Automatic generation of generalised regular factorial designs

Open Access for this article was paid for by the French Research Agency (ANR), project Escapade (ANR-12-AGRO-0003).The R package planor enables the user to search for, and construct, factorial designs satisfying given conditions. The user specifies the factors and their numbers of levels, the factorial terms which are assumed to be non-zero, and the subset of those which are to be estimated. Both block and treatment factors can be allowed for, and they may have either fixed or random effects, as well as hierarchy relationships. The designs are generalised regular designs, which means that each one is constructed by using a design key and that the underlying theory is that of finite abelian groups. The main theoretical results and algorithms on which planor is based are developed and illustrated, with the emphasis on mathematical rather than programming details. Sections 3–5 are dedicated to the elementary case, when the numbers of levels of all factors are powers of the same prime. The ineligible factorial terms associated with users’ specifications are defined and it is shown how they can be used to search for a design key by a backtrack algorithm. Then the results are extended to the case when different primes are involved, by making use of the Sylow decomposition of finite abelian groups. The proposed approach provides a unified framework for a wide range of factorial designs.Publisher PDFPeer reviewe

Sensitivity analysis of a hierarchical qualitative model – the analysis of MASC

AbstractSensitivity Analysis (SA) is applied to a hierarchical qualitative model built to assess the sustainability of cropping systems. Three approaches were tested to perform a first-order SA on such a model, assuming a fixed model structure and no correlation among input variables: (i) factorial designs combined with analysis of variance (ANOVA), (ii) conditional probabilities, (iii) Monte Carlo sampling (MC). If the complete factorial design is too large to be computed, MC and conditional probabilities represent efficient alternatives to perform an analysis of the overall qualitative model. Conditional probabilities exploit the hierarchical structure of the model to give exact first-order indices, while MC could be a more flexible approach for the introduction of correlations among variables. We discuss how such SA results can guide modellers and end-users in modelling and application phases

A completely random T-tessellation model and Gibbsian extensions

A revised version of this paper has been published in Spatial Statistics, 2013, volume 6, pages 118- 138.In their 1993 paper, Arak, Clifford and Surgailis discussed a new model of random planar graph. As a particular case, that model yields tessellations with only T-vertices (T-tessellations). Using a similar approach involving Poisson lines, a new model of random T-tessellations is proposed. Campbell measures, Papangelou kernels and Georgii-Nguyen-Zessin formulae are translated from point process theory to random T-tessellations. It is shown that the new model shows properties similar to the Poisson point process and can therefore be considered as a completely random T-tessellation. Gibbs variants are introduced leading to models of random T-tessellations where selected features are controlled. Gibbs random T-tessellations are expected to better represent observed tessellations. As numerical experiments are a key tool for investigating Gibbs models, we derive a simulation algorithm of the Metropolis-Hastings-Green family

Neutral modelling of agricultural landscapes by tessellation methods—Application for gene flow simulation.

International audienceNeutral landscape models are not frequently used in the agronomical domain, whereas they would be very useful for studying given agro-ecological or physical processes. Contrary to ecological neutral landscape models, agricultural models have to represent and manage geometrical patches and thus should rely on tessellation methods. We present a three steps approach that aimed at simulating such landscapes. Firstly, we characterized the geometry of three real field patterns; secondly, we generated simulated field patterns with two tessellation methods attempting to control the value of some of the observed characteristics and, thirdly, we evaluated the simulated field patterns. For this evaluation, we considered that good simulated field patterns should capture characteristics of real landscapes that are important for the targeted agro-ecological process. Real landscapes and landscapes simulated using either a Voronoi or a rectangular tessellation were thus compared when used as input data within a gene flow model. The results showed that neither tessellation method captured field shapes correctly, thus leading to over or (small) under estimation of gene flow. The Voronoi tessellation, though, performed better than the rectangular tessellation. Possible research directions are proposed to improve the simulated patterns, including the use of post processing, the control of cell orientation or the implementation of other tessellation techniques

Modeling protein network evolution under genome duplication and domain shuffling

<p>Abstract</p> <p>Background</p> <p>Successive whole genome duplications have recently been firmly established in all major eukaryote kingdoms. Such <it>exponential </it>evolutionary processes must have largely contributed to shape the topology of protein-protein interaction (PPI) networks by outweighing, in particular, all <it>time-linear </it>network growths modeled so far.</p> <p>Results</p> <p>We propose and solve a mathematical model of PPI network evolution under successive genome duplications. This demonstrates, from first principles, that evolutionary conservation and scale-free topology are intrinsically linked properties of PPI networks and emerge from <it>i) </it>prevailing <it>exponential </it>network dynamics under duplication and <it>ii) asymmetric divergence </it>of gene duplicates. While required, we argue that this asymmetric divergence arises, in fact, spontaneously at the level of protein-binding sites. This supports a refined model of PPI network evolution in terms of protein domains under exponential and asymmetric duplication/divergence dynamics, with multidomain proteins underlying the combinatorial formation of protein complexes. Genome duplication then provides a powerful source of PPI network innovation by promoting local rearrangements of multidomain proteins on a genome wide scale. Yet, we show that the overall conservation and topology of PPI networks are robust to extensive domain shuffling of multidomain proteins as well as to finer details of protein interaction and evolution. Finally, large scale features of <it>direct </it>and <it>indirect </it>PPI networks of <it>S. cerevisiae </it>are well reproduced numerically with only two adjusted parameters of clear biological significance (<it>i.e</it>. network effective growth rate and average number of protein-binding domains per protein).</p> <p>Conclusion</p> <p>This study demonstrates the statistical consequences of genome duplication and domain shuffling on the conservation and topology of PPI networks over a broad evolutionary scale across eukaryote kingdoms. In particular, scale-free topologies of PPI networks, which are found to be robust to extensive shuffling of protein domains, appear to be a simple consequence of the conservation of protein-binding domains under asymmetric duplication/divergence dynamics in the course of evolution.</p

Construction et randomisation de plans factoriels réguliers avec le package R PLANOR

Construction et randomisation de plans factoriels réguliers avec le package R PLANO

Méthodes pour l'analyse de sensibilité de modèles agro-écologiques à l'échelle du parcellaire agricole

National audienceLa structure spatiale et la composition de l'habitat ont une influence importante sur la propagation d'épidémies. Pour mieux évaluer et contrôler cette influence, les approches de modélisation et d'exploration numérique par simulations sont un complément incontournable d'approches entièrement analytiques. A partir de travaux menés en épidémiologie des plantes, nous présenterons les méthodes mathématiques et statistiques que nous mobilisons pour intégrer la structure et la composition du parcellaire agricole comme des facteurs à part entière de l'étude de phénomènes dynamiques à cette échelle. Nous en discuterons les principes les plus génériques, applicables en épidémiologie humaine ou animal