Toric and tropical Bertini theorems in positive characteristic

We generalize the toric Bertini theorem of Fuchs, Mantova, and Zannier to positive characteristic. A key part of the proof is a new algebraically closed field containing the field \kk(t_1,\dots,t_d) of rational functions over an algebraically closed field \kk of prime characteristic. As a corollary, we extend the tropical Bertini theorem of Maclagan and Yu to arbitrary characteristic, which removes the characteristic dependence from the d-connectivity result for tropical varieties from that paper

Pruning Algorithms for Pretropisms of Newton Polytopes

Pretropisms are candidates for the leading exponents of Puiseux series that represent solutions of polynomial systems. To find pretropisms, we propose an exact gift wrapping algorithm to prune the tree of edges of a tuple of Newton polytopes. We prefer exact arithmetic not only because of the exact input and the degrees of the output, but because of the often unpredictable growth of the coordinates in the face normals, even for polytopes in generic position. We provide experimental results with our preliminary implementation in Sage that compare favorably with the pruning method that relies only on cone intersections.Comment: exact, gift wrapping, Newton polytope, pretropism, tree pruning, accepted for presentation at Computer Algebra in Scientific Computing, CASC 201

Comparison of diagnostic accuracy of early screening for pre-eclampsia by NICE guidelines and a method combining maternal factors and biomarkers: results of SPREE

Objective To test the hypothesis that the performance of first-trimester screening for pre-eclampsia (PE) by a method that uses Bayes’ theorem to combine maternal factors with biomarkers is superior to that defined by current National Institute for Health and Care Excellence (NICE) guidelines. Methods This was a prospective multicenter study (screening program for pre-eclampsia (SPREE)) in seven National Health Service maternity hospitals in England, of women recruited between April and December 2016. Singleton pregnancies at 11–13weeks’ gestation had recording of maternal characteristics and medical history and measurements of mean arterial pressure (MAP), uterine artery pulsatility index (UtA-PI), serum placental growth factor (PlGF) and serum pregnancy-associated plasma protein-A (PAPP-A). The performance of screening for PE by the Bayes’ theorem-based method was compared with that of the NICE method. Primary comparison was detection rate (DR) using NICE method vs mini-combined test (maternal factors, MAP and PAPP-A) in the prediction of PE at any gestational age (all-PE) for the same screen-positive rate determined by the NICE method. Key secondary comparisons were DR of screening recommended by the NICE guidelines vs three Bayes’ theorem-based methods (maternal factors, MAP and PAPP-A; maternal factors, MAP and PlGF; and maternal factors, MAP, UtA-PI and PlGF) in the prediction of preterm PE, defined as that requiring delivery <37 weeks. Results All-PE developed in 473 (2.8%) of the 16 747 pregnancies and preterm PE developed in 142 (0.8%). The screen-positive rate by the NICE method was 10.3% and the DR for all-PE was 30.4% and for preterm PE it was 40.8%. Compliance with the NICE recommendation that women at high risk for PE should be treated with aspirin from the first trimester to the end of pregnancy was only 23%. The DR of the mini-combined test for all-PE was 42.5%, which was superior to that of the NICE method by 12.1% (95% CI, 7.9–16.2%). In screening for preterm PE by a combination of maternal factors, MAP and PlGF, the DR was 69.0%, which was superior to that of the NICE method by 28.2% (95% CI, 19.4–37.0%) and with the addition of UtA-PI the DR was 82.4%, which was higher than that of the NICE method by 41.6% (95% CI, 33.2–49.9%). Conclusions The performance of screening for PE as currently recommended by NICE guidelines is poor and compliance with these guidelines is low. The performance of screening is substantially improved by a method combining maternal factors with biomarkers

Neprilysin inhibition for pulmonary arterial hypertension: a randomized, double-blind, placebo-controlled, proof-of-concept trial

This is the peer reviewed version of the following article: Hobbs AJ, Moyes AJ, Baliga RS, et al. Neprilysin inhibition for pulmonary arterial hypertension: a randomized, double‐blind, placebo‐controlled, proof‐of‐concept trial. Br J Pharmacol. 2019. https://doi.org/10.1111/bph.14621, which has been published in final form at https://doi.org/10.1111/bph.14621. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived VersionsThis work was supported by a British Heart Foundation Project Grant (PG/11/88/28992) and the National Institutes for Health Research, Comprehensive Biomedical Research Centre award to UC

Determinants of impact : towards a better understanding of encounters with the arts

The article argues that current methods for assessing the impact of the arts are largely based on a fragmented and incomplete understanding of the cognitive, psychological and socio-cultural dynamics that govern the aesthetic experience. It postulates that a better grasp of the interaction between the individual and the work of art is the necessary foundation for a genuine understanding of how the arts can affect people. Through a critique of philosophical and empirical attempts to capture the main features of the aesthetic encounter, the article draws attention to the gaps in our current understanding of the responses to art. It proposes a classification and exploration of the factors—social, cultural and psychological—that contribute to shaping the aesthetic experience, thus determining the possibility of impact. The ‘determinants of impact’ identified are distinguished into three groups: those that are inherent to the individual who interacts with the artwork; those that are inherent to the artwork; and ‘environmental factors’, which are extrinsic to both the individual and the artwork. The article concludes that any meaningful attempt to assess the impact of the arts would need to take these ‘determinants of impact’ into account, in order to capture the multidimensional and subjective nature of the aesthetic experience

Exenatide once weekly versus placebo in Parkinson's disease: a randomised, double-blind, placebo-controlled trial

BACKGROUND: Exenatide, a glucagon-like peptide-1 (GLP-1) receptor agonist, has neuroprotective effects in preclinical models of Parkinson's disease. We investigated whether these effects would be apparent in a clinical trial. METHODS: In this single-centre, randomised, double-blind, placebo-controlled trial, patients with moderate Parkinson's disease were randomly assigned (1:1) to receive subcutaneous injections of exenatide 2 mg or placebo once weekly for 48 weeks in addition to their regular medication, followed by a 12-week washout period. Eligible patients were aged 25-75 years, had idiopathic Parkinson's disease as measured by Queen Square Brain Bank criteria, were on dopaminergic treatment with wearing-off effects, and were at Hoehn and Yahr stage 2·5 or less when on treatment. Randomisation was by web-based randomisation with a two strata block design according to disease severity. Patients and investigators were masked to treatment allocation. The primary outcome was the adjusted difference in the Movement Disorders Society Unified Parkinson's Disease Rating Scale (MDS-UPDRS) motor subscale (part 3) in the practically defined off-medication state at 60 weeks. All efficacy analyses were based on a modified intention-to-treat principle, which included all patients who completed any post-randomisation follow-up assessments. The study is registered at ClinicalTrials.gov (NCT01971242) and is completed. FINDINGS: Between June 18, 2014, and March 13, 2015, 62 patients were enrolled and randomly assigned, 32 to exenatide and 30 to placebo. Our primary analysis included 31 patients in the exenatide group and 29 patients in the placebo group. At 60 weeks, off-medication scores on part 3 of the MDS-UPDRS had improved by 1·0 points (95% CI -2·6 to 0·7) in the exenatide group and worsened by 2·1 points (-0·6 to 4·8) in the placebo group, an adjusted mean difference of -3·5 points (-6·7 to -0·3; p=0·0318). Injection site reactions and gastrointestinal symptoms were common adverse events in both groups. Six serious adverse events occurred in the exenatide group and two in the placebo group, although none in either group were judged to be related to the study interventions. INTERPRETATION: Exenatide had positive effects on practically defined off-medication motor scores in Parkinson's disease, which were sustained beyond the period of exposure. Whether exenatide affects the underlying disease pathophysiology or simply induces long-lasting symptomatic effects is uncertain. Exenatide represents a major new avenue for investigation in Parkinson's disease, and effects on everyday symptoms should be examined in longer-term trials. FUNDING: Michael J Fox Foundation for Parkinson's Research

A Grassmann algebra for matroids

We introduce an idempotent analogue of the exterior algebra for which the theory of tropical linear spaces (and valuated matroids) can be seen in close analogy with the classical Grassmann algebra formalism for linear spaces. The top wedge power of a tropical linear space is its Plucker vector, which we view as a tensor, and a tropical linear space is recovered from its Plucker vector as the kernel of the corresponding wedge multiplication map. We prove that an arbitrary d-tensor satisfies the tropical Plucker relations (valuated exchange axiom) if and only if the d-th wedge power of the kernel of wedge-multiplication is free of rank one. This provides a new cryptomorphism for valuated matroids, including ordinary matroids as a special case

Exenatide once weekly over 2 years as a potential disease-modifying treatment for Parkinson’s disease: protocol for a multicentre, randomised, double blind, parallel group, placebo controlled, phase 3 trial: The ‘Exenatide-PD3’ study

IntroductionParkinson’s disease (PD) is a common neurodegenerative disorder with substantial morbidity. No disease-modifying treatments currently exist. The glucagon like peptide-1 receptor agonist exenatide has been associated in single-centre studies with reduced motor deterioration over 1 year. The aim of this multicentre UK trial is to confirm whether these previous positive results are maintained in a larger number of participants over 2 years and if effects accumulate with prolonged drug exposure.Methods and analysisThis is a phase 3, multicentre, double-blind, randomised, placebo-controlled trial of exenatide at a dose of 2 mg weekly in 200 participants with mild to moderate PD. Treatment duration is 96 weeks. Randomisation is 1:1, drug to placebo. Assessments are performed at baseline, week 12, 24, 36, 48, 60, 72, 84 and 96 weeks.The primary outcome is the comparison of Movement Disorders Society Unified Parkinson’s Disease Rating Scale part 3 motor subscore in the practically defined OFF medication state at 96 weeks between participants according to treatment allocation. Secondary outcomes will compare the change between groups among other motor, non-motor and cognitive scores. The primary outcome will be reported using descriptive statistics and comparisons between treatment groups using a mixed model, adjusting for baseline scores. Secondary outcomes will be summarised between treatment groups using summary statistics and appropriate statistical tests to assess for significant differences.Ethics and disseminationThis trial has been approved by the South Central-Berkshire Research Ethics Committee and the Health Research Authority. Results will be disseminated in peer-reviewed journals, presented at scientific meetings and to patients in lay-summary format.Trial registration numbersNCT04232969, ISRCTN14552789.</jats:sec