Biological modeling of neural networks ‒ LCN ‐ EPFL

Neuronal networks, consisting of neurons and synapses that form changeable connexions between the neurons, are thought to be the basis of learning, memory, and thinking. In this course we develop and use mathematical modeling techniques to describe neuronal activity and discuss aspects of neuronal dynamics, learning, and memory.

Week 1: Introduction
- A First introduction and overview of course
- B Coding by Spikes (action potentials)
- C Model of a passive membrane
- D Leaky integrate-and-fire model
- E Nonlinear integrate-and-fire model
- F Quality of integrate-and-fire models: comparison with experiments
- Downloads, Exercises, Reading Assignments
  - Slides W1
  - Reading assignment, lecture 1b (Chapter 4.1) (Read chapter 4.1)
  - Reading assignment, lecture 1a (Chapter 1) (Read Chapter 1)
  - LIF.py
  - Handout – Python Install HowTo
  - Tutorial introduction slides
  - Questions Set 1
Week 2: Detailed Neuron Models
- A The Nernst Equation
- B Hodgkin-Huxley Model
- C Model of synaptic input
- Downloads, Exercises, Reading Assignments
  - Slides W2
  - Reading assignment Lecture 2 (Chapter 2) (Read Chapter 2.1-2.4)
  - HH.py
  - Questions Set 2
Week 3: Two dimensional neuron models:
- A Reduction of Hodgkin Huxley equations
- B Phase plane analysis
- C Type I and Type II models
- Downloads, Exercises, Reading Assignments
  - Slides W3
  - Reading assignment Lecture 3 (Chapter 3)
    (Two-dimensional models, reduction of hodgkin-huxley model, phase plane analysis, type 1 and type 2 model)
  - Tools.py
  - TypeX.py
  - TypeY.py
  - fvsI.py
  - demo_phaseplane.py
  - Questions Set 3
Week 4: Synaptic Plasticity
- Downloads, Exercises, Reading Assignments
  - Slides W4
  - Reading assignment: Chapter 10
    (Read chapter 10.1 and 10.2 and 10.3.1 and 10.4.1)
  - Reading assignment: Chapter 11.1.4
    (Read chapter 11.1.4 on Receptive Field development)
  - Set4.py
  - Questions Set 4
Week 5: Associative memory and population dynamics
- Downloads, Exercises, Reading Assignments
Week 6: Introduction to Reinforcement Learning
- Downloads, Exercises, Reading Assignments
Week 7: More on detailed neuron models —- Cable equation — simulation of compartmental models
- Downloads, Exercises, Reading Assignments
  - Slides W7
  - Neuron simulator
  - neuron_example.py
  - General Instructions for the Miniproject
  - Miniproject Reinforcement Learning
  - Miniproject – Hopfield networks
  - Miniproject – Neuron
  - mod file for NEURON miniproject
  - starter.py (for reinf. learning miniproject)
  - Questions set 7
Week 8: Variability and the Neural Code
- Downloads, Exercises, Reading Assignments
  - Slides W8
  - Reading assignment – Chapter 1.4-1.6 (Problem of neural coding)
  - Reading assignment – Chapter 5.1-5.3 (Noise and Variability)
  - Questions set 8
Week 9: Spike Response Model (SRM) and coding revisited
- Downloads, Exercises, Reading Assignments
  - Slides W9
  - Reading assignment (Spike Response Model and Coding, chapters 4.2, 4.3.1, 4.5, 4.6)
  - Reading assignment – Chapter 5 (chapters 5.5-5.10)
  - Questions set 9
Week 10: Population of Neurons – Fokker-Planck Equation
- Downloads, Exercises, Reading Assignments
Week 11: Population rate models and Coding — Reverse correlations, PSTH, rapid transients in populations of neurons, linear Poisson model
- Downloads, Exercises, Reading Assignments
  - Slides W11
  - Questions set 11
Week 12: Neural Networks with spatial structure, competition, field equations, decision processes
- Downloads, Exercises, Reading Assignments
Week 13: Connected Populations: perception, decision, and competition
- Downloads, Exercises, Reading Assignments
  - Slides W13
  - Questions set 13
Week 14: Population dynamics and associative memory; stable learning
- Downloads, Exercises, Reading Assignments
  - Slides W14
  - Past Exams
    - Exam 2010
    - Exam 2009
    - Exam 2008
    - Exam 2007
    - Exam 2005