VIGRE @ Rice

2006 PFUGs

• Computational Medical Image Processing

  • In this VIGRE research seminar we study mathematical and computational problems arising from image processing in medical and other applications. The activities will be in collaboration with researchers from the M.D. Anderson Cancer Center (MDACC).

• Simulation-Driven Optimization: Control, Design, and Inverse Problems (Data Assimilation)

  • Data assimilation (DA) refers to the reconciliation of the dynamical model of a physical process with measurements. This means that we want to estimate  parameters  in a dynamical model so that the solution of the dynamical model matches given observations.  DA arises in a variety of applications including weather forecasting  and process control.
    Of particular interest is the solution of DA problems in battery-powered sensor networks, an emerging technology.  Battery-powered sensor networks are very attractive for many applications, since they are inexpensive to deploy. However, their operation is challenging since in these networks energy and communication bandwidth is limited. We will study DA algorithms for battery-powered
    sensor  networks and explore their implementation in a testbed on the Rice campus.

• Developmental Biology

  • Our PFUG focuses on issues related to understanding the early development of fruit flies (drosophila melanogaster ). We discuss modeling the systems that help a young fly transition from an undifferentiated egg to an adult fly with body segments, eyes, wings and antennae in their proper places.
    We plan to pay particular attention to issues of precision. How is it that a simple system can take rough data like a protein gradient and decide exactly where a structural part of the fly should be built?
    Other issues will be discussed, too. Can one decipher the behavior of a protein network if one knows only its graph of interactions, but not the actual details of those interactions? Can one understand how the fly manages the complicated geometry involved in building a wing?
    There is ample opportunity to study these questions with both numerical and analytical techniques. The only prerequisite is some knowledge of differential equations (like Math 211 or 213).

2005 PFUGs

• Metabolic Engineering

  • Our Goal is to build a theory that permits the optimal design of both new organisms and new environmental niches. This semester we will investigate
    1) Statistical Mechanical Foundations of Molecular Interactions,
    2) Gillespie's Method for Estimating such Interactions in the low concentration limit,
    3) An adjoint method for inferring kinetic parameters from transient concentration data
    4) Methods for accelerating the computation of elementary flux modes in large systems.

2004 PFUGs

• Stochastic Processes in Molecular Biology

  • Many science and engineering topics involve the adjustment of model inputs or parameters to produce a desired predicted outcome, with the prediction being the result of a numerical simulation. Such problems arise in the Earth Sciences (seismology, meteorology, oceanography), Biology (CAT, PET, MRI imaging), and various branches of Engineering (control of complex systems, optimal design). This PFUG will study particular instances of simulation-driven optimization, and also provide an opportunity for those working on various such topics to communicate and cross-fertilize ideas.