Applied Computational Mathematics Division


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Exploration of a Random Dot Product Graph Model for Neuronal Connectivity

Rebecca Goldin
Department of Mathematical Sciences, George Mason University

Tuesday, March 20, 2012 15:00-16:00,
Building 101, Lecture Room C
Gaithersburg
Tuesday, March 20, 2012 13:00-14:00,
Room 1-4058
Boulder

Abstract: The mammalian brain is a large network of neurons (approximately 10^8 in rodents, up to 10^11 in humans), sparsely interconnected by synapses (approx. 10^4 per neuron). The common working assumption posits the existence of distinct "neuronal classes," where neurons in the same class share similar connectivity patterns compared to neurons in different classes. In this talk, I will introduce a probabilistic model that formalizes the concept of neuronal class based on network connectivity. Given a complete list of all neurons and their connections in a network, our techniques estimate the number of neuronal classes, and an assignment of each neuron to a class. We model the connectome using a random dot product model, in which the connection probability is determined by the dot product of latent vectors associated with the pre- and post-synaptic neurons. We fit the model using sparse singular value decomposition, and cluster the latent vectors into groups, which define the proposed neuronal classes. Using neurobiologically realistic surrogate data, we demonstrate that this approach is robust and computationally tractable. This model provides both a practical and theoretical foundation to bridge neuronal- and system-level neuroanatomy.

Speaker Bio: Rebecca Goldin holds a Ph.D. from Massachusetts Institute of Technology in Mathematics, and a B.A., cum laude from Harvard University. Dr. Goldin did postdoctoral work at University of Maryland with a National Science Foundation postdoctoral fellowship before she joined George Mason University, where she is currently an associate professor in the Department of Mathematical Sciences. She has published numerous research articles in internationally recognized mathematics journals, and regularly speaks at conferences across North America, Europe and Asia. She is the recipient of several grants from the National Science Foundation to support her research in mathematics and education. In 2007 she received the Ruth I. Michler Memorial Prize from the Associaton of Women in Mathematics and spent the fall semester of 2007 at Cornell University. In 2008, Dr. Goldin was an awardee of George Mason's Emerging Researcher, Scholar, Creator Awards, which recognizes excellence in academic achievement. Since 2004, Dr. Goldin has also been the Director of Research at Statistical Assessment Service (STATS), a nonprofit media education group that aims to improve the scientific discourse in the media. In this capacity she works with journalists and the public on a wide range of scientific and statistical topics. In 2008 she joined the advisory board of Math for America: DC, a non-profit organization dedicated to improving math education in secondary public schools in the U.S. She currently serves on the Association for Women in Mathematics Policy and Advocacy Committee, and several Mathematical Association of America and American Mathematical Society committees. Dr. Goldin is a 2012 Nifty Fifty speaker at the U.S. Science and Engineering Festival; she also coaches a Mathcounts team in Fairfax, VA.

Presentation Slides: PDF

Contact: B. Cloteaux

Note: Visitors from outside NIST must contact Cathy Graham; (301) 975-3668; at least 24 hours in advance.