A Perfect Match

Alla Borisyuk

Alla Borisyuk, associate professor of mathematics and the department’s director of undergraduate studies, has always been “good at math” and fascinated with the brain. When it came time to choose her major at Moscow State University, she seized the opportunity to study mathematics with a strong department. After completing a five-year master’s degree in pure mathematics, she found that neuroscience still held the greatest interest for her. She also recognized the math she had been learning could be used as a tool to study the brain, so she looked for a graduate school where she could complete a degree in math and do research in computational neuroscience. New York University (NYU) fit the bill, and she was able to do interdisciplinary study between NYU’s Courant Institute of Mathematical Sciences and its Center for Neural Science. She obtained a Ph.D. in mathematics from NYU in 2002 and spent time as a postdoc at the Mathematical Biosciences Institute at Ohio State University. In 2005, she and her husband, Firas Rassoul-Agha, who works in probability and stochastic processes, both joined the U’s Math Department.

“My research seeks to understand how different parts of the brain do what they do,” said Borisyuk. For that purpose, she and a team model brain processes by creating an idealized representation of them as a system of differential equations, or a stochastic process on a graph, for example. The choice of the model for a particular project depends on the biology of the system and the questions the team hopes to answer. She works with experimental neuroscientists to keep her models relevant to biology. Once a model is developed, it becomes a mathematical object suitable for analysis.

“For a long time, one of the most powerful tools we used was dynamical systems, which allowed us to characterize a system’s general behavior in different regions of parameter space,” said Borisyuk. “As experimental methods have evolved, it’s crucial now to treat many processes as stochastic, either because of the small number of components or because noise is an inseparable part of brain activity. The nature of the models we build often requires us to venture into different areas of mathematics—areas that I’m not an expert in—so I appreciate insight from my colleagues in math.”

National Institutes of Health Grant

Recently, Borisyuk and fellow researcher, Matt Wachowiak, a Utah Science Technology and Research (USTAR) professor of neurobiology and anatomy at the U, received a grant from the National Institutes of Health to investigate how olfactory information (different odors) is represented in the brain. Scientists know a lot about how the visual and auditory parts of the brain are organized, but less is known about olfaction. Borisyuk notes that math plays an important role in the research. “We use linear algebra, graph and network theory, and data analysis, in addition to ordinary differential equation model analysis and simulation,” she said. Understanding how the olfactory system encodes, processes, and decodes odors is likely to reveal new principles underlying brain function in general and will also facilitate future engineering applications.

Director of Undergraduate Studies

In addition to her teaching and research duties, Borisyuk directs the department’s undergraduate studies, which includes majors in math (including statistics and computing emphases), applied mathematics, and math education. “For me, the most interesting part of the undergraduate studies program is helping students find research projects through our Research Experience for Undergraduates program, or REU,” said Borisyuk. “For many students, the research experience is the highlight of their time at the U. While some take on projects to satisfy an honors degree or other program requirements, most do it for the experience.” Borisyuk works with the Math Department Curriculum Committee to ensure that class offerings and degree requirements remain relevant, interesting, and satisfying to students.

Borisyuk also gives her time to other programs at the U, including Mathematical Biology Research, Neuroscience, and the ACCESS Program for Women in Science & Mathematics. “I guess juggling all of this keeps me energized,” said Borisyuk. She credits her graduate students and collaborators in neuroscience with keeping her focused. “They motivate me, and our discussions keep me excited about the unknown we have to explore.”

When she isn’t teaching or doing research, she loves spending time with her husband and two sons. They like to travel, hike, and play board games.

As Borisyuk continues with her research, her priorities will remain focused on brain research and computational neuroscience. “We have a lot to learn, and, without a doubt, math will continue to play a central role in elucidating the principles of brain function,” she said.