Mathematical Contest in Modeling Talks
Come see the 2004 Mathematical Contest in Modeling Talks! This year we had four participating teams that all did an excellent job! Each team will be giving a short presentation on their solution to the problem they chose to work on.

QuickPass Systems:
QuickPass Systems are used in Amusement Parks to attempt to cut down on wait times in lines for popular attractions. The idea is that you can receive a pass to return at a later time in the day, where you will be able to wait in a shorter line to get on the ride. These systems have been plagued by various problems. The goal is to model an effective system for issuing these passes.
Three teams will present their solutions to this problem: 1) Arian Lalezari, Sarah Macumber, Matt Martin 2) Ian Derrington, Donovan Levinson, Karl Oberymeyer 3) Moorea Brega, Alejandro Cantarero, Corry Lee 

Fingerprints
It is a commonplace belief that the thumbprint of every human who has ever livedis different. Develop and analyze a model that will allow you to assess the probability that this is true. Compare the odds (that you found in this problem) of misidentification by fingerprint evidence against the odds of misidentification by DNA evidence.
One Team will present their solution to this problem: 1) Brian Camley, Pascal Getreuer, Brad Klingenberg

Srinath Vadlamani
Topic: The Gyrokinetic Equation for Strongly Magnetized Plasmas; an attempt at an intelligible derivation.
Abstract:
The modeling equations for most of controlled thermonuclear fusion research (CTR) via magnetic confinement are the "gyro"-equations of plasma. Many derivations have been developed with certain applications in mind. I will present the derivations that are closely related (ie. the "beginning" equations) to my research.

Kristian Sandberg
Topic: Analysis of fractals using wavelets
Abstract:
Wavelets have proven to be a powerful tool for image analysis. However, wavelets have many other applications as well, such as analyzing fractals. Such analysis has applications in e.g. studies of turbulence in fluid dynamics. In this talk I will describe how wavelets can be used to analyze the fractal-like function "the Devil's staircase".

Oliver Roehrle
Topic: Not Everything in this World is Linear - A Sample of Numerical Methods for Nonlinear Problems
Abstract:
The most simple models for physical processes are often based on linear partial differential equations. Improving the quality of the linear model usually results in a nonlinear model, often a system of nonlinear partial differential equations (PDEs). This presentation will give a brief overview on commonly used nonlinear solution techniques. Such techniques include basic nonlinear iterative solvers, Newton-like methods, as well as grid-continuation methods for Newton-like methods.

December 10th, 2003
4:45 - 6p.m. in ECOT 226 (The Applied Math Conference Room)
Undergraduate VIGRE Talks
A set of three talks by undergraduate students supported under the VIGRE grant will be given. Titles and abstracts for the talks follow:

Lauren Anderson and Ashley Moore
Topic: Non-linear Partial Differential Equations
Abstract:
Gearing up to solve discrete non-linear partial differential equations in various optics and Bose-Einstein Condensation situations, we are working on building the necessary foundation to solve these pde's. Initially we modeled the linear part of the Schrodinger equation (using ODE45), then we explored other pde's and their behavior. Directionally we are working on solving non-linear pde's using our own time-stepping integration method. These building blocks will lead us to the point where we can solve an array of non-linear pde's with different applications.

Pascal Getreuer
Topic: Generating Wavelet Transforms
Abstract:
The difficulty in feature extraction is that no one particular transform works well in representing all signals, instead, a transform must be created for a given signal or selected from a dictionary. My goal is to find methods, given a signal, to efficiently generate a biorthogonal wavelet that works well with the signal. I will discuss what wavelet qualities produce "good" transforms, and show how this along with the Lifting Scheme interpretation lead me to effecient methods for building up wavelet transforms in stages.

Ian Derrington and Mark Winter
Title: Behavior of Newton's Method as Applied to the Eigenvalue/Eigenvector Problem
Abstract:
We examine the qualitative differences in the Standard and Projected Newton's Method algorithms for solving the eigenvalue/eigenvector problem. We map the basins of attraction for various 2x2 and 3x3 symmetric and non-symmetric matrices. We superimpose the Jacobian singularity curve on top of the attraction maps and it appears to fit the basin boundaries for Standard Newton's Method. However in the case of Projected Newton's Method the Jacobian singularity curve does not accurately fit the basin boundaries. We try other methods to solve analytically for the basin boundaries of Projected Newton's Method.