Coursebooks 2016-2017

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Biological modeling of neural networks

BIO-465

Lecturer(s) :

Gerstner Wulfram

Language:

English

Summary

In this course we study mathematical models of neurons and neuronal networks in the context of biology and establish links to models of cognition.

Content

I. Models of single neurons 1. Introduction: brain vs computer and a first simple neuron model 2. Models on the level of ion current (Hodgkin-Huxley model) 3./4.  Two-dimensional models and phase space analysis II. Cognition, Learning, and Synaptic Plasticity  5. Associative Memory and Attractor Dynamics (Hopfield Model) 6:  Synaptic Plasticity and Long-term potentiation (Hebb rule, mathematical formulation)  7. Neuronal Populations and networks 8. Continuum models and perception 9. Competition and models of Decision making III. Noise and the neural code 10. Noise and variability of spike trains (point processes, renewal process, interval distribution) 11: Variance of membrane potentials and  Spike Response Models 12.  Population dynamics and membrane potential distribution (Fokker-Planck equation) 13. Dynamics in Plastic networks 14.  Neural Code: Generalized Linear Models and Reverse Correlations

Keywords

neural networks, neuronal dynamics, computational neuroscience, mathematical modeling in biology, applied mathematics, brain, cognition, neurons, memory, learning, plasticity

Learning Prerequisites

Required courses

undergraduate math at the level of electrical engineering or physics majors

undergraduate physics.

Recommended courses

Analysis I-III, linear algebra, probability and statistics
For SSV students: Dynamical Systems Theory for Engineers or "Mathematical and Computational Models in Biology" course, Felix Naef

Important concepts to start the course

Differential equations, stochastic processes,

Learning Outcomes

By the end of the course, the student must be able to:

Transversal skills

Teaching methods

Classroom teaching, exercises and miniproject

Expected student activities

miniprojects

Assessment methods

Written exam (67%) & miniproject (33%)

Resources

Bibliography

 Gerstner, Kistler, Naud, Pansinski : Neuronal Dynamics, Cambridge Univ. Press 2014

Ressources en bibliothèque
Videos

In the programs

Reference week

 MoTuWeThFr
8-9     
9-10INM200    
10-11    
11-12INM200    
12-13    
13-14     
14-15     
15-16     
16-17     
17-18     
18-19     
19-20     
20-21     
21-22     
 
      Lecture
      Exercise, TP
      Project, other

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  • Autumn semester
  • Winter sessions
  • Spring semester
  • Summer sessions
  • Lecture in French
  • Lecture in English
  • Lecture in German