This course provides the students with the numerical analysis tools most frequently used in modern theoretical physics, which will be needed in later courses, in particular Advanced Simulation Techniques. Moreover, the basic elements of computational neurosciences are introduced: models of neurons, learning, memory and computation, and their applications to the description of some fundamental neural subsystems.

The student must learn the basic tools of numerical analysis, with particular reference to those most frequently used in modern theoretical physics, like plotting data, root finding, numerical integration and random numbers. The student must also acquire a deep knowledge of the basic elements of computational neurosciences, in particular the basic models of neurons, learning, memory and computation, and learn how to apply these models to the description of some fundamental neural subsystems.

Mathematical analysis and general physics.

A. Introduction to numerical methods (4 credits) Unix/Linux and FORTRAN: simple programs, plotting data, input and output. Finding roots of equations: bisection, regula falsi, secant and Newton's methods. Numerical integration: trapezoid and Simpson's rule. Numerical differentiation: forward- and centred-difference methods. First order ordinary differential equations (ODE), initial value problems (IVP). Random numbers: definition and properties of pseudo-random numbers, classes of uniform random number generators, non-uniform random numbers. Applications of random numbers: Monte Carlo (MC) integration, percolation, random walks. B. Introduction to computational neuroscience (4 credits) Part 1. Physiology and functions of the mammalian visual system (an introduction to systems/computational neuroscience) 1. Introduction to anatomy and physiology of the visual system - A systems/computational approach to the study of the visual system - Anatomy of the visual system - Classic findings about physiology of lower-level visual areas - Data analysis approaches in Systems Neuroscience - Classic findings about physiology of higher-level visual areas 2. Descriptive models of visual neurons - How to build models of visual neuronal responses (i.e., stimulus/response maps) 3. Mechanistic models of the visual system - Infer the mechanisms underlying the response properties of visual neurons 4. Functional models of the visual system - Understanding neuronal population codes Part 2. Sensory Systems: Tactile Perception 1. Introduction to transduction and sensory systems 2. Maps... and somatosensory system I 3. somatosensory system II... and Pain 4. Signal detection theory and applications 5. Example of how to study sensory systems

Frontal lectures and computer lab sessions.

S.E. Koonin e D.C. Meredith, Computational physics, Addison-Wesley Numerical recipes online, http://www.nrbook.com Daniel Amit, Modeling Brain Function (Cambridge UP, 1989) ET Rolls & A Treves, Neural Networks and Brain Function (Oxford UP, 1998)

... The exam is made of 2 tests, of equal weight. The first test is a practical test that will require the solution of numerical problems, similar to those illustrated during the lectures, on a Unix/Linux platform. The second test is a written test on the topics of part B.

Gli studenti e le studentesse con disabilità o con Disturbi Specifici di Apprendimento (DSA), oltre alla segnalazione tramite procedura informatizzata, sono invitati a comunicare anche direttamente al/la docente titolare dell'insegnamento, con un preavviso non inferiore ad una settimana dall'avvio della sessione d'esame, gli strumenti compensativi concordati con l'Unità Special Needs, al fine di permettere al/la docente la declinazione più idonea in riferimento alla specifica tipologia di esame.