OUDOT , Steve

Given a continuous function $f:X\to\mathbb{R}$ and a cover $\mathcal{I}$ of its image by intervals, the Mapper is the nerve of a refinement of the pullback cover $f^{-1}(\mathcal{I})$. Despite its success in applications, little is known about the structure and stability of this construction from a theoretical point of view. As a pixelized...

For points sampled near a compact set X, the persistence barcode of the Rips filtration built from the sample contains information about the homology of X as long as X satisfies some geometric assumptions. The Rips filtration is prohibitively large, however zigzag persistence can be used to keep the size linear. We present several species of...

For points sampled near a compact set $X$, the persistence barcode of the Rips filtration built from the sample contains information about the homology of $X$ as long as $X$ satisfies some geometric assumptions. The Rips filtration is prohibitively large, however zigzag persistence can be used to keep the size linear. We present several species...

The notion of e-sample, as introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an e-sample of a smooth surface S for a sufficiently small e, then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in...

The notion of -sample, as introduced by Amenta and Bern, has proven to be a key concept in the theory of sampled surfaces. Of particular interest is the fact that, if E is an -sample of a smooth surface S for a sufficiently small , then the Delaunay triangulation of E restricted to S is a good approximation of S, both in a topological and in a...

We introduce a new algorithm for computing zigzag persis-tence, designed in the same spirit as the standard persistence algorithm. Our algorithm reduces a single matrix, maintains an explicit set of chains encoding the persistent homology of the current zigzag, and updates it under simplex insertions and removals. The total worst-case running...