The following paper is available in ps and ps.gz. It is about my talk at: 'Conference on Algebraic Topological Methods in Computer Science' Stanford, July 30 - August 3, 2001. 'Ordinary and directed combinatorial homotopy, applied to image analysis and concurrency' Marco Grandis Abstract. Combinatorial homotopical tools developed in previous works, and consisting essentially of intrinsic homotopy theories for simplicial complexes and directed simplicial complexes, can be applied to explore mathematical models representing images, or directed images, or concurrent processes. An image, represented by a metric space X, can be explored at a variable resolution e > 0, by equipping it with a structure t_eX of simplicial complex depending on e; this complex can be further analysed by homotopy groups \pi^e_n(X) = \pi_n(t_eX) and homology groups H^e_n(X) = H_n(t_eX). Loosely speaking, these objects detect singularities which can be captured by an n-dimensional grid, with edges bound by e; this works equally well for continuous or discrete regions of euclidean spaces. Similarly, a directed image, represented by an 'asymmetric metric space', produces a family of directed simplicial complexes f_eX and can be explored by the fundamental n-category of the latter. The same directed tools can be applied to mathematical models of concurrent automata, like Chu-spaces. AVAILABLE AT: ftp://www.dima.unige.it/Home/grandis/public/Cmb.App.ps ftp://www.dima.unige.it/Home/grandis/public/Cmb.App.ps.gz (18p, 260K) ***** With best regards Marco Grandis Dipartimento di Matematica Universita' di Genova via Dodecaneso 35 16146 GENOVA, Italy e-mail: grandis@dima.unige.it tel: +39.010.353 6805 fax: +39.010.353 6752 http://www.dima.unige.it/~grandis/ ftp://www.dima.unige.it/Home/grandis/public/ 1-Oct-2001 18:40:07 -0300,1032;000000000000-0000002b
From cat-dist@mta.ca Mon Oct 01 18:40:07 2001