 |
 |
 |
Presentation Seminar |
Pre-collegeUndergraduateREUGraduatePostdoctoralAdministrationHome |
Spring 2007 ScheduleMarch 6, 4:00 PM LCB 215Amy Richardson, Nathan Rickett, Sandy Shafer, Emily Weed RTG Group REU Mentor: Paul Bressloff Mathematical Models of AMPA Receptor Trafficking Abstract: AMPA receptors mediate the majority of fast excitatory synaptic transmission in the central nervous system, and recent experimental evidence suggests that AMPA receptor trafficking regulates synaptic strength, a phenomenon implicated in learning and memory. There are two major mechanisms of AMPA receptor trafficking: exo/endocytic exchange of surface receptors with intracellular receptor pools, and lateral diffusion of surface receptors within the plasma membrane. We will present our mathematical model of these trafficking mechanisms, and discuss how our model accounts for a variety of physiological data regarding plasticity. We will also present the results of our numerical simulations in MatLab. March 13, 4:00 PM LCB 215 Brent Hawker VIGRE Independent REU Mentor: Gordan Savin Continued Fractions and Pell's Equation Discussion of continued fractions in general, what they are and how they are constructed. Extend it to infinite continued fractions, and relate it to Pell's Equation. Explain Pell's Equation and the negative Pell's Equation, and how the sign is dependent upon the period of the continued fraction. Display an interesting result of my research which deals with this period. Discussion of sums of squares and their relevance to the problem and prime factorization. March 13, 4:45 PM LCB 215 Muhammed Adeel Mentor: Dan Margalit Geometry of Möbius Transformations The goal of the project is to explore the theory of groups generated by Möbius transformations of the Riemann sphere. This project has two aspects: Mathematical understanding and computer exploration. Computer exploration requires C++, though images will be generated using Metapost, a latex based tool. The task at present is to generate a double spiral which is a stereographic projection of the spiral from Riemman Sphere to complex extended plane. For this projection, we conjugate the Möbius transformation with some other Möbius transformation so that conjugating transformation maps each fixed point to some fixed point. March 26, 4:00 PM LCB 215 Nathan Mason VIGRE Independent REU Mentor: Fred Adler How Microglia respond to injury We are going to investigate a potential model of how microglia migrate to and surround a foreign object in the brain, like an electrode. Microglia are a type of glial cell that act as the immune cells of the Central nervous system (CNS). They act as type of phagocyte which works to remove foreign bodies in the CNS. The model we will be exploring is whether the cellular response of the microglia migrating to the foreign object, is in response to the object itself. Or alternatively if they respond to the cellular signals of neighboring microglia. A third option would be that the microglia migrate to the foreign object, learn that the foreign object is not a threat to the brain. They then move away from the object. We will be use chemotaxis and diffusion equations to model this behavior. March 26, 4:45 PM LCB 215 Tim Anderton VIGRE Independent REU Mentor: Eric Sharpe Broken Mirrors The method of compactifying or "rolling up" extra dimensions when doing theoretical physics has become common place. These extra dimensions are almost without exception assumed to be very small enabling them to be undetectable at suitably large distances. Most searches for these extra dimensions have taken the form of watching for deviations from an inverse square force law. Deviations which show up only at small distance scales however could also exist in systems with very large extra dimensions. If these large extra dimensions mirrored the information held in the others then they could leave the force law unchanged from that of a lower dimensional space. April 3, 4:00 PM LCB 215 Eric Heisler VIGRE Independent REU Mentor: Grady Wright Solving differential equations with radial basis functions Radial basis functions(RBFs) can be used to create very effective finite difference formulas for solving PDEs. The effectiveness of these methods is determined largely by a shape parameter which characterizes the RBF. Unfortunately, little is known about properties of the parameter, such as the effect on error bounds and convergence, or even how to choose the best value. This talk will be about finding a practical way to optimize this parameter, and will present numerical results to compare this method to the standard finite difference method. April 10, 4:00 PM LCB 215 Carl Tams VIGRE Independent REU Mentor: Fred Adler Drug diffusion models. There are bio-medical models and there are pharmacy models and in contrast with these we model drug diffusion. We have made a model to follow the drug travel through the body till it reaches its destination site. April 10, 4:45 PM LCB 215 Jake Grosek Mentor: Domingo Toledo Hyperbolic Tessellations Geometry in a hyperbolic space can be quite different than geometry in a Euclidean space. I plan to discuss some of the criteria for finding fundamental domains that tessellate various forms of hyperbolic space. I also plan on mentioning some of the patterns I have found in these fundamental domains. April 17, 4:00 PM LCB 215 Cory Steffen VIGRE Independent REU Mentor: Jingyi Zhu The Valuation of Mortgage-Backed Securities with PDEs A mortgage-backed security (MBS) is an asset-backed security whose cash flows are derived from the principal and interest payments of a set of mortgage loans. Total market value of all outstanding U.S. MBS at the end of the first quarter of 2006 was approximately $6.1 trillion, which highlights the need for proper valuation of these securities. I will discuss a PDE model to evaluate various facets of the pricing, returns, and risks of MBS relative to other types of fixed rate securities. April 24, 4:00 PM LCB 215 Alex Pruss VIGRE Independent REU Mentor: Peter Trapa Effects of Modular Arithmetic on Matrix Orders Applying a mod function to each element of a matrix will generally change the order of said matrix. Although it is difficult to say what effect the mod function will have on any given matrix, it is possible to determine this effect by using principles used in calculating the Crystallographic Restriction and by relating matrices to the Symmetric Group. For more information, contact: Hugo Rossi |
||