Rearranged Stochastic Heat Equation

The purpose of this work is to provide an explicit construction of a strong Feller semigroup on the space of probability measures over the real line that additionally maps bounded measurable functions into Lipschitz continuous functions, with a Lipschitz constant that blows up in an integrable manner in small time. Our construction relies on a rearranged version of the stochastic heat equation on the circle driven by a coloured noise. Formally, this stochastic equation writes as a reflected equation in infinite dimension, a topic that is known to be challenging. Under the action of the rearrangement, the solution is forced to live in a space of quantile functions that is isometric to the space of probability measures on the real line. We prove the equation to be solvable by means of an Euler scheme in which we alternate flat dynamics in the space of random variables on the circle with a rearrangement operation that projects back the random variables onto the subset of quantile functions. A first challenge is to prove that this scheme is tight. A second one is to provide a consistent theory for the limiting reflected equation and in particular to interpret in a relevant manner the reflection term. The last step in our work is to establish the aforementioned Lipschitz property of the semigroup by adapting earlier ideas from the Bismut-Elworthy-Li formula in stochastic analysis

Taille de la population d’Avahi laniger dans la réserve d’Ambodiriana-Manompana, Nord-est de Madagascar

Avahi laniger est le seul lémurien nocturne appartenant à la famille des Indriidae qui habite les forêts humides de l’est de Madagascar (Mittermeier et. al., 2010) dont une partie disparaît chaque année (exploitation du bois, pratique du «tavy» ou culture sur brûlis) (Beaucent and Fayolle, 2011; Lehman and Wright, 2000). La fragmentation et la destruction de leur habitat ainsi que la chasse menacent la survie de nombreuses espèces de lémuriens incluant celle de A. laniger (Jenkins et. al., 2011; Rakotondravony and Rabenandrasana, 2011; Anderson, Rowcliffe and Cowlishaw, 2007). Nous avons réalisé, entre fin Avril et Mai 2012, une étude de densité de la population de A. laniger au sein de l’aire protégée de Manompana-Ambodiriana afin d’estimer la taille de la population totale et de déterminer l’impact du projet de conservation menée par l’Association de Défense de la Forêt d’Ambodiriana (ADEFA) qui recherche l’évolution démographique à moyen terme de cette espèce."LABEX" TULIP: (ANR-10-LABX-41), fct fellowship: (SFRH/BD/64875/2009)

Evaluating postoperative rotator cuff healing: Prospective comparison of MRI and ultrasound

AbstractBackgroundThe objective of this prospective comparative single centre study was to compare postoperative rotator cuff healing rates as assessed by magnetic resonance imaging (MRI) versus ultrasonography (US).Material and methodsBetween October 2012 and February 2013, 61 patients underwent arthroscopic repair of postero-superior rotator cuff tears. Each patient underwent MRI and US 6 months later. The findings were assessed independently by two observers. We compared intra-observer and inter-observer levels of agreement regarding healing rates assessed by MRI and US.ResultsIntra-observer agreement regarding the MRI interpretation was 95% (κ coefficient, 0.83) for one observer and 98% (κ coefficient, 0.94) for the other. Values of κ for inter-observer agreement ranged across readings from 0.76 to 0.90. When MRI was taken as the reference, US had 80% sensitivity and 98% specificity.DiscussionMRI and US provide similar assessments of postoperative rotator cuff healing, although US is less sensitive. Intra-observer and inter-observer agreements are very good.Level of evidenceIII

Large Deviations Analysis for Distributed Algorithms in an Ergodic Markovian Environment

We provide a large deviations analysis of deadlock phenomena occurring in distributed systems sharing common resources. In our model transition probabilities of resource allocation and deallocation are time and space dependent. The process is driven by an ergodic Markov chain and is reflected on the boundary of the d-dimensional cube. In the large resource limit, we prove Freidlin-Wentzell estimates, we study the asymptotic of the deadlock time and we show that the quasi-potential is a viscosity solution of a Hamilton-Jacobi equation with a Neumann boundary condition. We give a complete analysis of the colliding 2-stacks problem and show an example where the system has a stable attractor which is a limit cycle

Probabilistic analysis of the upwind scheme for transport

We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical solution. We then understand that the error induced by the scheme is governed by the fluctuations of the Markov chain around the characteristics of the flow. We show, in various situations, that the fluctuations are of diffusive type. As a by-product, we prove that the scheme is of order 1/2 for an initial datum in BV and of order 1/2-a, for all a>0, for a Lipschitz continuous initial datum. Our analysis provides a new interpretation of the numerical diffusion phenomenon

Targeting intratumoral B cells with rituximab in addition to CHOP in angioimmunoblastic T-cell lymphoma. A clinicobiological study of the GELA.

Background In angioimmunoblastic T-cell lymphoma, symptoms linked to B-lymphocyte activation are common, and variable numbers of CD20(+) large B-blasts, often infected by Epstein-Barr virus, are found in tumor tissues. We postulated that the disruption of putative B-T interactions and/or depletion of the Epstein-Barr virus reservoir by an anti-CD20 monoclonal antibody (rituximab) could improve the clinical outcome produced by conventional chemotherapy. DESIGN AND METHODS: Twenty-five newly diagnosed patients were treated, in a phase II study, with eight cycles of rituximab + chemotherapy (R-CHOP21). Tumor infiltration, B-blasts and Epstein-Barr virus status in tumor tissue and peripheral blood were fully characterized at diagnosis and were correlated with clinical outcome. RESULTS: A complete response rate of 44% (95% CI, 24% to 65%) was observed. With a median follow-up of 24 months, the 2-year progression-free survival rate was 42% (95% CI, 22% to 61%) and overall survival rate was 62% (95% CI, 40% to 78%). The presence of Epstein-Barr virus DNA in peripheral blood mononuclear cells (14/21 patients) correlated with Epstein-Barr virus score in lymph nodes (P<0.004) and the detection of circulating tumor cells (P=0.0019). Despite peripheral Epstein-Barr virus clearance after treatment, the viral load at diagnosis (>100 copy/μg DNA) was associated with shorter progression-free survival (P=0.06). Conclusions We report here the results of the first clinical trial targeting both the neoplastic T cells and the microenvironment-associated CD20(+) B lymphocytes in angioimmunoblastic T-cell lymphoma, showing no clear benefit of adding rituximab to conventional chemotherapy. A strong relationship, not previously described, between circulating Epstein-Barr virus and circulating tumor cells is highlighted

A non-hybrid method for the PDF equations of turbulent flows on unstructured grids

In probability density function (PDF) methods of turbulent flows, the joint PDF of several flow variables is computed by numerically integrating a system of stochastic differential equations for Lagrangian particles. A set of parallel algorithms is proposed to provide an efficient solution of the PDF transport equation, modeling the joint PDF of turbulent velocity, frequency and concentration of a passive scalar in geometrically complex configurations. An unstructured Eulerian grid is employed to extract Eulerian statistics, to solve for quantities represented at fixed locations of the domain (e.g. the mean pressure) and to track particles. All three aspects regarding the grid make use of the finite element method (FEM) employing the simplest linear FEM shape functions. To model the small-scale mixing of the transported scalar, the interaction by exchange with the conditional mean model is adopted. An adaptive algorithm that computes the velocity-conditioned scalar mean is proposed that homogenizes the statistical error over the sample space with no assumption on the shape of the underlying velocity PDF. Compared to other hybrid particle-in-cell approaches for the PDF equations, the current methodology is consistent without the need for consistency conditions. The algorithm is tested by computing the dispersion of passive scalars released from concentrated sources in two different turbulent flows: the fully developed turbulent channel flow and a street canyon (or cavity) flow. Algorithmic details on estimating conditional and unconditional statistics, particle tracking and particle-number control are presented in detail. Relevant aspects of performance and parallelism on cache-based shared memory machines are discussed.Comment: Accepted in Journal of Computational Physics, Feb. 20, 200