Mathematics Faculty Projects
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.