Automated Regularized Deconvolution for Eliminating Extra-Column Effects in Fast High-Efficiency Separations.

With the introduction of ultrahigh efficiency columns and fast separations, the need to eliminate peak deformation contributed by the instrument must be effectively solved. Herein, we develop a robust framework to automate deconvolution and minimize its artifacts, such as negative dips, wild noise oscillations, and ringing, by combining regularized deconvolution and Perona-Malik (PM) anisotropic diffusion methods. A asymmetric generalized normal (AGN) function is proposed to model the instrumental response for the first time. With no-column data at various flow rates, the interior point optimization algorithm extracts the parameters describing instrumental distortion. The column-only chromatogram was reconstructed using the Tikhonov regularization technique with minimal instrumental distortion. For illustration, four different chromatography systems are used in fast chiral and achiral separations with 2.1 and 4.6 mm i.d. columns. Ordinary HPLC data can approach highly optimized UHPLC data. Similarly, in fast HPLC-circular dichroism (CD) detection, 8000 plates were gained for a fast chiral separation. Moment analysis of deconvolved peaks confirms correction of the center of mass, variance, skew, and kurtosis. This approach can be easily integrated and used with virtually any separation and detection system to provide enhanced analytical data.

Detecting outliers when fitting data with nonlinear regression - a new method based on robust nonlinear regression and the false discovery rate.

BACKGROUND: Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. RESULTS: We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in only about 1-3% of experiments. When analyzing data contaminated with one or several outliers, the ROUT method performs well at outlier identification, with an average False Discovery Rate less than 1%. CONCLUSION: Our method, which combines a new method of robust nonlinear regression with a new method of outlier identification, identifies outliers from nonlinear curve fits with reasonable power and few false positives.