Mathematics Faculty Projects


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Accurate Numerical Simulation of a Chromatography Column

Professor Dave Goulet

This project is an outshoot of another IPROP project, "Dimerization of the estrogen receptor protein." Chromatography is used to measure concentrations of chemicals within a solution. It is a key tool in understanding the time course of chemical reactions as they proceed to equilibrium. In this project, we use modern numerical techniques to simulate a mathematical model of diffusion, convection, and reactions as the chemical species move through the chromatography column. The model couples partial differential equations and ordinary differential equations into an optimization problem. The goal is to use chromatograph data to determine rate parameters for chemical reactions related to estrogen dimerization. The partial differential equations being used are exceptionally stiff, requiring a host of modern numerical methods in order to gain accurate solutions in a reasonable time. Any student who has taken classes in numerical analysis or computational science would have a chance to learn a great many new techniques and to see how their current techniques can be applied and adapted to a realistic scientific problem.

Visual Tracking and Interception of Flyballs

Professor Jameel Ahmed (ABBE)
Coach Jeff Jenkins
Professor John Rickert (MA)

How does a baseball player catch a flyball? Several theoretical models describing how people track flyballs exist, but experimental data is sparse. Digital imaging technology can be used to gather real-world data from people at several skill levels applying different techniques. The images can be processed, analyzed, and compared to proposed models.

Protein structure alignment

Professor Yosi Shibberu

Dr. Shibberu is investigating eigenvalue-based methods for the protein structure alignment problem. The goal is to align protein folds in order to identify fold families. These are computationally intensive problems requiring efficient algorithms and high-performance computers. Two alignment algorithms being used include one based on eigenvalues and dynamic programming to quickly compute a fold alignment, and another that iterates between an intrinsic geometry and the 3D geometry of a fold to make high-quality alignments.

Compressed Sensing for Geolocation of Radio Sources

Professor Kurt Bryan (MA)
Professor Deborah Walter (ECE) 

Compressed sensing (CS) is a new computational methodology that allows one to extract far more information from certain types of data than was thought possible using classical techniques.  The topic has connections to mathematics (especially linear algebra), computer science, and signal or image processing.  CS has shown great promise in many applications, and is currently a red-hot research area. One application in which CS seems to work well is that of locating a radio frequency (RF) source using data collected from a fairly small number of radio receivers with very simple antennas.  In conjunction with the Air Force Research Lab, we have made some progress on this problem in the case in which one or perhaps a few RF sources on the ground must be located using receivers mounted on unmanned aerial vehicles (UAVs), but much work remains to be done.

This project would, at the least, involve using an existing Matlab code and GUI to run simulations in order to understand when a CS approach to this problem is likely to be successful, e.g., how many RF sources can we locate using five UAVs?  What if the RF sources are in motion, or transmit intermittently?  The project could also involve developing new algorithms and incorporating them into the code, or carrying out a more rigorous analysis of existing algorithms.

If you accept this challenge, you will be working with an interdisciplinary team of researchers that may include professors, students, and professional engineers from Rose-Hulman, the Air Force Institute of Technology, and the Air Force Research Lab.  We anticipate that there may be future opportunities to take part in the development of a physical test-bed, conducting experiments, and applying algorithms to experimental data. This may result in an opportunity to focus your work into a senior math thesis, an engineering master's thesis, and/or a conference paper.

Image Enhancement for Thermal Nondestructive Testing

Professor Kurt Bryan

This project is concerned with finding small cracks in a metal object, for example, a boat's hull, using thermal imaging, and is based on some work I've been doing with Chris Earls in civil engineering at Cornell.  The object is heated with a low power laser while an infrared camera watches the object's surface.  From the infrared data we can infer the object's surface temperature.  The presence of cracks alters the flow of heat, which the camera can see.  However, we want to image cracks down to the one pixel or even sub-pixel level of the camera, and these are hard to see.  The right image enhancement techniques applied to the camera data make this a bit easier, but there is still room for improvement. For example, a good model of the camera optics (e.g., its point spread function) might allow more intelligent image processing techniques to be used. Additionally, maybe the experimental configuration can be improved, for example, should the heat source be held steady or swept over the object?  How long should we take data?  How often?  This project would involve exploring these issues, computationally and/or theoretically.

Atlas of protein fold space

Professor Yosi Shibberu (MA)
Professor Mark Brandt (CHEM)
Professor Allen Holder (MA)
Professor David Goulet (MA)

Proteins play a key role in nearly all the biochemical process of life. A protein sequence (translated from its corresponding gene sequence in DNA) collapses into a tightly packed, 3D structure called a fold. We are interested in developing an atlas of all known protein folds. Such an atlas will aid in identifying the function of individual proteins and potentially lead to the design of proteins with new functions. An atlas is built by comparing all pairs of proteins from a large database.  Our pairwise comparison technique uses eigenvalues and eigenvectors and has proven to be efficient and accurate on sizable test sets.

Dimerization of the estrogen receptor protein

Professor Yosi Shibberu (MA)
Professor Mark Brandt (CHEM)
Professor Allen Holder (MA)
Professor David Goulet (MA)

The estrogen receptor protein is the drug target of tamoxifen, one of the most successful drugs for treating breast cancer. We are interested in computer simulations of this protein to better understand how it functions. Some of our simulations have required more than a month of computation on the mathematics department's 48-core workstation. Each simulation generates several gigabytes of data to analyze. The project has important implications for both breast cancer research and for modeling protein-protein and protein-small molecule interactions.

Who painted this painting?  - a project in Image Registration

Professor Allen Broughton

An art collector possesses a "painting of unknown origin" which he suspects was painted by a "very famous painter".  The only possible evidence is a corner of the painting in an old  photograph taken in the painter's studio. Is there a way to match the two, such as matching fingerprints?  A proposed technique is to match the fragment to a modern image of the painting.  Since the the two images are taken by two different cameras, you just can't compare the two photos.  This problem is called image registration which is an optimization problem in multi-dimensional camera orientation space.  The novelty in this project is that we will try to implement the standard  image registration algorithms on advanced GPU's (graphical processing unit) which could yield  a much faster solution to the problem.


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