Triangulating non-Archimedean probability

We relate Popper functions to regular and perfectly additive such non-Archimedean probability functions by means of a representation theorem: every such non-Archimedean probability function is infinitesimally close to some Popper function, and vice versa. We also show that regular and perfectly additive non-Archimedean probability functions can be given a lexicographic representation. Thus Popper functions, a specific kind of non-Archimedean probability functions, and lexicographic probability functions triangulate to the same place: they are in a good sense interchangeable.publishe

Linguistic validation, validity and reliability of the British English versions of the Disabilities of the Arm, Shoulder and Hand (DASH) questionnaire and QuickDASH in people with rheumatoid arthritis

Background: Although the Disabilities of the Arm, Shoulder and Hand (DASH) questionnaire is widely used in the UK, no British English version is available. The aim of this study was to linguistically validate the DASH into British English and then test the reliability and validity of the British English DASH, (including the Work and Sport/Music DASH) and QuickDASH, in people with rheumatoid arthritis (RA). Methods: The DASH was forward translated, reviewed by an expert panel and cognitive debriefing interviews undertaken with 31 people with RA. Content validity was evaluated using the ICF Core Set for RA. Participants with RA (n=340) then completed the DASH, Health Assessment Questionnaire (HAQ), Short Form Health Survey v2 (SF36v2) and Measure of Activity Performance of the Hand (MAPHAND). We examined internal consistency and concurrent validity for the DASH, Work and Sport/Music DASH modules and QuickDASH. Participants repeated the DASH to assess test-retest reliability. Results: Minor wording changes were made as required. The DASH addresses a quarter of Body Function and half of Activities and Participation codes in the ICF RA Core Set. Internal consistency for DASH scales were consistent with individual use (Cronbach’s alpha = 0.94-0.98). Concurrent validity was strong with the HAQ (rs = 0.69-0.91), SF36v2 Physical Function (rs = -0.71 - -0.85), Bodily Pain (rs = -0.71 - -0.74) scales and MAPHAND (rs =0.71-0.93). Test-retest reliability was good (rs = 0.74-0.95). Conclusions: British English versions of the DASH, QuickDASH and Work and Sport/Music modules are now available to evaluate upper limb disabilities in the UK. The DASH, QuickDASH, Work and Sport/Music modules are reliable and valid to use in clinical practice and research with British people with RA

The importance of the intensive care unit environment in sleep-A study with healthy participants

Sleep disruption is common among intensive care unit patients, with potentially detrimental consequences. Environmental factors are thought to play a central role in ICU sleep disruption, and so it is unclear why environmental interventions have shown limited improvements in objectively assessed sleep. In critically ill patients, it is difficult to isolate the influence of environmental factors from the varying contributions of non-environmental factors. We thus investigated the effects of the ICU environment on self-reported and objective sleep quality in 10 healthy nurses and doctors with no history of sleep pathology or current or past ICU employment participated. Their sleep at home, in an unfamiliar environment ('Control'), and in an active ICU ('ICU') was evaluated using polysomnography and the Richard-Campbell Sleep Questionnaire. Environmental sound, light and temperature exposure were measured continuously. We found that the control and ICU environment were noisier and warmer, but not darker than the home environment. Sleep on the ICU was perceived as qualitatively worse than in the home and control environment, despite relatively modest effects on polysomnography parameters compared with home sleep: mean total sleep times were reduced by 48 min, mean rapid eye movement sleep latency increased by 45 min, and the arousal index increased by 9. Arousability to an awake state by sound was similar. Our results suggest that the ICU environment plays a significant but partial role in objectively assessed ICU sleep impairment in patients, which may explain the limited improvement of objectively assessed sleep after environmental interventions