Photo

D. Brian Walton

Assistant Professor
Department of Mathematics and Statistics
James Madison University

Address:
James Madison University
Department of Mathematics
MSC 1911
Harrisonburg VA 22807
Office:
 Roop 110
Hours: M 1-3 pm, T 11:30-1:30 pm, and W 1-2 pm or by appointment
Phone:
(540) 568-6387
Fax:
(540) 568-6857
E-Mail:
waltondb@jmu.edu

Quick Links

Here is a link to a PDF file containing the slides from my talk at JMM08: Biological Applications Illustrating Linear Algebra Concepts.
Here is a link to a PDF file to create a simple circular slide rule: Circular Slide Rule.
Here is a Java applet that finds all possible integer-valued solutions to the 24 Game: 24 Game Solver.

Current JMU Courses (Spring 2008): Course information is on Blackboard.

Previous JMU Courses

Research Interests:

Recent rapid advances in quantitative biology lead to the need for mathematically founded methods in analyzing these data and for models that predict behaviors. I am particularly interested in developing probabilistic models for experimental systems typically classified as biophysics, and more particularly, experiments relating to motor proteins. Such systems are fundamentally noisy because of thermal fluctuations, so that stochastic processes arise naturally in studying their behaviors.

One such motor protein, kinesin, is responsible for transporting essential cellular products that are stored in membrane-bound vesicles to distant regions of a cell. To do this, kinesin attaches to a microtubule and essentially walks along its lattice. Recent experiments allow biophysicists to track the progress of individual kinesin proteins as they walk along a microtubule by observing an attached microscopic sphere. I have developed a hidden Markov model filter for analyzing data coming from such experiments, working with biophysicist Koen Visscher to understand the biology and physics of the experiment properly.

Recently, I have begun considering another protein related to kinesin which is called mitotic centromere-associated kinesin (MCAK). Instead of transporting cargo along a microtubule, MCAK finds the ends of the microtubule and then proceeds to disassemble the microtubule. I am particularly interested in modeling how this protein reaches the microtubule ends and then how it contributes to the depolymerization of the microtubule.

Of course, other topics catch my attention. Working with Koen Visscher, I explored a topic referred to as "Noise Suppression by Noise" (Vilar and Rubi, Phys. Rev. Lett. 86, 950 (2001)). This has been typically regarded as an unintuitive phenomenon. Essentially, imagine an input/output device where the output is a function of the input but with additional noise, and where the size of the noise depends on the particular value of the input. Noise suppression says that the size of noise at the output can be reduced by increasing the fluctuations at the input. We demonstrated that noise suppression simply corresponds to spending a sufficiently large fraction of the time in low-noise input states that the average size of noise is reduced. More precisely, we explicitly compute the power spectrum of the output signal and provide exact conditions for a decrease in the spectrum.

Teaching Duties:

Prior to coming to James Madison University, I was a postdoctoral research fellow at the University of Washington. In the Department of Applied Mathematics, I taught a course titled "An Introduction to Continuous Modeling" in the Department of Applied Mathematics three times (Fall 2002, Spring 2003, and Fall 2003). This class uses case studies in modeling with differential equations to teach junior-level mathematical sciences students techniques in developing and analyzing differential equations for various systems. When I have taught this course, I have focused on population models, competition models, predator-prey models, Lanchester combat models, physical models with a potential energy, and traffic flow. This is a fun course to teach, and students are introduced to a variety of tools developed for dynamical systems such as bifurcations, phase-plane analysis, linear stability of equilibria, and dimensional analysis. This course also involves students preparing and writing a term project applying differential equations to a model system of their choice. I also taught one quarter of an Introduction to Numerical Methods.

Prior to coming to the UW, I taught three courses at the University of Arizona in the Math department. I taught the series for College Algebra (Math 116 and 117 at the time) as well as the introductory calculus course Elements of Calculus (Math 113). I also was an advanced TA for the graduate course in probability (Math 565), helping other graduate students in problem sessions.

Off-Topic Links

If you are interested in my life philosophy or hobbies, you might want to visit my personal web page.


This web-page was written by D. Brian Walton.