- Docente: Giovanna Citti
- Credits: 6
- SSD: MAT/05
- Language: English
- Moduli: Giovanna Citti (Modulo 1) Maria Carla Tesi (Modulo 2)
- Teaching Mode: Traditional lectures (Modulo 1) Traditional lectures (Modulo 2)
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Mathematics (cod. 5827)
Learning outcomes
At the end of the course, the student has knowledge of analytic approach to biomedical and biomechanical problems. The student is able to express these problems with instruments of geometrical analysis and differential equations.
Course contents
1) visual perception problems and models of the primary visual cortex.
Classical models as minima of functionals: Perona Malik and total variation functionals. Differential calculus in Banach spaces, steepest descent method, Palais Smale condition
Riemannian and subriemannian manifolds, exponential map. subriemannian distance, subriemannian models of cortext
2) Evolution of an electrical signal along nerve fibers: the Hodgkin-Huxley model and the FitzHug-Nagumo system. Models for the propagation of electrical impulses in heart cells.
Readings/Bibliography
Citti Sarti, Neuromathematics of vision, Springer
Corrado Mascia, Eugenio Montefusco, "Un invito alla biomatematica", Edizioni LaDotta
Office hours
See the website of Giovanna Citti
See the website of Maria Carla Tesi