# Search results

1. ### Anyone considering a career as a patent attorney?

I just want to say that I have been working for the USPTO for a while now and never would have considered patents if not for this thread. If anyone has any questions about the USPTO or working as a patent examiner I'll answer what I can.
2. ### General Optics Question

Yeah, its been several years since I've had any optics classes so I'm struggling to remember. I recall doing some matrix multiplication for compound lenses but I don't dare delve that deeply. I don't think it is impossible, just more effort.
3. ### General Optics Question

What 'd' should be used for calculating the power when including the third lens? So I have the first two lenses easy enough. But I'm not sure if I take the P12 to be the distance of the second lens, the average of the distance from 1->3 and 1->2 or just the total distance. I suspect it is the...
4. ### General Optics Question

I have all the dimensions of the lenses and distances between in the system.
5. ### General Optics Question

Homework Statement I have a compound thick lens problem that I need to find the sign of the refractive power. Homework Equations Thick lens equation and focal length equation. The Attempt at a Solution I believe all I need to do is calculate the focal length of the first two thick lenses and...
6. ### Relative Entropy or Kullback Leibler divergence

Nevermind, I've got it!
7. ### Relative Entropy or Kullback Leibler divergence

Homework Statement I am suppose to calculate the relative entropy between two sets of data: Base set Set 1: A C G T 0 0 0 10 0 0 0 10 0 0 10 0 0 10 0 0 10 0 0 0 * * * * //Randomized 0 0 0 10 0 10 0...
8. ### Hidden Markov Model

I think that I have found a way to do this, but I want to make sure it is correct. I believe that the equation is telling me to multiply the two probabilities (prob.to be ACGT within R or G and prob. that R or G changed) and then multiply all of those together. I'm just not sure about order...
9. ### Hidden Markov Model

Homework Statement Consider an HMM with two possible states, “R” and “G” (for “regulatory” and “gene” sequences respectively). Each state emits one character, chosen from the alphabet {A,C,G,T}. The transition probabilities of this HMM are: aRG = aGR = 1/4 aRR = aGG = 3/4 The emission...
10. ### DNA sequence evolution

You are right. I had a feeling that I was getting the opposite result that I was meaning to get. I should have realized I had them mixed up! Thanks!
11. ### DNA sequence modeled as 4 faced die

Oh, okay. I was worried for a second that I had done something else wrong. Thanks!
12. ### DNA sequence modeled as 4 faced die

Well, the ML method described in class was to take the binomial distribution's derivative, set it to 0 and solve for the probability. So that is the method I used. Is this not correct?
13. ### DNA sequence evolution

Homework Statement A strand of length L begins life as all A's. Assume that each letter evolves independent of all the rest until today, 1000 generations later. Within each generation there is a ##\mu## probability that the letter mutates to either C, G, T. Finally, assume that once a letter...
14. ### DNA sequence modeled as 4 faced die

I finally found time to sit and finish this, sorry it took so long. So, I found the maximum with the method I described initially and got the exact some result as if I had just taken the first "simple" method I thought of. It seems my first instinct was correct. Thanks for the help.
15. ### DNA sequence modeled as 4 faced die

My idea was handle each as either A or Not-A as you mentioned. Since I was explicitly given the hint to use the binomial and maximization likelihood. I don't believe we ever discussed the multinomial distribution but I can see how it works here. I think that since the problem is really just...
16. ### DNA sequence modeled as 4 faced die

Homework Statement I have a DNA sequence generated by L throws of a 4 faced die with probabilities ##\pi_A, \pi_C, \pi_G, \pi_T##. Each probability is unknown. Task: estimate the probability of each side of the die. Hint: use a random variable defined by the sequence that has a binomial...
17. ### Sequence Analysis (probability)

I'm struggling to understand the purpose of doing this when I just needed to get the Z score. I understand its significance otherwise.
18. ### Sequence Analysis (probability)

But every value I used for Poissons was already known from my earlier calculations and I didn't use the result for anything.. I feel like I missed something here.... Was I suppose to use the 0.00529 to find the expectation with 1024 strand (1024*.00529=5.42)?
19. ### Sequence Analysis (probability)

Okay, then using Poisson's: ##P(X)=\frac{\lambda^k e^{-\lambda}}{k!}=\frac{4^{10} e^{-4}}{10!}=0.00592## So, the probability of 10 occurrences here is just 0.00592.How does this relate to the Z factor though? If the variance is indeed the same as the expectation then my answer is exactly "3" ...
20. ### Sequence Analysis (probability)

Half correct. THe 1/256 isn't the expectation. Rather it is the probability of finding the 4 letter sequence at any given position within the sequence. Sorry, I kept getting interrupted as I was writing this (potty training my son). The question is asking just for the "Z-score" (standard...
21. ### Sequence Analysis (probability)

Homework Statement I have a 4-letter DNA sequence (AGGA) that appears 10 times in a strand that is 1027 letters long. The probability of finding this sequence at any random position is 1/256. What is the Z-score of this observation? Homework Equations ##Z=\frac{(X-E(X))}{\sqrt{Var(X)}}## The...
22. ### Coin flip deal (stats/probability)

Oh geez, I dunno why I did that. I got it, now. I'm going to think on this a bit and come back if I have any other questions. This is going to take some amount of googling to figure out. Thanks for the help, everyone!
23. ### Coin flip deal (stats/probability)

I promise I haven't missed a lecture (there was only 1 on this), we just didn't discuss anything in great detail as, apparently, it was expected that I have some background in this. It makes sense to me that the V(T) is the sum of the variances for each Xn and, likewise, it makes sense that...
24. ### Coin flip deal (stats/probability)

I honestly don't know what to do with this. I get that I know the variance of each Xn (1.2). But I don't know the total number of heads for each. I the expected value is 2, I think, but this just brings me in a giant circle. Somehow I need to get E(T) without know any X values... I feel like...
25. ### Coin flip deal (stats/probability)

For some reason I said 3.2 before, I think. But it is E(Y)=5.2. The variance was 3.2. Not sure if that was clear before.
26. ### Coin flip deal (stats/probability)

A bit more information then. I'm given the following data: (I couldnt get a latex table to work on here for some reason) X:-------- 0---------1---------2---------3---------4--------5 Pr(X): 0.07776 | 0.2592 | 0.3456 | 0.2304 | 0.0768 | 0.01024 X is the number of times heads appears in 5 rolls...
27. ### Coin flip deal (stats/probability)

Homework Statement Coin flip problem. I'm given the probability distribution of how many times a coin is heads out of 5 flips. From this, I need to determine if the following deal is worth it and, if not, how much it costs using variance: After flipping the coin 20 times I need to pay my...
28. ### Bloch sphere and mixed stats

Homework Statement What is reduced density matrix ##\rho_A## and the Bloch vector representation for a state that is 50% ##|0 \rangle## and 50% ##\frac{1}{\sqrt{2}}(|0 \rangle + |1 \rangle)## Homework Equations The Attempt at a Solution [/B] I haven't seen many (any?) examples of this so...
29. ### Finite Temperature matrix

I got it figured it out. I just couldn't find it in my textbook. Turns out in was in recommended reading I guess. Thanks for the help though.
30. ### Finite Temperature matrix

Homework Statement Consider the Hamiltonian ##H=\begin{bmatrix} 0& \frac{-iw}{2}\\ \frac{iw}{2} & 0 \end{bmatrix}## Write the finite temperature density of the matrix ##\rho(T)## Homework Equations ##\beta=\frac{1}{kT}## The Attempt at a Solution The initial part of the problem had me find...