Reduction and reconstruction of stochastic differential equations via symmetries

An algorithmic method to exploit a general class of infinitesimal symmetries for reducing stochastic differential equations is presented and a natural definition of reconstruction, inspired by the classical reconstruction by quadratures, is proposed. As a side result the well-known solution formula for linear one-dimensional stochastic differential equations is obtained within this symmetry approach. The complete procedure is applied to several examples with both theoretical and applied relevance

Genetically engineered bananas resistant to Xanthomonas wilt disease and nematodes

Banana is an important staple food crop feeding more than 100 million Africans, but is subject to severe productivity constraints due to a range of pests and diseases. Banana Xanthomonas wilt caused by Xanthomonas campestris pv. musacearum is capable of entirely destroying a plantation while nematodes can cause losses up to 50% and increase susceptibility to other pests and diseases. Development of improved varieties of banana is fundamental in order to tackle these challenges. However, the sterile nature of the crop and the lack of resistance in Musa germplasm make improvement by traditional breeding techniques either impossible or extremely slow. Recent developments using genetic engineering have begun to address these problems. Transgenic banana expressing sweet pepper Hrap and Pflp genes have demonstrated complete resistance against X. campestris pv. musacearum in the field. Transgenic plantains expressing a cysteine proteinase inhibitors and/or synthetic peptide showed enhanced resistance to a mixed species population of nematodes in the field. Here, we review the genetic engineering technologies which have potential to improve agriculture and food security in Africa

6-Meth­oxy-2,3,4,9-tetra­hydro-1H-carbazol-1-one

The carbazole unit of the title mol­ecule, C13H13NO2, is not planar. The dihedral angle between the benzene ring and the pyrrole ring is 1.69 (6)°. The cyclo­hexene ring adopts an envelope conformation. Inter­molecular C—H⋯O and N—H⋯O hydrogen bonds are present in the crystal structure. A C—H⋯π inter­action, involving the benzene ring, is also found in the crystal structure

Liver transplantation in the critically ill: a multicenter Canadian retrospective cohort study

Introduction: Critically ill cirrhosis patients awaiting liver transplantation (LT) often receive prioritization for organ allocation. Identification of patients most likely to benefit is essential. The purpose of this study was to examine whether the Sequential Organ Failure Assessment (SOFA) score can predict 90-day mortality in critically ill recipients of LT and whether it can predict receipt of LT among critically ill cirrhosis listed awaiting LT. Methods: We performed a multicenter retrospective cohort study consisting of two datasets: (a) all critically-ill cirrhosis patients requiring intensive care unit (ICU) admission before LT at five transplant centers in Canada from 2000 through 2009 (one site, 1990 through 2009), and (b) critically ill cirrhosis patients receiving LT from ICU (n = 115) and those listed but not receiving LT before death (n = 106) from two centers where complete data were available. Results: In the first dataset, 198 critically ill cirrhosis patients receiving LT (mean (SD) age 53 (10) years, 66% male, median (IQR) model for end-stage liver disease (MELD) 34 (26-39)) were included. Mean (SD) SOFA scores at ICU admission, at 48 hours, and at LT were 12.5 (4), 13.0 (5), and 14.0 (4). Survival at 90 days was 84% (n = 166). In multivariable analysis, only older age was independently associated with reduced 90-day survival (odds ratio (OR), 1.07; 95% CI, 1.01 to 1.14; P = 0.013). SOFA score did not predict 90-day mortality at any time. In the second dataset, 47.9% (n = 106) of cirrhosis patients listed for LT died in the ICU waiting for LT. In multivariable analysis, higher SOFA at 48 hours after admission was independently associated with lower probability of receiving LT (OR, 0.89; 95% CI, 0.82 to 0.97; P = 0.006). When including serum lactate and SOFA at 48 hours in the final model, elevated lactate (at 48 hours) was also significantly associated with lower likelihood of receiving LT (0.32; 0.17 to 0.61; P = 0.001). Conclusions: SOFA appears poor at predicting 90-day survival in critically ill cirrhosis patients after LT, but higher SOFA score and elevated lactate 48 hours after ICU admission are associated with a lower probability receiving LT. Older critically ill cirrhosis patients (older than 60) receiving LT have worse 90-day survival and should be considered for LT with caution

Boundary-crossing identities for diffusions having the time-inversion property

We review and study a one-parameter family of functional transformations, denoted by (S (β)) β∈ℝ, which, in the case β<0, provides a path realization of bridges associated to the family of diffusion processes enjoying the time-inversion property. This family includes Brownian motions, Bessel processes with a positive dimension and their conservative h-transforms. By means of these transformations, we derive an explicit and simple expression which relates the law of the boundary-crossing times for these diffusions over a given function f to those over the image of f by the mapping S (β), for some fixed β∈ℝ. We give some new examples of boundary-crossing problems for the Brownian motion and the family of Bessel processes. We also provide, in the Brownian case, an interpretation of the results obtained by the standard method of images and establish connections between the exact asymptotics for large time of the densities corresponding to various curves of each family

Regularity of Ornstein-Uhlenbeck processes driven by a L{\'e}vy white noise

The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by L\'evy white noise "obtained by subordination of a Gaussian white noise". Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general \cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.Comment: This is an updated version of the same paper. In fact, it has already been publishe

Phylogeny.fr: robust phylogenetic analysis for the non-specialist

Phylogenetic analyses are central to many research areas in biology and typically involve the identification of homologous sequences, their multiple alignment, the phylogenetic reconstruction and the graphical representation of the inferred tree. The Phylogeny.fr platform transparently chains programs to automatically perform these tasks. It is primarily designed for biologists with no experience in phylogeny, but can also meet the needs of specialists; the first ones will find up-to-date tools chained in a phylogeny pipeline to analyze their data in a simple and robust way, while the specialists will be able to easily build and run sophisticated analyses. Phylogeny.fr offers three main modes. The ‘One Click’ mode targets non-specialists and provides a ready-to-use pipeline chaining programs with recognized accuracy and speed: MUSCLE for multiple alignment, PhyML for tree building, and TreeDyn for tree rendering. All parameters are set up to suit most studies, and users only have to provide their input sequences to obtain a ready-to-print tree. The ‘Advanced’ mode uses the same pipeline but allows the parameters of each program to be customized by users. The ‘A la Carte’ mode offers more flexibility and sophistication, as users can build their own pipeline by selecting and setting up the required steps from a large choice of tools to suit their specific needs. Prior to phylogenetic analysis, users can also collect neighbors of a query sequence by running BLAST on general or specialized databases. A guide tree then helps to select neighbor sequences to be used as input for the phylogeny pipeline. Phylogeny.fr is available at: http://www.phylogeny.fr