Estimates for the Sobolev trace constant with critical exponent and applications

In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow \|u\|^p_{W^{1,p}(\Omega)} that are independent of $\Omega$. This estimates generalized those of [3] for general $p$. Here $p_* := p(N-1)/(N-p)$ is the critical exponent for the immersion and $N$ is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of [16]. Finally, we study an optimal design problem with critical exponent.Comment: 22 pages, submitte

H−H-convergence result for nonlocal elliptic-type problems via Tartar's method

In this work we obtain a compactness result for the $H-$convergence of a family of nonlocal and nonlinear monotone elliptic-type problems by means of Tartar's method of oscillating test functions.Comment: In this revision we added a new section that shows the Gamma-convergence of the associated energy functional

Energy nonconservation and relativistic trajectories: Unimodular gravity and beyond

Energy conservation has the status of a fundamental physical principle. However, measurements in quantum mechanics do not comply with energy conservation. Therefore, it is expected that a more fundamental theory of gravity -- one that is less incompatible with quantum mechanics -- should admit energy nonconservations. This paper begins by identifying the conditions for a theory to have an energy-momentum tensor that is not conserved. Then, the trajectory equation for pointlike particles that lose energy is derived, showing that energy nonconservation produces a particular acceleration. As an example, the unimodular theory of gravity is studied. Interestingly, in spherical symmetry, given that there is a generalized Birkhoff theorem and that the energy-momentum tensor divergence is a closed form, the trajectories of test particles that lose energy can be found using well known methods. Finally, limits on the energy nonconservation parameters are set using Solar system observations.Comment: 13 pages. Accepted in Phys. Rev.

A YY1-dependent increase in aerobic metabolism is indispensable for intestinal organogenesis

During late gestation, villi extend into the intestinal lumen to dramatically increase the surface area of the intestinal epithelium, preparing the gut for the neonatal diet. Incomplete development of the intestine is the most common gastrointestinal complication in neonates, but the causes are unclear. We provide evidence in mice that Yin Yang 1 (Yy1) is crucial for intestinal villus development. YY1 loss in the developing endoderm had no apparent consequences until late gestation, after which the intestine differentiated poorly and exhibited severely stunted villi. Transcriptome analysis revealed that YY1 is required for mitochondrial gene expression, and ultrastructural analysis confirmed compromised mitochondrial integrity in the mutant intestine. We found increased oxidative phosphorylation gene expression at the onset of villus elongation, suggesting that aerobic respiration might function as a regulator of villus growth. Mitochondrial inhibitors blocked villus growth in a fashion similar to Yy1 loss, thus further linking oxidative phosphorylation with late-gestation intestinal development. Interestingly, we find that necrotizing enterocolitis patients also exhibit decreased expression of oxidative phosphorylation genes. Our study highlights the still unappreciated role of metabolic regulation during organogenesis, and suggests that it might contribute to neonatal gastrointestinal disorders

Quantum Gravity Phenomenology without Lorentz Invariance Violation: a detailed proposal

We describe a scheme for the exploration of quantum gravity phenomenology focussing on effects that could be thought as arising from a fundamental granularity of space-time. In contrast with the simplest assumptions, such granularity is assumed to respect Lorentz Invariance but is otherwise left unspecified. The proposal is fully observer covariant, it involves non-trivial couplings of curvature to matter fields and leads to a well defined phenomenology. We present the effective Hamiltonian which could be used to analyze concrete experimental situations, some of which are briefly described, and we shortly discuss the degree to which the present proposal is in line with the fundamental ideas behind the equivalence principle.Comment: LaTeX, 24 pages. To be published in Classical and Quantum Gravit

Seawi—a sea urchin piwi/argonaute family member is a component of MT-RNP complexes

This is the publisher's version, also available electronically from http://rnajournal.cshlp.org/content/11/5/646.The piwi/argonaute family of proteins is involved in key developmental processes such as stem cell maintenance and axis specification through molecular mechanisms that may involve RNA silencing. Here we report on the cloning and characterization of the sea urchin piwi/argonaute family member seawi. Seawi is a major component of microtubule-ribonucleoprotein (MT-RNP) complexes isolated from two different species of sea urchin, Strongylocentrotus purpuratus and Paracentrotus lividus. Seawi co-isolates with purified ribosomes, cosediments with 80S ribosomes in sucrose density gradients, and binds microtubules. Seawi possesses the RNA binding motif common to piwi family members and binds P. lividus bep4 mRNA, a transcript that co-isolates with MT-RNP complexes and whose translation product has been shown to play a role in patterning the animal–vegetal axis. Indirect immunofluorescence studies localized seawi to the cortex of unfertilized eggs within granule-like particles, the mitotic spindle during cell division, and the small micromeres where its levels were enriched during the early cleavage stage. Lastly, we discuss how seawi, as a piwi/argonaute family member, may play a fundamentally important role in sea urchin animal–vegetal axis formation and stem cell maintenance

TaxMan : a server to trim rRNA reference databases and inspect taxonomic coverage

© The Author(s), 2012. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Nucleic Acids Research 40 (2012): W82-W87, doi:10.1093/nar/gks418.Amplicon sequencing of the hypervariable regions of the small subunit ribosomal RNA gene is a widely accepted method for identifying the members of complex bacterial communities. Several rRNA gene sequence reference databases can be used to assign taxonomic names to the sequencing reads using BLAST, USEARCH, GAST or the RDP classifier. Next-generation sequencing methods produce ample reads, but they are short, currently ∼100–450 nt (depending on the technology), as compared to the full rRNA gene of ∼1550 nt. It is important, therefore, to select the right rRNA gene region for sequencing. The primers should amplify the species of interest and the hypervariable regions should differentiate their taxonomy. Here, we introduce TaxMan: a web-based tool that trims reference sequences based on user-selected primer pairs and returns an assessment of the primer specificity by taxa. It allows interactive plotting of taxa, both amplified and missed in silico by the primers used. Additionally, using the trimmed sequences improves the speed of sequence matching algorithms. The smaller database greatly improves run times (up to 98%) and memory usage, not only of similarity searching (BLAST), but also of chimera checking (UCHIME) and of clustering the reads (UCLUST). TaxMan is available at http://www.ibi.vu.nl/programs/taxmanwww/.University of Amsterdam under the research priority area ‘Oral Infections and Inflammation’ (to B.W.B.); National Science Foundation [NSF/BDI 0960626 to S.M.H.]; the European Union Seventh Framework Programme (FP7/ 2007-2013) under ANTIRESDEV grant agreement no 241446 (to E.Z.)