Earlier this year, President Obama announced a major federal research initiative dubbed the “brain initiative.” According to the initial announcement, its goal was to develop and use imaging techniques to better understand neural processes and brain function.
Recently, the U.S. National Institutes of Health provided more details on a possible program in Brain Research through Advancing Innovative Neurotechnologies (BRAIN). Plans are for this initiative to begin in 2014 (the 2014 fiscal year starts October 1, 2013). The report lists various research priorities; among these, according to Science (Vol. 341, page 1325, 20 September 2013) are “classifying brain cells, studying how they connect, and identifying how patterns of activity among them produce behavior.”
Mathematics can play a crucial role in this research. Mathematicians Jennifer Chayes and Nancy Kopell were among the “expert consultants” in the study that led to the report (Report, page 56-57).
To get a sense of the role mathematics can play one need only look at the research of Nancy Kopell, one of many people studying neural activity from a dynamical systems perspective. Kopell studies rhythmic behavior in networks of neurons—what biophysical mechanisms produce them, and what functions they serve. Kopell delivered SIAM’s 2007 John von Neumann Lecture. A March 2007 article on Kopell in SIAM News describes some of this research. An earlier SIAM News article from May 2003, by Dana Mackenzie, also described possible implications of this research on understanding brain-related diseases, such as Parkinson’s disease.
Studying patterns of behavior through the dynamic interactions of neurons remains a very active of research among mathematicians in the field of applied dynamical systems.