Global exponential convergence to variational traveling waves in cylinders

We prove, under generic assumptions, that the special variational traveling wave that minimizes the exponentially weighted Ginzburg-Landau functional associated with scalar reaction-diffusion equations in infinite cylinders is the long-time attractor for the solutions of the initial value problems with front-like initial data. The convergence to this traveling wave is exponentially fast. The obtained result is mainly a consequence of the gradient flow structure of the considered equation in the exponentially weighted spaces and does not depend on the precise details of the problem. It strengthens our earlier generic propagation and selection result for "pushed" fronts.Comment: 23 page

Phase Slips and the Eckhaus Instability

We consider the Ginzburg-Landau equation, $\partial_t u= \partial_x^2 u + u - u|u|^2$, with complex amplitude $u(x,t)$. We first analyze the phenomenon of phase slips as a consequence of the {\it local} shape of $u$. We next prove a {\it global} theorem about evolution from an Eckhaus unstable state, all the way to the limiting stable finite state, for periodic perturbations of Eckhaus unstable periodic initial data. Equipped with these results, we proceed to prove the corresponding phenomena for the fourth order Swift-Hohenberg equation, of which the Ginzburg-Landau equation is the amplitude approximation. This sheds light on how one should deal with local and global aspects of phase slips for this and many other similar systems.Comment: 22 pages, Postscript, A

Interaction of vortices in viscous planar flows

We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations of the vortices do not depend on the viscosity parameter \nu, and we choose a time T > 0 such that the Helmholtz-Kirchhoff point vortex system is well-posed on the interval [0,T]. Under these assumptions, we prove that the solution of the Navier-Stokes equation converges, as \nu -> 0, to a superposition of Lamb-Oseen vortices whose centers evolve according to a viscous regularization of the point vortex system. Convergence holds uniformly in time, in a strong topology which allows to give an accurate description of the asymptotic profile of each individual vortex. In particular, we compute to leading order the deformations of the vortices due to mutual interactions. This allows to estimate the self-interactions, which play an important role in the convergence proof.Comment: 39 pages, 1 figur

Orbital stability of periodic waves for the nonlinear Schroedinger equation

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its phase over a period (Floquet exponent). In the defocusing case, we show that these travelling waves are orbitally stable within the class of solutions having the same period and the same Floquet exponent. This generalizes a previous work where only small amplitude solutions were considered. A similar result is obtained in the focusing case, under a non-degeneracy condition which can be checked numerically. The proof relies on the general approach to orbital stability as developed by Grillakis, Shatah, and Strauss, and requires a detailed analysis of the Hamiltonian system satisfied by the wave profile.Comment: 34 pages, 7 figure

Coherent vortex structures and 3D enstrophy cascade

Existence of 2D enstrophy cascade in a suitable mathematical setting, and under suitable conditions compatible with 2D turbulence phenomenology, is known both in the Fourier and in the physical scales. The goal of this paper is to show that the same geometric condition preventing the formation of singularities - 1/2-H\"older coherence of the vorticity direction - coupled with a suitable condition on a modified Kraichnan scale, and under a certain modulation assumption on evolution of the vorticity, leads to existence of 3D enstrophy cascade in physical scales of the flow.Comment: 15 pp; final version -- to appear in CM

Renormalizing Partial Differential Equations

In this review paper, we explain how to apply Renormalization Group ideas to the analysis of the long-time asymptotics of solutions of partial differential equations. We illustrate the method on several examples of nonlinear parabolic equations. We discuss many applications, including the stability of profiles and fronts in the Ginzburg-Landau equation, anomalous scaling laws in reaction-diffusion equations, and the shape of a solution near a blow-up point.Comment: 34 pages, Latex; [email protected]; [email protected]

Evaluation of NV556, a Novel Cyclophilin Inhibitor, as a Potential Antifibrotic Compound for Liver Fibrosis

Hepatic fibrosis can result as a pathological response to nonalcoholic steatohepatitis (NASH). Cirrhosis, the late stage of fibrosis, has been linked to poor survival and an increased risk of developing hepatocellular carcinoma, with limited treatment options available. Therefore, there is an unmet need for novel effective antifibrotic compounds. Cyclophilins are peptidyl-prolyl cis-trans isomerases that facilitate protein folding and conformational changes affecting the function of the targeted proteins. Due to their activity, cyclophilins have been presented as key factors in several stages of the fibrotic process. In this study, we investigated the antifibrotic effects of NV556, a novel potent sanglifehrin-based cyclophilin inhibitor, in vitro and in vivo. NV556 potential antifibrotic effect was evaluated in two well-established animal models of NASH, STAM, and methionine-choline-deficient (MCD) mice, as well as in an in vitro 3D human liver ECM culture of LX2 cells, a human hepatic stellate cell line. We demonstrate that NV556 decreased liver fibrosis in both STAM and MCD in vivo models and decreased collagen production in TGFβ1-activated hepatic stellate cells in vitro. Taken together, these results present NV556 as a potential candidate for the treatment of liver fibrosis

Why dig looted tombs? Two examples and some answers from Keushu (Ancash highlands, Peru)

Looted tombs at Andean archaeological sites are largely the result of a long tradition of trade in archaeological artefacts coupled with the 17th century policy of eradicating ancestor veneration and destroying mortuary evidence in a bid to “extirpate idolatry”. On the surface, looted funerary contexts often present abundant disarticulated and displaced human remains as well as an apparent absence of mortuary accoutrements. What kind of information can archaeologists and biological anthropologists hope to gather from such contexts? In order to gauge the methodological possibilities and interpretative limitations of targeting looted tombs, we fully excavated two collective funerary contexts at the archaeological site of Keushu (district and province of Yungay, Ancash, Peru; c. 2000 B.C.-A.D. 1600), which includes several dozen tombs, many built under large boulders or rock shelters, all of which appear disturbed by looting. The first is located in the ceremonial sector and excavation yielded information on four individuals; the second, in the funerary and residential sector, held the remains of seventy individuals - adults and juveniles. Here, we present and discuss the recovered data and suggest that careful, joint excavations by archaeologists and biological anthropologists can retrieve evidence of past mortuary practices, aid the biological characterisation of mortuary populations and help distinguish between a broad range of looting practices and post-depositional processes

A survey of primary care physician practices in antibiotic prescribing for the treatment of uncomplicated male gonoccocal urethritis

<p>Abstract</p> <p>Background</p> <p>The development of resistance to antimicrobial therapy by <it>Neisseria gonorrhoeae </it>causes on-going problems for individual case management of gonorrhoea. Surveillance data about <it>N. gonorrhoeae </it>have indicated an increase in the incidence of gonorrhoea in France in 2006. As a consequence of the development of antibiotic resistance in <it>N. gonorrhoeae</it>, French guidelines excluded fluoroquinolones as a standard treatment for <it>N. gonorrhoeae</it>. Ceftriaxone became the recommended treatment, associated with azithromycin for <it>Clamydia trachomatis </it>infection. Our aim was to describe the practice patterns of general practitioners (GPs) in managing the antibiotic treatment of patients with symptoms suggestive of uncomplicated male urethritis.</p> <p>Methods</p> <p>We developed a clinical vignette describing a man with typical gonococcal urethritis symptoms to elicit questions about antibiotic treatment. We mailed the electronic questionnaire to a random sample of 1000 French GPs belonging to the <it>Sentinelles </it>Network.</p> <p>Results</p> <p>By the end of the survey period, 350 vignettes were received, yielding a response rate of 35%. Sixty-six GPs (20.2%) prescribed the recommended antibiotics for the simultaneous treatment of <it>N</it>. <it>gonorrhoeae </it>and <it>C. trachomatis </it>infections, while 132 GPs (40.4%) prescribed only non-recommended antibiotics, including ciprofloxacin in 69 cases (21.1%). General practitioners with less than 10 years in practice showed better compliance to guidelines than those with more years in practice (p < 0.05).</p> <p>Conclusions</p> <p>The results suggest a mismatch between the guidelines and the antibiotic treatment of male uncomplicated urethritis by French GPs, mostly among the subgroup of physicians who have been in practice longer. Educational approaches based on practice feedback need to be developed to improve these deficits in the quality of care.</p

High-throughput CRISPRi phenotyping identifies new essential genes in Streptococcus pneumoniae.

Genome-wide screens have discovered a large set of essential genes in the opportunistic human pathogen &lt;i&gt;Streptococcus pneumoniae&lt;/i&gt; However, the functions of many essential genes are still unknown, hampering vaccine development and drug discovery. Based on results from transposon sequencing (Tn-seq), we refined the list of essential genes in &lt;i&gt;S. pneumoniae&lt;/i&gt; serotype 2 strain D39. Next, we created a knockdown library targeting 348 potentially essential genes by CRISPR interference (CRISPRi) and show a growth phenotype for 254 of them (73%). Using high-content microscopy screening, we searched for essential genes of unknown function with clear phenotypes in cell morphology upon CRISPRi-based depletion. We show that SPD_1416 and SPD_1417 (renamed to MurT and GatD, respectively) are essential for peptidoglycan synthesis, and that SPD_1198 and SPD_1197 (renamed to TarP and TarQ, respectively) are responsible for the polymerization of teichoic acid (TA) precursors. This knowledge enabled us to reconstruct the unique pneumococcal TA biosynthetic pathway. CRISPRi was also employed to unravel the role of the essential Clp-proteolytic system in regulation of competence development, and we show that ClpX is the essential ATPase responsible for ClpP-dependent repression of competence. The CRISPRi library provides a valuable tool for characterization of pneumococcal genes and pathways and revealed several promising antibiotic targets