CURL PROJECTS (Spring 2006)

Luke Berg & Joel Hestness

Project Title: Constructing an Intelligent System for Learning and Use of Language (ISL): A Prototype Project for Approach to Language Learning

URL 1: https://mywebspace.wisc.edu/jthestness/web/HilldaleResearchProposal.doc

Project Abstract: We propose to develop a proof-of-concept model for a prototype software-based intelligent system that can be used to do research in learning to generate English writing. As a byproduct, our model will also prove useful for:

(1) research on learning to write using interactive software,

(2) it will lead to a host of research opportunities into the effectiveness of teaching methods, and

(3) it could be used for our everyday word processing tasks.

We propose to develop this software through a bottom-up design, starting by constructing a simple ISL and making it more dynamic as we proceed. In this way, we will be able to evaluate, at each step, how closely the ISL shadows human learning. We want to show that it is possible for a computer to mimic the human learning process in writing. When this process has been completed, we hope to be able to implement a working interactive piece of software that can be used to experiment with ways of teaching writing to elementary students.

Abby Maki & Sheshali Wanchoo

Project Title: Mathematical Modeling of Biomolecular Mechanisms of Dopamine in Parkinson’s Disease and Drug Abuse.

URL 1: https://mywebspace.wisc.edu/aimaki/web/Proposal.html

URL 2: https://mywebspace.wisc.edu/sjwanchoo/web/Math491.html?uniq=xgof6

Abstract: Parkinson’s Disease (PD) is a progressive neurological disorder that is associated with the death of dopamine-producing neurons in the substantia nigra. The cause of the destruction of these neurons is not known. In our project, we will create mathematical models of neural networks of PD patients and that of drug abuse and compare the two, since similarity between PD and drug-abuse has been noted. Ultimately, our goal is to develop a quantitative method to hierarchically cluster associations between PD and drug abuse data. From this, we hope to identify the most significant families of genes that correlate best with improved behavioral responses.

Laura Legault and Rebecca Yale

Project Title: Dancing through life: a geometric analysis of biological movement and dynamic gene expression

URL: http://www.cs.wisc.edu/~legault/

Abstract: Perception of biological motion has long been studied in psychology – humans can identify the activity and identity of moving objects from a few reference points. Similarly, from a crowd of reference points, one can determine which points describe an individual. With the assistance of the Dance Department, utilizing motion capture technology, I will investigate the mathematical implications of this phenomenon, discover an analytic description of curves traced by human perambulation, and develop an algorithm (and computational implementation) to recognize patterns of motion in a group of points and classify the data into coherent subgroups. I hope to generalize the underlying mathematics to model dynamics in complex systems, such as patterns of dynamics in gene expression, and discover constraints on the architecture of gene networks.

Elizabeth Drilias

Project Title: The View of the United States Abroad: An Application of Complex Dynamical System Theory to Foreign Currency Exchange Rates

URL: https://mywebspace.wisc.edu/xythoswfs/webui/ejdrilias/web/Math491CURL

Abstract: Our goal for this project is to take exchange rate data and, using the tools of statistics and dynamical systems theory, find a set of equations or rules that govern the system. We used statistical smoothing to approximate daily data into a function with suitable analytic properties. We introduced a new concept of “catastrophe” for complex dynamical systems, and used it to find lengths over which predictions of behavior can correctly be made. We examined Japanese/U.S. exchange rates before and after a tumultuous week in the market. We found regular behavior before the “catastrophe” and great uncertainty afterward. Our research provides a new scheme for evaluating the behavior of international currency markets and the significance of “catastrophic” events.

George Foster

Project Title: Design of Intelligent System to Find and Track Web Users’ Eyes in Real-Time

URLhttps://mywebspace.wisc.edu/gfoster/CURL/Proposal/Report.html?uniq=1h7wss

Abstract: The project I wish to attempt is the following. Given an input image of a person, train a computer to:

a) Locate the exact position of the person's eyes

b) Determine the vector representing the direction the person is looking

To my knowledge, this has never been achieved, and if it could be it would have numerous applications.

Consider the following scenario: Webcams, like the one pictured above, cost about $20 at Best Buy. They are capable of capturing dozens of digital images a second. Imagine one of these hooked up to a computer program that can determine where a person is looking. In real time, the computer would be able to know where its user is looking. If the user looks at one part of the screen, something happens. If he looks at another part of the screen, something else happens. Or possibly if your son or daughter is using some educational software to do their homework and you want to know whether they are paying attention or looking out the window...

The point is, this would be tremendously useful if it could be done effectively, which I believe it can.

Adam Graves

Project Title: “The Insertion of Quantum Dots into Lipid Membranes”

URL: https://mywebspace.wisc.edu/amgraves/web/491Proposal/Proposal.htm?uniq=xjnt0

Abstract: It has recently been found that when quantum dots whose dipole moments are close to that of the peptaibol alamethicin are placed on a lipid bilayer membrane they insert themselves into the membrane when an external electric field is present. This leads to creation of QD pores on the membrane. It has been theorized that it takes at least three QDs to form such a pore. The purpose of my research is to model the behavior of the QD pore. To do this I plan to tailor the existing Markov models of alamethicin to the QD pore.

Jeremy Jacobson

Project Title: A Review of an Open Question Posed By A.D. Alexandrov in the Intrinsic Geometry of Surfaces.

URL https://mywebspace.wisc.edu/jajacobson/web/IntrinsicGeometry2006.html

Abstract: Here, in light of the---previously unavailable---English translation of his greatest works published this year, we review A.D. Alexandrov’s contributions to the intrinsic geometry of surfaces with the aim of understanding a question posed by Alexandrov over fifty years ago, asking which closed convex surface of a given diameter (diameter with respect to the inner metric) has maximal surface area. We summarize the original aims and methods of the intrinsic geometry, and then review how the subject, since its introduction by Gauss over two hundred years ago, was advanced by Alexandrov’s work in this last century. Finally, we work through one approach to resolving the question at hand.

Joseph Nelson

Project Title: Pattern Recognition in Complex Nonlinear Systems

URL: http://mywebspace.wisc.edu/jtnelson/web/491/

Abstract: In this project we will develop and implement new mathematical methods for capturing common nonlinear features for use in pattern classification of diverse complex systems. Specifically, we propose to develop a geometric approach in pattern recognition, and demonstrate its versatility within vastly different application domains: (a) recognizing handwritten symbols, and (b) classifying microarray gene expression. Our long-term plan beyond the Hilldale Project is to further develop these methods for pattern recognition problems in regenerative medicine, such as cellular re-engineering and the study of gene expression data measuring the dynamics of stem-cell differentiation. A potential application of our results is to solve the computational biology problems that hinder UW researchers’ experimental success in guiding stem cell differentiation to specific brain cells (Zhang, SC (2005) URL: http://www.news.wisc.edu/packages/stemcells/ .)

Richard Jensen

Project Title: Acoustical Search: it's potential use and value to society

URL https://mywebspace.wisc.edu/rjensen2/web/aud.htm

Abstract: Our focus of study for this research is to propose some sort of algorithm that takes a sample of acoustic data, a sung or hummed bit of a melody in this case, and, after comparing it with a database of songs, via a neural network or some other appropriate method, returns a list of potential matches in order of probability, ordered from highest probability to lowest probability. There are a number of specifics yet to be determined for this project, such as the song to use, where to get the data, and what format to store the data in, but these are minor details and will have little effect on the overall result of our research.

Joseph Oldenburg

Project Title: Perceptual Learning of Geometry from Observations of Dynamic Events

URL https://mywebspace.wisc.edu/jdoldenburg/web/ProjectProposalJDO.html?uniq=cqcjwa

Abstract: To what extent human discovery of the mathematics of "geometry" depend on the experience? Helmholtz, Henri Poincaré, Einstein and Gibson are pioneers in the theories of geometry as they arise from human interaction with the environment. We propose an empirical framework to explore the role of learning and memory in discovery of geometry from observation of events. The main idea is to design an intelligent system that discovers abstract properties of Euclidean and Riemannian geometry from physical experience despite presence of noise and other confounding factors in its environment.

Nick Stong

Project Title: Modeling of S. cerivasae Shmooing as a Means to Determine Response Rate to Chemical Factors

Abstract: S. cerivasae undergoes two life cycles. One is a diploid phase during which mitotic division, budding, can occur. If meiotic division occurs the cells spores develop into two separate “cell types” a and a. These cells release an a or a factor, a mating pheromone, that when binded by receptors in the opposite cell type creates a change in the cell membrane known as shmooing. My goal is to model and amount of shmooing to determine a rate of shmooing over time. To do this I will set out to model the change of a yeast cell from normal undisturbed condition based on a grayscale image of the cell. I will also need to determine whether the cell is budding or shmooing, which will be difficult in the case of bi-polar budding. I expect to be able to make an accurate comparison between a shmooing cell and a normal cell that will change over time as the cell shmoos more completely.

Raspanti,James

Project Title: Computational Modeling of Biological memory

URL

ABSTRACT

Isaac Schwabacher

Project Title: Best quadratic surface in approximating a given data set

URL

Abstract: Our objective is to find the best quadratic surface in approximating a given data set. We can transform the data to the lower dimensional space spanned by coordinate substitution from Singular Value Decomposition. We look for a least-squares solution for the best quadratic surface in this space, and from that solution we will be able to construct what we hope will be a good approximation. Ultimately, we hope to be able to project the data into the surface and apply the tools of differential geometry to our data so that we can find the best visualization of the data.