Dynamically affine maps in positive characteristic

We study fixed points of iterates of dynamically affine maps (a generalisation of Latt`es maps) over algebraically closed fields of positive characteristic p. We present and study certain hypotheses that imply a dichotomy for the Artin–Mazur zeta function of the dynamical system: it is either rational or non-holonomic, depending on specific characteristics of the map. We also study the algebraicity of the so-called tame zeta function, the generating function for periodic points of order coprime to p. We then verify these hypotheses for dynamically affine maps on the projective line, generalising previous work of Bridy, and, in arbitrary dimension, for maps on Kummer varieties arising from multiplication by integers on abelian varieties

Performance of commercially-available cholesterol self-tests

Background: Hypercholesterolemia (plasma cholesterol concentration ≥5.2 mmol/L) is a risk factor for cardiovascular disease and stroke. Many different cholesterol self-tests are readily available at general stores, pharmacies and web shops. However, there is limited information on their analytical and diagnostic performance. Methods: We included 62 adult patients who required a lipid panel measurement (cholesterol, high-density lipoprotein (HDL), triglycerides and LDLcalc) for routine care. The performance of five different cholesterol self-tests, three quantitative meters (Roche Accutrend Plus, Mission 3-in-1 and Qucare) and two semi-quantitative strip tests (Veroval and Mylan MyTest), was assessed according to the manufacturers’ protocol. Results: The average plasma cholesterol concentration was 5.2 ± 1.2 mmol/L. The mean absolute relative difference (MARD) of the five cholesterol self-tests ranged from 6 ± 5% (Accutrend Plus) to 20 ± 12% (Mylan Mytest). The Accutrend Plus cholesterol meter showed the best diagnostic performance with a 92% sensitivity and 89% specificity. The Qucare and Mission 3-in-1 are able to measure HDL concentrations and can thus provide a cholesterol:HDL ratio. The Passing-Bablok regression analyses for the ratio showed poor performance in both self-tests (Mission 3-in-1: y = 1.62x–1.20; Qucare: y = 0.61x + 1.75). The Accutrend Plus is unable to measure the plasma high-density lipoprotein concentration. Conclusions/interpretation: The Accutrend Plus cholesterol meter (Roche) had excellent diagnostic and analytic performance. However, several of the commercially-available self-tests had considerably poor accuracy and diagnostic performance and therefore do not meet the required qualifications, potentially leading to erroneous results. Better regulation, standardization and harmonization of cholesterol self-tests is warranted

Dynamically affine maps in positive characteristic

We study fixed points of iterates of dynamically affine maps (a generalisation of Latt`es maps) over algebraically closed fields of positive characteristic p. We present and study certain hypotheses that imply a dichotomy for the Artin–Mazur zeta function of the dynamical system: it is either rational or non-holonomic, depending on specific characteristics of the map. We also study the algebraicity of the so-called tame zeta function, the generating function for periodic points of order coprime to p. We then verify these hypotheses for dynamically affine maps on the projective line, generalising previous work of Bridy, and, in arbitrary dimension, for maps on Kummer varieties arising from multiplication by integers on abelian varieties

Rapid identification of SARS-CoV-2-infected patients at the emergency department using routine testing

Objectives: The novel coronavirus disease 19 (COVID-19), caused by SARS-CoV-2, spreads rapidly across the world. The exponential increase in the number of cases has resulted in overcrowding of emergency departments (ED). Detection of SARS-CoV-2 is based on an RT-PCR of nasopharyngeal swab material. However, RT-PCR testing is time-consuming and many hospitals deal with a shortage of testing materials. Therefore, we aimed to develop an algorithm to rapidly evaluate an individual's risk of SARSCoV-2 infection at the ED. Methods: In this multicenter retrospective study, routine laboratory parameters (C-reactive protein, lactate dehydrogenase, ferritin, absolute neutrophil and lymphocyte counts), demographic data and the chest X-ray/CT result from 967 patients entering the ED with respiratory symptoms were collected. Using these parameters, an easy-to-use point-based algorithm, called the corona-score, was developed to discriminate between patients that tested positive for SARS-CoV-2 by RT-PCR and those testing negative. Computational sampling was used to optimize the corona-score. Validation of the model was performed using data from 592 patients. Results: The corona-score model yielded an area under the receiver operating characteristic curve of 0.91 in the validation population. Patients testing negative for SARSCoV-2 showed a median corona-score of 3 vs. 11 (scale 0-14) in patients testing positive for SARS-CoV-2 (p<0.001). Using cut-off values of 4 and 11 the model has a sensitivity and specificity of 96 and 95%, respectively. Conclusions: The corona-score effectively predicts SARSCoV-2 RT-PCR outcome based on routine parameters. This algorithm provides the means for medical professionals to rapidly evaluate SARS-CoV-2 infection status of patients presenting at the ED with respiratory symptoms