277 research outputs found
The toric Hilbert scheme of a rank two lattice is smooth and irreducible
The toric Hilbert scheme of a lattice L in Z^n is the multigraded Hilbert
scheme parameterizing all ideals in k[x_1,...,x_n] with Hilbert function value
one for every degree in the grading monoid N^n/L. In this paper we show that if
L is two-dimensional, then the toric Hilbert scheme of L is smooth and
irreducible. This result is false for lattices of dimension three and higher as
the toric Hilbert scheme of a rank three lattice can be reducible.Comment: 19 pages, 4 figure
Euler characteristic of coherent sheaves on simplicial torics via the Stanley-Reisner ring
We combine work of Cox on the total coordinate ring of a toric variety and
results of Eisenbud-Mustata-Stillman and Mustata on cohomology of toric and
monomial ideals to obtain a formula for computing the Euler characteristic of a
Weil divisor D on a complete simplicial toric variety in terms of graded pieces
of the Cox ring and Stanley-Reisner ring. The main point is to use Alexander
duality to pass from the toric irrelevant ideal, which appears in the
computation of the Euler characteristic of D, to the Stanley-Reisner ideal of
the fan, which is used in defining the Chow ring. The formula also follows from
work of Maclagan-Smith.Comment: 9 pages 1 figur
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 Bayesâ 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 11â13weeksâ 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 Bayesâ 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 Bayesâ 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, 7.9â16.2%). 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, 19.4â37.0%) 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, 33.2â49.9%).
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, doubleâblind, placeboâcontrolled, proofâofâconcept 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 factorsâsocial, cultural and psychologicalâthat contribute to shaping the aesthetic experience, thus determining the possibility of impact. The âdeterminants of impactâ 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 âenvironmental factorsâ, 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 âdeterminants of impactâ into account, in order to capture the multidimensional and subjective nature of the aesthetic experience
On the Ethics of Trade Credit: Understanding Good Payment Practice in the Supply Chain
In spite of its commercial importance and signs of clear concern in public policy arenas, trade credit has not been subjected to systematic, extended analysis in the business ethics literature, even where suppliers as a stakeholder group have been considered. This paper makes the case for serious consideration of the ethics of trade credit and explores the issues surrounding slow payment of debts. It discusses trade debt as a kind of promise, butâ noting that not all promises are good onesâgoes on to develop an analysis of the ethics of trade credit grounded in an understanding of its fundamental purpose. Making a distinction between ââoperatingââ trade credit and ââfinancialââ trade credit, the paper provides an account of the maximum period for which it is appropriate for one company to delay payment to another from which it has purchased goods or services. The concern of commentators and policy makers that companies should not take too long to pay their debts is affirmed, but the understanding of what timely payment means is significantly finessed, with one conclusion being that, if debts have not already been settled according to acceptable standard terms of trade, cash should pass quickly back along the supply chain once the customer in the final product market has paid. The analysis has implications not only for companies that take credit but also for external parties that seek to rate companies or set regulations according to speed of paymentâan approach that is shown to be misleadingly simplistic, albeit well intentioned. A corresponding important responsibility for
suppliers, not to extend excessive credit (and thus act as a quasi-bank), also follows from the analysis developed. Having provided a novel analysis of an important business problem, the paper then discusses some of the related practical issues and makes suggestions for further research
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