Interior penalty discontinuous Galerkin FEM for the p(x)p(x)-Laplacian

In this paper we construct an "Interior Penalty" Discontinuous Galerkin method to approximate the minimizer of a variational problem related to the $p(x)-$Laplacian. The function $p:\Omega\to [p_1,p_2]$ is log H\"{o}lder continuous and $1<p_1\leq p_2<\infty$. We prove that the minimizers of the discrete functional converge to the solution. We also make some numerical experiments in dimension one to compare this method with the Conforming Galerkin Method, in the case where $p_1$ is close to one. This example is motivated by its applications to image processing.Comment: 26 pages, 2 figure

The Stokes and Poisson problem in variable exponent spaces

We study the Stokes and Poisson problem in the context of variable exponent spaces. We prove the existence of strong and weak solutions for bounded domains with C^{1,1} boundary with inhomogenous boundary values. The result is based on generalizations of the classical theories of Calderon-Zygmund and Agmon-Douglis-Nirenberg to variable exponent spaces.Comment: 20 pages, 1 figur

A Monte Carlo framework for denoising and missing wedge reconstruction in cryo-electron tomography

International audienceWe propose a statistical method to address an important issue in cryo electron to-mography image analysis: reduction of a high amount of noise and artifacts due to the presence of a missing wedge (MW) in the spectral domain. The method takes as an input a 3D tomogram derived from limited-angle tomography, and gives as an output a 3D denoised and artifact compensated tomogram. The artifact compensation is achieved by filling up the MW with meaningful information. The method can be used to enhance visualization or as a pre-processing step for image analysis, including segmentation and classification. Results are presented for both synthetic and experimental data

Interpolation in variable exponent spaces

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale

Variable exponent Besov-Morrey spaces

In this paper we introduce Besov-Morrey spaces with all indices variable and study some fundamental properties. This includes a description in terms of Peetre maximal functions and atomic and molecular decompositions. This new scale of non-standard function spaces requires the introduction of variable exponent mixed Morrey-sequence spaces, which in turn are defined within the framework of semimodular spaces. In particular, we obtain a convolution inequality involving special radial kernels, which proves to be a key tool in this work.publishe

DNA Damage during G2 Phase Does Not Affect Cell Cycle Progression of the Green Alga Scenedesmus quadricauda

DNA damage is a threat to genomic integrity in all living organisms. Plants and green algae are particularly susceptible to DNA damage especially that caused by UV light, due to their light dependency for photosynthesis. For survival of a plant, and other eukaryotic cells, it is essential for an organism to continuously check the integrity of its genetic material and, when damaged, to repair it immediately. Cells therefore utilize a DNA damage response pathway that is responsible for sensing, reacting to and repairing damaged DNA. We have studied the effect of 5-fluorodeoxyuridine, zeocin, caffeine and combinations of these on the cell cycle of the green alga Scenedesmus quadricauda. The cells delayed S phase and underwent a permanent G2 phase block if DNA metabolism was affected prior to S phase; the G2 phase block imposed by zeocin was partially abolished by caffeine. No cell cycle block was observed if the treatment with zeocin occurred in G2 phase and the cells divided normally. CDKA and CDKB kinases regulate mitosis in S. quadricauda; their kinase activities were inhibited by Wee1. CDKA, CDKB protein levels were stabilized in the presence of zeocin. In contrast, the protein level of Wee1 was unaffected by DNA perturbing treatments. Wee1 therefore does not appear to be involved in the DNA damage response in S. quadricauda. Our results imply a specific reaction to DNA damage in S. quadricauda, with no cell cycle arrest, after experiencing DNA damage during G2 phase