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Application of persistent homology to granular materials and sampled dynamical systems
Hiroshi Takeuchi, Chubu University
Location: Hill 425
Date & time: Friday, 14 February 2020 at 2:00PM - 3:00PM
Persistent homology is a tool describing the shape of data. In this talk, we apply persistent homology to two topics; granular materials and sampled dynamical systems. A granular material is a set of macroscopic particles, such as sand, nuts, or coffee beans. The simplest model of granular materials is monodisperse sphere packings. We utilize persistent homology to capture the change of topological configurations in the crystallization of sphere packings.
In the second application, we focus on a sampled map, which is a finite subset of a map. A notable example is that the map is a discrete dynamical system, then a sampled map is a sampling from the dynamical system. Our motivation is to retrieve topological information of the dynamical system only from the finite sampling data. Persistent homology can extract the robust topological changes in the underlying map, and the cycles of the homology generators provide the model of the underlying map.