J. P. Quadrat

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This paper is a brief introduction to idempotent and tropical mathematics. Tropical mathematics can be treated as the result of the so-called Maslov dequantization of the traditional mathematics over numerical fields as the Planck constant tends to zero taking imaginary values. Bibliography: 187 titles. To Anatoly Vershik with admiration and gratitude This(More)
| 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 deened on piecewise linear concave increasing functions, endowed(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)
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)
We revisit some results obtained recently in min-plus algebra following the ideas of statistical mechanics. Computation of geodes-ics in a graph can be done by min-plus matrix products. A min-plus matrix is seen as a kind of finite states mechanical system. The energy of this system is the eigenvalue of its min-plus matrix. The graph interpretation of the(More)