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A Symbolic Method to Analyse Patterns in Plant Structure

Published online by Cambridge University Press:  09 July 2014

C. LOI ,
P.-H. COURNÈDE  and
J. FRANÇON
C. LOI
Affiliation:
Ecole Centrale Paris, Laboratory of Applied Mathematics and Systems, Châtenay Malabry, France (e-mail: paul-henry.cournede@ecp.fr)
P.-H. COURNÈDE
Affiliation:
Ecole Centrale Paris, Laboratory of Applied Mathematics and Systems, Châtenay Malabry, France (e-mail: paul-henry.cournede@ecp.fr)
J. FRANÇON
Affiliation:
University of Strasbourg, ICube Laboratory, Team ‘Informatique Géométrique et Graphique’, France
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Abstract

Formal grammars such as L-systems have long been used to describe plant growth dynamics. In this article, they are used for a new purpose. The aim is to build a symbolic method that enables the computation of the stochastic distribution associated with the number of complex structures in plants whose organogenesis is driven by a multitype branching process. For that purpose, a new combinatorial framework is set in which plant structure is coded by a Dyck word. Moreover, organogenesis is represented by stochastic F0L-systems. In doing so, the problem is equivalent to determining the distribution of patterns in random words generated by a stochastic F0L-system. This method finds interesting applications in the parameter identification of stochastic models of plant development.

Keywords

Primary 05ASecondary 92B60J

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 23 , Issue 5: Honouring the Memory of Philippe Flajolet - Part 1 , September 2014 , pp. 842 - 860
Copyright
Copyright © Cambridge University Press 2014 

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