Semiparametric Bayesian inference for mean-covariance regression models

In this paper, we propose a Bayesian semiparametric mean-covariance regression model with known covariance structures. A mixture model is used to describe the potential non-normal distribution of the regression errors. Moreover, an empirical likelihood adjusted mixture of Dirichlet process model is constructed to produce distributions with given mean and variance constraints. We illustrate through simulation studies that the proposed method provides better estimations in some non-normal cases. We also demonstrate the implementation of our method by analyzing the data set from a sleep deprivation study.     

Sensitivity enhancing injection from a sample reservoir and channel interface in microchip electrophoresis

The stacking of a cationic analyte (i.e., rhodamine B) at the interface between a sample reservoir and channel in a microchip electrophoresis device is described for the first time. Stacking at negative polarity was by micelle to solvent stacking where the dye was prepared in a micellar solution (5 mM sodium dodecyl sulfate in 25 mM phosphoric acid, pH 2.5) and the channel was filled with high methanol content background solution (70% methanol in 50 mM phosphoric acid, pH 2.5). The injection of the stacked dye into the channel was by simple reversal of the voltage polarity with the sample solution and background solution at the anodic and cathodic reservoirs of the straight channel, respectively. The enrichment of rhodamine B at the interface and injection of the stacked dye into the channel was clearly visualized using an inverted fluorescence microscope. A notable sensitivity enhancement factor of up to 150 was achieved after 2 min at 1 kV of micelle to solvent stacking. The proposed technique will be useful as a concentration step for analyte mixtures in simple and classical cross‐channel microchip electrophoresis devices or for the controlled delivery of enriched reagents or analytes as narrow plugs in advanced microchip electrophoresis devices.     

Identification and analysis of chemical constituents and rat serum metabolites in Suan‐Zao‐Ren granule using ultra high performance liquid chromatography quadrupole time‐of‐flight mass spectrometry combined with multiple data processing approaches

Suan‐Zao‐Ren granule is widely used to treat insomnia in China. However, because of the complexity and diversity of the chemical compositions in traditional Chinese medicine formula, the comprehensive analysis of constituents in vitro and in vivo is rather difficult. In our study, an ultra high performance liquid chromatography with quadrupole time‐of‐flight mass spectrometry and the PeakView® software, which uses multiple data processing approaches including product ion filter, neutral loss filter, and mass defect filter, method was developed to characterize the ingredients and rat serum metabolites in Suan‐Zao‐Ren granule. A total of 101 constituents were detected in vitro. Under the same analysis conditions, 68 constituents were characterized in rat serum, including 35 prototype components and 33 metabolites. The metabolic pathways of main components were also illustrated. Among them, the metabolic pathways of timosaponin AI were firstly revealed. The bioactive compounds mainly underwent the phase I metabolic pathways including hydroxylation, oxidation, hydrolysis, and phase II metabolic pathways including sulfate conjugation, glucuronide conjugation, cysteine conjugation, acetycysteine conjugation, and glutathione conjugation. In conclusion, our results showed that this analysis approach was extremely useful for the in‐depth pharmacological research of Suan‐Zao‐Ren granule and provided a chemical basis for its rational.     

Advanced online mass spectrometry detection of proteins separated by capillary isoelectric focusing after sequential injection

Capillary isoelectric focusing hyphenated with mass spectrometry detection, following the sequential injection of the carrier ampholytes and the sample zone, is highly efficient for the characterization of proteins. The main advantage of the sequential injection protocol is that ampholytes, with pH ranges, which are not supposed to cover the isoelectric points of the sample components, can be used for separation. The method then allows online mass spectrometry detection of separated analytes either in the absence (substances that have left the pH gradient) or in the presence of low‐level ampholytes (substances that are migrating within the pH gradient). The appearance of the substances within, or outside the pH gradient depends on, e.g., the composition of the ampholytes (broad or narrow pH range) or on the composition of electrolyte solutions. The experiments performed in coated capillaries (with polyvinyl alcohol or with polyacrylamide) show that the amount and the injection length of the ampholytes influence the length of the pH gradient formed in the capillary.     

Phase II monitoring of changes in mean from high‐dimensional data

The generalized T² chart (GT‐chart), which is composed of the T² statistic based on a small number of principal components and the remaining components, is a popular alternative to the traditional Hotelling's T² control chart. However, the application of the GT‐chart to high‐dimensional data, which are now ubiquitous, encounters difficulties from high dimensionality similar to other multivariate procedures. The sample principal components and their eigenvalues do not consistently estimate the population values, and the GT‐chart relying on them is also inconsistent in estimating the control limits. In this paper, we investigate the effects of high dimensionality on the GT‐chart and then propose a corrected GT‐chart using the recent results of random matrix theory for the spiked covariance model. We numerically show that the corrected GT‐chart exhibits superior performance compared to the existing methods, including the GT‐chart and Hotelling's T² control chart, under various high‐dimensional cases. Finally, we apply the proposed corrected GT‐chart to monitor chemical processes introduced in the literature.     

Two optimization problems in linear regression with interval data

We consider a linear regression model where neither regressors nor the dependent variable is observable; only intervals are available which are assumed to cover the unobservable data points. Our task is to compute tight bounds for the residual errors of minimum-norm estimators of regression parameters with various norms (corresponding to least absolute deviations (LAD), ordinary least squares (OLS), generalized least squares (GLS) and Chebyshev approximation). The computation of the error bounds can be formulated as a pair of max–min and min–min box-constrained optimization problems. We give a detailed complexity-theoretic analysis of them. First, we prove that they are NP-hard in general. Then, further analysis explains the sources of NP-hardness. We investigate three restrictions when the problem is solvable in polynomial time: the case when the parameter space is known apriori to be restricted into a particular orthant, the case when the regression model has a fixed number of regression parameters, and the case when only the dependent variable is observed with errors. We propose a method, called orthant decomposition of the parameter space, which is the main tool for obtaining polynomial-time computability results.     

Uniqueness in potential scattering with reduced data

We consider inverse potential scattering problems where the source of the incident waves is located on a smooth closed surface outside of the inhomogeneity of the media. The scattered waves are measured on the same surface at a fixed value of the energy. We show that these data determine the bounded potential uniquely.     

The nonrelativistic limit of relativistic Vlasov–Maxwell system

We consider the one and one‐half dimensional multi‐species relativistic Vlasov–Maxwell system with non‐decaying (in space) initial data. We prove its well‐posedness and nonrelativistic limit as the speed of light . These results mainly rely on a delicate analysis of energy structure and application of estimates along the characteristic lines. Copyright © 2016 John Wiley & Sons, Ltd.     

Nonlinear anisotropic elliptic equations in with variable exponents and locally integrable data

In this paper, we prove existence and regularity results for weak solutions in the framework of anisotropic Sobolev spaces for a class of nonlinear anisotropic elliptic equations in the whole with variable exponents and locally integrable data. Our approach is based on the anisotropic Sobolev inequality, a smoothness, and compactness results. The functional setting involves Lebesgue–Sobolev spaces with variable exponents. Copyright © 2016 John Wiley & Sons, Ltd.