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We determine the reflexivity index of some closed set lattices by constructing maps relative to irrational rotations. For example, various nests of closed balls and some topological spaces, such as even-dimensional spheres and a wedge of two circles, have reflexivity index 2. We also show that a connected double of spheres has reflexivity index at most 2.
Coronavirus disease 2019 imposed dramatic changes on ENT service delivery. Pre-pandemic, such changes would have been considered potentially unsafe. This study outlines the impact of lockdown on the incidence and management of ENT emergencies at a large UK centre.
After modification of pre-pandemic guidelines, ENT emergency referrals data during the UK lockdown were prospectively captured. A comparative analysis was performed with retrospective data from a corresponding period in 2019.
An overall reduction (p < 0.001) in emergency referrals (n = 119) and admissions (n = 18) occurred during the lockdown period compared to the 2019 period (432 referrals and 290 admissions). Specifically, there were reduced admission rates for epistaxis (p < 0.0001) and tonsillar infection (p < 0.005) in the lockdown period. During lockdown, 90 per cent of patients requiring non-dissolvable nasal packing were managed as out-patients.
Coronavirus disease 2019 compelled modifications to pre-pandemic ENT guidelines. The enforced changes to emergency care appear to be safe and successfully adopted. Arguably, the measures have both economic and patient-related implications post-coronavirus disease 2019 and during future similar pandemics and lockdowns.
Antihypertensive drugs (AHTs) are associated with lowered risks of neurodegenerative diseases and stroke. However, the relative risks associated with different AHT classes are unclear. Using an electronic health record network with 34 million eligible patients, we compared rates of these disorders over a 2-year period, in propensity score-matched cohorts of people taking calcium channel blockers (CCBs) compared with those taking other AHT classes. CCBs were associated with a higher incidence of all disorders compared with renin-angiotensin system agents, and a higher incidence of dementia and cerebrovascular disease compared with diuretics. CCBs were associated with a lower incidence of movement disorders and cerebrovascular disease compared with beta-blockers. The data show that AHT classes confer differential risks of neurodegenerative and cerebrovascular diagnoses.