ECTS - University of Pisa
| Modules | Area | Type | Hours | Teacher(s) | |
| SISTEMI COMPLESSI - DINAMICHE NEURALI | FIS/03 | LEZIONI | 54 |
|
In questo corso si studiano esempi di modelli matematici, analitici e computazionali, di processi neuronali, che vanno dalla scala spaziale subcellulare a quella dell'intero sistema nervoso, al fine di cercare di comprendere alcuni meccanismi sottostanti la percezione, l'apprendimento, la memoria e il movimento. Gli strumenti matematici comprendono equazioni differenziali ordinarie e alle derivate parziali, deterministiche e stocastiche e loro soluzioni numeriche; metodi qualitativi per lo studio dei sistemi dinamici non lineari nel piano delle fasi; analisi dei segnali neuronali con metodi statistici e stocastici; elementi di teoria della informazione; elementi di graph theory; studio di fenomeni di auto-organizzazione e criticality; studio di fenomeni di sincronizzazione.
The course topics regard examples of mathematical models, analytical and computational, of neuronal processes, from subcellular scale to the scale of the whole nervous system, with the aim of improving the understanding of some mechanisms underlying perception, learning and memory, the movement. The mathematical tools include ordinary and partial differential equations, deterministic and stochastic, with numerical solutions; qualitative methods for the study of dynamical nonlinear systems in the phase space; analysis of the neuronal signals by means of statistical and stochastic methods; elements of the information theory; elements of the graph theory; study of self-organization phenomena and criticality; study of synchronization phenomena.
Gerstner W, Kistler W M, Naud R, Paninsky L. Neuronal Dynamics – From Single Neurons to Networks and Models of Cognition. Cambridge University Press, 2014.
Sterratt D, Graham B, Gillies A, Willshaw D. Principles of Computational Modelling in Neuroscience. Cambridge University Press, 2011.
Bressloff P. Neural field. Cambridge University Press, 2010.
Gabbiani F, Cox S J. Mathematics for Neuroscientists. Academic Press, 2010.
Dayan P, Abbott L F. Theoretical Neuroscience – Computational and Mathematical Modeling of Neural Systems. The MIT Press, 2001.
Gros C. Complex and Adaptive Dynamical Systems. Springer 2015.
Gerstner W, Kistler W M, Naud R, Paninsky L. Neuronal Dynamics – From Single Neurons to Networks and Models of Cognition. Cambridge University Press, 2014.
Sterratt D, Graham B, Gillies A, Willshaw D. Principles of Computational Modelling in Neuroscience. Cambridge University Press, 2011.
Bressloff P. Neural field. Cambridge University Press, 2010.
Gabbiani F, Cox S J. Mathematics for Neuroscientists. Academic Press, 2010.
Dayan P, Abbott L F. Theoretical Neuroscience – Computational and Mathematical Modeling of Neural Systems. The MIT Press, 2001.
Gros C. Complex and Adaptive Dynamical Systems. Springer 2015.
Seminario.
Seminar.
