26 citations · 42 across the 13 of their papers we have counts for
14 papers
Relative Gröbner bases of modules and applications in persistence theory
Fritz Grimpen, Matthias Orth, Anastasios Stefanou
Finitely generated modules over the polynomial ring in indeterminates are isomorphic to quotients of finite rank free modules. We introduce a theory of relative Gröbner bases f…
On the Hausdorff stability of barcodes over posets
Mujtaba Ali, Tom Needham, Anastasios Stefanou +1
The Isometry Theorem of Chazal et al. and Lesnick is a fundamental result in persistence theory, which states that the interleaving distance between two one-parameter persistence m…
On minimal flat-injective presentations over local graded rings
Fritz Grimpen, Anastasios Stefanou
Flat-injective presentations were introduced by Miller (2020) to provide combinatorial descriptions of -graded modules. We consider them in the setting of local graded…
Cofiltrations of spanning trees in multiparameter persistent homology
Fritz Grimpen, Anastasios Stefanou
Given a multiparameter filtration of simplicial complexes, we consider the problem of explicitly constructing generators for the multipersistent homology groups with arbitrary PID…
Stability of the persistence transformation
Gideon Klaila, Anastasios Stefanou, Lena Ranke
In this paper, we introduce the persistence transformation, a novel methodology in Topological Data Analysis (TDA) for applications in time series data which can be obtained in var…
Combinatorial Topological Models for Phylogenetic Networks and the Mergegram Invariant
Paweł Dłotko, Jan Felix Senge, Anastasios Stefanou
Mutations of genetic sequences are often accompanied by their recombinations, known as phylogenetic networks. These networks are typically reconstructed from coalescent processes t…
Supervised topological data analysis for MALDI mass spectrometry imaging applications
Gideon Klaila, Vladimir Vutov, Anastasios Stefanou
Background: Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) displays significant potential for applications in cancer research, especially in tumo…
Persistent Cup Product Structures and Related Invariants
Facundo Mémoli, Anastasios Stefanou, Ling Zhou
One-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from da…
Persistent Cup-Length
Marco Contessoto, Facundo Mémoli, Anastasios Stefanou +1
Cohomological ideas have recently been injected into persistent homology and have for example been used for accelerating the calculation of persistence diagrams by the software Rip…
Interleaving by Parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics
Woojin Kim, Facundo Mémoli, Anastasios Stefanou
Metrics of interest in topological data analysis (TDA) are often explicitly or implicitly in the form of an interleaving distance between poset maps (i.e. order-pr…
persistent homology estimates the topology from pointcloud datasets
Francisco Belchí, Anastasios Stefanou
Let be a closed subspace of a metric space . Under mild hypotheses, one can estimate the Betti numbers of from a finite set of points approximating . In…
Tree decomposition of Reeb graphs, parametrized complexity, and applications to phylogenetics
Anastasios Stefanou
Inspired by the interval decomposition of persistence modules and the extended Newick format of phylogenetic networks, we show that, inside the larger category of \textit{ordered R…
The -Cophenetic Metric for Phylogenetic Trees as an Interleaving Distance
Elizabeth Munch, Anastasios Stefanou
There are many metrics available to compare phylogenetic trees since this is a fundamental task in computational biology. In this paper, we focus on one such metric, the $\ell^\inf…
Theory of interleavings on categories with a flow
Vin de Silva, Elizabeth Munch, Anastasios Stefanou
The interleaving distance was originally defined in the field of Topological Data Analysis (TDA) by Chazal et al. as a metric on the class of persistence modules parametrized over…