paperclippy: (huh?)
I'm trying to understand a section of a paper. They're talking about the signal generated by a photomultiplier tube when photons from fluorescence are coming into it. The sentence says, "Since the number of photo-electrons ultimately captured by the PMT is finite, the signal quantitation is stochastic with a variance governed by the Poisson distribution."

  • Why does the fact that the number of photo-electrons is finite affect anything?
  • I forgot what stochastic means, please enlighten me.
  • Does "signal quantitation" mean the number of distinct waveforms coming out of the PMT?
  • Why is it governed by the Poisson distribution?


The next sentence says, "The square root of the number of captured photo-electrons is approximately the standard deviation of the error distribution." Is this because it is Poisson?

Also, explain the following sentences to me please: "Q is a measurement of efficiency and has units of number of photo-electrons per unit fluorescence intensity. The lower the Q value, the higher the amount of relative counting error associated with the signal."

I will admit that the primary reason I don't understand this is that I slacked off in prob/stat classes and I also never really learned how a PMT works. Unfortunately now it's important for me to understand what's going on!
paperclippy: (huh?)
So I have x and y velocities, and I want speed and angular velocity. Is the following correct?

r = sqrt(x^2 + y^2)
theta = invtan(y/x)

so

dr/dt = (1/2) * (1/sqrt(x^2+y^2)) * (2x(dx/dt) + 2y(dy/dt))
dtheta/dt = (1/(1 + (y/x)^2))*((x(dy/dt) - y(dx/dt))/x^2)

Assuming I took derivatives correctly. The question is: is there a way to get dr/dt and dtheta/dt without knowing x and y? What if I only know dx/dt and dy/dt?
paperclippy: (huh?)
I think there is a stupid obvious answer to this question, but I am at a total loss.

I have an array of length N. I want to divide it into D bins. N/D is not an integer. How do I do it without just taking the floor of N/D and then having a huge bin at the end?

Is the following a valid option? Let T = floor(N/D). First bin is length T. Then let T = floor((N-T)/(D-1)), etc? Does that work?

I really think this is something stupid that I used to know how to do but I have forgotton. If any of you know a matlab function that does exactly what I want, even better (I ultimately want a new array, length D, which has the average of each of those bins as its values).
paperclippy: (afroken)
someone please help me with some simple linear algebra )

If that's not clear enough, I can try to LaTeX it and convert it to an image to post instead. Thanks!!

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