Ceiling function considered harmful

Often in my 4th year mobile communications class, I'll ask a question like the following:

A cellular telephone system is intended to cover an area of 36 square km. Suppose FDMA is used, where the total system bandwidth is 100 MHz, and each call occupies 30 kHz. The system should support 40,000 simultaneous calls in the entire coverage area. Assuming a cluster size of 7, how many cells are needed?

This is a very easy question to solve, and I ask it to get students thinking about radio resources. (Granted that circuit-switched telephony is now obsolete with LTE.) The solution looks like this: at 30 kHz per call, 100 MHz supports 3333 calls; to get 40,000 calls, you need 40,000/3333, or about 12 times the system bandwidth (i.e. 12 cell clusters); with 7 cells per cluster, that's 12 x 7 = 84 cells.

But the problem is that 40000/3333 is slightly more than 12; it's exactly equal to 12 + 4/3333, or 12.00120012... . Multiplying this number by 7, we get 84 + 28/3333, or 84.00840084... .

Since the number of cells must be an integer, a typical student reaction is to take the ceiling of the answer: ceil(84.00840084...) = 85.

But that's bonkers. We "need" an extra 0.0084 of a cell, so the answer is to build a completely new cell tower to satisfy this tiny demand. Cell towers are expensive. And in fact, 12 clusters can cover 39,996 users, so the extra cell would serve a grand total of four calls. The revenue from that -- and even, let's say, the possible contractual penalties for not hitting exactly 40,000 calls -- would never be worth it.

Instead of blindly using the ceiling function in response to these questions, we should encourage students to think about the assumptions behind the question. Allowing a bit of flexibility (e.g., slightly relaxing the "40,000 call" assumption) would lead to a much more realistic and useful answer, and better engineering.

Thomas M. Cover, 1938-2012

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I never met Tom Cover. But like every PhD in information theory, I came to know him through his book.  

Elements of Information Theory, better known as Cover and Thomas, is the gold standard for a graduate-level mathematics textbook: always readable, rigorous but never tedious, and comprehensive; one that captures both the elements and the spirit of the discipline. You have to imagine that, if The Book has a section on information theory, it's just Cover and Thomas, verbatim.

Its influence on the field has been so vast, a colleague once said, that "we're not information theorists, we're Coverists."

Thomas M. Cover August 7, 1938 - March 26, 2012

Hidden York: Power generation and distribution facilities

The chimneystack is York's most widely ignored major landmark. Yet at the base of that chimney is enough heavy machinery to generate and distribute 10 MW of electrical power (about half of the university's maximum power needs), plus all of York's heating and cooling. Without it, we would all literally freeze -- or swelter -- in the dark.

Because the university's facilities department wants to play a role in our new electrical engineering program (especially our planned Power specialization), I had the rare opportunity to take a tour of the generation, distribution, and steam generation facilities. Many thanks to Brad Cochrane and Gary Gazo for showing me around. Pictures after the jump.

The zombie Sheppard subway must die: A rant

I ride transit to work. And like every Toronto transit rider, I have an opinion. Here it is.

Council has spoken: the Sheppard subway is a failure. It's costly and underused. It's not worth extending, even if it could be done for free. Now, east of Don Mills Road, Sheppard will be served by LRT; outside of the mayor's fever dreams, the Sheppard Subway will never be extended beyond its 5.5 km, five-stop stubby existence. It's dead.

But not really: council committed the key horror movie mistake of not finishing the job. After all that rhetoric of how terrible the Sheppard subway is, how short and pointless, how worthless it would be to extend (all good points!) ... it's still on the map. People are still going to ride it for the foreseeable future. The Sheppard LRT plan sets its undead, poorly designed, unexpandable failure in concrete for our childrens' children to admire.

This zombie subway will haunt every discussion about transit in the north end from now until kingdom come. Any time rapid transit north of Eglinton gets discussed, some bright-eyed person will ask, "Well, wouldn't it be better just to extend the Sheppard subway?" And then we get to have the very same knife fight about transit over and over, like that time Kelsey Grammer was on Star Trek.

There's only one solution: the zombie Sheppard subway must die.

How does that happen? We cut out its heart: convert the subway so that the LRT can use it. One seamless trip from the current subway tunnels, on to the surface and into the east end.

How do people tweet their Roll Up the Rim wins? They exaggerate (Update)

UPDATE:I had planned to make this a two-part series, with the mathematical details in the second part. Instead I'm going to turn the whole thing into a paper. I'll post more when the paper is written. Original post follows.

Canadians love them some Roll Up the Rim, the annual Tim Hortons coffee contest. They also love to tweet about it. And if ever there was a great experiment to see how people perceive -- and report -- random events, Roll Up the Rim and Twitter are it: known odds, random selection, and mass participation.

Last year around this time, I wrote a quick program that accessed Twitter's API, and extracted all available public tweets with the hashtag "#rolluptherim" (thanks twitter4j). I gathered 876 tweets covering Friday, March 18, to Wednesday, March 23, 2011. They were then promptly stored and forgotten about until a couple of weeks ago, when Roll Up the Rim began again in earnest.

So what do people tweet about, when they tweet #rolluptherim? For one thing, they tweet about their success rates: of the 876, I extracted 387 tweets containing something like "1/8", "3 for 10", and so on.

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So here's my question: how do people report their own success?

Semi-Hiatus

This is probably the most brutal semester of my academic career so far, so I'll be posting at reduced frequency until mid-April or so. I've got lots of stuff to talk about (Korea trip, thoughts about the BIRS workshop, my upcoming sabbatical) but no time to write.

The university at night

The university is a different place at night, as the boisterous crowds of the daytime give way to a very different quietness and studiousness.

Looking up at the few remaining lights from professors' offices, and the desks in the library where students are poring over books, I wonder what they're working on; I always imagine great research breakthroughs come after dark.