TITLE:

SYMMETRY IN COMPLEX SYSTEMS

DATE:

Friday, February 13th, 2009

TIME:

3:30 PM

LOCATION:

GMCS 214

SPEAKER:

Antonio Palacios, Professor, Nonlinear Dynamical Systems Group, Department of Mathematics and Statistics, San Diego State University

ABSTRACT:

Many sensory systems in animals are controlled by clusters of neuron cells physically interconnected to produce, somehow, an optimal response, which in many cases outperforms those of humans. A dog’s sense of smell is said to be a thousand times more sensitive than that of humans, thanks to the collective behavior of more than 220 olfactory receptor cells in its nose, while Sharks can sense extremely weak electric fields due to the collective output of thousands of specialized detectors in their snouts called ampullae of Lorenzini. In this talk, we will describe how we are trying to harness the optimality features of complex biological networks to develop nonlinear sensory devices. In particular, we wills discuss the realization of a√É¬Ç network for detecting weak electric-field signals and a network of gyroscopes for navigation systems.

A general approach for the analysis has been to derive a detailed model of the individual parts, connect the parts and note that the system contains some sort of symmetry, then attempt to exploit this symmetry in order to simplify numerical computations. This approach can result in very complicated models that are difficult to analyze even numerically. As an alternative approach, we use the symmetry of the system directly to formulate the appropriate models, and predict behavior without simulations.

HOST:

Jose Castillo

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