Computing the first eigenpair of the p-Laplacian via inverse iteration of sublinear supersolutions

We introduce an iterative method for computing the first eigenpair $(\lambda_{p},e_{p})$ for the $p$-Laplacian operator with homogeneous Dirichlet data as the limit of $(\mu_{q,}u_{q})$ as $q\rightarrow p^{-}$, where $u_{q}$ is the positive solution of the sublinear Lane-Emden equation $-\Delta_{p}u_{q}=\mu_{q}u_{q}^{q-1}$ with same boundary data. The method is shown to work for any smooth, bounded domain. Solutions to the Lane-Emden problem are obtained through inverse iteration of a super-solution which is derived from the solution to the torsional creep problem. Convergence of $u_{q}$ to $e_{p}$ is in the $C^{1}$-norm and the rate of convergence of $\mu_{q}$ to $\lambda_{p}$ is at least $O(p-q)$. Numerical evidence is presented.Comment: Section 5 was rewritten. Jed Brown was added as autho

Closing a gap in tropical forest biomass estimation : taking crown mass variation into account in pantropical allometries

Accurately monitoring tropical forest carbon stocks is a challenge that remains outstanding. Allometric models that consider tree diameter, height and wood density as predictors are currently used in most tropical forest carbon studies. In particular, a pantropical biomass model has been widely used for approximately a decade, and its most recent version will certainly constitute a reference model in the coming years. However, this reference model shows a systematic bias towards the largest trees. Because large trees are key drivers of forest carbon stocks and dynamics, understanding the origin and the consequences of this bias is of utmost concern. In this study, we compiled a unique tree mass data set of 673 trees destructively sampled in five tropical countries (101 trees > 100 cm in diameter) and an original data set of 130 forest plots (1 ha) from central Africa to quantify the prediction error of biomass allometric models at the individual and plot levels when explicitly taking crown mass variations into account or not doing so. We first showed that the proportion of crown to total tree aboveground biomass is highly variable among trees, ranging from 3 to 88 %. This proportion was constant on average for trees = 45 Mg. This increase coincided with a progressive deviation between the pantropical biomass model estimations and actual tree mass. Taking a crown mass proxy into account in a newly developed model consistently removed the bias observed for large trees (> 1 Mg) and reduced the range of plot- level error (in %) from [-23; 16] to [0; 10]. The disproportionally higher allocation of large trees to crown mass may thus explain the bias observed recently in the reference pantropical model. This bias leads to far- from- negligible, but often overlooked, systematic errors at the plot level and may be easily corrected by taking a crown mass proxy for the largest trees in a stand into account, thus suggesting that the accuracy of forest carbon estimates can be significantly improved at a minimal cost

Variables with time-varying effects and the Cox model: Some statistical concepts illustrated with a prognostic factor study in breast cancer

International audienceBACKGROUND: The Cox model relies on the proportional hazards (PH) assumption, implying that the factors investigated have a constant impact on the hazard - or risk - over time. We emphasize the importance of this assumption and the misleading conclusions that can be inferred if it is violated; this is particularly essential in the presence of long follow-ups. METHODS: We illustrate our discussion by analyzing prognostic factors of metastases in 979 women treated for breast cancer with surgery. Age, tumour size and grade, lymph node involvement, peritumoral vascular invasion (PVI), status of hormone receptors (HRec), Her2, and Mib1 were considered. RESULTS: Median follow-up was 14 years; 264 women developed metastases. The conventional Cox model suggested that all factors but HRec, Her2, and Mib1 status were strong prognostic factors of metastases. Additional tests indicated that the PH assumption was not satisfied for some variables of the model. Tumour grade had a significant time-varying effect, but although its effect diminished over time, it remained strong. Interestingly, while the conventional Cox model did not show any significant effect of the HRec status, tests provided strong evidence that this variable had a non-constant effect over time. Negative HRec status increased the risk of metastases early but became protective thereafter. This reversal of effect may explain non-significant hazard ratios provided by previous conventional Cox analyses in studies with long follow-ups. CONCLUSIONS: Investigating time-varying effects should be an integral part of Cox survival analyses. Detecting and accounting for time-varying effects provide insights on some specific time patterns, and on valuable biological information that could be missed otherwise

DRB2 Is Required for MicroRNA Biogenesis in Arabidopsis thaliana

Background The Arabidopsis thaliana (Arabidopsis) DOUBLE-STRANDED RNA BINDING (DRB) protein family consists of five members, DRB1 to DRB5. The biogenesis of two developmentally important small RNA (sRNA) species, the microRNAs (miRNAs) and trans-acting small interfering RNAs (tasiRNAs) by DICER-LIKE (DCL) endonucleases requires the assistance of DRB1 and DRB4 respectively. The importance of miRNA-directed target gene expression in plant development is exemplified by the phenotypic consequence of loss of DRB1 activity (drb1 plants). Principal Findings Here we report that the developmental phenotype of the drb235 triple mutant plant is the result of deregulated miRNA biogenesis in the shoot apical meristem (SAM) region. The expression of DRB2, DRB3 and DRB5 in wild-type seedlings is restricted to the SAM region. Small RNA sequencing of the corresponding tissue of drb235 plants revealed altered miRNA accumulation. Approximately half of the miRNAs detected remained at levels equivalent to those of wild-type plants. However, the accumulation of the remaining miRNAs was either elevated or reduced in the triple mutant. Examination of different single and multiple drb mutants revealed a clear association between the loss of DRB2 activity and altered accumulation for both the elevated and reduced miRNA classes. Furthermore, we show that the constitutive over-expression of DRB2 outside of its wild-type expression domain can compensate for the loss of DRB1 activity in drb1 plants. Conclusions/Significance Our results suggest that in the SAM region, DRB2 is both antagonistic and synergistic to the role of DRB1 in miRNA biogenesis, adding an additional layer of gene regulatory complexity in this developmentally important tissue

A Highly Conserved, Small LTR Retrotransposon that Preferentially Targets Genes in Grass Genomes

LTR retrotransposons are often the most abundant components of plant genomes and can impact gene and genome evolution. Most reported LTR retrotransposons are large elements (>4 kb) and are most often found in heterochromatic (gene poor) regions. We report the smallest LTR retrotransposon found to date, only 292 bp. The element is found in rice, maize, sorghum and other grass genomes, which indicates that it was present in the ancestor of grass species, at least 50–80 MYA. Estimated insertion times, comparisons between sequenced rice lines, and mRNA data indicate that this element may still be active in some genomes. Unlike other LTR retrotransposons, the small LTR retrotransposons (SMARTs) are distributed throughout the genomes and are often located within or near genes with insertion patterns similar to MITEs (miniature inverted repeat transposable elements). Our data suggests that insertions of SMARTs into or near genes can, in a few instances, alter both gene structures and gene expression. Further evidence for a role in regulating gene expression, SMART-specific small RNAs (sRNAs) were identified that may be involved in gene regulation. Thus, SMARTs may have played an important role in genome evolution and genic innovation and may provide a valuable tool for gene tagging systems in grass

Reconstructing the reproductive mode of an Ediacaran macro-organism.

Enigmatic macrofossils of late Ediacaran age (580-541 million years ago) provide the oldest known record of diverse complex organisms on Earth, lying between the microbially dominated ecosystems of the Proterozoic and the Cambrian emergence of the modern biosphere. Among the oldest and most enigmatic of these macrofossils are the Rangeomorpha, a group characterized by modular, self-similar branching and a sessile benthic habit. Localized occurrences of large in situ fossilized rangeomorph populations allow fundamental aspects of their biology to be resolved using spatial point process techniques. Here we use such techniques to identify recurrent clustering patterns in the rangeomorph Fractofusus, revealing a complex life history of multigenerational, stolon-like asexual reproduction, interspersed with dispersal by waterborne propagules. Ecologically, such a habit would have allowed both for the rapid colonization of a localized area and for transport to new, previously uncolonized areas. The capacity of Fractofusus to derive adult morphology by two distinct reproductive modes documents the sophistication of its underlying developmental biology.This work has been supported by the Natural Environment Research Council [grant numbers NE/I005927/1 to C.G.K., NE/J5000045/1 to J.J.M., NE/L011409/1 to A.G.L. and NE/G523539/1 to E.G.M.], and a Henslow Junior Research Fellowship from Cambridge Philosophical Society to A.G.L.This is the author accepted manuscript. The final version is available from NPG via http://dx.doi.org/10.1038/nature1464

Reflexões sobre as roças em São Tomé e Príncipe

O artigo tem como objetivo apresentar elementos constitutivos da história de São Tomé e Príncipe, segundo menor país do continente africano, que tem como língua oficial o português. Diversas leituras e dados coligidos auxiliaram na redação do texto, que define e contextualiza o universo do sistema latifundiário colonial construído nas duas ilhas e apresenta escolhas políticas e sociais realizadas em função desse sistema ao longo de sua história

Leveraging Signatures of Plant Functional Strategies in Wood Density Profiles of African Trees to Correct Mass Estimations From Terrestrial Laser Data

peer reviewedWood density (WD) relates to important tree functions such as stem mechanics and resistance against pathogens. This functional trait can exhibit high intraindividual variability both radially and vertically. With the rise of LiDAR-based methodologies allowing nondestructive tree volume estimations, failing to account for WD variations related to tree function and biomass investment strategies may lead to large systematic bias in AGB estimations. Here, we use a unique destructive dataset from 822 trees belonging to 51 phylogenetically dispersed tree species harvested across forest types in Central Africa to determine vertical gradients in WD from the stump to the branch tips, how these gradients relate to regeneration guilds and their implications for AGB estimations. We find that decreasing WD from the tree base to the branch tips is characteristic of shade-tolerant species, while light-demanding and pioneer species exhibit stationary or increasing vertical trends. Across all species, the WD range is narrower in tree crowns than at the tree base, reflecting more similar physiological and mechanical constraints in the canopy. Vertical gradients in WD induce significant bias (10%) in AGB estimates when using database-derived species-average WD data. However, the correlation between the vertical gradients and basal WD allows the derivation of general correction models. With the ongoing development of remote sensing products providing 3D information for entire trees and forest stands, our findings indicate promising ways to improve greenhouse gas accounting in tropical countries and advance our understanding of adaptive strategies allowing trees to grow and survive in dense rainforests. © 2020, The Author(s)