How could I have missed Vimperator until now? It’s a Firefox extension that gives the browser a modal interface like vim’s, with similar keybindings. To open a page in a new tab, for instance, you can type :tabopen sitename. A neat ...

Megabus.com adds Philadelphia-D.C. line, from the Daily Pennsylvanian.We learn from a Megabus spokesperson that their vehicles use "less than a pint of fuel per passenger mile".For those of you who don't have the misfortune of knowi...

We might not always want to lay out an entire algebra of sets in one go. Sometimes we can get away with a smaller collection that tells us everything we need to know. Suppose that is a subset of — a collection of subsets of — an...

articles on realism in the EMS newletter

We saw in the previous exercise that finding an exact solution for the traveling salesman problem is extremely time consuming, taking time O(n!). The alternative is a heuristic that delivers a reasonably good solution quickly. One...

I'm working on a certain problem, and I need to know more about the discrete Galton-Watson birth/death process. Say, start with one creature at step 0. It lays N eggs and then dies. Each egg has independent probability 1/N of produc...

This article by Mainardi and Rogosin gives the early history of infinitely divisible distributions. It includes a translation of Khintchine’s proof of the Lévy-Khintchine formula expressing the possible forms for the characteristic...

Recall that the Max-Cut problem is to, given a graph , find a division of into two sets such that the number of edges between the two sets is maximized. Here’s an interesting way, a la Lovasz, to motivate the Goemans-Williamson app...

Okay, now that root systems are behind us, I’m going to pick back up with some analysis. Specifically, more measure theory. But it’s not going to look like the real analysis we’ve done before until we get some abstract basics down...

The nCafé is currently affected by a bug that prevents comments to be posted. Here is a link to discussion on the nForum to alleviate this problem for the moment.

Tomasso Dorigo has a new, non-technical, post explaining muon decay. Tomasso characterized his description as “although not perfectly correct in the physics, was actually not devoid of some didactic power.”

In this final set of lecture notes for this course, we leave the realm of self-adjoint matrix ensembles, such as Wigner random matrices, and consider instead the simplest examples of non-self-adjoint ensembles, namely the iid matrix...

After last week’s sample from DJ Jazzy Jeff & The Fresh Prince, I thought I’d keep the old-school rolling with a true classic. In 1989, Marvin Young — known as Young MC — put out one of the best known rap songs ever. His breakout s...

You can actually buy a shirt with the Calkin-Wilf tree on it. I probably should buy it, if only so I can wear it when I inevitably give a talk on this subject again, either as a stand-alone talk (I've done it twice) or when I teach...

This is something I just need a little clarification on. I'm working through an exercise that goes approximately as follows: Let E have finite outer measure. Show that E is measurable if and only if [conditions X, Y, and Z]. The def...

Simon Willerton has written an introduction to the Weyl tube formula. More details can be found in this review of Alan Gray’s book on the subject.

For once I’m not the absolute last person on a fad. I’ve set up a page at Formspring. Any questions you have, you can ask there. No promises about answers, but it’s a nice anonymous feedback system. Now to figure out how to add i...

Could someone help with∫[dx/(rexp(ix) + z)]?The integral is from -π to πThis can be transformed into a constant (depending on r) multiple of the integral of the function z (conjugate of z) over the circle of radius r centered at zer...

I’ve mentioned earlier the first cases I had found of (almost) mod-Cauchy convergence (see this post for the definition). Yesterday, following from a citation in Sarnak’s note to one in a paper of Guivarc’h and Le Jan, I ended up l...

(this is part of an occasional series of essays on clustering: for all posts in this topic, click here) In the last post, we looked at the elbow method for determining the "right" number of clusters in data. Today, we'll look at ge...