Mathematics on (and of) the Mind — AMATH and a New Research Center

Submitted by Tony I Garcia on

Eric Shea-Brown, Adrienne Fairhall, and Christof Koch (President, Allen Institute for Brain Science) at the UW/Allen Institute Summer Workshop on the Dynamic Brain, which they co-direct together with Michael Buice and Shawn Olsen (Allen Institute).

By Eric Shea-Brown, Adrienne Fairhall, and Jessica Huszar

Recent years have found that mathematics, that wondrous invention of the brain, can be turned around to help understand the workings of the brain itself.  Neuroscience is changing more rapidly than anyone could have predicted. A wealth of novel recording technologies has opened up unprecedented 3-D views of brain activity and connectivity, revealing an incredibly dynamic system with complex patterns of activity that represent unknown features of the brain’s internal code. At the same time, stunning advances in neural network-driven computing systems have proved that brainlike components can be assembled to achieve human-level performance on perceptual and strategic tasks. Finding synergy between these twin advances requires fundamentally new ways of combining dynamical systems for networks, machine learning for big data, stochastic modeling for biophysics, and the theories of network-based computing.  

The UW Department of Applied Mathematics is seizing this extraordinary challenge -- and opportunity -- for the mathematical sciences.  The Department is a long-standing supporter of mathematical and computational neuroscience research at UW. This builds on a strong tradition of mathematical biology research in the department, including by former faculty such as Frederic Wan and James Murray -- author of the landmark text Mathematical Biology -- and current faculty including Ivana Bozic, Mark Kot, and Hong Qian. Over the past decade the Department hired key faculty to build the mathematical neuroscience community at UW, including Eric Shea-Brown, Eli Shlizerman, and Emo Todorov, and brought on adjunct and affiliate faculty Adrienne Fairhall, Bing Brunton, Stefan Mihalas, and Michael Buice. At the same time, Nathan Kutz moved part of his research program into the computational neuroscience field. The Department also co-supported a series of outstanding acting assistant professors in mathematical neuroscience including Andrea Barreiro (now at Southern Methodist University), Joel Zylberberg (now at York University), and Braden Brinkman (now at Stony Brook University), hosts recent National Institutes of Health (NIH) Pathway to Independence Award winners Gabrielle Gutierrez and Hannah Choi, and supported many PhD students in the field, many who have received university-wide and national recognition and are now also professors around the world, from École normale supérieure-Paris to Swarthmore to the University of Montreal to the Hong Kong University of Science and Technology.

In 2009, the Department provided visionary support to the first Computational Neuroscience Connection (now on its 11th year as the Neural Computation & Engineering Connection), an annual symposium celebrating neural computation and engineering research at UW and the Pacific Northwest. The department also supported the creation of new courses in computational neuroscience that span from beginning undergraduate to advanced graduate levels, including Introduction to Neural Coding and Computation (AMATH 342), and Dynamics of Neurons and Networks (AMATH 534). These courses provide unique opportunities for UW students to immerse themselves in the study of theoretical neuroscience and form the core of our programs at the interface of math and neuroscience.  

Building on the growing UW activity in the field, the UW Computational Neuroscience Center, currently housed in the Health Sciences Building, officially opened in 2017, sponsored by a generous investment from the College of Arts and Sciences (including funding from Applied Math), the School of Medicine, the College of Engineering, the Office of Research, and the Neuroscience Graduate Program. The Center’s goal is to catalyze interaction and research at the interface of mathematics and neuroscience by serving as a cross-departmental theory lab, nucleating joint grants, and hosting workshops, seminars, career development activities and journal clubs. The center is co-directed by Eric Shea-Brown and Adrienne Fairhall, with a leadership team of Eli Shlizerman, Emily Fox, and Michael Buice. The faculty are a mix of theorists and experimentalists, with interests that span many areas of mathematics, computation and data analysis and extensive interactions with colleagues in quantitative experimentation and imaging. They hold positions in many departments in the College of Arts and Sciences, the School of Medicine and the School of Engineering — giving students the chance to find their natural disciplinary home — but are closely connected through a dense web of interdisciplinary, cross-departmental collaboration.

The center runs programs for trainees at all different levels. This includes an undergraduate minor in Neural Computation and Engineering, an NIH-funded training program that provides research stipends for undergraduate and graduate students working in computational neuroscience, and a graduate certificate in Neural Computation. Fairhall also co-developed at UW the first MOOC in computational neuroscience, which has been that has enrolled over 50,000 students from around the world.  The CNC is also home to the Swartz Center for Theoretical Neuroscience, which provides funding for postdoctoral fellows, a yearly seminar series and summer visitors. The CNC has been able to support Applied Math researchers at all different levels. Some examples include recent funding for ACMS undergraduate student Zach McNulty who is working on training recurrent neural networks to make predictions, AMATH Ph.D. graduate student Iris Shi who is using neural network models to interpret brain-wide neural activity from the mouse visual cortex, and AMATH postdoctoral fellow Charles Delahunt who is studying rapid learning in neural networks inspired by insect olfactory systems. 

Prof. Anne Collins (UC Berkeley) delivers a CNC seminar on reinforcement learning algorithms. 

The doors are open for you to join us!  For more information on the Computational Neuroscience Center’s activities, please visit our website, and our Twitter feed. We host regular research events and seminars throughout the year, and, together with the Allen Institute for Brain Science, the Summer Workshop on the Dynamic Brain. Calls to join the training program are made every fall. Our website also has information on enrolling in the Neural Computation and Engineering Graduate Certificate and Minor, both of which are open to all interested students at UW.