Central Configurations and Mutual Differences

Central configurations are solutions of the equations λmjqj=∂U/∂qj, where U denotes the potential function and each qj is a point in the d-dimensional Euclidean space E≅Rd, for j=1,…,n. We show that the vector of the mutual differences qij=qi−qj satisfies the equation −(λ/α)q=Pm(Ψ(q)), where Pm is the orthogonal projection over the spaces of 1-cocycles and Ψ(q)=q/|q|α+2. It is shown that differences qij of central configurations are critical points of an analogue of U, defined on the space of 1-cochains in the Euclidean space E, and restricted to the subspace of 1-cocycles. Some generalizations of well known facts follow almost immediately from this approach

Simple choreographies of the planar Newtonian NN-body Problem

In the $N$-body problem, a simple choreography is a periodic solution, where all masses chase each other on a single loop. In this paper we prove that for the planar Newtonian $N$-body problem with equal masses, $N \ge 3$, there are at least $2^{N-3} + 2^{[(N-3)/2]}$ different main simple choreographies. This confirms a conjecture given by Chenciner and etc. in \cite{CGMS02}.Comment: 31pages, 6 figures. Refinements in notations and proof

SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks

We use supersymmetric Ward identities to relate multi-gluon helicity amplitudes involving a pair of massive quarks to amplitudes with massive scalars. This allows to use the recent results for scalar amplitudes with an arbitrary number of gluons obtained by on-shell recursion relations to obtain scattering amplitudes involving top quarks.Comment: 22 pages, references adde

Impact of proton pump inhibitors on efficacy of antiplatelet strategies with ticagrelor or aspirin after percutaneous coronary intervention : insights from the GLOBAL LEADERS trial

Background Several studies have suggested that proton pump inhibitors (PPIs) may reduce the antiplatelet effects of clopidogrel and/or aspirin, possibly leading to cardiovascular events. Aims We aimed to investigate the association between PPI and clinical outcomes in patients treated with ticagrelor monotherapy or conventional antiplatelet therapy after percutaneous coronary intervention (PCI). Methods This is a subanalysis of the randomized GLOBAL LEADERS trial, comparing the experimental antiplatelet arm (23-month ticagrelor monotherapy following 1-month dual antiplatelet therapy [DAPT]) with the reference arm (12-month aspirin monotherapy following 12-month DAPT) after PCI. Patient-oriented composite endpoints (POCEs: all-cause mortality, myocardial infarction, stroke, or repeat revascularization) and its components were assessed stratified by PPI use as a time-dependent covariate in patients with the experiment or reference antiplatelet arm. Results Among 15,839 patients, 2115 patients (13.5%) experienced POCE at 2 years. In the reference arm, the use of PPIs was independently associated with POCE (hazard ratio [HR]: 1.27; 95% confidence interval [CI]: 1.12–1.44) and its individual components, whereas it was not in the experimental arm (HR: 1.04; 95% CI: 0.92–1.19; pinteraction = 0.035). During the second-year follow-up, patients taking aspirin with PPIs had a significantly higher risk of POCE compared to those on aspirin without PPIs (HR: 1.57; 95% CI: 1.27–1.94), whereas the risk did not differ significantly irrespective of PPI in ticagrelor monotherapy group (HR: 1.03; 95% CI: 0.83–1.28; pinteraction = 0.008). Conclusions In contrast to conventional antiplatelet strategy, there were no evidence suggesting the interaction between ticagrelor monotherapy and PPIs on increased cardiovascular events, which should be confirmed in further studies. Clinical Trial Registration URL: https://clinicaltrials.go

SCORE2 risk prediction algorithms: new models to estimate 10-year risk of cardiovascular disease in Europe

Aims The aim of this study was to develop, validate, and illustrate an updated prediction model (SCORE2) to estimate 10-year fatal and non-fatal cardiovascular disease (CVD) risk in individuals without previous CVD or diabetes aged 40-69 years in Europe.Methods and results We derived risk prediction models using individual-participant data from 45 cohorts in 13 countries (677 684 individuals, 30 121 CVD events). We used sex-specific and competing risk-adjusted models, including age, smoking status, systolic blood pressure, and total- and HDL-cholesterol. We defined four risk regions in Europe according to country-specific CVD mortality, recalibrating models to each region using expected incidences and risk factor distributions. Region-specific incidence was estimated using CVD mortality and incidence data on 10 776 466 individuals. For external validation, we analysed data from 25 additional cohorts in 15 European countries (1 133 181 individuals, 43 492 CVD events). After applying the derived risk prediction models to external validation cohorts, C-indices ranged from 0.67 (0.65-0.68) to 0.81 (0.76-0.86). Predicted CVD risk varied several-fold across European regions. For example, the estimated 10-year CVD risk for a 50-year-old smoker, with a systolic blood pressure of 140 mmHg, total cholesterol of 5.5 mmol/L, and HDL-cholesterol of 1.3 mmol/L, ranged from 5.9% for men in low- risk countries to 14.0% for men in very high-risk countries, and from 4.2% for women in low-risk countries to 13.7% for women in very high-risk countries.Conclusion SCORE2-a new algorithm derived, calibrated, and validated to predict 10-year risk of first-onset CVD in European populations-enhances the identification of individuals at higher risk of developing CVD across Europe.Cardiolog