A Reilly formula and eigenvalue estimates for differential forms

We derive a Reilly-type formula for differential p-forms on a compact manifold with boundary and apply it to give a sharp lower bound of the spectrum of the Hodge Laplacian acting on differential forms of an embedded hypersurface of a Riemannian manifold. The equality case of our inequality gives rise to a number of rigidity results, when the geometry of the boundary has special properties and the domain is non-negatively curved. Finally we also obtain, as a by-product of our calculations, an upper bound of the first eigenvalue of the Hodge Laplacian when the ambient manifold supports non-trivial parallel forms.Comment: 22 page

Rigidity of compact Riemannian spin Manifolds with Boundary

In this article, we prove new rigidity results for compact Riemannian spin manifolds with boundary whose scalar curvature is bounded from below by a non-positive constant. In particular, we obtain generalizations of a result of Hang-Wang \cite{hangwang1} based on a conjecture of Schroeder and Strake \cite{schroeder}.Comment: English version of "G\'eom\'etrie spinorielle extrins\`eque et rigidit\'es", Corollary 6 in Section 3 added, to appear in Letters Math. Phy

Restricted and unrestricted Hartree-Fock calculations of conductance for a quantum point contact

Very short quantum wires (quantum contacts) exhibit a conductance structure at a value of conductance close to $0.7 \times 2e^2/h$. It is believed that the structure arises due to the electron-electron interaction, and it is also related to electron spin. However details of the mechanism of the structure are not quite clear. Previously we approached the problem within the restricted Hartree-Fock approximation. This calculation demonstrated a structure similar to that observed experimentally. In the present work we perform restricted and unrestricted Hartree-Fock calculations to analyze the validity of the approximations. We also consider dependence of the effect on the electron density in leads. The unrestricted Hartree-Fock method allows us to analyze trapping of the single electron within the contact. Such trapping would result in the Kondo model for the ``0.7 structure''. The present calculation confirms the spin-dependent bound state picture and does not confirm the Kondo model scenario.Comment: 6 pages, 9 figure

Extreme sensitivity of the spin-splitting and 0.7 anomaly to confining potential in one-dimensional nanoelectronic devices

Quantum point contacts (QPCs) have shown promise as nanoscale spin-selective components for spintronic applications and are of fundamental interest in the study of electron many-body effects such as the 0.7 x 2e^2/h anomaly. We report on the dependence of the 1D Lande g-factor g* and 0.7 anomaly on electron density and confinement in QPCs with two different top-gate architectures. We obtain g* values up to 2.8 for the lowest 1D subband, significantly exceeding previous in-plane g-factor values in AlGaAs/GaAs QPCs, and approaching that in InGaAs/InP QPCs. We show that g* is highly sensitive to confinement potential, particularly for the lowest 1D subband. This suggests careful management of the QPC's confinement potential may enable the high g* desirable for spintronic applications without resorting to narrow-gap materials such as InAs or InSb. The 0.7 anomaly and zero-bias peak are also highly sensitive to confining potential, explaining the conflicting density dependencies of the 0.7 anomaly in the literature.Comment: 23 pages, 7 figure

Interpreting physical performance in professional soccer match-play: Should we be more pragmatic in our approach?

Academic and practitioner interest in the physical performance of male professional soccer players in the competition setting determined via time-motion analyses has grown substantially over the last four decades leading to a substantial body of published research and aiding development of a more systematic evidence-based framework for physical conditioning. Findings have forcibly shaped contemporary opinions in the sport with researchers and practitioners frequently emphasising the important role that physical performance plays in match outcomes. Time-motion analyses have also influenced practice as player conditioning programmes can be tailored according to the different physical demands identified across individual playing positions. Yet despite a more systematic approach to physical conditioning, data indicate that even at the very highest standards of competition, the contemporary player is still susceptible to transient and end-game fatigue. Over the course of this article, the author suggests that a more pragmatic approach to interpreting the current body of time-motion analysis data and its application in the practical setting is nevertheless required. Examples of this are addressed using findings in the literature to examine: a) the association between competitive physical performance and ‘success’ in professional soccer, b) current approaches to interpreting differences in time-motion analysis data across playing positions and, c) whether data can realistically be used to demonstrate the occurrence of fatigue in match-play. Gaps in the current literature and directions for future research are also identified

Genetically determined height and coronary artery disease.

BACKGROUND: The nature and underlying mechanisms of an inverse association between adult height and the risk of coronary artery disease (CAD) are unclear. METHODS: We used a genetic approach to investigate the association between height and CAD, using 180 height-associated genetic variants. We tested the association between a change in genetically determined height of 1 SD (6.5 cm) with the risk of CAD in 65,066 cases and 128,383 controls. Using individual-level genotype data from 18,249 persons, we also examined the risk of CAD associated with the presence of various numbers of height-associated alleles. To identify putative mechanisms, we analyzed whether genetically determined height was associated with known cardiovascular risk factors and performed a pathway analysis of the height-associated genes. RESULTS: We observed a relative increase of 13.5% (95% confidence interval [CI], 5.4 to 22.1; P<0.001) in the risk of CAD per 1-SD decrease in genetically determined height. There was a graded relationship between the presence of an increased number of height-raising variants and a reduced risk of CAD (odds ratio for height quartile 4 versus quartile 1, 0.74; 95% CI, 0.68 to 0.84; P<0.001). Of the 12 risk factors that we studied, we observed significant associations only with levels of low-density lipoprotein cholesterol and triglycerides (accounting for approximately 30% of the association). We identified several overlapping pathways involving genes associated with both development and atherosclerosis. CONCLUSIONS: There is a primary association between a genetically determined shorter height and an increased risk of CAD, a link that is partly explained by the association between shorter height and an adverse lipid profile. Shared biologic processes that determine achieved height and the development of atherosclerosis may explain some of the association. (Funded by the British Heart Foundation and others.)

Limits on Gravitational-Wave Emission from Selected Pulsars Using LIGO Data

We place direct upper limits on the amplitude of gravitational waves from 28 isolated radio pulsars by a coherent multidetector analysis of the data collected during the second science run of the LIGO interferometric detectors. These are the first direct upper limits for 26 of the 28 pulsars. We use coordinated radio observations for the first time to build radio-guided phase templates for the expected gravitational-wave signals. The unprecedented sensitivity of the detectors allows us to set strain upper limits as low as a few times 10^(-24). These strain limits translate into limits on the equatorial ellipticities of the pulsars, which are smaller than 10^(-5) for the four closest pulsars