Computational neurosciences: neuronal dynamics

Lecturer: Wulfram Gerstner

Assistants: Louis Pezon (Head TA), Kasper Smeets (TA), Shuqi Wang (TA).

The course has a Ed Discussions page for questions.

In the first week Schedule is : Monday 9.15 am - 1 pm (in INM200) alternating between lecture and in-class exercises, Q&A and computer exercises.

In the second week and later weeks, the class meets Monday at 10.15am for an inverted classroom setting, after watching videos at home. The course consists of in-person Q&A session about the course contents, pen & pencil exercises, Python exercises, and graded miniprojects.

We meet at 9h15 for LECTURE 1 in the classroom.  

Introduction: brain vs. computer and a first simple neuron model as well as discussion of formalities

• First introduction and overview of the course
• Coding by spikes (action potentials)
• Model of a passive membrane
• Leaky integrate-and-fire model
• Nonlinear integrate-and-fire model
• Quality of integrate-and-fire models: comparison with experiments
  

Inverted classroom setting. Watch videos at home. We meet at 10h15 for questions exercises.

LECTURE 2. Detailed neuron models

• Nernst equation
• Hodgkin-Huxley model
• Models of synaptic input

Inverted classroom: watch videos to prepare for the inverted classroom session Monday 10h15.
LECTURE 3. Reduction of the Hodkgin-Huxley model from 4 to 2 dimensions.

For this, only watch the first 7 videos of Lecture 4 (not 3!), up to Math detour 3.
The 7 videos (102 min) can be found under Videos of all lectures above -> Two-dimensional models and phase plane analysis.

LECTURE 4.  Two-dimensional models and phase space analysis

• Complement to two-dimensional neuron models
• Separation of time scales
• Type I and Type II neurons

LECTURE 5. Introduction to Hopfield neural networks

We meet at 10h15 for inverted classroom followed by exercises.

The 6 videos to watch at home can be found under Videos of all lectures (above) -> Associative Memory in a Network of Neurons (57 min) (video lecture 10)

We meet at 10h15 for inverted classroom followed by exercises.

The 5 videos to watch at home can be found under Videos of all lectures (above) -> Attractor Networks and Generalizations of the Hopfield model (62 min) (video lecture 11)

LECTURE 7. Populations of neurons; population activity A(t); cortical connectivity; random connectivity models; mean-field method.

We meet at 10h15 for inverted classroom followed by exercises.

The 7 videos to watch at home can be found under Videos of all lectures (above) -> Neuronal Populations (85 min) (video lecture 8)

LECTURE 8. Continuum models: Cortical fields and perception

We meet at 10h15 for inverted classroom followed by exercises.

The 6 videos to watch at home can be found under Videos of all lectures (above) -> Continuum models: Cortical Fields and Perception (62 min) (video lecture 12)

LECTURE 9. Connected populations: perception, decision, and competition.

We meet at 10h15 for inverted classroom followed by exercises.

The 6 videos to watch at home can be found under Videos of all lectures (above) -> Decision models: Competitive Dynamics (66 min) (video lecture 13)

LECTURE 10. Noise and variability of spike trains

We meet at 10h15 for inverted classroom followed by exercises.

The videos to watch at home can be found under Videos of lectures (above) -> Variability of spike trains (96 min) (section II, lecture 5)

Reading: Neuronal Dynamic,  Ch. 7.1-7.3 and  Ch 8.1-8.3

LECTURE 11. Noise models: Escape Noise

We meet at 10h15 for inverted classroom followed by exercises.

The videos to watch at home can be found under Videos of lectures (above) -> Noise models (84 min) (section II, lecture 6).

Reading: Neuronal Dynamics: Ch. 7.5.1, Ch. 8.1-8.3 (part of this was also already in the previous week) Ch. 9.1-9.4

LECTURE 12. Fitting neural models to data

We meet at 10h15 for inverted classroom followed by exercises.

The videos to watch at home can be found under Videos of lectures (above) -> Modern phenomenological neuron models (94 min) (Section II, lecture 7)

LECTURE 13. Population of Neurons - Fokker-Planck Equation

We meet at 10h15 for inverted classroom followed by exercises.

The videos to watch at home can be found under Videos of lectures (above) -> Fokker-Planck equation for stochastic integrate-and-fire neurons (77 min) (section III, lecture 9)

LECTURE 14.
Low-dimensional manifolds

LECTURE 15. Summary and extensions. No exercises today, only Q/A on miniprojects

LECTURE 15. Networks of neurons, population activity, mean field argument

Date, time, place :  Please check on IS Academia.

Allowed material:

• Bring writing material (Pen, etc.). 
• Paper will be provided.
• You can bring a single A5 (half the size of A4) sheet, handwritten, on which you are allowed write (recto-verso) whatever you think might be useful.
• Nothing else. (In particular no books, lecture notes, mobile phones, laptops, calculators, etc.)

You must have your student card (CAMIPRO) with you for the exam.

You can find examples of exams from previous years below.

Neural Networks with spatial structure, competition, field equations, decision processes

LECTURE 8: Spike Response Model (SRM) and coding revisited

Lecture 10: Population rate models and Coding --- Reverse correlations, PSTH, rapid transients in populations of neurons, linear Poisson model

LECTURE 13

Lecture 9: Population of Neurons - Fokker-Planck Equation