2007-2008
Compact Courses
SPIKING NEURONS TO BEHAVIOR:
Dynamical Systems, the neuromechanics of animal locomotion and models of
decision making
by
Prof. Philip Holmes
Program in Applied and Computational Mathematics and Department of
Mechanical and Aerospace Engineering, Princeton University
4.00 pm - 5.15 pm
on Monday, Tuesday and Thursday
December 17, 18 and 20, 2007
(starting on December 17, 2007)
2.30pm - 3.30 pm
on Wednesday, December 19, 2007
at
L H � 3, Department of Mathematics
Indian Institute of Science, Bangalore
Abstract
I will describe how ideas and methods from the theories of deterministic and stochastic dynamical systems can be used to model and analyze the behaviors of running and thinking animals (including humans). I will show that simple energy-conserving mechanical models possess stable gaits similar to those seen in rapid running from insects to humans, and thoserealistic models of neural pattern generators and muscles can be added to such models, allowing the study of neural feedback. I will also show that one dimensional drift-diffusion processes can describe the accumulation of evidence in cortical areas during decision making. This permits explicit analyses of optimal decision strategies, to which human and animal behaviors can be compared. Throughout, I will emphasise how simple models can help reveal the dynamics of complex phenomena, and even provide partial explanations of them.
Background can be found in two extensive review articles:
P. Holmes, R.J. Full, D. Koditschek and J. Guckenheimer. The dynamics of legged locomotion: Models, analyses, and challenges. SIAM Review 48(2): 207-304, 2006.}
R. Bogacz, E. Shea-Brown, J. Moehlis, P. Holmes and J.D. Cohen. The physics of optimal decision making: A formal analysis of models of performance in two-alternative forced choice tasks. Psychological. Reveview 113(4): 700-765, 2006.
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