Cedric Loi ; Paul Henry Cournède
-
Generating Functions of Stochastic L-Systems and Application to Models of Plant Development
dmtcs:3574 -
Discrete Mathematics & Theoretical Computer Science,
January 1, 2008,
DMTCS Proceedings vol. AI, Fifth Colloquium on Mathematics and Computer Science
-
https://doi.org/10.46298/dmtcs.3574
Generating Functions of Stochastic L-Systems and Application to Models of Plant Development
Authors: Cedric Loi 1,2; Paul Henry Cournède 2,1
NULL##0000-0001-7679-6197
Cedric Loi;Paul Henry Cournède
1 Mathématiques Appliquées aux Systèmes - EA 4037
2 Modélisation de la croissance et de l'architecture des plantes
If the interest of stochastic L-systems for plant growth simulation and visualization is broadly acknowledged, their full mathematical potential has not been taken advantage of. In this article, we show how to link stochastic L-systems to multitype branching processes, in order to characterize the probability distributions and moments of the numbers of organs in plant structure. Plant architectural development can be seen as the combination of two subprocesses driving the bud population dynamics, branching and differentiation. By writing the stochastic L-system associated to each subprocess, we get the generating function associated to the whole system by compounding the associated generating functions. The modelling of stochastic branching is classical, but to model differentiation, we introduce a new framework based on multivariate phase-type random vectors.
Plants as Combinatorial Structures and Applications
4 Documents citing this article
Source : OpenCitations
Cournède, P.-H.; Chen, Yuting; Wu, Qiongli; Baey, Charlotte; Bayol, B., 2013, Development And Evaluation Of Plant Growth Models: Methodology And Implementation In The PYGMALION Platform, Mathematical Modelling Of Natural Phenomena, 8, 4, pp. 112-130, 10.1051/mmnp/20138407.
Cournède, P.-H.; Letort, V.; Mathieu, A.; Kang, M. Z.; Lemaire, S.; Trevezas, S.; Houllier, F.; De Reffye, P., 2011, Some Parameter Estimation Issues In Functional-Structural Plant Modelling, Mathematical Modelling Of Natural Phenomena, 6, 2, pp. 133-159, 10.1051/mmnp/20116205.
Loi, C.; Cournède, P.-H.; Françon, J., 2014, A Symbolic Method To Analyse Patterns In Plant Structure, Combinatorics, Probability And Computing, 23, 5, pp. 842-860, 10.1017/s0963548314000108.
Loi, Cédric; Cournède, Paul-Henry; Françon, Jean, 2009, Plants As Combinatorial Structures And Applications, 2009 Third International Symposium On Plant Growth Modeling, Simulation, Visualization And Applications, 10.1109/pma.2009.27.