Biological modeling of neural networks
Weekly outline
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Lecturer: Wulfram Gerstner.
Assistants: Martin Barry, Valentin Schmutz, Christos Sourmpis, Georgios Iatropoulos
Lectures on Monday 09:15-13:00 - INM200
Neuronal networks, consisting of neurons and synapses that form changeable connections between the neurons, are thought to be the basis of learning, memory, and thinking. In this course we develop and use mathematical modeling techniques to describe neuronal activity and discuss aspects of neuronal dynamics, learning, and memory.
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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 -
Easter Holidays
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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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Exam preparation / No lecture
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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.
