146 citations · 193 across the 10 of their papers we have counts for
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Algebraic Wasserstein distances and stable homological invariants of data
Jens Agerberg, Andrea Guidolin, Isaac Ren +1
Distances have a ubiquitous role in persistent homology, from the direct comparison of homological representations of data to the definition and optimization of invariants. In this…
Koszul complexes and relative homological algebra of functors over posets
Wojciech Chacholski, Andrea Guidolin, Isaac Ren +2
Under certain conditions, Koszul complexes can be used to calculate relative Betti diagrams of vector space-valued functors indexed by a poset, without the explicit computation of…
Homotopical decompositions of simplicial and Vietoris Rips complexes
Wojciech Chacholski, Alvin Jin, Martina Scolamiero +1
Motivated by applications in Topological Data Analysis, we consider decompositions of a simplicial complex induced by a cover of its vertices. We study how the homotopy type of suc…
Multidimensional Persistence and Noise
Martina Scolamiero, Wojciech Chachólski, Anders Lundman +2
In this paper we study multidimensional persistence modules [5,13] via what we call tame functors and noise systems. A noise system leads to a pseudo-metric topology on the categor…
Combinatorial presentation of multidimensional persistent homology
Wojciech Chacholski, Martina Scolamiero, Francesco Vaccarino
A multifiltration is a functor indexed by that maps any morphism to a monomorphism. The goal of this paper is to describe in an explicit and combinatorial way the na…
A presentation of general multipersistence modules computable in polynomial time?
Antonio Patriarca, Martina Scolamiero, Francesco Vaccarino
Multipersistence homology modules were introduced by G.Carlsson and A.Zomorodian which gave, together with G.Singh, an algorithm to compute their Groebner bases. Although their alg…
Combinatorial resolutions of multigraded modules and multipersistent homology
Wojciech Chacholski, Martina Scolamiero, Francesco Vaccarino
Let and a multigraded module. In this work we interpret as a multipersistent homology module and give a multigraded resolution of it. The construction…