Equations for determining aircraft motions for accident data

Procedures for determining a comprehensive accident scenario from a limited data set are reported. The analysis techniques accept and process data from either an Air Traffic Control radar tracking system or a foil flight data recorder. Local meteorological information at the time of the accident and aircraft performance data are also utilized. Equations for the desired aircraft motions and forces are given in terms of elements of the measurement set and certain of their time derivatives. The principal assumption made is that aircraft side force and side-slip angle are negligible. An estimation procedure is outlined for use with each data source. For the foil case, a discussion of exploiting measurement redundancy is given. Since either formulation requires estimates of measurement time derivatives, an algorithm for least squares smoothing is provided

Kernel dimension reduction in regression

We present a new methodology for sufficient dimension reduction (SDR). Our methodology derives directly from the formulation of SDR in terms of the conditional independence of the covariate $X$ from the response $Y$, given the projection of $X$ on the central subspace [cf. J. Amer. Statist. Assoc. 86 (1991) 316--342 and Regression Graphics (1998) Wiley]. We show that this conditional independence assertion can be characterized in terms of conditional covariance operators on reproducing kernel Hilbert spaces and we show how this characterization leads to an $M$-estimator for the central subspace. The resulting estimator is shown to be consistent under weak conditions; in particular, we do not have to impose linearity or ellipticity conditions of the kinds that are generally invoked for SDR methods. We also present empirical results showing that the new methodology is competitive in practice.Comment: Published in at http://dx.doi.org/10.1214/08-AOS637 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Analysis of severe atmospheric disturbances from airline flight records

Advanced methods were developed to determine time varying winds and turbulence from digital flight data recorders carried aboard modern airliners. Analysis of several cases involving severe clear air turbulence encounters at cruise altitudes has shown that the aircraft encountered vortex arrays generated by destabilized wind shear layers above mountains or thunderstorms. A model was developed to identify the strength, size, and spacing of vortex arrays. This model is used to study the effects of severe wind hazards on operational safety for different types of aircraft. The study demonstrates that small remotely piloted vehicles and executive aircraft exhibit more violent behavior than do large airliners during encounters with high-altitude vortices. Analysis of digital flight data from the accident at Dallas/Ft. Worth in 1985 indicates that the aircraft encountered a microburst with rapidly changing winds embedded in a strong outflow near the ground. A multiple-vortex-ring model was developed to represent the microburst wind pattern. This model can be used in flight simulators to better understand the control problems in severe microburst encounters

Coexistence of Antiferromagnetism and Superconductivity in Electron-doped High-Tc Superconductors

We present magnetotransport evidence for antiferromagnetism in films of the electron-doped cuprates Pr$_{2-x}$Ce$_x$CuO$_4$. Our results show clear signature of static antiferromagnetism up to optimal doping x=0.15, with a quantum phase transition close to x=0.16, and a coexistence of static antiferromagnetism and superconductivity for 0.12$\le$x$\le$0.15

Random vectors on the spin configuration of a Curie-Weiss model on Erdos-Renyi random graphs

This article is concerned with the asymptotic behaviour of random vectors in a diluted ferromagnetic model. We consider a model introduced by Bovier & Gayrard (1993) with ferromagnetic interactions on a directed Erd\H{o}s-R\'enyi random graph. Here, directed connections between graph nodes are uniformly drawn at random with a probability p that depends on the number of nodes N and is allowed to go to zero in the limit. If $Np\longrightarrow\infty$ in this model, Bovier & Gayrard (1993) proved a law of large numbers almost surely, and Kabluchko et al. (2020) proved central limit theorems in probability. Here, we generalise these results for $\beta<1$ in the regime $Np\longrightarrow\infty$. We show that all those random vectors on the spin configuration that have a limiting distribution under the Curie-Weiss model converge weakly towards the same distribution under the diluted model, in probability on graph realisations. This generalises various results from the Curie-Weiss model to the diluted model. As a special case, we derive a law of large numbers and central limit theorem for two disjoint groups of spins