A captcha problem

Hmm. Think it would cope with \( M_2(\mathbb{Z})\tilde m \)? Or $M_2(\mathbb{Z})\tilde m$? Or just plain M_2(\mathbb{Z})\tilde m? In principle it might, since recaptcha is crowd-sourced; if I came up with the same LaTeX representation all previous recaptcha users had, all would be fine...

Male contraception

The Pill — hormonal contraception for women — is sometimes credited with making possible the sexual revolution. There is as yet no hormonal contraception for men. My feeling is that this is for real biological reasons — the female reproductive system is more complicated and easier to interfere with. And of course in the era of HIV/AIDS and other STIs, condoms have a unique role. Other methods of contraception remain important. There's a new supposedly-reversible one for men and there's always vasectomy. But there's another method for men that I'd never heard of, but find amusing: testicular heating.
[update — pictures! sort of]

Source Code

No, I mean the movie. It's science fiction, of the Twilight Zone flavour: soft, set here and now, and with a little pointed topical relevance. Jake Gyllenhaal plays a soldier who gets sent into the "Source Code", eight minutes before a terrorist attack, and told that he must do whatever he can to figure out who the bomber is. He can retry it as many times as he likes. It's very like the brilliant interactive fiction Varicella (described below the jump).

The Core

I've worked with data from X-ray satellites before, and among the many messy things one has to deal with in real data were blocks of time marked SAA. I knew this stood for "South Atlantic Anomaly", but I had only the vague idea that it was a part of the sky that was geomagnetically inconvenient, so that I had to trim it out of my data. The other day I came across a fascinating BBC documentary, titled "The Core":

This documentary talks about the Earth's core and how we're studying it, from seismology to diamond anvils to huge liquid-sodium dynamo experiments. It makes very interesting watching, but I particularly liked that they used the South Atlantic Anomaly as a hook: it caused problems with certain instruments on Hubble, and the documentary is framed as an investigation into why. (More below the jump if you're not worried about spoilers.)

Mathjax

When looking at the ipython notebook interface, I came across a neat tool: mathjax. It's designed to allow embedding math in web documents. Now, MathML was supposed to do this, but support for MathML is still very spotty, and it's also really nasty trying to write MathML manually. So mathjax allows you to simply enter TeX format math and have it look okay in supposedly all browsers: both inline as \(e^{i\pi}=-1\) and displayed as $$\int_{-\infty}^{\infty}f(t)e^{2\pi i f t}dt. $$

The way that it does this is kind of amazing to me: it's essentially a TeX renderer written in javascript and running in your browser. I'm used to thinking of TeX as a batch-mode compiler that takes an appreciable time to run, but TeX has become the de facto standard way to write mathematics, and there are now several reimplementations of its renderer. Matplotlib has one, for example, though it can also call out to real TeX if you ask it to. But javascript!

Anyway, as you can see above, I've added it to the template for this blog, so I'll be a little freer with math from now on. Though I'm willing to bet it doesn't work in the RSS feed. Let me know if you have any problems with it.

Review: ipython notebooks

The development version of ipython recently added a "notebook" interface mode. This resembles the interface of MAPLE or Mathematica, in which you can intermingle blocks of formatted text, blocks of code and output, and plots. My feeling, after working with it for a bit, is that it is very well suited to the kind of work I do when (for example) writing blog posts demonstrating some algorithm. For developing actual reusable software, not so much.

In order to give it a proper test, I applied it to a problem that a friend asked me about. It's about the card game Set: how often do you run into a tableau with no sets? The game quotes a figure of one time in 25, but that's for tableaux dealt from scratch. As you play the game, you remove and replace sets, and it often seems as if no-set tableaux arise more often when the cards are not freshly-dealt. The game's rules are a lovely minimalist mathematical exercise, but once you start removing and replacing cards an analytical solution becomes impractical. Simulation to the rescue! And this seemed like a nice test problem for ipython.

You can see the results here (PDF). For my comments on ipython, read on.

Edited to add: notebooks have improved a lot since this review, or the later one.

Least squares and timing noise, part 2

Simulated time series

In my previous post I described a new paper about fitting pulsar parameters in the presence of timing noise using a general least-squares method. It seems like a good approach, but I'd like to look at it in more detail. So: python to the rescue!

The Mechanical Microbiologist

Laboratory automation has been growing more and more elaborate - multiwell tools for "parallel processing", and benchtop robot arms, for example, that will handle repetitive tasks. But flow cytometry offers some startling possibilities.

Least-squares and timing noise

Figure 4 from the paper: residuals and spectrum

Working with long-term pulsar timing data sets is a nuisance because of so-called "timing noise". Not only is this noise above and beyond the usual observational uncertainties, perhaps because it is torque noise, it tends to be strongest at low frequencies (it is very "red"). Often so much so that leakage from the very lowest frequencies dominates at all analysis frequencies. Various people, myself included, have tried various approaches for dealing with this noise, but a recent arxiv paper shows real promise:

Pulsar timing analysis in the presence of correlated noise

W. Coles, G. Hobbs, D. J. Champion, R. N. Manchester, J. P. W. Verbiest

Pulsar timing observations are usually analysed with least-square-fitting procedures under the assumption that the timing residuals are uncorrelated (statistically "white"). Pulsar observers are well aware that this assumption often breaks down and causes severe errors in estimating the parameters of the timing model and their uncertainties. Ad hoc methods for minimizing these errors have been developed, but we show that they are far from optimal. Compensation for temporal correlation can be done optimally if the covariance matrix of the residuals is known using a linear transformation that whitens both the residuals and the timing model. We adopt a transformation based on the Cholesky decomposition of the covariance matrix, but the transformation is not unique. We show how to estimate the covariance matrix with sufficient accuracy to optimize the pulsar timing analysis. We also show how to apply this procedure to estimate the spectrum of any time series with a steep red power-law spectrum, including those with irregular sampling and variable error bars, which are otherwise very difficult to analyse.

I'd like to look at it in more detail and try some of the techniques on test data.

Radio vortices

Quantum mechanics, no one will be surprised to hear, is weird. In particular, photons can carry angular momentum - circularly polarized light can set objects spinning. But it turns out that light can carry orbital angular momentum as well. It's really not very clear to me quite what this means in terms of photons. In terms of classical waves, it's weird but I think I get it: if you look at the spatial distribution of the light in a beam, you may find that the phase is constant across the whole beam. But you might also find that the phase varies. Now, it has to be continuous, but you can imagine that as you make a circle around the beam center, you find the phase increases by an integer multiple of two pi. This gives you a continuous phase in a way that is topologically different from the constant-phase situation. As I understand it, this is what is called wrapping number.

Now this would just be another weirdness from the world of (classical!) waves except that there seem to be applications for it. In particular there's a paper on the arxiv about using this for communications purposes.

Science fiction has no imagination, part 1

Every so often I come across something that makes me think that the supposedly imaginative field of science fiction can't hold a candle to reality for weirdness. Today's installment is an arxiv paper in which the authors are seriously discussing quantum teleportation as a way to combine signals from telescopes to form an interferometer:

Longer-Baseline Telescopes Using Quantum Repeaters

Daniel Gottesman, Thomas Jennewein, Sarah Croke

We present an approach to building interferometric telescopes using ideas of quantum information. Current optical interferometers have limited baseline lengths, and thus limited resolution, because of noise and loss of signal due to the transmission of photons between the telescopes. The technology of quantum repeaters has the potential to eliminate this limit, allowing in principle interferometers with arbitrarily long baselines.

A little SF vignette

Canada has these laws that require a certain fraction of the music that is broadcast to be Canadian. This caused a certain amount of screaming from radio stations, but I have this feeling that it actually works, that Canada as a result produces disproportionally more music, and more original music. I don't know about that (how would you quantify it?), but this band — You Say Party — is Canadian.

arXiv gleanings

I try to keep an eye on arxiv.org because interesting new pulsar papers generally appear there first. But there are often abstracts that catch my eye, whether because they have neat ideas, because they talk about neat object, or because they just seem peculiar. This week's batch had a few of each.

How tempo2 does its fitting

Pulsars can be difficult objects to study: for example, their radio pulses can randomly change in brightness, turn off, turn on, change shape, and we really don't know why. Nevertheless there has been some excellent science done by studying those very radio pulses. The trick has mostly been to simply not care how bright they are or what shape they have and focus on when they arrive. Since this comes from the rotation of the pulsar, this tends to be very regular. After all, for a ball 10 km across, with more mass than the sun, smoothed to within a millimeter by its own gravity, it takes an awful lot to change how fast it's spinning. What's more, time is the quantity we can make the best measurements of - world time standards drift by something like microseconds over decades, which is something like one part in ten to the fourteen. So pulsar timing is a powerful technique, that can measure pulsar positions and distances, spin-down rates and braking indices, and binary orbits. The standard software has been tempo, which is written in FORTRAN and has certain limitations. A new tool has recently appeared, tempo2, written in C++ and boasting good handling of timing effects down to the nanosecond level. Unfortunately the documentation on this tool is so far somewhat limited, so I've been figuring out how it works. I'd like to describe it, as best I understand it, here. This particular post will talk about how a timing solution is fit to a set of pulse arrival times.

Millisecond pulsar X-rays

Neutron stars are so tiny and so dense that the natural temperature scale for them has them glowing in the X-rays. What's more, they serve as powerful accelerators of electrons, which then naturally produce X-rays. So it turns out that X-ray telescopes provide a very interesting view of pulsars. In light of this, when we discovered my pet source, J1023, we took an X-ray observation of it. It's taken us considerable time to analyze the results and put together a paper describing them, but I think the result will be a valuable contribution to the literature. (More importantly for me, it should make a chapter of my PhD thesis.) The result is the cumbersomely-named "X-ray Variability and Evidence for Pulsations from the Unique Radio Pulsar/X-ray Binary Transition Object FIRST J102347.6+003841".

Much of the paper is devoted to details of data analysis, which I will spare you. But I think the gist is interesting, and not too hard to summarize. 

Ignition!

Recently, via Derek Lowe's In The Pipeline, I came across the book Ignition!, by John D. Clark. It's the story of the development of liquid rocket fuels, told by a man who was head of one of the programs. Even if you don't know much chemistry — I don't — the book makes a fascinating read. The image on the left is the first page you see when you open the book, and the image below is the second.

Ergo Proxy

As is obvious to regular readers of this blog, I read a lot of science fiction. I also enjoy science fiction movies and TV shows, but they're generally much harder to find. Or at least, ones I like are. But I came across an enjoyable new series recently: Ergo Proxy. It's a cyberpunk anime with a female protagonist that I came to rather like in spite of her cold and sometimes difficult personality. The series is obviously some sort of cousin to Ghost in the Shell (albeit without some of Shirow's particular obsessions) and Serial Experiments Lain (though thankfully free of schoolgirls). On the Western side, I suppose I'd compare it to The Matrix (or maybe the similar-but-better The Thirteenth Floor) and The Prisoner. 

As those analogies suggest, the series is sometimes a little heavy on the symbolism, mystery, and spouting of philosophy, but that's all part of the cyberpunk tradition, and this series carries it off well. I enjoy the visual style as well, though there are a few moments where the animation is a little off. The soundtrack is the kind of music I listen to anyway, which helps. I usually prefer subtitles to dubbed audio, but for this show the dub is better written and well-acted. All together a fun experience. 


[Edit: you can watch the whole thing online.]

Reporting FAIL

There's currently an item in the news about a British boy who managed to damage his eyesight with a "laser pointer". The news articles generally imply that any laser pointer is a lurking risk to your eyesight ready to blind you with a single incautious glance. But there are the ordinary 1-5 mW laser pointers you can buy in dollar stores, and then there are the pocket lasers you can buy online that have powers up to 500 mW and that can burn a hole in a credit card. If this kid managed to damage his eye with the former, well, that's surprising and alarming. But the articles don't describe the laser at all, beyond the fact that he ordered it on the internet. If you go to the original one in the British Medical Journal, though, you still don't get the power rating, but you find out that it was "high-powered", i.e. almost certainly one of the high-power ones you can get online. Of course you can damage your eyes with these; I strongly doubt it would be possible to get one without being made aware of the danger. What's more, the high-power ones are already arguably illegal in many places, not that that stops online companies from shipping them there.

The key point I'm getting at is that all the media coverage is missing the essential information that this is not a normal laser pointer, and that those are basically not dangerous.

[Edit: I emailed the corresponding author of the BMJ piece. Unfortunately the boy's guardian destroyed the laser before the doctor could see it, but the doctor is certain that it was one of the high-powered lasers I describe above. It's too bad none of the reporters bothered to check that detail, but I guess it doesn't make good copy.]

Virtual idol

Years ago, I'm not sure when or where, I saw the anime Macross Plus, which is about a pop star who is entirely a computer program that sings, but who has fans as devoted as any present-day pop star. Anime being anime, there was of course a whole plot line about her AI going rogue (plus giant robots of course), but I remember thinking "how weird, a pop star who doesn't exactly exist". Well, technology progresses, and sure enough, we have one now.

Laser rifles

Laser rifles have been a staple of science fiction for years, though now that cheap harmless (or nearly) lasers are everywhere writers are moving to other buzzwords. But I had no idea that anyone had come up with a more-or-less workable design until I stumbled across the "Stavatti SF-1" and "TIS-1".

(More below the jump.)