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Aims: The prognostic impact of heart rate (HR) in acute heart failure (AHF) patients is not well known especially in atrial fibrillation (AF) patients. The aim of the study was to evaluate the impact of admission HR, discharge HR, HR difference (admission-discharge) in AHF patients with sinus rhythm (SR) or AF on long- term outcomes. Methods: We included 1398 patients consecutively admitted with AHF between October 2013 and December 2014 from a national multicentre, prospective registry. Logistic regression models were used to estimate the association between admission HR, discharge HR and HR difference and one- year all-cause mortality and HF readmission. Results: The mean age of the study population was 72 ± 12 years. Of these, 594 (42.4%) were female, 655 (77.8%) were hypertensive and 655 (46.8%) had diabetes. Among all included patients, 745 (53.2%) had sinus rhythm and 653 (46.7%) had atrial fibrillation. Only discharge HR was associated with one year all-cause mortality (Relative risk (RR) = 1.182, confidence interval (CI) 95% 1.024–1.366, p = 0.022) in SR. In AF patients discharge HR was associated with one year all cause mortality (RR = 1.276, CI 95% 1.115–1.459, p ≤ 0.001). We did not observe a prognostic effect of admission HR or HRD on long-term outcomes in both groups. This relationship is not dependent on left ventricular ejection fraction. Conclusions: In AHF patients lower discharge HR, neither the admission nor the difference, is associated with better long-term outcomes especially in AF patients. Keywords: Heart rate, Acute heart failure, Sinus rhythm, Atrial fibrillation, Mortality

The identity of indiscernibles (PII) states that indiscernible objects must be identical. Many philosophers have held that the PII turns out to be either true but trivial, or non-trivial but false, depending on how the notion of (in)discernibility is spelled out. In this paper, I propose and defend an account of this notion which aims to yield a minimally non-trivial and yet plausible version of the PII. I argue moreover that this version of the principle is immune to a number of well-known and recent objections to the PII., (© The Author(s) 2021.)