Irrationally effective

Everyone knows that e has some nice combinatorial properties, but occasionally a counting result comes along that transcends the well-known mundanity of cute factorials.

Counting and Computing by e
M. Hassani

The problem that just won't go away

Do you like maps? Do you like colors? Do you like coloring maps? Do you like signed permutations? I like signed permutations because they describe genetic mutations. I also like the fact that maybe, just maybe, there's a connection between mutations and how many colors are necessary for map-making.

Signed permutations and the four color theorem
S. Eliahou, C. Lecouvey

Cubicles have no doors

While I, unlike the heroes of this comic strip, am quite productive at my workplace, I am highly attuned to passersby. My back is to the entry-break in the carpeted wall, so my reactions are as follows:

1. When I do not have headphones on, I turn to look every time someone passes by;
2. When I have headphones on, I am startled by a tap on my shoulder by whoever needs my attention.

The first is less disruptive, but more frequent, so there is clearly an optimization problem buried here. In either case, it is clear why the principles of feng shui dictate that one should always have a clear view of the entrance to their space.

When does a hiatus become a leave of absence?

Abject apologies to those who would like to have read more frequent musings in this space. You have witnessed the effect of finishing a doctoral dissertation. After a decent run of at-least-weekly posts, I realized that I wasn't going to be able to keep it up during my home stretch. Having recently begun a transition to a new phase of my career, I expect to be able to devote an appropriate amount of time to this pursuit again.

I guess you can write a paper about just about anything these days

But I really shouldn't be so harsh. The authors suggest that their work "rediscovers" a lost proof of a very interesting set theoretic result. And attention-grabbing titles can only help to spice up the literature-scape.

Division by three
Peter G. Doyle, John Horton Conway

The new generation of audio ransom note

Wired's music guy, E. Van Buskirk, interviewed S. König about his software project cum musical mash-up collage tool cum political statement on intellectual property, sCrAmBlEd?HaCkZ!. It's not only an interesting idea, but there are also numerous computational challenges to making it work, and work so well. I want to know how he does all that! I suppose I'll find out when it gets sourceforged.

Freed from economic and social constraints, I would volunteer to work on this without a second thought.

Limited options precipitate creativity

All mathematicians (and many others) immediately recognize the sequence 1, 1, 2, 3, 5, 8 as the first few Fibonacci numbers. In this article, G. K. Pincus proposes a new poetic form, the fib, whose line lengths (measured in syllables) are given by these numbers.

At first, I suspected that most such verses would simply be twenty syllables of English prose broken up to fit the "design parameters". After all, history is full of awkward attempts to use mathematical toys such as the Fibonacci senquence as a basis for art. However, after reading some contributions from the comments to the original post, as well as those featured in a follow-up article, I've found that this form has a real character to it. The first four lines are short and punchy, almost primal; the last two lines seem locquacious by comparison, allowing an outpour of articulate expression. It seems that Pincus struck that delicate balance of constraint; both sufficient to focus creative drive while relaxed enough to prevent the output from being artificial and bland.

Good?
Bad?
Great? Poor?
I'm no judge
Of this kind of thing,
But I know I like what I see.

Pants are one thing, but this is ridiculous

Pants to the power of two? And how did they get a a tree, anyway? Perhaps they were assisted by monkeys?

Squarepants in a Tree: Sum of Subtree Clustering and Hyperbolic Pants Decomposition
David Eppstein

Pachterian geometry

The hardest midterm I ever took was a Numerical Analysis take-home exam. One problem asked for a definition of "the circle that best approximates four co-planar points" and apply our definition to given data. This problem has clear applications to transceiver placement optimization; e.g., where to put a cell phone tower. The model discussed in this preprint describes not only multiple transciever locations, but also the cost to power a signal within a given radius from each tower. It's rare and wonderful to see a real world problem that translates so naturally to a mathematical model.

The professor for the above mentioned Numerical Analysis course, L. Pachter, has some geometric concerns of his own. In this case, the translation from real world problem to mathematical model is considerably harder to understand, mostly because the geometry does not take place in a plane or 3-space. The fundamental object is still a convex body, but it now lives in a larger number of dimensions. Don't let this scare you off; such models are extremely effective for countless applications.

But what about $K_5$ and $K_3,3$?

As a dear friend once told me, everyone should take time to play games. Here's one that I think my reader(s) will enjoy. In fact, I think (t)he(y) may have already. I'd really love to see it played on a 2-torus.

Human Experience Engineering

Last December C. Wetherell, a Google software engineer, told me that his next twenty-percent project would be an algorithm for love. It seems to have entered beta.

Complimentarily, Red Robot of Diesel Sweeties has been honing an algorithm for hate. While I would not take on such a research program myself, I commend him for this endeavor, as it progresses our overall understanding of emotional algorithms. Perhaps Google should recruit Red Robot to be their new Director of Human Experience Engineering.

Perhaps a more practical approach would be for Google to acquire an anti-social networking site, such as Snubster, or perhaps adapt Orkut to this end.

The high TeX arXiv

Numerous posts of mine point to the arXiv, the famous "e-print" server managed by Cornell University. Those at the helm of this marvelous resource have always ridden the leading edge of internet usage. For instance, consider this decade-old page, in which they point out that "... large databases such as this one (which has millions of distinct URL's that lead to gigabytes of data) are likely to grow ever more commonly exported via www." At the time, such archives were commonly hosted on an ftp server. How many of today's internet users even know what ftp stands for?

Fortunately, Cornell's e-librarians are eager to support new internet technologies, such as rss and trackback, at least on an experimental basis. For some reason, this is not widely publicized; perhaps they don't want too many users to become dependent on such features, ensuring that they can be removed without warning while causing minimal disruption. If you are a Physicist, Mathematician, Non-linear Dynamacist, Computer Scientist, or Quantitative Biologist, take advantage of these informational tools; they're there for the using.

Mathematics reaps the benefits of physical insight

A few days ago, slashdot linked to this essay by M. du Sautoy in Seed on the relationship between the Riemann Hypothesis and quantum physics. I've been consistently impressed by Seed's provision of scientific reporting that neither glosses over significant concepts nor drowns the non-specialist in technical details. I think it answers the scientist's perpetual complaint against journalists' relationship with science, as summarized by this recent opinion piece in the Notices of the AMS. Now, if only more media outlets would follow Seed's excellent example.

On a tenuously related note; the author's website is by far the most elaborate I've ever seen among academics. It's refreshing to see such an open rejection of the reverse snobbery so common among our ilk.

A formula for misery

R. Stevens does it again; this time, he illustrates why Math is Life.

The other side of the arXiv

It turns out that some decent papers are posted to arXiv:cs, where authors are not listed alphabetically.

Convex Separation from Optimization via Heuristics
L. M. Ioannou, B. C. Travaglione, D. Cheung

It's good to see convex geometry presented in a decidedly algorithmic setting, since it really thrives there.

No opportunity for subtle wordplay

The fourth Abel prize has been awarded to L. Carleson of the Royal Institute of Technology, Sweden "for his profound and seminal contributions to harmonic analysis and the theory of smooth dynamical systems." The Slashdot story mentions that "[h]is theorems have been helpful in creating [the] iPod," and includes a decent layman's explanation of Prof. Carleson's contributions to analysis. Essentially, he proved that using Fourier series to encode functions is theoretically sound, and not just "effective in practice."

I name my Apple products after mathematicians; my iPod shuffle is Diaconis, my Airport Express is Heddy (after H. Lamar), and my iPod (with video), after careful consideration, was christened Fourier, owing to its algorithmic dependence on Fourier series. Perhaps Carleson would have been a better choice. Well, there will probably be an iPod in need of a name in the future.

Watershed

The project I mentioned in some previous posts is now on the arXiv.

On the local structure of doubly laced crystals
P. Sternberg

It's good to have publicly visible work.

Non, c'est pas une Weezer logo

As part of a run of strips on superheroes, R. Stevens produced a comic in which a character points out that "... Justice League is not a reputable science journal." Buzzwords from mathematical physics puncuate the retort that follows.

I know what the golden "W" in the comic's header stands for, but I can't help but wish it was meant to recognize E. Witten as the strongest driving force in string theory.

Many scientifically concerned individuals bemoan the lack of public interest in science and mathematics. Perhaps what we need is better personal brand management, beginning with a broad campaign of brand identification.

Here, I'll start.

What's a five-letter word for "Surfaces of genus zero with three boundary cycles"?

Any situation can be made humorous (or more so, if it's already funny) by the addition or subtraction of pants or monkeys. At least, so said a dear friend of mine several years ago. I'm inclined to believe him.

As far as I know, there is no mathematical object known as a monkey; until last night, I thought the same was true of pants. As this nomenclature is due to W. Thurston, it has been suggested that they should be called Thurstonian pant-pairs.

A colleague of mine has written a paper on the subject.

Heegaard Splittings and the Pants Complex
J. Johnson

A nice round number

If you write dates with the month before the day, today is 3/14, or more affectionately, π day. Those who are especially meticulous celebrate at a moment about half a minute past 1:59. Yesterday, the Independent ran an article celebrating the wonderful properties and history of this number. Unfortunately, the following sentence appeared near the end of the story:

Pi, you see, is always going to be represented by an approximation because, like all irrational numbers, its digits never really end.

This is perfectly acceptable for a pre-calculus audience, but anyone who has been exposed to infinite sums deserves to see some of the miraculous closed-form expressions for π, such as the following, famously due to Ramanujan.

Happy π day!