  Information processing in certain neuronal networks in the brain can be
considered as a map of binary vectors, where ones (spikes) and zeros (no
spikes) of input neurons are transformed into spikes and no spikes of output
neurons. A simple but fundamental characteristic of such a map is how it
transforms distances between input vectors. In particular what is the mean
distance between output vectors given certain distance between input vectors?
Using combinatorial approach we found an exact solution to this problem for
networks of perceptrons with binary weights. he resulting formulas allow for
precise analysis how network connectivity and neuronal excitability affect the
transformation of distances between the vectors of neuronal spiking. As an
application, we considered a simple network model of information processing in
the hippocampus, a brain area critically implicated in learning and memory, and
found a combination of parameters for which the output neurons discriminated
similar and distinct inputs most effectively. A decrease of threshold values of
the output neurons, which in biological networks may be associated with
decreased inhibition, impaired optimality of discrimination.
