33 research outputs found
On the alleged simplicity of impure proof
Roughly, a proof of a theorem, is âpureâ if it draws only on what is âcloseâ or âintrinsicâ to that theorem. Mathematicians employ a variety of terms to identify pure proofs, saying that a pure proof is one that avoids what is âextrinsic,â âextraneous,â âdistant,â âremote,â âalien,â or âforeignâ to the problem or theorem under investigation. In the background of these attributions is the view that there is a distance measure (or a variety of such measures) between mathematical statements and proofs. Mathematicians have paid little attention to specifying such distance measures precisely because in practice certain methods of proof have seemed self- evidently impure by design: think for instance of analytic geometry and analytic number theory. By contrast, mathematicians have paid considerable attention to whether such impurities are a good thing or to be avoided, and some have claimed that they are valuable because generally impure proofs are simpler than pure proofs. This article is an investigation of this claim, formulated more precisely by proof- theoretic means. After assembling evidence from proof theory that may be thought to support this claim, we will argue that on the contrary this evidence does not support the claim
Omecamtiv mecarbil in chronic heart failure with reduced ejection fraction, GALACTICâHF: baseline characteristics and comparison with contemporary clinical trials
Aims:
The safety and efficacy of the novel selective cardiac myosin activator, omecamtiv mecarbil, in patients with heart failure with reduced ejection fraction (HFrEF) is tested in the Global Approach to Lowering Adverse Cardiac outcomes Through Improving Contractility in Heart Failure (GALACTICâHF) trial. Here we describe the baseline characteristics of participants in GALACTICâHF and how these compare with other contemporary trials.
Methods and Results:
Adults with established HFrEF, New York Heart Association functional class (NYHA)ââ„âII, EF â€35%, elevated natriuretic peptides and either current hospitalization for HF or history of hospitalization/ emergency department visit for HF within a year were randomized to either placebo or omecamtiv mecarbil (pharmacokineticâguided dosing: 25, 37.5 or 50âmg bid). 8256 patients [male (79%), nonâwhite (22%), mean age 65âyears] were enrolled with a mean EF 27%, ischemic etiology in 54%, NYHA II 53% and III/IV 47%, and median NTâproBNP 1971âpg/mL. HF therapies at baseline were among the most effectively employed in contemporary HF trials. GALACTICâHF randomized patients representative of recent HF registries and trials with substantial numbers of patients also having characteristics understudied in previous trials including more from North America (n = 1386), enrolled as inpatients (n = 2084), systolic blood pressureâ<â100âmmHg (n = 1127), estimated glomerular filtration rate <â30âmL/min/1.73 m2 (n = 528), and treated with sacubitrilâvalsartan at baseline (n = 1594).
Conclusions:
GALACTICâHF enrolled a wellâtreated, highârisk population from both inpatient and outpatient settings, which will provide a definitive evaluation of the efficacy and safety of this novel therapy, as well as informing its potential future implementation