The Research Experience for Undergraduates and Teachers Site on Computational Mathematics and Data Science provides exciting opportunities for summer research at Emory University in Atlanta, GA, USA. Under a common theme that changes every summer, the site hosts several teams who develop innovative mathematical solutions that help process, analyze, and generate data sets. The participants are mentored by leading experts within the Department of Mathematics.
With the application deadline for the summer 2022 program approaching, we’re delighted to announce the project topics and mentors. This year, we will have six projects centered on the theme models meet data. Applications include storm surge modeling and neuroscience and mathematical techniques cover a variety of topics ranging from data assimilation to deep neural networks and reinforcement learning. The teams will be mentored by faculty from Emory’s department of Mathematics and Computer Science and two former faculty and students who will join us as guest mentors. A full list of topics can be found on the Summer 2022 page. Applications for the REU and RET are due on March 1.
We are pleased to announce that applications for the summer research experience 2022 can now be submitted through mathprograms. Applications are due March 1 and we will send first offers around March 8 and continue until all positions are filled. Our theme this year is ‘Models meet Data’ and a list of projects will be posted in February.
Tensors are a a much better way to store and analyze multidimensional data than traditional, matrix-based representation. However, generalizations of effective numerical techniques for extracting features from matrices such as the Singular Value Decomposition to tensors are neither straightforward nor uniquely defined. Those techniques are crucial to identify relationships in high-dimensional data. In this project, we study tensor SVDs, propose a projection-based classification algorithm, and experiment with the four-dimensional StarPlus fMRI dataset.
Our group explored two methods - a machine learning method and an atlas-based image registration method - to automatically identify the cerebellum and brain stem in magnetic resonance image (MRI) data. Identifying these two brain regions is needed to analyze DENSE MRI data and quantify the brain movement caused by the subject’s heart beat. This in turn can help determine whether or not a subject has a Chiari Malformation. We compared the strengths and weaknesses of both methods, and how they might work in the future to improve Chiari diagnosis.
Our team has devised a way to improve point-of-care tomographic imaging and thereby making medical diagnoses more effectively. The work behind this new algorithm relies heavily upon mathematical techniques that connect numerical linear algebra with optimization methods.
Our team developed efficient numerical linear algebra techniques to improve generative models based on potential flows. We derive a preconditioner from the stochastic Lanzcos quadratures and found that it reduced the number of conjugate gradient (CG) iterations that CG requires to converge.
The role of mathematical modeling in clinics is particularly evident in cardiology, as computational mechanics for many historical reasons is a mature field of applied mathematics; on the other hand, many important cardiovascular pathologies have a significant mechanical component, in terms of fluid, structure and their interactions. The clinical impact of mathematical models strongly relies on reconstructing patient geometries to customize and personalize numerical simulations. Advances in medical image processing made over the last two decades have enabled virtual patient-specific models. A key step of the processing pipeline in Cardiology is the extraction of complex vascular geometries like an aortic dissection from medical images (typically, Computed Tomographies, Magnetic Resonance, and Optical Coherence Tomography). Our team evaluated the relation between PDEs and image segmentation/reconstruction through the level set method, and compared this segmentation approach with deep learning ones based on Convolutional Neural Networks.
This site is supported by the US National Science foundation awards DMS-2051019 and DMS-1751636. Any opinions, findings, and conclusions or recommendations expressed on this website are those of the author(s) and do not necessarily reflect the views of the funding agency.