TR: Embedding Recurrent Neural Networks into Predator-Prey Models (corrected URL)

[Yves Moreau]

Hello,

A number of people have been trying to download our technical report via
my home
page and list of publications; they were directed to a wrong URL (the
direct ftp URL
itself is correct) and thought the report was not available. I have
fixed this problem
and you can get the technical report whichever way you like.

My apologies to the other readers for the repeated posting.

Best regards,

Yves Moreau


Yves Moreau wrote:

> Dear Connectionists,
>
> The following technical report is available via ftp or the World Wide
> Web:
>
> EMBEDDING RECURRENT NEURAL NETWORKS INTO PREDATOR-PREY MODELS
>
> Yves Moreau and Joos Vandewalle, K.U.Leuven ESAT-SISTA
>
> K.U.Leuven, Elektrotechniek-ESAT, Technical report ESAT-SISTA TR98-02
>
ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/moreau/reports/lotka_volterra_tr98-02.ps

>
> Comments are more than welcome!
>
> ABSTRACT
> ========
>
>   We study changes of coordinates that allow the embedding of the
>   ordinary differential equations describing continuous-time recurrent

>   neural networks into differential equations describing predator-prey

>   models ---also called Lotka-Volterra systems. We do this by
transforming
>   the equations for the neural network first into quasi-monomial form,

>   where we express the vector field of the dynamical
>   system as a linear combination of products of powers of the
>   variables.  From this quasi-monomial form, we can directly
>   transform the system further into Lotka-Volterra equations.  The
>   resulting Lotka-Volterra system is of higher dimension than the
>   original system, but the behavior of its first variables is
>   equivalent to the behavior of the original neural network. We expect

>   that this transformation will permit the application of existing
>   techniques for the analysis of Lotka-Volterra systems to
recurrent-neural
>   networks. Furthermore, our result shows that Lotka-Volterra systems
>   are universal approximators of dynamical systems, just as
>   continuous-time neural networks.
>
> Keywords: Continuous-time neural networks,
> Equivalence of dynamical systems, Lotka-Volterra systems,
> Predator-prey models, Quasi-monomial forms.
>
> --------------------------------------------------------------
>
> To get it from the World Wide Web, point your browser at:
>
ftp://ftp.esat.kuleuven.ac.be/pub/SISTA/moreau/reports/lotka_volterra_tr98-02.ps

>
> To get it via FTP:
> ftp ftp.esat.kuleuven.ac.be
> cd pub/SISTA/moreau/reports
> get lotka_volterra_tr98-02.ps
>
> --------------------
>
> Yves Moreau
>
> Department of Electrical Engineering
> Katholieke Universiteit Leuven
> Leuven, Belgium
>
> email: moreau at esat.kuleuven.ac.be
>
> homepage: http://www.esat.kuleuven.ac.be/~moreau
>
> publications:
> http://www.esat.kuleuven.ac.be/~moreau/publication_list.html