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Computational Capacity of an Odorant Discriminator: The Linear Separability of Curves

nestor{at}if.usp.br, Instituto de Física, Universidade de São Paulo, CEP 05315-970, São Paulo, SP, Brazil

J. E. Palo Tejada

debianaqp{at}terra.com, Instituto de Física, Universidade de São Paulo, CEP 05315-970, São Paulo, SP, Brazil

D. Lancet

Doron.Lancet{at}weizmann.ac.il, Department of Membrane Research and Biophysics, Weizmann Institute of Science, Rehovot 76100, Israel

E. Domany

eytan.domany{at}weizmann.ac.il, Department of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel

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_c and calculate the critical capacity _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, together with a finite-size scaling analysis.

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