Dear all, here is a new preprint. Best regards. pg. Title: Directed algebraic topology and higher dimensional transition system Abstract : Cattani-Sassone's notion of higher dimensional transition system is interpreted as a small-orthogonality class of a locally finitely presentable topological category of weak higher dimensional transition systems. In particular, the higher dimensional transition system associated with the labelled $n$-cube turns out to be the free higher dimensional transition system generated by one $n$-dimensional transition. As a first application of this construction, it is proved that the category of higher dimensional transition systems is equivalent to a full reflective subcategory of the category of labelled symmetric precubical sets. As a second application, it is given a factorization of the mapping taking a CCS process name to a flow through higher dimensional transition systems. The second application of this paper can be easily adapted to other process algebras and to other topological models of concurrency than the one of flows. URL: http://www.pps.jussieu.fr/~gaucher/HDAparadigm.pdf