Persistent homology (PH) is a method used in topological data analysis (TDA) to study
qualitative features of data that persist across multiple scales. It is robust to perturbations of …

Comments• page viii, bottom of page: the following names should be added to the
acknowledgements:-Peter Landweber had an invaluable contribution to these notes. First …

Geometric and topological inference deals with the retrieval of information about a geometric
object using only a finite set of possibly noisy sample points. It has connections to manifold …

The Vietoris-Rips filtration is a versatile tool in topological data analysis. It is a sequence of
simplicial complexes built on a metric space to add topological structure to an otherwise …

Algorithms for persistent homology are well-studied where homomorphisms are induced by
inclusion maps. In this paper, we propose a practical algorithm for computing persistence …

This paper introduces a new data structure, called simplex tree, to represent abstract
simplicial complexes of any dimension. All faces of the simplicial complex are explicitly …

We associate with each compact set X of Rn two real-valued functions cX and hX defined on
R+ which provide two measures of how much the set X fails to be convex at a given scale …

We present a novel approach for the decimation of triangle surface meshes. Our algorithm
takes as input a triangle surface mesh and a set of planar proxies detected in a pre …

Co** with imbalanced data is a challenging task in practical classification problems. One
of effective methods to solve imbalanced problems is to oversample the minority class. Gls …

In this article, we extend the notions of dominated vertex and strong collapse of a simplicial
complex as introduced by J. Barmak and E. Miniam. We say that a simplex (of any …