Analyze connected networks in the mean-field limit
Formalize biological facts into mathematical models
Understand a simple mathematical model of memory formation in the brain
Understand a simple mathematical model of decision processes
Understand cortical field models of perception
What happens in your brain when you make a decision? And what happens if you recall a memory from your last vacation? Why is our perception of simple objects sometimes strangely distorted? How can millions of neurons in the brain work together without a central control unit?
This course explains the mathematical and computational models that are used in the field of theoretical neuroscience to answer the above questions. The core of the answer to cognition may lie in the collective dynamics of thousands of interacting neurons – and these dynamics are mathematically analyzed in this course using methods such as mean-field theory and non-linear differential equations.
Neuronal Dynamics - from single neurons to networks and models of cognition (W. Gerstner, W.M. Kistler, R. Naud and L. Paninski), Cambridge Univ. Press. 2014
online version: http://neuronaldynamics.epfl.ch/
The course will be based on Chapters 12 and 16-19.
Overview of contents over 6 weeks:
A) Associative Memory and Hopfield Model
B) Attractor networks and spiking neurons
C) Neuronal populations and mean-field theory
D) Perception and cortical field models
E) Decision making and competitive dynamics
F) Synaptic Plasticity and learning
Total duration and workload:
6 weeks of video lectures. Each weak comprises a series of 5-8 videos. Viewing time about 60-90 minutes per week. Self-learning time 90 minutes per week. Online exercises, quizzes, and a final exam.
Calculus and Differential equations at the level of a bachelor in physics, math, or electrical engineering.