The mixed problem for the Laplacian in Lipschitz domains

We consider the mixed boundary value problem or Zaremba's problem for the Laplacian in a bounded Lipschitz domain in R^n. We specify Dirichlet data on part of the boundary and Neumann data on the remainder of the boundary. We assume that the boundary between the sets where we specify Dirichlet and Neumann data is a Lipschitz surface. We require that the Neumann data is in L^p and the Dirichlet data is in the Sobolev space of functions having one derivative in L^p for some p near 1. Under these conditions, there is a unique solution to the mixed problem with the non-tangential maximal function of the gradient of the solution in L^p of the boundary. We also obtain results with data from Hardy spaces when p=1.Comment: Version 5 includes a correction to one step of the main proof. Since the paper appeared long ago, this submission includes the complete paper, followed by a short section that gives the correction to one step in the proo

M. Kontsevich's graph complex and the Grothendieck-Teichmueller Lie algebra

We show that the zeroth cohomology of M. Kontsevich's graph complex is isomorphic to the Grothendieck-Teichmueller Lie algebra grt_1. The map is explicitly described. This result has applications to deformation quantization and Duflo theory. We also compute the homotopy derivations of the Gerstenhaber operad. They are parameterized by grt_1, up to one class (or two, depending on the definitions). More generally, the homotopy derivations of the (non-unital) E_n operads may be expressed through the cohomology of a suitable graph complex. Our methods also give a second proof of a result of H. Furusho, stating that the pentagon equation for grt_1-elements implies the hexagon equation

Quantizing higher-spin gravity in free-field variables

We study the formulation of massless higher-spin gravity on AdS$_3$ in a gauge in which the fundamental variables satisfy free field Poisson brackets. This gauge choice leaves a small portion of the gauge freedom unfixed, which should be further quotiented out. We show that doing so leads to a bulk version of the Coulomb gas formalism for $W_N$ CFT's: the generators of the residual gauge symmetries are the classical limits of screening charges, while the gauge-invariant observables are classical $W_N$ charges. Quantization in these variables can be carried out using standard techniques and makes manifest a remnant of the triality symmetry of $W_\infty[\lambda]$. This symmetry can be used to argue that the theory should be supplemented with additional matter content which is precisely that of the Prokushkin-Vasiliev theory. As a further application, we use our formulation to quantize a class of conical surplus solutions and confirm the conjecture that these are dual to specific degenerate $W_N$ primaries, to all orders in the large central charge expansion.Comment: 31 pages + appendices. V2: typos corrected, reference adde

Strings on Bubbling Geometries

We study gauge theory operators which take the form of a product of a trace with a Schur polynomial, and their string theory duals. These states represent strings excited on bubbling AdS geometries which are dual to the Schur polynomials. These geometries generically take the form of multiple annuli in the phase space plane. We study the coherent state wavefunction of the lattice, which labels the trace part of the operator, for a general Young tableau and their dual description on the droplet plane with a general concentric ring pattern. In addition we identify a density matrix over the coherent states on all the geometries within a fixed constraint. This density matrix may be used to calculate the entropy of a given ensemble of operators. We finally recover the BMN string spectrum along the geodesic near any circle from the ansatz of the coherent state wavefunction.Comment: 41 pages, 12 figures, published version in JHE

The association between histamine 2 receptor antagonist use and Clostridium difficile infection: a systematic review and meta-analysis.

Background Clostridium difficile infection (CDI) is a major health problem. Epidemiological evidence suggests that there is an association between acid suppression therapy and development of CDI. Purpose We sought to systematically review the literature that examined the association between histamine 2 receptor antagonists (H2RAs) and CDI. Data source We searched Medline, Current Contents, Embase, ISI Web of Science and Elsevier Scopus from 1990 to 2012 for all analytical studies that examined the association between H2RAs and CDI. Study selection Two authors independently reviewed the studies for eligibility. Data extraction Data about studies characteristics, adjusted effect estimates and quality were extracted. Data synthesis Thirty-five observations from 33 eligible studies that included 201834 participants were analyzed. Studies were performed in 6 countries and nine of them were multicenter. Most studies did not specify the type or duration of H2RAs therapy. The pooled effect estimate was 1.44, 95% CI (1.22–1.7), I2 = 70.5%. This association was consistent across different subgroups (by study design and country) and there was no evidence of publication bias. The pooled effect estimate for high quality studies was 1.39 (1.15–1.68), I2 = 72.3%. Meta-regression analysis of 10 study-level variables did not identify sources of heterogeneity. In a speculative analysis, the number needed to harm (NNH) with H2RAs at 14 days after hospital admission in patients receiving antibiotics or not was 58, 95% CI (37, 115) and 425, 95% CI (267, 848), respectively. For the general population, the NNH at 1 year was 4549, 95% CI (2860, 9097). Conclusion In this rigorous systematic review and meta-analysis, we observed an association between H2RAs and CDI. The absolute risk of CDI associated with H2RAs is highest in hospitalized patients receiving antibiotics

Very special relativity as relativity of dark matter: the Elko connection

In the very special relativity (VSR) proposal by Cohen and Glashow, it was pointed out that invariance under HOM(2) is both necessary and sufficient to explain the null result of the Michelson-Morely experiment. It is the quantum field theoretic demand of locality, or the requirement of P, T, CP, or CT invariance, that makes invariance under the Lorentz group a necessity. Originally it was conjectured that VSR operates at the Planck scale; we propose that the natural arena for VSR is at energies similar to the standard model, but in the dark sector. To this end we provide an ab initio spinor representation invariant under the SIM(2) avatar of VSR and construct a mass dimension one fermionic quantum field of spin one half. This field turns out to be a very close sibling of Elko and it exhibits the same striking property of intrinsic darkness with respect to the standard model fields. In the new construct, the tension between Elko and Lorentz symmetries is fully resolved. We thus entertain the possibility that the symmetries underlying the standard model matter and gauge fields are those of Lorentz, while the event space underlying the dark matter and the dark gauge fields supports the algebraic structure underlying VSR.Comment: 19 pages. Section 5 is new. Published version (modulo a footnote, and a corrected typo

Multiple sclerosis risk variants regulate gene expression in innate and adaptive immune cells

At least 200 single-nucleotide polymorphisms (SNPs) are associated with multiple sclerosis (MS) risk. A key function that could mediate SNP-encoded MS risk is their regulatory effects on gene expression. We performed microarrays using RNA extracted from purified immune cell types from 73 untreated MS cases and 97 healthy controls and then performed Cis expression quantitative trait loci mapping studies using additive linear models. We describe MS risk expression quantitative trait loci associations for 129 distinct genes. By extending these models to include an interaction term between genotype and phenotype, we identify MS risk SNPs with opposing effects on gene expression in cases compared with controls, namely, rs2256814 MYT1 in CD4 cells (q = 0.05) and rs12087340 RF00136 in monocyte cells (q = 0.04). The rs703842 SNP was also associated with a differential effect size on the expression of the METTL21B gene in CD8 cells of MS cases relative to controls (q = 0.03). Our study provides a detailed map of MS risk loci that function by regulating gene expression in cell types relevant to MS

Mycotic aneurysm of the femoral artery complicating Staphylococcus aureus bacteremia: a case report

INTRODUCTION: Staphylococcus aureus is the major cause of bacteremia, with the potential for some complications, namely mycotic aneurysms, defined as irreversible dilatation of an artery due to destruction of the vessel wall by infection. CASE PRESENTATION: The authors present the case of a 52 year-old-Caucasian male, admitted with Staphylococcus aureus bacteremia and mycotic aneurysm of the right superficial femoral artery, associated with advanced atherosclerotic process. CONCLUSION: Mycotic aneurysms are rare, and a high index of suspicion is needed, because appropriate treatment will certainly affect the outcome, as they are associated with high morbidity and mortality