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SUMMARY:Detecting and Exploiting Non-Trivial Geometrical Data Structures f
or Obtaining Insights Into Biology
DTSTART;VALUE=DATE-TIME:20161107T100000Z
DTEND;VALUE=DATE-TIME:20161107T120000Z
DTSTAMP;VALUE=DATE-TIME:20210413T104701Z
UID:indico-event-1735@indico.math.cnrs.fr
DESCRIPTION:Thanks to recent progress in biotechnologies\, the high-throug
hput data\nin molecular biology are getting more\n and more interesting f
rom the point of view of application of advanced\nmethods for data analysi
s\, aimed\n at finding non-trivial topological characteristics in the dat
a such as\nbranching points and holes. Existence\n of such non-trivial st
ructures in the data can have direct biological\ninterpretations such as t
he process\n of cell fate decisions during cell differentiation or existe
nce of\ncyclic processes in a cell (e.g.\, cell cycle).\n\n I will presen
t examples of application of such methods in studying\nvarious biological
systems and explain their general\n principles. I will focus on the unive
rsal method of elatic principal\ngraphs for topological data analysis deve
loped by us.\n The method is based on application of the notion of harmon
ic graph\nembedding into a multi-dimensional space\,\n minimization of gr
aph elastic energy and using graph grammars defining\na family of possible
graph structures (such as trees).\n Simplest implementations of the appr
oach already give very usefull\ndata approximators such as principal curve
s\,\n principal closed curves\, principal manifolds and principal trees.\
nSeveral ideas for making these data approximators\n robust to the noise
and outliers in the biological data will be\npresented.\n\nhttps://indico.
math.cnrs.fr/event/1735/
LOCATION:IHES Amphithéâtre Léon Motchane
URL:https://indico.math.cnrs.fr/event/1735/
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