The persistent homology provides a mathematical tool to describe “features” in a principled manner. The persistence algorithm proposed by Edelsbrunner et al. [9] can compute n...
We develop a method for measuring homology classes. This involves three problems. First, we define the size of a homology class, using ideas from relative homology. Second, we defi...
In this note we discuss the information needed to compute the homology groups of a topological space. We argue that the natural class of spaces to consider are the compact absolut...
We define the robustness of a level set homology class of a function f : X R as the magnitude of a perturbation necessary to kill the class. Casting this notion into a group theor...
Paul Bendich, Herbert Edelsbrunner, Dmitriy Morozo...
Given a Newtonian coalgebra we associate to it a chain complex. The homology groups of this Newtonian chain complex are computed for two important Newtonian coalgebras arising in ...