The Operation of Memory Systems in the Brain - Computational Neuroscience: A Comprehensive Approach - page 512

modelled the experiments by giving the order parameters the following dynamics:

m a

t = − ∂ F

x a

t = − ∂ F

; . (16.14)

m a x a

These dynamics ensure that the stationary solutions, corresponding to the values
of the order parameters at the attractors, correspond also to minima of the free en-
ergy, and that, as the system evolves, the free energy is always minimized through its
gradient. The time constant of the macroscopical dynamics was chosen to be equal
to the time constant of the individual neurons, which reflects the assumption that
neurons operate in parallel. Equations (16.14) were solved by a simple discretizing
procedure (first order Runge-Kutta method). An appropriate value for the time in-
terval corresponding to one computer iteration was found to be

τ / 10 and the time

constant has been given the value 10 ms .

Since not all neurons in the network receive the same inputs, not all of them be-
have in the same way, i.e., have the same firing rates. In fact, the neurons in each
of the modules can be split into different sub-populations according to their state of
activity in each of the stored patterns. The mean firing rate of the neurons in each
sub-population depends on the particular state realized by the network (characterized
by the values of the order parameters). Associated with each pattern there are two
large sub-populations denoted as foreground (all active neurons) and background (all
inactive neurons) for that pattern. The overlap with a given pattern can be expressed
as the difference between the mean firing rate of the neurons in its foreground and
its background. The average was calculated over all other sub-populations to which
each neuron in the foreground (background) belonged to, where the probability of a
given sub-population is equal to the fraction of neurons in the module belonging to
it (determined by the probability distribution of the stored patterns as given above).
This partition of the neurons into sub-populations is appealing since, in neurophysi-
ological experiments, cells are usually classified in terms of their response properties
to a set of fixed stimuli, i.e., whether each stimulus is effective or ineffective in driv-
ing their response.
The modelling of the different experiments proceeded according to the macro-
scopic dynamics (16.14), where each stimulus was implemented as an extra current
into free energy for a desired period of time.
Using this model, results of the type described in Section 16.3.1 were found [67,
70]. The paper by [67] extended the earlier findings of [70] to integrate-and-fire
neurons, and it is results from the integrate-and-fire simulations that are shown in
Figures 16.10 and 16.11.

τ =

16.3.3 Computational necessity for a separate, prefrontal cortex, short-

term memory system

This approach emphasizes that in order to provide a good brain lesion test of pre-
frontal cortex short-term memory functions, the task set should require a short-term
memory for stimuli over an interval in which other stimuli are being processed, be-