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UID:20260622T005826EDT-4234VMPioc@132.216.98.100
DTSTAMP:20260622T045826Z
DESCRIPTION:Title: Topological data analysis of collective dynamics\n\nAbst
 ract:\n\nFrom nanoparticle assembly to synchronized neurons to locust swar
 ms\, collective behaviors abound anywhere in nature that objects or agents
  interact. Investigators modeling collective behavior face a variety of ch
 allenges involving data from simulation and/or experiment. These challenge
 s include exploring large\, complex data sets to understand and characteri
 ze the system\, inferring the model parameters that most accurately reflec
 t a given data set\, and assessing the goodness-of-fit between experimenta
 l data sets and proposed models. Topological data analysis provides a lens
  through which these challenges may be addressed. This talk consists of th
 ree parts. In the first part\, I apply topological data analysis to the se
 minal aggregation model of Vicsek et al. (1995) in order to identify dynam
 ical events that traditional methods do not. In the second part\, I use to
 pological data analysis to choose between unbiased correlated random walk 
 models that potentially describe motion tracking experiments on pea aphids
 . Finally\, moving towards a theory of reduced topological descriptions of
  complex behavior\, I present open questions on the topology of random dat
 a\, complementing research in random geometric graph theory. Throughout th
 e talk\, the key approach is to characterize a system's dynamics via the t
 ime-evolution of topological invariants called Betti numbers\, accounting 
 for persistence of topological features across multiple scales. No prior k
 nowledge of topology is necessary.\n
DTSTART:20190218T210000Z
DTEND:20190218T220000Z
LOCATION:Room 1104\, Burnside Hall\, CA\, QC\, Montreal\, H3A 0B9\, 805 rue
  Sherbrooke Ouest
SUMMARY:Chad Topaz (Williams College)
URL:/mathstat/channels/event/chad-topaz-williams-colle
 ge-294649
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