Information Technology Reference
In-Depth Information
1
0.5
3
2.5
1
1.5
2
μ
S
2
μ
P
1.5
2.5
1
3
Figure 7.10.
The asymptotic limit of the cross-correlation function, on the vertical axis, is displayed for the
range of power-law indices 1
<μ
P
,
S
<
3. The vertex
μ
S
=
μ
P
=
2 marks the transition from
the minimum to a condition of maximal input-output correlation. Adapted from [
6
].
correlated; that is, the cross-correlation function has the value one. This is the upper
plateau region of the cross-correlation cube in Figure
7.10
. If, on the other hand, web P is
ergodic, meaning that 2
2,
the cross-correlation of the two signals is zero. This is the lower plateau region of the
cross-correlation cube. The general argument for the shape of the cross-correlation cube
is given in full detail elsewhere [
6
,
68
].
This description of the perturbation and response of interacting complex webs sug-
gests what happens during dishabituation. The simple stimulus used in this section is
analogous to the ergodic perturbation and the effective synaptic weight is analogous
to the non-ergodic response, yielding an asymptotic response in the lower plateau.
The near-zero habituated response to the ergodic perturbation jumps to full strength,
the upper plateau, when a disruptive non-ergodic short-time perturbation is turned on.
This resetting of the effective synaptic weight is followed by the continuing ergodic
perturbation and the subsequent habituation of the revitalized effective synaptic weight.
<μ
P
<
3, and web S is non-ergodic, meaning that 1
<μ
S
<
7.4.3
Discussion
From the above arguments we see that aging, an unavoidable consequence of the event
probability density not having a finite average waiting time, that is,
2, has the effect
of suppressing the asymptotic response of the complex network of neurons to coherent
perturbations and consequently yields a habituated response. The intuitive explanation
of this effect is that a complex web, one described by a hyperbolic distribution such
as the neural web, generates signals through the interaction of many distinct neurons.
These neurons without characteristic frequencies are coupled by nonlinear interactions
that inhibit the formation of normal modes that would facilitate information transfer
μ<
