Knowledge of the main models of nervous activity, from the single neuron to networks of neurons, with particular emphasis on the role of noise
Curriculum
teacher profile teaching materials
In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Programme
A summary treatment of the structure and function of the components of the nervous system on various scales is proposed, as well as an overview of the experimental techniques for measuring nervous activity.In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Core Documentation
Textbook: W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, “Neuronal Dynamics”,Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Type of delivery of the course
Given the strongly interdisciplinary nature of the course, in the first part, after a short historical overview, a summary is given of the structure and function of the components of the nervous system on different scales, and an overview of experimental techniques used to measure the neural activity. Then, a bottom-up approach to physical-mathematical neural modeling is proposed. Emphasis is put on the fact that, contrary to a frequent situation in physics, in neural modeling it is not possible in generai neither perform a clear separation of scales, nor directly import techniques used in the statistica! mechanics of criticai systems. Starting from neuron models quite dose to biophysical evidence, a sequence of approximations and simplifications is described, allowing both a compact mathematical treatment of the single neuron, with the methods of dynamical systems theory, and building manageable network models. Given the many sources of irregularity and fluctuations of the neural activity, stochastic components are then incorporated in the models, both at the single neuron and network levels. In the final part of the course, relevant examples are illustrated, in which experimental evidence on complex cognitive functions are described. The scientific literature on the subject is characterized by great heterogeneity of style and language; to improve the ability of the students to autonomously acquire and absorb information, both for the purpose of the course and possibly for subsequent interdisciplinary studies, papers representative of important experimental and theoretical approaches are made available and discussed in the classroom. At the end of the course the students should possess a balanced knowledge of various approaches to modeling in the neurosciences, should be able to approach autonomously the scientific literature on the subject.Type of evaluation
Final oral examination The final evaluation consists in an oral exam in which students will be asked questions about the topics covered by the course. To pass the exam, the student must both illustrate the motivations of the models studied during the course, and develop the relevant calculations for the most important models. Given the interdisciplinary nature of the course, one criterion for the evaluation will also be the ability of the student to illustrate the specific relevance of the physical-mathematical models studied during the course, for the corresponding neuro-biological phenomena and experimental data reported during the course. teacher profile teaching materials
In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Programme
A summary treatment of the structure and function of the components of the nervous system on various scales is proposed, as well as an overview of the experimental techniques for measuring nervous activity.In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Core Documentation
Textbook: W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, “Neuronal Dynamics”,Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Type of delivery of the course
Given the strongly interdisciplinary nature of the course, in the first part, after a short historical overview, a summary is given of the structure and function of the components of the nervous system on different scales, and an overview of experimental techniques used to measure the neural activity. Then, a bottom-up approach to physical-mathematical neural modeling is proposed. Emphasis is put on the fact that, contrary to a frequent situation in physics, in neural modeling it is not possible in generai neither perform a clear separation of scales, nor directly import techniques used in the statistica! mechanics of criticai systems. Starting from neuron models quite dose to biophysical evidence, a sequence of approximations and simplifications is described, allowing both a compact mathematical treatment of the single neuron, with the methods of dynamical systems theory, and building manageable network models. Given the many sources of irregularity and fluctuations of the neural activity, stochastic components are then incorporated in the models, both at the single neuron and network levels. In the final part of the course, relevant examples are illustrated, in which experimental evidence on complex cognitive functions are described. The scientific literature on the subject is characterized by great heterogeneity of style and language; to improve the ability of the students to autonomously acquire and absorb information, both for the purpose of the course and possibly for subsequent interdisciplinary studies, papers representative of important experimental and theoretical approaches are made available and discussed in the classroom. At the end of the course the students should possess a balanced knowledge of various approaches to modeling in the neurosciences, should be able to approach autonomously the scientific literature on the subject.Type of evaluation
Final oral examination The final evaluation consists in an oral exam in which students will be asked questions about the topics covered by the course. To pass the exam, the student must both illustrate the motivations of the models studied during the course, and develop the relevant calculations for the most important models. Given the interdisciplinary nature of the course, one criterion for the evaluation will also be the ability of the student to illustrate the specific relevance of the physical-mathematical models studied during the course, for the corresponding neuro-biological phenomena and experimental data reported during the course. teacher profile teaching materials
In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Programme
A summary treatment of the structure and function of the components of the nervous system on various scales is proposed, as well as an overview of the experimental techniques for measuring nervous activity.In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Core Documentation
Textbook: W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, “Neuronal Dynamics”,Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Type of delivery of the course
Given the strongly interdisciplinary nature of the course, in the first part, after a short historical overview, a summary is given of the structure and function of the components of the nervous system on different scales, and an overview of experimental techniques used to measure the neural activity. Then, a bottom-up approach to physical-mathematical neural modeling is proposed. Emphasis is put on the fact that, contrary to a frequent situation in physics, in neural modeling it is not possible in generai neither perform a clear separation of scales, nor directly import techniques used in the statistica! mechanics of criticai systems. Starting from neuron models quite dose to biophysical evidence, a sequence of approximations and simplifications is described, allowing both a compact mathematical treatment of the single neuron, with the methods of dynamical systems theory, and building manageable network models. Given the many sources of irregularity and fluctuations of the neural activity, stochastic components are then incorporated in the models, both at the single neuron and network levels. In the final part of the course, relevant examples are illustrated, in which experimental evidence on complex cognitive functions are described. The scientific literature on the subject is characterized by great heterogeneity of style and language; to improve the ability of the students to autonomously acquire and absorb information, both for the purpose of the course and possibly for subsequent interdisciplinary studies, papers representative of important experimental and theoretical approaches are made available and discussed in the classroom. At the end of the course the students should possess a balanced knowledge of various approaches to modeling in the neurosciences, should be able to approach autonomously the scientific literature on the subject.Type of evaluation
Final oral examination The final evaluation consists in an oral exam in which students will be asked questions about the topics covered by the course. To pass the exam, the student must both illustrate the motivations of the models studied during the course, and develop the relevant calculations for the most important models. Given the interdisciplinary nature of the course, one criterion for the evaluation will also be the ability of the student to illustrate the specific relevance of the physical-mathematical models studied during the course, for the corresponding neuro-biological phenomena and experimental data reported during the course. teacher profile teaching materials
In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Programme
A summary treatment of the structure and function of the components of the nervous system on various scales is proposed, as well as an overview of the experimental techniques for measuring nervous activity.In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Core Documentation
Textbook: W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, “Neuronal Dynamics”,Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Type of delivery of the course
Given the strongly interdisciplinary nature of the course, in the first part, after a short historical overview, a summary is given of the structure and function of the components of the nervous system on different scales, and an overview of experimental techniques used to measure the neural activity. Then, a bottom-up approach to physical-mathematical neural modeling is proposed. Emphasis is put on the fact that, contrary to a frequent situation in physics, in neural modeling it is not possible in generai neither perform a clear separation of scales, nor directly import techniques used in the statistica! mechanics of criticai systems. Starting from neuron models quite dose to biophysical evidence, a sequence of approximations and simplifications is described, allowing both a compact mathematical treatment of the single neuron, with the methods of dynamical systems theory, and building manageable network models. Given the many sources of irregularity and fluctuations of the neural activity, stochastic components are then incorporated in the models, both at the single neuron and network levels. In the final part of the course, relevant examples are illustrated, in which experimental evidence on complex cognitive functions are described. The scientific literature on the subject is characterized by great heterogeneity of style and language; to improve the ability of the students to autonomously acquire and absorb information, both for the purpose of the course and possibly for subsequent interdisciplinary studies, papers representative of important experimental and theoretical approaches are made available and discussed in the classroom. At the end of the course the students should possess a balanced knowledge of various approaches to modeling in the neurosciences, should be able to approach autonomously the scientific literature on the subject.Type of evaluation
Final oral examination The final evaluation consists in an oral exam in which students will be asked questions about the topics covered by the course. To pass the exam, the student must both illustrate the motivations of the models studied during the course, and develop the relevant calculations for the most important models. Given the interdisciplinary nature of the course, one criterion for the evaluation will also be the ability of the student to illustrate the specific relevance of the physical-mathematical models studied during the course, for the corresponding neuro-biological phenomena and experimental data reported during the course. teacher profile teaching materials
In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Programme
A summary treatment of the structure and function of the components of the nervous system on various scales is proposed, as well as an overview of the experimental techniques for measuring nervous activity.In modeling in neuroscience it is not generally possible to clearly separate the scales of description of the problem, or simply import statistical mechanics techniques used for example in critical phenomena. We illustrate a series of approximations and simplifications that allow both a synthetic mathematical treatment of the single neuron, with the methods of the dynamical systems theory, and the construction of tractable models of networks of neurons.
Program
* Historical sketch
* Introduction to the structure of the central nervous system
* Neuron membrane and ionic channels
* Synaptic transmission
* Overview of experimental methods
* Ionic equilibrium and membrane potential
* Hodgkin-Huxley model of spike generation
* Features of dendrites
* Cable theory; elements of Rall's theory of dendritic trees
* Spike propagation
* 'Quasi-active' membrane; linearization of the Hodgkin-Huxley equations
* Bidimensional reduction of the Hodgkin-Huxley equations; phase plane analysis
* Elements of bifurcation theory and application to bidimensional neuron models
* Noise sources in neuronal dynamics
* Model of quantal release of neurotransmitters
* Stochastic dynamics of ionic channels
* General aspects of Poisson and renewal processes; application to the
description of spike trains
* ‘Integrate-and-fire’ (IF) neuron model with deterministic and stochastic
input
* Diffusion approximation for the IF neuron; Fokker-Planck equation
* Calculation of the mean firing rate in stationary regime; transfer function
* IF and ExpIF with spike frequency adaptation
* Elements of extensions of IF models
* Networks of IF neurons: mean field theory and attractors
* Excitation-inhibition balance
* Elements of synaptic plasticity and learning models
* Elements of Working Memory models
* Elements of perceptual decision models
* Elements of reservoir computing
* Elements of Deep Learning
Core Documentation
Textbook: W. Gerstner, W.M. Kistler, R. Naud, L. Paninski, “Neuronal Dynamics”,Cambridge University Press 2014
Chapter 1, Chapter 2, Chapter 3 (except 3.2.3), Chapter 4, Chapter 6 (6.1, 6.3.1),
Chapter 7 (till 7.5.3 included), Chapter 8, Chapter 12 (till 12.3.6 included,
12.4.1-12.4.4), Chapter 13 (till 13.4 included), Chapter 16 (16.1, 16.2), Chapter
17, Chapter 19 (19.1, 19.2), Chapter 20 (20.1).
The slides of the lectures will be distributed, with papers relevant to specific
aspects
Suggested references
B. Ermentrout, D. Terman, Mathematical foundations of neuroscience, Springer 2010
(Cap. 1, Cap. 6)
H. Tuckwell, Introduction to theoretical neurobiology, Cambridge University Press
1988 (Vol. 1 Cap. 4, Vol. 2 Cap.9)
D. Johnston, S. Wu, Foundations of cellular neurophysiology, MIT Press 1995 (Cap. 2,
Cap. 5, Cap. 9, Cap. 10)
S.H. Strogatz, Nonlinear dynamics and chaos, Perseus 1994 (Cap. 3, Cap. 6, Cap. 7,
Cap. 8)
D. Sterrat, B. Graham, A. Gillies, D. Willshaw, Principles of computational modeling
in neuroscience, Cambridge University Press 2011
Type of delivery of the course
Given the strongly interdisciplinary nature of the course, in the first part, after a short historical overview, a summary is given of the structure and function of the components of the nervous system on different scales, and an overview of experimental techniques used to measure the neural activity. Then, a bottom-up approach to physical-mathematical neural modeling is proposed. Emphasis is put on the fact that, contrary to a frequent situation in physics, in neural modeling it is not possible in generai neither perform a clear separation of scales, nor directly import techniques used in the statistica! mechanics of criticai systems. Starting from neuron models quite dose to biophysical evidence, a sequence of approximations and simplifications is described, allowing both a compact mathematical treatment of the single neuron, with the methods of dynamical systems theory, and building manageable network models. Given the many sources of irregularity and fluctuations of the neural activity, stochastic components are then incorporated in the models, both at the single neuron and network levels. In the final part of the course, relevant examples are illustrated, in which experimental evidence on complex cognitive functions are described. The scientific literature on the subject is characterized by great heterogeneity of style and language; to improve the ability of the students to autonomously acquire and absorb information, both for the purpose of the course and possibly for subsequent interdisciplinary studies, papers representative of important experimental and theoretical approaches are made available and discussed in the classroom. At the end of the course the students should possess a balanced knowledge of various approaches to modeling in the neurosciences, should be able to approach autonomously the scientific literature on the subject.Type of evaluation
Final oral examination The final evaluation consists in an oral exam in which students will be asked questions about the topics covered by the course. To pass the exam, the student must both illustrate the motivations of the models studied during the course, and develop the relevant calculations for the most important models. Given the interdisciplinary nature of the course, one criterion for the evaluation will also be the ability of the student to illustrate the specific relevance of the physical-mathematical models studied during the course, for the corresponding neuro-biological phenomena and experimental data reported during the course.