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<td>[math-ias] Reminder for today's Members' Seminar</td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">Date: </th>
<td>Mon, 4 Feb 2019 10:32:24 -0500</td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">From: </th>
<td>Kristina Phillips <a class="moz-txt-link-rfc2396E" href="mailto:kphillips@ias.edu"><kphillips@ias.edu></a></td>
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<th valign="BASELINE" nowrap="nowrap" align="RIGHT">To: </th>
<td>'Seminars' <a class="moz-txt-link-rfc2396E" href="mailto:seminars@math.ias.edu"><seminars@math.ias.edu></a></td>
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<p class="MsoNormal">INSTITUTE FOR ADVANCED STUDY<o:p></o:p></p>
<p class="MsoNormal">School of Mathematics<o:p></o:p></p>
<p class="MsoNormal">Princeton, NJ 08540<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><b>Members' Seminar<o:p></o:p></b></p>
<p class="MsoNormal"><b>Monday, February 4<o:p></o:p></b></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">To view mathematics in titles and
abstracts, please click on the talk's link.<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Topic: The Sample
Complexity of Multi-Reference Alignment<o:p></o:p></p>
<p class="MsoNormal">Speaker: Philippe Rigollet,
Massachusetts Institute of Technology; Visiting Professor,
School of Mathematics<o:p></o:p></p>
<p class="MsoNormal">Time/Room: 2:00pm - 3:00pm/Simonyi
Hall 101<o:p></o:p></p>
<p class="MsoNormal"><span lang="FR">Abstract Link: </span><a
href="http://www.math.ias.edu/seminars/abstract?event=129413"
moz-do-not-send="true"><span lang="FR">http://www.math.ias.edu/seminars/abstract?event=129413</span></a><span
lang="FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="FR"><o:p> </o:p></span></p>
<p class="MsoNormal">How should one estimate a signal, given
only access to noisy versions of the signal corrupted by
unknown cyclic shifts? This simple problem has surprisingly
broad applications, in fields from aircraft radar imaging to
structural biology with the ultimate goal of understanding the
sample complexity of Cryo-EM. We describe how this model can
be viewed as a multivariate Gaussian mixture model whose
centers belong to an orbit of a group of orthogonal
transformations. This enables us to derive matching lower and
upper bounds for the optimal rate of statistical estimation
for the underlying signal. These bounds show a striking
dependence on the signal-to-noise ratio of the problem. We
also show how a tensor based method of moments can solve the
problem efficiently. Based on joint work with Afonso Bandeira
(NYU), Amelia Perry (MIT), Amit Singer (Princeton) and
Jonathan Weed (MIT).<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"> <a href="http://www.math.ias.edu/seminars"
moz-do-not-send="true">http://www.math.ias.edu/seminars</a><o:p></o:p></p>
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