This Project Grant award from the National Science Foundation (NSF) Mathematical and Physical Sciences (MPS) program in the amount of $199,555 supports collaborative research on stochastic shape processes and inference. Led by a team of investigators from the U.S. and U.K., the project will develop methods for modeling how biological and other shapes change over time, using statistical frameworks to capture shape variations across objects and populations. This research aims to advance the...
This National Science Foundation (NSF) Project Grant award, under the Mathematical and Physical Sciences (CFDA 47.049) program, will support research on stochastic methods and isoperimetric inequalities at Texas A&M University. The $238,406 award, active from July 2024 to June 2027, will develop techniques to bridge fundamental conjectures in Brunn-Minkowski theory and dual Brunn-Minkowski theory, with a focus on intersection bodies and higher-dimensional generalizations. The research aims...
The National Science Foundation (NSF) awarded a $498,229 Project Grant under its Mathematical and Physical Sciences program (CFDA 47.049) to Yale University. The grant will fund research to develop new mathematical and machine learning techniques for analyzing complex, high-dimensional biomedical data such as single-cell sequencing and gene regulatory networks. Key research thrusts include creating data geometric features and neural network models to characterize point cloud data, preserving...
The National Science Foundation (NSF) awarded a $305,850 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) federal grant program to the University of Houston System. The grant, titled "CAREER: SHAPE ANALYSIS IN SUBMANIFOLD SPACES: NEW DIRECTIONS FOR THEORY AND ALGORITHMS," will support research to advance the analysis and comparison of relaxed shape matching problems, investigate deep learning approaches to improve the efficiency of manifold registration...
This National Science Foundation project grant of $239,962 will support the development of novel statistical methods for analyzing functional and imaging data supported on complex geometries through the Mathematical and Physical Sciences program (CFDA 47.049). Led by the University of Washington with a completion date of June 2025, key products include generalized linear models and regularized linear models to predict outcomes from functional predictors on multidimensional non-linear domains....
This $100,011 Project Grant award from the National Science Foundation's (NSF) Mathematical and Physical Sciences program (CFDA 47.049) supports research on stochastic growth models and mathematical structures called line ensembles, which have applications in fields ranging from magnetization to protein synthesis. The research aims to expand knowledge of line ensembles and related techniques, leading to solutions for previously intractable problems. The award includes organizing conferences...
This $196,255 Project Grant from the National Science Foundation Division of Mathematical Sciences will fund the development of a new computational method called Shape-Morphing Modes for efficiently simulating multiscale evolution partial differential equations with conserved quantities. Shape-Morphing Modes are computational elements that adaptively change shape and location to efficiently capture various temporal and spatial scales in solutions to partial differential equations describing...
The National Science Foundation awarded a $252,937 Project Grant under its Mathematical and Physical Sciences program (CFDA 47.049) to the University of Chicago. The purpose of this 3-year grant, which runs from September 1, 2023 to August 31, 2026, is to enhance statistical methods for analyzing temporally observed, multi-sample data in fields such as environmental science, epidemiology, and economics. The research team will develop innovative approaches to estimate and infer trends in data...
The National Science Foundation (NSF) awarded a $419,962 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of North Carolina at Chapel Hill (UNC-CH), effective August 1, 2024 through July 31, 2027. The funding will support the development and analysis of algorithms to uncover low-dimensional intrinsic data structures within Wasserstein space, a mathematical framework for representing and analyzing distributional or point-cloud datasets. The...
The National Science Foundation (NSF) awarded a $343,850 Project Grant under the Mathematical and Physical Sciences (CFDA 47.049) program to the University of Cincinnati. This 3-year grant, effective September 1, 2024, will fund research to develop new mathematical tools for analyzing the large-scale geometric behavior of non-smooth metric measure spaces, which have diverse applications across fields like fluid mechanics, neurophysiology, and fractal geometry. The project aims to enhance the...
This National Science Foundation (NSF) Project Grant under the Mathematical and Physical Sciences (CFDA# 47.049) program will fund a collaborative research effort between U.S. and U.K. investigators to develop new statistical methods for modeling dynamic changes in biological and other complex shapes. The $200,000 award, effective August 1, 2024 through July 31, 2027, will focus on integrating spatiotemporal registration of objects and their evolution into the statistical formulation to enable deeper study of the link between form and function. Key objectives include advancing stochastic differential equations on shape manifolds, time series models for shapes, shape-based functional data analysis, and modeling on infinite-dimensional shape spaces. Example applications will explore changes in cell morphology/topology during division and human posture during activities. This project aims to provide practitioners with general, useful tools for a range of scientific domains.