Clas Blomberg - Physics of life-Elsevier Science (2007)

Chapter 29. Noise and non-linear phenomena 311
Figure 29.1 Due to irregular processes in the brain, a picture of a cube like this seems to oscillate
between two forms, characterised by which surface is the forward one.
one of the wells depending on where it started. With noise, fluctuations, on the other hand,
a particle would with a relatively small probability cross the barrier. This would be the case for
any model with several stable states, separated by some kind of threshold regions. Typically,
the time course would be such that they start close to one such state, vary around that, irregularly
for some time, then, suddenly move over a threshold to a new state, stay there for some
time, and then again move back or to another state. There may be several states of that kind.
It is feasible that neural networks, artificial ones but also real ones can show that kind of
behaviour. Signals in the networks may go towards some stable states which might be identified
with some kind of recognised pattern, then go away and find another related pattern.
Signals may move from pattern to pattern. This is fully consistent with the well-known
oscillating interpretation of certain pictures, we see them for some time in one particular way,
then suddenly, that is changed and we interpret them in a new way. A cube like the one below
which, when one looks at it oscillates between two states is among the most typical examples,
but there are numerous ones (Figure 29.1).
What is advantageous? To have a sensitive system with clear thresholds and clear transitions
or the noisy one with softer, sometimes completely in distinct transitions? Probably both features
are relevant in biological systems. There are certainly cases, where there should be possibilities
of different types of behaviour triggered by some kind of influence. An external
influence shall cause a response only if it passes a certain threshold. In such cases, noise is a disadvantage,
and its effects should be avoided. If the cell shall make a certain task, it shall do that
and not be influenced by any effects that may change the result. On the other hand, noise effects
are always there. What can they do? Can they trigger unwanted effects if they cause the system
to pass thresholds and provide unwanted behaviour? Certainly, this is a very relevant question.
Stochastic effects have been studied in regulatory networks, see e.g. Paulsson and Ehrenberg
(2001), Paulsson (2005), and many studies have taken up noise and general stochastic
processes in the brain. See, e.g. Holden (1976), Buchman and Schulete (1987), Liljenström
(1996), Liljenström and Århem (1997), Tuckwell (1989), Århem (2000) as well as the articles
in the book edited by Århem et al. (2000).
29B
Stochastic resonance
Stochastic resonance was treated above with a Brownian motion kind of method. There are
several variants of that scheme, which means that noise in some way triggers oscillations