EPFL Graduate Course (Master program):
Neural Networks and Biological modeling
I. Models of Single Neurons
- Neural Networks and Biological Modeling (Summer
term; 2h of lectures and 2h of exercises per week), taught by Prof. W. Gerstner
This course for Physicists and Life Scientists
focuses on biological modeling, in particular
the dynamics of neurons and learning in neural systems.
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.
II. Synpatic changes and Learning
- week 1. Brain versus Computer
and a first simple neuron model (integrate-and-fire)
- week 2. Detailed ion-current based neuron models
(Reversal potential, Hodgkin-Huxley model)
- week 3. Two-dimensional models and phase plane analysis
and Morris-Lecar model)
III. Noise and the Neural Code
- week 4. Synaptic Plasticity and Long-term potentiation
(Hebb rule, spike-time dependent learning)
- week 5. Network Dynamics and
Associative Memory (Hopfield Model, spin analogy)
- week 6: Introduction to Detailed Modeling and the Blue Brain Project
- week 7: Hand-out of miniproject and more
on topics of week 2,5, and 6.
IV. Structured Networks: Competition, Decision, Field Equations
- 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)
- week 11. Signal transmission and coding (rapid transients,oscillations)
Recommanded text books
- week 12. Spatially structured networks (field equations, working memory,formation of activity bumps)
- week 13. Decision Making
- week 14: Associative Memory, Mean-Field, and Population Dynamics
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.
Or as 45 minutes of lecture; 20 minutes of exercise,
10 minutes discussion of exercise and 45 minutes of lecture.
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.
Video Lectures are available for this
Slides, Python Exercises, and Paper and Pencil Exercises are available for this
Students taking the course for credit find additional material
on the Moodle page. The Moodle page is the official page
for any course announcements.
go to LCN Home Page
go to EPFL-I&C Home Page
go to Life Sciences -