Recent content by rynlee

Sure, suppose your Gaussian mixture model only has one mixed state for the sake of argument: N(mu_i, sigma_i, Ot) = 1/(sqrt(2*pi)*sigma_i) * exp(-(Ot-mu_i)^2/(2*sigma_i^2) ) and b_i(Ot) = N(mu_i, sigma_i, Ot) for each state 1<= i <= N Because of the leading term in the gaussian, b_i(Ot) has...

So I am working with a Hidden Markov Model with continuous observation, and something has been bothering me that I am hoping someone might be able to address. Going from a discrete-observation HMM to continuous-observation HMM is actually quite straightforward (for example see Rabiner's 1989...

Alright, i think I've figured it out. While null observations typically pertain to HMMs where you treat observations as made on the transitions as opposed to the regular time intervals (i.e. when you set self-transitions, a_ii in common nomenclature, to zero, and instead assign duration pdfs to...

My idea above, in the third paragraph, could be described as a HMM with missing observations. I've looked a bit at the literature on null observations, but that is really pertaining to when observations are made on the arcs/transitions, not at regular time intervals.

Hello All, I'm building a HMM for some data where there are two different time delays. Specifically, I collect data in consecutive traces, such that the time delay between each data point within a trace is approximately fixed, and the time delay between each trace is approximately fixed, but...

That's a good point, really this could be viewed as two coupled DEQs, one defined on [0,a] and the other defined on [a,c], each with a set of Robin BCs, with one of them shared (at a). The two DEQs aren't independent though, since the BCs are Robin not Neumann. If we instead had...

don't I have 2 BCs in a second order DEQ? If you stick with the original 2D problem I have 2BCs (those) and in the steady state assumption no longer need an initial conditions since I eliminate t, leaving me with the 2nd order DEQ and two robin BCs. For a simpler problem Neumann BCs could be...

Properly I should title this more like "diffusion-reaction DEQ with delta reaction term in steady state with homogenous generation"

Hi All, so I'm trying to tackle this DEQ: f''[x] = f[x] DiracDelta[x - a] - b, with robin boundary conditions f'[0] == f[0], f'[c] == f[c] where a,b, and c are constants. If you're curious, I'm getting this because I'm trying to treat steady state in a 1D diffusion system where...

thanks! that really did the trick, I'm amazed at how few points mathematica actually takes. That said I'm glad for its low plot points by default - cranking it up really increases the calculation time, it looks like when PlotPoints is set to automatic, it tries to keep the calculation time...

I've had this problem many times in the past, and haven't thought of a way to fix it. Sometimes when I plot a function that requires quite a bit of effort on mathematica's part, (for example, one time the function was a sum of about a thousand terms, each of which was multiplied complex terms...

The final function (just to show what it should look like if anyone else has the same problem):

yep the evaluate[] did it! Thanks!

Hi All, running into a bit of a mathematica issue. I put the following code into plot: Plot[Im[correlationList], {t, 0, timeEnd}, PlotStyle -> ColorList] correlationList is a list of complex functions that have been evaluated at t. It correctly plots all of them (if I change it to...

Nevermind, the length of the time vector was too long, I fixed it and things seem to work now.