Department of Mathematics and Statistics

James Madison University

Address: |
James Madison University Department of Mathematics MSC 1911 Harrisonburg VA 22807 |

Office: |
Roop 110 |

Spring 2013 Office Hours: | MW 9:00-10:00 am, Tu 9:00-11:00 am and 3:30-4:30 pm, and by appointment |

Phone: |
(540) 568-6387 |

Fax: |
(540) 568-6857 |

E-Mail: |
waltondb at jmu.edu |

Quick Links

Here is a link to a PDF file containing the slides from my talk at JMM13:

UBM Group Seminar Discussions: Grappling with Issues beyond the Curriculum.

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. (Note: This only deals with solutions where intermediate values are also integers.)

**Current JMU Courses**: Spring 2013. Official course information is on Blackboard.

- Math 232 (Sections 5 and 6): Calculus with Functions II
- Math 423: Stochastic Processes

I have some teaching blogs on which I occasionally post things.

- http://waltonsjmumathblog.blogspot.com/
- An out of date and incomplete site for Math 231-232

- Math 231: Fa04, Su05, Fa05, Sp09, Fa09, Fa10, Fa11, Fa12
- Math 232: Sp05, Sp06, Sp10, Sp11, Sp12
- Math 235: Su06, Fa06, Fa08
- Math 236: Sp07
- Math 238: Fa07
- Math 248: Fa05
- Math 318: Sp08, Fa12
- Math/Physics 341: Sp07
- Math/Biology 342: Sp05, Sp06, Fa06, Sp09, Sp11

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.

- Dissertation: "Analysis of Single-Molecule Kinesin Assay Data by
Hidden Markov Model Filtering," The University of Arizona, 2002. (PDF
version)

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.

- D. Brian Walton and Koen Visscher, "Noise Suppression and Spectral Decomposition for State-Dependent Noise in the Presence of a Stationary Fluctuating Input", submitted 2003 (PDF preprint)

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.

If you are interested in my life philosophy or hobbies, you might want to visit my blogs:

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