15 citations · 80 across the 24 of their papers we have counts for
30 papers
On the support of Betti tables of multiparameter persistent homology modules
Andrea Guidolin, Claudia Landi
Persistent homology encodes the evolution of homological features of a multifiltered cell complex in the form of a multigraded module over a polynomial ring, called a multiparamete…
Abelian and model structures on tame functors
Wojciech Chachólski, Barbara Giunti, Claudia Landi +1
In this paper, we discuss certain circumstances in which the category of tame functors inherits an abelian category structure with minimal resolutions and a model category structur…
Computing the Matching Distance of 2-Parameter Persistence Modules from Critical Values
Asilata Bapat, Robyn Brooks, Celia Hacker +3
The exact computation of the matching distance for multi-parameter persistence modules is an active area of research in computational topology. Achieving an easily obtainable exact…
Morse inequalities for the Koszul complex of multi-persistence
Andrea Guidolin, Claudia Landi
In this paper, we define the homological Morse numbers of a filtered cell complex in terms of relative homology of nested filtration pieces, and derive inequalities relating these…
Decomposing filtered chain complexes: geometry behind barcoding algorithms
Wojciech Chachólski, Barbara Giunti, Alvin Jin +1
In Topological Data Analysis, filtered chain complexes enter the persistence pipeline between the initial filtering of data and the final persistence invariants extraction. It is k…
Morse-based Fibering of the Persistence Rank Invariant
Asilata Bapat, Robyn Brooks, Celia Hacker +2
Although there is no doubt that multi-parameter persistent homology is a useful tool to analyse multi-variate data, efficient ways to compute these modules are still lacking in the…