We show that although the algebraic semantics of place/transition Petri nets under the collective token philosophy can be fully explained in terms of strictly symmetric monoidal categories, the analogous construction under the individual token philosophy is not completely satisfactory, because it lacks universality and also functoriality. We introduce the notion of pre-net to recover these aspe...

In children pre-anaesthetic medications are frequently administered as pharmacological adjunctions to help alleviate the stress and fear of surgery as well as to ease child parental separation and promote a smooth induction. Oral, rectal, intravenous and intramuscular route has been used; however each route has its disadvantage. Pre-anaesthetic medication administered intranasal for avoidance o...

In this work a theory is developed for unifying large classes of nonlinear discrete-time dynamical systems obeying a superposition of a weighted maximum or minimum type. The state vectors and input-output signals evolve on nonlinear spaces which we call complete weighted lattices and include as special cases the nonlinear vector spaces of minimax algebra. Their algebraic structure has a polygon...

A quantaloid is a sup-lattice-enriched category; our subject is that of categories, functors and distributors enriched in a base quantaloid Q. We show how cocomplete Q-categories are precisely those which are tensored and conically cocomplete, or alternatively, those which are tensored, cotensored and ‘order-cocomplete’. In fact, tensors and cotensors in a Q-category determine, and are determin...

We investigate the phenomenon that every monad is a linear state monad. We do this by studying a fully-complete state-passing translation from an impure call-by-value language to a new linear type theory: the enriched call-by-value calculus. The results are not specific to store, but can be applied to any computational effect expressible using algebraic operations, even to effects that are not ...

Sounds in VRML are spatialized (i.e. located in space) but no room effects can be described to make them more realistic. In this paper we present a solution we have implemented for extending the simple sound management within a VRML browser. The first aspect is the description of sound related materials in VRML format using new nodes and fields. We describe the different elements we have introd...

We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coin-ductively deened types. Our main results provide suucient criteria for the validity of such principles: in the presence of comprehension, the induction principle for initial algebras is admissible, and dually, in the presence of quotient types, the coinduction principle fo...

The expectation monad is introduced abstractly via two composable adjunctions, but concretely captures measures. It turns out to sit in between known monads: on the one hand the distribution and ultrafilter monad, and on the other hand the continuation monad. This expectation monad is used in two probabilistic analogues of fundamental results of Manes and Gelfand for the ultrafilter monad: alge...

We present a categorical logic formulation of induction and coinduction principles for reasoning about inductively and coin-ductively deened types. Our main results provide suucient criteria for the validity of such principles: in the presence of comprehension, the induction principle for initial algebras is admissible, and dually, in the presence of quotient types, the coinduction principle fo...

To work effectively with simplicial sets, which provide useful algebraic or combinatorial models of topological spaces, we need to get serious about geometric realization, colimits, limits, and adjunctions. A first step is to recall the Yoneda Lemma. Given any pair of functors F,G : D−→C, denote by Nat(F,G) := {φ| φ : F−→G} the collection of all natural transformations from F to G. Denote by sS...