Mardi 13 mai, 11:30
Université de Sherbrooke, Département de
mathématiques
2500 boul. de l'Université, Pavillon D6-2046
Afra Zomorodian, Dartmouth College
Topological
Data Analysis
Conférence
conjointe du séminaire GRTC avec le Colloque
de Mathématiques du DM
Mercredi
27 février, 15:30
Université de Sherbrooke, Département de
mathématiques
2500 boul. de l'Université, Pavillon D7-2016
Konstantin Mischaikow, Rutgers
University
Homology
of Random Fields
Abstract:
It is fairly easy to collect large amounts of high dimensional data
describing the time dependent spatial structures of materials or fluids
either through experimentation or numerical simulation. Techniques from
computational homology can be used to reduce both the size and
dimension of the data sets and still provide useful statistics for
parameter identification, model selection, and quantification of the
spatio-temporal complexity of the dynamics. In many applications the
structures of interest arise as nodal domains of real-valued functions,
but the homology computations are based on suitable
discretizations. This raises the question of how accurate the
resulting homology computations are. I will discuss a
probabilistic approach to quantifying the validity of homology
computations for nodal domains of random fields in one and two space
dimensions, which furnishes explicit probabilistic a-priori bounds for
the suitability of certain discretization sizes.