Persistent homology (PH) provides topological descriptors for geometric ...
The notion of rank decomposition of a multi-parameter persistence module...
Multigraded Betti numbers are one of the simplest invariants of
multipar...
We introduce a novel gradient descent algorithm extending the well-known...
In this paper we introduce the signed barcode, a new visual representati...
This paper addresses two questions: (1) can we identify a sensible class...
We define notions of differentiability for maps from and to the space of...
Merge trees are a type of graph-based topological summary that tracks th...
In this paper we provide an explicit connection between level-sets
persi...
The matching distance is a pseudometric on multi-parameter persistence
m...
In this survey, we review the literature on inverse problems in topologi...
Persistence diagrams (PDs) are now routinely used to summarize the under...
Persistence diagrams (PDs) play a key role in topological data analysis
...
In this article, we study the question of the statistical convergence of...
In this paper, we propose a new fuzzy clustering algorithm based on the
...