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which can be solved if the time course of the activity of
S
i
is known. This,
however, may depend on the state of elements acting upon
e
i
, which in turn
may depend on states of elements acting upon those, etc. If we consider
such a hierarchy of
k
levels we may eventually get:
d
d
S
t
j
[
[
[
(
)
]
]
]
=
FYY
...
St kt
-
D
,
ij
hi
gh
o
which is clearly a mess. Nevertheless, there are methods of solving this tele-
scopic set of equations under certain simplifying assumptions, the most
popular one being the assumption of linear dependencies.
This brief excursion into the conceptual machinery that permit us to
manipulate the various states of individual elements was undertaken solely
for the purpose of showing the close interdependence of the concepts of
“active connection” and “elements”. A crucial role in this analysis is played
by the time interval D
t
within which we expected some changes to take place
in the reacting element as a consequence of some states of the acting
element. Clearly, if we enlarge this time interval, say, to 2D
t
,3D
t
,4D
t
,...we
shall catch more and more elements in a network which may eventually
contribute to some changes of our element. This observation permits us to
define “action neighbours” of the
k
th order, irrespective of their topo-
graphical neighborhood. Hence, in
e
j
we simply have an action neighbor of
k
th order for
e
i
if at least one of the states of
e
j
at time
t
-
k
D
t
causes a state
transition in
e
i
at time
t
.
With these remarks about networks in general we are sufficiently pre-
pared to deal with some structural properties of the networks whose
operations we wish to discuss in our third chapter. In our outline of the
structural skeleton of networks we kept abstract the two concepts
“element” and “agent”, for which we carefully avoided reference to con-
crete entities. However, the abstract framework of the interplay of these
concepts permits us to interpret them according to our needs, taking for
instance, “general receptors” for receptors proper (e.g., cones, rods, outer
hair cells, Meissner's corpuscles, Krause's end-bulbs, Merkel's discs; or
for intermediate relays receiving afferent information, bipolar cells, cells of
the cochlear nucleus, or for cells in various cortical layers). “General effec-
tors” may be interpreted as effectors proper (e.g., muscle fibers), and
also as glia cells, which act in one way on neurons but in another way on
each other.
Furthermore, we are free to interpret “agent” in a variety of ways, for
instance, as a single volley on a neuron, as a pulse frequency, as a single
burst of pulses, as pressure, as light intensity. This freedom is necessary,
because in some instances we do not yet know precisely which physical
property causes the change of state in some elements, nevertheless, we
know which element causes this state change. A commitment to a particu-
lar interpretation would favor a particular hypothesis, and would thus mar
the general applicability of our concepts.
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