Vol. 15, No. 1, 2022

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Periodic neural codes and sound localization in barn owls

Lindsey S. Brown and Carina Curto

Vol. 15 (2022), No. 1, 1–37

Inspired by the sound localization system of the barn owl, we define a new class of neural codes, called periodic codes, and study their basic properties. Periodic codes are binary codes with a special patterned form that reflects the periodicity of the stimulus. Because these codes can be used by the owl to localize sounds within a convex set of angles, we investigate whether they are examples of convex codes, which have previously been studied for hippocampal place cells. We find that periodic codes are typically not convex, but can be completed to convex codes in the presence of noise. We introduce the convex closure and Hamming distance completion as ways of adding codewords to make a code convex, and describe the convex closure of a periodic code. We also find that the probability of the convex closure arising stochastically is greater for sparser codes. Finally, we provide an algebraic method using the neural ideal to detect if a code is periodic. We find that properties of periodic codes help to explain several aspects of the behavior observed in the sound localization system of the barn owl, including common errors in localizing pure tones.

neural coding, convex codes, periodic codes, sound localization, neural ideal
Mathematical Subject Classification 2010
Primary: 92B05
Secondary: 05E45
Received: 13 June 2019
Revised: 15 June 2021
Accepted: 19 July 2021
Published: 14 March 2022

Communicated by Kenneth S. Berenhaut
Lindsey S. Brown
Princeton Neuroscience Institute
Princeton University
Princeton, NJ
United States
Carina Curto
Department of Mathematics
The Pennsylvania State University
State College, PA
United States