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The Weyl group of a crystallographic root system has a multiplicative action on the ring of multivariate trigonometric polynomials. We study the problem of minimizing an invariant trigonometric polynomial. This problem can be written as a polynomial optimization problem on a compact basic semi-algebraic set. Lasserre's moment-SOS hierarchy is formulated in the basis of generalized Chebyshev polynomials, leading to a different notion of the polynomial degree and smaller matrices in the arising semi-definite program. Bilevel optimization techniques are applied to solve max-min problems. Optimal values of trigonometric polynomials appear in spectral bounds for chromatic numbers and independence numbers of geometric distance graphs. We study the quality of these bounds for polytope norms and prove sharpness in several cases.

This thesis studies the problem of optimizing a trigonometric polynomial with crystallographic symmetry. Optimization of trigonometric polynomials has been subject to many recent works, but a theory for exploiting symmetries has hardly been developed or generalized. We consider the action of a crystallographic group, also known as a Weyl group, on the exponents. This action admits a definition of generalized Chebyshev polynomials. If a trigonometric polynomial is invariant under the action, then it can be written as a sum of generalized Chebyshev polynomial in fundamental invariants.By rewriting an invariant trigonometric polynomial as a classical polynomial, the region of optimization is transformed into the orbit space of the multiplicative Weyl group action. This orbit space is the image of fundamental invariants and we show that, for the Weyl groups of types A, B, C, D and G, it is a compact basic semi-algebraic set. Furthermore, we give the describing polynomial inequalities through a positive semi-definite Hermite matrix polynomial.Concerning the optimization problem, our rewriting approach transforms the trigonometric optimization problem into a classical polynomial optimization problem on a basic semi-algebraic set. To solve such problems, one can apply Lasserre's hierarchy of moment and sum of squares relaxations. We adapt and implement this hierarchy in the basis of generalized Chebyshev polynomials with a new notion of degree. The optimal value of the original trigonometric optimization problem is then approximated through solutions of semi-definite programs, which are solved numerically.In classical polynomial optimization and other applications, symmetry adaptation has been studied and implemented, but crystallographic symmetries have not been exploited in trigonometric optimization before. With our approach, we provide an alternative to known strategies for trigonometric optimization. Where other techniques utilize sums of Hermitian squares or generalizations of Lasserre's hierarchy to the complex setting, we exploit symmetry first and then apply techniques from classical polynomial optimization. This reduces the size of arising semi-definite relaxations and can also improve the quality of the approximation.As an application, we study the problem of computing lower bounds for the chromatic number of geometric distance graphs. Given a norm and a set of vertices, this problem asks to find the minimal number of colors needed to paint the vertices, so that no two of those of distance 1 between them have the same color. The spectral bound was generalized from finite to infinite graphs to deal with such problems. This bound involves the optimization of a trigonometric polynomial. We focus on norms which are given by polytopes with crystallographic symmetry. Then the problem can be tackled with the techniques developed in this thesis. We give several bounds through analytical and numerical computations., Cette thèse étudie le problème de l'optimisation d'un polynôme trigonométrique avec symétrie cristallographique. L'optimisation des polynômes trigonométriques était l'objet de nombreux travaux récents, mais une théorie permettant d'exploiter les symétries n'a pas été développée ou généralisée. Nous considérons l'action d'un groupe cristallographique, également connu sous le nom de groupe de Weyl, sur les exposants. Cette action admet une définition des polynômes de Chebychev généralisés. Si un polynôme trigonométrique est invariant sous l'action, il peut être écrit comme une somme de polynômes de Chebyshev généralisés dans les invariants fondamentaux.En réécrivant un polynôme trigonométrique invariant comme un polynôme classique, la région d'optimisation est transformée en l'espace d'orbite de l'action du groupe de Weyl multiplicatif. Cet espace d'orbite est l'image des invariants fondamentaux et nous montrons que, pour les groupes de Weyl de types A, B, C, D et G, il s'agit d'un ensemble compact basique semi-algébrique. En plus, nous donnons les inégalités polynomiales descriptives à par un matrix polynomial positif de Hermite.En ce qui concerne l'optimisation, notre approche de réécriture transforme le problème d'optimisation trigonométrique dans un problème d'optimisation polynomiale sur un ensemble basique semi-algébrique. Pour résoudre de tels problèmes, on peut appliquer la hiérarchie des relaxations de moment et de somme de carrés de Lasserre. Nous adaptons et implémentons cette hiérarchie sur la base de polynômes de Chebyshev généralisés avec une nouvelle notion de degré. La valeur optimale du problème d'optimisation trigonométrique original est alors approximée par des solutions de programmes semi-définis, qui sont résolus numériquement.Dans l'optimisation polynomiale classique et d'autres applications, l'adaptation des symétries a été étudiée et implémenté, mais les symétries cristallographiques n'ont pas été exploitées en optimisation trigonométrique auparavant. Avec notre approche, nous fournissons une alternative aux stratégies connues pour l'optimisation trigonométrique. Alors que d'autres techniques utilisent des sommes de carrés Hermitiens ou en généralisant l'hiérarchie de Lasserre au cadre complexe, nous exploitons d'abord la symétrie et appliquons ensuite des techniques d'optimisation polynomiale classique. Cela réduit la taille des relaxations semi-définies qui en découlent et peut également améliorer la qualité de l'approximation.En guise d'application, nous étudions le problème de calcul des bornes inférieurs pour le nombre chromatique des graphes géométriques. Étant donné une norme et un ensemble de sommets, ce problème demande de trouver le nombre minimal de couleurs nécessaires pour peindre les sommets, de sorte que deux de ceux de distance 1 entre eux n'aient pas la même couleur. La borne spectrale a été généralisée des graphes finis aux graphes infinis pour traiter de tels problèmes. Cette limite implique l'optimisation d'un polynôme trigonométrique. Nous nous concentrons sur les normes qui sont données par des polytopes avec une symétrie cristallographique. Le problème peut alors être abordé avec les techniques développées dans cette thèse. Nous donnons plusieurs bornes à travers des calculs analytiques et numériques.

International audience; Summary Soil aggregates are critical to soil functionality, but there remain many uncertainties with respect to the role of biotic factors in forming aggregates. Understanding the interacting effects of soil, land use type, vegetation and microbial communities is a major challenge that needs assessment in both field and controlled laboratory conditions, as well as in bulk and rhizosphere soils. To address these effects and their feedbacks, we first examined the influence of soil, root and litter characteristics along a land use gradient (ancient woodland, secondary woodland, grassland, pasture and arable land) on microbial community structure (in both bulk and rhizosphere soil), as well as on aggregate stability. Then, we performed an inoculation experiment where we extracted soil columns from the arable and secondary woodland and used a third unstructured loamy soil as a control. We sterilized these three soils to remove microbial communities, and then either inoculated the tops of sterilized soil columns with soil from the secondary woodland or the arable field sites. Control columns of all soil types were not inoculated. In a fully-crossed design, we planted two species possessing distinct root system morphological traits: Brachypodium sylvaticum (fibrous system with many thin and fine roots) and Urtica dioica (taproot system with few fine roots). After four months, microbial communities (in bulk and rhizospheric soil) and aggregate stability were measured, along with root traits. In both the field and laboratory experiments, bacterial (16S) and fungal (ITS) biodiversity was determined using high throughput sequencing. In the field study we found that: i) there were strong relationships between aggregate stability and microbial community composition that were driven by land use, ii) the relationship between aggregate stability along the land use gradient and the trophic nature of bacterial communities was not significant, but that certain soil, root and litter parameters shaped bacterial phyla, with oligotrophic bacteria conditioned by the rhizosphere niche, and copiotrophic phyla more dependent on bulk soil conditions, iii) land use gradient (from woodland to arable), reduced the relative abundance of saprotrophic and ectomycorrhizal fungi with an increase in the relative abundance of Ascomycota and a reduction in the relative abundance of Basidiomycota. In the laboratory experiment we found that: i) the inoculation of sterilized soils with soils from the field significantly increased aggregate stability in control soil that was initially poorly structured, ii) the effects of inoculation on aggregate stability were similar when either secondary woodland or arable soils were used as inoculums and iii) these effects were affected significantly by root length density. Our results show that microbial communities influence soil structure and that bacterial communities are intimately associated to rhizospheric conditions and root traits (of which root length density was the most pertinent).

National audience; Phénotypage haut débit de l'architecture du système racinaire du blé. Journée scientifique de l'Association des Sélectionneurs Français

Le développement du système racinaire résulte de l’équilibre entre les interactions physiques et chimiques avec le sol et la perception de conditions environnementales plus globales comme, par exemple, la gravité terrestre qui permet à la racine de percevoir la verticale. La morphogenèse du système racinaire est en particulier conditionnée par l’apex racinaire qui oriente la croissance longitudinale des racines. L’apex racinaire est connu pour être une zone influencée par les propriétés chimiques et mécaniques de son environnement. Cependant, la rhéologie de l’apex racinaire (lien entre ses déformations et les contraintes auxquelles il est soumis) lors de la progression des racines demeure mal connue. Étudier cette rhéologie nécessite l’observation de la déformation à l’échelle cellulaire de l’apex racinaire dans des conditions in-vivo au sein de milieux aux propriétés mécaniques mesurables et contrôlables. Pour ce faire nous avons développé un microscope à feuillet de lumière (SPIM : Selective Plane Illumination Microscopy) en nous appuyant sur le projet OpenSPIM qui propose des plans sous licence libre pour sa construction. Cette technique d’imagerie par fluorescence connait un gain d’intérêt depuis une dizaine d’années du fait de ses capacités d’imagerie 3D in-vivo permises par une vitesse d’acquisition rapide accompagnée d’une faible phototoxicité. Nous présenterons ici cette technique de microscopie, la construction de cet instrument et ce qu’il apporte pour l’étude de la croissance des racines in-vivo.

International audience; Rapid adjustment of plant physiology and development to external fluctuations is critical for sessile organism, giving a singular interest to network signaling controlling these mechanisms. Among many adaptation processes, root plasticity is primordial to optimize nutrient acquisition but relies on a complex network integrating local and systemic (root shoot) signaling. Indeed, locally, plants invest resource in soil area where nutrients are available and systemically they adjust nutrient acquisition to the whole plant demand.Our main goal is to decipher systemic signaling underlying the perception of nitrate heterogeneous provision, in Arabidopsis. Using the split-root system, in which physically isolated root systems of the same plant were challenged with different environments, we previously demonstrated that cytokinin biosynthesis constitutes one critical component of root-shoot-root communication. By combining the use of cytokinin mutants with hormone measurements, transcriptomic analysis, nitrate uptake assays, and root growth measurements, we show that root to shoot trans-zeatin (tZ) translocation is likely crucial for long distance signaling controlling rapid sentinel gene regulation and long-term functional acclimation to heterogeneous nitrate supply. Interestingly, shoot transcriptome profiling revealed that glutamate/glutamine metabolism is likely a target of tZ root-to-shoot translocation, prompting an interesting hypothesis regarding shoot-to-root communication. Finally, this study also highlights tZ-independent pathways triggered by variation into nitrogen supply.

Nutrient fluctuations are more a rule rather than an exception in the life of sessile organisms such as plants. Despite this constraint that adds up to abiotic and biotic stresses, plants are able to accomplish their life cycle thanks to an efficient signaling network that reciprocally controls nutrient acquisition and use with growth and development. The majority of nutrients are acquired by the root system where multiple local signaling pathways that rely on nutrient-sensing systems are implemented to direct root growth toward soil resources. Moreover, long-distance signaling plays an essential role in integrating nutrient availability at the whole-plant level and adjusting nutrient acquisition to plant growth requirements. By studying the signaling network for single mineral nutrients, several long-distance signals traveling between roots and shoots and taking a diversity of forms have been identified and are summarized here. However, the nutritional environment is multifactorial, adding a tremendous complexity for our understanding of the nutrient signaling network as a unique system. For instance, long-distance signals are expected to support this nutrient cross-talk in part, but the mechanisms are still largely unknown. Therefore, the involvement of possible long-distance signals as conveyers of nutrient cross-talk is discussed here together with approaches and strategies that are now considered to build a picture from the nutrient signaling puzzle.

http://www.heldermann.de/JLT/JLT28/JLT281/jlt28010.htm; International audience; Let G be a split real connected simple Lie group and S a semigroup of G that contains a subgroup G(α) for an arbitrary root α, isomorphic to SL(2,R). We present a Cartan decomposition of the Lie algebra of G, related to α, invariant by the adjoint action of the Lie algebra sl(2,R) that allows to characterize some properties of the Lie saturate of the semigroup S. We give necessary and sufficient conditions for S to be equal to the whole group G.

International audience; One of the most challenging computer vision problems in the plant sciences is the segmentation of roots and soil in X-ray tomography. So far, this has been addressed using classical image analysis methods. In this paper, we address this soil-root segmentation problem in X-ray tomography using a variant of supervised deep learning-based classification called transfer learning where the learning stage is based on simulated data. The robustness of this technique, tested for the first time with this plant science problem, is established using soil-roots with very low contrast in X-ray tomography. We also demonstrate the possibility of efficiently segmenting the root from the soil while learning using purely synthetic soil and roots.

Let Γ be a finite subgroup of SU2(ℂ). Then the quotient ℂ2/Γ can be embedded in ℂ3 as a surface with an isolated singularity. The quotient ℂ2/Γ is called a Kleinian singularity, after F. Klein who studied them first in 1884. Through their minimal resolutions, these singularities have a deep connection with simply-laced Dynkin diagrams of types Ar, Dr and Er. In the 1970's E. Brieskorn and P. Slodowy took advantage of this connection to describe the resolutions and deformations of these singularities in terms of Lie theory. In 1998 P. Slodowy and H. Cassens constructed the semiuniversal deformations of the Kleinian singularities using quiver theory and work from 1989 by P.B. Kronheimer on symplectic geometry. In Lie theory, the classification of simple Lie algebras allows for a separation in two classes: those simply-laced of types Ar, Dr and Er, and those of types Br, Cr, F4 and G2 called inhomogeneous. With the use of a second finite subgroup Γ’ of SU2(ℂ) such that Γ ⊲ Γ’, P. Slodowy extended in 1978 the definition of a Kleinian singularity to the inhomogeneous types by adding to ℂ2/Γ the group of automorphisms Ω= Γ’/Γ of the Dynkin diagram associated to the singularity. The purpose of this thesis is to generalize H. Cassens' and P. Slodowy's construction to the singularities of types Br, Cr, F4 and G2. It will lead to explicit semiuniversal deformations of inhomogeneous types on the fibers of which the group Ω acts. By quotienting such a map we obtain a deformation of a singularity ℂ2/Γ’, Soit Γ un sous-groupe fini de SU2(ℂ). Alors le quotient ℂ2/Γ peut être plongé dans ℂ3 sous la forme d'une surface munie d'une singularité isolée. Le quotient ℂ2/Γ est appelé singularité de Klein, d'après F. Klein qui fut le premier à les décrire en 1884. A travers leurs résolutions minimales, ces singularités ont un lien étroit avec les diagrammes de Dynkin simplement lacés de types Ar, Dr et Er. Dans les années 1970, E. Brieskorn et P. Slodowy ont tiré profit de cette connection pour décrire les résolutions et les déformations de ces singularités à l'aide de la théorie de Lie. En 1998 P. Slodowy et H. Cassens ont construit les déformations semiuniverselles des ℂ2/Γ à l'aide de la théorie des carquois ainsi que des travaux de P.B. Kronheimer en géométrie symplectique datant de 1989. En théorie de Lie, la classification des algèbres de Lie simples divisent ces dernières en deux classes: les algèbres de Lie de types Ar, Dr et Er qui sont simplement lacées, et celles de types Br, Cr, F4 et G2 appelées non-homogènes. A l'aide d'un second sous-groupe fini Γ' de SU2(ℂ) tel que Γ ⊲ Γ', P. Slodowy a étendu en 1978 la notion de singularité de Klein aux algèbres de Lie non-homogènes en ajoutant à ℂ2/Γ le groupe d'automorphismes Ω= Γ'/Γ du diagramme de Dynkin associé à la singularité. L'objectif de cette thèse est de généraliser la construction de H. Cassens et P. Slodowy à ces singularités de types Br, Cr, F4 et G2. Il en résultera des constructions explicites des déformations semiuniverselles de types inhomogènes sur les fibres desquelles le groupe Ω agit. Le passage au quotient d'une telle application révèle alors une déformation d'une singularité de type ℂ2/Γ'

Growth under water deficit is controlled by short-term mechanisms but, because of numerous feedbacks, the combination of these mechanisms over time often results in outputs that cannot be deduced from the simple inspection of individual mechanisms. It can be analysed with dynamic models in which causal relationships between variables are considered at each time-step, allowing calculation of outputs that are routed back to inputs for the next time-step and that can change the system itself. We first review physiological mechanisms involved in seven feedbacks of transpiration on plant growth, involving changes in tissue hydraulic conductance, stomatal conductance, plant architecture and underlying factors such as hormones or aquaporins. The combination of these mechanisms over time can result in non-straightforward conclusions as shown by examples of simulation outputs: ‘over production of abscisic acid (ABA) can cause a lower concentration of ABA in the xylem sap ’, ‘decreasing root hydraulic conductance when evaporative demand is maximum can improve plant performance’ and ‘rapid root growth can decrease yield’. Systems of equations simulating feedbacks over numerous time-steps result in logical and reproducible emergent properties that can be viewed as ‘meta-mechanisms’ at plant level, which have similar roles as mechanisms at cell level.

We thank Pascal Chapon for his dedicated technical help, the experimental station 'INRA LA Fage' as well as the 'Terrain d'experience' and 'PACE' platforms at CEFE (technical facilities of the Labex Centre Mediterranean de l'Environnement et de la Biodiversite, CEMEB) for providing all the facilities and technical support. F.F. was supported by a grant from; 1. Understanding the water-use of plants is timely under increasing drought stress due to climate change. Despite the crucial role of roots in water uptake, relationships between water-use and root traits are seldom considered. 2. Combining a functional trait-based approach with a water balance model, we tested whether root functional traits are related to spatial and temporal water-use among 12 Mediterranean rangeland species grown in common garden monocultures. Soil water content was monitored for 10 months, and the dynamics of water uptake of each species was modelled at a daily time step. Root functional traits were measured at two soil depths (shallow and deep soil). 3. Species with fast resource acquisition strategies in shallow soil, i.e. thin roots, maximised water uptake in a short period and consumed large amounts of water during periods of low water availability. Conversely, species with a more conservative root strategy, i.e. coarse roots, took up less water during the peak-growing season, maintained water uptake over a longer period of time and consumed less water during periods of low water availability. Deep root traits are strongly related to species' ability to take up water from deep soil. Deep roots with large diameters and low specific root length improve species' ability to reach water from deep soil. Biomass investment in the deep soil layer was positively related to the amount of water consumed during periods of low water availability. 4. Our results highlight that root functional traits influence a range of spatial and temporal water-use among Mediterranean rangeland species. They account for the amount of water taken up during dry periods but not during the entire growing season.

Better managing crop : weed competition in cropping systems while reducing both nitrogen and herbicide inputs is a real challenge that requires a better understanding of crop and weed root architecture in relation to soil-nitrogen availability. An original approach was used which considered the parameters of a simulation model of root architecture as traits to analyse (a) the interspecific diversity of root system architecture, and (b) its response to soil-nitrogen availability. Two greenhouse experiments were conducted using three crop and nine weed species grown at two contrasted concentrations of soil-nitrogen availability. Plant traits were measured to characterise both overall plant growth and root architecture, with a focus on primary root emergence, root elongation and branching. The studied root traits varied among species (from a twofold to a fourfold factor, depending on the trait), validating their use as indicators to analyse the interspecific variability of root architecture. The largest interspecies differences were for two traits: ‘maximal apical root diameter’ and ‘interbranch distance’ (distance between two successive laterals on the same root). Conversely, most of the studied root traits varied little with soil-nitrogen availability (from no variation to a 1.1-fold factor, depending on the trait) even though soil-nitrogen availability varied with a 17-fold factor and impacted the overall shoot and root biomass. So, the root traits used in this article are stable whatever soil-nitrogen availability. As they reflect processes underlying root system architecture, this low effect of nitrogen suggests that the rules governing root architecture are little affected by plant nitrogen status and soil-nitrogen availability. We propose that the determinants of differences in root system architecture between soils with contrasted nitrogen availability mainly originate from differences in the amount of carbon allocated to and within the root system. Characterising each plant species by a combination of root traits gave insights regarding the potential species competitive ability for soil resources in agroecosystems.

The roles of potassium channels from the Shaker family in stomatal movements have been investigated by reverse genetics analyses in Arabidopsis (Arabidopsis thaliana), but corresponding information is lacking outside this model species. Rice (Oryza sativa) and other cereals possess stomata that are more complex than those of Arabidopsis. We examined the role of the outward Shaker K+ channel gene OsK5.2. Expression of the OsK5.2 gene (GUS reporter strategy) was observed in the whole stomatal complex (guard cells and subsidiary cells), root vasculature, and root cortex. In stomata, loss of OsK5.2 functional expression resulted in lack of time-dependent outward potassium currents in guard cells, higher rates of water loss through transpiration, and severe slowdown of stomatal closure. In line with the expression of OsK5.2 in the plant vasculature, mutant plants displayed a reduced K+ translocation from the root system toward the leaves via the xylem. The comparison between rice and Arabidopsis show that despite the strong conservation of Shaker family in plants, substantial differences can exist between the physiological roles of seemingly orthologous genes, as xylem loading depends on SKOR and stomatal closure on GORK in Arabidopsis, whereas both functions are executed by the single OsK5.2 Shaker in rice. Since a waxy cuticle covers outer leaf tissues, water vapor diffusion into the atmosphere occurs mainly through the stomatal pores at the leaf surface. The size of the stomatal aperture is tightly regulated to optimize gas exchanges between the leaf inner tissues and the atmosphere, including CO2 intake for photosynthesis and water loss by transpiration (Lawson and Blatt, 2014). This is achieved by fine tuning of the turgor pressure of the two guard cells that surround the stomatal pore and involves a complex coordinated activity of transport systems at the guard cell plasma membrane and vacuolar membrane (Hedrich, 2012; Chen et al., 2012; Hills et al., 2012; Kollist et al., 2014). This control also affects long-distance transport of mineral nutrients from the roots, which take up these nutrients, to the aerial parts, to support plant growth (Marschner et al., 1996). Potassium ion (K+), as a major inorganic constituent of the plant cells and the most abundant cation in the cytosol, is an essential macronutrient for growth and development. It is involved in various functions, including electrical neutralization of negative charges, control of cell membrane polarization, and osmoregulation (Clarkson and Hanson, 1980; Leigh and Wyn Jones, 1984). K+ is thus the main cation absorbed by the roots and circulating within the plant at the cellular or long-distance levels. In guard cells, it is well known as a major contributor, with Cl-, NO3− and malate, to the osmolarity (Raschke and Schnabl, 1978; Willmer and Fricker, 1996). Stomatal opening is initiated by activation of plasma membrane proton pumps in guard cells, which promotes K+ influx through voltage-gated inward K+ channels, as well as anion uptake through H+-anion symporters (Blatt, 1987a; Schroeder et al., 1987; Roelfsema and Prins, 1997; Talbott and Zeiger, 1998; Guo et al., 2003; Jezek and Blatt, 2017). Conversely, stomatal closure requires inhibition of proton pumping at the guard cell membrane and activation of both anion channels and voltage-gated outward K+ channels. The molecular mechanisms responsible for inward and outward K+ fluxes across the plasma membrane have been extensively investigated in Arabidopsis (Arabidopsis thaliana). Shaker channel subunits, present as a nine-member family in Arabidopsis, have been shown to form the major pathways for these fluxes throughout the plant (Véry and Sentenac, 2003). In the Arabidopsis model species, four genes encoding Shaker channel subunits have been identified as playing a major role in root to shoot K+ translocation and in stomatal movements. The SKOR subunit, which is expressed in root pericycle and xylem parenchyma, forms outwardly rectifying channels involved in K+ secretion into the xylem sap (Gaymard et al., 1998). In stomata, the inward Shaker channel subunits KAT1 and KAT2 are involved in guard cell K+ uptake, and the outward Shaker channel GORK mediates guard cell K+ release (Ache et al., 2000; Pilot et al., 2001; Szyroki et al., 2001; Hosy et al., 2003; Lebaudy et al., 2008). Whereas these Shaker subunits have been deeply characterized in Arabidopsis, and the Shaker family, as a whole, can be considered as the best characterized family of plant membrane transport systems, little information at the molecular genetic level is yet available on this family outside Arabidopsis. The stomatal complex in rice (Oryza sativa), the current model cereal, is very different from that of Arabidopsis (Itoh et al., 2005; Franks and Farquhar, 2007; Roelfsema and Hedrich, 2009). In rice, like in other cereals, it comprises two subsidiary cells in addition to the two guard cells. Substantial differences may thus exist between rice and Arabidopsis in stomatal functioning (Mumm et al., 2011). Rice possesses two putative outward Shaker channel subunits (Pilot et al., 2003; Véry et al., 2014), named OsK5.1 (or OsSKOR) and OsK5.2 (or OsGORK; Pilot et al., 2003; Kim et al., 2015). OsK5.1 was reported to be mainly expressed in root vasculature, just as SKOR in Arabidopsis (Kim et al., 2015). In contrast, OsK5.2 was found to be expressed both in roots and shoots (Kim et al., 2015). The expression pattern of this gene at the tissue level has, however, not been described. Here, we investigate the expression pattern and role of this rice outward Shaker gene. OsK5.2 is shown to play two important roles in rice plants: it mediates K+ translocation into the xylem sap toward the shoots, and it is involved in K+ release from guard cells and stomatal movements.

Background and aims Soil-plant models always oversimplified the representation of soil chemical processes or root system. The objectives of the study were (i) to present a model overcoming such limitations, and (ii) to illustrate its relevance for the modelling of soil-plant interactions. Methods We coupled a root system architecture (RSA) model with a reactive transport model using a macroscopic approach. The two models were coupled sequentially using Fortran-C++ interoperability. We used the resulting model to investigate the case of phosphorus (P) acquisition from hydroxyapatite (HA) in an alkaline soil as induced by P and calcium (Ca) uptake and pH variations in the root zone. Important model parameters were issued of the literature and we tested its sensitivity to selected soil properties. Model sensitivity to grid size and time increment was evaluated as well. Results The simulations revealed that HA dissolution can contribute very substantially to P nutrition in case of rhizosphere alkalisation thanks to Ca and P uptake. Root-induced acidification was much more efficient at acquiring P, suggesting that ammonium-fed plants should be more P efficient. The variations of dissolved P in the root zone partly agreed with the observations, suggesting that P release was rather controlled by desorption when alkalisation occurs. The presence of more soluble minerals as well as the increase of Ca uptake should enhance P acquisition by crops. Conclusion We developed a new model and demonstrated the interest of the mechanistic description of geochemical processes with a spatially-explicit distribution of roots in soil while modelling soil-plant interactions. Results of its first application to P acquisition from a mineral source in an alkaline soil were overall consistent with the literature.

This study tested a method to quantify and locate hydraulic lift (HL, defined as the passive upward water flow from wetter to dryer soil zones through the plant root system) by combining an experiment using the stable water isotope 1H218O as a tracer with a soil–plant water flow model. Our methodology consisted in (i) establishing the initial conditions for HL in a large rhizobox planted with Italian ryegrass (Lolium multiflorum Lam.), (ii) labeling water in the deepest soil layer with an 18O-enriched solution, (iii) monitoring the water O isotopic composition in soil layers to find out changes in the upper layers that would reflect redistribution of 18O-enriched water from the bottom layers by the roots, and (iv) comparing the observed soil water O isotopic composition to simulation results of a three-dimensional model of water flow and isotope transport in the soil–root system. Our main findings were that (i) the depth and strength of the observed changes in soil water O isotopic composition could be well reproduced with a modeling approach (RMSE = 0.2‰, i.e., equivalent to the precision of the isotopic measurements), (ii) the corresponding water volume involved in HL was estimated to account for 19% of the plant transpiration of the following day, i.e., 0.45 mm of water, and was in agreement with the observed soil water content changes, and (iii) the magnitude of the simulated HL was sensitive to both plant and soil hydraulic properties.

International audience; The purpose of this article is to generalize a construction by H. Cassens and P. Slodowy of the semiuniversal deformations of the simple singularities of types A_r , D_r , E_6 , E_7 and E_8 to the singularities of inhomogeneous types B_r , C_r , F_4 and G_2 defined in 1978 by P. Slodowy. Let Γ be a finite subgroup of SU_2. Then C^2/ Γ is a simple singularity of type ∆(Γ). By studying the representation space of a quiver defined from Γ via the McKay correspondence , and a well chosen finite subgroup Γ ′ of SU_2 containing Γ as normal subgroup, we will use the symmetry group Ω = Γ′/Γ of the Dynkin diagram ∆(Γ) and explicitly compute the semiuniversal deformation of the singularity (C^2/Γ, Ω) of inhomogeneous type. The fibers of this deformation are all equipped with an induced Ω-action. By quotienting we obtain a deformation of a singularity C^2/Γ′ with some unexpected fibers.

International audience; The purpose of this article is to generalize a construction by H. Cassens and P. Slodowy of the semiuniversal deformations of the simple singularities of types A_r , D_r , E_6 , E_7 and E_8 to the singularities of inhomogeneous types B_r , C_r , F_4 and G_2 defined in 1978 by P. Slodowy. Let Γ be a finite subgroup of SU_2. Then C^2/ Γ is a simple singularity of type ∆(Γ). By studying the representation space of a quiver defined from Γ via the McKay correspondence , and a well chosen finite subgroup Γ ′ of SU_2 containing Γ as normal subgroup, we will use the symmetry group Ω = Γ′/Γ of the Dynkin diagram ∆(Γ) and explicitly compute the semiuniversal deformation of the singularity (C^2/Γ, Ω) of inhomogeneous type. The fibers of this deformation are all equipped with an induced Ω-action. By quotienting we obtain a deformation of a singularity C^2/Γ′ with some unexpected fibers.

Above and below-ground relationships in hybrid walnut growing in agroforests along a climatic gradient. EcoSummit 2016 Ecological Sustainability: Engineering Change

UMR AGAP - équipe AFEF - Architecture et fonctionnement des espèces fruitières; Global climate change may lead to longer or more frequent episodes of extreme temperatures and drought, thus threatening plant crops. Thus, we focused on apple tree aiming to identify the molecular mechanisms that are triggered when trees face water soil deficit. We focused on differentially expressed transcripts (DET) in roots, between well-watered trees compared to trees grown under soil water deficit either moderate (MS) and severe (SS). Two apple cultivars, ‘Starkrimson’ (ST) and ‘Granny Smith’ (GS), with contrasted behavior under water deficit, were grafted on M9 rootstock and grown in pots under controlled conditions. Roots were sampled when transpirable soil water (FTSW)=0.5 and FTSW=0.2 were reached, for MS and SS stress, respectively. RNA was extracted and analyzed using the AryANE micro-array apple chip to identify DET response to moderate and severe soil water deprivation. Among DET in roots, 209 up and 137 down-regulated genes were common to both cultivars under MS while 148 up and 542 down-regulated genes were common to both cultivars under SS. DET linked to the response to osmotic stress were observed at MS, especially signal sensors proteins kinases and phosphatases which were up-regulated. As expected, DET related to abscissic acid (ABA) were highly expressed under water deficit conditions, both ABA-dependent (ADP) and ABA-independent pathways (AIP) being stimulated. ABA biosynthesis was activated in both genotypes in MS, even though to a lesser extent in ST than in GS. However, these transcripts were no more differentially expressed in SS, suggesting that other mechanisms are involved under SS. Specific DET to each genotype were also observed. ST had a higher number of upregulated DET at MS and downregulated DET at SS than GS. Such results prove that even when grafted on the same rootstock, we notice a significant difference on the ST and GS roots system response to the soil water deficit evidencing that root systems (here M9) response to the soil water deficit depends on the grafted scion, probably because of different transpiration and regulation in response to soil water deprivation of the two scion genotypes. Further analyses are currently performed to decipher DET in aerial organs.

Root quality is one of the main drivers of fine root decomposition, an important process controlling soil carbon (C) and nutrient cycling in most terrestrial ecosystems. Root quality is defined by chemical and morphological traits, which differ across species and thus communities. This trait variation is assumed to follow a trade-off between resource acquisition and conservation (i.e. the root economics spectrum). To what extent root quality or the economics spectrum influence fine root decomposition rates at the community level remains poorly understood, particularly within the context of land use change. Changes in land use induce shifts in plant community composition, which also affect root distribution within the soil profile, resulting in changes in root quality. We hypothesize that at the community level, i) root decomposability is driven by community root functional parameters (i.e. root traits measured at the community level), ii) changes in root functional parameters among land use types and with soil depth translate into changes in root decomposability. We collected shallow and deep fine roots (< 2 mm) from 20 plant communities across contrasting land use types in 7 sites worldwide, ranging from agricultural crops to natural forests and determined their decomposition rate in standard conditions. Fine root quality was related to known values of functional parameters for these communities, including carbon (C), nitrogen (N) and lignin concentrations. A combination of chemical functional parameters (lignin, C and N concentrations) best explained root decomposition rates at the community level, whereas root economics remained a poorer predictor of decomposability rates. Among land use gradients, roots from agricultural and agroforestry communities decomposed faster than roots from forest sites. Across and within plant communities, a consistently greater decomposability in shallow roots was observed. Both land use and depth effects were explained by changes in root chemical traits at the community level. Synthesis. Our results suggest that the conversion of plant communities from forests to agricultural lands leads to changes in root functional parameters, that drastically increase root decomposition rates and may lead to major soil C losses, especially in shallow soil layers.

We consider deformations of the Weyl arrangement of type $A_2$, which include the extended Shi and Catalan arrangements. These last ones are well-known to be free. We study their sheaves of logarithmic vector fields in all other cases, and show that they are Steiner bundles. Also, we determine explicitly their unstable lines. As a corollary, some counter-examples to the shift isomorphism problem are given., Comment: 13 pages

In this thesis, we show that, for any root system $\mathcal{R}$ in the Euclidean space $\R^d$ and for any nonnegative multiplicity function $k$ on $\mathcal{R}$, we can develop in this geometric framework a Newtonian type or more generally a Riesz type potential theory which coincide with the classical theories when $k$ is the zero function.; Dans cette th\`{e}se, nous montrons que pour tout syst\`{e}me de racines $\mathcal{R}$ de l'espace euclidien $\R^d$ et pour toute fonction de multiplicit\'{e} positive $k$ sur $\mathcal{R}$, on peut d\'{e}velopper dans ce cadre g\'{e}om\'{e}trique une th\'{e}orie du potentiel de type newtonien et plus g\'{e}n\'{e}ralement de type Riesz qui co\"{\i}ncident avec les th\'{e}ories classiques lorsque la fonction $k$ est identiquement nulle.

A whole plant model was build up based on programmable and self-organised morphogenesis processes. The coupling between aboce- and below- ground components of the system is based on two principles: i) self regulation rules from shoot architecture trigger the initiation of new nodal roots, and ii) carbon allocation drives root development.

Ectomycorrhizal (ECM) symbiosis is defined as a mutual association between fungal symbionts and roots of woody plants. This symbiosis is strongly represented in temperate and boreal forests and is considered to be the most widespread means of increasing P acquisition by trees. Despite the importance of the ECM association, current knowledge about molecular mechanisms involved in membrane transport between the two partners is still limited. Therefore, the identification of the mechanisms essential for the symbiosis is a major issue. To better understand these mechanisms, we used a model association between the ECM basidiomycete Hebeloma cylindrosporum and the maritime pine Pinus pinaster. The fungal genome contains three transporters of Pi (HcPT1.1, HcPT1.2, and HcPT2), which have been already characterized as H+ Pi carriers. We hypothesized that one of these carriers could be responsible for both influx and efflux of Pi from the soil to the fungus and from the fungus to the plant. Our results suggest that HcPT2 would be the best candidate to fill both roles. An in vitro ectomycorrhizal system was used to investigate phosphate flux from H. cylindrosporum toward a liquid compartment containing pine roots. Interestingly, the expression pattern of HcPT2 was correlated to fungal phosphate efflux. Moreover, immuno-localization experiments showed that the protein is located (i) in the extraradical hyphae and the fungal sheath, compatible with Pi uptake, and (ii) within the Hartig net, which is the place of exchange between fungal and host cells. In order to study more specifically the role of HcPT2 at the fungus-plant interface, overexpressing and knock-down transgenic H. cylindrosporum strains were produced. Fungal strains with up regulated expression of HcPT2 increased phosphate efflux within the interaction medium, supporting a role of HcPT2 in phosphate transfer to the plant. In addition, the modification of HcPT2 expression strongly affects Pi nutrition of P. pinaster.

Agroforestry is a land use type where crops and trees are grown together in the same place and at the same time. Agroforestry systems have the advantage of providing multiple products (e.g. wood, fruits) or services (e.g. biodiversity enhancement, erosion control) whilst maintaining agricultural production. If they are known to store carbon into the biomass of the trees, they could also increase soil organic carbon (SOC) stocks. However their impact has rarely been studied under temperate conditions and has mostly concerned superficial soil layers. Our objectives were (i) to quantify and spatialize SOC stocks in an agroforestry system and in an adjacent agricultural plot, (ii) to assess what SOC fractions are responsible for possible additional carbon storage, and (iii) to quantify all organic inputs entering the soil. The trial was established in 1995 in southern France. Hybrid walnut trees are intercropped with durum wheat. SOC stocks were measured on 200 soil cores down to 2 m soil depth, and particle-size fractionation was performed on 64 soil samples. Carbon stocks of trees and of the herbaceous vegetation in the tree rows were also quantified. A trench was dug to 4 m soil depth to quantify tree fine root distribution and biomass. Minirhizotrons were installed at different depths to study tree fine root turnover. Annual additional SOC storage rates were estimated at 259 ± 59 kg C ha-1 yr-1 (0-30 cm) and at 350 ± 88 kg C ha-1 yr-1 (0-100 cm), and were mainly due to particulate organic matter fractions (> 50 μm). Only 10 to 15% was associated to clay particles. When the biomass of the trees was taken into account, total organic carbon storage rate reached 1.2 Mg C ha-1 yr-1. High tree root densities were observed at depth, but root turnover decreased with depth. Agroforestry systems provide higher amounts of carbon at depth than other agricultural practices, like no-till farming, and could therefore provide a more stable C storage in the long-term.

Weak order on a Coxeter group W is a partial order on W appearing in many areas of algebraic combinatorics. In this thesis, we propose a new general model for the study of the weak order and other related partially ordered sets (also called “posets”) and we explore various algebraic and combinatorial consequences of this construction. We begin with studying a restricted version of this model in Chapter 3. More precisely, we explain how one can associate a poset to any simple acyclic digraph together with a valuation on its vertices (also called “valued digraph”). We then prove that these posets are complete meet semi-lattices in general, complete lattices when the underlying digraph is finite, and we give an explicit formula to compute the value of their Möbius functions. Then, we show that the weak order on Coxeter groups of type A, B and A, the flag weak order, and the up-set (resp. down-set) lattices of any finite poset can be described within this theory. This description naturally leads to associate a quasi-symmetric function to any element of An And An, and we demonstrate that this function is in fact the corresponding Stanley symmetric function. In Chapter 4 we introduce the main results of this thesis. Indeed, we introduce in this chapter the generalization of the construction made in Chapter 3 to the case of any valued digraph, that is without the simplicity and acyclicity condition. Furthermore, this new definition allows us to get rid of some constraints of the definition of Chapter 3, allowing us to associate a complete lattice to each valued digraph. In particular, the meet semi-lattices of Chapter 3 are naturally extended into complete lattices. This leads us to the study of some conjectures of Dyer about the properties of an extension of the weak order having a lot of the properties conjecturally attached to Dyer’s extensions, and we prove that each one of our extensions contains Dyer’s extension as a sub-poset. We make the conjecture that one of this extension coincide with the one of Dyer, and we provide tools in order to test this conjecture. Finally, we study various consequences of out theory : we provide extensions of Cambrian semi-lattices into complete lattices (end of Chapter 4), we construct a new combinatorial model for Tamari and m-Tamari lattices (Chapter 5), and we finish with an application to tableaux combinatorics (Chapter 6), L'ordre faible sur un groupe de Coxeter W est un ordre partiel sur les éléments de W, intervenant dans de nombreux domaines de la combinatoire algébrique. Dans cette thèse, on propose un nouveau modèle général pour l'étude de cet ordre ainsi que d'autres ensembles ordonnés affiliés, et on explore diverses conséquences aussi bien algébriques que combinatoires de cette construction. On commence, dans le chapitre 3, par étudier une version restreinte de ce modèle. Plus précisément, on explique comment on peut associer un ensemble ordonné (aussi appelé « poset » à tout graphe orienté, simple, acyclique et muni d'une valutation sur ses sommets (aussi appelé « graphe valué »). On montre ensuite que ces posets sont en général des semi-treillis inférieurs, des treillis quand le graphe est fini, et on donne une formule explicite pour les valeurs de leurs fonctions de Möbius. On prouve ensuite que l'ordre faible sur les groupes de Coxeter de type A, B et A, le « flag weak order », ainsi que le treillis des idéaux supérieurs et inférieurs de tout poset fini peuvent être décrit avec notre modèle. Cette description amène naturellement à associer une série quasi-symétrique à chaque élément de An et An et on montre que cette série est en fait la série de Stanley associée. On présente dans le chapitre 4 les résultats centraux de la thèse, en effet on y introduit la généralisation de la construction faite au chapitre précédent au cas de tout graphe valué, c'est-à-dire sans condition s'acyclicité et de simplicité. On s'affranchit également de certaines contraintes imposées par la définition du chapitre 3, ce qui nous permet d'associer à tout graphe valué un treillis complet, et non plus un semi-treillis. En particulier, les semi-treillis du chapitre 3 se retrouvent naturellement plongés dans un treillis complet. Ceci nous amène à nous intéresser à des conjectures de Dyer portant sur l'étude d'une extension de l'ordre faible sur tout groupe de Coxeter (entre autres, il est conjecturé que ces extensions sont des treillis complets). On construit alors, à l'aide de notre formalisme, des extensions de l'ordre faible ayant beaucoup des propriétés conjecturalement attachées aux extensions de Dyer, et contenant ces dernières comme sous-poset. On conjecture que l'une de ces extensions coïncide avec celle de Dyer, et on fournit des outils pour le tester. Finalement, on étudie diverses conséquences de notre théorie : la construction d'extensions des semi-treillis cambriens (fin du chapitre 4), la construction d'un nouveau modèle combinatoire pour le treillis de Tamari et m-Tamari (chapitre 5), et enfin on propose une application à la combinatoire des tableaux (chapitre 6)

[Departement_IRSTEA]Territoires [TR1_IRSTEA]SEDYVIN [TR2_IRSTEA]RIVAGE; International audience; Background and Aims. Tree root system structure and development are difficult to assess and poorly understood in natural conditions because of soil heterogeneity and the difficulty in extracting mature tree root systems without damaging them. The purpose of this study was to understand root system development plasticity according to biological and physical parameters: species tree age and size, soil material, water availability, slope angle, and climate. Methods. Two hundred and forty-three mature trees from twelve species were uprooted from homogeneous French dikes fills. Root system structure (root number and size, root system span, depth and volume) was compared between two contrasting soil materials: fine and coarse. Results.Tree species had little influence on root system structure: all root system types and root size could be found for most of the species according to site conditions. Heart root systems were limited to fine material while mixed and tap root systems were found on coarse material. In coarse materials, trees developed few but rather large roots (> 5 cm in diameter and >4 m in length). In fine materials, root systems had three times more roots but they were 40% smaller and shorter. Roots were 20% more numerous and 65% larger on the downslope side due to water availability at dike or riverbank toe. Conclusion. Root system structure was mainly influenced by soil material and water availability and far less by tree species. Tree root systems are opportunistic in developing in the direction where water and nutrients are plentiful: whatever the species, predicting its dimensions and structure requires a thorough investigation of soil and other environmental conditions. This study gives a new insight in root development: it will help predict tree root growth in various environments and particularly on dikes.

International audience; Aims: This study aimed at disentangling the respective influence of species, environment, root size and root type in tree root architecture.Method: The root system of 106 adult trees from ten species was carefully extracted from French dikes. Root length and proximal diameter, length and diameter of root segments and branch insertion diameter were measured. Root branching and tapering rates, segment taper, classical (P) and new architectural parameters related to branching patterns were computed.Results: Two contrasting root types called "running" (R) and "short" (S), were identified from growth and architectural parameters. Compared to S roots, R roots were longer for an equivalent proximal diameter and singled out with lower tapering rate, branching rate and segment taper and with smaller branches. Their main axis lost less in diameter at branching point for branches of the same size. Tree species had little influence on these architectural parameters. The effect of soil material (coarse vs fine) was significant mainly on root size, on branching rate in fine material, and only secondarily on some branching patterns for running roots and on segment taper. The new architectural parameters describe branching patterns more accurately than classical ones.Conclusion: This study provides an original insight in tree root architectural analysis, proposing a new root typology and innovative parameters for the description and modelling of root architecture.

Summary Our objective was to calibrate a model of the root system architecture on several Poaceae species and to assess its value to simulate several ‘integrated’ traits measured at the root system level: specific root length (SRL), maximum root depth and root mass. We used the model ArchiSimple, made up of sub-models that represent and combine the basic developmental processes, and an experiment on 13 perennial grassland Poaceae species grown in 1.5-m-deep containers and sampled at two different dates after planting (80 and 120 d). Model parameters were estimated almost independently using small samples of the root systems taken at both dates. The relationships obtained for calibration validated the sub-models, and showed species effects on the parameter values. The simulations of integrated traits were relatively correct for SRL and were good for root depth and root mass at the two dates. We obtained some systematic discrepancies that were related to the slight decline of root growth in the last period of the experiment. Because the model allowed correct predictions on a large set of Poaceae species without global fitting, we consider that it is a suitable tool for linking root traits at different organisation levels.

Cited Reference Count: 40 ref.International Formulae Group (IFG)Dschang, Cameroon; L’étude in situ de l’architecture et la croissance des systèmes racinaires ont été réalisées sur des jeunes plants en milieu naturel et en station. Les fronts racinaires verticaux et horizontaux sont déterminés à partir de la méthode d’excavation. Les coordonnées spatiales obtenues manuellement sur le terrain alimentent un logiciel AMAPmod de modélisation qui transforme d’une part les coordonnées spatiales en coordonnées standards puis d’autre part, donne les représentations 3D des systèmes racinaires des jeunes plants. En milieu naturel, les systèmes racinaires sont constitués de 3 ordres de racines. Les racines d’ordre 2 sont les plus abondantes. La profondeur d’enracinement de B. aegyptiaca est la plus importante. A. tortilis développe une longueur totale racinaire plus importante. La longueur totale des racines d’ordre 2 d’A. tortilis est plus importante que celle de B. aegyptiaca. En station, l’ordre maximal des ramifications est de 5 chez A. tortilis et Z. mauritiana et de 7 chez B. aegyptiaca. Les types 2 et 3 chez A. tortilis et Z. mauritiana et les types 2, 3 et 4 chez B. aegyptiaca forment l’essentiel du système racinaire. La densité totale des racines de B. aegyptiaca est plus importante. Les profondeurs d’enracinement d’A. tortilis et de B. aegyptiaca sont différentes de celle de Z. mauritiana. B. aegyptiaca dispose une longueur totale plus importante. Les ordres 2 et 3 sont les plus longs du système racinaire. Ensuite suivent les racines d’ordre 4. Celles des racines d’ordre 1, 5, 6 et 7 sont de longueurs égales

International audience; Ramanujan's Master theorem states that, under suitable conditions, the Mellin transform of an alternating power series provides an interpolation formula for the coefficients of this series. Ramanujan applied this theorem to compute several definite integrals and power series, which explains why it is referred to as the "Master Theorem". In this paper we prove an analogue of Ramanujan's Master theorem for the hypergeometric Fourier transform on root systems. This theorem generalizes to arbitrary positive multiplicity functions the results previously proven by the same authors for the spherical Fourier transform on semisimple Riemannian symmetric spaces.

Non toxic ecotypes of Jatropha curcas L. (NTJC) have been poorly documented at the national or international scales, despite having higher potential as energy and food sources when compared with the toxic forms (TJC). Therefore, the objective of this research was to analyze the properties and performance of NTJC seeds and seedlings in soils with different textures and nutritional contents, as well as their response to a locally important pathogen, Pythium aphanidermatum. This research included the study of: 1) seeds, 2) seedlings, 3) roots and 4) seeds and plants inoculated with the pathogen. The study of seeds was performed by literature research on the oleic qualities of NTJC and TJC; allometric measurements on four sources and three experiments to determine the effects of seed weight on germination and vigor. Plant growth was observed beginning at germination and through several periods (daily, weekly and monthly) in eight different substrates and nutritional content. Roots were analyzed in six different substrates using optic and electronic microscopes, and a study of root structure was performed using three dimensional techniques. Pathogenic response was studied by inoculating seeds and seedlings in three different substrates and at two periods in time. The results on literature review found similar oleic quality between NTJC and TJC seeds; the allometric characters of NTJC were highly variable, and a positive correlation between seed weight and vigor was found. Seedling development proceeded more rapidly in substrates with organic matter content (OM) greater than 1.0% and in medium to fine textures, whereas NTJC forms survived but had inhibited growth in substrates with OM less than 1.0% and coarse textures. Root systems showed higher soil fixation capabilities in medium to fine textures, and a strong morpho-genetic structural pattern adapted to explore poor soils, and not affected by the substrate composition. Inoculation with P. aphanidermatum determined that NTJC was able to survive in contaminated soils when it entered the post-germination stage. In conclusion NTJC and TJC seeds have similar energetic properties. Dispersed allometry in seeds and their capability to survive despite a local pathogen and poor soils indicate a good genetic diversity and adaptability to the Mexican tropical and subtropical environments. However, the establishment of NTJC forms in commercial plantations would require additional fertilization on poor soils., Las formas o ecotipos no tóxicos de Jatropha curcas L. (NTJC) poco han sido documentadas a nivel nacional e internacional, a pesar de su mayor potencial como fuentes energéticas y alimenticias, comparadas con las formas tóxicas (TJC). Es por ello que esta investigación tiene como objetivo analizar las propiedades y desempeño de semillas y plántulas NTJC en suelos con diferentes texturas y contenido nutrimental; así como su respuesta ante un patógeno localmente importante, como es Pythium aphanidermatum. La investigación comprendió el estudio de: 1) semillas, 2) plántulas, 3) raíces y 4) la inoculación del patógeno en semillas y plántulas. El estudio de las semillas se realizó mediante la documentación de las cualidades oleicas de semillas NTJC y TJC; mediciones alométricas de cuatro accesiones, y tres experimentos para determinar los efectos de sus pesos sobre su germinación y vigor. Se observó el crecimiento de las plántulas desde su germinación y durante varios periodos (diario, semanal y mensual) en ocho sustratos con diferentes condiciones texturales y nutrimentales. Las raíces y su relación con la parte aérea fueron analizadas en seis sustratos diferentes mediante microscopios óptico y electrónico, y un enfoque sobre su estructura aplicando técnicas tri-dimensionales. La respuesta al patógeno se estudió mediante su inoculación en semillas y plántulas en tres sustratos y durante dos periodos de tiempo diferentes. Los resultados de las investigaciones disponibles sobre las semillas NTJC encontraron cualidades oleicas similares a las semillas TJC; alométricamente las semillas NTJC fueron muy dispersas y tuvieron una relación positiva entre su peso y su vigor. El desarrollo de las plántulas fue mayor en sustratos con contenidos de materia orgánica (MO) superiores al 1.0% y texturas finas a medias, en relación con texturas gruesas y contenidos de MO inferiores, donde las formas NTJC sobrevivieron, pero inhibieron su crecimiento. Su sistema de raíces demostró una mayor capacidad de fijación en suelos con texturas medias a finas, y una fuerte tendencia morfo-genética que permitió mantener su estructura original independiente del sustrato y adaptada para explorar suelos pobres. La inoculación con P. aphanidermatum determinó que la forma NTJC fue capaz de sobrevivir en suelos contaminados con este fitopatógeno durante la etapa posterior a la germinación. Por lo que se concluyó que las semillas NTJC energéticamente tienen propiedades similares a las semillas TJC. La dispersión en la alometría de sus semillas y su capacidad para adaptarse a un patógeno local y a suelos pobres son caracteres indicativos de una buena diversidad genética y de ecotipos aptos a las condiciones del trópico y subtrópico mexicano. Sin embargo, su establecimiento en plantaciones comerciales requeriría de fertilizantes en suelos con muy baja fertilidad.

We investigate some aspects of some matrix-valued diffusions and use Harmonic analysis tools to answer some probabilistic questions. We start with the Laguerre process then study the radial Dunkl process which generalizes the eigenvalues process of these diffusions. Next, we define and study the free Jacobi process, which is the infinite dimensional limiting process of the complex Jacobi-matrix. The last chapter deals with large deviations principle for statistics of one-dimensional Jacobi processes.; On étudie quelques aspects de certaines diffusions matricielles pour lesquelles on utilise des outils d'analyse harmonique pour répondre à des questions de nature probabiliste : on commence par le processus de Laguerre, puis on s'intéresse au processus de Dunkl radial qui généralise le processus des valeurs propres de ces diffusions. On regarde ensuite le processus de Jacobi dans le cas où la taille de la matrice tend vers l'infini, ceci nous plonge dans le monde des probabilités libres. Le dernier chapitre est consacré à la résolution d'un problème de grandes déviations pour des statistiques de processus de Jacobi univariés.

We investigate some aspects of some matrix-valued diffusions and use Harmonic analysis tools to answer some probabilistic questions. We start with the Laguerre process then study the radial Dunkl process which generalizes the eigenvalues process of these diffusions. Next, we define and study the free Jacobi process, which is the infinite dimensional limiting process of the complex Jacobi-matrix. The last chapter deals with large deviations principle for statistics of one-dimensional Jacobi processes.; On étudie quelques aspects de certaines diffusions matricielles pour lesquelles on utilise des outils d'analyse harmonique pour répondre à des questions de nature probabiliste : on commence par le processus de Laguerre, puis on s'intéresse au processus de Dunkl radial qui généralise le processus des valeurs propres de ces diffusions. On regarde ensuite le processus de Jacobi dans le cas où la taille de la matrice tend vers l'infini, ceci nous plonge dans le monde des probabilités libres. Le dernier chapitre est consacré à la résolution d'un problème de grandes déviations pour des statistiques de processus de Jacobi univariés.

In this thesis, we are interested inthe study of analytical and probabilistic aspects ofHeckman--Opdam and affine buildings of type $\tilde{A}_r$theories. We also study the Poisson boundary of rationaltriangular matrices.One of our main results, is to obtain new estimates of thehypergeometric functions of Heckman--Opdam. Our proofs arerelatively more elementary than in the particular case ofsymmetric spaces $G/K$. For instance for the proof of the basicestimates of spherical functions, obtained by Harish-Chandra orGangolli and Varadarajan, and for the recent estimate of theelementary spherical function $\phi_0$ by Anker, Bougerol andJeulin.Another main result is the estimate of the heat kernel associatedwith some combinatorial Laplacian on an affine building oftype $\tilde{A}_r$., Cette thèse porte sur une étudeanalytique et probabiliste des théories de Heckman--Opdam et desimmeubles affines de type $\tilde{A}_r$. On étudie aussi lafrontière de Poisson des matrices triangulaires inversiblesrationnelles.Un de nos principaux résultats est l'obtention de nouvellesestimations des fonctions hypergéométriques de Heckman--Opdam. Nospreuves sont relativement plus simples que dans le cas particulierdes espaces symétriques $G/K$. Par exemple pour les estimations debase des fonctions sphériques, obtenues par Harish-Chandra, ouGangolli et Varadarajan, ainsi que pour les estimations récentesde la fonction sphérique élémentaire $\phi_0$ par Anker, Bougerolet Jeulin.Un des autres principaux résultats est l'estimation du noyau de lachaleur associé à un certain laplacien combinatoire sur unimmeuble affine de type $\tilde{A}_r$.

Under the assumption of positive multiplicity, we obtain basic estimates of the hypergeometric functions F\_\la and G\_\la of Heckman and Opdam, and sharp estimates of the particular functions F\_0 and G\_0. Next we prove the Paley-Wiener theorem for the Schwartz class, solve the heat equation and estimate the heat kernel.

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42 ref.

International audience; One-year-old peach trees (Prunus persica (L.) Batsch) were severely pruned in July by removing 60% of the shoots. Tree responses were analyzed in terms of architecture and nutritional status. Tree growth was recorded from July to September by nondestructive (leaf production, thickening and branching of the remaining secondary axes) and destructive measurements (biomass partitioning and concentrations of total nitrogen (N) and nonstructural carbohydrates (NC) in specific tissues). The dry weights of pruned trees were lower than those of control trees at the end of the growing season (i.e., 2.5 months after pruning), whereas shoot:root ratios were restored to the initial values. Tree response occurred in two stages. During the first 24 days following pruning, the growth components of the remaining secondary axes were similar to the control, and new secondary axes were produced. During the next 17 days, increases in both diameter and branching of secondary axes contributed to the maintenance of pruned tree growth rate (similar to that of control trees) and restoration of initial shoot:root ratios. No significant effect of pruning was observed on NC concentrations, whereas N concentrations increased in several organs of the pruned trees during the first growth period. The transient increase in internal N availability contributed to the initiation of new axes and the restoration of a more functional biomass partitioning between shoots and roots.

Mesure et analyse de la répartition de la conductance hydraulique dans le système racinaire du maïs

Effets interactifs de l'enrichissement en CO2 et de la nutrition azotée sur la croissance et la sensibilité à la sécheresse du pin maritime (Pinus pinaster Ait.)

Culture of Bartlett on its own roots. Comparaisons with Quince and French seedling rootstocks

Essais de bouturage herbacé de la variété Williams (Pyrus communis[/i] L.).