Graduate Course (Master program): Neural Networks and Biological modeling

• Neural Networks and Biological Modeling (Summer term; 2h of lectures and 2h of exercises per week)
 

This course for Physicists and Life Scientists focuses on biological modeling, in particular the dynamics of neurons and learning in neural systems.

Objectifs:

Neural networks are a fascinating interdisciplinary field where physicists, biologists, and computer scientists work together in order to better understand the information processing in biology. In this course, mathematical models of biological neural networks are presented and analyzed.

Contents:

• week 1. Brain versus Computer and a first simple neuron model (integrate-and-fire) Reading: Ch. 1
• week 2. Detailed ion-current based neuron models (Reversal potential, Hodgkin-Huxley model) Reading: Ch. 2.
• week 3. Two-dimensional models and phase plane analysis (Fitzhugh-Nagumo and Morris-Lecar model) Reading: Ch. 3

• week 4. Synaptic Plasticity and Long-term potentiation (Hebb rule, spike-time dependent learning) Reading: Ch. 10
• week 5. Network Dynamics and Associative Memory (Hopfield Model, spin analogy) Reading Here is a simple demo of the Hopfield model
• week 6: Introduction to Reinforcement learning
• week 7: Hand-out of miniproject and more on topics of week 2,5, and 6.

• week 8: Variability of Spike trains, noise and the neural code (Interval distribution, Poisson process, Renewal process)
• week 9: Spike Response Models and the neural code revisited (Reliability of neurons, predicting spike times, timing codes)
• week 10. Population dynamics and membrane potential distribution (diffusive noise/stochastic spike arrival; Fokker-Planck equation, neuron in subthreshold regime) Reading: Ch. 5.5
• week 11. Signal transmission and coding (rapid transients,oscillations) Reading: Ch. 7

• week 12. Spatially structured networks (field equations, working memory,formation of activity bumps) Reading: Ch. 6.5 as well as Ch. 9.1 and 9.2
• week 13. Current research topics

• Spiking Neuron Models by W. Gerstner and W. Kistler (Cambridge Univ. Press).
• Theoretical Neuroscience by P. Dayan and L.F. Abbott (MIT Press).

Exercises.
Attention. Many of the Exercises will be integrated in the lectures. For example a Monday session from 10h15 to 13h00 can be structured as 35 minutes course + 10 minutes exercise + break + 25 minutes course + 20 minutes exercise + break + 20 minutes course + 15 minutes exercise. Most exercises are paper-and-pencil, but bring your labtop, because some exercises will also be computer-based demonstrations that you will do in class.

Some slides The main part of the course is taught using the blackboard, yet transparencies and computer animations are occasionally used. Here are some slides to Intro , Part I , Part II , Part III , Hopfield Model.