Mathematics for 2d Interfaces

We present here a survey of recent results concerning the mathematical analysis of instabilities of the interface between two incompressible, non viscous, fluids of constant density and vorticity concentrated on the interface. This configuration includes the so-called Kelvin-Helmholtz (the two densities are equal), Rayleigh-Taylor (two different, nonzero, densities) and the water waves (one of the densities is zero) problems. After a brief review of results concerning strong and weak solutions of the Euler equation, we derive interface equations (such as the Birkhoff-Rott equation) that describe the motion of the interface. A linear analysis allows us to exhibit the main features of these equations (such as ellipticity properties); the consequences for the full, non linear, equations are then described. In particular, the solutions of the Kelvin-Helmholtz and Rayleigh-Taylor problems are necessarily analytic if they are above a certain threshold of regularity (a consequence is the illposedness of the initial value problem in a non analytic framework). We also say a few words on the phenomena that may occur below this regularity threshold. Finally, special attention is given to the water waves problem, which is much more stable than the Kelvin-Helmholtz and Rayleigh-Taylor configurations. Most of the results presented here are in 2d (the interface has dimension one), but we give a brief description of similarities and differences in the 3d case.Comment: Survey. To appear in Panorama et Synth\`ese

Valid auto-models for spatially autocorrelated occupancy and abundance data

Auto-logistic and related auto-models, implemented approximately as autocovariate regression, provide simple and direct modelling of spatial dependence. The autologistic model has been widely applied in ecology since Augustin, Mugglestone and Buckland (J. Appl. Ecol., 1996, 33, 339) analysed red deer census data using a hybrid estimation approach, combining maximum pseudo-likelihood estimation with Gibbs sampling of missing data. However Dormann (Ecol. Model., 2007, 207, 234) questioned the validity of auto-logistic regression, giving examples of apparent underestimation of covariate parameters in analysis of simulated "snouter" data. Dormann et al. (Ecography, 2007, 30, 609) extended this analysis to auto-Poisson and auto-normal models, reporting similar anomalies. All the above studies employ neighbourhood weighting schemes inconsistent with conditions (Besag, J. R. Stat. Soc., Ser. B, 1974, 36, 192) required for auto-model validity; furthermore the auto-Poisson analysis fails to exclude cooperative interactions. We show that all "snouter" anomalies are resolved by correct auto-model implementation. Re-analysis of the red deer data shows that invalid neighbourhood weightings generate only small estimation errors for the full dataset, but larger errors occur on geographic subsamples. A substantial fraction of papers applying auto-logistic regression to ecological data use these invalid weightings, which are default options in the widely used "spdep" spatial dependence package for R. Auto-logistic analyses using invalid neighbourhood weightings will be erroneous to an extent that can vary widely. These analyses can easily be corrected by using valid neighbourhood weightings available in "spdep". The hybrid estimation approach for missing data is readily adapted for valid neighbourhood weighting schemes and is implemented here in R for application to sparse presence-absence data.Comment: Typos corrected in Table 1. Note that defaults in R package 'spdep' have changed in response to this paper; some results using defaults are therefore now version-dependen

Modeling stream fish distributions using interval-censored detection times

Controlling for imperfect detection is important for developing species distribution models (SDMs). Occupancy-detection models based on the time needed to detect a species can be used to address this problem, but this is hindered when times to detection are not known precisely. Here, we extend the time-to-detection model to deal with detections recorded in time intervals and illustrate the method using a case study on stream fish distribution modeling. We collected electrofishing samples of six fish species across a Mediterranean watershed in Northeast Portugal. Based on a Bayesian hierarchical framework, we modeled the probability of water presence in stream channels, and the probability of species occupancy conditional on water presence, in relation to environmental and spatial variables. We also modeled time-to-first detection conditional on occupancy in relation to local factors, using modified interval-censored exponential survival models. Posterior distributions of occupancy probabilities derived from the models were used to produce species distribution maps. Simulations indicated that the modified time-to-detection model provided unbiased parameter estimates despite interval-censoring. There was a tendency for spatial variation in detection rates to be primarily influenced by depth and, to a lesser extent, stream width. Species occupancies were consistently affected by stream order, elevation, and annual precipitation. Bayesian P-values and AUCs indicated that all models had adequate fit and high discrimination ability, respectively. Mapping of predicted occupancy probabilities showed widespread distribution by most species, but uncertainty was generally higher in tributaries and upper reaches. The interval-censored time-to-detection model provides a practical solution to model occupancy-detection when detections are recorded in time intervals. This modeling framework is useful for developing SDMs while controlling for variation in detection rates, as it uses simple data that can be readily collected by field ecologistsinfo:eu-repo/semantics/publishedVersio

Controllability under positivity constraints of multi-d wave equations

We consider both the internal and boundary controllability problems for wave equations under non-negativity constraints on the controls. First, we prove the steady state controllability property with nonnegative controls for a general class of wave equations with time-independent coefficients. According to it, the system can be driven from a steady state generated by a strictly positive control to another, by means of nonnegative controls, when the time of control is long enough. Secondly, under the added assumption of conservation and coercivity of the energy, controllability is proved between states lying on two distinct trajectories. Our methods are described and developed in an abstract setting, to be applicable to a wide variety of control systems

China's soil and groundwater management challenges: Lessons from the UK's experience and opportunities for China

There are a number of specific opportunities for UK and China to work together on contaminated land management issues as China lacks comprehensive and systematic planning for sustainable risk based land management, encompassing both contaminated soil and groundwater and recycling and reuse of soil. It also lacks comprehensive risk assessment systems, structures to support risk management decision making, processes for verification of remediation outcome, systems for record keeping and preservation and integration of contamination issues into land use planning, along with procedures for ensuring effective health and safety considerations during remediation projects, and effective evaluation of costs versus benefits and overall sustainability. A consequence of the absence of these overarching frameworks has been that remediation takes place on an ad hoc basis. At a specific site management level, China lacks capabilities in site investigation and consequent risk assessment systems, in particular related to conceptual modelling and risk evaluation. There is also a lack of shared experience of practical deployment of remediation technologies in China, analogous to the situation before the establishment of the independent, non-profit organisation CL:AIRE (Contaminated Land: Applications In Real Environments) in 1999 in the UK. Many local technology developments are at lab-scale or pilot-scale stage without being widely put into use. Therefore, a shared endeavour is needed to promote the development of technically and scientifically sound land management as well as soil and human health protection to improve the sustainability of the rapid urbanisation in China

Imagerie quantitative de bioluminescence appliquée à un modèle murin syngénique de lymphone exprimant le CD20 humain (analyses de l'influence du volume tumoral sur la réponse au rituximab, et de l'effet thérapeutique de neutrons et de nanoparticules chargées.)

L objectif général du travail de thèse a donc été d analyser le rôle respectif du volume tumoral et des paramètres pharmacocinétiques dans la réponse au rituximab en utilisant des moyens d imagerie adaptés aux modèles murins et à la cancérologie. Dans une première partie nous avons utilisé une lignée lymphomateuse T (El4) syngénique de souris C57Bl6J, transduite par le CD20 humain et transfectée avec le gène de la luciférase. Dans une seconde partie une seule injection de rituximab a été réalisée et la concentration a été évaluée par une méthode ELISA. L analyse des concentrations au cours du temps nous a permis de montrer une très grande variabilité d exposition au rituximab semblable à l observation faite chez l homme. Nous avons pu modéliser les concentrations de rituximab et la progression des foyers tumoraux par la construction d un modèle concentration/effet nous permettant de démontrer l existence d une relation entre l efficacité du rituximab et le volume tumoral. Enfin dans un troisième volet nous avons utilisé le modèle cellulaire afin d évaluer in vitro l usage de particules d oxydes de gadolinium ou de bore.The overall objective of this work of thesis was to analyze the respective role of tumor burden and pharmacokinetic parameters in the response to the rituximab by using systems of imagery adapted to murine models and to cancerology. In a first part of development of the model we used a T lymphoma cell line (El4) syngenic of mouse C57Bl6J, transduted by the human CD20 and transfected with luciferase gene. In a second part, one injection of rituximab was carried out and the circulating concentration was evaluated by an ELISA method. The analysis of the rituximab concentrations in the course of time enabled us to show a very important variability of exposure to the rituximab similar to the observation made for the human. We realized a model of the rituximab concentrations and of the tumors evolution by the construction of a concentration/effect model allowing us to show the existence of a relation between the effectiveness of the rituximab and tumor burden before treatment. Finally in a third part we used the cellular model El4-huCD20-Luc in order to evaluate in vitro the use of gadolinium oxide particles or boron and gadolinium oxide particles.TOURS-Bibl.électronique (372610011) / SudocSudocFranceF