EPFLx: Computational Neuroscience: Neuronal Dynamics of Cognition

by École polytechnique fédérale de Lausanne

Theoretical Neuroscience

Course Description

Are you fascinated by the intricate workings of the human brain? Do you want to unravel the mysteries behind decision-making, memory recall, and perception? Welcome to the cutting-edge world of Theoretical Neuroscience! This advanced course delves deep into the mathematical and computational models that explain how our brain functions at a neural level. You'll explore the collective dynamics of thousands of interacting neurons and learn how to analyze these complex systems using sophisticated mathematical techniques.

What Students Will Learn

Analyzing connected networks in the mean-field limit
Formalizing biological facts into mathematical models
Understanding simple mathematical models of memory formation in the brain
Comprehending mathematical models of decision processes
Grasping cortical field models of perception

Pre-requisites

To succeed in this course, you should have a strong foundation in:

Calculus
Differential equations

These should be at the level typically acquired in a bachelor's degree in physics, mathematics, or electrical engineering.

Course Content

Associative Memory and Hopfield Model
Attractor networks and spiking neurons
Neuronal populations and mean-field theory
Perception and cortical field models
Decision making and competitive dynamics
Synaptic Plasticity and learning

Who This Course Is For

Graduate students in neuroscience, physics, mathematics, or computer science
Researchers looking to expand their knowledge in theoretical neuroscience
Professionals in fields such as artificial intelligence or cognitive science seeking to understand brain-inspired computing

Real-World Applications

In neuroscience research, to develop more accurate models of brain function
In artificial intelligence, to create more brain-like algorithms and neural networks
In medicine, to better understand neurological disorders and potential treatments
In cognitive science, to model and predict human behavior and decision-making
In data science, to apply advanced mathematical techniques to complex systems

Syllabus

Textbook: "Neuronal Dynamics - from single neurons to networks and models of cognition" by W. Gerstner, W.M. Kistler, R. Naud and L. Paninski, Cambridge Univ. Press. 2014

Online version available at: http://neuronaldynamics.epfl.ch/

The course is based on Chapters 12 and 16-19 and is structured over 6 weeks:

Week 1: Associative Memory and Hopfield Model

Week 2: Attractor networks and spiking neurons

Week 3: Neuronal populations and mean-field theory

Week 4: Perception and cortical field models

Week 5: Decision making and competitive dynamics

Week 6: Synaptic Plasticity and learning

Each week includes: