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UID:cb75f2a647ccd63cb0c41a80e03925b0
CATEGORIES:Math and Data Seminar
CREATED:20260828T181006
SUMMARY:Crystallographic Phase Retreival, Multi-Reference Alignment and Second Moments
LOCATION:Hill 705
DESCRIPTION:Abstract: X-ray crystallography is a widely used technology for reconstruct
 ing the lattice structure of crystallized protein molecules from the diffra
 ction patterns produced when the crystal is bombarded with X-rays. This tec
 hnology plays a critical role in drug discovery and medicine. At the heart 
 of this method lies the so-called "phase problem": if we treat the protein'
 s electron density as the signal to be reconstructed, the diffraction patte
 rn fails to captures any phase information of this signal. The crystallogra
 phic phase retrieval problem therefore seeks to recover an unknown signal f
 rom its crystallographic phase-less measurements. In this talk, we will int
 roduce the crystallographic phase retrieval problem, discuss its well-posed
 -ness, and outline a few results that determine if and when recovery is pos
 sible. To establish these recovery results, we will outline how the crystal
 lographic phase retrieval problem is a special instance of a problem seekin
 g to invert the second moment measurements of a more general framework know
 n as the Multi-Reference Alignment (MRA) model.\nThis talk is based on join
 t works with Dan Edidin, Nadav Dym and Tamir Bendory.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Abstract: X-ray crystallography is a widely used technology for reconstr
 ucting the lattice structure of crystallized protein molecules from the dif
 fraction patterns produced when the crystal is bombarded with X-rays. This 
 technology plays a critical role in drug discovery and medicine. At the hea
 rt of this method lies the so-called "phase problem": if we treat the prote
 in's electron density as the signal to be reconstructed, the diffraction pa
 ttern fails to captures any phase information of this signal. The crystallo
 graphic phase retrieval problem therefore seeks to recover an unknown signa
 l from its crystallographic phase-less measurements. In this talk, we will 
 introduce the crystallographic phase retrieval problem, discuss its well-po
 sed-ness, and outline a few results that determine if and when recovery is 
 possible. To establish these recovery results, we will outline how the crys
 tallographic phase retrieval problem is a special instance of a problem see
 king to invert the second moment measurements of a more general framework k
 nown as the Multi-Reference Alignment (MRA) model.</p><p>This talk is based
  on joint works with Dan Edidin, Nadav Dym and Tamir Bendory.</p>
CONTACT:Arun Suresh (Rutgers)
DTSTAMP:20260829T213127
DTSTART;TZID=America/New_York:20260909T140000
DTEND;TZID=America/New_York:20260909T150000
SEQUENCE:0
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