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- Francis Bailly, Giuseppe Longo Hermann
- 2010

Deuxième point : la méthode. Les concepts de temps et d'espace pris en compte par nos mathématiques ont été conçus à partir d'un enracinement dans des problèmes propres aux sciences physiques. Il n'est pas étonnant qu'il faille les réviser : l'approche méthodologique des auteurs consiste en une révision critique à la fois historique et généalogique des… (More)

- N Destainville, R Mosseri, F Bailly
- 2001

Some combinatorial properties of fixed boundary rhombus random tilings with octagonal symmetry are studied. A geometrical analysis of their configuration space is given as well as a description in terms of discrete dynamical systems, thus generalizing previous results on the more restricted class of codimension-one tilings. In particular this method gives… (More)

This paper is a conceptual analysis of the role of the mathematical continuum vs. the discrete in the understanding of randomness, as a notion with a physical meaning or origin. The presentation is " informal " , as we will not write formulas; yet, we will refer to non-obvious technical results from various scientific domains. And we will propose a… (More)

This paper proposes an abstract mathematical frame for describing some features of biological time. The key point is that usual physical (linear) representation of time is insufficient, in our view, for the understanding key phenomena of life, such as rhythms, both physical (circadian, seasonal...) and properly biological (heart beating, respiration,… (More)

- M Widom, N Destainville, R Mosseri, F Bailly
- 1998

Random tilings of the plane by rhombi are projections into the plane of corrugated two-dimensional surfaces in a higher dimensional hypercubic crystal. We consider tilings of 2D-fold symmetry projected from D-dimensional space. Thermodynamic properties depend on the relative numbers of tiles with diierent angles and ori-entations, and also on the boundary… (More)

This paper proposes a systemic perspective for some aspects of both phylogenesis and ontogenesis, in the light of the notion of " biological organization " as negative entropy, following some hints by Schrödinger. To this purpose, we introduce two extra principles to the thermodynamic ones, which are (mathematically) compatible with the traditional… (More)

- N Destainville, R Mosseri, F Bailly
- 2003

We propose the first algebraic determinantal formula to enumerate random rhombus tilings filling a centro-symmetric octagon of any size. This result uses the Gessel-Viennot technique and generalizes to any octagon a former specialized formula by Elnitsky.

We show how a simple nonlinear dynamical system (the discrete quadratic iteration on the unit segment) can be the basis for modelling the embryogenesis process. Such an approach, even though being crude, can nevertheless prove to be useful when looking with the two main involved processes: (i) on one hand the cell proliferation under successive divisions;… (More)

- Jean-Pierre Fouque, Josselin Garnier, F Bailly, J Chillan, J F Clouet, J P Fouque +1 other
- 2007

The aim of this contribution is to present recent results obtained at the "Centre de Math ematiques Appliqu ees de l' Ecole Polytechnique" by the group working on waves in random media (These results are based on various generalizations of classical diiusion-approximation results. In the rst section we study the spreading of an acoustic pulse travelling… (More)

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