Algebraic models for proper homotopy types : Lectures at Logronno
Abstract:
The aim of this workshop on Proper Homotopy Theory
was to provide an opportunity to present and discuss
various approaches to proper homotopy theory.
My current work in this area is with Luis Javier Hernandez
and I have attempted to explain the "philosophy" behind our approach.
Why "philosophy"?
Simply, because all too seldom do mathematicians put in writing their
overall view of a subject and how it may evolve.
This theme would seem particularly important given
the aim of the workshop.
Published in:
Proceedings of the workshop on Proper Homotopy Theory,
Universidad de la Rioja, 1993.
Catgorical shape theory as a formal language for pattern recognition?
Abstract:
Can categorical shape theory be regarded as a formal language for
pattern regognition?
In an attempt to move towards an answer to this question,
in this paper I will briefly investigate
what the question might mean.
What is a "formal language"?
How is it formed?
What is it useful for?
I also want to ask what aspects of pattern recognition might be described
by such a language.
This has two aspects:
(i) can the language handle at least some of the sorts of argument
used in pattern recognition, e.g. use of invariants?
(ii) does the model "predict" or "explain" known properties
of natural or artificial pattern recognition systems?
We will partially examine these as we develop the language.
Published in:
Annals of Mathematics and Artificial Intelligence,
10 (1994) 25-54
