Information Technology Reference
In-Depth Information
Figure 2.10.
The complex pattern of the neuronal web is seen to interleave the brain mass and interconnect
spatially distant regions of the brain.
regular. However, most biological networks, and many physical ones, are discontinu-
ous, inhomogeneous and irregular and are necessarily that way in order to perform a
particular function, such as gas exchange in lungs and arteries.
The branching trees of neurons such as those depicted in Figure 2.10 interleave the
brain and form the communication web within the body. In the neurophysiology lit-
erature the radius of the branches from one bifurcation to the next was given in 1959
by Rall's law [ 61 ], where
5. In this case the ratio of the number of branches in
successive generations is given by
α =
1
.
N n
N n + 1 =
2 1
R
=
(2.23)
independently of branching number. More recent measurements of the scaling index,
at each generation of dendritic branching, revealed a change with generation number,
that is, the single ratio parameter R discussed in the previous section is replaced with
a parameter that is dependent on generation number. This non-constant ratio coefficient
implies that Thompson's principle of similitude is violated.
The dendrite branches of a neuron can take weeks to grow under the best of condi-
tions, and the spatial scales are millimeters to meters in length. These space and time
scales can be compared with the hundreds of meters or kilometers of the lightning bolt or
river bed. However, even with the differences in the space and time scales the structures
are remarkably similar to one another.
It is reasonable to point out that classical scaling disregards the irregular surfaces
and structures seen in the heart, intestine and brain and the corresponding time series
generated by their dynamics. The classical approach relies on the assumption that the
processes of interest, whether biological, social or physical, are continuous, homoge-
neous and regular. It is quite remarkable then that this assumption that is so often made
is very quickly shown by experiment and observation to be invalid. Most complex webs
 
Search WWH ::




Custom Search