Add to ORKGIn the thesis simplicial complexes as a means for representing topological spaces are presented. In particular, the Vietoris-Rips complex, which is used in computer science for data reconstruction and analysis, is described. A two-phase algorithm for constructing the Vietoris-Rips complex on a given data set is described. In the first phase, the algorithms constructs the neighborhood graph on a set of points, and in the second phase the graph is extended to a simplicial complex. Three approaches, inductive, incremental and maximal, for the second phase are described and proofs of their correctness are given. The algorithms are tested on an example, and their efficiency is analyzed
In this thesis, we look for methods for reconstructing an approximation of a manifold known only thr...
A point cloud can be endowed with a topological structure by constructing a simplicial complex using...
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up...
In the thesis simplicial complexes as a means for representing topological spaces are presented. In...
Motivated by applications in Topological Data Analysis, we consider decompositionsof a simplicial co...
In recent years, a new approach to data analysis has been developed, based on topological methods. T...
The field of computational topology has developed many powerful tools to describe the shape of data,...
Inspired by an early work of Muldoon et al., Physica D 65, 1-16 (1993), we present a general method ...
International audienceWe study the simplification of simplicial complexes by repeated edge contracti...
The Vietoris–Rips filtration is a versatile tool in topological data analysis. It is a sequence of s...
International audienceThe Vietoris–Rips filtration is a versatile tool in topological data analysis....
9 pagesInternational audienceWe study the simplification of simplicial complexes by repeated edge co...
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of...
In this thesis, we look for methods for reconstructing an approximation of a manifold known only thr...
In many applications, the first step into the topological analysis of a discrete point set P sampled...
In this thesis, we look for methods for reconstructing an approximation of a manifold known only thr...
A point cloud can be endowed with a topological structure by constructing a simplicial complex using...
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up...
In the thesis simplicial complexes as a means for representing topological spaces are presented. In...
Motivated by applications in Topological Data Analysis, we consider decompositionsof a simplicial co...
In recent years, a new approach to data analysis has been developed, based on topological methods. T...
The field of computational topology has developed many powerful tools to describe the shape of data,...
Inspired by an early work of Muldoon et al., Physica D 65, 1-16 (1993), we present a general method ...
International audienceWe study the simplification of simplicial complexes by repeated edge contracti...
The Vietoris–Rips filtration is a versatile tool in topological data analysis. It is a sequence of s...
International audienceThe Vietoris–Rips filtration is a versatile tool in topological data analysis....
9 pagesInternational audienceWe study the simplification of simplicial complexes by repeated edge co...
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of...
In this thesis, we look for methods for reconstructing an approximation of a manifold known only thr...
In many applications, the first step into the topological analysis of a discrete point set P sampled...
In this thesis, we look for methods for reconstructing an approximation of a manifold known only thr...
A point cloud can be endowed with a topological structure by constructing a simplicial complex using...
A graph complex is a finite family of graphs closed under deletion of edges. Graph complexes show up...