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

346 Part VIII. Applications
The next important stage appears when a pulse reaches a connection to another nerve
cell, a synapse. There, the electric pulse is converted to a chemical pulse which is transferred
to the neighbouring synapse. In this, also calcium ions are involved. At the synapse,
the electric ion pulse is converted to a chemical signal that influences an adjacent neuron
cell. It may give rise to an electric pulse in the new cell by, for instance opening of sodium
channels. In other synapses, the influence may be the opposite, a signal can inhibit activity
in the adjacent neuron.
What happens in a cell depends on the combined action of connecting synapses, taking
into account excitatory and inhibitory tendencies with varying strengths. This is the basis
for models of neural networks. There nerve cells are considered as parts in a network connected
to other cells via excitatory and inhibitory synapses. An excitation in one cell can
generate new excitations (nerve signals in the connected cells by excitatory synapses and
absence of inhibitory ones). The inhibitory synapses are crucial to prevent exited nerve
pulses to spread over all nerve cells.
In the model neural network, the nerve cells are centres which are excited, with moving
pulses of the described type or silent, resting. These influence other cells by the synapses
of different characters and different strengths, and thus excite new cells or prevent excitation.
It is common here to regard the cells of various types in different layers to produce
certain propagation of excitation in the network. In that way, new cells (centres are excited,
and also inhibited), eventually lead to a stationary pattern where cells cannot excite or
inhibit further cells (Wilson and Cowan, 1972).
A common view is that such a resulting stationary pattern of excited cells can be apprehended
as “memories” of a certain stimulus, a basic input as pulse generation of certain cells.
Such a pattern can be generated again by the same or a very similar stimulus—in order to
retrieve a certain memory, all details must not be present. By slower connections patterns of
this kind can be further transferred and associated with other memory patterns—there is a
kind of associative network (Kohonen, 1987, Kleinfeld, D. and Sompolinsky, H., 1989).
The common view is also that here is a mechanism, that the network when influenced by
various stimuli can modify the synapse strengths in order to provide stronger stationary patterns,
stronger possible memories. These modifications of the synapses are then considered
as parts of a “learning” procedure, a way to “learn the system features of an original stimulus
and to provide stronger and more easily retrieved memories” (Levy and Steward, 1979).
The number of possible “memories” in this kind of network is much larger than the number
of network centres, of nerve cells. And as the number of cells in the brain is very large
and further the number of synapses, connections of each cell also is large, the possibilities
of a neural network are very large (Levy, 1985, Alexander and Moron, 1991).
32B
Spin-glass analogy
Hopfield (1982) described an interesting analogy to a kind of magnetic model, the spinglass
model, in order to accomplish a basis for the characterisation of a neural network.
Although not really correct in its details, this work opened, in particular among physicists,
important parts of this field and clarified basic concepts. See, e.g. the book on spin glasses
and applications by Mezard et al. (1987).