Local linear spatial quantile regression

Copyright @ 2009 International Statistical Institute / Bernoulli Society for Mathematical Statistics and Probability.Let {(Yi,Xi), i ∈ ZN} be a stationary real-valued (d + 1)-dimensional spatial processes. Denote by x → qp(x), p ∈ (0, 1), x ∈ Rd , the spatial quantile regression function of order p, characterized by P{Yi ≤ qp(x)|Xi = x} = p. Assume that the process has been observed over an N-dimensional rectangular domain of the form In := {i = (i1, . . . , iN) ∈ ZN|1 ≤ ik ≤ nk, k = 1, . . . , N}, with n = (n1, . . . , nN) ∈ ZN. We propose a local linear estimator of qp. That estimator extends to random fields with unspecified and possibly highly complex spatial dependence structure, the quantile regression methods considered in the context of independent samples or time series. Under mild regularity assumptions, we obtain a Bahadur representation for the estimators of qp and its first-order derivatives, from which we establish consistency and asymptotic normality. The spatial process is assumed to satisfy general mixing conditions, generalizing classical time series mixing concepts. The size of the rectangular domain In is allowed to tend to infinity at different rates depending on the direction in ZN (non-isotropic asymptotics). The method provides muchAustralian Research Counci

Is GRO J1744-28 a Strange Star?

The unusal hard x-ray burster GRO J1744-28 recently discovered by the Compton Gamma-ray Observatory (GRO) can be modeled as a strange star with a dipolar magnetic field $\le 10^{11}$Gauss. When the accreted mass of the star exceeds some critical mass, its crust may break, resulting in conversion of the accreted matter into strange matter and release of energy. Subsequently, a fireball may form and expand relativistically outward. The expanding fireball may interact with the surrounding interstellar medium, causing its kinetic energy to be radiated in shock waves, producing a burst of x-ray radiation. The burst energy, duration, interval and spectrum derived from such a model are consistent with the observations of GRO J1744-28.Comment: Latex, has been published in SCIENCE, Vol. 280, 40

Beaming Effects in Gamma-Ray Bursts

Based on a refined generic dynamical model, we investigate afterglows from jetted gamma-ray burst (GRB) remnants numerically. In the relativistic phase, the light curve break could marginally be seen. However, an obvious break does exist at the transition from the relativistic phase to the non-relativistic phase, which typically occurs at time 10 to 30 days. It is very interesting that the break is affected by many parameters, especially by the electron energy fraction (xi_e), and the magnetic energy fraction (xi_B^2). Implication of orphan afterglow surveys on GRB beaming is investigated. The possible existence of a kind of cylindrical jets is also discussed.Comment: Minor changes; 10 pages, with 9 eps figures embedded. Talk given at the Sixth Pacific Rim Conference on Stellar Astrophysics (Xi'an, China, July 11-17, 2002). A slightly revised version will appear in the proceeding

Pair loading in Gamma-Ray Burst Fireball And Prompt Emission From Pair-Rich Reverse Shock

Gamma-ray bursts (GRBs) are believed to originate from ultra-relativistic winds/fireballs to avoid the "compactness problem". However, the most energetic photons in GRBs may still suffer from $\gamma-\gamma$ absorption leading to electron/positron pair production in the winds/fireballs. We show here that in a wide range of model parameters, the resulting pairs may dominate those electrons associated with baryons. Later on, the pairs would be carried into a reverse shock so that a shocked pair-rich fireball may produce a strong flash at lower frequencies, i.e. in the IR band, in contrast with optical/UV emission from a pair-poor fireball. The IR emission would show a 5/2 spectral index due to strong self-absorption. Rapid responses to GRB triggers in the IR band would detect such strong flashes. The future detections of many IR flashes will infer that the rarity of prompt optical/UV emissions is in fact due to dust obscuration in the star formation regions.Comment: 8 pages, 2 figures, ApJ accepte

Comparisons and Applications of Four Independent Numerical Approaches for Linear Gyrokinetic Drift Modes

To help reveal the complete picture of linear kinetic drift modes, four independent numerical approaches, based on integral equation, Euler initial value simulation, Euler matrix eigenvalue solution and Lagrangian particle simulation, respectively, are used to solve the linear gyrokinetic electrostatic drift modes equation in Z-pinch with slab simplification and in tokamak with ballooning space coordinate. We identify that these approaches can yield the same solution with the difference smaller than 1\%, and the discrepancies mainly come from the numerical convergence, which is the first detailed benchmark of four independent numerical approaches for gyrokinetic linear drift modes. Using these approaches, we find that the entropy mode and interchange mode are on the same branch in Z-pinch, and the entropy mode can have both electron and ion branches. And, at strong gradient, more than one eigenstate of the ion temperature gradient mode (ITG) can be unstable and the most unstable one can be on non-ground eigenstates. The propagation of ITGs from ion to electron diamagnetic direction at strong gradient is also observed, which implies that the propagation direction is not a decisive criterion for the experimental diagnosis of turbulent mode at the edge plasmas.Comment: 12 pages, 10 figures, accept by Physics of Plasma

A spectroscopic study of the cycling transition 4s[3/2]_2-4p[5/2]_3 at 811.8 nm in Ar-39: Hyperfine structure and isotope shift

Doppler-free saturated absorption spectroscopy is performed on an enriched radioactive Ar-39 sample. The spectrum of the 3s^2 3p^5 4s [3/2]_2 - 3s^2 3p^5 4p [5/2]_3 cycling transition at 811.8 nm is recorded, and its isotope shift between Ar-39 and Ar-40 is derived. The hyperfine coupling constants A and B for both the 4s [3/2]_2 and 4p [5/2]_3 energy levels in Ar-39 are also determined. The results partially disagree with a recently published measurement of the same transition. Based on earlier measurements as well as the current work, the isotope shift and hyperfine structure of the corresponding transition in Ar-37 are also calculated. These spectroscopic data are essential for the realization of laser trapping and cooling of Ar-37 and Ar-39