Research Projects:
I'm currently working on a number of research projects. Undergraduate or
graduate students who are interested in working on one of these projects
should contact me. We might be able to arrange a directed study, thesis,
or dissertation project. In some cases I might even be able to pay you
for your work on the project.
- Semidefinite programming. For the last ten years, I've been working
on a code that solves problems in semidefinite programming. This open
source software package, called
CSDP, uses a primal-dual interior point method. It
has been
used by researchers in many disciplines. Along with my former student
Joseph Young, I've modified the code to run in parallel on shared memory
systems using OpenMP. One student project would be to extend the
software by incorporating a sparse Cholesky factorization routine. A somewhat
larger project or possible thesis topic would be implementing a first
order algorithm for solving very large SDP problems.
- Maximum Independent Set Problems. The maximum independent set
problem is an extremely difficult (NP-Hard) combinatorial optimization
problem. However, it is possible to use semidefinite programming to
obtain bounds on the size of the MIS. Together with former students
Richard Hahn and Aaron Wilson, I've developed an SDP based branch and bound code for the solution of
MIS problems and used it to solve some problems that have never been solved
by other approaches. A possible student project in this area would be the
development of a parallelized version of the code that would run on a
distributed memory cluster (e.g. a Beowulf.)
- Cosmogenic Nuclide Dating. In an NSF funded project called
CRONUS,
a group of researchers at several universities is working to improve the
accuracy of exposure age dating of samples from measurements of rare
isotopes that are produced by cosmic rays that begin to bombard rock after
it is exposed on the surface. My part of the project is the calibration
of production rates from independently dated samples. I'm currently working
with a student, Robert Aumer, who is developing a code for aging depth
profile samples.
- Remote sensing of soil moisture. I'm currently working with Jan Hendrickx and his
students in the hydrology department on analysis of remote sensing data
with applications to hydrology and soil science. In one project, we're using
an algorithm called SEBAL to estimate root zone soil moisture from LANDSAT
and MODIS images. Several current and former students have been involved in
the development of our MATLAB code for soil moisture estimation.
We've also investigated the use of radar images for
estimation of soil moisture. This research has also included an
investigation of the spatial variability of soil moisture at scales ranging
from 30m to tens of kilometers and methods for up and downscaling images
at different scales.
- Landmine detection.
I've also done work with Jan Hendrickx and his students in the hydrology
program on
modeling
the effects of soil physical properties on landmine detection sensors.
This project has largely wound down.
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