Rachid Boumaza

Coordinated Development of the Architecture of the Primary Shoot in Bush Rose

The development of the architecture of ornamental bushes needs to be explicitly described because it defines both their visual appearance and their interface with the environment. The aim of this work was to describe the dynamics of organ development in the primary shoot of rose bushes and their coordination. Rosa hybrida L. ‘Radrazz’ was grown in a glasshouse in two seasons. Internodes and leaflets were measured frequently and elongation curves were fitted to a linear-plateau model. The number of leaflets per leaf displayed clear patterns of organization along the shoot. Allometric relationships linked all leaf dimensions to terminal leaflet length. The differences in internode length between successive phytomers resulted from differences in the extension rate and the duration of extension. Conversely, the differences in the terminal leaflet size resulted almost solely from differences in extension rate. Internodes and terminal leaflets extensions were closely coordinated. This work provides the basic elements for establishing a virtual plant model.

Rose bush leaf and internode expansion dynamics: analysis and development of a model capturing interplant variability

Rose bush architecture, among other factors, such as plant health, determines plant visual quality. The commercial product is the individual plant and interplant variability may be high within a crop. Thus, both mean plant architecture and interplant variability should be studied. Expansion is an important feature of architecture, but it has been little studied at the level of individual organs in rose bushes. We investigated the expansion kinetics of primary shoot organs, to develop a model reproducing the organ expansion of real crops from non-destructive input variables. We took interplant variability in expansion kinetics and the models ability to simulate this variability into account. Changes in leaflet and internode dimensions over thermal time were recorded for primary shoot expansion, on 83 plants from three crops grown in different climatic conditions and densities. An empirical model was developed, to reproduce organ expansion kinetics for individual plants of a real crop of rose bush primary shoots. Leaflet or internode length was simulated as a logistic function of thermal time. The model was evaluated by cross-validation. We found that differences in leaflet or internode expansion kinetics between phytomer positions and between plants at a given phytomer position were due mostly to large differences in time of organ expansion and expansion rate, rather than differences in expansion duration. Thus, in the model, the parameters linked to expansion duration were predicted by values common to all plants, whereas variability in final size and organ expansion time was captured by input data. The model accurately simulated leaflet and internode expansion for individual plants (RMSEP = 7.3 and 10.2% of final length, respectively). Thus, this study defines the measurements required to simulate expansion and provides the first model simulating organ expansion in rosebush to capture interplant variability.

RTIL-system: a Real-Time Interactive L-system for 3D interactions with virtual plants

The L-system is a rewriting process based on formal grammar and is used to generate 3D, dynamic structures such as virtual plants and fractal graphics. In previous works, we highlighted that existing L-system software applications and programs are limited, either in terms of human interaction or in terms of modelling. In particular, few of them allow the user to interact with virtual plants during their growth. Our own L-system engine was developed and called the real-time interactive L-system (RTIL-system). The RTIL-system covers most important L-system extensions such as parametric and context-sensitive features. Furthermore, real-time interactions with the user and the environment with respect to L-system formalism are available. This paper presents an RTIL-system focusing on human interaction, the Partial Interactive Derivation (PID) concept and further progress by the extension of PID to context-sensitive rules. To illustrate the potential of the RTIL-system, the effect of various interactive tasks such as sub-axis additions, pruning and bending on the subsequent dynamic development of virtual plants is described.

Optimal bandwidth matrices in functional principal component analysis of density functions

In order to explore and compare a finite number T of data sets by applying functional principal component analysis (FPCA) to the T associated probability density functions, we estimate these density functions by using the multivariate kernel method. The data set sizes being fixed, we study the behaviour of this FPCA under the assumption that all the bandwidth matrices used in the estimation of densities are proportional to a common parameter h and proportional to either the variance matrices or the identity matrix. In this context, we propose a selection criterion of the parameter h which depends only on the data and the FPCA method. Then, on simulated examples, we compare the quality of approximation of the FPCA when the bandwidth matrices are selected using either the previous criterion or two other classical bandwidth selection methods, that is, a plug-in or a cross-validation method.