Bayesian Multiscale Smoothing for Making Inferences About Features in Scatterplots

A rather common problem of data analysis is to find interesting features, such as local minima, maxima, and trends in a scatterplot. Variance in the data can then be a problem and inferences about features must be made at some selected level of significance. The recently introduced SiZer technique uses a family of nonparametric smooths of the data to uncover features in a whole range of scales. To aid the analysis, a color map is generated that visualizes the inferences made about the significance of the features. The purpose of this article is to present Bayesian versions of SiZer methodology. Both an analytically solvable regression model and a fully Bayesian approach that uses Gibbs sampling are presented. The prior distributions of the smooths are based on a roughness penalty. Simulation based algorithms are proposed for making simultaneous inferences about the features in the data.     

Mixed mode fracture of a piezoelectric–piezomagnetic bi-layer structure with two un-coaxial cracks parallel to the interface and each in a layer

The purpose of the present work is to study the mixed mode fracture of a piezoelectric–piezomagnetic composite with two un-coaxial cracks parallel to the interface and each in a layer. Methods of generalized dislocation simulation, Green’s function, Cauchy singular integral equation and Lobatto–Chebyshev collocation are combined together to get the numerical results of mechanical strain energy release rate (MSERR). Three kinds of effects are revealed by parametric studies, i.e., the free-surface effect, the shielding effect and the interference effect, and they are used to interpret the characteristics of COD and MSERR curves. In addition, the effects of shear loading, magnetic loading and electric loading on MSERR are also disclosed, respectively, by varying the corresponding loading factor.     

Synthesis, Structure and H+/K+-ATPase Inhibitory Activity of Novel Triazolyl Substituted Tetrahydrobenzofuran Derivatives via One-pot Three-component Click Reaction

Eleven triazolyl substituted tetrahydrobenzofuran derivatives were synthesized in high yields as novel H⁺/K⁺‐ATPase inhibitor via one‐pot CuI‐catalyzed three‐component click reaction of azide, secondary amine and 3‐bromopropyne under mild conditions in water. Their structures were characterized by NMR, IR, ESI‐MS, elemental analysis and single‐crystal X‐ray diffraction analysis. Most of the target compounds exhibited better H⁺/K⁺‐ATPase inhibitory activity than commercial omeprazole with IC₅₀ values less than 15 µmol·L^?1. The initial structure‐activity analysis suggested that the triazole substituted by cycloalkyl, aromatic ring or O‐containing side‐chain seemed to be beneficial for enhancing the activity.     

Estimating Precision in Functional Images

Abstract

Functional imaging of biologic parameters like in vivo tissue metabolism is made possible by Positron Emission Tomography (PET). Many techniques have been suggested for extracting such images from dynamic time-course sequences of reconstructed PET scans. Quantitating the precision of these estimates is important for drawing inferences on the biologic parameters. Analytic variance formulas are not immediate owing to the nonlinear methods used in extraction. The usual resampling approach is infeasible because each image reconstruction in PET is a computationally demanding solution to a high-dimensional linear inverse problem. We suggest an alternative simulation approach that approximates the distribution of reconstructed PET scans and performs a parametric bootstrap in the imaging domain. Results on a simplified model chosen to match the characteristics of PET reconstruction are very encouraging. Mixture analysis is used to estimate functional images; however, the suggested approach is general enough to extend to other techniques or imaging methods.     

Importance Sampling for p-value Computations in Multivariate Tests

Abstract

An importance sampling procedure is developed to approximate the distribution of an arbitrary function of the eigenvalues for a matrix beta random matrix or a Wishart random matrix. The procedure is easily implemented and provides confidence intervals for the p-values of many of the commonly used test statistics in multivariate analysis. An adaptive procedure allows for the control of either absolute error or relative error in this p-value estimation through the choice of importance sample size.     

Nonasymptotic analysis of robust regression with modified Huber's loss

To achieve robustness against the outliers or heavy-tailed sampling distribution, we consider an Ivanov regularized empirical risk minimization scheme associated with a modified Huber's loss for nonparametric regression in reproducing kernel Hilbert space. By tuning the scaling and regularization parameters in accordance with the sample size, we develop nonasymptotic concentration results for such an adaptive estimator. Specifically, we establish the best convergence rates for prediction error when the conditional distribution satisfies a weak moment condition.     

Voltammetric Determination of Allura Red AC onto Carbone-paste Electrode Modified by Silica with Embedded Cetylpyridinium Chloride

In current study the carbon-paste electrode modified by silica with embedded cetylpyridinium chloride for determination of Allura Red AC have been developed. The optimal conditions were determined to be for the square-wave voltammetric quantification: pH=2, E_ads=300 mV, t_ads=300 s, amplitude – 40 mV, frequency – 25 Hz and potential scan rate is 250 mV sec⁻¹. The calibration plot has linearity in the concentration ranges 0.04–0.2 μM and 0.2–1.00 μM. The LOD and LOQ are equal to 0.005 μM and 0.015 μM respectively. The crafted sensor has been applied successfully to model solutions and in jelly candies analysis with RSD no more than 10 %.     

Detection of ochratoxin A contamination in stored wheat using near-infrared hyperspectral imaging

Near-infrared (NIR) hyperspectral imaging system was used to detect five concentration levels of ochratoxin A (OTA) in contaminated wheat kernels. The wheat kernels artificially inoculated with two different OTA producing Penicillium verrucosum strains, two different non-toxigenic P. verrucosum strains, and sterile control wheat kernels were subjected to NIR hyperspectral imaging. The acquired three-dimensional data were reshaped into readable two-dimensional data. Principal Component Analysis (PCA) was applied to the two dimensional data to identify the key wavelengths which had greater significance in detecting OTA contamination in wheat. Statistical and histogram features extracted at the key wavelengths were used in the linear, quadratic and Mahalanobis statistical discriminant models to differentiate between sterile control, five concentration levels of OTA contamination in wheat kernels, and five infection levels of non-OTA producing P. verrucosum inoculated wheat kernels. The classification models differentiated sterile control samples from OTA contaminated wheat kernels and non-OTA producing P. verrucosum inoculated wheat kernels with a 100% accuracy. The classification models also differentiated between five concentration levels of OTA contaminated wheat kernels and between five infection levels of non-OTA producing P. verrucosum inoculated wheat kernels with a correct classification of more than 98%. The non-OTA producing P. verrucosum inoculated wheat kernels and OTA contaminated wheat kernels subjected to hyperspectral imaging provided different spectral patterns.     

The numerical radius and specttural matrices

In this paper we investigate spectral matrices, i.e., matrices with equal spectral and numerical radii. Various characterizations and properties of these matrices are given.