Cauchy Approximation Research Articles

Quasi-likelihood analysis for Student-Lévy regression

We consider the quasi-likelihood analysis for a linear regression model driven by a Student-t Lévy process with constant scale and arbitrary degrees of freedom. The model is observed at high frequency over an extending period, under which we can quantify how the sampling frequency affects estimation accuracy. In that setting, joint estimation of trend, scale, and degrees of freedom is a non-trivial problem. The bottleneck is that the Student-t distribution is not closed under convolution, making it difficult to estimate all the parameters fully based on the high-frequency time scale. To efficiently deal with the intricate nature from both theoretical and computational points of view, we propose a two-step quasi-likelihood analysis: first, we make use of the Cauchy quasi-likelihood for estimating the regression-coefficient vector and the scale parameter; then, we construct the sequence of the unit-period cumulative residuals to estimate the remaining degrees of freedom. In particular, using full data in the first step causes a problem stemming from the small-time Cauchy approximation, showing the need for data thinning.

Induced gyrotropy in thin PET films before and after swift heavy ion irradiation evidenced from analysis of optical interference fringes

We present here experimental studies of the UV/vis/near IR transmission spectra of polyethylene terephthalate (PET) films before and after irradiation with Kr+15 ions of energy 1.75 MeV/a.u. and fluence of 1.9 × 10 10 cm−2. Our data show small variations (∼0.5%) in transmission between individual pristine PET film samples in the IR region of the spectrum, as would be expected for films produced to certain manufacturing tolerances. Swift heavy ion (SHI) irradiation of a sample reduces transmission in this region, but by less than the observed variation in transmission between individual pristine samples, and does not affect local transmission variations in the spectrum, indicating that SHI irradiation has not destroyed the molecular structure of the PET film responsible for these variations. We use established methods to separate our experimental spectra into interference-free transmission spectra and isolated interference fringes and estimate the absorption coefficient and dispersion of the refractive index for pristine and irradiated PET films. We show that the observed amplitude modulation of the interference fringes is due to the optical activity of our PET samples and is a signature of induced gyrotropy. In some spectral regions, we observe a refractive index that is negative relative to the Cauchy approximation. We provide evidence that this is due to the ordering/texture of chiral molecules in PET films, suggesting that very highly textured PET films may exhibit a greater degree of negativity.

An Ellipsometric Study of Thin-Film Structures of Amorphic Hydrogenized Carbon and Gold Nanoparticles

Optical сonstants of an amorphous hydrogenated carbon (a-C:H) film and its hybrid structure with granular gold film before and after annealing at 300°C have been investigated by spectral ellipsometry. Dispersions n(λ) and k(λ) of the a-C:H film and its thickness have been identified using the Cauchy approximation. The spectral features of the layer of Au plasmon nanoparticles deposited on the a-C:H surface have been modeled in the form of an effective medium and Lorentz oscillator. The parameters of the films and their thickness have been determined by fitting the calculated spectra to the ψ(λ) and Δ(λ) ellipsometric spectra. The obtained data have been used to determine the Lorentz oscillator parameters in the model of an a‑C:H/Au two-layer structure. The intensity of the maxima in the n and k spectra increased, their position shifted to the blue region, and the half-width of the bands decreased as a result of the a-C:H/Au structure annealing. The observed changes in ellipsometric spectra are fully consistent with the spectrophotometric data of this structure.

Эллипсометрическое исследование тонкопленочных структур аморфного гидрогенизированного углерода и наночастиц золота

In this work, the optical constant films of amorphous hydrogenated carbon (a-C: H) and a hybrid structure based on it with a granulated gold film before and after their annealing at 300 °C were studied by spectral ellipsometry. The dispersions n (λ) and k (λ) of the a-C:H film were established using the Cauchy approximation and its thickness. The spectral features of the Au plasmon nanoparticle layer deposited on the a-C:H surface were modeled as an effective medium and a Lorentz oscillator. The parameters of the films and their thickness were determined by fitting the calculated spectra to the ellipsometric spectra  (λ) and  (λ). The obtained data were used to determine the parameters of the Lorentz oscillator in the model of a-C:H / Au two-layer structure. As a result of the a-C:H / Au structure annealing, the intensity of the maxima in the spectra n and k increased, their position shifted to the blue region, and the half-width of the bands decreased. The observed changes in the ellipsometric spectra are completely consistent with the spectrophotometric data of this structure.

Broadening Microstructure Analysis Program(BMAP): an isotropic and anisotropic crystallite size and strain calculator

BMAPcalculator is a simplified software tool to obtain microstructure characteristics and to investigate their isotropic and anisotropic nature using some common broadening methods. The Scherrer and Stokes–Wilson methods as well as the Williamson–Hall plot (microstructure isotropy) and modified Williamson–Hall models (strain anisotropy) are implemented in the calculations. TheBMAPinput data are the X-ray diffraction peak parameters (the full width at half-maximum or integral breadth and peak position) of a measured line profile and of a reference one. The components of the measured line profile or corrected broadening are based on several approximations (Cauchy, Gauss or Voigt). The linear least-squares fit is used to calculate the size–strain values, and the correlation coefficient for accepting the results. The calculator is applied to an X-ray diffraction experiment of NiO nanoparticles prepared by a sol–gel method for testing. The results ofBMAPcalculator and theMAUDprogram, combined with an anisotropic Popa rules approach, are compared. The uniform stress model based on the Cauchy approximation is the most suitable one in cubic nanostructure nickel oxide, with an average crystallite size of 24 nm and anisotropic strains of 1.54 × 10−3, 0.61 × 10−3, 1.77 × 10−3and 1.49 × 10−3using the {111}, {200}, {220} and {311} reflections, respectively. Generally, for non-Rietveld users, it is useful to collect different methods into one program to depict the anisotropic nature of materials.

Support Vector Regression Modeling for LTCC Interconnection Based on Prior Knowledge

This paper presents a prior knowledge based support vector regression modeling method to characterize the RF performance of the low temperature co-fired ceramic (LTCC) structure. A coarse surrogate is formed by multidimensional Cauchy approximation as the prior knowledge to improve the accuracy of modeling. 3D LTCC based vertical interconnection model is developed as an example using the proposed method. Experimental results show that the developed SVR model perform a better predictive ability.

Antenna modeling using space‐mapping corrected cauchy approximation surrogates

AbstractIn this work, a computationally efficient antenna modeling technique. Our methodology is a two‐stage approach is present. In the first stage, a Cauchy‐based approximation model is constructed using coarsely discretized full‐wave simulation. The accuracy of this model is improved using a space mapping (SM) approach. A limited number of high‐fidelity antenna simulations are used in the SM phase. We show that our approach obtains a modeling accuracy comparable to that provided by direct Cauchy approximation of the high‐fidelity electromagnetic simulation data. The computational cost is, however, much lower. We successfully illustrate our approach through a number of antenna modeling examples. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:37–40, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.26455

Computationally efficient design optimization of wideband planar antennas using Cauchy approximation and space mapping

Computationally efficient simulation-driven design of ultra-wideband planar antennas is presented using Cauchy-based surrogate models of the coarsely-discretized antenna electromagnetic models.Verification of the proposed methodology is performed with satisfactory designs obtained at a computational cost of a few evaluations of high-fidelity antenna models. © 2011 Wiley Periodicals, Inc. Microwave Opt Technol Lett 53:618–622, 2011; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.25814

VARIABLE-FIDELITY DESIGN OPTIMIZATION OF MICROWAVE DEVICES USING MULTI-DIMENSIONAL CAUCHY APPROXIMATION AND COARSELY DISCRETIZED ELECTROMAGNETIC MODELS

Application of multi-dimensional Cauchy approximation and coarse-discretization electromagnetic (EM) models to surrogate- based optimization of microwave structures is discussed. Space mapping is used as an optimization engine with the surrogate model constructed as a Cauchy approximation of the coarsely discretized device EM model. The proposed approach allows us to perform computationally e-cient optimization of microwave structures without using circuit-equivalent coarse models traditionally exploited by space mapping algorithms. We demonstrate our technique through design of a range of microwave devices, including fllters, antennas, and transitions. Comprehensive numerical veriflcation of the proposed methodology is carried out with satisfactory designs obtained | for all considered devices | at a computational cost corresponding to a few full-wave simulations.

Cauchy approximation for sums of independent random variables

We use Stein′s method to find a bound for Cauchy approximation. The random variables which are considered need to be independent.

First-order and conditional statistics of rain attenuation fade slope

In accordance with the assumptions of Maseng and Bakken (1981), the distribution of rain fade slope on high frequency GSO links is calculated and its Cauchy approximation is presented. The conditional PDF of the fade slope is finally modelled for application to predictive rain fade mitigation techniques (FMTs).

Reliability of the Simplified Integral-Breadth Methods in Diffraction Line-Broadening Analysis

A comparison between different simplified integral-breadth methods, often used in the Rietveld-refinement programs to calculate coherent domain size and lattice strain, is carried out. It is shown that systematic differences exist for both domain size and strain, when they simultaneously broaden diffraction lines. Among different approximations, the values of domain size exceptionally scatter and sometimes are completely false (negative or not real). A comparison to the alternative Fourier method shows that all the simplified integral-breadth methods overestimate domain size, but especially the Cauchy–Cauchy approximation. The root-mean-square strain and the upper limit of strain are related in the general case of the Voigt strain-broadened line profile. It is shown that they should not differ much as the profile changes between the Gauss and Cauchy extremes. The pure-Gauss size-broadened profile is incompatible with the definitions of surface-weighted domain size and column-length distribution function.

Characterization of the Thin Oxide-Nitride-Oxide (ONO) Structure Using Spectroscopic Ellipsometry

ABSTRACTSpectroscopic ellipsometry has been used to characterize thin oxide/nitride/oxide (ONO) layer structures. Films were deposited on top of the Si/oxide/polysilicon filmstack using a low-pressure chemical vapor deposition (LPCVD) technique. Different approaches to modeling this structure are compared to select an adequate representation. Analysis of the data for the three-layer-with-abrupt-interfaces ONO model using an effective-medium or Cauchy approximation shows strong correlation of the parameters and ambiguity of the results. A more robust and physically plausible model of the ONO structure as an inhomogeneous oxynitride film with Gaussian distribution of the silicon nitride component is suggested. This interpretation of the ONO structure is supported by the results of Auger electron spectroscopy (AES) and transmission electron microscopy (XTEM).