Numerical Solution of a parabolic system with blowup of the solution

In this paper, the author proposes a numerical method to solve a parabolic system of two quasilinear equations of nonlinear heat conduction with sources. The solution of this system may blow up in finite time. It is proved that the numerical solution also may blow up in finite time and an estimate of this time is obtained. The convergence of the scheme is obtained for particular values of the parameters.Comment: 22 page

Analysis of completely discrete finite element method for a free boundary diffusion problem with absorption

AbstractConvergence of truncation methods is obtained for a free boundary problem in R2 with an absorption depending on space and time. Error estimates are derived for the discretization, in space by a P1-finite element method and in time by a backward Euler method

Spectral Dimensionality Reduction

In this paper, we study and put under a common framework a number of non-linear dimensionality reduction methods, such as Locally Linear Embedding, Isomap, Laplacian Eigenmaps and kernel PCA, which are based on performing an eigen-decomposition (hence the name 'spectral'). That framework also includes classical methods such as PCA and metric multidimensional scaling (MDS). It also includes the data transformation step used in spectral clustering. We show that in all of these cases the learning algorithm estimates the principal eigenfunctions of an operator that depends on the unknown data density and on a kernel that is not necessarily positive semi-definite. This helps to generalize some of these algorithms so as to predict an embedding for out-of-sample examples without having to retrain the model. It also makes it more transparent what these algorithm are minimizing on the empirical data and gives a corresponding notion of generalization error. Dans cet article, nous étudions et développons un cadre unifié pour un certain nombre de méthodes non linéaires de réduction de dimensionalité, telles que LLE, Isomap, LE (Laplacian Eigenmap) et ACP à noyaux, qui font de la décomposition en valeurs propres (d'où le nom "spectral"). Ce cadre inclut également des méthodes classiques telles que l'ACP et l'échelonnage multidimensionnel métrique (MDS). Il inclut aussi l'étape de transformation de données utilisée dans l'agrégation spectrale. Nous montrons que, dans tous les cas, l'algorithme d'apprentissage estime les fonctions propres principales d'un opérateur qui dépend de la densité inconnue de données et d'un noyau qui n'est pas nécessairement positif semi-défini. Ce cadre aide à généraliser certains modèles pour prédire les coordonnées des exemples hors-échantillons sans avoir à réentraîner le modèle. Il aide également à rendre plus transparent ce que ces algorithmes minimisent sur les données empiriques et donne une notion correspondante d'erreur de généralisation.non-parametric models, non-linear dimensionality reduction, kernel models, modèles non paramétriques, réduction de dimensionalité non linéaire, modèles à noyau

Boundary feedback controller over a bluff body for prescribed drag and lift coefficients

This paper presents an improved boundary feedback controller for the two and three-dimensional Navier-Stokes equations, in a bounded domain Ω, for prescribed drag and lift coefficients. In order to determine the feedback control law, we consider an extended system coupling the equations governing the Navier-Stokes problem with an equation satisfied by the control on the bluff body, which is a part of the domain boundary. By using the Faedo-Galerkin method and a priori estimation techniques, a stabilizing boundary control is built. This control law ensures the stability of the controlled discrete system. A compactness result then allows us to pass to the limit in the non linear system satisfied by the approximated solutions

Conservation planning with spatially explicit models : a case for horseshoe bats in complex mountain landscapes

This work was partly Funded by the French Ministry of Ecology, Sustainable Development and Energy, France in support of the development of the DEB-MOCHAB project (2013–2015) (Species distribution modelling: a tool for evaluation the conservation of species’ habitats and ecological continuities). This work was also partially supported by the OpenNESS project funded from the European Union’s Seventh Programme for research, technological development and demonstration under grant agreement n° 308428.Context Bats are considered as an ecological indicator of habitat quality due to their sensitivity to human-induced ecosystem changes. Hence, we will focus the study on two indicator species of bats as a proxy to evaluate structure and composition of the landscape to analyze anthropic pressures driving changes in patterns. Objectives This study develops a spatially-explicit model to highlight key habitat nodes and corridors which are integral for maintaining functional landscape connectivity for bat movement. We focus on a complex mountain landscape and two bat species: greater (Rhinolophus ferrumequinum) and lesser (Rhinolophus hipposideros) horseshoe bats which are known to be sensitive to landscape composition and configuration. Methods Species distribution models are used to delineate high-quality foraging habitat for each species using opportunistic ultrasonic bat data. We then performed connectivity analysis combining (modelled) suitable foraging habitat and (known) roost sites. We use graph-theory and the deviation in the probability of connectivity to quantify resilience of the landscape connectivity to perturbations. Results Both species were confined to lowlands (<1000 m elevation) and avoided areas with high road densities. Greater horseshoe bats were more generalist than lesser horseshoe bats which tended to be associated with broadleaved and mixed forests. Conclusions The spatially-explicit models obtained were proven crucial for prioritizing foraging habitats, roost sites and key corridors for conservation. Hence, our results are being used by key stakeholders to help integrate conservation measures into forest management and conservation planning at the regional level. The approach used can be integrated into conservation initiatives elsewhere.PostprintPeer reviewe

Mycoplasma genitalium : a brief review

Mycoplasma genitalium belongs to the class Mollicutes and is the smallest prokaryote capable of independent replication. It was originally isolated from the urethras of two men with non-gonococcal urethritis (NGU). It has a number of characteristics which are similar to its genetically close relative, Mycoplasma pneumoniae, which is an established pathogen of the respiratory tract. M. genitalium lacks a cell wall and has a characteristic pear/flask shape with a terminal tip organelle. This organelle enables M. genitalium to glide along and adhere to moist/mucous surfaces, including host cells. M. genitalium has minimal metabolism, and when compared to the other genital mycoplasmas, has the ability to metabolise glucose. The organism is the smallest self-replicating prokaryote with a genome of only 580 kb pairs and was the second bacterium to have its genome fully sequenced. Its DNA falls under the low G+C category and thus has a lower melting temperature during denaturation in polymerase chain reaction (PCR) assays. The target genes for PCR assays include MgPa, rRNA and gap. M. genitalium has several virulence factors that are responsible for its pathogenicity. These include the ability to adhere to host epithelial cells using the terminal tip organelle with its adhesins, the release of enzymes and the ability to evade the host immune response by antigenic variation.Financial support for this study was obtained from the National Research Foundation of South Africa