On Trudinger\u2013Moser type inequalities involving Sobolev\u2013Lorentz spaces

Generalizations of the Trudinger-Moser inequality to Sobolev-Lorentz spaces with weights are considered. The weights in these spaces allow for the addition of certain lower order terms in the exponential integral. We prove an explicit relation between the weights and the lower order terms; furthermore, we show that the resulting inequalities are sharp, and that there are related phenomena of concentration-compactness

Optimal Sobolev type inequalities in Lorentz spaces

It is well known that the classical Sobolev embeddings may be improved within the framework of Lorentz spaces L p,q : the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, embeds into L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e. However, the value of the best possible embedding constants in the corresponding inequalities is known just in the case L p 17 ,p (R n ) . Here, we determine optimal constants for the embedding of the space D 1,p (R n ) , 1\u2009<\u2009p\u2009<\u2009n, into the whole Lorentz space scale L p 17 ,q (R n ) , p\u2009 64\u2009q\u2009 64\u2009 1e, including the limiting case q\u2009=\u2009p of which we give a new proof. We also exhibit extremal functions for these embedding inequalities by solving related elliptic problems

Salmonella Biofilm Formation on Aspergillus niger Involves Cellulose – Chitin Interactions

Salmonella cycles between host and nonhost environments, where it can become an active member of complex microbial communities. The role of fungi in the environmental adaptation of enteric pathogens remains relatively unexplored. We have discovered that S. enterica Typhimurium rapidly attaches to and forms biofilms on the hyphae of the common fungus, Aspergillus niger. Several Salmonella enterica serovars displayed a similar interaction, whereas other bacterial species were unable to bind to the fungus. Bacterial attachment to chitin, a major constituent of fungal cell walls, mirrored this specificity. Pre-incubation of S. Typhimurium with N-acetylglucosamine, the monomeric component of chitin, reduced binding to chitin beads by as much as 727-fold and inhibited attachment to A. niger hyphae considerably. A cellulose-deficient mutant of S. Typhimurium failed to attach to chitin beads and to the fungus. Complementation of this mutant with the cellulose operon restored binding to chitin beads to 79% of that of the parental strain and allowed for attachment and biofilm formation on A. niger, indicating that cellulose is involved in bacterial attachment to the fungus via the chitin component of its cell wall. In contrast to cellulose, S. Typhimurium curli fimbriae were not required for attachment and biofilm development on the hyphae but were critical for its stability. Our results suggest that cellulose–chitin interactions are required for the production of mixed Salmonella-A. niger biofilms, and support the hypothesis that encounters with chitinaceous alternate hosts may contribute to the ecological success of human pathogens

Comparative effectiveness and safety of non-vitamin K antagonists for atrial fibrillation in clinical practice: GLORIA-AF Registry

Background and purpose: Prospectively collected data comparing the safety and effectiveness of individual non-vitamin K antagonists (NOACs) are lacking. Our objective was to directly compare the effectiveness and safety of NOACs in patients with newly diagnosed atrial fibrillation (AF). Methods: In GLORIA-AF, a large, prospective, global registry program, consecutive patients with newly diagnosed AF were followed for 3&nbsp;years. The comparative analyses for (1) dabigatran vs rivaroxaban or apixaban and (2) rivaroxaban vs apixaban were performed on propensity score (PS)-matched patient sets. Proportional hazards regression was used to estimate hazard ratios (HRs) for outcomes of interest. Results: The GLORIA-AF Phase III registry enrolled 21,300 patients between January 2014 and December 2016. Of these, 3839 were prescribed dabigatran, 4015 rivaroxaban and 4505 apixaban, with median ages of 71.0, 71.0, and 73.0&nbsp;years, respectively. In the PS-matched set, the adjusted HRs and 95% confidence intervals (CIs) for dabigatran vs rivaroxaban were, for stroke: 1.27 (0.79–2.03), major bleeding 0.59 (0.40–0.88), myocardial infarction 0.68 (0.40–1.16), and all-cause death 0.86 (0.67–1.10). For the comparison of dabigatran vs apixaban, in the PS-matched set, the adjusted HRs were, for stroke 1.16 (0.76–1.78), myocardial infarction 0.84 (0.48–1.46), major bleeding 0.98 (0.63–1.52) and all-cause death 1.01 (0.79–1.29). For the comparison of rivaroxaban vs apixaban, in the PS-matched set, the adjusted HRs were, for stroke 0.78 (0.52–1.19), myocardial infarction 0.96 (0.63–1.45), major bleeding 1.54 (1.14–2.08), and all-cause death 0.97 (0.80–1.19). Conclusions: Patients treated with dabigatran had a 41% lower risk of major bleeding compared with rivaroxaban, but similar risks of stroke, MI, and death. Relative to apixaban, patients treated with dabigatran had similar risks of stroke, major bleeding, MI, and death. Rivaroxaban relative to apixaban had increased risk for major bleeding, but similar risks for stroke, MI, and death. Registration: URL: https://www.clinicaltrials.gov. Unique identifiers: NCT01468701, NCT01671007. Date of registration: September 2013

Anticoagulant selection in relation to the SAMe-TT2R2 score in patients with atrial fibrillation. the GLORIA-AF registry

Aim: The SAMe-TT2R2 score helps identify patients with atrial fibrillation (AF) likely to have poor anticoagulation control during anticoagulation with vitamin K antagonists (VKA) and those with scores &gt;2 might be better managed with a target-specific oral anticoagulant (NOAC). We hypothesized that in clinical practice, VKAs may be prescribed less frequently to patients with AF and SAMe-TT2R2 scores &gt;2 than to patients with lower scores. Methods and results: We analyzed the Phase III dataset of the Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation (GLORIA-AF), a large, global, prospective global registry of patients with newly diagnosed AF and ≥1 stroke risk factor. We compared baseline clinical characteristics and antithrombotic prescriptions to determine the probability of the VKA prescription among anticoagulated patients with the baseline SAMe-TT2R2 score &gt;2 and ≤ 2. Among 17,465 anticoagulated patients with AF, 4,828 (27.6%) patients were prescribed VKA and 12,637 (72.4%) patients an NOAC: 11,884 (68.0%) patients had SAMe-TT2R2 scores 0-2 and 5,581 (32.0%) patients had scores &gt;2. The proportion of patients prescribed VKA was 28.0% among patients with SAMe-TT2R2 scores &gt;2 and 27.5% in those with scores ≤2. Conclusions: The lack of a clear association between the SAMe-TT2R2 score and anticoagulant selection may be attributed to the relative efficacy and safety profiles between NOACs and VKAs as well as to the absence of trial evidence that an SAMe-TT2R2-guided strategy for the selection of the type of anticoagulation in NVAF patients has an impact on clinical outcomes of efficacy and safety. The latter hypothesis is currently being tested in a randomized controlled trial. Clinical trial registration: URL: https://www.clinicaltrials.gov//Unique identifier: NCT01937377, NCT01468701, and NCT01671007

Uniqueness of positive solutions of nonlinear elliptic equations with exponential growth

By combining a technique inspired to the theory of sublinear elliptic equations with the Emden-Fowler inversion technique of Atkinson and Peletier, we obtain uniqueness of positive solutions of the following equation -\u394u = \u3bbueu \u3b8 in B, u > 0, u = 0 on 02B, where B 82 \u211dn is the ball of radius one, \u3bb > 0 and 1 < \u3bd 64 2