7,883 research outputs found

    Indexed induction and coinduction, fibrationally.

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    This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we present a sound coinduction rule for any data type arising as the final coalgebra of a functor, thus relaxing Hermida and Jacobs’ restriction to polynomial data types. For this we introduce the notion of a quotient category with equality (QCE), which both abstracts the standard notion of a fibration of relations constructed from a given fibration, and plays a role in the theory of coinduction dual to that of a comprehension category with unit (CCU) in the theory of induction. Second, we show that indexed inductive and coinductive types also admit sound induction and coinduction rules. Indexed data types often arise as initial algebras and final coalgebras of functors on slice categories, so our key technical results give sufficent conditions under which we can construct, from a CCU (QCE) U : E -> B, a fibration with base B/I that models indexing by I and is also a CCU (QCE)

    Methods of a large prospective, randomised, open-label, blinded end-point study comparing morning versus evening dosing in hypertensive patients:the Treatment In Morning versus Evening (TIME) study

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    Introduction: Nocturnal blood pressure (BP) appears to be a better predictor of cardiovascular outcome than daytime BP. The BP lowering effects of most antihypertensive therapies are often greater in the first 12 h compared to the next 12 h. The Treatment In Morning versus Evening (TIME) study aims to establish whether evening dosing is more cardioprotective than morning dosing. Methods and analysis: The TIME study uses the prospective, randomised, open-label, blinded end-point (PROBE) design. TIME recruits participants by advertising in the community, from primary and secondary care, and from databases of consented patients in the UK. Participants must be aged over 18 years, prescribed at least one antihypertensive drug taken once a day, and have a valid email address. After the participants have self-enrolled and consented on the secure TIME website (http://www.timestudy.co.uk) they are randomised to take their antihypertensive medication in the morning or the evening. Participant follow-ups are conducted after 1 month and then every 3 months by automated email. The trial is expected to run for 5 years, randomising 10 269 participants, with average participant follow-up being 4 years. The primary end point is hospitalisation for the composite end point of non-fatal myocardial infarction (MI), non-fatal stroke (cerebrovascular accident; CVA) or any vascular death determined by record-linkage. Secondary end points are: each component of the primary end point, hospitalisation for non-fatal stroke, hospitalisation for non-fatal MI, cardiovascular death, all-cause mortality, hospitalisation or death from congestive heart failure. The primary outcome will be a comparison of time to first event comparing morning versus evening dosing using an intention-to-treat analysis. The sample size is calculated for a two-sided test to detect 20% superiority at 80% power. Ethics and dissemination: TIME has ethical approval in the UK, and results will be published in a peer-reviewed journal. Trial registration number: UKCRN17071; Pre-results
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