arXiv subjects

Rafael Cavalcanti

Publications and source records attributed to Rafael Cavalcanti.

3 recordsLinked to original sources

arXiv2025

Geometric Obstructions in Finsler Spaces and Torsion-Free Persistent Homology

We relate the novel concept of Topological Data Analysis in Finsler space with representability property, which is a natural obstruction to prevent spurious features in high dimensions. We use decomposition of integer matrix in order to find suitable prime integer $p$ such that persistent homology module over $\mathbb{Z}_p$ encompasses only the holes associated to the free part, in agreement with the rational case.

math.AT↗

arXiv2025

Topological Data Analysis in Finsler Spaces

We introduce a new approach to Topological Data Analysis (TDA) based on Finsler metrics and we also generalize the classical concepts of Vietoris-Rips and Cech complexes within this framework. In particular, we propose a class of directionally dependent Finsler metrics and establish key results demonstrating their relevance to TDA. Moreover, we show that several Information Theoretic perspectives on TDA can often be recovered through the lens of Finsler geometry.

math.DG↗

arXiv2025

Modeling Coral Reef Bleaching Recovery Through KCC-Theory

We use Volterra-Hamilton systems theory and their associated cost functional to study the population dynamics and productive processes of coral reefs in recovery from bleaching and show that the cost of \mbox{production} remains the same after the process. The geometrical KCC-invariants are determined for the model proposed to describe the renewed symbiotic interaction between coral and algae.

math.DS↗