Propagation of chaos for rank-based interacting diffusions and long time behaviour of a scalar quasilinear parabolic equation

We study a quasilinear parabolic Cauchy problem with a cumulative distribution function on the real line as an initial condition. We call 'probabilistic solution' a weak solution which remains a cumulative distribution function at all times. We prove the uniqueness of such a solution and we deduce the existence from a propagation of chaos result on a system of scalar diffusion processes, the interactions of which only depend on their ranking. We then investigate the long time behaviour of the solution. Using a probabilistic argument and under weak assumptions, we show that the flow of the Wasserstein distance between two solutions is contractive. Under more stringent conditions ensuring the regularity of the probabilistic solutions, we finally derive an explicit formula for the time derivative of the flow and we deduce the convergence of solutions to equilibrium.Comment: Stochastic partial differential equations: analysis and computations (2013) http://dx.doi.org/10.1007/s40072-013-0014-

Fractal analysis of urban catchments and their representation in semi-distributed models: imperviousness and sewer system

Fractal analysis relies on scale invariance and the concept of fractal dimension enables one to characterize and quantify the space filled by a geometrical set exhibiting complex and tortuous patterns. Fractal tools have been widely used in hydrology but seldom in the specific context of urban hydrology. In this paper, fractal tools are used to analyse surface and sewer data from 10 urban or peri-urban catchments located in five European countries. The aim was to characterize urban catchment properties accounting for the complexity and inhomogeneity typical of urban water systems. Sewer system density and imperviousness (roads or buildings), represented in rasterized maps of 2m  ×  2m pixels, were analysed to quantify their fractal dimension, characteristic of scaling invariance. The results showed that both sewer density and imperviousness exhibit scale-invariant features and can be characterized with the help of fractal dimensions ranging from 1.6 to 2, depending on the catchment. In a given area consistent results were found for the two geometrical features, yielding a robust and innovative way of quantifying the level of urbanization. The representation of imperviousness in operational semi-distributed hydrological models for these catchments was also investigated by computing fractal dimensions of the geometrical sets made up of the sub-catchments with coefficients of imperviousness greater than a range of thresholds. It enables one to quantify how well spatial structures of imperviousness were represented in the urban hydrological models

The novel curcumin analog FLLL32 decreases STAT3 DNA binding activity and expression, and induces apoptosis in osteosarcoma cell lines

<p>Abstract</p> <p>Background</p> <p>Curcumin is a naturally occurring phenolic compound shown to have a wide variety of antitumor activities; however, it does not attain sufficient blood levels to do so when ingested. Using structure-based design, a novel compound, FLLL32, was generated from curcumin. FLLL32 possesses superior biochemical properties and more specifically targets STAT3, a transcription factor important in tumor cell survival, proliferation, metastasis, and chemotherapy resistance. In our previous work, we found that several canine and human osteosarcoma (OSA) cell lines, but not normal osteoblasts, exhibit constitutive phosphorylation of STAT3. Compared to curcumin, we hypothesized that FLLL32 would be more efficient at inhibiting STAT3 function in OSA cells and that this would result in enhanced downregulation of STAT3 transcriptional targets and subsequent death of OSA cells.</p> <p>Methods</p> <p>Human and canine OSA cells were treated with vehicle, curcumin, or FLLL32 and the effects on proliferation (CyQUANT^®), apoptosis (SensoLyte^®Homogeneous AMC Caspase- 3/7 Assay kit, western blotting), STAT3 DNA binding (EMSA), and vascular endothelial growth factor (VEGF), survivin, and matrix metalloproteinase-2 (MMP2) expression (RT-PCR, western blotting) were measured. STAT3 expression was measured by RT-PCR, qRT- PCR, and western blotting.</p> <p>Results</p> <p>Our data showed that FLLL32 decreased STAT3 DNA binding by EMSA. FLLL32 promoted loss of cell proliferation at lower concentrations than curcumin leading to caspase-3- dependent apoptosis, as evidenced by PARP cleavage and increased caspase 3/7 activity; this could be inhibited by treatment with the pan-caspase inhibitor Z-VAD-FMK. Treatment of OSA cells with FLLL32 decreased expression of survivin, VEGF, and MMP2 at both mRNA and protein levels with concurrent decreases in phosphorylated and total STAT3; this loss of total STAT3 occurred, in part, via the ubiquitin-proteasome pathway.</p> <p>Conclusions</p> <p>These data demonstrate that the novel curcumin analog FLLL32 has biologic activity against OSA cell lines through inhibition of STAT3 function and expression. Future work with FLLL32 will define the therapeutic potential of this compound <it>in vivo</it>.</p

Crk and CrkL adaptor proteins: networks for physiological and pathological signaling

The Crk adaptor proteins (Crk and CrkL) constitute an integral part of a network of essential signal transduction pathways in humans and other organisms that act as major convergence points in tyrosine kinase signaling. Crk proteins integrate signals from a wide variety of sources, including growth factors, extracellular matrix molecules, bacterial pathogens, and apoptotic cells. Mounting evidence indicates that dysregulation of Crk proteins is associated with human diseases, including cancer and susceptibility to pathogen infections. Recent structural work has identified new and unusual insights into the regulation of Crk proteins, providing a rationale for how Crk can sense diverse signals and produce a myriad of biological responses

MÖSSBAUER EMISSION SPECTRA OF 119mSnCl2 ADDUCTS WITH SOME OXYGEN AND NITROGEN COMPOUNDS

Des expériences de source Mössbauer ont été réalisées sur le système 119mSnCl2 additionné de composés contenant de l'oxygène ou de l'azote. Les effets chimiques de la réaction nucléaire sont l'apparition d'une faible proportion de l'espèce aliovalente oxydée Sn4+ losque le ligand ajouté est l'eau ou l'aniline; cette proportion devient très importante avec le diméthyl sulfoxyde, le diphényle sulfoxyde, oxyde de pyridine ou les oxydes de picoline.The Mössbauer source experiments of 119mSnCl2 adducts with some oxygen and nitrogen containing compounds were carried out. For the chemical after-effects a small portion of the oxidized alliovalent species of Sn4+ was observed in the spectra of the adducts with the ligands such as water and aniline, whereas a very large portion of the aliovalent charge state was observed in the spectra of the adducts with dimethyl sulfoxide, diphenyl sulfoxide, pyridine N-oxide, and picoline N-oxides