Grants and Awards
For fiscal year ending July 1, 2007, the WPI Department of Mathematical Sciences research funding totaled over $1.1 million.
Below is a list (by P.I.s and co-P.I.s) of the newly awarded and continuing grants in 2006-2007.
The newly awarded grants were (listed in chronological order of the award dates):
Nandram, B.
Propensity Score Method for Nonignorable Nonresponse Adjustment for Health Survey Data
Centers for Disease Control and Prevention/Department of Health and Human Services
We develop a robust method to do Bayesian predictive inference for the finite population quantile of a sub-area (an area within a small area) when there is nonresponse. A robust logistic regression model is used to relate the response indicators to the covariates for the sample, providing propensity scores used to construct adjustment cells. The nonrespondents' values are filled in by drawing a random sample from a kernel density estimator, formed from the respondents' values within the adjustment cells. Prediction uses a linear spline rank-based regression of the response variable on the covariates by areas, sampling the errors from another kernel density estimator; thereby further robustifying our method. We use Markov chain Monte Carlo methods to fit our model. The posterior distribution of a quantile of the response variable is obtained within each sub-area using the order statistic over all the individuals (sampled and nonsampled). Our application is on the third National Health and Nutrition Examination survey in which the response variable is body mass index (BMI), and age, race and sex are the covariates; data are available from thirty five large counties. Bayesian predictive inference of the finite population BMI quantiles for each age-race-sex domain within each county is of interest.
Martin, W.
Problems in Association Schemes
National Security Agency
In this project, we study problems related to the structure of association schemes and their applications. The problems fall under two main themes: a study of cometric (or Q-polynomial) association schemes and a study of Delsarte's linear programming bound and its recent extension to a semidefinite programming context.
Cometric association schemes are very important in combinatorial design theory and digital coding theory, yet they are not well understood. In this project, we search for new examples, further structure, and new applications. The second half of the project deals with the famous linear programming bound of Delsarte. This bound gives the strongest known non-existence results for error-correcting codes, but also applies to a wide variety of problems in combinatorics, such as the study of (t,m,s)-nets used in numerical integration and global optimization. The project aims to extend recent work applying Delsarte's approach to the Terwilliger algebras of the n-cubes as well as to other Terwilliger algebras such as the ordered Hamming scheme.
Tang, D., Petruccelli, J., Walker, H.
Multi-Physics Modeling and Meshless Method for Atherosclerotic Plaque Progression
National Science Foundation
The objective of this project is to combine computational modeling, magnetic resonance imaging (MRI) and pathological analysis to simulate plaque progression and quantify critical blood flow and plaque stress/strain conditions under which plaque rupture is likely to occur. MRI and pathological analysis will be used to quantify human carotid plaque morphology and progression and to assess plaque vulnerability. For the first time, multi-year MRI patient-tracking data will be obtained to quantify human atherosclerotic plaque progression. MRI-based three-dimensional (3D) computational models with multi-component plaque structure and fluid-structure interactions (FSI) will be developed and solved by numerical methods based on the meshless local Petrov-Galerkin
(MLPG) method to obtain critical flow and plaque stress/strain conditions, to identify suitable plaque rupture risk indicators for more accurate plaque assessment, and to simulate plaque progression for early prediction and diagnosis of related cardiovascular diseases. The computational model, MLPG method, and a better understanding of plaque progression and rupture will be considerable contributions to computational mathematics, biological sciences, bioengineering, especially in the cardiovascular research area with realistic potential clinical applications.
Wilbur, J., Weekes, S.
REU Site: Research Experience for Undergraduates in Industrial Mathematics and Statistics
National Science Foundation
The Research Experience for Undergraduates in Industrial Mathematics and Statistics at WPI provides a unique educational experience for students of mathematics by introducing them to research in an industrial environment. The students work in teams on problems provided by local business and industry. They work closely with a company representative to define the problem and develop solutions of immediate value to the company. They work closely with a faculty advisor to maintain a clear focus on the mathematics and statistics at the core of the project.
Twelve undergraduates will participate each summer. A team of three-four students will work on each of the industrial projects. Students are assigned to a project according to their interest and course background, but in most cases the work requires knowledge and tools from several areas of mathematics and statistics. Each team makes weekly progress reports to the full group and all students participate in these presentations. At the end of the program, each team provides a final written report as well as a final public oral presentation summarizing the results of their research.
The site is supported by the Department of Defense in partnership with the NSF REU program.
Fehribach, J.
Vector Spaces and Kirchhoff Graphs
National Science Foundation
The aim of this proposal is to allow the PI to continue research begun as a part of his year in the WPI Chemical Engineering Department funded through IGMS grant DMS 0426132. During his time in Chemical Engineering, the PI was introduced to a number of interesting problems. The present proposal focuses on one of these problems; it concerns chemical/electrochemical/biochemical reaction networks, reaction routes (reaction pathways) through these networks, and the depiction of these networks using what are herein called Kirchhoff graphs. Kirchhoff graphs allow one to study reversible reaction networks using approaches that traditionally are used to study electrical circuits. As do circuit diagrams, Kirchhoff graphs must satisfy the Kirchhoff laws: (1) the net change in potential around any cycle in a Kirchhoff graph must be zero, and (2) the net reaction rate (current) into/out of any node in a Kirchhoff graph must be zero. The main work proposed here is (1) showing that one or more Kirchhoff graphs exist for any given reaction network, (2) developing a method for constructing these Kirchhoff graphs. Neither of these results is obvious for arbitrary reaction networks. If funded, the proposed work will build on a vector space approach to reaction routes already developed.
Lui, R.
Mathematics of Molecular and Cellular Biology
University of Minnesota and National Science Foundation
This grant, from the Institute of Mathematics and Its Applications (IMA) at the University of Minnesota, is to support my visit to the IMA for its thematic year on Mathematics of Molecular and Cellular Biology. The IMA is a mathematics research center supported by the National Science Foundation and its participating institutions. WPI has been a participating insitution since 2006.
In addition to the above, several continuing multi-year grants have contributed to the total of awards received (listed in chronological order of the award dates):
Larsen, C.
Variational Methods for Material Damage: Fracture, Fatigue and Debonding
National Science Foundation
The investigator uses variational methods to study material damage, with an emphasis on properties of damaged regions and their time evolution. Examples of damage include brittle cracks, cracking due to fatigue, and debonding of thin films. Some discrete-time models for damage evolution exist in the engineering community, but these are generally ad hoc and not known to correspond to limiting continuous-time models. The investigator studies the existence of the limiting models, basic properties of the damage regions, and the justification for extending numerical methods for static problems to methods for the quasi-static, continuous-time problems. Damage to materials is of great technological importance not only because it results in material failure, but also because it plays an important role in building certain nanostructures, for example by selectively debonding thin films. The project seeks to greatly improve our understanding of these materials by improving the mathematical models and studying basic properties of their solutions, as well as by developing and justifying numerical methods. Mathematics Ph.D. students are included in the project, and are trained in the mathematical modeling and analysis of important interdisciplinary problems.
Walker, H.
Algorithms and Software for C-SAFE
University of Utah
This award represents an additional increase in funding for a portion of year 5 of a current research program from the University of Utah's Department of Chemical and Fuels Engineering under its prime award from the Lawrence Livermore National Laboratory (funded by the Department of Energy). The total program, which is to run for 5 years, is expected to total $437,500. During this period of performance for this program, promising avenues of research are being pursued while exploiting proven algorithms and software when feasible and appropriate.
More specifically, this study includes both collaborative research with members of the C-SAFE team and closely coordinated complementary research that will provide guidance to the team. The main areas of investigation are scalable linear and non-linear solvers, implicit methods for time-dependent problems, higher-order time-stepping schemes, and operator splitting issues. This activity will leverage and be leveraged by major research efforts at Sandia National Laboratory, Lawrence Livermore National Laboratory, and Argonne National Laboratory. The award also provides support for one full-time graduate student in each of the five years of the program.
Heinricher, A., Vernescu, B., Weekes, S.
Focus on Mathematics: Creating Learning Culture for High Student Achievement
Boston University and National Science Foundation
This award represents year 4 funding from Boston University under its prime grant from the National Science Foundation (NSF) for a five-year program, the purpose of which is to provide high school teachers with the resources for integrating projects into their classes. The WPI team is, during regular visits to schools, meeting with selected students who are developing projects and graduate students are being made available online for mentoring. In addition, WPI is leading the effort to organize a Mathematics Exposition that will be a yearly event in which students and teachers can present the results of their research to their peers, to panels of mathematicians, and to the media. The WPI team is also organizing a Visitors Program to spark student and teacher interest in working on a research project and contribute to the Summer Institute Program.
The main components of the work being performed in this program include: 1.) development of industrial projects for teachers and students, 2.) presentation of the projects to teachers during the Mathematics in Industry Institutes (MII) in the summer, 3.) support for the teachers during the academic year as they use the projects in classes, and 4.) development of a cohort of industrial partners that will act as the client for students and teachers using the projects during the school year.
Tang, D., Co-PIs: Sotak, C., Hoffman, A., Woodard, PK.
MRI-Based Computational Modeling for Carotid Plaque Rupture and Stroke
Department of Health and Human Services
The objectives of this project are to integrate computational modeling, Magnetic Resonance Imaging (MRI) technology, ultrasound/Doppler technology (US), mechanical testing, and pathological analysis to perform quantitative mechanical analysis to atherosclerotic carotid plaques, to quantify critical blood flow and plaque stress/strain conditions under which plaque rupture is likely to occur, and to seek the potential that quantitative mechanical analysis can be integrated into state-of-the-art imaging technologies for better screening and diagnostic applications.
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Last modified: March 17, 2008 11:53:12