Persistent Homology of functional data in aleatory metric spaces

• Grant number: 18/17240-8
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2018
• End date: September 30, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Carlos Biasi
• Grantee: Sergio Tsuyoshi Ura
• Host Institution: Instituto de Geociências e Ciências Exatas (IGCE). Universidade Estadual Paulista (UNESP). Campus de Rio Claro. Rio Claro , SP, Brazil
• Associated research grant: 16/24707-4 - Algebraic, geometric and differential topology, AP.TEM

Abstract

Many sets of data that comes from scientific and practical problems consists of maps defined in different domains, displaying a complex geometry or topology. For example, in plant biology, functional can be defined on leaves or roots with complex forms. Typically, the roots and leaves of different specimen have different shapes, that makes the variational analysis difficult. In development biology, functional data associated to the proliferation or gene expression provides other interesting examples. We will address fundamental issues using persistent homology that arises in the analysis of such data applying topological methods.

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BIASI, CARLOS; LIBARDI, ALICE KIMIE MIWA; DE MATTOS, DENISE; URA, SERGIO TSUYOSHI. Borsuk-Ulam theorem for filtered spaces. FORUM MATHEMATICUM, v. 33, n. 2, p. 419-426, MAR 2021. (16/24707-4, 18/17240-8)

VILAMAIOR PAIVA, THALES FERNANDO; DOS SANTOS, EDIVALDO LOPES. ohomology Algebra of Orbit Spaces of Free Involutions on Some Wall Manifold. BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, v. 53, n. 1, p. 281-294, MAR 2022. (18/17240-8)