UCLA short course on Fuzzy Logic, Chaos, and Neural Networks

[Goodin, Bill]

On May 22-24, 1995, UCLA Extension will present the short course,
"Fuzzy Logic, Chaos, and Neural Networks: Principles and
Applications", on the UCLA campus in Los Angeles.

The instructor is Harold Szu, PhD, Research Physicist,
Washington, DC.

This course presents the principles and applications of
several different but related disciplines--neural
networks, fuzzy logic, chaos--in the context of pattern
recognition, control of engineering tolerance
imprecision, and the prediction of fluctuating time
series.  Since research into these areas has contributed
to the understanding of human intelligence, researchers
have dramatically enhanced their understanding of fuzzy
neural systems and in fact may have discovered the
"Rosetta stone" to decipher and unify these intelligence
functions.  For example, complex neurodynamic patterns
may be understood and modelled by Artificial Neural
Networks (ANN) governed by fixed-point attractor dynamics
in terms of a Hebbian learning matrix among bifurcated
neurons.  Each node generates a low dimensional
bifurcation cascade towards the chaos but together they
form collective ambiguous outputs; e.g., a fuzzy set
called the Fuzzy Membership Function (FMF).  This
feature becomes particularly powerful for real world
applications in signal processing, pattern recognition
and/or prediction/control.  The course delineates the
difference between the classical sigmoidal squash function
of the typical neuron threshold logic and the new N-shaped
sigmoidal function having a "piecewise negative logic" that can
generate a Feigenbaum cascade of bifurcation outputs of which
the overall envelope is postulated to be the triangle FMF.  The
course also discusses applications of chaos and collective
chaos for spatiotemporal information processing that has been
embedded through an ANN bifurcation cascade of those collective
chaotic outputs generated from piecewise negative logic neurons.
These chaotic outputs learn the FMF triangle-shape with a
different degree of fuzziness as defined by the scaling function of
the multiresolution analysis (MRA) used often in wavelet transforms.
Another advantage of this methodology is information processing
in a synthetic nonlinear dynamical environment.  For example,
nonlinear ocean waves can be efficiently analyzed by nonlinear
soliton dynamics, rather than traditional Fourier series.
Implementation techniques in chaos ANN chips are given.

The course covers essential ANN learning theory and the
elementary mathematics of chaos such as the bifurcation cascade
route to chaos and the rudimentary Fuzzy Logic (FL) for those
interdisciplinary participants with only basic knowledge of the
subject areas.  Various applications in chaos, fuzzy logic, and
neural net learning are illustrated in terms of spatiotemporal
information processing, such as:

 --Signal/image de-noise
 --Control device/machine chaos
 --Communication coding
 --Chaotic heart and biomedical applications.

For additional information and a complete course description,
please contact Marcus Hennessy at:
(310) 825-1047
(310) 206-2815  fax
mhenness at unex.ucla.edu