Generating Functions of Stochastic L-Systems and Application to Models of Plant Development

International audienceIf 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

A symbolic method to analyse patterns in plant structure whose organogenesis is driven by a multitype branching process

International audienceFormal grammars like 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 derived from computer science that enables the computation of the distribution associated to the number of complex structures in plants whose organogenesis is driven by a multitype branching process. To that purpose, a new combinatorial framework is set in which plant structure is coded by a Dyck word. Moreover, the organogenesis is represented by stochastic F0L-systems. By doing so, the problem is equivalent to determining the distribution of patterns in random words generated by stochastic F0L-system. This method leads directly to numerous applications like parametric identication for plant growth model

Plants as Combinatorial Structures and Applications

International audienceIn this article, we introduce a new method allowing the computation of the distribution associated to the number of complex structures in plants deriving from GreenLab type growth model. In order to use this method, we set a new mathematical framework based on combinatorics. We show how plants can be seen as plane rooted trees and how their topology can be described by Dyck words. Moreover, we integrate plant growth in the formalism by adapting stochastic F0L-systems to the framework. This new representation enables not only the computation of the distribution associated to all types of organ but also the analysis of particular patterns thanks to a symbolic method. This approach gives new kinds of applications such as estimating the age of a plant from a set of botanical data

A stochastic growth model of grapevine with full interaction between environment, trophic competition and plant development.

International audienceGrapevine development is mainly determined by environmental factors whose effects are modulated by its complex topological structure. The trophic relationships between all the organs of the different axes appear to be the main underlying process which drive axis organogenesis in fluctuating environment. A new modelling approach is proposed based on GreenLab formalism in which axis organogenesis is controlled by stochastic processes according to trophic competition between the different axes. In this model, a water budget was also implemented to account for the effects of water depletion. The model was validated at organ and axis scales on a large range of environmental conditions in terms of photosynthetic active radiation, temperature and soil water supply. The efficiency of the model to simulate plant development at a detailed scale proved its ability to further analyse of the retroactions between plant development and the different environmental variables in order to improve crop management

Transfer printing of AlGaInAs/InP etched facet lasers to Si substrates

InP-etched facet ridge lasers emitting in the optical C-band are heterogeneously integrated on Si substrates by microtransfer printing for the first time. 500 μm × 60 μm laser coupons are fabricated with a highly dense pitch on the native InP substrate. The laser epitaxial structure contains a 1-μm-thick InGaAs sacrificial layer. A resist anchoring system is used to restrain the devices while they are released by selectively etching the InGaAs layer with FeCl3:H2O (1:2) at 8 °C. Efficient thermal sinking is achieved by evaporating Ti-Au on the Si target substrate and annealing the printed devices at 300 °C. This integration strategy is particularly relevant for lasers being butt coupled to polymer or silicon-on-insulator (SOI) waveguides

A Symbolic Method to Analyse Patterns in Plant Structure

International audienceFormal grammars like 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 derived from computer science that enables the computation of the distribution associated to the number of complex structures in plants whose organogenesis is driven by a multitype branching process. To that purpose, a new combinatorial framework is set in which plant structure is coded by a Dyck word. Moreover, the organogenesis is represented by stochastic F0L-systems. By doing so, the problem is equivalent to determining the distribution of patterns in random words generated by stochastic F0L-system. This method leads directly to numerous applications like parametric identication for plant growth model

A symbolic method to compute the probability distribution of the number of pattern occurences in random texts generated by stochastic 0L-systems

International audienceThe analysis of pattern occurrences has numerous applications, in particular in biology. In this article, a symbolic method is proposed to compute the distribution associated to the number of occurences of a specific pattern in a random text generated by a stochastic 0L-system. To that purpose, a semiring structure is set for combinatorial classes composed of weighted words. This algebraic structure relies on new union and concatenation operators which, under some assumptions, are admissible constructions. Decomposing the combinatorial classes of interest by using these binary operators enables the direct translation of specifications into a set of functional equations relating generating functions thanks to transformation rules. The article ends with two examples. The first one deals with unary patterns and the connection with multitype branching process is established. The second one is about a pattern composed of two letters and underlines the importance of writing a proper specification

Measurement of the inelastic pppp cross-section at a centre-of-mass energy of 13 TeV

The cross-section for inelastic proton-proton collisions at a centre-of-mass energy of 13 TeV is measured with the LHCb detector. The fiducial cross-section for inelastic interactions producing at least one prompt long-lived charged particle with momentum p > 2 GeV/c in the pseudorapidity range 2 < η < 5 is determined to be σ$_{acc}$ = 62.2 ± 0.2 ± 2.5 mb. The first uncertainty is the intrinsic systematic uncertainty of the measurement, the second is due to the uncertainty on the integrated luminosity. The statistical uncertainty is negligible. Extrapolation to full phase space yields the total inelastic proton-proton cross-section σ$_{inel}$ = 75.4 ± 3.0 ± 4.5 mb, where the first uncertainty is experimental and the second due to the extrapolation. An updated value of the inelastic cross-section at a centre-of-mass energy of 7 TeV is also reported

Measurement of C ⁣PC\!P asymmetries in two-body B(s)0B_{(s)}^{0}-meson decays to charged pions and kaons

International audienceThe time-dependent CP asymmetries in B0→π+π- and Bs0→K+K- decays are measured using a data sample of p p collisions corresponding to an integrated luminosity of 3.0  fb-1, collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV. The same data sample is used to measure the time-integrated CP asymmetries in B0→K+π- and Bs0→π+K- decays. The results are Cπ+π-=-0.34±0.06±0.01, Sπ+π-=-0.63±0.05±0.01, CK+K-=0.20±0.06±0.02, SK+K-=0.18±0.06±0.02, AK+K-ΔΓ=-0.79±0.07±0.10, ACPB0=-0.084±0.004±0.003, and ACPBs0=0.213±0.015±0.007, where the first uncertainties are statistical and the second systematic. Evidence for CP violation is found in the Bs0→K+K- decay for the first time