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TZID:Asia/Jerusalem
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DTSTART:20171029T020000
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DTSTART:20180323T020000
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UID:calendar.49191.field_date.0@mathematics.huji.ac.il
DTSTAMP:20200710T101854Z
CREATED:20171228T134155Z
DESCRIPTION:Date: \n\n12:00pm to 1:00pm\n\n\n\n\nSee also: Analysis\, Eve
nts & Seminars\, SeminarsLocation: \n\nRoss 70\n\n\nAbstract: Cryo-EM is a
n imaging technology that is revolutionizing structural biology\; the Nobe
l Prize in Chemistry 2017 was recently awarded to Jacques Dubochet\, Joach
im Frank and Richard Henderson “for developing cryo-electron microscopy fo
r the high-resolution structure determination of biomolecules in solution'
. \nCryo-electron microscopes produce a large number of very noisy two-dim
ensional 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 o
f noise and additional technical factors\, make the determination of the s
tructure of molecules challenging. \nWhile other methods for structure det
ermination\, such as x-ray crystallography and nuclear magnetic resonance
(NMR)\, measure ensembles of molecules together\, cryo-EM produces measure
ments of individual molecules. Therefore\, cryo-EM could potentially be us
ed to study mixtures of different conformations of molecules. Indeed\, cur
rent 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\, continuu
ms of similar conformations (continuous heterogeneity)\, remains one of th
e open problems in cryo-EM. \nI will discuss a one-dimensional discrete mo
del 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 first mathematical formulation of truly continuo
usly heterogeneous molecules\, 2. The optimal representation of objects th
at are highly concentrated in both the spatial domain and the frequency do
main using high-dimensional Prolate spheroidal functions\, and 3. Bayesian
algorithms for inverse problems with an unsupervised-learning component f
or recovering such hyper-molecules in cryo-EM.\n\n Export\n \n\n \nsubs
cribe iCal
DTSTART;TZID=Asia/Jerusalem:20171122T120000
DTEND;TZID=Asia/Jerusalem:20171122T130000
LAST-MODIFIED:20191103T200056Z
SUMMARY:Jerusalem Analysis Seminar: 'Inverse Problems with applications to
Cryo-Electron Microscopy (cryo-EM)'\,Roy Lederman
URL;TYPE=URI:https://mathematics.huji.ac.il/event/jerusalem-analysis-semina
r-inverse-problems-applications-cryo-electron-microscopy-cryo
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