Organizers:
Richard Zemel (Computing Science, Toronto),
Frances Skinner (Toronto Western Research and UT)
Randy McIntosh (Rotman Research Institute and UT)
Conversations over coffee gave rise to a small group in southern
Ontario with an interest in methods and problems in computational
neuroscience. The primary motivation is to exchange information
between experimentalists and computational modellers in order
to investigate how computational and mathematical approaches have
been-or could be-used to address critical issues in neuroscience.
The talks are either in tutorial style, geared to general scientists,
or more problem-oriented, where an issue is presented and the
floor is then opened for discussion on how to deal with the issue
(e.g., we have all this data from brain imaging; how do we characterize
the dynamics?).
Nov. 10, 2004 --10:00 am
Michael Breakspear
(School of Physics at the University of Sydney & Brain Dynamics
Centre at Westmead Hospital, Sydney, Australia)
http://www.brain-dynamics.net/about/personal/michael.php
Dynamics of a neural system with a multiscale architecture
The architecture of the brain is characterised by a modular
organization repeated across a hierarchy of spatial scales - neurons,
minicolumns, cortical columns, functional brain regions, etc.
It is important to consider that the processes governing neural
dynamics at any given scale are not only determined by the behaviour
of other neural structures at that scale, but also by the emergent
behaviour of smaller scales and the constraining influence of
activity at larger scales. In this paper, we introduce a theoretical
framework for neural systems in which the dynamicsare nested within
a multiscale architecture. In essence the dynamics at each scale
are determined by a coupled ensemble of nonlinear oscillators
which embody the principle scale-specific neurobiological processes.
The dynamics at larger scales are 'slaved' to the emergent behaviour
of smaller scales through a coupling function that depends on
a multiscale wavelet decomposition. The approach is first explicated
mathematically. Numerical examples are then given to illustrate
phenomena such as between-scale bifurcations and how synchronization
in small-scale structures influences the dynamics in larger structures
in an intuitive manner that cannot be captured by existing modelling
approaches.
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