The amino acid and hydrocarbon contents of the Paris meteorite: Insights into the most primitive CM chondrite

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A Mathematical Approach Estimating Source and Sink Functioning of Competing Organs

in pressPlant growth and development depend on both organogenesis and photosynthesis. Organogenesis sets in place various organs (leaves, internodes, fruits, roots) that have their own sinks. The sum of these sinks corresponds to the plant demand. Photosynthesis of the leaves provides the biomass supply (source) that is to be shared among the organs according to their sink strength. Here we present a mathematical model – GreenLab – that describes dynamically plant architecture in a resource-dependent way. The source and sink functions of the various organs control the biomass acquisition and partitioning during plant development and growth, giving the sizes and weights of organs according to their position in the plant architecture. Non-linear least-square method was used to estimate the numerical values of (hidden) parameters that control the organ sink variation and leaf functioning. Through simultaneous fitting of data from several developmental stages (multi-fitting), plant growth could be described satisfactorily with just a few parameters. Examples of application on cotton and maize are shown in this article

Bayesian Estimation for the GreenLab Plant Growth Model with Deterministic Organogenesis

Plant growth modeling has attracted a lot of attention due to its potential applications. Many scientific disciplines are involved, and a lot of research effort and intensive computer methods were needed to understand better the complex mechanisms underlying plant evolution. Among the numerous challenges, one can cite mathematical modeling, parameterization, estimation and prediction. One of the most promising models that have been proposed in the literature is the GreenLab functional–structural plant growth model. In this study, we focus only on one of its versions, named GreenLab-1, particularly adapted to a certain class of plants with known organogenesis, such as sugar beet, maize, rapeseed and other crop plants. The parameters of the model are related to plant functioning, and the vector of observations consists of organ masses measured only once at a given observation time. Previous efforts for parameter estimation in GreenLab-1 include Kalman-type filters, stochastic variants of EM and/or ECM algorithms, and hybrid sequential importance sampling algorithms with Bayesian estimation only for the functional parameters of the model. In this paper, the first purely Bayesian approach for parameter estimation of the GreenLab-1 model is proposed. This approach has much more flexibility in handling complex structures, thus providing a useful tool for analyzing such types of models. In order to sample from the posterior distribution an MCMC algorithm is used and its implementation issues are also discussed. The performance of this method is illustrated on a simulated and a real dataset from the sugar beet plant, and a comparison is made with the MLE approach. © 2021, International Biometric Society

Modélisation mathématique de l'hématopoïèse et des hémopathies : développement, dynamique et traitement

National audienceL'étude de l'hématopoïèse normale et pathologique, de par la complexité du sujet, requiert une approche multi-disciplinaire. L'utilisation de modèles mathématiques, lorsqu'il s'agit de comprendre la dynamique de populations de cellules, le développement de cancers ou l'effet d'un traitement, est particulièrement appropriée. Les modèles mathématiques, calibrés à partir d'observations expérimentales, peuvent être des outils d'aide à la décision en clinique, permettant par exemple de prédire l'effet d'un traitement ou d'en optimiser le dosage. Dans cette revue, nous commencerons par présenter différents modèles et formalismes mathématiques qui se sont développés au cours des décennies pour modéliser l'hématopoïèse, et qui sont encore pour certains à la base des travaux les plus récents. Nous aborderons ensuite les enjeux méthodologiques liés à l'inférence mathématique, permettant de s'assurer de la validité et robustesse des résultats. Enfin, nous terminerons par illustrer l'utilisation de modèles mathématiques dans trois champs d'application : l'initiation et le développement des hémopathies malignes, la dérégulation de leur hématopoïèse et leurs traitements

Achievement of Global Second Order Mesh Convergence for Discontinuous Flows with Adapted Unstructured Meshes

In the context of steady CFD computations, some numerical experiments point out that only a global mesh convergence order of one is numerically reached on a sequence of uniformly refined meshes although the considered numerical scheme is second order. This is due to the presence of genuine discontinuities or sharp gradients in the modelled flow. In order to address this issue, a continuous mesh adaptation framework is proposed based on the metric notion. It relies on a L p control of the interpolation error for twice differentiable functions. This theory provides an optimal bound of the interpolation error involving the Hessian of the solution. From this estimate, an optimal metric is exhibited to govern the adapted mesh generation. As regards steady flow computations with discontinuities, a global second order mesh convergence should be obtained. To this end, a higher order smooth approximation of the solution is reconstructed providing an accurate and reliable Hessian evaluation. Several numerical examples in two and three dimensions illustrate that the global convergence order is recovered using this mesh adaptation strategy

Mixed-Effects Estimation in Dynamic Models of Plant Growth for the Assessment of Inter-individual Variability

Modeling inter-individual variability in plant populations is a key issue to understand crop heterogeneity and its variations in response to the environment. Being able to describe the interactions among plants and explain the variability observed in the population could provide useful information on how to control it and improve global plant growth. We propose here a method to model plant variability within a field, by extending the so-called GreenLab functional-structural plant model from the individual to the population scale via nonlinear mixed-effects modeling. Parameter estimation of the population model is achieved using the stochastic approximation expectation maximization algorithm, implemented in the platform for plant growth modeling and analysis PyGMAlion. The method is first applied on a set of simulated data and then on a real dataset from a population of 34 winter oilseed rape plants at the rosette stage. Results show that our method allows for a good characterization of the variability in the population with only a limited number of parameters, which is a key point for plant models. Results on simulated data show that parameters associated with a low sensitivity index are inaccurately estimated by the algorithm when considered as random effects, but a good stability of the results can be obtained by considering them as fixed effects. These results open new ways for the analysis of inter-plant variability within a population and the study of plant–plant competition.Supplementary materials accompanying this paper appear online. © 2018, International Biometric Society