## Friday, December 22, 2006

### The inaugural post

The hardest thing about starting a blog is coming up with a good name. It has to be whimsical yet not cheesy, and somehow encapsulate the ethos of the blog. At first, I was discouraged by the thought that all the clever ones were taken. Then one day I managed to crank out a whole bunch of potential blog names (I won't say what they were-- wouldn't want to ruin the fun for other newcomers). Finally, I settled on what you see here.

An explanation is in order. The name is an amalgamation of two of my main research interests: stochastic processes and automata theory. "Absolutely regular" is a type of strong mixing condition, and I've done a bit of work on that. "Regular" is also the name of a fundamental class of formal languages (in a well-defined sense, it is the simplest nontrivial class of languages with natural closure properties). I have some results regarding these as well.

"Regularity" is one of those abused terms in math (cf. "space" and "kernel") that means everything and nothing. Roughly speaking, regularity is whatever conditions we need to impose to exclude the pathologies that prevent intuitive/desirable statements from being true. Mathematical analysis is full of instances where the naive claim is inaccurate or plain false (integration and differentiation are inverse operations) but becomes true once the right (usually, mild) conditions are imposed. In some sense, analysis is the study of such conditions. Regularity also crops up in more applied areas, such as statistical machine learning. No one can learn arbitrary functions -- there are simply too many of them. However, once a regularity condition is imposed (VC-dimension, Sobolev norm, Tsybakov noise condition, etc) -- learning becomes possible. In some sense, machine learning theory is the study of the regularity conditions that enable learning.

And finally, "absolutely regular" might just conjure up an image of a relaxed, easy-going everyday joe-shmoe blogging away in his pajamas.

I'll close with a mission statement. This is mainly a research blog. I'll post about problems I'm working on, current and past, and invite readers to join in. Recently, my work has been generating a slew of open problems, so if you're looking for a good problem to work on, you've come to the right place.

I'll resist the temptation to post about personal stuff because (1) my friends shouldn't have to read my blog to get an update (2) everyone else really has no business even being curious. I'll try to keep the politics near zero, but I see myself occasionally lapsing into a mini-rant (what blogger worth his salt doesn't? At least I'm honest and upfront about it).

Finally, I'm a novice at this "web-logging" on "the inter-net" so please do bear with me. I don't even know how to make formulas, such as $f:\mathcal{X}^n\to\mathbb{R}$ come out right. I'm glad that русский and עברית seem to work.