A Universal Characterization of the Double Powerlocale

This is a version from 29 Sept 2003 of the paper published under the same name in Theoretical Computer Science 316 (2004) 297{321. The double powerlocale P(X) (found by composing, in either order,the upper and lower powerlocale constructions PU and PL) is shown to be isomorphic in [Locop; Set] to the double exponential SSX where S is the Sierpinski locale. Further PU(X) and PL(X) are shown to be the subobjects P(X) comprising, respectively, the meet semilattice and join semilattice homomorphisms. A key lemma shows that, for any locales X and Y , natural transformations from SX (the presheaf Loc

An overview of the modeling of crowd dynamics

In this chapter we review some of the most important models at microscopic, macroscopic, and mesoscopic scale, which, in our opinion, represent milestones in their respective fields or are of particular interest for this book. We also report some models for rational pedestrians, which make use of techniques from optimal control theory. For the sake of convenience, we present all models in two space dimensions