17 research outputs found
General Spectral Flow Formula for Fixed Maximal Domain
We consider a continuous curve of linear elliptic formally self-adjoint
differential operators of first order with smooth coefficients over a compact
Riemannian manifold with boundary together with a continuous curve of global
elliptic boundary value problems. We express the spectral flow of the resulting
continuous family of (unbounded) self-adjoint Fredholm operators in terms of
the Maslov index of two related curves of Lagrangian spaces. One curve is given
by the varying domains, the other by the Cauchy data spaces. We provide
rigorous definitions of the underlying concepts of spectral theory and
symplectic analysis and give a full (and surprisingly short) proof of our
General Spectral Flow Formula for the case of fixed maximal domain. As a side
result, we establish local stability of weak inner unique continuation property
(UCP) and explain its role for parameter dependent spectral theory.Comment: 22 page
Strichartz estimates on Schwarzschild black hole backgrounds
We study dispersive properties for the wave equation in the Schwarzschild
space-time. The first result we obtain is a local energy estimate. This is then
used, following the spirit of earlier work of Metcalfe-Tataru, in order to
establish global-in-time Strichartz estimates. A considerable part of the paper
is devoted to a precise analysis of solutions near the trapping region, namely
the photon sphere.Comment: 44 pages; typos fixed, minor modifications in several place
Long-term cardiovascular safety of febuxostat compared with allopurinol in patients with gout (FAST): a multicentre, prospective, randomised, open-label, non-inferiority trial
Background:
Febuxostat and allopurinol are urate-lowering therapies used to treat patients with gout. Following concerns about the cardiovascular safety of febuxostat, the European Medicines Agency recommended a post-licensing study assessing the cardiovascular safety of febuxostat compared with allopurinol.
Methods:
We did a prospective, randomised, open-label, blinded-endpoint, non-inferiority trial of febuxostat versus allopurinol in patients with gout in the UK, Denmark, and Sweden. Eligible patients were 60 years or older, already receiving allopurinol, and had at least one additional cardiovascular risk factor. Those who had myocardial infarction or stroke in the previous 6 months or who had severe congestive heart failure or severe renal impairment were excluded. After a lead-in phase in which allopurinol dose was optimised towards achieving a serum urate concentration of less than 0·357 mmol/L (<6 mg/dL), patients were randomly assigned (1:1, with stratification according to previous cardiovascular events) to continue allopurinol (at the optimised dose) or start febuxostat at 80 mg/day, increasing to 120 mg/day if necessary to achieve the target serum urate concentration. The primary outcome was a composite of hospitalisation for non-fatal myocardial infarction or biomarker-positive acute coronary syndrome; non-fatal stroke; or cardiovascular death. The hazard ratio (HR) for febuxostat versus allopurinol in a Cox proportional hazards model (adjusted for the stratification variable and country) was assessed for non-inferiority (HR limit 1·3) in an on-treatment analysis. This study is registered with the EU Clinical Trials Register (EudraCT 2011-001883-23) and ISRCTN (ISRCTN72443728) and is now closed.
Findings:
From Dec 20, 2011, to Jan 26, 2018, 6128 patients (mean age 71·0 years [SD 6·4], 5225 [85·3%] men, 903 [14·7%] women, 2046 [33·4%] with previous cardiovascular disease) were enrolled and randomly allocated to receive allopurinol (n=3065) or febuxostat (n=3063). By the study end date (Dec 31, 2019), 189 (6·2%) patients in the febuxostat group and 169 (5·5%) in the allopurinol group withdrew from all follow-up. Median follow-up time was 1467 days (IQR 1029–2052) and median on-treatment follow-up was 1324 days (IQR 870–1919). For incidence of the primary endpoint, on-treatment, febuxostat (172 patients [1·72 events per 100 patient-years]) was non-inferior to allopurinol (241 patients [2·05 events per 100 patient-years]; adjusted HR 0·85 [95% CI 0·70–1·03], p<0·0001). In the febuxostat group, 222 (7·2%) of 3063 patients died and 1720 (57·3%) of 3001 in the safety analysis set had at least one serious adverse event (with 23 events in 19 [0·6%] patients related to treatment). In the allopurinol group, 263 (8·6%) of 3065 patients died and 1812 (59·4%) of 3050 had one or more serious adverse events (with five events in five [0·2%] patients related to treatment). Randomised therapy was discontinued in 973 (32·4%) patients in the febuxostat group and 503 (16·5%) patients in the allopurinol group.
Interpretation:
Febuxostat is non-inferior to allopurinol therapy with respect to the primary cardiovascular endpoint, and its long-term use is not associated with an increased risk of death or serious adverse events compared with allopurinol.
Funding:
Menarini, Ipsen, and Teijin Pharma Ltd
Unique Continuation from Infinity in Asymptotically Anti-de Sitter Spacetimes
The authors acknowledge support through a grant of the European Research Counci