Convex domains of Finsler and Riemannian manifolds

A detailed study of the notions of convexity for a hypersurface in a Finsler manifold is carried out. In particular, the infinitesimal and local notions of convexity are shown to be equivalent. Our approach differs from Bishop's one in his classical result (Bishop, Indiana Univ Math J 24:169-172, 1974) for the Riemannian case. Ours not only can be extended to the Finsler setting but it also reduces the typical requirements of differentiability for the metric and it yields consequences on the multiplicity of connecting geodesics in the convex domain defined by the hypersurface.Comment: 22 pages, AMSLaTex. Typos corrected, references update

Braided Matrix Structure of the Sklyanin Algebra and of the Quantum Lorentz Group

Braided groups and braided matrices are novel algebraic structures living in braided or quasitensor categories. As such they are a generalization of super-groups and super-matrices to the case of braid statistics. Here we construct braided group versions of the standard quantum groups $U_q(g)$. They have the same FRT generators $l^\pm$ but a matrix braided-coproduct \und\Delta L=L\und\tens L where $L=l^+Sl^-$, and are self-dual. As an application, the degenerate Sklyanin algebra is shown to be isomorphic to the braided matrices $BM_q(2)$; it is a braided-commutative bialgebra in a braided category. As a second application, we show that the quantum double D(\usl) (also known as the `quantum Lorentz group') is the semidirect product as an algebra of two copies of \usl, and also a semidirect product as a coalgebra if we use braid statistics. We find various results of this type for the doubles of general quantum groups and their semi-classical limits as doubles of the Lie algebras of Poisson Lie groups.Comment: 45 pages. Revised (= much expanded introduction

TRY plant trait database – enhanced coverage and open access

Plant traits—the morphological, anatomical, physiological, biochemical and phenological characteristics of plants—determine how plants respond to environmental factors, affect other trophic levels, and influence ecosystem properties and their benefits and detriments to people. Plant trait data thus represent the basis for a vast area of research spanning from evolutionary biology, community and functional ecology, to biodiversity conservation, ecosystem and landscape management, restoration, biogeography and earth system modelling. Since its foundation in 2007, the TRY database of plant traits has grown continuously. It now provides unprecedented data coverage under an open access data policy and is the main plant trait database used by the research community worldwide. Increasingly, the TRY database also supports new frontiers of trait‐based plant research, including the identification of data gaps and the subsequent mobilization or measurement of new data. To support this development, in this article we evaluate the extent of the trait data compiled in TRY and analyse emerging patterns of data coverage and representativeness. Best species coverage is achieved for categorical traits—almost complete coverage for ‘plant growth form’. However, most traits relevant for ecology and vegetation modelling are characterized by continuous intraspecific variation and trait–environmental relationships. These traits have to be measured on individual plants in their respective environment. Despite unprecedented data coverage, we observe a humbling lack of completeness and representativeness of these continuous traits in many aspects. We, therefore, conclude that reducing data gaps and biases in the TRY database remains a key challenge and requires a coordinated approach to data mobilization and trait measurements. This can only be achieved in collaboration with other initiatives

Clinical characteristics of women captured by extending the definition of severe postpartum haemorrhage with 'refractoriness to treatment': a cohort study

Background: The absence of a uniform and clinically relevant definition of severe postpartum haemorrhage hampers comparative studies and optimization of clinical management. The concept of persistent postpartum haemorrhage, based on refractoriness to initial first-line treatment, was proposed as an alternative to common definitions that are either based on estimations of blood loss or transfused units of packed red blood cells (RBC). We compared characteristics and outcomes of women with severe postpartum haemorrhage captured by these three types of definitions. Methods: In this large retrospective cohort study in 61 hospitals in the Netherlands we included 1391 consecutive women with postpartum haemorrhage who received either ≥4 units of RBC or a multicomponent transfusion. Clinical characteristics and outcomes of women with severe postpartum haemorrhage defined as persistent postpartum haemorrhage were compared to definitions based on estimated blood loss or transfused units of RBC within 24 h following birth. Adverse maternal outcome was a composite of maternal mortality, hysterectomy, arterial embolisation and intensive care unit admission. Results: One thousand two hundred sixty out of 1391 women (90.6%) with postpartum haemorrhage fulfilled the definition of persistent postpartum haemorrhage. The majority, 820/1260 (65.1%), fulfilled this definition within 1 h following birth, compared to 819/1391 (58.7%) applying the definition of ≥1 L blood loss and 37/845 (4.4%) applying the definition of ≥4 units of RBC. The definition persistent postpartum haemorrhage captured 430/471 adverse maternal outcomes (91.3%), compared to 471/471 (100%) for ≥1 L blood loss and 383/471 (81.3%) for ≥4 units of RBC. Persistent postpartum haemorrhage did not capture all adverse outcomes because of missing data on timing of initial, first-line treatment. Conclusion: The definition persistent postpartum haemo