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Mathematical Sciences

Student Research Presentations

Date: 3:30pm PDT September 13, 2011 Location: Howard Hall, Room 244

Howard Hall, Room 244

Presentations by Buck Fisk, Alison Fankhauser, Jenny Louthan about their summer research.

Modeling Learning in the Zebra Finch

Presented by Buck Fisk (’12)

Sequences of neural spiking underlie song production in the brain of the Zebra Finch. A recent com-putational model of the pre-motor nucleus HVC uses a binary neural network to implement biologically based neural response and learning that apparently gives rise to a permutation matrix in the space of synaptic weights. This presentation provides insight in a model that predicts the distribution of lengths of firing sequences in the binary neural network.

Numerical Evolution of Reaction-Diffusion Equations Arising in Chemistry

Presented by Allison Fankhauser (‘12) and Jenny Louthan (‘13)

The Belousov-Zhabotinsky (BZ) reaction is a chemical reaction in which intermediate concentrations oscillate repeatedly instead of immediately tending toward equilibrium. We make use of the Oregonator model of the Field-Körös-Noyes mechanism to model the unusual behavior of this reaction in two-dimensional space by combining ordinary differential equations (ODEs) to represent the reaction and partial differential equations (PDEs) to represent the diffusion components of the process. We apply numerical methods to examine the oscillatory behavior in the ODE case and the effects of diffusion on oscillatory reactions in the PDE case. We find traveling wave solutions present in the PDE system arising from Murray’s model. We also examine the model of Field and Noyes—which is more sensitive to numerical error—and obtain a stable simulation for the ODE case.