Exponential convergence rate of ruin probabilities for level-dependent L\'evy-driven risk processes

We explicitly find the rate of exponential long-term convergence for the ruin probability in a level-dependent L\'evy-driven risk model, as time goes to infinity. Siegmund duality allows to reduce the pro blem to long-term convergence of a reflected jump-diffusion to its stationary distribution, which is handled via Lyapunov functions.Comment: 20 pages, 5 figure

PathExpress: a web-based tool to identify relevant pathways in gene expression data

PathExpress is a web-based tool developed to interpret gene expression data obtained from microarray experiments by identifying the most relevant metabolic pathways associated with a subset of genes (e.g. differentially expressed genes). A graphical pathway representation permits the visualization of the expressed genes in a functional context. Based on the publicly accessible KEGG Ligand database, PathExpress can be adapted to any organism and is currently available for seven Affymetrix genome arrays. About 20% of the probe sets of each array have been assigned to Enzyme Commission numbers by homology relationship and linked to corresponding metabolic pathways

Polynomial approximations for bivariate aggregate claims amount probability distributions

A numerical method to compute bivariate probability distributions from their Laplace transforms is presented. The method consists in an orthogonal projection of the probability density function with respect to a probability measure that belongs to a Natural Exponential Family with Quadratic Variance Function (NEF-QVF). A particular link to Lancaster probabilities is highlighted. The procedure allows a quick and accurate calculation of probabilities of interest and does not require strong coding skills. Numerical illustrations and comparisons with other methods are provided. This work is motivated by actuarial applications. We aim at recovering the joint distribution of two aggregate claims amounts associated with two insurance policy portfolios that are closely related, and at computing survival functions for reinsurance losses in presence of two non-proportional reinsurance treaties

Approximate Bayesian Computations to fit and compare insurance loss models

Approximate Bayesian Computation (ABC) is a statistical learning technique to calibrate and select models by comparing observed data to simulated data. This technique bypasses the use of the likelihood and requires only the ability to generate synthetic data from the models of interest. We apply ABC to fit and compare insurance loss models using aggregated data. We present along the way how to use ABC for the more common claim counts and claim sizes data. A state-of-the-art ABC implementation in Python is proposed. It uses sequential Monte Carlo to sample from the posterior distribution and the Wasserstein distance to compare the observed and synthetic data

The 2HA line of Medicago truncatula has characteristics of an epigenetic mutant that is weakly ethylene insensitive

BACKGROUND The Medicago truncatula 2HA seed line is highly embryogenic while the parental line Jemalong rarely produces embryos. The 2HA line was developed from one of the rare Jemalong regenerates and this method for obtaining a highly regenerable genotype in M. truncatula is readily reproducible suggesting an epigenetic mechanism. Microarray transcriptomic analysis showed down regulation of an ETHYLENE INSENSITIVE 3-like gene in 2HA callus which provided an approach to investigating epigenetic regulation of genes related to ethylene signalling and the 2HA phenotype. Ethylene is involved in many developmental processes including somatic embryogenesis (SE) and is associated with stress responses. RESULTS Microarray transcriptomic analysis showed a significant number of up-regulated transcripts in 2HA tissue culture, including nodule and embryo specific genes and transposon-like genes, while only a few genes were down-regulated, including an EIN3-like gene we called MtEIL1. This reduced expression was associated with ethylene insensitivity of 2HA plants that was further investigated. The weak ethylene insensitivity affected root and nodule development. Sequencing of MtEIL1 found no difference between 2HA and wild-type plants. DNA methylation analysis of MtEIL1 revealed significant difference between 2HA and wild-type plants. Tiling arrays demonstrated an elevated level of miRNA in 2HA plants that hybridised to the antisense strand of the MtEIL1 gene. AFLP-like methylation profiling revealed more differences in DNA methylation between 2HA and wild-type. Segregation analysis demonstrated the recessive nature of the eil1 phenotype and the dominant nature of the SE trait. CONCLUSIONS We have demonstrated that EIL1 of Medicago truncatula (MtEIL1) is epigenetically silenced in the 2HA seed line. The possible cause is an elevated level of miRNA that targets its 3'UTR and is also associated with DNA methylation of MtEIL1. Down regulation of MtEIL1 makes it possible to form nodules in the presence of ethylene and affects root growth under normal conditions. Segregation analysis showed no association between MtEIL1 expression and SE in culture but the role and mechanism of ethylene signalling in the process of plant regeneration through SE requires further investigation. The work also suggests that epigenetic changes to a particular gene induced in culture can be fixed in regenerated plants.This work was funded by the Australian Research Council (CEO348212) through the ARC Centre of Excellence for Integrative Legume Research (CILR)

A polynomial expansion to approximate the ultimate ruin probability in the compound Poisson ruin model

International audienceA numerical method to approximate ruin probabilities is proposed within the frame of a compound Poisson ruin model. The defective density function associated to the ruin probability is projected in an orthogonal polynomial system. These polynomials are orthogonal with respect to a probability measure that belongs to Natural Exponential Family with Quadratic Variance Function (NEF-QVF). The method is convenient in at least four ways. Firstly, it leads to a simple analytical expression of the ultimate ruin probability. Secondly, the implementation does not require strong computer skills. Thirdly, our approximation method does not necessitate any preliminary discretisation step of the claim sizes distribution. Finally, the coefficients of our formula do not depend on initial reserves

Des programmes de chimie à leur mise en oeuvre

Depuis la rentrée scolaire 1993-1994, au collège et au lycée, sont entrés en vigueur de nouveaux programmes de chimie. Cet article présente quelques-unes des raisons qui ont motivé l'écriture de ceux-ci autour de thèmes liés à des problèmes de la vie quotidienne. Si les programmes sont novateurs, l'innovation est-elle obligatoirement au bout du chemin ? Pas sûr..

Genome-wide transcriptional analysis of super-embryogenic Medicago truncatula explant cultures

Background. The Medicago truncatula (M. truncatula) line 2HA has a 500-fold greater capacity to regenerate plants in culture by somatic embryogenesis than its wild type progenitor Jemalong. To understand the molecular basis for the regeneration capacity of this super-embryogenic line 2HA, using Affymetrix GeneChip, we have compared transcriptomes of explant leaf cultures of these two lines that were grown on media containing the auxin NAA (1-naphthaleneacetic acid) and the cytokinin BAP (6-benzylaminopurine) for two weeks, an early time point for tissue culture proliferation. Results. Using Affymetrix GeneChip, GCRMA normalisation and statistical analysis, we have shown that more than 196 and 49 probe sets were significantly (p < 0.05) up- or down-regulated respectively more than 2 fold in expression. We have utilised GeneBins, a database for classifying gene expression data to distinguish differentially displayed pathways among these two cultures which showed changes in number of biochemical pathways including carbon and flavonoid biosynthesis, phytohormone biosynthesis and signalling. The up-regulated genes in the embryogenic 2HA culture included nodulins, transporters, regulatory genes, embryogenesis related arabinogalactans and genes involved in redox homeostasis, the transition from vegetative growth to reproductive growth and cytokinin signalling. Down-regulated genes included protease inhibitors, wound-induced proteins, and genes involved in biosynthesis and signalling of phytohormones auxin, gibberellin and ethylene. These changes indicate essential differences between the super-embryogenic line 2HA and Jemalong not only in many aspects of biochemical pathways but also in their response to auxin and cytokinin. To validate the GeneChip results, we used quantitative real-time RT-PCR to examine the expression of the genes up-regulated in 2HA such as transposase, RNA-directed DNA polymerase, glycoside hydrolase, RESPONSE REGULATOR 10, AGAMOUS-LIKE 20, flower promoting factor 1, nodulin 3, fasciclin and lipoxygenase, and a down-regulated gene ETHYLENE INSENSITIVE 3, all of which positively correlated with the microarray data. Conclusion. We have described the differences in transcriptomes between the M. truncatula super-embryogenic line 2HA and its non-embryogenic progenitor Jemalong at an early time point. This data will facilitate the mapping of regulatory and metabolic networks involved in the gaining totipotency and regeneration capacity in M. truncatula and provides candidate genes for functional analysis