The AF structure of non commutative toroidal Z/4Z orbifolds

For any irrational theta and rational number p/q such that q|qtheta-p|<1, a projection e of trace q|qtheta-p| is constructed in the the irrational rotation algebra A_theta that is invariant under the Fourier transform. (The latter is the order four automorphism U mapped to V, V mapped to U^{-1}, where U, V are the canonical unitaries generating A_theta.) Further, the projection e is approximately central, the cut down algebra eA_theta e contains a Fourier invariant q x q matrix algebra whose unit is e, and the cut downs eUe, eVe are approximately inside the matrix algebra. (In particular, there are Fourier invariant projections of trace k|qtheta-p| for k=1,...,q.) It is also shown that for all theta the crossed product A_theta rtimes Z_4 satisfies the Universal Coefficient Theorem. (Z_4 := Z/4Z.) As a consequence, using the Classification Theorem of G. Elliott and G. Gong for AH-algebras, a theorem of M. Rieffel, and by recent results of H. Lin, we show that A_theta rtimes Z_4 is an AF-algebra for all irrational theta in a dense G_delta.Comment: 35 page

Cohort profile of the UK Biobank: diagnosis and characteristics of cerebrovascular disease

Purpose: The UK Biobank is a large-scale biomedical resource, containing sociodemographic and medical information, including data on a previous diagnosis of stroke or transient ischaemic attack (TIA). We described these participants and their medication usage. Participants: We identified participants who either self-reported or were identified from a nurse-led interview, having suffered a stroke or a TIA and compared them against participants without stroke ort TIA. We assessed their risk factor burden (sex, age, deprivation, waist to hip ratio (WHR), hypertension, smoking, alcohol intake, diabetes, physical exercise and oral contraception use (oral contraceptive pill, OCP)) and medication usage. Findings: to date We studied 502 650 people (54.41% women), 6669 (1.23%) participants self-reported a stroke. The nurse-led interview identified 7669 (1.53%) people with stroke and 1781 (0.35%) with TIA. Hypertension, smoking, higher WHR, lower alcohol consumption and diabetes were all more common in people with cerebrovascular disease (p&lt;0.0001 for each). Women with cerebrovascular disease were less likely to have taken the OCP (p=0.0002). People with cerebrovascular disease did more exercise (p=0.03). Antithrombotic medication was taken by 81% of people with stroke (both self-report and nurse-led responders) and 89% with TIA. For self-reported stroke, 63% were taking antithrombotic and cholesterol medications, 54% taking antithrombotic and antihypertensive medications and 46% taking all 3. For the nurse-led interview and TIA, these figures were 65%, 54% and 46%, and 70%, 53% and 45%, respectively. Future plans: The UK Biobank provides a large, generalisable and contemporary data source in a young population. The characterisation of the UK Biobank cohort with cerebrovascular disease will form the basis for ongoing research using this data source

Deriving modified rankin scores from medical records

&lt;p&gt;&lt;b&gt;Background and Purpose:&lt;/b&gt; Modified Rankin score (mRS) is traditionally graded using a face-to-face or telephone interview. Certain stroke assessment scales can be derived from a review of a patient’s case-record alone. We hypothesized that mRS could be successfully derived from the narrative within patient case-records.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Methods:&lt;/b&gt; Sequential patients attending our cerebrovascular outpatient clinic were included. Two independent, blinded clinicians, trained in mRS, assessed case-records to derive mRS. They scored “certainty” of their grading on a 5-point Likert scale. Agreement between derived and traditional face-to-face mRS was calculated using attribute agreement analysis.&lt;/p&gt; &lt;p&gt;&lt;b&gt;Results:&lt;/b&gt; Fifty patients with a range of disabilities were included. Case-record appraisers were poor at deriving mRS (k=0.34 against standard). Derived mRS grades showed poor agreement between observers (k=0.33). There was no relationship between certainty of derived mRS and proportion of correct grades (P=0.727).&lt;/p&gt; &lt;p&gt;&lt;b&gt;Conclusion:&lt;/b&gt; Accurate mRS cannot be derived from standard hospital records. Direct mRS interview is still required for clinical trials.&lt;/p&gt

Cost effectiveness of community leg ulcer clinics: randomised controlled trial

Objectives: To establish the relative cost effectiveness of community leg ulcer clinics that use four layer compression bandaging versus usual care provided by district nurses. Design: Randomised controlled trial with 1 year of follow up. Setting: Eight community based research clinics in four trusts in Trent. Subjects: 233 patients with venous leg ulcers allocated at random to intervention (120) or control (113) group. Interventions: Weekly treatment with four layer bandaging in a leg ulcer clinic (clinic group) or usual care at home by the district nursing service (control group). Main outcome measures: Time to complete ulcer healing, patient health status, and recurrence of ulcers. Satisfaction with care, use of services, and personal costs were also monitored. Results: The ulcers of patients in the clinic group tended to heal sooner than those in the control group over the whole 12 month follow up (log rank P=0.03). At 12 weeks, 34% of patients in the clinic group were healed compared with 24% in the control. The crude initial healing rate of ulcers in intervention compared with control patients was 1.45 (95% confidence interval 1.04 to 2.03). No significant differences were found between the groups in health status. Mean total NHS costs were £878.06 per year for the clinic group and £859.34 for the control (P=0.89). Conclusions: Community based leg ulcer clinics with trained nurses using four layer bandaging is more effective than traditional home based treatment. This benefit is achieved at a small additional cost and could be delivered at reduced cost if certain service configurations were used

Settlement and Early Post-Settlement Survival of Sessile Marine Invertebrates on Topographically Complex Surfaces: The Importance of Refuge Dimensions and Adult Morphology

We predicted that both refuge dimension and growth form would influence settlement and short-term post-settlement success (≤7 d) of sessile marine invertebrates that live attached to hard substrata in low energy environments. Individuals with unlimited attachment to the substrata should rapidly be protected by their growth form, thus decreasing their need to settle in refuges and limiting the length of time any locations on heterogeneous substrata act as refuges. Alternatively, organisms with limited attachment to the substrata should remain susceptible to the causes of mortality for a longer time, and as a result should settle in high quality refuges (sites that protect individuals from competitors, predators or physical disturbance events until either a size refuge or reproductive maturity is obtained). Results agreed with these predictions for 4 species of invertebrates examined on both the topographically complex surface of the solitary ascidian Styela plicata (hereafter Styela) and on settlement plates with uniformly spaced roughness elements that mimicked the heights of roughness elements (2.0 and 5.0 rnm) found on Styela in Beaufort, North Carollna, USA. On all surfaces, the 2 species with limited attachment to the substrata, Balanus sp. (aclonal, solitary) and Bugula neritina (clonal, arborescent), settled almost exclusively in the location that provided individuals with the best refuge: the crevices formed where the bases of roughness elements intersect with the flat surfaces. Additionally, when roughness elements of various heights were present (Styela, range: 0 6 to 8.8 mm), intermediate size roughness elements (2.0 ˂ x ≤15.0 mm) were picked over 72% of the time. Settlement locations and locations where survival were enhanced were less consistent for the 2 species with unlimited attachment to the substrata: a clonal, encrusting form (Schjzoporella errata) and a clonal stolon-mat form (Tubularia crocea). Fewer individuals of these 2 species settled on roughness elements on Styela and when they did, they were not restricted to the bases of the roughness elements. On the plate surfaces, most settlement did occur in crevices, but both species grew away from this location within days and short-term survival was not consistently greater in this location. Additional trials were run on plates with pits of the same maximum dimensions as the tested roughness elements (2.0 and 5.0 mm depth) to see if crevices and pits provide refuges of equal quality for newly settled individuals. Only survival of Balanus sp. recruits was greatest in both crevices and pits. Evidence for active choice of settlement location comes from consistent results in trials in which some larvae settled in greater numbers on specific size roughness elements on Styela and in areas of high erosion. Overall, these results show that one must be very cautious when generalizing about refuge quality on heterogeneous surfaces, and to determine if a location is a spatial refuge, it is critical to consider: (1) the dimensions of the larva, (2) the relative dimensions of the individual and potential refuge location at any point in time from the moment settlement occurred, and (3) the growth form of the individual which is related to its need for protection from biotic and abiotic sources of mortality

Quantifying Spatial Patterns of Overgrowth in Epibenthic Communities

A method is presented that allows rapid and accurate measurement of changes in the spatial pattern of space occupation in encrusting organisms. The boundaries of organisms are represented as polygons, and geometric difference calculations are used to establish the perimeters of the areas gained or vacated between sampling dates. The influence of interspecific interactions on occupation of space is also quantified: geometric intersection calculations are used to define the perimeters of the areas gained or lost in overgrowth interactions. A method is presented for estimating the sampling frequency necessary for detection of significant changes in occupation of space. The method provides a means of quantifying not only changes in percent cover and diversity but also the dynamics of colony movement and the rates and outcomes of competitive interactions

Black Hole Entropy, Topological Entropy and the Baum-Connes Conjecture in K-Theory

We shall try to exhibit a relation between black hole entropy and topological entropy using the famous Baum-Connes conjecture for foliated manifolds which are particular examples of noncommutative spaces. Our argument is qualitative and it is based on the microscopic origin of the Beckenstein-Hawking area-entropy formula for black holes, provided by superstring theory, in the more general noncommutative geometric context of M-Theory following the Connes- Douglas-Schwarz article.Comment: 17 pages, Latex, contains an important paragraph in section 2 which gives a better understandin

Olive Schreiner at 150: some thoughts on re-editing Cronwright's The Reinterment on Buffelskop

[From the introduction]: The original edition of Cronwright’s The Reinterment on Buffelskop (1983) was produced by Guy Butler and Nick Visser to commemorate the centenary of the 1883 publication of The Story of an African Farm. The Butler-Visser text was a photographic reproduction of a typed carbon copy of the first part of Cronwright’s extant diaries plus a special diary he had kept covering in detail the events of the actual reinterment. (The originals are now at the National English Literary Museum [NELM].) Butler included a comprehensive and illuminating introduction to these texts, as well as – under separate soft cover – a set of “Provisional Notes” which draw deeply on his own and his family’s accumulated knowledge of Cradock, its environs and inhabitants. In addition, Butler and Visser included two passages excised by Cronwright from the typescript of his Life of Olive Schreiner: a word picture of Charles Heathcote, and the longer account of “The Nienaber Incident” – pages which deal with the execution of three innocent men at De Aar on 19 March 1901, and Cronwright’s subsequent attempts at legal reparation for them and their families. The substantive text of the Butler-Visser edition is often difficult to read because of the method of reproduction; moreover, because it also reproduces Cronwright’s emendations (in ink) of the typescript, it is frankly uninviting. Thus, when the NELM Council proposed a publication commemorating the 150th anniversary of Olive Schreiner’s birth on 24 March 1855, it seemed appropriate that a second attempt be made to give students of Olive Schreiner’s works easier access to Cronwright’s detailed account of this “bizarre, romantic” episode. Furthermore, from the perspective of text history, the typescript of the Reinterment antedates both Cronwright’s Life and The Letters of Olive Schreiner. Parts of it are clearly Cronwright’s preliminary ‘notes towards’ his Life, and, as Butler hypothesizes, the whole of the Reinterment might have been intended as a separate (and earlier) publication. Finally, the sarcophagus on Buffelskop is one of South Africa’s more noteworthy literary shrines: while the idea of re-editing an account of Olive Schreiner’s reinterment might be thought to be a futile exercise in intellectual recycling, our intention is that both husband and wife should live again through a rediscovery of the thoughts and feelings that led them to this dramatic final resting-place