ESAM 495

Hermann Riecke

TuTh 9:30-11:00 M177 Technological Institute

This class is intended for an interdisciplinary
audience of applied mathematicians, biologists, engineers, physicists.

For detailed class information see bottom of the page

**Outline **

- Introduction
- Single Neurons:
- Passive properties
- Ion Channels, Nernst-Planck equation and equilibrium, Goldman-Hodgkin-Katz equation
- Hodgkin-Huxley model
- Conductance-Based Models: Additional currents , ,
- Integrate-and-Fire model (Type-I vs Type-II neurons)

- Cable equation
- Linear Cable Theory
- Axons and Active Dendrites

Movie

- Synapses
- gap junctions
- chemical synapses, facilitation and depression

- Firing-Rates
- Poisson spike trains
- Spike-triggered average, receptive fields

- Networks:
- Rate Models
- Feed-forward Networks
- V1: Hubel-Wiesel model Long Movie Short Movie
- Compensation of gaze direction

- Recurrent Networks
- Limulus vision: center-surround cells, temporal on/off cells, selective amplification
- Associate memory: Hopfield network

- Networks: Spiking Neurons
- Synchronization: weak coupling and phase-response curve
- Gamma-rhythm

- Unsupervised Learning
- Hebbian rule, Oja rule, BCM rule
- Development of ocular dominance

- Synaptic Plasticity, Spike-Timing-Dependent Plasticity
- Neural Decoding

discrimination, population decoding, optimal decoding, Fisher information - Information theory

entropy maximization, decorrelation, whitening filter

The class will be based largely on the book

Lecture notes are also available online for Northwestern students or for general audience. They will
be updated as the class proceeds. Therefore it is highly recommended only to
download the currently used section, even if more sections should already
be available. Please note that the notes are only available from computers
on the northwestern.edu subnet.

Other recommended sources:

- The class has substantial overlap with the class W.L. Kath taught in Winter 2007. His notes are at Kath's Notes.
- J. Keener and J. Sneyd,
*Mathematical Physiology*

It is available online at Mathematical Physiology. This is also a good book. The overlap with the class is, however, smaller and from that perspective the online version will be fine. We'll mostly use it for the derivation of the Goldmann-Hodgkin-Katz equation. - P. Churchland, T.J. Sejnowski,
*The Computational Brain*

It is available online at The Computational Brain. It has a good overview of brain function and basic anatomy. *Brain Facts*published by the Society for Neuroscience, available online at Brain Facts- hhsim simulator by D. Touretzky et al. for Hodgkin-Huxley model with exercises (see also HHsim home page)

There won't be class on October 16 and November 18. The time will be made up.

Mo 3-4, Tu 11-12, Thu 11-12 in M458

HW 1

Matlab programs for this assignment: Problem 2 Problem 3 sketch of solutions

HW 2 You will need to obtain a few journal articles, as discussed in the assignment. Partial Solutions

HW 3 Partial Solutions Sample Matlab program

HW 4 Partial Solutions HW 5 pattern 1 pattern 2 pattern 3 pattern 4

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The translation was initiated by Hermann Riecke on 2008-09-05

Hermann Riecke 2008-09-05