## SCIENTIFIC ORGANIZERS

S. Coombes (Nottingham)

A. Longtin (Ottawa)

J. Rubin (Pittsburgh)

Thematic Semester on

Applied Dynamical Systems

June-December 2007

and the Center for Neural Dynamics, University of Ottawa

The goal of this workshop is to provide an overview of the current state of research in mathematical approaches to neuroscience. This vibrant area, seeded by successes in understanding nerve action potentials, dendritic processing, and the neural basis of EEG, has moved on to encompass increasingly sophisticated tools of modern applied mathematics. Included among these are Evans functions techniques for studying wave stability and bifurcation in tissue level models of synaptic and EEG activity, heteroclinic cycling in theories of olfactory coding, the use of geometric singular perturbation theory in understanding rhythmogenesis, stochastic differential equations describing inherent sources of neuronal noise, spike-density approaches to modelling network evolution, weakly nonlinear analysis of pattern formation, and the role of canards in organising neural dynamics. Importantly the workshop will also address the novel application of such techniques in two half-day sessions, one on audition and the other on Parkinsonian tremor and deep brain stimulation. Hence, participants will be drawn from both the mathematical and experimental sciences. ## Mathematics of Parkinson's Disease and deep brain stimulationParkinson's disease (PD) is a well known degenerative disorder characterized primarily by motor manifestations, such as muscle rigidity, slowing or loss of movement, and resting tremor. While it is known that parkinsonism results from the degeneration of neurons that supply the brain with dopamine, surprisingly little else about PD has been firmly characterized, such that experimental investigation relating to PD remains a very active area of research. ## Mathematics of HearingThe auditory system has attracted the attention of mathematical modelers for over four decades. The availability of much experimental data from a number of species (cat, gerbils, monkey etc...) and the ability to control the inputs to the auditory systems has made it very exciting to model. Consequently there has been a strong interaction between experiment and theory. Another reason for the attraction of this system is the wealth of new data on humans following cochlear implant procedures, where nerves are directly stimulated by electrodes receiving acoustic signals that have been processed by “mathematical algorithms”. |