A mathematical model for resolution enhancement in layered sensory systems

Abstract

Heiligenberg (1987) recently proposed a model to explain how the representation of a stimulus variable through an ordered array of broadly tuned receptors could allow a degree of stimulus resolution greatly exceeding the resolution of the individual receptors which make up the array. In his model, this “hyperacuity” is achieved by connecting the receptors to a higher level pool interneuron according to a linear synaptic weighting function. We have extended this model to the general case of arbitrary polynomial synaptic weighting functions, and showed that the response function of this higher level interneuron is a polynomial of the same order as the weighting function. We also proved that Hermite polynomials are eigen-functions of the system. Further, by allowing multiple interneurons in the higher level pool, each of which is connected to the receptors according to a different orthogonal weighting function, we demonstrated that extended stimulus functions can be represented with enhanced precision, rather than just the value of individual point stimuli. Finally, we suggest a solution to the problem of “edge effect” errors arising near the ends of finite receptor arrays.