Structures in a class of magnetized scale-free discs

We construct analytically stationary global configurations for both aligned and logarithmic spiral coplanar magnetohydrodynamic (MHD) perturbations in an axisymmetric background MHD disc with a power-law surface mass density $\Sigma_0\propto r^{-\alpha}$, a coplanar azimuthal magnetic field $B_0\propto r^{-\gamma}$, a consistent self-gravity and a power-law rotation curve $v_0\propto r^{-\beta}$ where $v_0$ is the linear azimuthal gas rotation speed. The barotropic equation of state $\Pi\propto\Sigma^{n}$ is adopted for both MHD background equilibrium and coplanar MHD perturbations where $\Pi$ is the vertically integrated pressure and $n$ is the barotropic index. For a scale-free background MHD equilibrium, a relation exists among $\alpha$, $\beta$, $\gamma$ and $n$ such that only one parameter (e.g., $\beta$) is independent. For a linear axisymmetric stability analysis, we provide global criteria in various parameter regimes. For nonaxisymmetric aligned and logarithmic spiral cases, two branches of perturbation modes (i.e., fast and slow MHD density waves) can be derived once $\beta$ is specified. To complement the magnetized singular isothermal disc (MSID) analysis of Lou, we extend the analysis to a wider range of $-1/4<\beta<1/2$. As an example of illustration, we discuss specifically the $\beta=1/4$ case when the background magnetic field is force-free. Angular momentum conservation for coplanar MHD perturbations and other relevant aspects of our approach are discussed.Comment: 25 page

Stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs

We construct aligned and unaligned stationary perturbation configurations in a composite system of stellar and coplanarly magnetized gaseous singular isothermal discs (SIDs) coupled by gravity. In comparison with SID problems studied earlier, there exist three possible classes of stationary solutions allowed by more dynamic freedoms. Our exact global perturbation solutions and critical points are valuable for testing numerical magnetohydrodynamic codes. For galactic applications, our model analysis contains more realistic elements and offer useful insights for structures and dynamics of disc galaxies consisting of stars and magnetized gas.Comment: 25 pages, 31 figures, accepted by Monthly Notices of Royal Astronomical Society, style files include

Periodicities in Solar Coronal Mass Ejections

Mid-term quasi-periodicities in solar coronal mass ejections (CMEs) during the most recent solar maximum cycle 23 are reported here for the first time using the four-year data (February 5, 1999 to February 10, 2003) of the Large Angle Spectrometric Coronagraph (LASCO) onboard the Solar and Heliospheric Observatory (SOHO). In parallel, mid-term quasi-periodicities in solar X-ray flares (class >M5.0) from the Geosynchronous Operational Environment Satellites (GOES) and in daily averages of Ap index for geomagnetic disturbances from the World Data Center (WDC) at the International Association for Geomagnetism and Aeronomy (IAGA) are also examined for the same four-year time span. Several conceptual aspects of possible equatorially trapped Rossby-type waves at and beneath the solar photosphere are discussed.Comment: Accepted by MNRAS, 6 figure

Energy, angular momentum and wave action associated with density waves in a rotating magnetized gas disc

Both fast and slow magnetohydrodynamic (MHD) density waves propagating in a thin rotating magnetized gas disc are investigated. In the tight-winding or WKBJ regime, the radial variation of MHD density-wave amplitude during wave propagation is governed by the conservation of wave action surface density N which travels at a relevant radial group speed Cg. The wave energy surface density ℰ and the wave angular momentum surface density J are related to N by ℰ=ωN and J=mN respectively, where ω is the angular frequency in an inertial frame of reference and the integer m, proportional to the azimuthal wavenumber, corresponds to the number of spiral arms. Consequently, both wave energy and angular momentum are conserved for spiral MHD density waves. For both fast and slow MHD density waves, net wave energy and angular momentum are carried outward or inward for trailing or leading spirals, respectively. The wave angular momentum flux contains separate contributions from gravity torque, advective transport and magnetic torque. While the gravity torque plays an important role, the latter two can be of comparable magnitudes to the former. Similar to the role of gravity torque, the part of MHD wave angular momentum flux by magnetic torque (in the case of either fast or slow MHD density waves) propagates outward or inward for trailing or leading spirals, respectively. From the perspective of global energetics in a magnetized gas sheet in rotation, trailing spiral structures of MHD density waves are preferred over leading ones. With proper qualifications, the generation and maintenance as well as transport properties of MHD density waves in magnetized spiral galaxies are discusse

Communication-Efficient Distributed Estimation and Inference for Cox's Model

Motivated by multi-center biomedical studies that cannot share individual data due to privacy and ownership concerns, we develop communication-efficient iterative distributed algorithms for estimation and inference in the high-dimensional sparse Cox proportional hazards model. We demonstrate that our estimator, even with a relatively small number of iterations, achieves the same convergence rate as the ideal full-sample estimator under very mild conditions. To construct confidence intervals for linear combinations of high-dimensional hazard regression coefficients, we introduce a novel debiased method, establish central limit theorems, and provide consistent variance estimators that yield asymptotically valid distributed confidence intervals. In addition, we provide valid and powerful distributed hypothesis tests for any coordinate element based on a decorrelated score test. We allow time-dependent covariates as well as censored survival times. Extensive numerical experiments on both simulated and real data lend further support to our theory and demonstrate that our communication-efficient distributed estimators, confidence intervals, and hypothesis tests improve upon alternative methods

Robust High-dimensional Tuning Free Multiple Testing

A stylized feature of high-dimensional data is that many variables have heavy tails, and robust statistical inference is critical for valid large-scale statistical inference. Yet, the existing developments such as Winsorization, Huberization and median of means require the bounded second moments and involve variable-dependent tuning parameters, which hamper their fidelity in applications to large-scale problems. To liberate these constraints, this paper revisits the celebrated Hodges-Lehmann (HL) estimator for estimating location parameters in both the one- and two-sample problems, from a non-asymptotic perspective. Our study develops Berry-Esseen inequality and Cram\'{e}r type moderate deviation for the HL estimator based on newly developed non-asymptotic Bahadur representation, and builds data-driven confidence intervals via a weighted bootstrap approach. These results allow us to extend the HL estimator to large-scale studies and propose \emph{tuning-free} and \emph{moment-free} high-dimensional inference procedures for testing global null and for large-scale multiple testing with false discovery proportion control. It is convincingly shown that the resulting tuning-free and moment-free methods control false discovery proportion at a prescribed level. The simulation studies lend further support to our developed theory.Comment: In this paper, we develop tuning-free and moment-free high dimensional inference procedures