[Comp-neuro] "realistic models"
G. Bard Ermentrout
bard at math.pitt.edu
Sun Aug 17 15:30:23 CEST 2008
Carson Chow, a former colleague, has an interesting summary of this
doscussion on
sciencehouse.blogspot.com
- Years ago Carson and I would go to neuro lectures (which I generally
find far more accessible than math colloquia - and I am a professional
mathematician! - which speaks on the issue that I think it is far easier
form a mathematician to gain an appreciation for biology than vice versa,
but I digress) and there were a number on the complex channels found in
dendrites which from an evolutionary point of view, must be quite costly.
However, in almost all the cases, the final point of the speaker was that
this was to compensate fro being out at the end of the dendrite, so that
we used to say that nature is trying to make all neurons point neurons.
Computationally, we can put as many inputs as we want into a point - but
anatomy and physiology prevent this in real cells, hence the complex
structure.
- This leads to a second point - the neural turing test. (There have been
contests related to this). I recently heard Eugene Izhikevich give a talk
and he showed a picture of a recording froma cortical pyramidal cell
receiving a complex stimulus pattern (whatever that means, Jim) and his
2 variable 4 parameter model - the sub and super threshold behavior was
almost indistinguishable and this model was fit for the FI curve only. I
realize that the pyramidal cell stimulus was quite simplistic, but one
could presumably do the same stim mixed with other stimuli in the
dendrites. maybe there are complex dendritic calculations going on - but
the bottom line is what is the output of the cell - that is all that
matters. So any model that does this in a reasonable way will, to me, be a
realistic model since the cell on the other side of the wall cannot
distinguish it. I would guess that Jim Bower would claim there is no such
model that does this except the most delatiled model with all the channels
and structure. However, I am less pessimistic about this for the following
reason:
-Yannis Kevrikides has deveolped some very useful numerical tools that
exploit a common freature in many complex physical and biological systems
(here, I am a strong reductionist and believe with every fiber of my body
that biology is describable by physical pronciples - I lost all shreds of
mysticism in Nov 1969 - although I continued to exploit others making
money casting horoscopes - a mathematical exercise, in fact)
basically, most systems, even complex ones, behave in such a manner as to
drastically reduce dimensionality. They are strongly contracting or
dissipative and as a consequence, are captured by far fewer degrees of
freedom. Kevrikides methods allow one to compute in these lower degrees
without knowing the underlying reduced equations. Nevertheless, they are
there. Mathematicians and physicists have used these ideas for years and
call it averaging, mean field reduction, etc and of course
experimentalists do use these ideas as well and call it PCA in which they
show that only a few modes capture the majority of the variance. Thus, the
Turing test neuron is not pie in the sky and I believe that there are
reduced models that will do what the "realistic" model does with as much
precision as you would like.
Regards
Bard Ermentrout
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