A general wavelet-based profile decomposition in the critical embedding of function spaces

We characterize the lack of compactness in the critical embedding of functions spaces $X\subset Y$ having similar scaling properties in the following terms : a sequence $(u_n)_{n\geq 0}$ bounded in $X$ has a subsequence that can be expressed as a finite sum of translations and dilations of functions $(\phi_l)_{l>0}$ such that the remainder converges to zero in $Y$ as the number of functions in the sum and $n$ tend to $+\infty$. Such a decomposition was established by G\'erard for the embedding of the homogeneous Sobolev space $X=\dot H^s$ into the $Y=L^p$ in $d$ dimensions with $0<s=d/2-d/p$, and then generalized by Jaffard to the case where $X$ is a Riesz potential space, using wavelet expansions. In this paper, we revisit the wavelet-based profile decomposition, in order to treat a larger range of examples of critical embedding in a hopefully simplified way. In particular we identify two generic properties on the spaces $X$ and $Y$ that are of key use in building the profile decomposition. These properties may then easily be checked for typical choices of $X$ and $Y$ satisfying critical embedding properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, H\"older and BMO spaces.Comment: 24 page

Agrometerological study of semi-arid areas : an experiment for analysing the potential of time series of FORMOSAT-2 images (Tensift-Marrakech plain)

Earth Observing Systems designed to provide both high spatial resolution (10m) and high capacity of time revisit (a few days) offer strong opportunities for the management of agricultural water resources. The FORMOSAT-2 satellite is the first and only satellite with the ability to provide daily high-resolution images over a particular area with constant viewing angles. As part of the SudMed project, one of the first time series of FORMOSAT-2 images has been acquired over the semi-arid Tensift-Marrakech plain. Along with these acquisitions, an experimental data set has been collected to monitor land-cover/land-use, soil characteristics, vegetation dynamics and surface fluxes. This paper presents a first analysis of the potential of these data for agrometerological study of semi-arid areas

Entrainment of the Mammalian Cell Cycle by the Circadian Clock: Modeling Two Coupled Cellular Rhythms

The cell division cycle and the circadian clock represent two major cellular rhythms. These two periodic processes are coupled in multiple ways, given that several molecular components of the cell cycle network are controlled in a circadian manner. For example, in the network of cyclin-dependent kinases (Cdks) that governs progression along the successive phases of the cell cycle, the synthesis of the kinase Wee1, which inhibits the G2/M transition, is enhanced by the complex CLOCK-BMAL1 that plays a central role in the circadian clock network. Another component of the latter network, REV-ERBα, inhibits the synthesis of the Cdk inhibitor p21. Moreover, the synthesis of the oncogene c-Myc, which promotes G1 cyclin synthesis, is repressed by CLOCK-BMAL1. Using detailed computational models for the two networks we investigate the conditions in which the mammalian cell cycle can be entrained by the circadian clock. We show that the cell cycle can be brought to oscillate at a period of 24 h or 48 h when its autonomous period prior to coupling is in an appropriate range. The model indicates that the combination of multiple modes of coupling does not necessarily facilitate entrainment of the cell cycle by the circadian clock. Entrainment can also occur as a result of circadian variations in the level of a growth factor controlling entry into G1. Outside the range of entrainment, the coupling to the circadian clock may lead to disconnected oscillations in the cell cycle and the circadian system, or to complex oscillatory dynamics of the cell cycle in the form of endoreplication, complex periodic oscillations or chaos. The model predicts that the transition from entrainment to 24 h or 48 h might occur when the strength of coupling to the circadian clock or the level of growth factor decrease below critical values

Lack of group X secreted phospholipase A₂ increases survival following pandemic H1N1 influenza infection

The role of Group X secreted phospholipase A2 (GX-sPLA2) during influenza infection has not been previously investigated. We examined the role of GX-sPLA2 during H1N1 pandemic influenza infection in a GX-sPLA2 gene targeted mouse (GX−/−) model and found that survival after infection was significantly greater in GX−/− mice than in GX+/+ mice. Downstream products of GX-sPLA2 activity, PGD2, PGE2, LTB4, cysteinyl leukotrienes and Lipoxin A4 were significantly lower in GX−/− mice BAL fluid. Lung microarray analysis identified an earlier and more robust induction of T and B cell associated genes in GX−/− mice. Based on the central role of sPLA2 enzymes as key initiators of inflammatory processes, we propose that activation of GX-sPLA2 during H1N1pdm infection is an early step of pulmonary inflammation and its inhibition increases adaptive immunity and improves survival. Our findings suggest that GX-sPLA2 may be a potential therapeutic target during influenza

Sub-terahertz, microwaves and high energy emissions during the December 6, 2006 flare, at 18:40 UT

The presence of a solar burst spectral component with flux density increasing with frequency in the sub-terahertz range, spectrally separated from the well-known microwave spectral component, bring new possibilities to explore the flaring physical processes, both observational and theoretical. The solar event of 6 December 2006, starting at about 18:30 UT, exhibited a particularly well-defined double spectral structure, with the sub-THz spectral component detected at 212 and 405 GHz by SST and microwaves (1-18 GHz) observed by the Owens Valley Solar Array (OVSA). Emissions obtained by instruments in satellites are discussed with emphasis to ultra-violet (UV) obtained by the Transition Region And Coronal Explorer (TRACE), soft X-rays from the Geostationary Operational Environmental Satellites (GOES) and X- and gamma-rays from the Ramaty High Energy Solar Spectroscopic Imager (RHESSI). The sub-THz impulsive component had its closer temporal counterpart only in the higher energy X- and gamma-rays ranges. The spatial positions of the centers of emission at 212 GHz for the first flux enhancement were clearly displaced by more than one arc-minute from positions at the following phases. The observed sub-THz fluxes and burst source plasma parameters were found difficult to be reconciled to a purely thermal emission component. We discuss possible mechanisms to explain the double spectral components at microwaves and in the THz ranges.Comment: Accepted version for publication in Solar Physic

Le FORUM, Vol. 38 No. 4

https://digitalcommons.library.umaine.edu/francoamericain_forum/1043/thumbnail.jp

Le Forum, Vol. 41 No. 1

https://digitalcommons.library.umaine.edu/francoamericain_forum/1090/thumbnail.jp

LIPH Expression in Skin and Hair Follicles of Normal Coat and Rex Rabbits

Natural mutations in the LIPH gene were shown to be responsible for hair growth defects in humans and for the rex short hair phenotype in rabbits. In this species, we identified a single nucleotide deletion in LIPH (1362delA) introducing a stop codon in the C-terminal region of the protein. We investigated the expression of LIPH between normal coat and rex rabbits during critical fetal stages of hair follicle genesis, in adults and during hair follicle cycles. Transcripts were three times less expressed in both fetal and adult stages of the rex rabbits than in normal rabbits. In addition, the hair growth cycle phases affected the regulation of the transcription level in the normal and mutant phenotypes differently. LIPH mRNA and protein levels were higher in the outer root sheath (ORS) than in the inner root sheath (IRS), with a very weak signal in the IRS of rex rabbits. In vitro transfection shows that the mutant protein has a reduced lipase activity compared to the wild type form. Our results contribute to the characterization of the LIPH mode of action and confirm the crucial role of LIPH in hair production

Le FORUM, Vol. 39 No. 1

https://digitalcommons.library.umaine.edu/francoamericain_forum/1044/thumbnail.jp