Asymptotic behavior of general M-estimates for regression and scale with random carriers

Summary Let (xini, y _i be a sequence of independent identically distributed random variables, where x _i R ^p and y _i R, and let R ^p be an unknown vector such that y _i =x _i +u _i (^*), where u _i is independent of x _i and has distribution function F(u/), where >0 is an unknown parameter. This paper deals with a general class of M-estimates of regression and scale, ( ^*,^*), defined as solutions of the system: , where r= (y _i –x _i ^1*/)^*, with R ^p ×RR and RR. This class contains estimators of (, ) proposed by Huber, Mallows and Krasker and Welsch. The consistency and asymptotic normality of the general M-estimators are proved assuming general regularity conditions on and and assuming the joint distribution of (x _i , y _i ) to fulfill the model (^*) only approximately.     

In situ 2-D piezoelectric wafer active sensors arrays for guided wave damage detection

This paper presented development work of an in situ method for damage detection in thin-wall structures using embedded two-dimensional ultrasonic phased arrays. Piezoelectric wafer active sensors were used to generate and receive guided Lamb waves propagating in the plate-like structure. The development of a generic beamforming algorithm that does not require parallel ray assumption through using full wave propagation paths is described. A virtual beam steering method and device, the embedded ultrasonic structural radar, was implemented as a signal post-processing procedure. Several two-dimensional configurations were investigated and compared with beamforming simulation. Finally, rectangular shape arrays were developed for verifying the generic formulas and omnidirectionality. The rectangular arrays yield good directionality within the 360° full range and are able to detect damage anywhere in the entire plate.     

Prescriptions for gravitational initial data as judged by a simple radiating model

Several methods of prescribing initial data for gravitational and matter fields, which are intended to eliminate extraneous radiation that is not produced by the matter source, are analysed in a simple exactly soluble radiating model. The model consists of an harmonic oscillator coupled to a scalar field along future light cones of Minkowski space time. In particular we analyze the asymptotic regime of the oscillator and find it is characterized essentially by two distinct decay modes. They differ in the way they behave both in the limit of small coupling constant and in a certain Newtonian limit. As a criterion to select initial data for the field with no extra radiation, we require that these initial data sets should put the oscillator from the start into the asymptotic regime. The underlying hypothesis here is that initial transients result from excitation of the oscillator by incoming radiation. We then see that the requirement of a uniform Newtonian limit leads to unique data for the scalar field for each arbitrary data set for the oscillator. We further find that this unique data set indeed satisfies our criterion.     

Stable radially symmetric and azimuthally modulated vortex solitons supported by localized gain

We discover that a spatially localized gain supports stable vortex solitons in media with cubic nonlinearity and two-photon absorption. The interplay between nonlinear losses and gain in amplifying rings results in the suppression of otherwise ubiquitous azimuthal modulation instabilities of radially symmetric vortex solitons. We find that the topology of the gain profile imposes restrictions on the maximal possible charge of vortex solitons. Symmetry breaking occurs at high gain levels, resulting in the formation of necklace vortex solitons composed of asymmetric bright spots.     

Wide dynamic range detection of bidirectional flow in Doppler optical coherence tomography using a two-dimensional Kasai estimator

We demonstrate extended axial flow velocity detection range in a time-domain Doppler optical coherence tomography (DOCT) system using a modified Kasai velocity estimator with computations in both the axial and transverse directions. For a DOCT system with an 8 kHz rapid-scanning optical delay line, bidirectional flow experiments showed a maximum detectable speed of >56 cm/s using the axial Kasai estimator without the occurrence of aliasing, while the transverse Kasai estimator preserved the approximately 7 microm/s minimum detectable velocity to slow flow. By using a combination of transverse Kasai and axial Kasai estimators, the velocity detection dynamic range was over 100 dB. Through a fiber-optic endoscopic catheter, in vivoM-mode transesophageal imaging of the pulsatile blood flow in rat aorta was demonstrated, for what is for the first time to our knowledge, with measured peak systolic blood flow velocity of >1 m/s, while maintaining good sensitivity to detect aortic wall motion at <2 mm/s, using this 2D Kasai technique.     

Morphological predictability and acoustic duration of interfixes in Dutch compounds

This study explores the effects of informational redundancy, as carried by a word's morphological paradigmatic structure, on acoustic duration in read aloud speech. The hypothesis that the more predictable a linguistic unit is, the less salient its realization, was tested on the basis of the acoustic duration of interfixes in Dutch compounds in two datasets: One for the interfix -s- (1155 tokens) and one for the interfix -e(n)- (742 tokens). Both datasets show that the more probable the interfix is, given the compound and its constituents, the longer it is realized. These findings run counter to the predictions of information-theoretical approaches and can be resolved by the Paradigmatic Signal Enhancement Hypothesis. This hypothesis argues that whenever selection of an element from alternatives is probabilistic, the element's duration is predicted by the amount of paradigmatic support for the element: The most likely alternative in the paradigm of selection is realized longer.     

Phase-matched third-harmonic UV generation using low-order modes in a glass micro-fiber

We observe phase-matched third-harmonic generation at 355 nm in a low-order mode of a sub-micron diameter glass fiber. The third-harmonic signal exhibits a sharp resonance for a fiber diameter d = 0.49 ± 0.02 μm, in excellent agreement with the value d = 0.506 μm predicted by theory. The third-harmonic conversion efficiency is 2 × 10⁻⁶, and is limited by the pump power (1 kW) and effective fiber length (100 μm).     

Tunable soliton self-bending in optical lattices with nonlocal nonlinearity

We address the phenomenon of soliton self-bending in Kerr-type nonlocal nonlinear media with an imprinted transverse periodic modulation of the linear refractive index. We show that the imprinted optical lattice makes possible to control the mobility of soliton by varying the depth and the frequency of the linear refractive index modulation.     

Micromachined array tip for multifocus fiber-based optical coherence tomography

High-resolution optical coherence tomography demands a large detector bandwidth and a high numerical aperture for real-time imaging, which is difficult to achieve over a large imaging depth. To resolve these conflicting requirements we propose a novel multifocus fiber-based optical coherence tomography system with a micromachined array tip. We demonstrate the fabrication of a prototype four-channel tip that maintains a 9-14-microm spot diameter with more than 500 microm of imaging depth. Images of a resolution target and a human tooth were obtained with this tip by use of a four-channel cascaded Michelson fiber-optic interferometer, scanned simultaneously at 8 kHz with geometric power distribution across the four channels.