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SUMMARY:Twisted paths in Euclidean groups: Keeping track of total orientat
 ion while traversing DNA - Chirikjian\, G S (Johns Hopkins University)
DTSTART:20120905T103000Z
DTEND:20120905T105000Z
UID:TALK39540@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:This talk introduces a new mathematical structure for modeling
  global twist in DNA. The relative rigid-body motion between reference fra
 mes attached either to a backbone curve\, bi-rods\, or individual bases in
  DNA\, can be described well using elements of the Euclidean motion group\
 , SE(n). However\, the group law for Euclidean motions does not keep track
  of overall twist. In the planar case\, the universal covering group of SE
 (2) identifies orientation angle as a quantity on the real line rather tha
 n on the circle\, and hence keeps track of ``global'' rotations (not modul
 o 360 degrees). However\, in the three-dimensional case\, no such structur
 e exists since the the orientational part of the universal cover of SE(3) 
 can be identified with the quaternion sphere. In this talk a new mathemati
 cal structure for ``adding'' framed curves and extracting global twist is 
 present. Though reminiscent of the group operation in braid theory and in 
 homotopy theory\, this structure is distinctly different\, as it is geomet
 ric in nature\, rather than topological. The motivation for this mathemati
 cal structure and its applications to DNA conformation will be presented.\
 n
LOCATION:Seminar Room 1\, Newton Institute
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