NSF REU/RET Computational Mathematics for Data Science
The Emory Research Experience for Undergraduates and Teachers site focuses on computational mathematics and its applications in data science. One of our site’s unique features is that undergraduate students and high-school teachers will collaborate on research projects in teams. The program will train approximately twelve undergraduates and four teachers annually in the summers of 2021, 2022, and 2023. Our site will introduce the participants to the mathematical theory and computational tools used in applications ranging from data assimilation to machine learning. Our site emphasizes developing research and professional skills that will increase the participants' ability to understand, conduct, and effectively communicate mathematical research in data science.
The site is organized by Lars Ruthotto and Bree Ettinger and also involve other mentors from the Departments of Mathematics and Computer Science, including: Joyce Ho, Manuela Manetta, Talea Mayo, James Nagy, Elizabeth Newman, Alessandro Veneziani, Yuanzhe Xi.
Our site’s research projects are accessible to teachers and undergraduate students with a strong background in Linear Algebra, Vector Calculus, Differential Equations, and elementary programming experience. To help participants learn other project-specific materials, our site includes a comprehensive research training plan. Our activities include professional development, a weekly lunch seminar, and social excursions in Atlanta.
Themes and Timeline
The site’s activities are centered around a six-week research stay at Emory during which teams work on projects under an umbrella theme that differs each year:
- Summer 2021: Learning from Images
- Summer 2022: Combining Models with Data
- Summer 2023: Data Science for Social Justice
This year’s timeline is:
- Apply by March 1, 2021, for full consideration via the application sites for students and teachers.
- May 24 - June 11, 2021: Virtual pre-REU/RET phase. We will host one meeting per week to help organize teams, take care of administrative items, and give participants an overview of the educational materials.
- June 14 - July 30, 2021: On-campus phase (depending on covid restrictions).
2021 Theme: Learning From Images
The amount of imaging data generated on a single day, let alone a year, exceeds human imagination. With their ability to statistically analyze such large datasets, computational algorithms can enhance our ability to discover patterns. Key advances in image classification, image segmentation, and object recognition have fueled applications like image search and self-driving cars. In the medical realm, computational approaches have led to efficient and accurate diagnostic tools, support of treatment decisions, and accelerated drug discovery.
Our 2021 theme sheds light on the mathematical methods behind the above success stories, and our projects seek to bring similar advances to new applications. Some projects will develop machine learning (ML) approaches for analyzing image datasets, while others will develop partial differential equations (PDE) models for image processing. Our projects include:
- Image-Based Diagnosis of Chiari Disease (led by Lars Ruthotto): Chiari malformation is a condition in which brain tissue extends into the spinal canal. While it can be difficult to diagnose Chari from anatomical images, a promising direction is a novel functional Magnetic Resonance Imaging (MRI) technique developed by Dr. Oshinsky’s group at Emory’s Dept. of Radiology. However, the large number of manual processing steps prohibit its use as a wide-spread screening tool. The team will develop machine learning algorithms to automize the process, for example, tools that help label and align the images.
- From Images to Patient-Specific Models in Cardiology (led by Alessandro Veneziani): 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). The team will discover the relation between PDEs and image segmentation/reconstruction through the level set method
- Tensors and Data Modeling (led by Elizabeth Newman in collaboration with Yuanzhe Xi, Joyce Ho): Advances in the neuroimaging technology of functional Magnetic Resonance Imaging (fMRI) have provided large amounts of digital data, which can be used to study the complex functionality of the human brain. A whole-brain fMRI image sample consists of a discrete-time series of 3D image scans, where each scan consists of hundreds of thousands of voxels. The size of the dataset and additional problems such as measurement noise render fMRI analysis very challenging computationally. The team will investigate the use of tensor representations to represent and analyze the fMRI data. Here, an fMRI brain image sample can be organized as a fourth-order tensor, with three space and one time dimension. This viewpoint allows for extracting information using various tensor decomposition methods.
- Point-of-Care Tomographic Imaging (led by James Nagy): Computed tomography (CT) is well known for its ability to produce high-quality images needed for medical diagnostic purposes. Unfortunately, standard CT machines are extremely large, heavy, require careful and regular calibration, and are expensive, limiting their availability in many parts of the world. An alternative approach is to use portable machines. Still, parameters related to the geometry of these devices (e.g., the distance between source and detector, the orientation of the source to the detector) cannot always be precisely calibrated in point-of-care situations. These parameters may change slightly when the machine is adjusted during the image acquisition process, which causes severe degradations in the resulting image. The team working on this project will develop a numerical method to jointly estimate the geometry parameters of the portable device and to reconstruct the image.
Our NSF grant DMS 2051019 supports twelve undergraduate students, who are US citizens or permanent residents and are currently enrolled at a college in the US (including two-year college) and four in-service high-school teachers. Some additional funds may be available to support international students currently enrolled at US colleges. All participants will receive a stipend, housing, and travel support. To find more details and submit your application visit our mathprograms.org application sites for students and teachers.
Emory students that are interested in summer research should read about the Emory Summer Undergraduate Research Experience (SURE). Applications for the SURE program are reviewed in the spring semester and interested students should identify and talk to a faculty mentor about their project plan ahead of time. The SURE program allows students to work on their project during the summer at the end of which they will present their progress in a poster symposium. Participants receive a stipend and housing support.
In the summer of 2019, we hosted a cohort of eight undergraduate students from across the US and Europe. The students were advised by Drs. Veneziani, Xi, Nagy, Ruthotto, and Newman. We provided some boot camps in the beginning, but the main part was the students exploring and working on three projects. Projects were mathematical methods in hemodynamics, efficient estimation methods for log determinants in Gaussian processes, and numerical methods for optimal mass transport. The picture above shows this amazing group of students and should convey how much fun we had. We thank the National Science Foundation and Emory College for providing the financial support to host the students.
In the summer of 2018, we hosted a small group of four students from Emory, UC Merced, and U Houston. The students were advised by Dr. Ruthotto and working on new applications of deep neural networks in classification and inverse problems. This productive summer has led to two Honors theses.