---------- Forwarded message ----------
From: *Ryan Adams* <rpa(a)seas.harvard.edu
Date: Monday, April 28, 2014
Subject: Fwd: [Seas-faculty] TODAY: Amit Singer will give a talk at the
Applied Mathematics Colloquium on Monday, April 28 at 3 pm in MD G125.
To: Dougal Maclaurin <maclaurin(a)physics.harvard.edu>du>, Martin Blood-Forsythe
<mbloodforsythe(a)physics.harvard.edu
Begin forwarded message:
*From: *"Stevens, Arlene S."
<astevens@seas.harvard.edu<javascript:_e(%7B%7D,'cvml','astevens@seas.harvard.edu');
*Subject: **[Seas-faculty] TODAY: Amit Singer will give a talk at the
Applied Mathematics Colloquium on Monday, April 28 at 3 pm in MD G125.*
*Date: *April 28, 2014 at 9:06:46 AM EDT
*To: *seas-faculty
<seas-faculty@seas.harvard.edu<javascript:_e(%7B%7D,'cvml','seas-faculty@seas.harvard.edu');
*APPLIED MATHEMATICS COLLOQUIUM*
*Monday**, April 28, 2014*
*3 pm in MD G125*
*Amit Singer,*
*Princeton University*
*Three-dimensional Structure **Determination of Molecules **without
Crystallization*
In cryo-electron microscopy (cryo-EM), a microscope generates a top view
of a sample of randomly-oriented copies of a molecule. The cryo-EM problem
is to use the resulting set of noisy 2D tomographic projection images taken
at unknown directions to reconstruct the 3D structure of the molecule. We
will discuss methods for estimating the unknown orientations using variants
of semidefinite programs (SDP) that were originally proposed in the
theoretical computer science community for solving problems such as Max-Cut
and Unique Games. Numerical evidence suggests that the SDP method is many
cases tight, that is, it provides the maximum likelihood estimator despite
the fact that the parameter space is exponentially large and non-convex. If
time permit, we will also discuss the problem of heterogeneity, which is
the task of mapping the space of conformational states of a molecule. Here
we are able to estimate the covariance matrix of the 3D structures from
their 2D projections. The proposed solutions has applications beyond
cryo-EM such as low-rank matrix completion and determination of ground
states of interacting particle systems. The analysis combines tools from
tomography, convex optimization, group theory, and random matrix theory. No
prior knowledge in these areas will be assumed.
--
---------------------------------------------------
Martin Blood-Forsythe
Graduate Student in Physics
Harvard University
Aspuru-Guzik Lab