Computational Neuroscience: Neuronal Dynamics of Cognition

This course explains the mathematical and computational models that are used in the field of theoretical neuroscience to analyze the collective dynamics of thousands of interacting neurons.

Description

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.

What you will learn

• 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.

Prerequisites

Calculus and Differential equations at the level of a bachelor in physics, math, or electrical engineering.

Plan

• 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