The compression theorem I

This the first of a set of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie, made parallel to the given R direction) by an isotopy of M and normal field in Q X R. The theorem can be deduced from Gromov's theorem on directed embeddings [M Gromov, Partial differential relations, Springer-Verlag (1986); 2.4.5 C'] and is implicit in the preceeding discussion. Here we give a direct proof that leads to an explicit description of the finishing embedding. In the second paper in the series we give a proof in the spirit of Gromov's proof and in the third part we give applications.Comment: This is a shortened version of "The compression theorem": applications have been omitted and will be published as part III. For a preliminary version of part III, see section 5 onwards of version 2 of this paper. This version (v3) is published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper14.abs.htm

Developing clinical guidelines: a challenge to current methods.

Current methods for producing clinical guidelines are cumbersome and not always reliable. Could a more streamlined approach improve coverage and make decisions more transparent

Impact on mortality of prompt admission to critical care for deteriorating ward patients: an instrumental variable analysis using critical care bed strain.

PURPOSE: To estimate the effect of prompt admission to critical care on mortality for deteriorating ward patients. METHODS: We performed a prospective cohort study of consecutive ward patients assessed for critical care. Prompt admissions (within 4 h of assessment) were compared to a 'watchful waiting' cohort. We used critical care strain (bed occupancy) as a natural randomisation event that would predict prompt transfer to critical care. Strain was classified as low, medium or high (2+, 1 or 0 empty beds). This instrumental variable (IV) analysis was repeated for the subgroup of referrals with a recommendation for critical care once assessed. Risk-adjusted 90-day survival models were also constructed. RESULTS: A total of 12,380 patients from 48 hospitals were available for analysis. There were 2411 (19%) prompt admissions (median delay 1 h, IQR 1-2) and 9969 (81%) controls; 1990 (20%) controls were admitted later (median delay 11 h, IQR 6-26). Prompt admissions were less frequent (p < 0.0001) as strain increased from low (22%), to medium (15%) to high (9%); the median delay to admission was 3, 4 and 5 h respectively. In the IV analysis, prompt admission reduced 90-day mortality by 7.4% (95% CI 1.7-18.5%, p = 0.117) overall, and 16.2% (95% CI 1.1-31.3%, p = 0.036) for those recommended for critical care. In the risk-adjust survival model, 90-day mortality was similar. CONCLUSION: After allowing for unobserved prognostic differences between the groups, we find that prompt admission to critical care leads to lower 90-day mortality for patients assessed and recommended to critical care

Improving long-term disaster recovery research in Australia through boosting dataset comparability

Emergencies and disasters are increasing in frequency and complexity in Australia and around the world.1 It is well established that the effects of these events take a long time to recover from. There is strong and growing evidence to show that different segments of society are exposed to disasters in different ways, with people and communities affected in interconnected and compounding ways