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Computational Neuroscience: Neuronal Dynamics of Cognition

About This Course

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.

By the end of the course, you will be able to:

  • 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.

Textbook:

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:

  • 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

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.

Requirements

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

Course Staff

Course Staff Image #1

Wulfram Gerstner

After studies of Physics in Tübingen and at the Ludwig-Maximilians-University Munich (Master 1989), Wulfram Gerstner spent a year as a visiting researcher at UC Berkeley. He received his PhD in Theoretical Physics from the Technical University Munich in 1993 with a thesis on associative memory in networks of spiking neurons. After short postdoctoral stays at Brandeis University and the TU Munich, he joined the EPFL in 1996 as Assistant Professor. Promoted to Associate Professor in 2001, he is since 2006 a full professor with double appointment in Computer Science and Life Sciences. Wulfram Gerstner has been invited speaker at numerous international conferences and workshops. He has served on the editorial board of the 'Journal of Computational Neuroscience', and 'Science', as well as other journals. He conducts research in computational neuroscience with special emphasis on models of spiking neurons, spike-timing dependent plasticity, and reward-based learning in spiking neurons.

  1. Course Number

    BIO_465.b
  2. Classes Start

  3. Classes End

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