I occasionally enjoy Thai cooking, so I appreciated some of the comments made by Andy Ricker.

I recently learned about India’s Clean Currency Policy which went into effect this year. I still have some money (in an unpacked box, probably) from my trip this last fall, and I wonder if any of it will be still usable when I go to SPCOM 2014 this year. That sounded a bit crazy to me though, further investigation indicates that an internal circular leaked and it sounds like a more sensible multi-year plan to phase in more robust banknotes. My large-ish pile of Rs. 1 coins remains useless, however.

An Astounding Result — some may have seen this before, but it’s getting some press now. It’s part of the Numberphile series. Terry Tao (as usual) has a pretty definitive post on it.

Avi Wigderson is giving a talk at Rutgers tomorrow, so I thought about this nice lecture of his on Randomness (and pseudorandomness).

There’s been a lot of blogging about the MIT Mystery Hunt (if I wasn’t so hosed starting up here at Rutgers I’d probably blog about it earlier) but if you want the story and philosophy behind this year’s Hunt, look no further than the writeup of Erin Rhode, who was the Director of the whole shebang.

Last year I did a lot of flying, and as a result had many encounters with the TSA. This insider account should be interesting to anyone who flies regularly.

This came up as sub-problem during Young-Han’s group meeting today and we mulled over it for a few minutes but didn’t come up with a non-ugly answer. I’m sure, given the number of Real Mathematicians ™ who read this, that someone out there knows of an “obvious” explanation.

Suppose I give you p integers in an arbitrary order (where p is prime). While maintaining the order and using only addition, multiplication, and parenthesis, is it always possible to make an expression which evaluates to 0 mod p?

I think it’s true, but I’m sure there’s some special property of \mathbb{F}_p that I have forgotten. I guess further generalizations would include whether or not it’s possible for arbitrary p (not necessarily prime), how many elements of an arbitrary field you would need, and so on. I’d ask this on MathOverflow but… meh. It’s probably a homework problem.

My friend Reno has a California Bankruptcy Blog.

The ISIT 2010 site seems quite definitive, no? (h/t Pulkit.)

The Times has a nice profile of Martin Gardner.

My buddy, buildingmate at UCSD, and fellow MIT thespian Stephen Larson premiered the Whole Brain Catalog at the Society for Neuroscience conference.

A fascinating article on the US-Mexico border (h/t Animikwaan.)

Kanye West is an oddly compelling trainwreck. (via MeFi).

Obviously it’s clear I’m a big nerd, but thinking back on the wonder that was Square One, I am astonished at how much work they put into their cultural references/parodies. You can dance if you want to… as long it is the Angle Dance!

On the official website you can watch the some other clips. If they ever released this show on DVD I would queue up to buy it.

I am trying to figure out a rather simple question but I’m sure it’s known already. Suppose I have a the minimizer of the following regularized optimization:

f^{\ast}(\lambda) = \arg \min_{f \in \mathcal{F}} L(f) + \lambda \|f\|^2

Here L(f) is a continuous convex function of f. Is f^{\ast}(\lambda) a continuous function of \lambda? I want to say yes, but maybe I need more assumptions on L(f).

I’ve been catching up on my magazine reading and an ad from the AMS Book & Journal Donation Program in the December issue of the Notices of the AMS caught my eye. The program is designed to improve access to mathematical materials in developing countries via donations. The AMS already has discounted membership fees for those in developing countries, and in general the mathematics community seems more sensitive to these kinds of disparities.

I looked around a bit to see if the IEEE had any sort of book donation program, but it doesn’t seem to be an institutionally supported thing. The scalable computing people have a page on donations, but I didn’t see one for the main IEEE page. There are no discounts listed on the subscription price list. It seems like more could and should be done. Just putting more things online isn’t going to fix everything. There is a value in having actual books in a library too.

So what can be done? In terms of textbooks, there are already cheaper editions available from most of the major publishers, so that doesn’t seem to be the bottleneck. Setting up a clearinghouse (as the AMS has done) for more research-oriented titles seems like a relatively simple thing to do. Providing a tiered-pricing scheme for journals would be a next good step. If the impetus for this comes at a high level in the IEEE, it might get chapters (and undergrads!) engaged in helping gather materials, solicit requests for donations, and so on.

Here’s a little problem that Halyun brought up in group meeting today — a little googling showed that it’s a Putnam prep problem, but I won’t hold that against it. The problem is “Determinant Tic-Tac-Toe.” This is like regular Tic-Tac-Toe except that Player One puts a “1″ in the square and Player Two puts a “0.” The grid forms a 3×3 matrix (call it A), and Player Two wants to make \det(A) = 0, whereas Player One wants to make \det(A) \ne 0. Player One gets to move first. Is there a winning strategy for either player? What if both players can place arbitrary real numbers? What about a general n \times n grid?

I seem to have a penchant for picking books with amusing footnotes. Or maybe most math books have them and I’ve been remarkably unlucky. Here’s one from Random Fields and Geometry, by R.J. Adler and J.E. Taylor:

The use of T comes from the prehistory of Gaussian processes, and probably stands for “time.” While the whole point of this book is to get away from the totally ordered structure of \mathbb{R}, the notation is too deeply entombed into the collective psyche of probabilists to change it now. Later on, however, when we move to manifolds as parameter spaces, we shall emphasize this by replacing T by M. Nevertheless, points in M will still be denoted by t. We hereby make the appropriate apologies to geometers.

It’s a good book so far, and may help me solve some pesky technical point in a new problem I’ve been working on. Hooray for new problems!

I had an interesting conversation two weeks ago about the working process for doing theory work in CS and EE. We discussed two extremes of working styles. In one, you meticulously prove small statements, type them up as you go along, getting the epsilons and deltas right and not working on the next step until the current step is totally set. I call this “prove as you go.” The other is that you sketch out some proofs to convince yourself that they are probably true (in some form) and then try to chase down the implications until you have the big result. When some deadline rolls around, you then build up the proofs for real. This could be thought of as “scaffolding first.” Fundamentally, these are internal modes of working, but because of the pressure to publish in CS and EE they end up influencing how people view theory work.

(more…)

In I.G. Macdonald’s Symmetric Functions and Hall Polynomials, on page 2 there is the following comment on the standard way to write down diagrams of partitions and tableaux:

Some authors (especially Francophones) prefer the convention of coordinate geometry (in which the first coordinate increases from left to right and the second coordinate from bottom to top) and define the diagram of \lambda to be the set of (i,j) \in \mathbf{Z}^2 such that 1 \le i \le \lambda_j. Readers who prefer this convention should read this book upside down in a mirror.

Oh, snap!

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