It is well known that the nerve (or Čech complex) of a covering consisting of metric balls with a common fixed radius is nicely approximated by the Vietoris-Rips complex. Being a f …

I have a data set that essentially looks like the picture below, i.e., it's given by sets of points in $\mathbb{R}^3$ that sample the cross-sections of a certain surface that in pr …

If you generate points in $\mathbb R^n$ via a process that respects a Gaussian normal distribution, then compute the persistent homology / barcodes, to my eye something fairly regu …

Hi I am delving into the field of Computational Topology. I am aware of the books in this field, but could anybody tell me a nice relevant paper in this field which tackles a "t …

Consider a dynamical system $(T,X)$ that admits a Markov partition $\mathcal{M}$ (e.g., an Anosov map), and consider the corresponding 0-1 transition matrix $A$. It is commonplace …