document: Computational capacity of an odorant discriminator : the linear separability of curves We introduce and study an artificial neural network inspired by the probabilistic receptor affinity distribution model of olfaction . Our system consists of 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/sub c / and calculate the critical capacity alpha c =p / sub 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 , together with a finite-size scaling analysis
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