i dont know much physics but i know math. Trying to understand this so i can get a better understanding of what is being talked about in the computational neuroscience reading group. This video is awesome thank you
Excellent explanation, thank you. Wproking towards a different application of the Fokker-Planck equation but even though i can't use all the assumptions, your video made the subject much clearer to me. I'll be going back to this movie
I'm stuck trying to figure out how you prepared the dirac delta to integrate over the v_old s. I used the property for a scaled argument in the delta delta(bx-a), but I can't quite get what you ended up with in the argument of P(v,t) in the next step.
@@StratosFair I think what happened might be: we have v_old = (1/lambda)(v - R(t)del t), then write it as v + (...) * del t + O(\det t^2). The higher-order terms don't matter after Taylor expansion, so it's enough to have what's written in the video.
Really great explanation, thanks a lot! One thing I did not get was why 2nd order Taylor expansion was sufficient. I suspect it is because the higher order terms are tiny as they have higher powers of delta_t in them, but I'd have to do the math to convince myself that they indeed are negligible
You are on the right track....keep in mind that he only needs a delta_t in the rhs to factor it out after applying all probabilistic relations, then devide all by delta_t and through a limit process get dP/dt on the lhs, if higher order derivatives in the Taylor expansion were used you would end up with higher than 1 order in delta_t in the rhs, or by multiplying gamma delta_t, which will get to zero faster than delta_t...THE KEY IS TO SEE HE WROTE "TO THE ORDER OF DELTA_T"...in minute 26:40...
Thank you for your question. The only ingredients going into the calculations are the first and second moments of the distribution, the first moment being zero. If you have an alternative distribution with first moment zero, you obtain the same form. For a non-vanishing first moment, you can probably do a similar calculation, where the first moment would appear as an extra contribution to the drift force.
Thank you very much...I have seen this equation appearing in many books...but nobody explained the derivation as detailed as you did it here...
i dont know much physics but i know math. Trying to understand this so i can get a better understanding of what is being talked about in the computational neuroscience reading group. This video is awesome thank you
Great explanation to me as a beginner on the area. I hope to see the written media for me to understand more clearly on some places. Thank you~
Beautiful explanation
Can someone please explain the passage at 26:15? How does the (1+gamma Delta t) appears?
binomial approximation
Thank you so much.
Excellent explanation, thank you. Wproking towards a different application of the Fokker-Planck equation but even though i can't use all the assumptions, your video made the subject much clearer to me. I'll be going back to this movie
I'm stuck trying to figure out how you prepared the dirac delta to integrate over the v_old s. I used the property for a scaled argument in the delta delta(bx-a), but I can't quite get what you ended up with in the argument of P(v,t) in the next step.
did you ever figure out what he did?
did you figure this out?
Whoever figures it out please come and tell is 😭
@@StratosFair I think what happened might be: we have v_old = (1/lambda)(v - R(t)del t), then write it as v + (...) * del t + O(\det t^2). The higher-order terms don't matter after Taylor expansion, so it's enough to have what's written in the video.
Clear exposition; thanks.
Really great explanation, thanks a lot! One thing I did not get was why 2nd order Taylor expansion was sufficient. I suspect it is because the higher order terms are tiny as they have higher powers of delta_t in them, but I'd have to do the math to convince myself that they indeed are negligible
You are on the right track....keep in mind that he only needs a delta_t in the rhs to factor it out after applying all probabilistic relations, then devide all by delta_t and through a limit process get dP/dt on the lhs, if higher order derivatives in the Taylor expansion were used you would end up with higher than 1 order in delta_t in the rhs, or by multiplying gamma delta_t, which will get to zero faster than delta_t...THE KEY IS TO SEE HE WROTE "TO THE ORDER OF DELTA_T"...in minute 26:40...
Thank you very much for this, it helped me a lot
What would it be if P(R) was not a Gaussian function? Would we still get the FP equation?
Thank you for your question. The only ingredients going into the calculations are the first and second moments of the distribution, the first moment being zero. If you have an alternative distribution with first moment zero, you obtain the same form. For a non-vanishing first moment, you can probably do a similar calculation, where the first moment would appear as an extra contribution to the drift force.
Sir, How can we convolute the Fokker plank equation with the signal(sine)? how to write Matlab code for that?
Kya Fokker Planck equation he lengavine equation h