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The following article is now available at <br>
<a
href="http://calabreselx.biology.emory.edu/andrey/pub/olypher_calabrese_07_jnphys_epub.pdf">http://calabreselx.biology.emory.edu/andrey/pub/olypher_calabrese_07_jnphys_epub.pdf</a>
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<a class="moz-txt-link-freetext"
href="http://www.cns.bu.edu/Profiles/Grossberg:"></a>Using constraints
on neuronal activity to reveal compensatory changes in neuronal
parameters.<br>
Andrey V. Olypher and Ronald L. Calabrese<br>
J Neurophysiol, 2007 (in press). <br>
<br>
ABSTRACT:
<br>
In this study, we developed a general description of parameter<sup> </sup>combinations
for which specified characteristics of neuronal<sup> </sup>or network
activity are constant. Our approach is based on<sup> </sup>the
implicit function theorem and is applicable to activity<sup> </sup>characteristics
which smoothly depend on parameters. Such smoothness<sup> </sup>is
often intrinsic to neuronal systems when they are in stable<sup> </sup>functional
states. The conclusions about how parameters compensate<sup> </sup>each
other, developed in this study, can thus be used even without<sup> </sup>regard
to the specific mathematical model describing a particular<sup> </sup>neuron
or neuronal network. We showed that near a generic point<sup> </sup>in
the parameter space there are infinitely many other points,<sup> </sup>or
parameter combinations, for which specified characteristics<sup> </sup>of
activity are the same as in the original point. These parameter<sup> </sup>combinations
form a smooth manifold. This manifold can be extended<sup> </sup>as
long as the gradients of characteristics are defined and<sup> </sup>independent.
All possible variations of parameters compensating<sup> </sup>each
other are simply all possible charts of the same manifold.<sup> </sup>
The number of compensating parameters (but not parameters themselves)<sup>
</sup>is fixed and equal to the number of the independent
characteristics<sup> </sup>maintained. The algorithm that we developed
shows how to find<sup> </sup>compensatory functional dependencies
between parameters numerically.<sup> </sup> Our method can be used in
the analysis of the homeostatic regulation,<sup> </sup>neuronal
database search, model tuning and other applications.<br>
<br>
<pre class="moz-signature" cols="72">--
Andrei Olifer (Andrey Olypher)
Biology Department
Emory University
1510 Clifton Rd
Atlanta, GA 30322
<a class="moz-txt-link-abbreviated" href="mailto:aolifer@emory.edu">aolifer@emory.edu</a>
tel: 404-727-4202
fax: 404-727-2880
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