J . - P . Quadrat

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|We study uid analogues of a subclass of Petri nets, called Fluid Timed Event Graphs with Multipliers, which are a timed extension of weighted T-Systems studied in the Petri Net literature. These event graphs can be studied naturally, with a new algebra, analogous to the min-plus algebra, but de ned on piecewise linear concave increasing functions, endowed(More)
To Anatoly Vershik with admiration and gratitude This paper is a brief introduction, practically without exact theorems and proofs, to the Maslov dequantization and idempotent and tropical mathematics. Our list of references is not complete (not at all). Additional references can be found, e.g., in the electronic archive http://arXiv.org and in [9, 17, 21,(More)
The article describes a stochastic formal language adapted to the botanical concepts underlying the GreenLab organogenesis model. It is based on stochastic L-systems (parallel rewriting grammars) and on multi-type branching processes: stochastic processes control bud productions and at each growth cycle, each new growth unit is the result of a random(More)
In maxplus algebra, linear projectors on an image of a morphism B parallel to the kernel of another morphism C can be built under transversality conditions of the two morphisms. The existence of a transverse to an image or a kernel of a morphism is obtained under some regularity conditions. We show that those regularity and transversality conditions can be(More)
We show that car traffic on a town can be modeled using a Petri net extension where arcs have negative weights. The corresponding minplus dynamics is not linear but homogeneous of degree one. Possibly depending on the initial condition, homogeneous of degree 1 minplus systems may be periodic or have a chaotic behavior (to which corresponds a constant(More)
We study here the min-plus analogues of Jacksonnetworks of queues and show that the corresponding geodesic problems on Zm can be reduced to minimal cost flow problems on complete graphs having m nodes. In some particular cases, these flow problems can be solved explicitly giving formulae analogue, in the min-plus algebra, to the standard product forms. Nous(More)