Partial actions of monoids

We investigate partial monoid actions, in the sense of Megrelishvili and Schroeder [12]. These are equivalent to a class of premorphisms, which we call strong premorphisms. We describe two distinct methods for constructing a monoid action from a partial monoid action: the expansion method provides a generalisation of a result of Kellendonk and Lawson [10] in the group case, whilst the approach via globalisation extends results of both [12] and [10]

Oxford mathematics at a low ebb? an 1855 dispute over examination results

Between December 1855 and March 1856, a public dispute raged, in British national newspapers and locally published pamphlets, between two teachers at the University of Oxford: the mathematical lecturer Francis Ashpitel and Bartholomew Price, the professor of natural philosophy. The starting point for these exchanges was the particularly poor results that had come out of the final mathematics examinations in Oxford that December. Ashpitel, as one of the examiners, stood accused of setting questions that were too difficult for the ordinary student, with the consequence that, in Price’s view, further mathematical study in Oxford – never as robust as in Cambridge – would be discouraged. We examine this short-lived affair, and use it not only to gain insight into the status of mathematical study in Oxford in the mid-nineteenth century, but also to point towards the increasing importance of competitive examinations in British public life at that time

Extending the Ehresmann-Schein-Nambooripad Theorem

We extend the `join-premorphisms' part of the Ehresmann-Schein-Nambooripad Theorem to the case of two-sided restriction semigroups and inductive categories, following on from a result of Lawson (1991) for the `morphisms' part. However, it is so-called `meet-premorphisms' which have proved useful in recent years in the study of partial actions. We therefore obtain an Ehresmann-Schein-Nambooripad-type theorem for meet-premorphisms in the case of two-sided restriction semigroups and inductive categories. As a corollary, we obtain such a theorem in the inverse case.Comment: 23 pages; final section on Szendrei expansions removed; further reordering of materia

Avaliação ecocardiográfica e auscultação electrónica de 27 casos de gatos por presença de sopro à auscultação cardíaca convencional

Dissertação de Mestrado Integrado em Medicina VeterináriaContexto: ao longo dos anos, as doenças cardíacas do paciente felino têm recebido menos atenção do que as doenças cardíacas em cães pela classe médico-veterinária (Fuentes, 2015). Numa avaliação comparativa sobre o tema, o Journal of Veterinary Cardiology conteve cerca de quatro vezes mais estudos relacionados com cães do que com gatos durante os últimos dez anos (Fuentes, 2015). Para além disso, a presença de sopro à auscultação num cão é um indicador de doença cardíaca muito mais fidedigno do que um sopro ouvido num gato (Wagner, Fuentes, Payne, McDermott & Brodbelt, 2010), o que dificulta ainda mais a interpretação deste som que, muitas vezes, é dinâmico (Dirven, Cornelissen, Barendse, Van Mook & Sterenborg, 2010). Objectivos [principais (P) e secundários (S)] deste estudo: Ρ Compreender a prevalência das doenças cardíacas numa população representativa de gatos que se apresentaram à consulta com sopro à auscultação; Ρ Aferir qualitativamente a relevância clínica do uso do estetoscópio electrónico quando comparado com o método convencional; Ρ Tentativa de compreender a presença de sopro cardíaco em gatos cujos exames ecocardiográficos não fundamentam a presença de sopro; S Calcular a sensibilidade e especificidade da auscultação cardíaca em gatos; S Tentar compreender a ausência de sopro cardíaco em gatos cujos exames ecocardiográficos fundamentam a presença de sopro; S Sensibilizar a classe médico-veterinária para a importância de uma auscultação detalhada no paciente felino. Principais conclusões e relevância clínica: cerca de 70% (n=20) dos 27 gatos com sopro cardíaco apresentaram algum tipo de hipertrofia do ventrículo esquerdo (SIVd ≥ 0,50cm), destes, 50% (n=10) possuíam concomitantemente algum grau de regurgitação valvular, sendo a regurgitação mitral a mais prevalente. Apenas um gato se apresentou com sopro (II/VI) e sem achados ecocardiográficos significativos, podendo este dever-se à sedação administrada, a alterações hemodinâmicas (anemia, estados infecciosos) ou outras alterações sistémicas. Dos 27 gatos, houve apenas dois casos (7%) de cardiomiopatia restritiva e um caso (4%) de cardiomiopatia dilatada. Sete porcento (n=2) apresentou doença cardíaca congénita. O uso do estetoscópio electrónico provou-se indispensável, principalmente, na detecção de ruídos de galope e na análise morfológica das ondas e seu relacionamento com a doença cardíaca presente; na classificação da intensidade de sopros, contudo, mostrou-se ineficiente.ABSTRACT - Echocardiographic assessment and electronic auscultation of 27 cases of cats by presence of heart murmur on conventional cardiac auscultation - Background: throughout the years, feline heart diseases have received less attention than dog’s heart disease by the veterinary professionals (Fuentes, 2015). In one comparative assessment regarding the subject, the ‘Journal of Veterinary Cardiology’ has about four times more research related to dogs than cats during the last ten years (Fuentes, 2015). Besides, a murmur auscultated on a dog is a much more reliable marker of heart disease than the same sound heard on a cat (Wagner, Fuentes, Payne, McDermott & Brodbelt, 2010), what makes the interpretation of murmurs, sometimes dynamic, much harder (Dirven, Cornelissen, Barendse, Van Mook & Sterenborg, 2010). Objectives [prime (P) and secondary (S)]: Ρ Comprehension of the prevalence of cardiac diseases on a population of cats that were present with heart murmur at auscultation; Ρ Understanding the clinical relevance of the use of electronic stethoscopes compared with the conventional method; Ρ Explanation for the presence of heart murmur in cats which have no significant alteration on echocardiographic examination; S Sensitivity and sensibility calculation for cats’ auscultation; S Explanation for the absence of heart murmurs in cats with alterations on echocardiographic examination; S Sensitize veterinary professionals for the importance of a thorough auscultation of the feline patient. Leading conclusions and clinical significance: about 70% (n=20) of the 27 cats presented with a heart murmur showed some kind of hypertrophy of the left ventricle (SIVd ≥ 0,50cm), half of which (n=10) had some degree of valvular regurgitation at the same time, being mitral regurgitation the most common. Only 1 cat was present with a murmur (II/VI) and no significant echocardiographic findings, probably due to the tranquilization that was administered, hemodynamic alterations (anaemia, infectious states, stress) or other systemic disorders. Of the 27 cats, there were only two cases (7%) of restrictive cardiomyopathy and one case (4%) of dilated cardiomyopathy. Seven percent (n=2) were present with a congenital heart disease. The use of an electronic stethoscope proved itself useful, mainly at the detection of gallop sounds and analysis of wave morphologies and its connection with each cardiac disease; for the classification of the intensity of the murmur, however, it proved itself inefficient.N/

Predicting farm-level animal populations using environmental and socioeconomic variables

Accurate information on the geographic distribution of domestic animal populations helps biosecurity authorities to efficiently prepare for and rapidly eradicate exotic diseases, such as Foot and Mouth Disease (FMD). Developing and maintaining sufficiently high-quality data resources is expensive and time consuming. Statistical modelling of population density and distribution has only begun to be applied to farm animal populations, although it is commonly used in wildlife ecology. We developed zero-inflated Poisson regression models in a Bayesian framework using environmental and socioeconomic variables to predict the counts of livestock units (LSUs) and of cattle on spatially referenced farm polygons in a commercially available New Zealand farm database, Agribase. Farm-level counts of cattle and of LSUs varied considerably by region, because of the heterogeneous farming landscape in New Zealand. The amount of high quality pasture per farm was significantly associated with the presence of both cattle and LSUs. Internal model validation (predictive performance) showed that the models were able to predict the count of the animal population on groups of farms that were located in randomly selected 3 km zones with a high level of accuracy. Predicting cattle or LSU counts on individual farms was less accurate. Predicted counts were statistically significantly more variable for farms that were contract grazing dry stock, such as replacement dairy heifers and dairy cattle not currently producing milk, compared with other farm types. This analysis presents a way to predict numbers of LSUs and cattle for farms using environmental and socio-economic data. The technique has the potential to be extrapolated to predicting other pastoral based livestock species

Evaluation of antithrombotic use and COVID-19 outcomes in a nationwide atrial fibrillation cohort

OBJECTIVE: To evaluate antithrombotic (AT) use in individuals with atrial fibrillation (AF) and at high risk of stroke (CHA2DS2-VASc score ≥2) and investigate whether pre-existing AT use may improve COVID-19 outcomes. METHODS: Individuals with AF and CHA2DS2-VASc score ≥2 on 1 January 2020 were identified using electronic health records for 56 million people in England and were followed up until 1 May 2021. Factors associated with pre-existing AT use were analysed using logistic regression. Differences in COVID-19-related hospitalisation and death were analysed using logistic and Cox regression in individuals with pre-existing AT use versus no AT use, anticoagulants (AC) versus antiplatelets (AP), and direct oral anticoagulants (DOACs) versus warfarin. RESULTS: From 972 971 individuals with AF (age 79 (±9.3), female 46.2%) and CHA2DS2-VASc score ≥2, 88.0% (n=856 336) had pre-existing AT use, 3.8% (n=37 418) had a COVID-19 hospitalisation and 2.2% (n=21 116) died, followed up to 1 May 2021. Factors associated with no AT use included comorbidities that may contraindicate AT use (liver disease and history of falls) and demographics (socioeconomic status and ethnicity). Pre-existing AT use was associated with lower odds of death (OR=0.92, 95% CI 0.87 to 0.96), but higher odds of hospitalisation (OR=1.20, 95% CI 1.15 to 1.26). AC versus AP was associated with lower odds of death (OR=0.93, 95% CI 0.87 to 0.98) and higher hospitalisation (OR=1.17, 95% CI 1.11 to 1.24). For DOACs versus warfarin, lower odds were observed for hospitalisation (OR=0.86, 95% CI 0.82 to 0.89) but not for death (OR=1.00, 95% CI 0.95 to 1.05). CONCLUSIONS: Pre-existing AT use may be associated with lower odds of COVID-19 death and, while not evidence of causality, provides further incentive to improve AT coverage for eligible individuals with AF

COVID-19 trajectories among 57 million adults in England:a cohort study using electronic health records

Background: Updatable estimates of COVID-19 onset, progression, and trajectories underpin pandemic mitigation efforts. To identify and characterise disease trajectories, we aimed to define and validate ten COVID-19 phenotypes from nationwide linked electronic health records (EHR) using an extensible framework. Methods: In this cohort study, we used eight linked National Health Service (NHS) datasets for people in England alive on Jan 23, 2020. Data on COVID-19 testing, vaccination, primary and secondary care records, and death registrations were collected until Nov 30, 2021. We defined ten COVID-19 phenotypes reflecting clinically relevant stages of disease severity and encompassing five categories: positive SARS-CoV-2 test, primary care diagnosis, hospital admission, ventilation modality (four phenotypes), and death (three phenotypes). We constructed patient trajectories illustrating transition frequency and duration between phenotypes. Analyses were stratified by pandemic waves and vaccination status. Findings: Among 57 032 174 individuals included in the cohort, 13 990 423 COVID-19 events were identified in 7 244 925 individuals, equating to an infection rate of 12·7% during the study period. Of 7 244 925 individuals, 460 737 (6·4%) were admitted to hospital and 158 020 (2·2%) died. Of 460 737 individuals who were admitted to hospital, 48 847 (10·6%) were admitted to the intensive care unit (ICU), 69 090 (15·0%) received non-invasive ventilation, and 25 928 (5·6%) received invasive ventilation. Among 384 135 patients who were admitted to hospital but did not require ventilation, mortality was higher in wave 1 (23 485 [30·4%] of 77 202 patients) than wave 2 (44 220 [23·1%] of 191 528 patients), but remained unchanged for patients admitted to the ICU. Mortality was highest among patients who received ventilatory support outside of the ICU in wave 1 (2569 [50·7%] of 5063 patients). 15 486 (9·8%) of 158 020 COVID-19-related deaths occurred within 28 days of the first COVID-19 event without a COVID-19 diagnoses on the death certificate. 10 884 (6·9%) of 158 020 deaths were identified exclusively from mortality data with no previous COVID-19 phenotype recorded. We observed longer patient trajectories in wave 2 than wave 1. Interpretation: Our analyses illustrate the wide spectrum of disease trajectories as shown by differences in incidence, survival, and clinical pathways. We have provided a modular analytical framework that can be used to monitor the impact of the pandemic and generate evidence of clinical and policy relevance using multiple EHR sources. Funding: British Heart Foundation Data Science Centre, led by Health Data Research UK.</p

COVID-19 trajectories among 57 million adults in England:a cohort study using electronic health records

Background: Updatable estimates of COVID-19 onset, progression, and trajectories underpin pandemic mitigation efforts. To identify and characterise disease trajectories, we aimed to define and validate ten COVID-19 phenotypes from nationwide linked electronic health records (EHR) using an extensible framework. Methods: In this cohort study, we used eight linked National Health Service (NHS) datasets for people in England alive on Jan 23, 2020. Data on COVID-19 testing, vaccination, primary and secondary care records, and death registrations were collected until Nov 30, 2021. We defined ten COVID-19 phenotypes reflecting clinically relevant stages of disease severity and encompassing five categories: positive SARS-CoV-2 test, primary care diagnosis, hospital admission, ventilation modality (four phenotypes), and death (three phenotypes). We constructed patient trajectories illustrating transition frequency and duration between phenotypes. Analyses were stratified by pandemic waves and vaccination status. Findings: Among 57 032 174 individuals included in the cohort, 13 990 423 COVID-19 events were identified in 7 244 925 individuals, equating to an infection rate of 12·7% during the study period. Of 7 244 925 individuals, 460 737 (6·4%) were admitted to hospital and 158 020 (2·2%) died. Of 460 737 individuals who were admitted to hospital, 48 847 (10·6%) were admitted to the intensive care unit (ICU), 69 090 (15·0%) received non-invasive ventilation, and 25 928 (5·6%) received invasive ventilation. Among 384 135 patients who were admitted to hospital but did not require ventilation, mortality was higher in wave 1 (23 485 [30·4%] of 77 202 patients) than wave 2 (44 220 [23·1%] of 191 528 patients), but remained unchanged for patients admitted to the ICU. Mortality was highest among patients who received ventilatory support outside of the ICU in wave 1 (2569 [50·7%] of 5063 patients). 15 486 (9·8%) of 158 020 COVID-19-related deaths occurred within 28 days of the first COVID-19 event without a COVID-19 diagnoses on the death certificate. 10 884 (6·9%) of 158 020 deaths were identified exclusively from mortality data with no previous COVID-19 phenotype recorded. We observed longer patient trajectories in wave 2 than wave 1. Interpretation: Our analyses illustrate the wide spectrum of disease trajectories as shown by differences in incidence, survival, and clinical pathways. We have provided a modular analytical framework that can be used to monitor the impact of the pandemic and generate evidence of clinical and policy relevance using multiple EHR sources. Funding: British Heart Foundation Data Science Centre, led by Health Data Research UK.</p