  We present a complete mean field theory for a balanced state of a simple
model of an orientation hypercolumn. The theory is complemented by a
description of a numerical procedure for solving the mean-field equations
quantitatively. With our treatment, we can determine self-consistently both the
firing rates and the firing correlations, without being restricted to specific
neuron models. Here, we solve the analytically derived mean-field equations
numerically for integrate-and-fire neurons. Several known key properties of
orientation selective cortical neurons emerge naturally from the description:
Irregular firing with statistics close to -- but not restricted to -- Poisson
statistics; an almost linear gain function (firing frequency as a function of
stimulus contrast) of the neurons within the network; and a contrast-invariant
tuning width of the neuronal firing. We find that the irregularity in firing
depends sensitively on synaptic strengths. If Fano factors are bigger than 1,
then they are so for all stimulus orientations that elicit firing. We also find
that the tuning of the noise in the input current is the same as the tuning of
the external input, while that for the mean input current depends on both the
external input and the intracortical connectivity.
