Tiling groupoids and Bratteli diagrams

Let T be an aperiodic and repetitive tiling of R^d with finite local complexity. Let O be its tiling space with canonical transversal X. The tiling equivalence relation R_X is the set of pairs of tilings in X which are translates of each others, with a certain (etale) topology. In this paper R_X is reconstructed as a generalized "tail equivalence" on a Bratteli diagram, with its standard AF-relation as a subequivalence relation. Using a generalization of the Anderson-Putnam complex, O is identified with the inverse limit of a sequence of finite CW-complexes. A Bratteli diagram B is built from this sequence, and its set of infinite paths dB is homeomorphic to X. The diagram B is endowed with a horizontal structure: additional edges that encode the adjacencies of patches in T. This allows to define an etale equivalence relation R_B on dB which is homeomorphic to R_X, and contains the AF-relation of "tail equivalence".Comment: 34 pages, 4 figure

Cowries in the archaeology of West Africa: the present picture

Despite the perceived importance of cowrie shells as indicators of long-distance connections in the West African past, their distribution and consumption patterns in archaeological contexts remain surprisingly underexplored, a gap that is only partly explicable by the sparse distribution of archaeological sites within the sub-continent. General writings on the timeline of importation of cowries into West Africa often fail to take into account the latest archaeological evidence and rely instead on accounts drawn from historical or ethnographic documents. This paper is based on a first-hand assessment of over 4500 shells from 78 sites across West Africa, examining chronology, shell species and processes of modification to assess what distribution patterns can tell us about the history of importation and usage of cowries. These first-hand analyses are paralleled by a consideration of published materials. We re-examine the default assumption that two distinct routes of entry existed — one overland from North Africa before the fifteenth century, another coming into use from the time sea links were established with the East African coast and becoming predominant by the middle of the nineteenth century. We focus on the eastern part of West Africa, where the importance of imported cowries to local communities in relatively recent periods is well known and from where we have a good archaeological sample. The conclusion is that on suitably large assemblages shell size can be an indication of provenance and that, while the present archaeological picture seems largely to confirm historical sources, much of this may be due to the discrepancy in archaeological data available from the Sahara/Sahel zone compared to the more forested regions of the sub-continent. Future archaeological work will clarify this matter

Evaluating the Effects of SARS-CoV-2 Spike Mutation D614G on Transmissibility and Pathogenicity

Global dispersal and increasing frequency of the SARS-CoV-2 spike protein variant D614G are suggestive of a selective advantage but may also be due to a random founder effect. We investigate the hypothesis for positive selection of spike D614G in the United Kingdom using more than 25,000 whole genome SARS-CoV-2 sequences. Despite the availability of a large dataset, well represented by both spike 614 variants, not all approaches showed a conclusive signal of positive selection. Population genetic analysis indicates that 614G increases in frequency relative to 614D in a manner consistent with a selective advantage. We do not find any indication that patients infected with the spike 614G variant have higher COVID-19 mortality or clinical severity, but 614G is associated with higher viral load and younger age of patients. Significant differences in growth and size of 614G phylogenetic clusters indicate a need for continued study of this variant

The Cholecystectomy As A Day Case (CAAD) Score: A Validated Score of Preoperative Predictors of Successful Day-Case Cholecystectomy Using the CholeS Data Set

Background Day-case surgery is associated with significant patient and cost benefits. However, only 43% of cholecystectomy patients are discharged home the same day. One hypothesis is day-case cholecystectomy rates, defined as patients discharged the same day as their operation, may be improved by better assessment of patients using standard preoperative variables. Methods Data were extracted from a prospectively collected data set of cholecystectomy patients from 166 UK and Irish hospitals (CholeS). Cholecystectomies performed as elective procedures were divided into main (75%) and validation (25%) data sets. Preoperative predictors were identified, and a risk score of failed day case was devised using multivariate logistic regression. Receiver operating curve analysis was used to validate the score in the validation data set. Results Of the 7426 elective cholecystectomies performed, 49% of these were discharged home the same day. Same-day discharge following cholecystectomy was less likely with older patients (OR 0.18, 95% CI 0.15–0.23), higher ASA scores (OR 0.19, 95% CI 0.15–0.23), complicated cholelithiasis (OR 0.38, 95% CI 0.31 to 0.48), male gender (OR 0.66, 95% CI 0.58–0.74), previous acute gallstone-related admissions (OR 0.54, 95% CI 0.48–0.60) and preoperative endoscopic intervention (OR 0.40, 95% CI 0.34–0.47). The CAAD score was developed using these variables. When applied to the validation subgroup, a CAAD score of ≤5 was associated with 80.8% successful day-case cholecystectomy compared with 19.2% associated with a CAAD score >5 (p < 0.001). Conclusions The CAAD score which utilises data readily available from clinic letters and electronic sources can predict same-day discharges following cholecystectomy

Line intensity ratios in electron spin resonance spectra. A remarkable change accompanying saturation

In certain large organic radicals having a highly localized unpaired electron the intensities, even at moderate levels of microwave power, of the 13C satellite lines relative to the main line(s) may be very much greater than would be anticipated from the number of contributing 13C nuclei. This phenomenon, which can complicate attempts to identify organic radicals, can be qualitatively accounted for in terms of differential saturation behavior. The species producing the main line(s) has only weak relaxation mechanisms while the nuclear hyperfine interaction in the 13C containing radicals provides much stronger relaxation. \ua9 1978 American Chemical Society.Peer reviewed: YesNRC publication: Ye