Anastasios Stefanou
YOU?
Author Swipe
View article: On minimal flat-injective presentations over local graded rings
On minimal flat-injective presentations over local graded rings Open
Flat-injective presentations were introduced by Miller (2020) to provide combinatorial descriptions of $\mathbb Z^n$-graded modules. We consider them in the setting of local graded rings $R$, with grading over an abelian group, and give a …
View article: Cofiltrations of spanning trees in multiparameter persistent homology
Cofiltrations of spanning trees in multiparameter persistent homology Open
Given a multiparameter filtration of simplicial complexes, we consider the problem of explicitly constructing generators for the multipersistent homology groups with arbitrary PID coefficients. We propose the use of spanning trees as a too…
View article: Stability of the persistence transformation
Stability of the persistence transformation Open
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 various areas such as science, politics, economy, healthcare, …
View article: Persistent cup product structures and related invariants
Persistent cup product structures and related invariants Open
One-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from datasets by studying multi-dimensional persistence modules an…
View article: Combinatorial Topological Models for Phylogenetic Networks and the Mergegram Invariant
Combinatorial Topological Models for Phylogenetic Networks and the Mergegram Invariant Open
Mutations of genetic sequences are often accompanied by their recombinations, known as phylogenetic networks. These networks are typically reconstructed from coalescent processes that may arise from optimal merging or fitting together a gi…
View article: Supervised topological data analysis for MALDI mass spectrometry imaging applications
Supervised topological data analysis for MALDI mass spectrometry imaging applications Open
Background: Matrix-assisted laser desorption/ionization mass spectrometry imaging (MALDI MSI) displays significant potential for applications in cancer research, especially in tumor typing and subtyping. Lung cancer is the primary cause of…
View article: Persistent Cup Product Structures and Related Invariants
Persistent Cup Product Structures and Related Invariants Open
One-dimensional persistent homology is arguably the most important and heavily used computational tool in topological data analysis. Additional information can be extracted from datasets by studying multi-dimensional persistence modules an…
View article: Persistent Cup-Length
Persistent Cup-Length Open
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 Ripser. The cup product operation which is available at cohomo…
View article: The persistent cup-length invariant.
The persistent cup-length invariant. Open
We define a persistent cohomology invariant called persistent cup-length
which is able to extract non trivial information about the evolution of the
cohomology ring structure across a filtration. We also devise algorithms for
the computati…
View article: Interleaving by Parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics
Interleaving by Parts: Join Decompositions of Interleavings and Join-Assemblage of Geodesics Open
Metrics of interest in topological data analysis (TDA) are often explicitly or implicitly in the form of an interleaving distance $d_{\mathrm{I}}$ between poset maps (i.e. order-preserving maps), e.g. the Gromov-Hausdorff distance between …
View article: The metric structure of the formigram interleaving distance
The metric structure of the formigram interleaving distance Open
\textit{Formigrams} are a natural generalization of the notion of \textit{dendrograms}. This notion has recently been proposed as a signature for studying the evolution of clusters in dynamic datasets across different time scales. Although…
View article: Interleaving by parts for persistence in a poset
Interleaving by parts for persistence in a poset Open
Metrics in computational topology are often either (i) themselves in the form of the interleaving distance $d_{\mathrm{I}}(\mathbf{F},\mathbf{G})$ between certain order-preserving maps $\mathbf{F},\mathbf{G}:(\mathcal{P},\leq)\rightarrow (…
View article: $A_\infty$ persistent homology estimates the topology from pointcloud datasets
$A_\infty$ persistent homology estimates the topology from pointcloud datasets Open
Let $X$ be a closed subspace of a metric space $M$. Under mild hypotheses, one can estimate the Betti numbers of $X$ from a finite set $P \subset M$ of points approximating $X$. In this paper, we show that one can also use $P$ to estimate …
View article: Classification of Phylogenetic Networks
Classification of Phylogenetic Networks Open
By considering rooted Reeb graphs as a model for phylogenetic networks, using tools from category theory we construct an injection that assigns to each phylogenetic network with $n$-labelled leaves and $s$ cycles a finite set of phylogenet…
View article: Tree decomposition of Reeb graphs, parametrized complexity, and\n applications to phylogenetics
Tree decomposition of Reeb graphs, parametrized complexity, and\n applications to phylogenetics Open
Inspired by the interval decomposition of persistence modules and the\nextended Newick format of phylogenetic networks, we show that, inside the\nlarger category of \\textit{ordered Reeb graphs}, every Reeb graph with $n$\nleaves and first…
View article: The $\ell^\infty$-Cophenetic Metric for Phylogenetic Trees as an Interleaving Distance
The $\ell^\infty$-Cophenetic Metric for Phylogenetic Trees as an Interleaving Distance Open
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 $\ell^\infty$-cophenetic metric introduced by Cardona et al. This met…
View article: Theory of interleavings on categories with a flow
Theory of interleavings on categories with a flow Open
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 the real line. Bubenik et al. subsequently extended the def…
View article: Theory of interleavings on categories with a flow
Theory of interleavings on categories with a flow Open
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 the real line. Bubenik et al. subsequently extended the def…
View article: Theory of interleavings on $[0,\infty)$-actegories
Theory of interleavings on $[0,\infty)$-actegories Open
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 the real line. Bubenik et al. subsequently extended the def…