Adelle Coster
School of Electrical Engineering, University of New South Wales,
Sydney, 2052, Australia
A Hamiltonian for the neural activity in an interconnected net was
developed (Cowan, 1970). This formed the basis for the statistical mechanics
of a biologically consistent neural net. This formulation included an analogue
to temperature for such a system. Here we report an investigation to explore
the thermodynamics of such a neural net.
The model simulated differs from the "spin-glass" models of neural networks (see for example Amit, 1989), in that the parameters of the neurons, such as the voltage across the neuronal membrane, are continuous (not just in one of two states). This seems to be more appropriate for modelling biological systems. The simulation developed for the "experiments" on the system was also based on a continuous time platform.
In this paper we present the results of the simulations performed to assess the validity of the basic statistical mechanics model and extensions which may be required for more generic systems.
Cowan, J.D., 1970, "A Statistical Mechanics of Nervous Activity", in Am. Math. Soc., Some Mathematical Questions in Biology, Providence, R.I., pp. 1-57
Kerner, E.H., 1972, "Gibbs Ensemble: Biological Ensemble", Gordon and Breach, NY
See also
Amit, D.J., 1989, "Modeling Brain Function The world of attractor neural networks", Cambridge University Press for references to the spin-glass statistical models for neural networks.