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1. Rate Coding in the Nervous System.

A number of websites provide a good working introduction to the integrate and fire model. Most use Matlab as a platform to run the models.

Gabbiani and Koch provide a number of matlab routines for illustrating integrate and fire properties of neurons. To run them, you must have Matlab 6 with the simulink program running. (This is available with a Cornell Matlab site licence). The integrate and fire routine illustrated in the seminar was Tutorial 2, Download the desired files from their download site, and run using Matlab.

Emilio Salinas provides examples of Matlab routines that run integrate and fire with noisy inputs. In one of these routines, a perfect integrator is considered, in a second, a leaky integrator is employed.

Each of these demonstrations that you download files from the website and run the program on a local matlab program.

Nelson provides a java-script integrate and fire model which runs from a web page, but there is not much flexibility. Susan Becker at McMaster University has a good web site for neuronal computation that has a simple integrate and fire program for matlab.

2. Neural Assemblies.

For more information on Alexa Riehle, see her web site at the CNRS in Marseille, France. For more on the research of Ad Aertsen, please check his home page at the University of Freiberg. Ad Aertsen provides a web-page for more on the neural modeling of synchronized spikes.

3 & 4 . Analysis of Spike Trains.

For basic analysis of spike trains, try the "ORBITAL SPIKE 3" program written by Attila Szücs. This program, written for Windows platforms, operates on Win95, Win98, and Win2000. It generates spike density functions, inter-spike interval histograms, plots of sequences, histograms, scatter plots, color maps, mutual spike intervals (phases), cumulative ISI-histograms, firing rate estimation using rectangular, Gaussian and sinc filters, auto- and crosscorrelation from interspike or SDF data, Fourier-transform from ISI or SDF data, and much more. You can import your own spike data, transformed into time-stamped data, simply by writing a text file and importing it into OSW3.

One of the previous metrics developed for stability and similarity of two spike trains was developed by Jonathan Victor at Cornell Wiel Medical College in New York. Victor works on visual cortex and has had a long interest in temporal coding in the brain. His algorithm is described in his web site. A mat-lab implementation is avialable.

Here is a link to Bruce Land's seminar.

5. Temporal Hyperacuity.

For some time-coding systems, the precision of temporal analysis is far less than the duration of a single spike. For example, sound localization using interaural time differences requires estimating time to an accurary of 10 microseconds or so, while the duratino of the action potential is 100 times greater. In vision, the ability to resolve spatial information finer than that of the spacing of the individual cones is referred to as visual hyperacuity. By analogy, measurements of timing with great accuracy is called temporal hyperacuity. Some of the best acknowledged cases of temporal hyperacuity come from the auditory and electrosenory systems of bats, owls and electric fish. In this meeting, we discuss the jamming avoidance response of electric fish which has a temporal acuity of 0.2 microseconds.

Reading:

Kawasaki, M. (1997). Sensory hyperacuity in the jamming avoidance response of weakly electric fish. Current Opinion in Neurobiology 7, 473-479.

Rose, G. and Heiligenberg, W. (1985). Temporal hyperacuity in the electric sense of fish. Nature 318, 178-80.

9. Decoding Time II: Spike timing dependent learning rules. Hebbian and Anti-Hebbian Learning.

Symmetic and antisymmetric learning rules, both Hebbian and Anti-Hebbian are discussed. Dr. Patrick Roberts, Oregon Health and Sciences University has written about and modeled the anti-Hebbian learning rules extracted from electric fish, and combined this with general asymmetric versus symmetric learning rules applying to other systesm. See his modeling efforts here (Macintosh only). Alternatively, see a Flash slide demonstration of the various learning rules.