Component Selection in the Additive Regression Model

Similar to variable selection in the linear regression model, selecting significant components in the popular additive regression model is of great interest. However, such components are unknown smooth functions of independent variables, which are unobservable. As such, some approximation is needed. In this paper, we suggest a combination of penalized regression spline approximation and group variable selection, called the lasso-type spline method (LSM), to handle this component selection problem with a diverging number of strongly correlated variables in each group. It is shown that the proposed method can select significant components and estimate nonparametric additive function components simultaneously with an optimal convergence rate simultaneously. To make the LSM stable in computation and able to adapt its estimators to the level of smoothness of the component functions, weighted power spline bases and projected weighted power spline bases are proposed. Their performance is examined by simulation studies across two set-ups with independent predictors and correlated predictors, respectively, and appears superior to the performance of competing methods. The proposed method is extended to a partial linear regression model analysis with real data, and gives reliable results

Harmonically-related diffraction gratings-based interferometer for quadrature phase measurements

We demonstrate the use of shallow diffraction gratings for quadrature phase interferometry. A single shallow diffraction grating-based Michelson interferometer yields only trivial (0° or 180°) phase shift between different output ports. In comparison, a combination of two parallel shallow diffraction gratings can be useful to achieve desired phase shifts (e.g., 90° for quadrature phase interferometry). We show that the phase at different output ports of a grating-pair based interferometer can be adjusted by shearing the two gratings with respect to each other. Two harmonically-related diffraction gratings are used to demonstrate phase shift control at the output ports of a modified Michelson interferometer. Our experimental data is in good agreement with theory

Anisotropic Rabi model

We define the anisotropic Rabi model as the generalization of the spin-boson Rabi model: The Hamiltonian system breaks the parity symmetry; the rotating and counter-rotating interactions are governed by two different coupling constants; a further parameter introduces a phase factor in the counter-rotating terms. The exact energy spectrum and eigenstates of the generalized model is worked out. The solution is obtained as an elaboration of a recent proposed method for the isotropic limit of the model. In this way, we provide a long sought solution of a cascade of models with immediate relevance in different physical fields, including i) quantum optics: two-level atom in single mode cross electric and magnetic fields; ii) solid state physics: electrons in semiconductors with Rashba and Dresselhaus spin-orbit coupling; iii) mesoscopic physics: Josephson junctions flux-qubit quantum circuits.Comment: 5 pages+ 6 pages supplementary, 7 figures, accepted by Phys. Rev.

Surface-wave-enabled darkfield aperture for background suppression during weak signal detection

Sensitive optical signal detection can often be confounded by the presence of a significant background, and, as such, predetection background suppression is substantively important for weak signal detection. In this paper, we present a novel optical structure design, termed surface-wave-enabled darkfield aperture (SWEDA), which can be directly incorporated onto optical sensors to accomplish predetection background suppression. This SWEDA structure consists of a central hole and a set of groove pattern that channels incident light to the central hole via surface plasmon wave and surface-scattered wave coupling. We show that the surface wave component can mutually cancel the direct transmission component, resulting in near-zero net transmission under uniform normal incidence illumination. Here, we report the implementation of two SWEDA structures. The first structure, circular-groove-based SWEDA, is able to provide polarization-independent suppression of uniform illumination with a suppression factor of 1230. The second structure, linear-groove-based SWEDA, is able to provide a suppression factor of 5080 for transverse-magnetic wave and can serve as a highly compact (5.5 micrometer length) polarization sensor (the measured transmission ratio of two orthogonal polarizations is 6100). Because the exact destructive interference balance is highly delicate and can be easily disrupted by the nonuniformity of the localized light field or light field deviation from normal incidence, the SWEDA can therefore be used to suppress a bright background and allow for sensitive darkfield sensing and imaging (observed image contrast enhancement of 27 dB for the first SWEDA)