Zobrazeno 1 - 10
of 30
pro vyhledávání: '"Stefanou, Anastasios"'
Autor:
Grimpen, Fritz, Stefanou, Anastasios
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 criterion f
Externí odkaz:
http://arxiv.org/abs/2410.17667
Autor:
Grimpen, Fritz, Stefanou, Anastasios
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 tool to identi
Externí odkaz:
http://arxiv.org/abs/2312.00235
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, engineering
Externí odkaz:
http://arxiv.org/abs/2310.05559
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 given set of
Externí odkaz:
http://arxiv.org/abs/2305.04860
Publikováno v:
BMC Bioinformatics 24, 279 (2023)
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 tumor-rela
Externí odkaz:
http://arxiv.org/abs/2302.13948
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 and by utiliz
Externí odkaz:
http://arxiv.org/abs/2211.16642
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 cohomology level
Externí odkaz:
http://arxiv.org/abs/2107.01553
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 metric spac
Externí odkaz:
http://arxiv.org/abs/1912.04366
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 much more d
Externí odkaz:
http://arxiv.org/abs/1902.09138
Autor:
Stefanou, Anastasios
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 Reeb graphs}, every Reeb graph with $n$ leaves and first Betti number $
Externí odkaz:
http://arxiv.org/abs/1902.05855