Math Researcher Provides New Tool to Study the Brain

Assistant Professor of Mathematics Iris Yoon first became intrigued by topology—a branch of mathematics concerned with the study of shapes—as an undergraduate student.  

“I took a topology class in undergrad which was fascinating to me,” said Yoon. “And I found this field by accident. I went on Google and searched ‘applications of topology’ and found that it was an actual field of research.” 

That fascination led Yoon to contact a researcher at the University of Pennsylvania, who invited her to join his weekly research seminars and ultimately served as advisor for her Ph.D. in applied mathematics and computation science.  

In her work as a mathematician and applied topologist at Wesleyan, Yoon ponders questions like, “How is high-dimensional data—a dataset with a large number of variables—organized? What is its shape? What insight can we gain from understanding the structure and shape?” she said. 

Most recently, Yoon focused her expertise on neurons, or the billions of nerve cells that fire off messages throughout the body. In a new paper, published in Proceedings of the National Academy of Sciences (PNAS), Yoon and her co-authors developed a new tool for examining the topology, or structure, of neurons in the human brain. The technique could lead to further research into how the brain encodes and organizes the enormous amount of information flowing through it. One potential implication of this study—though much more research will need to be done—is insight into neurological disorders, such as schizophrenia, that may stem from disrupted communication across neural populations. 

Advancements in imaging technologies allow scientists like Yoon to analyze data collected from multiple regions of the brain simultaneously. With these tools, researchers can explore more complex issues. “This raises new scientific questions such as, how are the neural structures in multiple brain regions related to one another?” said Yoon. 

The computational method Yoon and her colleagues developed further expands possibilities for researching the brain. “It provides a new tool to study how information flows across different brain regions,” said Yoon, and may even lead to understanding differences across healthy and diseased brains.   

Her research—which draws from topology, network theory, and machine learning—develops novel methods for capturing the complexities of data in cancer research and genomics, as well as neuroscience.  

 “Advancements in experimental techniques make it common for experimentalists to record from multiple brain regions simultaneously. This raises new scientific questions: How is the information encoded in multiple brain regions related to one another?” said Yoon. Understanding the structure and meaning of that data is a “non-trivial task that demands the development of new approaches,” she said.