21,249 research outputs found

    An optimal gap theorem

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    By solving the Cauchy problem for the Hodge-Laplace heat equation for dd-closed, positive (1,1)(1, 1)-forms, we prove an optimal gap theorem for K\"ahler manifolds with nonnegative bisectional curvature which asserts that the manifold is flat if the average of the scalar curvature over balls of radius rr centered at any fixed point oo is a function of o(r−2)o(r^{-2}). Furthermore via a relative monotonicity estimate we obtain a stronger statement, namely a `positive mass' type result, asserting that if (M,g)(M, g) is not flat, then lim inf⁥r→∞r2Vo(r)∫Bo(r)S(y) dÎŒ(y)>0\liminf_{r\to \infty} \frac{r^2}{V_o(r)}\int_{B_o(r)}\mathcal{S}(y)\, d\mu(y)>0 for any o∈Mo\in M

    Real-time standard scan plane detection and localisation in fetal ultrasound using fully convolutional neural networks

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    Fetal mid-pregnancy scans are typically carried out according to fixed protocols. Accurate detection of abnormalities and correct biometric measurements hinge on the correct acquisition of clearly defined standard scan planes. Locating these standard planes requires a high level of expertise. However, there is a worldwide shortage of expert sonographers. In this paper, we consider a fully automated system based on convolutional neural networks which can detect twelve standard scan planes as defined by the UK fetal abnormality screening programme. The network design allows real-time inference and can be naturally extended to provide an approximate localisation of the fetal anatomy in the image. Such a framework can be used to automate or assist with scan plane selection, or for the retrospective retrieval of scan planes from recorded videos. The method is evaluated on a large database of 1003 volunteer mid-pregnancy scans. We show that standard planes acquired in a clinical scenario are robustly detected with a precision and recall of 69 % and 80 %, which is superior to the current state-of-the-art. Furthermore, we show that it can retrospectively retrieve correct scan planes with an accuracy of 71 % for cardiac views and 81 % for non-cardiac views

    Temperature dependence of electron-spin relaxation in a single InAs quantum dot at zero applied magnetic field

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    The temperature-dependent electron spin relaxation of positively charged excitons in a single InAs quantum dot (QD) was measured by time-resolved photoluminescence spectroscopy at zero applied magnetic fields. The experimental results show that the electron-spin relaxation is clearly divided into two different temperature regimes: (i) T < 50 K, spin relaxation depends on the dynamical nuclear spin polarization (DNSP) and is approximately temperature-independent, as predicted by Merkulov et al. (ii) T > about 50 K, spin relaxation speeds up with increasing temperature. A model of two LO phonon scattering process coupled with hyperfine interaction is proposed to account for the accelerated electron spin relaxation at higher temperatures.Comment: 10 pages, 4 figure

    Ellipsometry noise spectrum, suspension transfer function measurement and closed-loop control of the suspension system in the Q & A experiment

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    The Q & A experiment, aiming at the detection of vacuum birefringence predicted by quantum electrodynamics, consists mainly of a suspended 3.5 m Fabry-Perot cavity, a rotating permanent dipole magnet and an ellipsometer. The 2.3 T magnet can rotate up to 10 rev/s, introducing an ellipticity signal at twice the rotation frequency. The X-pendulum gives a good isolation ratio for seismic noise above its main resonant frequency 0.3 Hz. At present, the ellipsometry noise decreases with frequency, from 1*10^{-5} rad Hz^{-1/2} at 5 Hz, 2*10^{-6} rad Hz^{-1/2} at 20 Hz to 5*10^{-7} rad Hz^{-1/2} at 40 Hz. The shape of the noise spectrum indicates possible improvement can be made by further reducing the movement between the cavity mirrors. From the preliminary result of yaw motion alignment control, it can be seen that some peaks due to yaw motion of the cavity mirror was suppressed. In this paper, we first give a schematic view of the Q & A experiment, and then present the measurement of transfer function of the compound X-pendulum-double pendulum suspension. A closed-loop control was carried out to verify the validity of the measured transfer functions. The ellipsometry noise spectra with and without yaw alignment control and the newest improvement is presented.Comment: 7 pages, 5 figures, presented in 6th Edoardo Amaldi Conference on Gravitational Waves, June 2005, Okinawa Japan and submitted to Journal of Physics: Conference Series. Some modifications are made according to the referee's comments: mainly to explain the relation between the displacement of cavity mirror and the ellipticity noise spectru

    Non-minimal coupling of photons and axions

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    We establish a new self-consistent system of equations accounting for a non-minimal interaction of gravitational, electromagnetic and axion fields. The procedure is based on a non-minimal extension of the standard Einstein-Maxwell-axion action. The general properties of a ten-parameter family of non-minimal linear models are discussed. We apply this theory to the models with pp-wave symmetry and consider propagation of electromagnetic waves non-minimally coupled to the gravitational and axion fields. We focus on exact solutions of electrodynamic equations, which describe quasi-minimal and non-minimal optical activity induced by the axion field. We also discuss empirical constraints on coupling parameters from astrophysical birefringence and polarization rotation observations.Comment: 31 pages, 2 Tables; replaced with the final version published in Classical and Quantum Gravit

    Non-exponential London penetration depth in Ba1−_{1-}Kx_{x}Fe2_{2}As2_{2} single crystals

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    We have studied the in- and out-of-plane magnetic penetration depths in the hole- doped iron based superconductor Ba1−x_{1-x}Kx_{x}Fe2_{2}As2_{2} (Tc≈T_{c}\approx 30K). The study was performed on single crystals grown from different fluxes and we find that the results are nearly the same. The in-plane London penetration depth λab\lambda_{ab} does not show exponential saturation at low temperature, as would be expected from a fully gapped superconductor. Instead, λab(T)\lambda_{ab}(T) shows a power-law behavior, λ∝Tn\lambda\propto T^{n} (n≈2n\approx 2), down to T≈0.02TcT\approx 0.02 T_{c}, similar to the electron doped Ba(Fe1−x_{1-x}Cox_{x})2_{2}As2_{2}. The penetration depth anisotropy γλ=λc(T)/λab(T)\gamma_{\lambda}=\lambda_{c}(T)/\lambda_{ab}(T) increases upon cooling, opposite to the trend observed in the anisotropy of the upper critical field, ÎłÎŸ=Hc2⊄c(0)/Hc2∄c(0)\gamma_{\xi}=H_{c2}^{\perp c}(0)/H_{c2}^{\parallel c}(0). These are universal characteristics of both the electron and hole doped 122 systems, suggesting unconventional superconductivity. The behavior of the in-plane superfluid density ρab(T)\rho_{ab}(T) is discussed in light of existing theoretical models proposed for the iron pnictides superconductors

    A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates

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    We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters

    Magnetic properties of Gd_xY_{1-x}Fe_2Zn_{20}: dilute, large, S\textbf {S} moments in a nearly ferromagnetic Fermi liquid

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    Single crystals of the dilute, rare earth bearing, pseudo-ternary series, Gd_xY_{1-x}Fe_2Zn_{20} were grown out of Zn-rich solution. Measurements of magnetization, resistivity and heat capacity on Gd_xY_{1-x}Fe_2Zn_{20} samples reveal ferromagnetic order of Gd^{3+} local moments across virtually the whole series (x≄0.02x \geq 0.02). The magnetic properties of this series, including the ferromagnetic ordering, the reduced saturated moments at base temperature, the deviation of the susceptibilities from Curie-Weiss law and the anomalies in the resistivity, are understood within the frame work of dilute, S\textbf {S} moments (Gd^{3+}) embedded in a nearly ferromagnetic Fermi liquid (YFe_2Zn_{20}). The s-d model is employed to further explain the variation of TCT_{\mathrm{C}} with x as well as the temperature dependences of of the susceptibilities
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