AMSC Ph.D. student Shashank Sule (M.S. ’24, applied mathematics & statistics, and scientific computation) helps develop methods that could improve brain disease diagnostics and molecular simulations.

Shashank Sule (M.S. ’24, applied mathematics & statistics, and scientific computation) considers himself a latecomer to math. As an Amherst College freshman in 2016, he wanted to pursue chemistry research but wasn’t accepted into his preferred lab. 

Undeterred, he enrolled in a Fourier analysis math class to learn the basic tenets of Fourier transform infrared spectroscopy, an analysis technique used in chemistry, to bolster his skill set before reapplying. He didn’t expect this math class to change his plans completely. “I took that class and thought, ‘Okay, I don't want to major in chemistry anymore. I'd like to do mathematics instead,’” Sule recalled. “I liked how a lot of the arguments in Fourier analysis fit together elegantly and how far-reaching the applications of that subject were.”

Sule has been studying math ever since and is now a Ph.D. student in the University of Maryland’s applied mathematics & statistics, and scientific computation (AMSC) program. With applications in medical imaging and drug discovery, Sule’s research blends machine learning with mathematical techniques like applied harmonic analysis—a method that includes Fourier analysis and breaks functions down into smaller pieces for further study. Sule’s love of dissecting problems has aided his research, which aims to identify techniques for improving brain disease diagnostics and molecular simulations.

“I've always had a tendency to deconstruct or analyze things, and I also liked seeing how arguments fit together,” Sule said. “I think that is something that attracted me to math in the first place.”

Breaking it down

Though Sule pursued math later than some of his peers, a study abroad program in fall 2018 helped to bring him up to speed. As an undergraduate student, he spent a semester learning from Hungarian mathematicians in Budapest—a humbling and rewarding experience, according to Sule. “They’re famous for their problem-solving culture, so there were a lot of Olympiad-style problems,” Sule said. “I wasn’t used to that since I wasn't in the math world as a kid, but at some point, I started getting the hang of it and it became really fun.”

When Sule returned to Amherst, his advisor, University of Maryland alum Karamatou Yacoubou Djima (M.S. ’11, Ph.D. ’15, applied mathematics & statistics, and scientific computation) suggested that he focus on harmonic analysis for his undergraduate thesis. Sule was instantly captivated by the field’s applications in everything from medical imaging to machine learning—so much so that he decided to keep pursuing this research after earning his bachelor’s degree in mathematics in 2020. He chose UMD’s AMSC program because of his advisor’s recommendation and the Norbert Wiener Center for Harmonic Analysis. Since joining UMD, Sule has had the chance to explore both sides of his mathematical interests—pure and applied. “What gives me a lot of joy is finding good proofs but also finding mathematical arguments that lend themselves well to computation,” Sule said. “I think that's a really interesting side of harmonic analysis.”

Real-world research

In his current research, Sule works closely with his co-advisors, Mathematics Professors Wojciech Czaja and Maria Cameron. With Czaja, he uses a mix of classical and deep learning methods to develop better methods of identifying changes in myelin—a protective layer around nerve fibers and an important biomarker for brain disease. “If you want to diagnose Alzheimer's, traumatic brain injury or multiple sclerosis, there is this component in the brain called myelin, and researchers want to measure how much myelin each part of the brain has,” Sule said of their research, which was funded by the National Institutes of Health.
Specifically, their research approach aims to improve estimates of a patient’s myelin water fraction (MWF), which describes the amount of water within myelin and can indicate brain health. Their method would complement MRI, which is often imperfect at separating myelin from other features in the brain. Sule co-authored a paper showing that a machine learning technique called regularization can help tune out “noise” in the MRI data and improve the accuracy of MWF measurements. “This could serve as an additional diagnostic tool,” Sule said of the potential applications. “For instance, when a radiologist looks at a copy of a brain scan, they could have a tool on their screen that says the estimated myelin content. This could help them figure out what's going on in the brain.”

In separate research with Cameron, Sule develops new ways to speed up simulations of rare molecular events. Many processes that interest researchers—like how proteins fold or how chemicals react—happen too slowly to study on their actual timescales.  “It's like trying to see how a glacier melts by observing every centimeter of where the glacier is every week—you’re never going to see it in real life,” Sule said. “A lot of my work with Maria Cameron is about developing new mathematical techniques to understand these rare events.” While Sule focuses on getting the mechanics right, his research could one day advance the search for new and improved drugs to target a variety of human diseases. “One of our target goals is to find what's called the transition rate, which is connected to the rate of a chemical reaction,” Sule said. “It’s super relevant to drug design or studying chemical reactions.”

As Sule sharpens his research skills and reflects on everything he’s learned at UMD so far, he’s surprised by how far he’s come—as a mathematician and as a researcher working on real-world problems.
“Coming to graduate school, I never would have imagined the research I've worked on, especially the applications,” Sule said. “I very much still think of myself as a mathematician, but the exposure I've gotten to medical imaging, drug discovery and just knowing what things people outside of the math world care about has been really exciting and important to learn.”

Written by Emily Nunez