Random Planar Lattices and Integrated SuperBrownian Excursion

In this paper, a surprising connection is described between a specific brand of random lattices, namely planar quadrangulations, and Aldous' Integrated SuperBrownian Excursion (ISE). As a consequence, the radius r_n of a random quadrangulation with n faces is shown to converge, up to scaling, to the width r=R-L of the support of the one-dimensional ISE. More generally the distribution of distances to a random vertex in a random quadrangulation is described in its scaled limit by the random measure ISE shifted to set the minimum of its support in zero. The first combinatorial ingredient is an encoding of quadrangulations by trees embedded in the positive half-line, reminiscent of Cori and Vauquelin's well labelled trees. The second step relates these trees to embedded (discrete) trees in the sense of Aldous, via the conjugation of tree principle, an analogue for trees of Vervaat's construction of the Brownian excursion from the bridge. From probability theory, we need a new result of independent interest: the weak convergence of the encoding of a random embedded plane tree by two contour walks to the Brownian snake description of ISE. Our results suggest the existence of a Continuum Random Map describing in term of ISE the scaled limit of the dynamical triangulations considered in two-dimensional pure quantum gravity.Comment: 44 pages, 22 figures. Slides and extended abstract version are available at http://www.loria.fr/~schaeffe/Pub/Diameter/ and http://www.iecn.u-nancy.fr/~chassain

From Oncogenetic Pedigrees to Family Profiles: A Necessary Step to Enable Statistics

International audienceBackground: Cancer has always been a major domain requiring progress in statistics, methodology and bio-informatics. Oncogenetic, focusing on the relationship between genetics and cancer, is particularly concerned with “big data” issues, which includes genealogical pedigrees: their special structure – made of relations between members and possible clinical annotations - is too complex to be directly used for statistical purpose. This article describes a way to condense pedigrees so that they can be handled more easily and compared together.Method: our approach aggregates the genealogical and clinical information of pedigrees containing many generations. Condensed pedigrees, called “subtrees”, are composed of basic 2 or 3-generation pedigrees: for one whole pedigree, a subtree is calculated by the mean of all basic pedigrees it contains. These subtrees can then be grouped together for different subsets of families (for example breast/ovarian cancer families with or without BRCA mutation carrier). Such a grouping named “profile”, besides its reduced structure, is particularly interesting because for each studied characteristic, means and standard deviations are available. Moreover, distances between each subtree and various profiles can be calculated and used as a discriminant index.Results: Subtrees and profiles were validated using a subset of 454 families (22.348 members) with a Lynch syndrome: in 84, at least one member carried an MMR deleterious mutation. Two profiles were computed depending on the presence or the absence of MMR mutation in the families. An ROC analysis showed that distances between each family subtree and both profiles were significant predictors for MMR mutations.Conclusion: Subtrees and profiles show interesting discriminant properties to study pedigree data. This method seems suitable to search for population differences between monogenic cancer risk models and multigenic ones

Cover crops and their erosion-reducing effects during concentrated flow erosion

Cover crops are a very effective erosion control and environmental conservation technique. When cover crops freeze at the beginning of the winter period, the above-ground biomass becomes less effective in protecting the soil from water erosion, but roots can still play an important role in improving soil strength. However, information on root properties of common cover crops growing in temperate climates (e.g. Sinapis alba (white mustard), Phacelia tanacetifoli (phacelia), Lolium perenne (ryegrass), Avena sativa (oats), Secale cereale (rye), Raphanus sativus subsp. oleiferus (fodder radish)) is very scarce. Therefore, root density distribution with soil depth and the erosion-reducing effect of these cover crops during concentrated flow erosion were assessed by conducting root auger measurements and controlled concentrated flow experiments with 0.1m topsoil samples. The results indicate that root density of the studied cover crops ranges between 1.02 for phacelia and 2.95kg m-3 for ryegrass. Cover crops with thick roots (e.g. white mustard and fodder radish) are less effective than cover crops with fine-branched roots (e.g. ryegrass and rye) in preventing soil losses by concentrated flow erosion. Moreover, after frost, the erosion-reducing potential of phacelia and oats roots decreased. Amoeba diagrams, taking into account both below-ground and above-ground plant characteristics, identified ryegrass, rye, oats and white mustard as the most suitable species for controlling concentrated flow erosion. © 2011 Elsevier B.V

Cover crops and their erosion-reducing effects during concentrated flow erosion

Cover crops are a very effective erosion control and environmental conservation technique. When cover crops freeze at the beginning of the winter period, the above-ground biomass becomes less effective in protecting the soil from water erosion, but roots can still play an important role in improving soil strength. However, information on root properties of common cover crops growing in temperate climates (e.g. Sinapis alba (white mustard), Phacelia tanacetifoli (phacelia), Lolium perenne (ryegrass), Avena sativa (oats), Secale cereale (rye), Raphanus sativus subsp. oleiferus (fodder radish)) is very scarce. Therefore, root density distribution with soil depth and the erosion-reducing effect of these cover crops during concentrated flow erosion were assessed by conducting root auger measurements and controlled concentrated flow experiments with 0.1 m topsoil samples. The results indicate that root density of the studied cover crops ranges between 1.02 for phacelia and 2.95 kgm−3 for ryegrass. Cover crops with thick roots (e.g. white mustard and fodder radish) are less effective than cover crops with fine-branched roots (e.g. ryegrass and rye) in preventing soil losses by concentrated flow erosion. Moreover, after frost, the erosion-reducing potential of phacelia and oats roots decreased. Amoeba diagrams, taking into account both below-ground and above-ground plant characteristics, identified ryegrass, rye, oats and white mustard as the most suitable species for controlling concentrated flow erosion.status: publishe

Comparative Wood Anatomy of the Primuloid Clade (Ericales s.l.)

The wood structure of 78 species from 27 genera representing the woody primuloids (Maesaceae, Myrsinaceae, and Theophrastaceae) was investigated using light microscopy (LM) and scanning electron microscopy (SEM). Results indicated that the ray structure, the nature of mineral inclusions, and the occurrence of breakdown areas in rays can be used to separate the three primuloid families from each other. Within Ericales, the presence of exclusively multiseriate rays is synapomorphic for Myrsinaceae and Theophrastaceae, and the occurrence of breakdown areas in rays is synapomorphic for Myrsinaceae. Within Myrsinaceae, the wood structure of the mangrove genus Aegiceras differs because it has short vessel elements that are storied, non-septate fibers, a combination of low uni- and multiseriate rays, and multiseriate rays with exclusively procumbent body ray cells. The aberrant wood anatomy of Coris and Lysimachia can be explained by their secondary woodiness. Within Theophrastaceae, Clavija and Theophrasta can be distinguished from Bonellia, Jacquinia, and Deherainia. The recent division of Jacquinia s.l. into Jacquinia s.s. and Bonellia is supported by a difference in mineral inclusions

Comparative Wood Anatomy of the Primuloid Clade (Ericales s.l.)

The wood structure of 78 species from 27 genera representing the woody primuloids (Maesaceae, Myrsinaceae, and Theophrastaceae) was investigated using light microscopy (LM) and scanning electron microscopy (SEM). Results indicated that the ray structure, the nature of mineral inclusions, and the occurrence of breakdown areas in rays can be used to separate the three primuloid families from each other. Within Ericales, the presence of exclusively multiseriate rays is synapomorphic for Myrsinaceae and Theophrastaceae, and the occurrence of breakdown areas in rays is synapomorphic for Myrsinaceae. Within Myrsinaceae, the wood structure of the mangrove genus Aegiceras differs because it has short vessel elements that are storied, non-septate fibers, a combination of low uni- and multiseriate rays, and multiseriate rays with exclusively procumbent body ray cells. The aberrant wood anatomy of Coris and Lysimachia can be explained by their secondary woodiness. Within Theophrastaceae, Clavija and Theophrasta can be distinguished from Bonellia, Jacquinia, and Deherainia. The recent division of Jacquinia s.l. into Jacquinia s.s. and Bonellia is supported by a difference in mineral inclusions