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.