Applications of Computational and Topological Methods to Dynamical Systems

• Grant number: 19/06249-7
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2019
• End date: May 31, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Marcio Fuzeto Gameiro
• Grantee: Marcio Fuzeto Gameiro
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• City of the host institution: São Carlos

Abstract

The goal of this research project is to rigorously compute implicitly defined curves and manifolds of solutions of nonlinear equations and to use these solution manifolds to rigorously compute bifurcation of solutions to differential equations. (AU)

Scientific publications

(6)

(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)

CASTELO, ANTONIO; BUENO, LUCAS MOUTINHO; GAMEIRO, MARCIO. A combinatorial marching hypercubes algorithm. COMPUTERS & GRAPHICS-UK, v. 102, p. 67-77, FEB 2022. (13/07375-0, 19/06249-7, 19/07316-0, 17/25631-4)

GAMEIRO, MARCIO; GEDEON, TOMAS; KEPLEY, SHANE; MISCHAIKOW, KONSTANTIN. Rational design of complex phenotype via network models. PLOS COMPUTATIONAL BIOLOGY, v. 17, n. 7, JUL 2021. (19/06249-7)

CALCINA, SABRINA S.; GAMEIRO, MARCIO. Parameter estimation in systems exhibiting spatially complex solutions via persistent homology and machine learning. MATHEMATICS AND COMPUTERS IN SIMULATION, v. 185, p. 719-732, JUL 2021. (19/06249-7)

RAMOS, EDUARDO; NOLASCO, VICTOR; GAMEIRO, MARCIO. Rigorous enclosures of solutions of Neumann boundary value problems. APPLIED NUMERICAL MATHEMATICS, v. 180, p. 16-pg., 2022-06-02. (19/06249-7)

DIEGMILLER, ROCKY; ZHANG, LUN; GAMEIRO, MARCIO; BARR, JUSTINN; ALSOUS, JASMIN IMRAN; SCHEDL, PAUL; SHVARTSMAN, STANISLAV Y.; MISCHAIKOW, KONSTANTIN. Mapping parameter spaces of biological switches. PLOS COMPUTATIONAL BIOLOGY, v. 17, n. 2, FEB 2021. (19/06249-7)

CUMMINS, BREE; GAMEIRO, MARCIO; GEDEON, TOMAS; KEPLEY, SHANE; MISCHAIKOW, KONSTANTIN; ZHANG, LUN. Extending Combinatorial Regulatory Network Modeling to Include Activity. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 21, n. 3, p. 30-pg., 2022-01-01. (19/06249-7)