Marco Antonio de Freitas Contessoto

• Abstract

  One of the recent trends in the applied algebraic topology field has been the development of algorithmic techniques that can efficiently compute the persistence barcodes associated with a given simplicial tower K. There are very recent indications that ideas related to coomology often lead to algorithms that present higher memory efficiency and lower overall computational complexity in pr…

  Persistent cohomology, BP.DR

• Abstract

  Gunnar Carlsoon discusses the adaptation of the theory of homology from the Algebraic Topology to topological pattern recognition problems in point cloud data sets. This adaptation leads to the concept of persistence homology and bar codes. Several applications have been obtained using this method. We will present several cases where persistence homology is used, illustrating different…

  An adaptation of homology theory to problems of topological pattern recognition, BP.MS

• Abstract

  This project aims to give an overview of applications of Algebraic Topology. Simple examples of applications of the following topics will be presented: Manifolds, Euler Characteristic, Homology and Cohomology, Morse Theory and Conley Index. All topics, except for Morse theory, have been developed formally by the student previously. The student will learn new concepts with the reading of a…

  Some applications of algebraic topology, BP.IC

(Only some records are available in English at this moment)

• Abstract

  One of the recent trends in the Applied Algebraic Topology field has been the development of algorithmic techniques that can efficiently compute the persistence barcodes associated with a given simplicial tower K. There are very recent indications that ideas related to cohomology often lead to algorithms that present higher memory efficiency and lower overall computational complexity in …

  Persistent cohomology, BE.EP.DR

• Abstract

  In the paper "Barcodes: the persistent topology data" is presented the primary mathematical tool considered in a homology theory for point- cloud data sets (persistent homology) and a novel representation of this algebraic characterization (barcodes) and in "Persistent Homology - a survey" is given a short history of persistent homology and present its basic concepts. (AU)

  Barcodes: the persistent topology of data, BE.EP.IC