Zipf's law and cortical areas

Darragh Smyth smyth at zorro
Tue Aug 15 11:22:03 EST 1995


doug fitzpatrick writes:
 
> My question is: what is the relationship between the size of the cortex 
> as a whole and the distribution of size of functional areas?  Can it be 
> expected to follow Zipf's law*?

My understanding was that different functional areas will vary in size and
relative size across species, depending on how important they're for that
species. Different species will use different sensory modalities as their
prime source of information and so this is likely to maybe affect their
relative sizes. Someone please holler if I am wrong on this.

> This question is prompted by the following.  I study the mustached bat 
> auditory cortex, which is quite small (about 13 sq mm).  Despite its 
> size, it contains more thandiscrete areas, some of them specialized 
> to process biosonar signals.  I have evidence from corticocortical 
> connections for a columnar organization in this cortex (i.e., labeled 
> patches about 0.5 mm wide).  However, some of the areas are so small 
> that they may be composed of as few as 1 column.

Do you know whether these areas are close or far from the auditory
stimuli? I know nothing about auditory cortex but in the language of
visual cortex, how do you know that you are not just seeing a column
responding to a particular orientation in a particular position of the
retinal image, rather than a complex object cell?

> I therefore wonder, do the larger cortices of more commonly studied 
> animals contain extremely small areas that process some specific signal 
> attribute?  If so, the potential for a very large number of areas would 
> exist.

I think face recognition is probably an example here in humans. I believe
the relative area is quite small from studies of brain damaged patients.
I reckon there probably is a large number of areas that do specialize in
particular types of tasks. Of course whether it goes all the way to a 
full blown grandmother theory, nobody knows? Cells in higher areas do
have specialized functions, but we also know they are probably not
unique. How we find out if the columns are unique is another days work!

> Yet, it is clear that in larger brains there are some areas that are 
> large, much larger than any in the mustached bat.  If the size of the  
> largest areas scaled with brain and body size, while the size of the 
> smallest areas stayed constant at one or a few columns, could 
> predictions be made about how many areas are likely to exist as a 
> function of brain size? Has this been done? 

The number of specialized areas will also depend on the cognitive or
sensorimotor capabilities of the creature. Maybe there are animals with
large brains but not much power. I don't know, any answers to that one?
There are other factors such as connectivity complexity which control
how many areas there were.
 
> *  As I understand it, Zipfs law is a purely empirical observation that 
> many things in biological systems scale according to the rule that as 
> larger maximum values occur then more and more intermediate and small 
> values also arise, to fill in the distribution.  Is this description 
> close?  Are there equations with parameters?

Is this the law they apply to the distribution of word usage in language
or something like that?

ok, that was my penny's worth, sorry for no knowledge of Zipf's applications.


Darragh

--
Darragh Smyth               smyth at informatik.uni-leipzig.de
Institut fur Informatik,    http://www.informatik.uni-leipzig.de/~smyth/
Universitat Leipzig,        voice : +49-341-97-32242 
Pf. 920, Leipzig 04009,     fax   : +49-341-97-32209
Germany.

``Each of us is sometimes a cretin, a fool, a moron or a lunatic.
  A normal person is just a reasonable mix of the these components.''
  (Umberto Eco, Foucault's Pendulum)
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