Tuesday, February 22, 2011

A quick update

I'll be liveblogging the India trip over here. (Written from Pearson, waiting for my flight to Frankfurt.)

Friday, February 18, 2011

A very short presentation on email etiquette

After receiving lots of questionable emails, today I gave a presentation on email etiquette to my first year class. I think they got the picture. Please feel free to use and/or modify it yourself.

PPT version, PDF version

Whirlwind Tour of India

A couple of months ago, I agreed to join a delegation to India from York's Faculty of Science and Engineering.  The idea is to make contact with Indian researchers, sign memoranda of understanding (MOUs) (e.g., covering graduate students and visiting faculty), and possibly to explore joint research projects through bilateral partnership programs.

We're going next week.  My schedule includes a day of meetings at the Bose Institute and University of Calcutta on the 24th; then off to Mumbai for meetings at TIFR on the 25th and IIT Bombay on the 26th, then off to Delhi that evening; a day off on the 27th (the plan is to visit the Taj Mahal); and then a workshop in Delhi from the 28th to the 2nd, with side visits to IIT Delhi and JNU. It'll be my first trip to India.

The trip is partially funded by a government agency. On the one hand, this is great: research is increasingly an international activity, but research funding remains annoyingly nationalistic.  In the absence of partnership programs like this one, it is almost impossible to construct international collaborative research teams, and breaking down those walls is a good thing.  On the other hand, it's surprising how eagerly universities are jumping at this money: we've been told this is "delegation season" in Inda; we're arriving shortly after another Canadian delegation, and we're being told which other universities have signed MOUs, hoping not to miss out on our chance.  You could argue this is symptomatic of general research underfunding in Canada; one wonders what Ghoussoub would have to say about it.

The blog is on hiatus for a bit, but I'll post about the trip when I get back.

Wednesday, February 16, 2011

How about a redesign?

Everybody's doing it, so why not me? Hopefully this will go down better than theirs.  I'll probably twiddle with the colors and so forth, but my main goal was to restrict the column width of the posts.

Thursday, February 10, 2011

A famous communication theorist

I was reading a paper on MIMO recently, when I noticed that one of the authors was Maher Arar.  Surely it can't be that Maher Arar, I thought to myself. But in fact it is: here he is getting a PhD in EE from the University of Ottawa.

Congratulations, Dr. Arar! He even has a nice blog.

Thursday, February 3, 2011

Pigeonholes and entropy, a work in progress

The pigeonhole principle is probably the simplest lemma in combinatorics:
  • Say you want to sort k objects into n bins.  If n < k, then at least one bin must contain at least two objects.  
For example, a person can have only one of 366 possible birthdays (counting Feb 29).  By the pigeonhole principle, any gathering of 367 or more people must have people who share a birthday.

The lemma is obvious almost to the point of triviality, so it comes as a surprise that you can use it to prove powerful results; there are some examples in the book.

Lately I've been wondering whether it can be used to say anything interesting about entropy.  Here's the first thing I thought of: let X and Y be random variables on a discrete alphabet, and let S(X) and S(Y) represent the support of the probabilities of X and Y, respectively (i.e., x is in S(X) if and only if p(x) > 0). Then
  • Theorem. If |S(X)| > |S(Y)|, then H(X|Y) > 0.
  • Proof. By definition of entropy, H(X|Y) >= 0. If H(X|Y) = 0, then there must exist an injective map from S(X) --> S(Y).  However, since |S(X)| > |S(Y)|, no such map exists (by the pigeonhole principle).  Thus, H(X|Y) != 0, and the theorem follows.
 Not very exciting, I will admit.  I'm still thinking about it, any other ideas?