  We introduce and study an artificial neural network, inspired by the
probabilistic Receptor Affinity Distribution model of olfaction. Our system
consists on N sensory neurons whose outputs converge on a single processing
linear threshold element. The system's aim is to model discrimination of a
single target odorant from a large number p of background odorants, within a
range of odorant concentrations. We show that this is possible provided p does
not exceed a critical value p_c, and calculate the critical capacity \alpha_c =
p_c/N. The critical capacity depends on the range of concentrations in which
the discrimination is to be accomplished. If the olfactory bulb may be thought
of as a collection of such processing elements, each responsible for the
discrimination of a single odorant, our study provides a quantitative analysis
of the potential computational properties of the olfactory bulb. The
mathematical formulation of the problem we consider is one of determining the
capacity for linear separability of continuous curves, embedded in a large
dimensional space. This is accomplished here by a numerical study, using a
method that signals whether the discrimination task is realizable or not,
together with a finite size scaling analysis.
