Spectral isolation of naturally reductive metrics on simple Lie groups

We show that within the class of left-invariant naturally reductive metrics $\mathcal{M}_{\operatorname{Nat}}(G)$ on a compact simple Lie group $G$, every metric is spectrally isolated. We also observe that any collection of isospectral compact symmetric spaces is finite; this follows from a somewhat stronger statement involving only a finite part of the spectrum.Comment: 19 pages, new title and abstract, revised introduction, new result demonstrating that any collection of isospectral compact symmetric spaces must be finite, to appear Math Z. (published online Dec. 2009

Gallot-Tanno Theorem for closed incomplete pseudo-Riemannian manifolds and applications

We extend the Gallot-Tanno Theorem to closed pseudo-Riemannian manifolds. It is done by showing that if the cone over a manifold admits a parallel symmetric $(0,2)-$tensor then it is Riemannian. Applications of this result to the existence of metrics with distinct Levi-Civita connections but having the same unparametrized geodesics and to the projective Obata conjecture are given. We also apply our result to show that the holonomy group of a closed $(O(p+1,q),S^{p,q})$-manifold does not preserve any nondegenerate splitting of $\R^{p+1,q}$.Comment: minor correction

The utility of Ki-67 as a prognostic biomarker in pulmonary neuroendocrine tumours: protocol for a systematic review and meta-analysis

INTRODUCTION: The omission of the immunohistochemical proliferation marker Ki-67 labelling index (henceforth, simply Ki-67) from the 2015 WHO classification system of pulmonary neuroendocrine tumours (Lung-NETs) as a prognostic and grading criterion remains controversial. This systematic review along with meta-analysis will be conducted to assess the prognostic/grading utility of Ki-67 in Lung-NETs.METHODS: This systematic review will be conducted in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analysis guidelines. A systematic search of MEDLINE Ovid, Embase, Scopus and the Cochrane Library will be performed from the inception of each database to 28 February 2019 for studies investigating any role of Ki-67 in Lung-NETs. Only full papers published in English detailing survival outcomes and HRs according to Ki-67 will be included. The primary endpoint will be establishing whether Ki-67 is a reliable marker in determining prognosis and thus assessing grade of Lung-NETs patients.ETHICS AND DISSEMINATION: Ethical approval will not be required as this is an academic review of published literature. Findings will be disseminated through the preparation of a manuscript for publication in a peer-reviewed journal as well as presentation at national and international conferences.PROSPERO REGISTRATION NUMBER: CRD42018093389.</p

First and second variation formulae for the sub-Riemannian area in three-dimensional pseudo-hermitian manifolds

We calculate the first and the second variation formula for the sub-Riemannian area in three dimensional pseudo-hermitian manifolds. We consider general variations that can move the singular set of a C^2 surface and non-singular variation for C_H^2 surfaces. These formulas enable us to construct a stability operator for non-singular C^2 surfaces and another one for C2 (eventually singular) surfaces. Then we can obtain a necessary condition for the stability of a non-singular surface in a pseudo-hermitian 3-manifold in term of the pseudo-hermitian torsion and the Webster scalar curvature. Finally we classify complete stable surfaces in the roto-traslation group RT .Comment: 36 pages. Misprints corrected. Statement of Proposition 9.8 slightly changed and Remark 9.9 adde

Perfectionism and self-conscious emotions in British and Japanese students: Predicting pride and embarrassment after success and failure

Regarding self-conscious emotions, studies have shown that different forms of perfectionism show different relationships with pride, shame, and embarrassment depending on success and failure. What is unknown is whether these relationships also show cultural variations. Therefore, we conducted a study investigating how self-oriented and socially prescribed perfectionism predicted pride and embarrassment after success and failure comparing 363 British and 352 Japanese students. Students were asked to respond to a set of scenarios where they imagined achieving either perfect (success) or flawed results (failure). In both British and Japanese students, self-oriented perfectionism positively predicted pride after success and embarrassment after failure whereas socially prescribed perfectionism predicted embarrassment after success and failure. Moreover, in Japanese students, socially prescribed perfectionism positively predicted pride after success and self-oriented perfectionism negatively predicted pride after failure. The findings have implications for our understanding of perfectionism indicating that the perfectionism–pride relationship not only varies between perfectionism dimensions, but may also show cultural variations

Genomic analysis in the study of drought tolerance using recombinant inbred lines and recurrent selection.

Plant breeding for drought tolerance is one of the approaches that can be applied in order to improve water use efficiency in agriculture

Let's agree to disagree: learning highly debatable multirater labelling

Classification and differentiation of small pathological objects may greatly vary among human raters due to differences in training, expertise and their consistency over time. In a radiological setting, objects commonly have high within-class appearance variability whilst sharing certain characteristics across different classes, making their distinction even more difficult. As an example, markers of cerebral small vessel disease, such as enlarged perivascular spaces (EPVS) and lacunes, can be very varied in their appearance while exhibiting high inter-class similarity, making this task highly challenging for human raters. In this work, we investigate joint models of individual rater behaviour and multirater consensus in a deep learning setting, and apply it to a brain lesion object-detection task. Results show that jointly modelling both individual and consensus estimates leads to significant improvements in performance when compared to directly predicting consensus labels, while also allowing the characterization of human-rater consistency.Comment: Accepted at MICCAI 201

Bifurcation and local rigidity of homogeneous solutions to the Yamabe problem on spheres

We study existence and non-existence of constant scalar curvature metrics conformal and arbitrarily close to homogeneous metrics on spheres, using variational techniques. This describes all critical points of the Hilbert-Einstein functional on such conformal classes, near homogeneous metrics. Both bifurcation and local rigidity type phenomena are obtained for 1-parameter families of U(n+1), Sp(n+1) and Spin(9)-homogeneous metrics.Comment: LaTeX2e, 18 pages, 1 figure, revised version. To appear in Calc. Var. and PDE