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Introduction to numerical methods and computational neuroscience

01RLJPF

A.A. 2023/24

Course Language

Inglese

Course degree

Master of science-level of the Bologna process in Physics Of Complex Systems (Fisica Dei Sistemi Complessi) - Torino/Trieste/Parigi

Course structure
Teaching Hours
Teachers
Teacher Status SSD h.Les h.Ex h.Lab h.Tut Years teaching
Teaching assistant
Espandi

Context
SSD CFU Activities Area context
FIS/03
ING-INF/06
4
4
D - A scelta dello studente
D - A scelta dello studente
A scelta dello studente
A scelta dello studente
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.
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.
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.
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
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.
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)
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 disabilitÓ 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'UnitÓ Special Needs, al fine di permettere al/la docente la declinazione pi¨ idonea in riferimento alla specifica tipologia di esame.
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.
In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.
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