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

SINE RNA Induces Severe Developmental Defects in Arabidopsis thaliana and Interacts with HYL1 (DRB1), a Key Member of the DCL1 Complex

The proper temporal and spatial expression of genes during plant development is governed, in part, by the regulatory activities of various types of small RNAs produced by the different RNAi pathways. Here we report that transgenic Arabidopsis plants constitutively expressing the rapeseed SB1 SINE retroposon exhibit developmental defects resembling those observed in some RNAi mutants. We show that SB1 RNA interacts with HYL1 (DRB1), a double-stranded RNA-binding protein (dsRBP) that associates with the Dicer homologue DCL1 to produce microRNAs. RNase V1 protection assays mapped the binding site of HYL1 to a SB1 region that mimics the hairpin structure of microRNA precursors. We also show that HYL1, upon binding to RNA substrates, induces conformational changes that force single-stranded RNA regions to adopt a structured helix-like conformation. Xenopus laevis ADAR1, but not Arabidopsis DRB4, binds SB1 RNA in the same region as HYL1, suggesting that SINE RNAs bind only a subset of dsRBPs. Consistently, DCL4-DRB4-dependent miRNA accumulation was unchanged in SB1 transgenic Arabidopsis, whereas DCL1-HYL1-dependent miRNA and DCL1-HYL1-DCL4-DRB4-dependent tasiRNA accumulation was decreased. We propose that SINE RNA can modulate the activity of the RNAi pathways in plants and possibly in other eukaryotes

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

Separate and combined analysis of successive dependent outcomes after breast-conservation surgery: recurrence, metastases, second cancer and death

<p>Abstract</p> <p>Background</p> <p>In the setting of recurrent events, research studies commonly count only the first occurrence of an outcome in a subject. However this approach does not correctly reflect the natural history of the disease. The objective is to jointly identify prognostic factors associated with locoregional recurrences (LRR), contralateral breast cancer, distant metastases (DM), other primary cancer than breast and breast cancer death and to evaluate the correlation between these events.</p> <p>Methods</p> <p>Patients (n = 919) with a primary invasive breast cancer and treated in a cancer center in South-Western France with breast-conserving surgery from 1990 to 1994 and followed up to January 2006 were included. Several types of non-independent events could be observed for the same patient: a LRR, a contralateral breast cancer, DM, other primary cancer than breast and breast cancer death. Data were analyzed separately and together using a random-effects survival model.</p> <p>Results</p> <p>LRR represent the most frequent type of first failure (14.6%). The risk of any event is higher for young women (less than 40 years old) and in the first 10 years of follow-up after the surgery. In the combined analysis histological tumor size, grade, number of positive nodes, progesterone receptor status and treatment combination are prognostic factors of any event. The results show a significant dependence between these events with a successively increasing risk of a new event after the first and second event. The risk of developing a new failure is greatly increased (RR = 4.25; 95%CI: 2.51-7.21) after developing a LRR, but also after developing DM (RR = 3.94; 95%CI: 2.23-6.96) as compared to patients who did not develop a first event.</p> <p>Conclusion</p> <p>We illustrated that the random effects survival model is a more satisfactory method to evaluate the natural history of a disease with multiple type of events.</p

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

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