like wavelets. Anyway, this technique may also be relevant to our foreground removal problem because we might be able to use it to construct the minimal foreground model implied by our data. For synchrotron emission, which should have smoothly varying spatial structure with frequency, I envision that this could construct a maximally smooth model that would allow us to use sparse frequency coverage to remove the foreground emission to the extent that it is possible to do so.

Is Tenure a Problem in Science Departments?

Somewhat belatedly, I wanted to comment on the New York Times Op-Ed by Mark Taylor that addresses some of the flaws of the current academic system and proposes some solutions. The central problems that Taylor highlights in his article are that academic departments are too isolated from one another and from the world, and that there aren't enough academic positions for all of the people who are getting doctoral degrees these days. Taylor makes some very good points, but his article is strongly influenced by his experiences in a humanities department, and I am not sure how relevant his suggestions are for a science department.

Astronomy suffers from many of the same problems Taylor describes. There are far more graduate students and post-doctoral researchers than there are tenured professorial positions, and yet students are trained as if they were all to be professors. However, science students are often not paying their own tuition (it is paid by the grant of a supporting professor) and there are more options for science students outside of tenure-track positions because of the many sources of external funding that support scientific research. Unlike the humanities, there are a variety of scientific programming and research positions for graduates who are not seeking professorial positions. These positions are aligned with the education students receive through their doctoral research.

This isn't to say that there is not a major problem in scientific disciplines concerning the ratio of student positions to professional positions. Rather, it is that the problem may not be as closely tied to tenure and the longevity of tenured professors as in the humanities. The problem may be that professional positions available to graduating students are being occupied by the students themselves. Scientific research in the United States relies on a large pool of skilled labor. Currently, this labor is being bought at well under market price in the form of cheap graduate student researchers. If more of these positions were filled by full-time research professionals, we might have a healthier employment system for scientific academia.

The problem is that this raises the price of research in the United States and may result in a reduction in the total number of projects (and therefore, researchers) that can be supported. From the perspective of researchers, this may be a healthier state of affairs--to not be misled into spending 5-7 years underpaid as a graduate student only to find that the only way to continue to do what you've been trained to do is to continue to be underpaid. But unlike in the humanities, science graduate students usually have not accumulated debt beyond their undergraduate education and they have been supported (however cheaply) through this process. The solution, then, may simply be to ensure that prospective graduate students in science are well-informed about what employment prospects they should expect after they file their dissertation.

Interferometry File Formats

When astronomers talk about software done right, they often hold up FITS as the gold standard. I'll admit, FITS has done more to live up to its namesake (Flexible Image Transport System) than many believed possible. But unfortunately, there can be too much of a good thing. Sometimes too much emphasis is put on defining an end-all-be-all file format, when all we really need are good tools for converting between file formats.

Data formats are a problem in radio astronomy software. Currently, there are at least three major formats (MIRIAD, UVFITS, and MeasurementSets), each linked to a major software package (MIRIAD, AIPS, and CASA), with rudimentary/non-existant tools for converting between them. Many have taken this current state of affairs as a sign that multiple file formats are bad and that the community should decide on a single format. Since each format is intimately tied to major software package, this battle over file formats has escalated to a war between software packages.

The mistake made here was blaming the file formats. File formats are not the problem. The problem is that the software for reading them has not been circulated in easily accessible modules. I am encountering this problem as I'm trying to get AIPY to be agnostic about file formats by wrapping them all into Python. Here's where I am:

The MIRIAD file format was actually easily wrapped up, owing to MIRIAD having a developed programmer's API.

MeasurementSets (with CASA) are giving me a lot more trouble. It seems that CASA, with all of it's C++ objects that are passed between functions, is something of an "all or nothing" deal. If I want to read a MeasurementSet, I apparently need to wrap up the entirety of CASA. The failing here is code modularity.

UVFITS is giving me the opposite problem.
UVFITS was cooked up as a FITS-conforming file format to handle raw interferometric data. Unfortunately, interferometric data isn't in picture form yet, so an extension of the FITS format (the binary table) was cooked up to accommodate that (Cotton et al. 1995). The result was a file format that is so general that it does not tell the programmer what the data actually means.

File formats exist to support the needs of different applications. They've been created out of need, and should not be dismissed as unnecessary. I recommend to the radio astronomy software community that we embrace these file formats and work on modular code so that they are accessible from any software package.

PAPER: 8 Station Results

Yesterday I submitted our paper on the 4- and 8-antenna deployments of PAPER to the Astronomical Journal & astro-ph. Although it does not place any meaningful constraints on cosmic reionization (when light from the first stars broke up the bulk of the hydrogen gas that had been sitting around since it originally formed), it nonetheless illustrates a first level of calibration and analysis towards that goal. This paper should have some impact in the community, as it shows that we are fairly well along in our experiment and it provides a first look at some of the astrophysical foregrounds that will interfere with detecting reionization. This paper also will double as the last chapter of my dissertation, so publishing it puts me in the endgame of my doctoral studies... This fall I'm going to take an NSF postdoc back at Berkeley. Basically, that just means I'll be doing the same research (along with some teaching), but with better pay.

More on MCMC in Python

Markov-Chain Monte Carlo (MCMC) seems to be a promising technique for the calibration/imaging problem that we are facing with our experiment the Precision Array for Probing the Epoch of Reionization (PAPER). Yesterday, in addition to taking a crash-course in MCMC, I also started playing with PyMC, which implements, among other things, MCMC using Metropolis-Hastings chains. A first shot at a simple fitter using PyMC went something like this:

import pymc, numpy as n, pylab as p
from pymc import deterministic

x = n.arange(-10., 10, .01)

def actual_func(a, b, c): return a*x**2 + b*x + c

sig = .1
tau = 1/sig**2
noise = n.random.normal(0, scale=sig, size=x.size)
mdata = actual_func(1., 2., 3.)
mdata += noise

a_fit = pymc.Uniform('a', 0., 2.)
b_fit = pymc.Uniform('b', 1., 3.)
c_fit = pymc.Uniform('c', 2., 4.)
tau_fit = pymc.Uniform('tau', tau/3, 3*tau)

@deterministic
def func(a=a_fit, b=b_fit, c=c_fit): return actual_func(a, b, c)

mdata_var = pymc.Normal('mdata', mu=func, tau=tau_fit,
    value=mdata, observed=True)

mdl = pymc.Model([a_fit, b_fit, c_fit, d_fit, mdata_var, tau_fit])
mc = pymc.MCMC(mdl)
mc.sample(iter=1000,burn=250)  

a_hist, a_edges = n.histogram(a_fit.trace(), 40, (0,2))
a_bins = (a_edges[:-1] + a_edges[1:])/2
p.plot(a_bins, a_hist)

p.show()

I chose this example over the ones that came with PyMC because it was much closer to the kind of calibration problems we will be trying to solve with PAPER. An interesting point that came up early on was the reliance of MCMC on an estimate of noise levels in the data. I remember this from the Maximum Entropy Method (MEM) for deconvolution that I coded up in AIPY. An interesting technique, used here, is to actually include the noise level (tau_fit) as a variable that is fit for. This way you can specify a starting guess for noise, along with a confidence interval, and not have to pull a magic number out of a hat. In this example, the fitter does a good job of accurately determining noise levels. I think what happens in this code is that the current guess for the noise level is used as part of the calculation that determines the next state to jump to in the Markov chain, and that new state make include a revision of the noise level. This clearly might be instable for more complex systems, so I imagine some amount of care must be exercised in leaving noise as a free parameter.

Image Deconvolution with Markov-Chain Monte Carlo

I've decided to morph this blog to be more about short updates pertaining to current ideas I'm thinking about, rather than the long-winded philosophical rants I've posted so far. Hopefully this might keep me more engaged as a blogger and maybe even help me keep better track of the things I'm working on. Starting up this blog again, by the way, is a shameless procrastination technique, since my dissertation is due in about 1 month, and all my writing energy should really be focused on that...

After attending an SKA Imaging Workshop in Socorro, NM a couple of weeks ago, I've developed an interest in Bayesian statistics and Markov-Chain Monte Carlo (MCMC) techniques as they pertain to interferometric imaging. Having never taken a stats course, I'm scrambling a little to absorb the vocabulary I need to understand papers written on the subject. Fortunately, in this era of wikipedia, getting up to speed isn't that hard. After reading wiki articles on MCMC, Markov Chains, and the Metropolis-Hastings algorithm, I dived into EVLA Memo 102, which talks about a first shot at using MCMC for image deconvolution.

The Maximum Entropy Method (MEM) is a classic deconvolution technique (one I've already reimplemented for AIPY), but I'd like to go a bit further down this road. According to the standard implementation (which I gleaned from reading Cornwell & Evans (1984) and Sault (1990)) this algorithm uses a steepest descent minimization technique based on the assumption of a nearly diagonal pixel covariance matrix (i.e. the convolution kernel is approximately a single pixel). While this is an effective computation-saving assumption, I found that for the data I was working with, this assumption lead to the fit diverging when I started imaging at finer resolutions.

I think MCMC, by not taking the steepest decent, might be able to employ the diagonality assumption more robustly. I also think it's high time that deconvolution algorithms make better use of priors. The spatial uniformity prior in MEM makes it powerful for deconvolving extended emission, while the brightest-pixel selection technique in CLEAN makes it effective for deconvolving point sources. There's no reason we can't build a prior explicitly for a deconvolution algorithm that tells it to prefer single strong point sources over many weaker point sources, but also tells it that when all else is equal, entropy should be maximized.

Playing, and Why The Fast Track Wasn't the Best Track

A NY Times article on playing today got me thinking about the indirect path I took to being an astronomer. I went to school at Harvard with a lot of very bright people (and even managed to marry one of them). The undergraduate academic experience at Harvard was a little hard on me, though it took me several years after I graduated to fully understand why. The first reason is pretty common to undergraduates at Harvard--intelligent and accomplished people who are used to being the best at what they do are suddenly brought into contact with quite a few people who are better than they are. For driven students, this blow to the ego can undercut some of the self-assurance necessary to work productively.

What was harder on me than turning in my "big fish" status as I moved to a larger pond was the cultural mismatch that existed between myself and the faculty with whom I came into contact. Harvard physics (or at least physics instruction) has a strongly theoretical bent to it, and while some modicum of application is maintained through the 2 lab courses we were required to take, I was always given the impression that applied fields were a cop-out for theoreticians who couldn't make the cut. The culture of disdain for experimentalists kept me on a theoretical track throughout college, long past the point at which I was "having fun". I can tell when I'm having fun, because I play. Playing, as defined in the article above, is "apparently purposeless activity." For me, that means trying to answer questions that aren't on the homework, just out of curiosity. It means starting projects, building things, and enjoying it. The farther I went down the theory track, I less I played with what I was learning. The undergraduate curriculum left little time for doing anything that wasn't strictly required, which was one problem, but the larger problem was that the path I was taking wasn't supporting the kind of playing I like to do.

I got lucky when I enrolled in an introductory electronics class with Paul Horowitz. I found myself, outside of class, trying to teach the computer I'd built to shoot a dart at a mechanical dinosaur. I modified a remote sensing, squawking penguin to spit water at passers-by. I didn't realize it at the time, but I was playing. After I graduated, somewhat at a loss for what to do, and burnt out with physics, I asked Paul if he knew anyone I could work for. He introduced me to Dan Werthimer at Berkeley, where I started designing and building electronics for SETI. Out of school, I suddenly had a lot more time for diversions, and I began learning Python and using it to write evolving programs that mutated their own source code. I tried writing speech recognition (I'll post someday about language acquisition, one of my favorite diversions). I made a guitar website to learn cgi programming. Most telling, I (mostly) gave up video games for computer programming, which indicates the degree to which this really was playing for me.

Eventually I stumbled into radio astronomy, where the physics that I learned (and really did love), met with the electronics and programming that I loved playing with. An incredible number of skills that I currently use were developed during my diversions, including Python programming, soldering, web programming, and signal processing. I never took classes in any of these things, I just learned them from my projects. What I didn't understand as an undergraduate was that working can really be "playing" if you find the right job, and that if you don't play with what you're doing, you might be barking up the wrong tree. Moreover, I was able to learn and accomplish much more when I was in a laboratory environment, playing with what I was learning, than in a classroom listening to lectures. Of course, you can't learn everything from playing--you need people to take you beyond what you have immediately at hand--but for me at least, I would rather this be the exception to the rule. Playing shouldn't just be for kids.

Hidden Variables

I've been having a few conversations about hidden variables lately, so I thought I would post about it. First a little background:

Quantum mechanics (QM), as we know it, is weird. It is a classic example of science as a selection process, as I talked about in the previous post. It set about to solve the problem of predicting the locations, energies, and other microscopic attributes of fundamental particles. When the dust settled, we had one of the most accurate theories ever made (it predicts the mass of the electron to 14 decimal places), but the model used to make these predictions countermanded a lot of things we'd thought were true but never actually got around to testing--intuitive things like "a particle can only be one place at a time", well-established things like "no particle may carry information faster than the speed of light" (which is true, but can be violated over short distances), and most importantly for this post "if you had enough information, you could determine the outcome of any experiment." Nature's rejection of this last idea comes dangerously close to undermining the pillar of scientific philosophy that the universe is predictable insofar as it can be modeled and tested, and it offended a lot of scientists (including Einstein).

What QM says is that there are certain pieces of information that are not simultaneously knowable. If you know a particle's position perfectly accurately, then it is impossible to know its momentum. If you know a particle's orientation along one axis, you can't know it along any other axis. For a long time, many people (including Einstein) thought that this was a shortcoming of QM--that these particles have "actual, hidden values" that QM just didn't know how to predict, and eventually there would be a better theory that could tell us what these values are. Those hopes were shattered in 1964 when John S. Bell proved that there can exist no hidden variables in a way that is compatible with QM. His predictions have been validated by experiment, showing that the reason we don't know the state of a particle is because the universe hasn't made up its mind (excuse the anthropomorphification) until you measure the particle. Crazy.

I like to think of QM like a black curtain at a magic show that allows the universe (the magician) to perform all sorts of sleight-of-hand shielded from the eyes of the audience. On our side of the curtain, there are rules you have to follow--conservation of energy, speed of light, definity of location and state, etc. On the other side of the curtain, anything can happen, so long as when you pull it back out (when we make a measurement), the rules have been obeyed. The "curtain" idea isn't so far-fetched; it's an analogy to Feynman's well-tested theory that the outcome of an interaction is the sum over all possible interaction pathways. The universe takes advantage of this curtain to do things that we think should be impossible, like transmitting information about a measurement instantaneously between two particles that share a quantum state. Furthermore, the universe relies on the fact that we can never see behind the curtain (this is an interpretation of Bell's theorem) because if we could, we could use that machinery to transmit our own information faster than the speed of light, and that violates causality. Causality, by the way, is another principle that we cling to because it seems self-evident, but may in fact be wrong. It will take a unification of the theories of QM and general relativity to sort that out.

Shifting gears into philosophy, I was talking with my uncle, who came to visit last week, about how people look for meaning in their lives. His argument was that back in human history, when the universe seemed a jumble of arbitrary events, a physical, all-powerful deity with direct control over all that happened was a powerful metaphor for finding meaning in the events of ones life. However, as scientific knowledge has gradually encroached on the idea that a god can take direct physical action in the universe, religion has had to respond to the sense that science is pushing away meaning in life. My uncle's thoughts were that a physical deity is becoming an outdated way of looking for meaning in life, and that we need to think about a more spiritual, humanistic God. I agree with this philosophy, but I wonder if the rejection of the hidden variable hypothesis (the magician's curtain) provides a home for religions that require a physical deity.

Philosophy of Science (a Rant)

I read an article today that got my back up a little. Let me give a little background to explain why.

I grew up in the rural, conservatively religious town of Rangely, CO. The first real experience I remember having that set me apart from the majority of the town came in 7th grade science class when we where discussing (you guessed it) evolution. Presented with another in the series of assertions that seems to constitute science education, I blithely bought in. My peers, who had been privately informed that evolution was not to be "believed in", discovered by waywardness, they dubbed me Monkey Boy. Yes, I know. Hilarious.

This was certainly not the last time that I butted heads with conservatives in my town, and it stands at the base of a growing sense of disconcert that I have felt towards organized religion. In the meantime, I went on to study physics in college, and am now a graduate student in astronomy (I do experimental cosmology). It has been surprising to me, now that I have started being introduced as an astronomer, to suddenly to have became an "Interpreter of the Voice of Science" (preacher) for people who want to know how our universe came to be.

The reason the above article got my back up was that I've always been careful, in these situations where I find myself describing the history (as we know it) of the universe, to stress the differences between science and religion. It's confusing terrain because cosmology has only recently come into the realm of science. My "what is science" speech usually ends up something like the following: science isn't a body of knowledge (despite what constitutes science education), or a belief system, or a religion. It is a methodology. Its groundings are philosophical, but that doesn't make its results philosophical. Science started from the philosophy that the universe is predictable: that one can predict the outcome of an experiment if one knows the initial conditions to sufficient accuracy.

Out of this philosophy (which the microscopic, quantum universe has helped us to understand is not strictly correct), a method was devised for arriving at an understanding of the predictability of the universe. Hypothesize, Predict, Experiment, Analyze, Conclude. Elementary school science fair stuff (except that "conclude" now means "peer review"), but still confusing. Science is a level playing field where anyone can make up any theory they want, in the face of all current knowledge if they want, using any strange force or being or Flying Spaghetti Monster, and science has nothing to say about it until you make predictions, devise an experiment to test them, and peer review to make sure it's reproducible. Science works like infants learning shapes--pick a block, try to jam it through the hole, and repeat until you succeed.

The framework that seems to work best for predicting the outcomes of experiments involves math. I'll save a discussion of why this might be for another blog, but it's important to realize that it didn't have to be this way. The universe could have chosen to play by different rules, or perhaps there are even models that can predict the outcomes of all the various experiments we've tried without using math. Math is just a model we have that works. Once you have two models that have equivalent predictive power, science has nothing to say again. Yes, I know about "Occam's Razor", but that's philosophy again, despite its popular portrayal as a pillar of science.

I get frustrated when people (even scientists and cosmologists) misunderstand science to be a body of knowledge, or a set of "transcendental laws", because (it seems to me) it's putting the cart before the horse. Whatever laws and rules we have are only as good as the degree of testing they have undergone, and are subject to revision and replacement as new experiments reveal their flaws. And we know they're flawed. The two most accurate physical models we have--gravity and quantum mechanics--are mutually inconsistent, and neither of them are able to account for an accelerating expansion of the universe (the "Dark Energy" problem) or for motions on galactic scales (the "Dark Matter" problem). So how can a self-respecting scientist hold up a "transcendental law" and claim it is more than our current best model?

My personal opinion is that referring to science as a body of knowledge makes it akin to religion--something transcendental and immutable (and inaccurate) handed down from above. What makes science science are the error bars: little reminders that our models are only as good as the extent to which they have been tested.