We show that the persistent homology of a filtered ddimensional simplicial complex is simply the standard homology of a particular graded module over a polynomial ring. Our analy...
Inference of topological and geometric attributes of a hidden manifold from its point data is a fundamental problem arising in many scientific studies and engineering application...
: We present a method to compute the exact topology of a real algebraic surface S, implicitly given by a polynomial f Q[x,y,z] of arbitrary total degree N. Additionally, our analy...