Zobrazeno 1 - 10
of 118
pro vyhledávání: '"Skraba, Primoz"'
Metric magnitude is a measure of the "size" of point clouds with many desirable geometric properties. It has been adapted to various mathematical contexts and recent work suggests that it can enhance machine learning and optimization algorithms. But
Externí odkaz:
http://arxiv.org/abs/2409.04411
Autor:
Bobrowski, Omer, Skraba, Primoz
In this paper, we prove a universality result for the limiting distribution of persistence diagrams arising from geometric filtrations over random point processes. Specifically, we consider the distribution of the ratio of persistence values (death/b
Externí odkaz:
http://arxiv.org/abs/2406.05553
Multiparameter persistence modules can be uniquely decomposed into indecomposable summands. Among these indecomposables, intervals stand out for their simplicity, making them preferable for their ease of interpretation in practical applications and t
Externí odkaz:
http://arxiv.org/abs/2403.11939
Autor:
Onus, Adam, Skraba, Primoz
Let $K$ be a periodic cell complex endowed with a covering $q:K\to G$ where $G$ is a finite quotient space of equivalence classes under translations acting on $K$. We assume $G$ is embedded in a space whose homotopy type is a $d$-torus for some $d$,
Externí odkaz:
http://arxiv.org/abs/2312.00709
Autor:
Bobrowski, Omer, Skraba, Primoz
Persistent homology is a natural tool for probing the topological characteristics of weighted graphs, essentially focusing on their $0$-dimensional homology. While this area has been substantially studied, we present a new approach to constructing a
Externí odkaz:
http://arxiv.org/abs/2310.00350
Autor:
Patel, Amit, Skraba, Primoz
This paper introduces M\"obius homology, a homology theory for representations of finite posets into abelian categories. While the connection between poset topology and M\"obius functions is classical, we establish a direct connection between poset t
Externí odkaz:
http://arxiv.org/abs/2307.01040
Autor:
Bobrowski, Omer, Skraba, Primoz
One of the most elusive challenges within the area of topological data analysis is understanding the distribution of persistence diagrams. Despite much effort, this is still largely an open problem. In this paper, we present a series of novel conject
Externí odkaz:
http://arxiv.org/abs/2207.03926
Autor:
Skraba, Primoz, Yogeshwaran, D.
We investigate asymptotics for the minimal spanning acycles of the (Alpha)-Delaunay complex on a stationary Poisson process on $\mathbb{R}^d, d \geq 2$. Minimal spanning acycles are topological (or higher-dimensional) generalization of minimal spanni
Externí odkaz:
http://arxiv.org/abs/2205.12348
Autor:
Skraba, Primoz, Turner, Katharine
These notes are a self-contained short proof of the stability of persistence diagrams.
Externí odkaz:
http://arxiv.org/abs/2103.10723
Autor:
Beltramo, Gabriele, Andreeva, Rayna, Giarratano, Ylenia, Bernabeu, Miguel O., Sarkar, Rik, Skraba, Primoz
We study the use of the Euler characteristic for multiparameter topological data analysis. Euler characteristic is a classical, well-understood topological invariant that has appeared in numerous applications, including in the context of random field
Externí odkaz:
http://arxiv.org/abs/2102.08260