Error Kernel Research Articles

Nonlinear flexure mechanics of beams: stress gradient and nonlocal integral theory

In order to study the intrinsic size-effects, the stress gradient theory is implemented to a nano-scale beam model in nonlinear flexure. The nonlocal integral elasticity model is considered as a suitable counterpart to examine the softening behavior of nano-beams. Reissner variational principle is extended consistent with the stress gradient theory and applied to establish the differential, constitutive and boundary conditions of a nano-sized beam in nonlinear flexure. The nonlinear integro-differential and boundary conditions of inflected beams in the framework of the nonlocal integral elasticity are determined utilizing the total elastic strain energy formulation. A practical series solution approach in terms of Chebyshev polynomials is introduced to appropriately estimate the kinematic and kinetic field variables. A softening structural behavior is observed in the flexure of the stress gradient and the nonlocal beam in terms of the characteristic parameter and the smaller-is-softer phenomenon is, therefore, confirmed. The flexural response associated with the stress gradient theory is demonstrated to be in excellent agreement with the counterpart results of the nonlocal elasticity model equipped with the Helmholtz kernel function. The nonlocal elasticity theory endowed with the Error kernel function is illustrated to underestimate the flexural results of the stress gradient beam model. Detected numerical benchmark can be efficiently exploited for structural design and optimization of pioneering nano-engineering devices broadly utilized in advanced nano-electro-mechanical systems.

A Generalized Continuous-Multinomial Response Model with a t-distributed Error Kernel

In multinomial response models, idiosyncratic variations in the indirect utility are generally modeled using Gumbel or normal distributions. This study makes a strong case to substitute these thin-tailed distributions with a t-distribution. First, we demonstrate that a model with a t-distributed error kernel better estimates and predicts preferences, especially in class-imbalanced datasets. Our proposed specification also implicitly accounts for decision-uncertainty behavior, i.e. the degree of certainty that decision-makers hold in their choices relative to the variation in the indirect utility of any alternative. Second – after applying a t-distributed error kernel in a multinomial response model for the first time – we extend this specification to a generalized continuous-multinomial (GCM) model and derive its full-information maximum likelihood estimation procedure. The likelihood involves an open-form expression of the cumulative density function of the multivariate t-distribution, which we propose to compute using a combination of the composite marginal likelihood method and the separation-of-variables approach. Third, we establish finite sample properties of the GCM model with a t-distributed error kernel (GCM-t) and highlight its superiority over the GCM model with a normally-distributed error kernel (GCM-N) in a Monte Carlo study. Finally, we compare GCM-t and GCM-N in an empirical setting related to preferences for electric vehicles (EVs). We observe that accounting for decision-uncertainty behavior in GCM-t results in lower elasticity estimates and a higher willingness to pay for improving the EV attributes than those of the GCM-N model. These differences are relevant in making policies to expedite the adoption of EVs.

A Novel Path Planning Method for Articulated Road Roller Using Support Vector Machine and Longest Accessible Path With Course Correction

Aiming at Articulated Road Roller (ARR) path planning near the construction area, a novel path planning method using Support Vector Machine (SVM) and Longest Accessible Path with Course Correction (LAP-CC) is proposed. First, the feasible path selected by Goal-Directed RRT (GDRRT) will be repeated 20 times to determine which category the obstacle belongs to, and then the error penalty factor and kernel parameter of SVM are selected by the grid search and cross-validation parameter optimization algorithm. Then, A set of different virtual obstacles are used on both sides of ARR to control the start and end points of the zero-potential decision boundary. Next, Longest Accessible Path (LAP) is presented to search critical turning points on the decision boundary. Finally, Course Correction (CC) corrects ARR course at these critical turning points. Simulation experiments show that the novel path planning method for ARR using SVM and LAP-CC has the advantages of simplicity, feasibility, low computational cost and good repeatability.

Variable Selection in Kernel Regression Using Measurement Error Selection Likelihoods

ABSTRACTThis article develops a nonparametric shrinkage and selection estimator via the measurement error selection likelihood approach recently proposed by Stefanski, Wu, and White. The measurement error kernel regression operator (MEKRO) has the same form as the Nadaraya–Watson kernel estimator, but optimizes a measurement error model selection likelihood to estimate the kernel bandwidths. Much like LASSO or COSSO solution paths, MEKRO results in solution paths depending on a tuning parameter that controls shrinkage and selection via a bound on the harmonic mean of the pseudo-measurement error standard deviations. We use small-sample-corrected AIC to select the tuning parameter. Large-sample properties of MEKRO are studied and small-sample properties are explored via Monte Carlo experiments and applications to data. Supplementary materials for this article are available online.

JPEG false contour reduction using error diffusion

This study presents an approach to effectively suppress the annoying false contour inherently introduced in a JPEG compressed image. The false contour is mainly caused by the discrepancy between the original DCT coefficient prior quantization in the encoder and the inverse quantization coefficient in the decoder. In this study, the error diffusion with the optimized error kernels is involved to compensate the quantization errors to the pixels in the neighboring blocks. As documented in the experimental results, the proposed method has been proven to significantly reduce the false contour in a JPEG image.

TR ADJOINT IMAGING METHOD FOR MITAT

Most of the current imaging methods in microwave induced thermoacoustic tomography (MITAT) system assume that the heterogeneous sound velocity (SV) and density distribution are given or subject to Gaussian distribution. These situations generally are not satisfled. To improve multi-targets thermoacoustic sources imaging quality in a heterogeneous tissue, an iterative TR adjoint imaging method is proposed. The proposed iterative TR adjoint method can reconstruct thermoacoustic sources from the measured data even if the prior heterogeneous information of the tissue is unknown. This method estimates misflt between synthesized and observed measured signals, and iteratively updates supposed model parameters which give the heterogeneous tissue structure. In this iterative procedure, error kernels of SV, density and the approximate point source position information can be obtained independently. After the time of ∞ight (TOF) convergence criterion is reached, a regular time reversal (TR) method with updated model will give out the flnal imaging result. The proposed TR adjoint imaging method is based on strictly theoretical derivation, and some simulations are presented to validate the method.

Quartic Box-Spline Reconstruction on the BCC Lattice

This paper presents an alternative box-spline filter for the body-centered cubic (BCC) lattice, the seven-direction quartic box-spline M7 that has the same approximation order as the eight-direction quintic box-spline M8 but a lower polynomial degree, smaller support, and is computationally more efficient. When applied to reconstruction with quasi-interpolation prefilters, M7 shows less aliasing, which is verified quantitatively by integral filter metrics and frequency error kernels. To visualize and analyze distributional aliasing characteristics, each spectrum is evaluated on the planes and lines with various orientations.

Quantitative Error Analysis for the Reconstruction of Derivatives

We present a general Fourier-based method which provides an accurate prediction of the approximation error, when the derivative of a signal s(t) is continuously reconstructed from uniform point samples or generalized measurements on s. This formalism applies to a wide class of convolution-based techniques. It provides a key tool, the frequency error kernel, for designing computationally efficient reconstruction schemes which are near optimal in the least-squares sense.

Gradient Estimation Revitalized

We investigate the use of a Fourier-domain derivative error kernel to quantify the error incurred while estimating the gradient of a function from scalar point samples on a regular lattice. We use the error kernel to show that gradient reconstruction quality is significantly enhanced merely by shifting the reconstruction kernel to the centers of the principal lattice directions. Additionally, we exploit the algebraic similarities between the scalar and derivative error kernels to design asymptotically optimal gradient estimation filters that can be factored into an infinite impulse response interpolation prefilter and a finite impulse response directional derivative filter. This leads to a significant performance gain both in terms of accuracy and computational efficiency. The interpolation prefilter provides an accurate scalar approximation and can be re-used to cheaply compute directional derivatives on-the-fly without the need to store gradients. We demonstrate the impact of our filters in the context of volume rendering of scalar data sampled on the Cartesian and Body-Centered Cubic lattices. Our results rival those obtained from other competitive gradient estimation methods while incurring no additional computational or storage overhead.

Non-rigid registration with missing correspondences in preoperative and postresection brain images.

Registration of preoperative and postresection images is often needed to evaluate the effectiveness of treatment. While several non-rigid registration methods exist, most would be unable to accurately align these types of datasets due to the absence of tissue in one image. Here we present a joint registration and segmentation algorithm which handles the missing correspondence problem. An intensity-based prior is used to aid in the segmentation of the resection region from voxels with valid correspondences in the two images. The problem is posed in a maximum a posteriori (MAP) framework and optimized using the expectation-maximization (EM) algorithm. Results on both synthetic and real data show our method improved image alignment compared to a traditional non-rigid registration algorithm as well as a method using a robust error kernel in the registration similarity metric.

Constraining the black hole mass spectrum with gravitational wave observations - I. The error kernel

Many scenarios have been proposed for the origin of the supermassive black holes (SMBHs) that are found in the centres of most galaxies. Many of these formation scenarios predict a high-redshift population of intermediate-mass black holes (IMBHs), with masses in the range 100 to 100000 times that of the Sun. A powerful way to observe these IMBHs is via gravitational waves the black holes emit as they merge. The statistics of the observed black hole population should, in principle, allow us to discriminate between competing astrophysical scenarios for the origin and formation of SMBHs. However, gravitational wave detectors such as LISA will not be able to detect all such mergers nor assign precise black hole parameters to the merger, due to weak gravitational wave signal strengths. In order to use LISA observations to infer the statistics of the underlying population, these errors must be taken into account. We describe here a method for folding the LISA gravitational wave parameter error estimates into an `error kernel' designed for use at the population model level. The effects of this error function are demonstrated by applying it to several recent models of black hole mergers, and some tentative conclusions are made about LISA's ability to test scenarios of the origin and formation of supermassive black holes.

$L^1$-Norm Convergence Properties of Correlogram Spectral Estimates

This paper establishes the following results concerning the estimation of the power spectrum of a single, deterministic, infinitely long signal. a) If S x is the signal's power spectral density, correlogram spectral estimates obtained from increasingly longer signal segments tend to S x * ? x/2p in the L 1-norm, where ? is the Fourier transform of the window used to generate the estimates. b) The L 1-norm of S x - S x * ? x/2p can be made arbitrarily small by an appropriate choice of window. It is further shown that the accuracy of the spectral estimates generated by a given window is related to a newly introduced function, termed the windowing error kernel and that this function yields bounds on the asymptotic error of the estimates. As an example, correlogram spectral estimates are used to analyze spectral regrowth in an amplifier.

A fluence-convolution method to calculate radiation therapy dose distributions that incorporate random set-up error

The International Commission on Radiation Units and Measurements Report 62 (ICRU 1999) introduced the concept of expanding the clinical target volume (CTV) to form the planning target volume by a two-step process. The first step is adding a clinically definable internal margin, which produces an internal target volume that accounts for the size, shape and position of the CTV in relation to anatomical reference points. The second is the use of a set-up margin (SM) that incorporates the uncertainties of patient beam positioning, i.e. systematic and random set-up errors. We propose to replace the random set-up error component of the SM by explicitly incorporating the random set-up error into the dose-calculation model by convolving the incident photon beam fluence with a Gaussian set-up error kernel. This fluence-convolution method was implemented into a Monte Carlo (MC) based treatment-planning system. Also implemented for comparison purposes was a dose-matrix-convolution algorithm similar to that described by Leong (1987 Phys. Med. Biol. 32 327–34). Fluence and dose-matrix-convolution agree in homogeneous media. However, for the heterogeneous phantom calculations, discrepancies of up to 5% in the dose profiles were observed with a 0.4 cm set-up error value. Fluence-convolution mimics reality more closely, as dose perturbations at interfaces are correctly predicted (Wang et al 1999 Med. Phys. 26 2626–34, Sauer 1995 Med. Phys. 22 1685–90). Fluence-convolution effectively decouples the treatment beams from the patient, and more closely resembles the reality of particle fluence distributions for many individual beam-patient set-ups. However, dose-matrix-convolution reduces the random statistical noise in MC calculations. Fluence-convolution can easily be applied to convolution/superposition based dose-calculation algorithms.

Relational object recognition from large structural libraries

This paper presents a probabilistic similarity measure for object recognition from large libraries of line-patterns. We commence from a structural pattern representation which uses a nearest neighbour graph to establish the adjacency of line-segments. Associated with each pair of line-segments connected in this way is a vector of Euclidean invariant relative angle and distance ratio attributes. The relational similarity measure uses robust error kernels to compare sets of pairwise attributes on the edges of a nearest neighbour graph. We use the relational similarity measure in a series of recognition experiments which involve a library of over 2500 line-patterns. A sensitivity study reveals that the method is capable of delivering a recognition accuracy of 94%. A comparative study reveals that the method is most effective when either a Gaussian kernel or Huber's robust kernel is used to weight the attribute relations. Moreover, the method consistently outperforms the standard and the quantile Hausdorff distance.

Improved convergence rates for the truncation error in gravimetric geoid determination

When Stokes's integral is used over a spherical cap to compute a gravimetric estimate of the geoid, a truncation error results due to the neglect of gravity data over the remainder of the Earth. Associated with the truncation error is an error kernel defined over these two complementary regions. An important observation is that the rate of decay of the coefficients of the series expansion for the truncation error in terms of Legendre polynomials is determined by the smoothness properties of the error kernel. Previously published deterministic modifications of Stokes's integration kernel involve either a discontinuity in the error kernel or its first derivative at the spherical cap radius. These kernels are generalised and extended by constructing error kernels whose derivatives at the spherical cap radius are continuous up to an arbitrary order. This construction is achieved by smoothly continuing the error kernel function into the spherical cap using a suitable degree polynomial. Accordingly, an improved rate of convergence of the spectral series representation of the truncation error is obtained.

Correction functions and statistical noises in transverse section picture reconstruction

An analysis of image reconstruction with one- and two-dimensional convolution methods is presented in an outline of the relationship among the correction functions, the point spread function and the statistical noise. The correction functions are derived which maximize the ratio of one-dimensional signal power to noise power for a given r.m.s. resolution width in a uniform image. The texture of the image noise is expressed by the autocovariance function. For emission images, the variance of noise is expressed by the convolution of the source distribution with the “error kernel” which is determined from the one-dimensional correction function.