Asymptotic power of sphericity tests for high-dimensional data

This paper studies the asymptotic power of tests of sphericity against perturbations in a single unknown direction as both the dimensionality of the data and the number of observations go to infinity. We establish the convergence, under the null hypothesis and contiguous alternatives, of the log ratio of the joint densities of the sample covariance eigenvalues to a Gaussian process indexed by the norm of the perturbation. When the perturbation norm is larger than the phase transition threshold studied in Baik, Ben Arous and Peche [Ann. Probab. 33 (2005) 1643-1697] the limiting process is degenerate, and discrimination between the null and the alternative is asymptotically certain. When the norm is below the threshold, the limiting process is nondegenerate, and the joint eigenvalue densities under the null and alternative hypotheses are mutually contiguous. Using the asymptotic theory of statistical experiments, we obtain asymptotic power envelopes and derive the asymptotic power for various sphericity tests in the contiguity region. In particular, we show that the asymptotic power of the Tracy-Widom-type tests is trivial (i.e., equals the asymptotic size), whereas that of the eigenvalue-based likelihood ratio test is strictly larger than the size, and close to the power envelope.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1100 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

System Concepts for Bi- and Multi-Static SAR Missions

The performance and capabilities of bi- and multistatic spaceborne synthetic aperture radar (SAR) are analyzed. Such systems can be optimized for a broad range of applications like frequent monitoring, wide swath imaging, single-pass cross-track interferometry, along-track interferometry, resolution enhancement or radar tomography. Further potentials arises from digital beamforming on receive, which allows to gather additional information about the direction of the scattered radar echoes. This directional information can be used to suppress interferences, to improve geometric and radiometric resolution, or to increase the unambiguous swath width. Furthermore, a coherent combination of multiple receiver signals will allow for a suppression of azimuth ambiguities. For this, a reconstruction algorithm is derived, which enables a recovery of the unambiguous Doppler spectrum also in case of non-optimum receiver aperture displacements leading to a non-uniform sampling of the SAR signal. This algorithm has also a great potential for systems relying on the displaced phase center (DPC) technique, like the high resolution wide swath (HRWS) SAR or the split antenna approach in the TerraSAR-X and Radarsat II satellites

Comparison of young swimmer’s active drag coefficient using three methods to compute trunk transverse surface area.

The purpose of this study was to compare the active drag coefficient (CDa) of young swimmers using three different ways of measuring the trunk transverse surface area (TTSA). 23 young swimmers, including 12 boys and 11 girls were analyzed. The velocity perturbation method of Kolmogorov was used to compute CDa. The TTSA was calculated based on three methods: (i) measured by photogrammetric; (ii) estimated by the equation developed by Clarys and; (iii) estimated from the equations developed by Morais et al.. Three procedures were used in the comparison CDa values: (i) T-Student test; (ii) simple linear regression analysis and; (iii) Bland Altman plots. All paired samples showed significant differences (p <0.001) when comparing mean values. However, there were significant correlations (p <0.001) between the paired samples in the simple linear regression analysis, and the in the Bland Altman plots for all conditions studied. At least 80% of the plots were within the ± 1.96 standard deviation of the difference. As a conclusion, the mean values of CDa computed with TTSA estimated with the equations developed by Morais et al. were the ones with lower difference compared with TTSA measured directly. Those should be used by coaches and investigators in order to estimate TTSA for CDa computing

A Fr\'{e}chet law and an Erd\"os-Philipp law for maximal cuspidal windings

In this paper we establish a Fr\'{e}chet law for maximal cuspidal windings of the geodesic flow on a Riemannian surface associated with an arbitrary finitely generated, essentially free Fuchsian group with parabolic elements. This result extends previous work by Galambos and Dolgopyat and is obtained by applying Extreme Value Theory. Subsequently, we show that this law gives rise to an Erd\"os-Philipp law and to various generalised Khintchine-type results for maximal cuspidal windings. These results strengthen previous results by Sullivan, Stratmann and Velani for Kleinian groups, and extend earlier work by Philipp on continued fractions, which was inspired by a conjecture of Erd\"os

Bistatic Experiment Using TerraSAR-X and DLR’s new F-SAR System

A bistatic X-band experiment was successfully performed early November 2007. TerraSAR-X was used as transmitter and DLR’s new airborne radar system F-SAR, which was programmed to acquire data in a quasi-continuous mode to avoid echo window synchronization issues, was used as bistatic receiver. Precise phase and time referencing between both systems, which is essential for obtaining high resolution SAR images, was derived during the bistatic processing. Hardware setup and performance analyses of the bistatic configuration are pre-sented together with first processing results that verify the predicted synchronization and imaging performance

Tentativa preliminar para desenvolver um modelo de análise (path-flow) da performance em jovens nadadoras

O objectivo do presente trabalho foi desenvolver um modelo de análise da performance (path flow) em jovens nadadoras, com base em parâmetros antropométricos, hidrodinâmicos, biomecânicos e bioenergéticos

How informative are the vertical buoyancy and the prone gliding tests to assess young swimmers hydrostatic and hydrodynamic profiles?

The aim of this research was to develop a path-flow analysis model to highlight the relationships between buoyancy and prone gliding tests and some selected anthropometrical and biomechanical variables. Thirty-eight young male swimmers (12.97 ± 1.05 years old) with several competitive levels were evaluated. It were assessed the body mass, height, fat mass, body surface area, vertical buoyancy, prone gliding after wall push-off, stroke length, stroke frequency and velocity after a maximal 25 [m] swim. The confirmatory model included the body mass, height, fat mass, prone gliding test, stroke length, stroke frequency and velocity. All theoretical paths were verified except for the vertical buoyancy test that did not present any relationship with anthropometrical and biomechanical variables nor with the prone gliding test. The good-of-fit from the confirmatory path-flow model, assessed with the standardized root mean square residuals (SRMR), is considered as being close to the cut-off value, but even so not suitable of the theory (SRMR = 0.11). As a conclusion, vertical buoyancy and prone gliding tests are not the best techniques to assess the swimmer’s hydrostatic and hydrodynamic profile, respectively

Remarks on the exact energy functional for fermions: an analysis using the Löwdin partitioning technique

A comparison model based in the Löwdin partitioning technique is used to analyse the differences between the wave function and density functional models. This comparison model provides a tool, the Löwdin function f (E), to understand the structure of both theories and its discrepancies in terms of the subjacent mathematical structure and the necessary conditions of variationality required for the energy functional. It is argued that density functional theory (DFT) can be compared to the wave function theory (WFT) using the expressions of f (E) at E = 0. The WFT provides an explicit form of the exact energy functional for a fermion system from the full configuration interaction approach. The DFT can be seen as a special case of Löwdin function that does not satisfy all variational conditions on ρ(r) and also on the EXC[ρ] term. This analysis shows that ignoring the restrictions imposed by the spin and space symmetry requirements of the solutions when making a variational calculation implies that the correlations expressed by the ρ(r) function will be inconsistent with a γ1(r1; r′1) function derivable from a spin and space symmetry adapted wave function Ψ(r1s1, ¿, rnsn), even for a closed-shell system (i.e. an energy minimum that will exhibit the phenomenon of 'overcorrelation'). The comparison scheme also provides a new insight on the variational requirements in order to achieve a consistent description of the molecular electronic structure of both ground and excited states. Some numerical results are reported