Biological modeling of neural networks
Weekly outline
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Lecturer: Wulfram Gerstner.
Assistants: Sophia Becker, Shuqi Wang, Valentin Schmutz, Christos Sourmpis, Martin Barry
Exercise session: Monday 11 am - 1 pm (On Wonder)
Q&A with Prof. Gerstner: Monday 11.30 - 11.50 am (On Zoom)
General office hours: Friday 4 pm - 6 pm (On Wonder)
The course has a Piazza page for questions.
In this course, we study mathematical models of neurons and neuronal networks in the context of biology and establish links to models of cognition.
The course consists of video lectures, pen & pencil exercises, Python exercises, and graded miniprojects.
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LECTURE 1:
A First introduction and overview of course.
B Coding by Spikes (action potentials).
C Model of a passive membrane.
D Leaky integrate-and-fire model.
E Nonlinear integrate-and-fire model.
F Quality of integrate-and-fire models: comparison with experiments. -
LECTURE 2: Detailed Neuron Models:
A The Nernst Equation.
B Hodgkin-Huxley Model.
C Model of synaptic input. -
LECTURE 3: Two dimensional neuron models:
- Reduction of Hodgkin Huxely equations
- FitzHugh-Nagumo
- Phase plane analysis.
- Reduction of Hodgkin Huxely equations
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LECTURE 4:
- Complement to 2-dimensional neuron models
- Separation of time scales
- Type I and Type II neurons
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LECTURE 5: Introduction to Hopfield neural networks
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LECTURE 6: Generalization of the Hopfield model and Attractor Networks
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LECTURE 7:
Networks of Neurons, Population Activity, mean field argument
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Lecture 8:
Continuum models: Cortical fields and perception -
LECTURE 9:
Connected Populations: perception, decision, and competition
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LECTURE 10:
Variability and Noise: The question of the neural code
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LECTURE 11:
Variability and noise: Autocorrelation
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LECTURE 12:
Optimizing Neuron Models For Coding and Decoding
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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.
