The impact of VIGRE in the CAAM department

About VIGRE

In 2003 the National Science Foundation (NSF) awarded a Vertical Integration of Research and Education in the Mathematical Science (VIGRE) grant to the departments of Mathematics, Statistics and our own Computational and Applied Mathematics.

This grant allowed our department to

Visit the VIGRE at Rice website, or continue with us below for a glimpse at the PFUGs our department has particularly enjoyed.

Computational Neuroscience PFUG

Neuron morphology
Neuron morphology

This PFUG is extremely active, with a lot of eager and talented undergraduates joining more senior researchers. That collaboration includes researchers in the Houston Medical Center, which is conveniently located across the street from Rice University. The PFUG focuses on mathematical problems that arise when simulating the behavior of neurons, either by themselves or as a network. Their work will lead to one of the most tantalizing and elusive goals of the 21st century: an understanding of the human brain.

Some of the topics studied are the role of calcium in neuronal signaling, ion channel distribution in neurons, and neuronal networks of the hippocampus. For an updated overview of this PFUG, you may visit the Computational Neuroscience PFUG webpage.

Metabolic Engineering PFUG

E coli electron microscope
Escherichia coli (source: NIAID, NIH)

The objective of this PFUG is to investigate sensor mechanisms that exist in bacteria such as E. Coli. These bacteria are able to thrive in harsh conditions by adapting their metabolism to their environment. To learn more about this subject, you may visit the Metabolic Engineering PFUG webpage.

Simulation-Driven Optimization: Control, Design, and Inverse Problems PFUG

Weather forecast, southwest US
A weather forecast (source: weather channel)

You do not have to be told how lousy weather forecasts can be. At best, weathermen manage to accurately predict the weather a week ahead of time, but just as often you get wet when they tell you to leave your umbrella at home. Let's not be too harsh; weather forecasting is a tricky business!

We have models that predict how the main influences of weather -- ocean currents, the jet stream, areas of high and low pressure, and so on -- will evolve over time. Unlike ideal models, however, we cannot access that information everywhere at once. We have to assimilate measurements from scattered weather stations, meteorological balloons, satellites, and other sensors to provide some semblance of what is actually going on out there. This process, common to other applications as well, is called data assimilation and its mathematical foundations are one of the main subjects of this PFUG.

Other problems tackled in this PFUG are those where the adjustment of model inputs or parameters is needed to produce a desired predicted outcome, with the prediction being the result of a numerical simulation. This is often refereed to as optimal control or optimal design. To learn about these topics, you may visit this PFUGs homepage.

Computational Image Processing PFUG

Lung cancer tumor
How can we track a lung tumor as the patient breathes?

The name of this PFUG belies just how close to home the problem it addresses is. A particular problem in cancer treatments is pinpointing the location of a tumor over time so as to not radiate nearby healthy tissue. Considering that doctors must locate the tumor days before the treatment via medical images such as CT scans, and the patient may have to move during the radiation treatment, this problem is far from being solved. For example, merely the act of breathing is going to change the location of a lung tumor during radiation procedures. The purpose of this newly created PFUG is to study mathematical and computational problems arising from image processing in medical and other applications.

One of these applications, known as image registration, consists of identifying the same feature in different images. For example, one could track a lung tumor during the respiratory cycle of a patient, and use that information to predict where the tumor will be when radiating. This PFUG regularly involves researchers from our neighbors, the MD Anderson Cancer Center. For more information, visit the Medical Image Processing PFUG webpage.

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