Recent content by Cexy

Here's one idea You have two databases of texts, one containing texts written by humans (genuine), one containing texts written by computers (spam). For every word appearing in the texts, you calculate the probability of it appearing in a message, conditional on the message being genuine...

Yup. Finite unions of finite sets are finite. Countable unions of finite sets are countable. Finite unions of countable sets are countable. Countable unions of countable sets are countable.

Do you have a mistake in calculating the final probabiity P(R|E)? It seems as though you've calculated P(R|E) = \sum_i P(R|Hi, E) whereas you should really be calculating P(R|E) = \sum_i P(R|Hi,E) P(Hi|E) It seems intuitively obvious (and I'm pretty sure I have a proof) that if we...

Cross-validation to test the accuracy of the model? To test how well the observations fit the probability distribution produced by the model you could construct a test statistic (eg Pearson's chi square statistic) and repeatedly sample from your model's prob distribution to produce a...

I have a data set {X(t) = (x(t), y(t))}_t=1,...,N and I'm interested in modelling the changes from t to t+1, using some metric d(X(t),X(t+1)) The issue is that x(t) has some dependence on y(t), and I'd like to account for this: if there is a large change in y(t) we expect there to be a...

It sounds as though you're trying to rotate the complex plane around the point 2+i, rather than rotating the point 2+i around the origin. In this case you're doing the right thing: Given a complex number z, you first translate so that 2+i is at the origin (ie subtract 2+i) then you rotate by 90...

Nothing on Wikipedia or Google? http://en.wikipedia.org/wiki/Julian_Barbour http://www.google.com/search?q=julian+barbour

I was assuming that by "finance" the OP meant a good IB job. More like depending on what job you do. I worked ~60 hrs a week which I don't consider to be awful, and earned good money.

Not impossible, but it depends on (a) when he left (6M ago? 10 Y ago?) and (b) what currency... I doubt that.

Yes.

For me: finance, no question about it. Why? Because computer science is dull and finance pays 3-10x more.

I did original research when I was working at an investment bank.

You certainly can't do research in mathematical physics with a computer science degree. But you can do a master's degree in mathematics, physics or mathematical physics and try to get into research that way. It will involve a lot of work and extra reading though. Also consider that...

Undergraduate degree at 21, Masters at 22, PhD at 25 (hopefully...) all in maths.

You hit the nail on the head with "From my (limited) experience, it seems that the truley interesting and meaningful things in this world are rarely linear" It's true. There are no interesting linear problems to solve, because we already know how to solve linear problems. And also there are no...