3 papers
math.AT2026
A data structure for quotient flag complexes
Konstantin Sorokin, Aleksandr Levin, Maxim Beketov +1
Vietoris-Rips filtrations, which are standard in topological data analysis, are flag complexes, and a simplex tree stores these without any attaching data. In this paper we ask wha…
math.AT2025
Sheaf theory: from deep geometry to deep learning
Anton Ayzenberg, Thomas Gebhart, German Magai +1
This paper provides an overview of the applications of sheaf theory in deep learning, data science, and computer science in general. The primary text of this work serves as a frien…
math.AT2023
Coverings by open and closed hemispheres
Anton Ayzenberg, Maxim Beketov, German Magai
In this paper we study the nerves of two types of coverings of a sphere : (1) coverings by open hemispheres; (2) antipodal coverings by closed hemispheres. In the first ca…