Questions deemed too ‘technical’ at Q&A session on W3D1 “Real Neurons”.
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Why do both the mean and the standard deviation of the GWN affect the slope of the correlation transfer function?
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Thanks for posting my question here! Hope the community can help with an answer
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Another question out of the tutorials lot - What was the tutorial 3 first exercise about? We were supposed to give a really high threshold (to prevent spiking I guess), yet there were spikes and the graph didn’t reflect the higher threshold that was set up
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Another Q from the crowdcast Q&A: Can some uncorrelated inputs generate correlated outputs? If yes, how?
My related Q: When can output correlation become larger than output correlation?
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What is point process dedicated to spike train and gamma process for refractoriness ? Whats the purpose and significance of it?
Difficult to answer. You should really look into the paper by La Rocha (it was referenced in the tutorial). But intuitively (also being at the risk of being wrong in an attempt to make it intuitive), think of it like this: spikes are elicited when there are large enough fluctuations in the input. Some of these fluctuations will be common (due to input correlations). By varying the size (not number) of fluctuations in both side (not by increasing the input correlations) you increase the probability that the neuron will spike when those common fluctuations occur.
Same way we can imagine that increasing the mean will bring the common fluctuation closer to the threshold.
But of course these changes will also affect other uncorrelated fluctuations (thats why this simple way of thinking is not completely correct).
Mathematically speaking, output correlation in proportional to the input variance and the slope of the F-I curve of the neuron. Mean input determines where exactly we are operating on the F-I curve. But please look into the paper by La Rocha.
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Can uncorrelated inputs generate correlated output – NO.
But output correlation can be bigger than input corr. Spike threshold means that beyond a certain input correlation output correlation will be always 1. In the tutorials we kept the weight low so you perhaps did not see that. A nice example of such increase in correlation is the SYNFIRE CHAIN.
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One can use Poisson process with dead time to model spike trains with refractoriness.
We figured that the red trace showed the timecourse of the membrane potential, assuming no spiking mechanisms existed - assuming that the membrane dynamics are always described by the differential equation, instead of spiking and resetting when a threshold is reached. So this is the one we concentrate on in this exercise.
The blue trace is neuron as usual.
maybe not a ‘technical’ question, but after finishing the outro video (specifically the plots around 28:30) I am left wondering why nonlinear integration is so much more efficient than linear processes. Is it because nonlinear transformations allow you to compress information into a smaller space than possible with simply linear transformations?
The idea of free membrane potential (FMP) is a an abstract one. But it makes a lot of sense for mathematical analysis. The FMP distribution gives you an idea of what is the distribution of input current to the neuron. Knowing the area of the FMP distribution above the spike threshold give a fairly good estimate of the firing rate of the neuron. Also provides a good heuristics whether the neuron will spike in a regular or irregular way.
So that was the reason to show you the FMP trace.
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