I’ve been reading up on graph cuts methods for low-level vision. These are methods that, when properly applied, can de-noise an image as was done in the original paper: D. M. Greig, B. T. Porteous, and A. H. Seheult, “Exact maximum a posteriori estimation for binary images,” Journal of the Royal Statistical Society. Series B [...]
Entropy has always struck me as a somewhat puzzling concept. The definition is simple enough but raises all kinds of puzzling questions. What is with the minus sign? Why use the logarithm? Imagine for a moment that you do not know anything about logarithms, and you were trying to understand the definition above where . [...]
Now, I wish that was all I needed to say. But, the point rather cogently made by the comic above is that that isn’t good enough, that an unexamined “it just happened that we were all men” is never good enough. All of us, men and women both need to examine whether they’re being that [...]
I just watched an online presentation of SAGE, a nifty toolkit for doing mathematics. One of the really neat things about SAGE is that it glues together a ton of existing open source packages. We’re beginning to transition into the stage of software engineering where software development starts (in the minds of many futurists) to [...]
I’m clearing out my draft posts, without actually trying to flesh them out. Anyway, here’s some questions I’m thinking about. As you may be able to infer, I’m trying to teach myself statistics. Natural conjugate priors – prior has the same functional form as the likelihood. Is there a category theoretical explanation of “natural” in [...]
I’m happy about this post because I understood it, as opposed to say, most of the stuff at n-Category Cafe. I’m especially happy because at one time or another, I knew the statement of, and the corresponding proof of: 1. The Hairy Ball Theorem 2. Cauchy Integral Theorem 3. Nash Equilibrium Theorem I just hope [...]
I was a math major in college. Though I’m sure the experience was beneficial, upon reflection I can’t identify how any content I learned in the math classes I took applies to computer science. I’m using a lot of Bayesian inference stuff right now, and PCA, but these two topics never came up in the [...]
How can you have inverses but still have zero divisors, you may wonder? It’s because nonassociativity is bad juju. From a comment on this. Then there’s the following from the same comment thread: There are illegal primes, but being prime numbers, they are inevitably real, positive, rational, integral, natural and wholesome. A goldmine! And here’s [...]