4 papers
Canopies: A Generalization of Vines and Vineyards for Parameterized Persistence
Barbara Giunti, Elizabeth Munch
In this paper, we provide a new construction for studying parameterized persistence, called a canopy. We give two versions of this construction: the A-canopy, retaining all informa…
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…
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…
Invariants for tame parametrised chain complexes
Wojciech Chachólski, Barbara Giunti, Claudia Landi
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes level. We present the category of tame parametrised cha…