An Application of Abstract Algebra to the Neural Code for Sound Localization in the Barn Owl

Abstract

Patterns of neural firing can be viewed as a binary code with each neuron as a bit, with neurons which actively fire in response to a stimulus associated to a 1 and those which do not fire associated to a 0. In previous work, Curto et al. demonstrate that by studying the neural code as a ring, information can be recovered about the ways the regions over which the different neurons fire intersect as well as the convexity of these regions. In this work, these ideas are applied to the system of sound localization in the owl. One of the properties of the sound used to determine its location is the interaural time difference, which is represented in the nucleus laminaris when a neuron fires in response to being stimulated by signals coming from both ears at the same time. Though the signals arrive at the same time at the neuron, it is still ambiguous by how many periods the two sound waves differ, resulting in periodic firing in the columns of the nucleus laminaris and behavioral errors in the owl's response in locating the sound. Using the concepts from neural coding theory, it is demonstrated that neural codes with a perfectly patterned periodic form do not correspond to a set of convex sets, reflecting this ambiguity. It is further shown that by introducing stochasticity into these patterns, hence introducing new codewords, the new code may have a convex realization. This suggests that the stochastic nature of neural firing may be necessary for disambiguating stimuli.