Data analysis of complex networks by sparse recovery techniques

• Grant number: 19/10920-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: August 01, 2019
• End date: July 31, 2020
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Tiago Pereira da Silva
• Grantee: Kevin Felipe Kühl Oliveira
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

This project aims to develop the relevant mathematical basis to the reconstruction of the dynamics of dynamical systems from a dataset using the Sparse Recovery technique. For this purpose, the project is divided into three stages, which include the study of the properties and applications of the Hilbert Transform in signal processing, the understanding and simulation of Rössler's attractor systems, the introduction to chaos models and, finally, the Sparse Recovery technique and its application conditions. The subject is meaningful given the dependence of several areas of science on the prediction of behavior of dynamical systems. It is expected that, at the end of the research period, the student will be able to perform the analysis and interpretation of electroencephalogram data of epileptic patients, as a practical model of the studied theory.