On the Persson-Strang’s Identity for the Legendre Polynomials

We show an alternative proof of an identity given by Persson-Strang for the well known Legendre polynomials.&nbsp

Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases

The production of peroxide and superoxide is an inevitable consequence of aerobic metabolism, and while these particular "reactive oxygen species" (ROSs) can exhibit a number of biological effects, they are not of themselves excessively reactive and thus they are not especially damaging at physiological concentrations. However, their reactions with poorly liganded iron species can lead to the catalytic production of the very reactive and dangerous hydroxyl radical, which is exceptionally damaging, and a major cause of chronic inflammation. We review the considerable and wide-ranging evidence for the involvement of this combination of (su)peroxide and poorly liganded iron in a large number of physiological and indeed pathological processes and inflammatory disorders, especially those involving the progressive degradation of cellular and organismal performance. These diseases share a great many similarities and thus might be considered to have a common cause (i.e. iron-catalysed free radical and especially hydroxyl radical generation). The studies reviewed include those focused on a series of cardiovascular, metabolic and neurological diseases, where iron can be found at the sites of plaques and lesions, as well as studies showing the significance of iron to aging and longevity. The effective chelation of iron by natural or synthetic ligands is thus of major physiological (and potentially therapeutic) importance. As systems properties, we need to recognise that physiological observables have multiple molecular causes, and studying them in isolation leads to inconsistent patterns of apparent causality when it is the simultaneous combination of multiple factors that is responsible. This explains, for instance, the decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference

Enoxaparin followed by once-weekly idrabiotaparinux versus enoxaparin plus warfarin for patients with acute symptomatic pulmonary embolism: a randomised, double-blind, double-dummy, non-inferiority trial

BACKGROUND: Treatment of pulmonary embolism with low-molecular-weight heparin and vitamin K antagonists, such as warfarin, is not ideal. We aimed to assess non-inferiority of idrabiotaparinux, a reversible longlasting indirect inhibitor of activated factor X, to warfarin in patients with acute symptomatic pulmonary embolism. METHODS: In our randomised, double-blind, double-dummy, non-inferiority trial, we enrolled adults with objectively documented acute symptomatic pulmonary embolism attending 291 centres in 37 countries. We excluded patients who were pregnant, had active bleeding, kidney failure, or malignant hypertension, or were at high risk of death, bleeding, or adverse reactions to study drugs. We randomly allocated patients to receive 5-10 days' enoxaparin 1\ub70 mg/kg twice daily followed by subcutaneous idrabiotaparinux (starting dose 3\ub70 mg) or adjusted-dose warfarin (target international normalised ratio 2\ub70-3\ub70); regimens lasted 3 months or 6 months dependent on clinical presentation. Block randomisation was done with a central interactive computerised system, stratified by study centre and intended treatment duration. The primary efficacy outcome was recurrent venous thromboembolism at 99 days after randomisation. We estimated the odds ratio and 95% CI with a Mantel-Haenzsel \u3c7(2) analysis (non-inferiority margin 2\ub70) in the intention-to-treat population. The main safety outcome was clinically relevant bleeding (major or non-major) in all patients at day 99. This study is registered with ClinicalTrials.gov, number NCT00345618. FINDINGS: Between Aug 1, 2006, and Jan 31, 2010, we enrolled 3202 patients aged 18-96 years. 34 (2%) of 1599 patients randomly allocated to receive enoxaparin-idrabiotaparinux and 43 (3%) of 1603 patients randomly allocated to receive enoxaparin-warfarin had recurrent venous thromboembolism (odds ratio 0\ub779, 95% CI 0\ub750-1\ub725; p(non-inferiority)=0\ub70001). 72 (5%) of 1599 patients in the enoxaparin-idrabiotaparinux group and 106 (7%) of 1603 patients in the enoxaparin-warfarin group had clinically relevant bleeding (0\ub767, 0\ub749-0\ub791; p(superiority)=0\ub70098). We noted similar differences in outcomes in those patients treated to 6 months. INTERPRETATION: Idrabiotaparinux could provide an attractive alternative to warfarin for the long-term treatment of pulmonary embolism, and seems to be associated with reduced bleeding

Rivaroxaban with or without aspirin in stable cardiovascular disease

BACKGROUND: We evaluated whether rivaroxaban alone or in combination with aspirin would be more effective than aspirin alone for secondary cardiovascular prevention. METHODS: In this double-blind trial, we randomly assigned 27,395 participants with stable atherosclerotic vascular disease to receive rivaroxaban (2.5 mg twice daily) plus aspirin (100 mg once daily), rivaroxaban (5 mg twice daily), or aspirin (100 mg once daily). The primary outcome was a composite of cardiovascular death, stroke, or myocardial infarction. The study was stopped for superiority of the rivaroxaban-plus-aspirin group after a mean follow-up of 23 months. RESULTS: The primary outcome occurred in fewer patients in the rivaroxaban-plus-aspirin group than in the aspirin-alone group (379 patients [4.1%] vs. 496 patients [5.4%]; hazard ratio, 0.76; 95% confidence interval [CI], 0.66 to 0.86; P<0.001; z=−4.126), but major bleeding events occurred in more patients in the rivaroxaban-plus-aspirin group (288 patients [3.1%] vs. 170 patients [1.9%]; hazard ratio, 1.70; 95% CI, 1.40 to 2.05; P<0.001). There was no significant difference in intracranial or fatal bleeding between these two groups. There were 313 deaths (3.4%) in the rivaroxaban-plus-aspirin group as compared with 378 (4.1%) in the aspirin-alone group (hazard ratio, 0.82; 95% CI, 0.71 to 0.96; P=0.01; threshold P value for significance, 0.0025). The primary outcome did not occur in significantly fewer patients in the rivaroxaban-alone group than in the aspirin-alone group, but major bleeding events occurred in more patients in the rivaroxaban-alone group. CONCLUSIONS: Among patients with stable atherosclerotic vascular disease, those assigned to rivaroxaban (2.5 mg twice daily) plus aspirin had better cardiovascular outcomes and more major bleeding events than those assigned to aspirin alone. Rivaroxaban (5 mg twice daily) alone did not result in better cardiovascular outcomes than aspirin alone and resulted in more major bleeding events

Edoxaban versus warfarin for the treatment of symptomatic venous thromboembolism.

BACKGROUND: Whether the oral factor Xa inhibitor edoxaban can be an alternative to warfarin in patients with venous thromboembolism is unclear. METHODS: In a randomized, double-blind, noninferiority study, we randomly assigned patients with acute venous thromboembolism, who had initially received heparin, to receive edoxaban at a dose of 60 mg once daily, or 30 mg once daily (e.g., in the case of patients with creatinine clearance of 30 to 50 ml per minute or a body weight below 60 kg), or to receive warfarin. Patients received the study drug for 3 to 12 months. The primary efficacy outcome was recurrent symptomatic venous thromboembolism. The principal safety outcome was major or clinically relevant nonmajor bleeding. RESULTS: A total of 4921 patients presented with deep-vein thrombosis, and 3319 with a pulmonary embolism. Among patients receiving warfarin, the time in the therapeutic range was 63.5%. Edoxaban was noninferior to warfarin with respect to the primary efficacy outcome, which occurred in 130 patients in the edoxaban group (3.2%) and 146 patients in the warfarin group (3.5%) (hazard ratio, 0.89; 95% confidence interval [CI], 0.70 to 1.13; P&lt;0.001 for noninferiority). The safety outcome occurred in 349 patients (8.5%) in the edoxaban group and 423 patients (10.3%) in the warfarin group (hazard ratio, 0.81; 95% CI, 0.71 to 0.94; P=0.004 for superiority). The rates of other adverse events were similar in the two groups. A total of 938 patients with pulmonary embolism had right ventricular dysfunction, as assessed by measurement of N-terminal pro-brain natriuretic peptide levels; the rate of recurrent venous thromboembolism in this subgroup was 3.3% in the edoxaban group and 6.2% in the warfarin group (hazard ratio, 0.52; 95% CI, 0.28 to 0.98). CONCLUSIONS: Edoxaban administered once daily after initial treatment with heparin was noninferior to high-quality standard therapy and caused significantly less bleeding in a broad spectrum of patients with venous thromboembolism, including those with severe pulmonary embolism. (Funded by Daiichi-Sankyo; Hokusai-VTE ClinicalTrials.gov number, NCT00986154.)

Ezetimibe added to statin therapy after acute coronary syndromes

BACKGROUND: Statin therapy reduces low-density lipoprotein (LDL) cholesterol levels and the risk of cardiovascular events, but whether the addition of ezetimibe, a nonstatin drug that reduces intestinal cholesterol absorption, can reduce the rate of cardiovascular events further is not known. METHODS: We conducted a double-blind, randomized trial involving 18,144 patients who had been hospitalized for an acute coronary syndrome within the preceding 10 days and had LDL cholesterol levels of 50 to 100 mg per deciliter (1.3 to 2.6 mmol per liter) if they were receiving lipid-lowering therapy or 50 to 125 mg per deciliter (1.3 to 3.2 mmol per liter) if they were not receiving lipid-lowering therapy. The combination of simvastatin (40 mg) and ezetimibe (10 mg) (simvastatin-ezetimibe) was compared with simvastatin (40 mg) and placebo (simvastatin monotherapy). The primary end point was a composite of cardiovascular death, nonfatal myocardial infarction, unstable angina requiring rehospitalization, coronary revascularization ( 6530 days after randomization), or nonfatal stroke. The median follow-up was 6 years. RESULTS: The median time-weighted average LDL cholesterol level during the study was 53.7 mg per deciliter (1.4 mmol per liter) in the simvastatin-ezetimibe group, as compared with 69.5 mg per deciliter (1.8 mmol per liter) in the simvastatin-monotherapy group (P<0.001). The Kaplan-Meier event rate for the primary end point at 7 years was 32.7% in the simvastatin-ezetimibe group, as compared with 34.7% in the simvastatin-monotherapy group (absolute risk difference, 2.0 percentage points; hazard ratio, 0.936; 95% confidence interval, 0.89 to 0.99; P = 0.016). Rates of pre-specified muscle, gallbladder, and hepatic adverse effects and cancer were similar in the two groups. CONCLUSIONS: When added to statin therapy, ezetimibe resulted in incremental lowering of LDL cholesterol levels and improved cardiovascular outcomes. Moreover, lowering LDL cholesterol to levels below previous targets provided additional benefit