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Fig. 4.11 Pozin (a) and
Grossberg (b) neural
networks
The main result obtained in these investigations was that a rectangular pulse
could be sharpened or broadened, or a contour of the signal could be enhanced
depending on the shape of the coupling function F ( p i ). Numerical simulation of
these effects performed using the technique of Pozin is shown in Fig. 4.12 . Con-
volution integrals of the rectangular distribution with the coupling function were
computed, with the latter approximated by the expression:
:
x 2
x 2
gx
ðÞ ¼
A 1exp
=
B 1
A 2exp
=
B 2
Constants A 1, A 2, B 1, B 2 are shown in Fig. 4.12 .
In the end of the 1960s of the last century, American mathematician Stephen
Grossberg began a series of studies on neural networks essentially similar to Pozin
networks.
In order to explain the mechanisms of information processing by visual cortex,
Stephen Grossberg proposed the concept of specialized neural networks, incorpo-
rating particular features of visual fields.
Based on psychobiological and neurobiological data, Grossberg concluded that
neural networks with a central activation and lateral inhibition (Fig. 4.11 ) can be
used to interpret a variety of phenomena of human vision, including optical
illusions. Neural networks of this type are described by kinetic equations:
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