A convergent scheme for a non local Hamilton-Jacobi equation modelling dislocation dynamic

We study dislocation dynamics with a level set point of view. The model we present here looks at the zero level set of the solution of a non local Hamilton Jacobi equation, as a dislocation in a plane of a crystal. The front has a normal speed, depending on the solution itself. We prove existence and uniqueness for short time in the set of continuous viscosity solutions. We also present a first order finite difference scheme for the corresponding level set formulation of the model. The scheme is based on monotone numerical Hamiltonian, proposed by Osher and Sethian. The non local character of the problem makesit not monotone. We obtain an explicit convergence rate of the approximate solution to the viscosity solution. We finally provide numerical simulations

Finite-Element Discretization of Static Hamilton-Jacobi Equations Based on a Local Variational Principle

We propose a linear finite-element discretization of Dirichlet problems for static Hamilton-Jacobi equations on unstructured triangulations. The discretization is based on simplified localized Dirichlet problems that are solved by a local variational principle. It generalizes several approaches known in the literature and allows for a simple and transparent convergence theory. In this paper the resulting system of nonlinear equations is solved by an adaptive Gauss-Seidel iteration that is easily implemented and quite effective as a couple of numerical experiments show.Comment: 19 page

Fast Marching Method for Generic Shape from Shading

International audienceWe develop a fast numerical method to approximate the solutions of a wide class of equations associated to the Shape From Shading problem. Our method, which is based on the control theory and the interfaces propagation, is an extension of the ?Fast Marching Method? (FMM) [30,25]. In particular our method extends the FMM to some equations for which the solution is not systematically decreasing along the optimal trajectories. We apply with success our one-pass method to the Shape From Shading equations which are involved by the most relevant and recent modelings [22,21] and which cannot be handled by the most recent extensions of the FMM [26,8]

Efficient Algorithms for Image and High Dimensional Data Processing Using Eikonal Equation on Graphs

International audienceIn this paper we propose an adaptation of the static eikonal equation over weighted graphs of arbitrary structure using a framework of discrete operators. Based on this formulation, we provide explicit solu- tions for the L1,L2 and L∞ norms. Efficient algorithms to compute the explicit solution of the eikonal equation on graphs are also described. We then present several applications of our methodology for image processing such as superpixels decomposition, region based segmentation or patch- based segmentation using non-local configurations. By working on graphs, our formulation provides an unified approach for the processing of any data that can be represented by a graph such as high-dimensional data

Biomarkers of Extracellular Matrix Metabolism (MMP-9 and TIMP-1) and Risk of Stroke, Myocardial Infarction, and Cause-Specific Mortality: Cohort Study

Objective: Turnover of the extracellular matrix in all solid organs is governed mainly by a balance between the degrading matrix metalloproteinases (MMPs) and their tissue inhibitors (TIMPs). An altered extracellular matrix metabolism has been implicated in a variety of diseases. We investigated relations of serum levels of MMP-9 and TIMP-1 to mortality risk from an etiological perspective. Design: The prospective Uppsala Longitudinal Study of Adult Men (ULSAM) cohort, followed from 1991–1995 for up to 18.1 years. A random population-based sample of 1,082 71-year-old men, no loss to follow-up. Endpoints were all-cause (n = 628), cardiovascular (n = 230), non-cardiovascular (n = 398) and cancer mortality (n = 178), and fatal or non-fatal myocardial infarction (n = 138) or stroke (n = 163). Results: Serum MMP-9 and TIMP-1 levels were associated with risk of all-cause mortality (Cox proportional hazard ratio [HR] per standard deviation 1.10, 95% confidence interval [CI] 1.03–1.19; and 1.11, 1.02–1.20; respectively). TIMP-1 levels were mainly related to risks of cardiovascular mortality and stroke (HR per standard deviation 1.22, 95% CI 1.09–1.37; and 1.18, 1.04–1.35; respectively). All relations except those of TIMP-1 to stroke risk were attenuated by adjustment for cardiovascular disease risk factors. Relations in a subsample without cardiovascular disease or cancer were similar to those in the total sample. Conclusion: In this community-based cohort of elderly men, serum MMP-9 and TIMP-1 levels were related to mortality risk. An altered extracellular matrix metabolism may be involved in several detrimental pathways, and circulating MMP-9 or TIMP-1 levels may be relevant markers thereof

Lifelong testicular differentiation in Pleurodeles waltl (Amphibia, Caudata)

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The Entomopathogenic Bacterial Endosymbionts Xenorhabdus and Photorhabdus: Convergent Lifestyles from Divergent Genomes

Members of the genus Xenorhabdus are entomopathogenic bacteria that associate with nematodes. The nematode-bacteria pair infects and kills insects, with both partners contributing to insect pathogenesis and the bacteria providing nutrition to the nematode from available insect-derived nutrients. The nematode provides the bacteria with protection from predators, access to nutrients, and a mechanism of dispersal. Members of the bacterial genus Photorhabdus also associate with nematodes to kill insects, and both genera of bacteria provide similar services to their different nematode hosts through unique physiological and metabolic mechanisms. We posited that these differences would be reflected in their respective genomes. To test this, we sequenced to completion the genomes of Xenorhabdus nematophila ATCC 19061 and Xenorhabdus bovienii SS-2004. As expected, both Xenorhabdus genomes encode many anti-insecticidal compounds, commensurate with their entomopathogenic lifestyle. Despite the similarities in lifestyle between Xenorhabdus and Photorhabdus bacteria, a comparative analysis of the Xenorhabdus, Photorhabdus luminescens, and P. asymbiotica genomes suggests genomic divergence. These findings indicate that evolutionary changes shaped by symbiotic interactions can follow different routes to achieve similar end points

Azospirillum Genomes Reveal Transition of Bacteria from Aquatic to Terrestrial Environments

Fossil records indicate that life appeared in marine environments ∼3.5 billion years ago (Gyr) and transitioned to terrestrial ecosystems nearly 2.5 Gyr. Sequence analysis suggests that “hydrobacteria” and “terrabacteria” might have diverged as early as 3 Gyr. Bacteria of the genus Azospirillum are associated with roots of terrestrial plants; however, virtually all their close relatives are aquatic. We obtained genome sequences of two Azospirillum species and analyzed their gene origins. While most Azospirillum house-keeping genes have orthologs in its close aquatic relatives, this lineage has obtained nearly half of its genome from terrestrial organisms. The majority of genes encoding functions critical for association with plants are among horizontally transferred genes. Our results show that transition of some aquatic bacteria to terrestrial habitats occurred much later than the suggested initial divergence of hydro- and terrabacterial clades. The birth of the genus Azospirillum approximately coincided with the emergence of vascular plants on land