In this package you find the following items:

1. Folder MG17 (zipped)
   
Contains the Matlab code I used for the chaotic attractor prediction
documented in the paper 

H. Jaeger and H. Haas, Harnessing Nonlinearity: Predicting Chaotic
Systems and Saving Energy in Wireless Communication. Science 304, 2
April 2004

Together with the helper functions from the folder common, this
provides a complete Matlab package for re-running the simulations from
the Science paper. 

2. RefutationES.pdf

A text document in which I refute the objections of a Science reviewer
who objected that the Mackey-Glass data that I used might be
generated incorrectly and in fact not be chaotic. This is of interest
only for those with a deeper interest in the subtelties of chaotic
time series simulation.  

3. Folder MG17Lyapunov (zipped)

Matlab code for checking the leading Lyapunov exponent for the
Mackey-Glass time series that I generated for the investigations
documented in the Science paper. This again will be of interest
only for those with a deeper interest in the subtelties of chaotic
time series simulation. 

4. Folder common (zipped)

Some Matlab helper routines that are called by functions and scripts
in MG17 and MG17Lyapunov. Make sure that these helpers are in your
Matlab search paths when you work with MG17 or MG17Lyapunov.


General comment. I have received a number of messages from people who
were unable to replicate the results reported in the Science
paper. These problems apparently are mostly due to improper generation
of the training and testing data. Specifically, if one uses the delay
differential equation solvers that come shipped with Matlab for
generating Mackey-Glass data, their quality is insufficient because
the Matlab solvers are precise only on far-spaced support points, with
unreliable interpolated values in between. The inaccuracies are large
enough to disrupt the high-precision prediction possible with
ESNs. Therefore I used self-generated Mackey-Glass data for training
and testing, whose setup (and quality assessment) is detailed out in
the document RefutationES.pdf. -- Another possible reason why some may
have difficulties with replicating the Science paper results is that
they might not use long enough washout times for the dynamical
reservoir. Make sure that both in training and testing, about 1,000
iterations are "wasted" before network states are used for training
output weights or making predictions (if one uses networks as large as
1,000 units).