Families of strictly pseudoconvex domains and peak functions

We prove that given a family $(G_t)$ of strictly pseudoconvex domains varying in $\mathcal{C}^2$ topology on domains, there exists a continuously varying family of peak functions $h_{t,\zeta}$ for all $G_t$ at every $\zeta\in\partial G_t.

Dense Packings of Congruent Circles in Rectangles with a Variable Aspect Ratio

We use computational experiments to find the rectangles of minimum area into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. Most of the packings found have the usual regular square or hexagonal pattern. However, for 1495 values of n in the tested range n =< 5000, specifically, for n = 49, 61, 79, 97, 107,... 4999, we prove that the optimum cannot possibly be achieved by such regular arrangements. The evidence suggests that the limiting height-to-width ratio of rectangles containing an optimal hexagonal packing of circles tends to 2-sqrt(3) as n tends to infinity, if the limit exists.Comment: 21 pages, 13 figure

Quantification of crypt and stem cell evolution in the normal and neoplastic human colon.

Human intestinal stem cell and crypt dynamics remain poorly characterized because transgenic lineage-tracing methods are impractical in humans. Here, we have circumvented this problem by quantitatively using somatic mtDNA mutations to trace clonal lineages. By analyzing clonal imprints on the walls of colonic crypts, we show that human intestinal stem cells conform to one-dimensional neutral drift dynamics with a "functional" stem cell number of five to six in both normal patients and individuals with familial adenomatous polyposis (germline APC(-/+)). Furthermore, we show that, in adenomatous crypts (APC(-/-)), there is a proportionate increase in both functional stem cell number and the loss/replacement rate. Finally, by analyzing fields of mtDNA mutant crypts, we show that a normal colon crypt divides around once every 30-40 years, and the division rate is increased in adenomas by at least an order of magnitude. These data provide in vivo quantification of human intestinal stem cell and crypt dynamics.This study was supported by Cancer Research UK (to A.-M.B. and N.A.W.), the Medical Research Council (to B.C. and S.A.C.M.), the Engineering and Physical Sciences Research Council (to A.G.F.), Microsoft Research (to A.G.F.), the National Institute for Health Research University College London Hospitals Biomedical Research Centre (to M.R.J.), the Dutch Cancer Research Foundation (to M.J.), the Wellcome Trust (to B.D.S.), and Higher Education Funding Council for England (to T.A.G.)

Palmaria palmata (Dulse) as an unusual maritime aetiology of hyperkalemia in a patient with chronic renal failure: a case report

<p>Abstract</p> <p>Introduction</p> <p>Hyperkalemia is rare in individuals with normal renal function, regardless of dietary intake. This is due to the ability of the kidneys to adapt to increasing serum potassium concentrations. In patients with renal compromise, potassium homeostasis can become impaired. <it>Palmaria palmata </it>(dulse) is an edible seaweed known to be very rich in potassium. We report a case of hyperkalemia precipitated by the consumption of dulse by a patient with known renal disease.</p> <p>Case Presentation</p> <p>A 66-year-old Caucasian woman with diabetes and chronic renal disease presented to our emergency department with nausea, vomiting, and worsening malaise, which had been present for less than a day. She had undergone electrocardiogram monitoring, which showed bradycardia, and periods of asystole. Our patient denied any other symptoms. Laboratory analysis revealed a serum potassium level of 8.6 mmol/L (normal range 3.5 to 4.9 mmol/L). Although our patient was taking some medications known to influence renal function, the only recent change that she could recount was that she had consumed approximately 200 g of dulse within the preceding 24 hours. A diagnosis of hyperkalemia was made, and the patient was treated successfully, and discharged home in her pre-morbid state.</p> <p>Conclusion</p> <p>To the best of our knowledge, this is the first published report of hyperkalemia due to dulse consumption. Dulse is high in potassium, with concentrations upwards of 34 times greater than that found in bananas. Caution should be taken in prescribing medications with potential adverse renal effects for patients with known renal impairment. In such instances, renal function should be monitored closely. Patients should be counseled to avoid dietary sources high in potassium, with particular attention paid to unusual geographical dietary variations.</p

Cross-species gene expression analysis of species specific differences in the preclinical assessment of pharmaceutical compounds

Animals are frequently used as model systems for determination of safety and efficacy in pharmaceutical research and development. However, significant quantitative and qualitative differences exist between humans and the animal models used in research. This is as a result of genetic variation between human and the laboratory animal. Therefore the development of a system that would allow the assessment of all molecular differences between species after drug exposure would have a significant impact on drug evaluation for toxicity and efficacy. Here we describe a cross-species microarray methodology that identifies and selects orthologous probes after cross-species sequence comparison to develop an orthologous cross-species gene expression analysis tool. The assumptions made by the use of this orthologous gene expression strategy for cross-species extrapolation is that; conserved changes in gene expression equate to conserved pharmacodynamic endpoints. This assumption is supported by the fact that evolution and selection have maintained the structure and function of many biochemical pathways over time, resulting in the conservation of many important processes. We demonstrate this cross-species methodology by investigating species specific differences of the peroxisome proliferatoractivator receptor (PPAR) a response in rat and human

Development and validation of a multivariable risk factor questionnaire to detect oesophageal cancer in 2-week wait patients

INTRODUCTION: Oesophageal cancer is associated with poor health outcomes. Upper GI (UGI) endoscopy is the gold standard for diagnosis but is associated with patient discomfort and low yield for cancer. We used a machine learning approach to create a model which predicted oesophageal cancer based on questionnaire responses. METHODS: We used data from 2 separate prospective cross-sectional studies: the Saliva to Predict rIsk of disease using Transcriptomics and epigenetics (SPIT) study and predicting RIsk of diSease using detailed Questionnaires (RISQ) study. We recruited patients from National Health Service (NHS) suspected cancer pathways as well as patients with known cancer. We identified patient characteristics and questionnaire responses which were most associated with the development of oesophageal cancer. Using the SPIT dataset, we trained seven different machine learning models, selecting the best area under the receiver operator curve (AUC) to create our final model. We further applied a cost function to maximise cancer detection. We then independently validated the model using the RISQ dataset. RESULTS: 807 patients were included in model training and testing, split in a 70:30 ratio. 294 patients were included in model validation. The best model during training was regularised logistic regression using 17 features (median AUC: 0.81, interquartile range (IQR): 0.69-0.85). For testing and validation datasets, the model achieved an AUC of 0.71 (95% CI: 0.61-0.81) and 0.92 (95% CI: 0.88-0.96) respectively. At a set cut off, our model achieved a sensitivity of 97.6% and specificity of 59.1%. We additionally piloted the model in 12 patients with gastric cancer; 9/12 (75%) of patients were correctly classified. CONCLUSIONS: We have developed and validated a risk stratification tool using a questionnaire approach. This could aid prioritising patients at high risk of having oesophageal cancer for endoscopy. Our tool could help address endoscopic backlogs caused by the COVID-19 pandemic

Non-opaque soft tissue foreign body: sonographic findings

<p>Abstract</p> <p>Background</p> <p>Soft tissue foreign bodies are a common cause of orthopedic consultation in emergency departments. It is difficult to confirm their existence because conventional radiology only detects radio-opaque foreign bodies. Sonography can be a useful diagnostic method. The aim of this study is to evaluate diagnostic accuracy of sonography in detection and localization of non-opaque foreign bodies.</p> <p>Methods</p> <p>We evaluated 47 patients with suspected foreign body retention in soft tissues by 10 MHz linear array transducer. A single radiologist performed all examinations with 6 years' experience in musculoskeletal Sonography. We detected and localized the presence of the foreign body in the soft tissue as guidance for facilitating the surgery.</p> <p>Results</p> <p>We detected soft tissue foreign body in 45 cases as hyperechoic foci. Posterior acoustic shadowing was seen in 36 cases and halo sign was seen in 5 cases due to abscess or granulation tissue formation. Surgery was performed in 39 patients and 44 foreign bodies were removed.</p> <p>Conclusion</p> <p>Sonography is a useful modality in detection and localization of radiolucent foreign bodies in soft tissue which can avoid misdiagnosis during primary emergency evaluation.</p

Consistent phenological shifts in the making of a biodiversity hotspot: the Cape flora

Background The best documented survival responses of organisms to past climate change on short (glacial-interglacial) timescales are distributional shifts. Despite ample evidence on such timescales for local adaptations of populations at specific sites, the long-term impacts of such changes on evolutionary significant units in response to past climatic change have been little documented. Here we use phylogenies to reconstruct changes in distribution and flowering ecology of the Cape flora - South Africa's biodiversity hotspot - through a period of past (Neogene and Quaternary) changes in the seasonality of rainfall over a timescale of several million years. Results Forty-three distributional and phenological shifts consistent with past climatic change occur across the flora, and a comparable number of clades underwent adaptive changes in their flowering phenology (9 clades; half of the clades investigated) as underwent distributional shifts (12 clades; two thirds of the clades investigated). Of extant Cape angiosperm species, 14-41% have been contributed by lineages that show distributional shifts consistent with past climate change, yet a similar proportion (14-55%) arose from lineages that shifted flowering phenology. Conclusions Adaptive changes in ecology at the scale we uncover in the Cape and consistent with past climatic change have not been documented for other floras. Shifts in climate tolerance appear to have been more important in this flora than is currently appreciated, and lineages that underwent such shifts went on to contribute a high proportion of the flora's extant species diversity. That shifts in phenology, on an evolutionary timescale and on such a scale, have not yet been detected for other floras is likely a result of the method used; shifts in flowering phenology cannot be detected in the fossil record