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From: Osher Doctorow on 16 May 2010 10:51
From Osher Doctorow

The remarkable relationship between expansive-contractive properties
of the Universe and biological properties, partially noticed by
Schrodinger, has been made more precise for the enhancement of visual
perception by Ajanta Kundu and Sandip Sarkar of Saha Institute of
Nuclear Physics Kolkata India, in "Can Centre Surround Model Explain
the Enhancement of Visual Perception Through Stochastic Resonance?",
arXiv: 1005.1830 [physics.comp-ph, q-bio.NC] May 2010.

As with our equation of Section 395:

1) y = y(0)[exp(kt) - exp(ku)]

for two-time expansion of the Universe (t, u being two independent
time dimensions), Kundu and Sarkar obtain a difference of exponentials
equation with t and u respectively replaced by:

2) -(x^2 + y^2)/((2sigma_1) ^2) and -(x^2 + y^2)/((2sigma_2) ^2)
respectively

with weighted respective prefactors of the exponentials being A1 and
A2 (presumably constants).

This process of Stochastic Resonance occurs in many physical and
biological systems including:

3) dithering systems
4) Schmitt trigger
5) ring laser
6) Cray fish mechanoreceptor
7) cricket
8) human vision

Stochastic Resonance is roughly adding external noise to a weak signal
which significantly enhances the performance of nonlinear signal
processing systems, especially when adding to a weak signal which
enhances its detect ability by peripherical nervous system.

The differs of Gaussians in (2), or DOG model, looks in resultant like
a Mexican hat in 2 dimensions and was modified by the authors to
accomodate the concept of narrow channels and extended classical
receptive field (ECRF) into:

9) -DOG(x, y) - m delta(x, y), where m is a constant factor and
delta(x, y) is 2-dimensional Dirac delta function.

The "Center Surround Model" involves "antagonistic" effects of
successive layers of cells which in the human retinal model looks
like:

10) PP --> BC --> GC --> Cortex, where PP are primary photoreceptors
(2-dimensional array), BC is a layer of bipolar cells, GC is a layer
of ganglion cells, and PP involve rods and cones information. The
Cortex gets the information through the visual pathway.

Notice that although (2) does not look as general as (1), the
different variances sigma_i ^2 for i = 1, 2 in fact yield spatial
analogs of t and u respectively with u < = t except that u is a
function of t for the proper choices of variances, and this can be
generalized to more general scenarios where u is not a function of t.
The x^2 + y^2 can also be related to t and u under various models,
although the authors do not do this.

Osher Doctorow

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