An algebraic formula for the index of a vector field on an isolated complete intersection singularity

Let (V,0) be a germ of a complete intersection variety in \CC^{n+k}, n>0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on \CC^{n+k} tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space \CC^{n+k} we give a formula for the homological index in terms of local linear algebra.Comment: 18 pages; added an example which is not quasi homogeneous. A script calculating this example can be found at http://www.iag.uni-hannover.de/~bothmer/gobelin/ or at the and of the source file of this articl

Flags in zero dimensional complete intersections and indices of real vector fields

We introduce bilinear forms in a flag in a complete intersection local $\mathbb R$-algebra of dimension 0, related to the Eisenbud-Levine, Khimshiashvili bilinear form. We give a variational interpretation of these forms in terms of Jantzen's filtration and bilinear forms. We use the signatures of these forms to compute in the real case the constant relating the GSV-index with the signature function of vector fields tangent to an even dimensional hypersurface singularity, one being topologically defined and the other computable by finite dimensional commutative algebra methods.Comment: 17 pages. v2: Some changes in the introduction. A few typos corrected. To appear in Mathematische Zeitschrif

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 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 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 >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 >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 >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 >2. The proportion of patients prescribed VKA was 28.0% among patients with SAMe-TT2R2 scores >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

Measurement of ϒ production in pp collisions at √s = 2.76 TeV

The production of ϒ(1S), ϒ(2S) and ϒ(3S) mesons decaying into the dimuon final state is studied with the LHCb detector using a data sample corresponding to an integrated luminosity of 3.3 pb−1 collected in proton–proton collisions at a centre-of-mass energy of √s = 2.76 TeV. The differential production cross-sections times dimuon branching fractions are measured as functions of the ϒ transverse momentum and rapidity, over the ranges pT < 15 GeV/c and 2.0 < y < 4.5. The total cross-sections in this kinematic region, assuming unpolarised production, are measured to be σ (pp → ϒ(1S)X) × B ϒ(1S)→μ+μ− = 1.111 ± 0.043 ± 0.044 nb, σ (pp → ϒ(2S)X) × B ϒ(2S)→μ+μ− = 0.264 ± 0.023 ± 0.011 nb, σ (pp → ϒ(3S)X) × B ϒ(3S)→μ+μ− = 0.159 ± 0.020 ± 0.007 nb, where the first uncertainty is statistical and the second systematic

Study of the doubly charmed tetraquark T+cc

Quantum chromodynamics, the theory of the strong force, describes interactions of coloured quarks and gluons and the formation of hadronic matter. Conventional hadronic matter consists of baryons and mesons made of three quarks and quark-antiquark pairs, respectively. Particles with an alternative quark content are known as exotic states. Here a study is reported of an exotic narrow state in the D0D0π+ mass spectrum just below the D*+D0 mass threshold produced in proton-proton collisions collected with the LHCb detector at the Large Hadron Collider. The state is consistent with the ground isoscalar T+cc tetraquark with a quark content of ccu⎯⎯⎯d⎯⎯⎯ and spin-parity quantum numbers JP = 1+. Study of the DD mass spectra disfavours interpretation of the resonance as the isovector state. The decay structure via intermediate off-shell D*+ mesons is consistent with the observed D0π+ mass distribution. To analyse the mass of the resonance and its coupling to the D*D system, a dedicated model is developed under the assumption of an isoscalar axial-vector T+cc state decaying to the D*D channel. Using this model, resonance parameters including the pole position, scattering length, effective range and compositeness are determined to reveal important information about the nature of the T+cc state. In addition, an unexpected dependence of the production rate on track multiplicity is observed

International Consensus Statement on Rhinology and Allergy: Rhinosinusitis

Background: The 5 years since the publication of the first International Consensus Statement on Allergy and Rhinology: Rhinosinusitis (ICAR‐RS) has witnessed foundational progress in our understanding and treatment of rhinologic disease. These advances are reflected within the more than 40 new topics covered within the ICAR‐RS‐2021 as well as updates to the original 140 topics. This executive summary consolidates the evidence‐based findings of the document. Methods: ICAR‐RS presents over 180 topics in the forms of evidence‐based reviews with recommendations (EBRRs), evidence‐based reviews, and literature reviews. The highest grade structured recommendations of the EBRR sections are summarized in this executive summary. Results: ICAR‐RS‐2021 covers 22 topics regarding the medical management of RS, which are grade A/B and are presented in the executive summary. Additionally, 4 topics regarding the surgical management of RS are grade A/B and are presented in the executive summary. Finally, a comprehensive evidence‐based management algorithm is provided. Conclusion: This ICAR‐RS‐2021 executive summary provides a compilation of the evidence‐based recommendations for medical and surgical treatment of the most common forms of RS