MATH CLUB Off on a Tangent The AU Math Club and the Division of Mathematics present APPLICATION OF TUNING CURVES IN NEUROSCIENCE By AU student TYLER COYE Wednesday, November 17, 2010 12:20 – 1:10 p.m. Myers Hall, Room 228 Pizza and soda will be served. All are welcome. Abstract. “Neurons are remarkable among the cells of the body in their ability to propagate signals over large distances. They do this by generating characteristic electrical impulses called action potentials or, more simply, spikes that can travel down nerve fibers. Neurons represent and transmit information by firing sequences of spikes in various temporal patterns.” – Theoretical Neuroscience (Dayan & Abbot, p.3) The present discussion hopes to demonstrate and discuss the importance of applied mathematics in the understanding of the stimulus-response duality. More specifically we will discuss how tuning curves are used to model neuronal response (spike) patterns. A tuning curve is a curve which describes how neurons respond to stimuli in terms of values. We will introduce the application of Gaussian, cosine and sigmoidal tuning curves by mapping each to a set of data points gathered from neural responses in the motor and visual cortex of cats and monkeys. Finally, we will end our discussion with a mathematical description of stimuli found in and extending from Weber’s law and Fechner’s law.