**UBC Mathematics Department**

*http://www.math.ubc.ca*

## Colloquium Abstract: Dr. Andre Longtin,
Dept. of Physics, Univ. of Ottawa

*Biological Point Processes: Assessing Determinism and Validating Models
*

Nerve cell firings, cell division and epileptic seizures are examples of
``events'' in the time evolution of the corresponding biological systems.
The characterization of interevent interval sequences using nonlinear
dynamical rather than statistical methods is of interest when one suspects a
strong deterministic component in the underlying dynamics. In this talk I
will discuss results of applying dynamical methods to interval sequences
from experimental and model neural systems.

The first example involves intervals measured from mammalian cold receptors.
The goal is to elucidate the nature of the cellular dynamics giving rise to
specific firing patterns at different temperatures. We study this problem
using biophysically motivated nonlinear dynamical models, with and without
stochastic inputs. Combined with nonlinear prediction techniques, our
analysis points to noise-induced firing as the main source of aperiodicity.
The second example analyzes the nonlinear dynamical information which can
``in principle'' be extracted from interval sequences. Specifically,
conditions are given under which the properties of a chaotic input to a
neuron are detectable in the output interval sequence.

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