Persistent homology generators and applications

Author(s)

Carlos Henrique Venturi Ronchi

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2019-11-13

Examining board members

Oziride Manzoli Neto; Denise de Mattos; Thiago de Melo; Afonso Paiva Neto

• Advisor: Márcio Fuzeto Gameiro

Abstract

In the recent year data has been produced in a large scale and rapidly. It is becoming ever difficult to analyse it all through the current methods. Thus, it is necessary to develop and apply new methods. Topological data analysis is a whole new field in computational mathematics/ algebraic topology that studies the topological properties of data through tools like persistent homol- ogy. This tool searches for components, holes and cavities in the data. In this dissertation we show the basic ideas of persistent homology, its theory as well as some related tools, such as optimal cycles and persistence images. We propose using these tools models to the protein folding problem. The first one is a stability score predictor for a protein dataset. We show some results close to the state of art and new perspectives to the design of new proteins. In the second method we study the designed protein landscape energy. We show how persistent homology can be used as an aid to macromolecular designing softwares to get more stable proteins. (AU)

• FAPESP's process: 17/14678-0 - Persistent homology generators and applications
• Grantee: Carlos Henrique Venturi Ronchi
• Support Opportunities: Scholarships in Brazil - Master