Recent content by coolnessitself

Thanks for the quick response! So once I have an expansion in terms of a Fourier series or orthogonal polynomials over the disk, how do I then "take into account" the holes? Or is this not what you mean? Since I'm not familiar, do you know a name for these?

Hi all, I have a smooth f(x,y) in some region of ℝ2 that I know to be 0\le f(x,y)\le 1. The region has holes. I also know that inside the holes, f(x,y)=0, and outside of the region, f(x,y)=0. I'm looking for a good choice of polynomials or other functions I can expand f on in order to fit my...

Hi all, I feel like there's a missing link in my understanding of brownian motion. I'm comfortable with the "method of http://fraden.brandeis.edu/courses/phys39/simulations/Uhlenbeck%20Brownian%20Motion%20Rev%20Mod%20Phys%201945.pdf" where the signal is written as a Fourier series, and with...

Hi, thanks for the link. So the bessel function simply appears in a bivariate laplace distribution, which I'm dealing with. I guess from an intuitive standpoint, I'm confused about its pdf. If the pdf becomes infinite at some point, how does that relate to probability? If the pdf maps R to some...

Hi Stephen, Essentially I guess it's #1. I have a jump diffusion process x(t) - x(0) = \int\limits_0^t f(x(s))ds + \int\limits_0^t g(x(s))dw(s) + J(t) where J(t) specifies both the Pr(jump in [t,t+Delta]) as well as a distribution of the resulting jumps. That latter distribution is my...

Hi all, I have a question about the actual value associated with the probability p(r) where p(r) is infinite for r=0. I realize that this p(r) can only be a distribution and only exist under an integral, and can't represent a pdf. My p(r) is a radially symmetric laplace distribution in 2d...

ps. two profs that came to mind with interesting work: Todorov: computations the brain must perform for limb movement and sensory information processing http://www.cs.washington.edu/homes/todorov/ Krumhansl: cognitive processes in music perception and memory...

Well I'm not saying that studying Fourier series makes you better at violin, and I'm not talking about the change in IQ or some other ability that is affected by listening to Mozart prenatal or otherwise, but instead, maybe there's some link (possibly related to spatial abilities? just a guess)...

There is a great depth to the mathematics associated with music in terms of chord structure and progression, but clearly the brain does not primarily compute frequencies, ratios and sequences when improvising. However, there is clearly a correlation between mathematical abilities and musical...

I'm working with a cartestian system that has certain periodic properties I'd like to exploit with a new coordinate system, but I don't know one that would work. The trajectory of the state of the system is symmetric across non-adjacent squares (ie a checkerboard of sorts), so that (x,y) can...

Aside from what the name of those iterative distributions might be, here's another question. I'm trying to actually find the distribution of \max(c/f(x)) so I can fit it, where f(x) is a N(\mu,\sigma^2). If I have more peaks I can just sum up my mus and sigmas, so this seems general enough. So...

I think I would need something like cellfun, but my version of MATLAB doesn't allow anonymous functions in cellfun, just built-in functions, so that won't work. But anyways, that's all fine and good. Followup question: Is there a term or subject or something I can look into to describe the...

I haven't gotten the x_2=x_1+\delta to work yet, but I like your c/f(x) suggestion since it can work for multiple peaks, as you say. I can get 2 equally-weighted peaks to work fairly well. I know this isn't a coding forum, but maybe this MATLAB can help someone clc maxVal=1000; %interval from 1...

cei-ing the c/f(x) does an adequate job for my purposes, so I'm set for now, but I guess I'm still curious about this problem in general. A motivation: Given some bus station has buses arriving throughout the day (or here, seconds 1 to 1000). About noon (500), there are a lot of buses, whereas...

But can you make that interval follow some distribution, but with a minimum interval? I have matlab, and I could easily obtain R, but I'm looking for some math behind it, really. Maybe this is more of an algorithmic thing than a statistics thing...