Dept. of Statistics, University of Chicago
The human brain connectome is an ambitious project to provide a complete map of neural
connectivity and a recent source of excitement in the neuroscience community. Just as
the human genome is a triumph of marrying technology (high throughput sequencers) with
theory (dynamic programming for sequence alignment), the human connectome is a result
of a similar union. The technology in question is that of diffusion magnetic resonance
imaging (dMRI) while the requisite theory, we shall argue, comes from three areas:
PDE, harmonic analysis, and convex algebraic geometry.
The underlying mathematical model in dMRI is the Bloch-Torrey PDE but we will approach
the 3-dimensional imaging problem directly. The main problems are (i) to reconstruct a
homogeneous polynomial representing a real-valued function on a sphere from dMRI data;
and (ii) to analyze the homogeneous polynomial via a decomosition into a sum of powers
of linear forms. We will focus on the nonlinear approximation associated with (ii) and
discuss a technique that combines (i) and (ii) for mapping neural fibers.
This is joint work with T. Schultz of MPI Tubingen.
Tuesday, May 22, 2012
11:00AM AP&M 2402
Center for Computational Mathematics9500 Gilman Dr. #0112La Jolla, CA 92093-0112Tel: (858)534-9813