- 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)
-
from Nov 05, 2024 to Dec 17, 2024
-
from Sep 16, 2024 to Oct 22, 2024
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
L'effetto retinex e le illusioni ottiche
Riemannian and subriemannian manifolds, exponential map. subriemannian distance, subriemannian models of the cortext: the Kanitza triangle
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
Teaching methods
The course will take place through in-person frontal lectures.
For the description of the functional and physiological structure of neurons and the visual cortex, as well as the presentation of optical illusions, extensive use will be made of slides, images, and some videos.
The modeling part and the description of mathematical properties will instead be presented in detail on the blackboard.
The lessons will always be highly interactive, and students will be involved and encouraged to actively participate by asking questions and requesting further explanations.
Assessment methods
The learning assessment is conducted through an oral exam designed to evaluate the student’s acquisition of the expected knowledge and skills.
The exam begins from a topic choosen by the student from those covered in class, followed by questions from the instructor that may extend beyond the chosen topic to encompass the entire course content.
Teaching tools
Office hours and tutoring.
PDF notes from the virtual board, covering some parts of the program
textbooks on different part of the program
Office hours
See the website of Giovanna Citti
See the website of Maria Carla Tesi