Evaluation of automated sample preparation, retention time locked gas chromatography-mass spectrometry and data analysis methods for the metabolomic study of Arabidopsis species

In this paper, automated sample preparation, retention time locked gas chromatography-mass spectrometry (GC-MS) and data analysis methods for the metabolomics study were evaluated. A miniaturized and automated derivatisation method using sequential oximation and silylation was applied to a polar extract of 4 types (2 types×2 ages) of Arabidopsis thaliana, a popular model organism often used in plant sciences and genetics. Automation of the derivatisation process offers excellent repeatability, and the time between sample preparation and analysis was short and constant, reducing artifact formation. Retention time locked (RTL) gas chromatography-mass spectrometry was used, resulting in reproducible retention times and GC-MS profiles. Two approaches were used for data analysis. XCMS followed by principal component analysis (approach 1) and AMDIS deconvolution combined with a commercially available program (Mass Profiler Professional) followed by principal component analysis (approach 2) were compared. Several features that were up- or down-regulated in the different types were detected.     

Analysis of Iranian rosemary essential oil: application of gas chromatography-mass spectrometry combined with chemometrics

This paper focuses on characterization of the components of Iranian rosemary essential oil using gas chromatography-mass spectrometry (GC-MS). Multivariate curve resolution (MCR) approach was used to overcome the problem of background, baseline offset and overlapping/embedded peaks in GC-MS. The analysis of GC-MS data revealed that sixty eight components exist in the rosemary essential oil. However, with the help of MCR this number was extended to ninety nine components with concentrations higher than 0.01%, which accounts for 98.23% of the total relative content of the rosemary essential oil. The most important constituents of the Iranian rosemary are 1,8-cineole (23.47%), α-pinene (21.74%), berbonone (7.57%), camphor (7.21%) and eucalyptol (4.49%).     

Discrete-time orthogonal spline collocation methods for the nonlinear Schrödinger equation with wave operator

In this paper, discrete-time orthogonal spline collocation schemes are proposed for the nonlinear Schrödinger equation with wave operator. These schemes are constructed by using orthogonal spline collocation approaches combined with finite difference methods. The conservative property, the convergence, and the stability of these methods are theoretically analyzed and also verified by extensive numerical experiments. In addition, some interesting phenomena which require further theoretical analysis are discussed numerically.     

Centrality as a gradual notion: A new bridge between fuzzy sets and statistics

This paper aims at formalizing the intuitive idea that some points are more central in a probability distribution than others. Our proposal relies on fuzzy events to define a fuzzy set of central points for a distribution (or a family of distributions, including imprecise probability models). This framework has a natural interpretation in terms of fuzzy logic and unifies many known notions from statistics, including the mean, median and mode, interquantile intervals, the Lorenz curve, the halfspace median, the zonoid and lift zonoid, the coverage function and several expectations and medians of random sets, and the Choquet integral against an infinitely alternating or infinitely monotone capacity.     

用样条逼近Sobolev函数类W_p~1(R)的逼近误差

作者研究了定义在全实轴上的Sobolev函数类W_p~1(R)的逼近问题.以一次样条函数作为逼近工具,给出了p=1和p=∞时的逼近误差.     

Design of experiments on 135 cloned poplar trees to map environmental influence in greenhouse

To find and ascertain phenotypic differences, minimal variation between biological replicates is always desired. Variation between the replicates can originate from genetic transformation but also from environmental effects in the greenhouse. Design of experiments (DoE) has been used in field trials for many years and proven its value but is underused within functional genomics including greenhouse experiments. We propose a strategy to estimate the effect of environmental factors with the ultimate goal of minimizing variation between biological replicates, based on DoE. DoE can be analyzed in many ways. We present a graphical solution together with solutions based on classical statistics as well as the newly developed OPLS methodology.In this study, we used DoE to evaluate the influence of plant specific factors (plant size, shoot type, plant quality, and amount of fertilizer) and rotation of plant positions on height and section area of 135 cloned wild type poplar trees grown in the greenhouse. Statistical analysis revealed that plant position was the main contributor to variability among biological replicates and applying a plant rotation scheme could reduce this variation.     

Factors that affect quantification of diode array data in comprehensive two-dimensional liquid chromatography using chemometric data analysis

There has been a tremendous increase in research on comprehensive two dimensional LC (LC×LC); however, to date, the central analytical issue, quantification, has received only minimal attention. It is vital to the further development of LC×LC that a greater understanding of the specific factors affecting peak quantification in LC×LC be attained. This work focuses on the following factors: data complexity, retention time shifting, dynamic range issues, chromatographic and spectral peak overlap and difficulties related to background signal removal. The above mentioned factors that affect peak quantification are investigated using fourteen replicate analyses of a urine sample, representing the effects of such factors when analyzing samples in complex matrices. We demonstrate that quantification of LC×LC data is improved following implementation of chemometric techniques that minimized the deleterious effects on quantification due to chromatographically overlapped peaks, retention time shifting and background signal interference. The chemometrically resolved data shows a 2.5-fold increase in precision of quantification over the quantification of the raw data. It is also demonstrated that the method quantifies sixteen peaks that were not visually evident prior to chemometric analysis. The purpose of this paper is to determine the impact of these issues on the effectiveness of LC×LC as a technique for the quantitative analysis of complex samples.     

Two-component Brownian coagulation: Monte Carlo simulation and process characterization

The compositional distribution within aggregates of a given size is essential to the functionality of composite aggregates that are usually enlarged by rapid Brownian coagulation. There is no analytical solution for the process of such two-component systems. Monte Carlo method is an effective numerical approach for two-component coagulation. In this paper, the differentially weighted Monte Carlo method is used to investigate two-component Brownian coagulation, respectively, in the continuum regime, the free-molecular regime and the transition regime. It is found that (1) for Brownian coagulation in the continuum regime and in the free-molecular regime, the mono-variate compositional distribution, i.e., the number density distribution function of one component amount (in the form of volume of the component in aggregates) satisfies self-preserving form the same as particle size distribution in mono-component Brownian coagulation; (2) however, for Brownian coagulation in the transition regime the mono-variate compositional distribution cannot reach self-similarity; and (3) the bivariate compositional distribution, i.e., the combined number density distribution function of two component amounts in the three regimes satisfies a semi self-preserving form. Moreover, other new features inherent to aggregative mixing are also demonstrated; e.g., the degree of mixing between components, which is largely controlled by the initial compositional mass fraction, improves as aggregate size increases.     

Numerical solution of the Rosenau–KdV–RLW equation by operator splitting techniques based on B‐spline collocation method

In the present study, the operator splitting techniques based on the quintic B‐spline collocation finite element method are presented for calculating the numerical solutions of the Rosenau–KdV–RLW equation. Two test problems having exact solutions have been considered. To demonstrate the efficiency and accuracy of the present methods, the error norms L₂ and L_∞ with the discrete mass Q and energy E conservative properties have been calculated. The results obtained by the method have been compared with the exact solution of each problem and other numerical results in the literature, and also found to be in good agreement with each other. A Fourier stability analysis of each presented method is also investigated.     

Operator splitting for numerical solution of the modified Burgers' equation using finite element method

The aim of this study is to obtain numerical behavior of a one‐dimensional modified Burgers' equation using cubic B‐spline collocation finite element method after splitting the equation with Strang splitting technique. Moreover, the Ext4 and Ext6 methods based on Strang splitting and derived from extrapolation have also been applied to the equation. To observe how good and effective this technique is, we have used the well‐known the error norms L₂ and L_∞ in the literature and compared them with previous studies. In addition, the von Neumann (Fourier series) method has been applied after the nonlinear term has been linearized to investigate the stability of the method.