Computational design and multivariate optimization of an electrochemical metoprolol sensor based on molecular imprinting in combination with carbon nanotubes

This work describes the development of an electrochemical sensor based on a new molecularly imprinted polymer for detection of metoprolol (MTP) at ultra-trace level. The polypyrrole (PPy) was electrochemically synthesized on the tip of a pencil graphite electrode (PGE) which modified whit functionalized multi-walled carbon nanotubes (MWCNTs). The fabrication process of the sensor was characterized by cyclic voltammetry (CV) and the measurement process was carried out by differential pulse voltammetry (DPV). A computational approach was used to screening functional monomers and polymerization solvent for rational design of molecularly imprinted polymer (MIP). Based on computational results, pyrrole and water were selected as functional monomer and polymerization solvent, respectively. Several significant parameters controlling the performance of the MIP sensor were examined and optimized using multivariate optimization methods such as Plackett–Burman design (PBD) and central composite design (CCD). Under the selected optimal conditions, MIP sensor was showed a linear range from 0.06 to 490 μmol L⁻¹ MTP, a limit of detection of 2.88 nmol L⁻¹, a highly reproducible response (RSD 3.9%) and a good selectivity in the presence of structurally related molecules. Furthermore, the applicability of the method was successfully tested with determination of MTP in real samples (tablet, and serum).     

Rapid multivariate analysis of 3D ToF‐SIMS data: graphical processor units (GPUs) and low‐discrepancy subsampling for large‐scale principal component analysis

Principal component analysis (PCA) and other multivariate analysis methods have been used increasingly to analyse and understand depth‐profiles in XPS, AES and SIMS. For large images or three‐dimensional (3D) imaging depth‐profiles, PCA has been difficult to apply until now simply because of the size of the matrices of data involved. In a recent paper, we described two algorithms, random vector 1 (RV1) and random vector 2 (RV2), that improve the speed of PCA and allow datasets of unlimited size, respectively. In this paper, we now apply the RV2 algorithm to perform PCA on full 3D time‐of‐flight SIMS data for the first time without subsampling. The dataset we process in this way is a 128 × 128 pixel depth‐profile of 120 layers, each voxel having a 70 439 value mass spectrum associated with it. This forms over a terabyte of data when uncompressed and took 27 h to process using the RV2 algorithm using a conventional windows desktop personal computer (PC). While full PCA (e.g. using RV2) is to be preferred for final reports or publications, a much more rapid method is needed during analysis sessions to inform decisions on the next analytical step. We have therefore implemented the RV1 algorithm on a PC having a graphical processor unit (GPU) card containing 2880 individual processor cores. This increases the speed of calculation by a factor of around 4.1 compared with what is possible using a fast commercially available desktop PC having central processing units alone, and full PCA is performed in less than 7 s. The size of the dataset that can be processed in this way is limited by the size of the memory on the GPU card. This is typically sufficient for two‐dimensional images but not 3D depth‐profiles without sampling. We have therefore examined efficient sampling schemes that allow a good approximate solution to the PCA problem for large 3D datasets. We find that low‐discrepancy series such as Sobol series sampling gives more rapid convergence than random sampling, and we recommend such methods for routine use. Using the GPU and low‐discrepancy series together, we anticipate that any time‐of‐flight SIMS dataset, of whatever size, can be efficiently and accurately processed into PCA components in a maximum of around 10 s using a commercial PC with a widely available GPU card, although the longer RV2 approach is still to be preferred for the presentation of final results, such as in published papers. Copyright © 2016 The Authors Surface and Interface Analysis Published by John Wiley & Sons Ltd     

基于盲数理论和随机模拟的河流水环境容量计算

针对水环境系统的不确定性,将延拓盲数引入到水环境容量计算模型中,并运用随机模拟方法对盲参数进行模拟,把盲数之间的运算转化为普通实数之间的运算,从而建立了水环境容量的延拓盲数与随机模拟的耦合模型.经实例研究,得到研究对象的水环境容量随机模拟分布以及在不同保证率下的水环境容量值,为研究对象当地的水环境规划和保护提供丰富可靠的依据.     

Fluctuations in the homogenization of semilinear equations with random potentials

We study the stochastic homogenization and obtain a random fluctuation theory for semilinear elliptic equations with a rapidly varying random potential. To first order, the effective potential is the average potential and the nonlinearity is not affected by the randomness. We then study the limiting distribution of the properly scaled homogenization error (random fluctuations) in the space of square integrable functions, and prove that the limit is a Gaussian distribution characterized by homogenized solution, the Green’s function of the linearized equation around the homogenized solution, and by the integral of the correlation function of the random potential. These results enlarge the scope of the framework that we have developed for linear equations to the class of semilinear equations.     

A higher-order large-scale regularity theory for random elliptic operators

We develop a large-scale regularity theory of higher order for divergence-form elliptic equations with heterogeneous coefficient fields a in the context of stochastic homogenization. The large-scale regularity of a-harmonic functions is encoded by Liouville principles: The space of a-harmonic functions that grow at most like a polynomial of degree k has the same dimension as in the constant-coefficient case. This result can be seen as the qualitative side of a large-scale C^k,α-regularity theory, which in the present work is developed in the form of a corresponding C^k,α-“excess decay” estimate: For a given a-harmonic function u on a ball B_R, its energy distance on some ball B_r to the above space of a-harmonic functions that grow at most like a polynomial of degree k has the natural decay in the radius r above some minimal radius r₀.

Though motivated by stochastic homogenization, the contribution of this paper is of purely deterministic nature: We work under the assumption that for the given realization a of the coefficient field, the couple (φ, σ) of scalar and vector potentials of the harmonic coordinates, where φ is the usual corrector, grows sublinearly in a mildly quantified way. We then construct “kth-order correctors” and thereby the space of a-harmonic functions that grow at most like a polynomial of degree k, establish the above excess decay, and then the corresponding Liouville principle.     

Barzilai–Borwein method with variable sample size for stochastic linear complementarity problems

A smoothing method for solving stochastic linear complementarity problems is proposed. The expected residual minimization reformulation of the problem is considered, and it is approximated by the sample average approximation (SAA). The proposed method is based on sequential solving of a sequence of smoothing problems where each of the smoothing problems is defined with its own sample average approximation. A nonmonotone line search with a variant of the Barzilai–Borwein (BB) gradient direction is used for solving each of the smoothing problems. The BB search direction is efficient and low cost, particularly suitable for nonmonotone line search procedure. The variable sample size scheme allows the sample size to vary across the iterations and the method tends to use smaller sample size far away from the solution. The key point of this strategy is a good balance between the variable sample size strategy, the smoothing sequence and nonmonotonicity. Eventually, the maximal sample size is used and the SAA problem is solved. Presented numerical results indicate that the proposed strategy reduces the overall computational cost.     

一类带乘性噪声随机分数阶微分方程Euler方法的弱收敛性与弱稳定性

本文主要在带加性噪声随机分数阶微分方程的基础上,研究了一类更为困难的带乘性噪声随机分数阶微分方程Euler方法的弱收敛性与弱稳定性,并得到了类似的结论.首先构造了数值求解带乘性噪声随机分数阶微分方程的Euler方法,然后证明当分数阶α满足0α1/2时,该方法是1/2-α阶弱收敛的和弱稳定的,文末数值试验的结果验证了理论结果的正确性.     

HPLC–TOF‐MS and HPLC–MS/MS combined with multivariate analysis for the characterization and discrimination of phenolic profiles in nonfumigated and sulfur‐fumigated rhubarb

Sulfur fumigation has recently been used during the postharvest handling of rhubarb to reduce the drying duration and control pests. However, a few reports question the effect of sulfur fumigation on the bioactive components of rhubarb, which is crucial for the quality evaluation of the herbal medicine. The bottleneck limiting the study comes from the complex compounds that exist in herb samples with diverse structural features, wide concentration range and the difficulty to obtain all the reference standards. In this study, an integrated strategy based on the highly effective separation and analysis by liquid chromatography coupled with diode‐array detection and time‐of‐flight/triple‐quadruple tandem mass spectrometry combined with multivariate analysis was established. 68 phenolic compounds that exist in nonfumigated and sulfur‐fumigated herb samples of rhubarb were tentatively assigned based on their retention behavior, UV spectra, accurate molecular weight, and mass spectral fragments. Qualitative and semiquantitative comparison revealed a serious reduction of the majority of phenolic compounds in sulfur‐fumigated rhubarb. Furthermore, multivariate analysis was applied to holistically discriminate nonfumigated from sulfur‐fumigated rhubarb and explore the characteristic chemical markers. The established approach was specific and rapid for characterizing and screening sulfur‐fumigated rhubarb among commercial samples and could be applied for the quality assessment of other sulfur‐fumigated herbs.     

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??In this paper, we prove the existence and uniqueness of solutions for reflected backward stochastic differential equations driven by a Levy process, in which the reflecting barriers are just right continuous with left limits whose jumps are arbitrary. To derive the above results, the monotonic limit theorem of Backward SDE associated with Levy process is established.