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Nicholas Cain
Graduate Student
Address: University of Washington
Department of Applied Mathematics
Box 352420
Seattle, WA 98195-2420
USA
Phone: 206-685-9395 Fax: 206-685-1440 E-mail: nicain at amath washington edu
Office: Guggenheim Hall 407 (29)
Biographical Information
I was born in Fairbanks, Alaska, and moved to sunny Tacoma, WA at a young age. Many years went by, until I arrived at Davidson College in Carlotte, North Carolina, before I discovered the joys of mathematics and my life really began. As of March '09, I am a third-year graduate student in the Department of Applied Mathematics, at the University of Washington. You can find out more on Facebook, or just stop by Guggenheim and say hello!
Research Interests
My research focuses on modeling simple decision tasks in using a variety of mathematical techniques, ranging from bifurcation analysis of systems of ordinary differential equations, to analysis of stochastic systems using a variety of methods. In particular, my current research area involves neural integration and the drift-diffusion model (DDM). In the area of cognitive neuroscience, the drift-diffusion model (DDM) has been proposed for many years as a model to explain observations in the two-alternative forced-choice (2AFC) task. Implicit in this model is a neural mechanism implementing the mathematical operation of integration. I study some of the important challenges that must be overcome to implement such a model in the brain, some possible strategies that have recently been suggested in the literature, and the impact of these strategies on predictions from model.
Papers
- Brown G., Patterson, T., and Cain, N. The Devil in the Details:Non-convexities in Ecosystem Service Provision , Resources and Energy Economics, Publication Pending.
- Cain, N. Learning Mathematics with a Strip of Paper. , Math Horizons, Submitted.
Presentations
- Neural Integration and the DDM , SIAMUW Student Seminar, February 2009, University of Washington
- CMMI: Sequence Motif Recognition Using Artificial Neural Networks , Carolinas Mathematics Undergraduate Research Conference, March 2006, Furman University
- Sequence Motif Recognition in S. cerevisiae, Mathematical Association of America Southeast Section Meeting, April 2006, Auburn University
- On the Application of Neural Network Techniques to the Brachistochrone Problem , 3rd Annual Pacific-Coast Variational Conference, February 2007, University of Washington
- Honors Thesis Presentation/Defense , SIAMUW Student Seminar, May 2006, Davidson College
Honors and Awards
- VIGRE Fellowship, 2007-2008.
- GK-12 Fellowship, 2008-2009.
Teaching
- Current: GK-12 Fellow
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