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U.W. Bangor - School of Informatics - Mathematics Preprints 1992

Category Theory & Homotopy Theory

92.09 : PORTER, T.

Can catgorical shape theory handle grey level images?

Published in:

"Shape in picture", Proc. NATO advanced research workshop, NATO ASI Series F 126 (1994) Springer-Verlag, Berlin Heidelberg.

92.10 : PORTER, T.

Algebraic models for proper homotopy types : Lectures at Logronno


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.

92.18 : PORTER, T.

Catgorical shape theory as a formal language for pattern recognition?


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

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