# Seminars & Colloquia Calendar

## Inverse Problems and Unsupervised Learning with applications to Cryo-Electron Microscopy

#### Roy Lederman, PACM, Princeton University

Location: ** Hill 705**

Date & time: Wednesday, 17 January 2018 at 3:30PM - 4:30PM

Abstract: Cryo-Electron Microscopy (cryo-EM) is an imaging technology that is revolutionizing structural biology; the Nobel Prize in Chemistry 2017 was recently awarded to Jacques Dubochet, Joachim Frank and Richard Henderson "for developing cryo-electron microscopy for the high-resolution structure determination of biomolecules in solution".

Cryo-electron microscopes produce a large number of very noisy two-dimensional projection images of individual frozen molecules. Unlike related methods, such as computed tomography (CT), the viewing direction of each image is unknown. The unknown directions, together with extreme levels of noise and additional technical factors, make the determination of the structure of molecules challenging. While other methods for structure determination, such as x-ray crystallography and nuclear magnetic resonance (NMR), measure ensembles of molecules, cryo-electron microscopes produce images of individual molecules. Therefore, cryo-EM could potentially be used to study mixtures of different conformations of molecules. Indeed, current algorithms have been very successful at analyzing homogeneous samples, and can recover some distinct conformations mixed in solutions, but, the determination of multiple conformations, and in particular, continuums of similar conformations (continuous heterogeneity), remains one of the open problems in cryo-EM.

I will discuss a one-dimensional discrete model problem, Heterogeneous Multireference Alignment, which captures many of the group properties and other mathematical properties of the cryo-EM problem. I will then discuss different components which we are introducing in order to address the problem of continuous heterogeneity in cryo-EM: 1. "hyper-molecules," the mathematical formulation of truly continuously heterogeneous molecules, 2. Computational and numerical tools for formulating associated priors, and 3. Bayesian algorithms for inverse problems with an unsupervised-learning component for recovering such hyper-molecules in cryo-EM.

R. Shapiro Organizer's Page

Charles Weibel Organizer's Page

Brooke Logan

Wujun Zhang Organizer's webpage

Xiaojun Huang and Purvi Gupta Organizer's webpage

Pranjal Awasthi, Shubhangi Saraf Organizer's Page

Jeffry Kahn, Bhargav Narayanan, Jinyoung Park Organizer's webpage

Mingjia Yang, Doron Zeilberger home page

Paul Feehan, Manousos Maridakis, Natasa Sesum Organizer's webpage

Lev Borisov, Emanuel Diaconescu, Angela Gibney, Nicolas Tarasca, and Chris Woodward Organizer's webpage

Alejandro Ginory Organizer's Page

Louis Gaudet, Yael Davidov Organizer's webpage

Erik De Amorim Organizer's Page

Corrine Yap Organizer's webpage

Edna Jones Organizer's webpage

Yanyan Li, Zheng-Chao Han, Jian Song, Natasa Sesum

Lisa Carbone, Yi-Zhi Huang, James Lepowsky, Siddhartha Sahi Organizer's page

Simon Thomas website

Kasper Larsen, Daniel Ocone and Kim Weston Organizer's page

Joel Lebowitz, Michael Kiessling

Yanyan Li, Haim Brezis

Edna Jones website

Stephen D. Miller, John C. Miller, Alex V. Kontorovich, Claire Burrin seminar website

Stephen D. Miller

Organizers: Yanyan Li, Z.C. Han, Jian Song, Natasa Sesum

Matthew Charnley Organizer's Page

Hongbin Sun Organizer's page

Ebru Toprak, Organizer

Organizer: Luochen Zhao

Organizers: Marco Castronovo - website

Organizer: Vladimir Retakh Organizer's webpage

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