Martin's Blog

Some slides and a movie

martinleslie — Tue, 12 Jan 2010 06:35:38 +0000

Talks I gave last semester:

- A talk about LDPC codes. This explains why I was making those perplexing pictures a few posts down.
- A talk about using a neural network to solve the 8 queens problem. These might not make a whole bunch of sense as the talk was for a course so requires background and when I gave the talk my network didn’t actually work. (Since then I managed to make it pretty much work so I’ve changed the ending of the talk).
- A movie of my neural network converging to a solution. It’s mp4 format which I can play in quicktime or VLC so hopefully you can play it in something*. The exciting swirly part is slightly before halfway.

*It’s unlikely you guys will be able to help me with this but do you know a good way to do video on a mac? I get a 430mb uncompressed avi file out of matlab and I used QTamateur then iSquint to compress it down to 600k. I’m sure there’s a better way to do this.

Running byes straight to the wicketkeeper

martinleslie — Wed, 30 Sep 2009 16:21:34 +0000

We once again* saw an international cricket team have no idea what to do when the score is tied with one ball to go (actually Younus Khan looked like he had no idea what was going on at all).

*England had a whole over of missing easy runouts against The Netherlands, I think, in the World T20. That may have been Stuart Broad at the bowler’s end but the same principle applies.

Some simple ideas:
- wicketkeeper up at the stumps
- if you can’t do that, train your keeper so that he can hit the striker’s end stumps 3/4 of the time
- if that doesn’t work, have a short leg there to receive the ball
- also have a short midoff to receive the throw to the other end to prevent the delayed steal*

*This would work, right? The non-striker takes the absurd lead he is allowed under current rules and then the striker waits until the non-striker arrives before setting off on the run. There’s no way to get an out at the striker’s end.

Your team needs to practice this for about 15 minutes once and then they’ll know what to do.

Animated gifs

martinleslie — Tue, 29 Sep 2009 00:39:53 +0000

You might say that I could have spent my time better but after a few hours of work I was able to make this rather inscrutable picture. Any guesses as to what it’s doing?

Shane Warne

martinleslie — Mon, 14 Sep 2009 00:48:08 +0000

With my recent thoughts and endeavours not leading to interesting blog posts (even by the low standards of this site) I will merely give you a youtube video of Shane Warne.

Later in his career Warney was ‘just’ an accurate bowler of legbreaks that turned enough to be dangerous who also had a psychological hold over batsmen and umpires. But circa 1994 he was an absolute bamboozler – the flipper especially was unplayable for people that grew up in South Africa, England, West Indies…

This video from 1994 against South Africa is worth watching:

Quiz answer & discussion

martinleslie — Thu, 03 Sep 2009 21:16:02 +0000

1/3 is ‘correct’ by exactly Dave’s solution. I was going to provide a more detailed and motivated exposition but I don’t think I can be bothered. My knowledge of Bayesian inference comes exclusively from reading the first half of section two of McKay’s textbook Information Theory, Inference and Learning Algorithms so you can read that and know as much as I do.

So, points for Dave for doing what the book did, Yuliya for getting approximately the right answer first and Leesa for having both the worst and possibly the best answer.

The answer of 0.3 is clearly terrible: if you are a frequentist that doesn’t believe in probability representing belief then your real answer should be that the 10 flips are not at all significant.

But the 0.3485 might be pretty good. What was your prior Leesa? I can certainly believe that a prior that is normal with mean 0.5 and some smallish standard deviation is perhaps more reasonable than a uniform prior and that should give us an answer above 1/3.

A quiz

martinleslie — Mon, 31 Aug 2009 15:47:43 +0000

You toss a (not necessarily fair) coin 10 times and get three heads. What is the probability of getting a head on the next toss?

Guesses and answers with some calculations are both acceptable.

The argument of a complex number

martinleslie — Sun, 30 Aug 2009 19:56:24 +0000

The argument of a complex number is defined to be a number which represents the angle of the vector corresponding to the number measured from the positive real axis. If you draw a picture of this setup your first thought is that . Unfortunately this can't work because the range of is . It is true that but ever since I learnt about complex numbers 8 years ago or so I just knew that you had to draw the picture and think about it to solve this equation for .

But just a few days ago I discovered* that there does exist a formula! (well, it can’t give you an answer of but apart from that it works). It is the rather mysterious statement . Wikipedia says that it’s related to half angle trigonometry but looking at the formula you should also be able to get it from a picture of a circle.

*reading something on Wikipedia is a form of discovery, right?

So here’s one way to come up with it: Draw the point in the complex plane and then draw the circle centred at the origin that goes through the point. Now consider the following diagram.

The angle at the boundary of the circle is half of that at the centre (that’s a theorem from circle geometry but it’s pretty easy to see from the picture in this case). The radius of the circle is so you have and this time you can invert with the standard function.

This seems quite weird to me: that this function works but the other doesn’t. It’s a stereographic projection I guess and is a better coordinate than …

This formula isn’t actually that useful but it was just what I wanted to find to do a question from my complex analysis homework 0, so it was helpful to someone somewhere.

It’s hard to take ratemyprofessors.com seriously

martinleslie — Tue, 25 Aug 2009 15:33:19 +0000

My two most recent reviews on my ratemyprofessors.com profile (a hugely biased sample of four students out of about 150).

Simply he’z a great teacher. he makes Calculus as an easy material you ever expected. Just study for review study and you’ll do fine. An A is acheivable since his exams is a pretty easy.

I sincerely hope that this student speaks English as a second language.

Martin is a mathematical genius. His stories of kangaroos killing people are funny too. The class is tough, tests are tricky, study and an A is achievable. Good teacher!

I don’t recall telling any stories of kangaroos killing people.

Also, if any readers want to add fake reviews (are those two above fake?) I’d appreciate one of those little chili pepper icons saying i’m ‘hot’.

My new favourite family picture

martinleslie — Mon, 24 Aug 2009 05:15:57 +0000

Well sure, it’s actually only got one member of my family in it…

My sister Ellen on the left, Tali White in the middle

The Lucksmiths played their last ever Brisbane gig later tonight*. Hope you enjoyed it Elle.

*grammar problems caused by the international date line

Bad predictions

martinleslie — Sat, 22 Aug 2009 22:28:04 +0000

After my last two cricket posts have shown my complete lack of predictive power (I thought Australia would chase 500 last time they had that target and that Stuart Clark should play over Hauritz) I should probably keep my mouth shut.

But I really think Australia has a chance of chasing a world record total this time. Somebody is going to do it some time and this Australian team is probably most likely to do it. They can score dominant test match centuries from 1-8 in the order and the pitch isn’t that bad…

So I’ll be waking up at 3 am tomorrow morning. Hopefully I won’t be going back to sleep at 4:30.