An algorithm for three-way data analysis that alternatively minimizes coupled vector (COV) resolution error and PARAFAC error.

A novel algorithm, alternatively minimizing coupled vector (COV) resolution error and PARAFAC error algorithm, is proposed in this paper. This algorithm can overcome the problem of slow convergence and is insensitive to the estimation of component number, such problems are unavoidable while using the traditional parallel factors analysis (PARAFAC) algorithm. In other words, this algorithm is capable of improving the computing speed and providing accurate resolutions provided that the number of factors used in the computation is no less than that of the actual underlying ones. The characteristic performances were demonstrated with a novel fluorescence data array.     

Vertex vector sequential projection for the resolution of three-way data

Usually, the PARAFAC2 method is utilized for handling retention time shifts in resolving chromatographic three-way data. It requires all profiles shift the same amount, which, unfortunately, seems unlikely the case in the practice of chromatographic analysis of multi-component samples. The present authors deal with the problem by unfolding the three-way data array along a certain direction into one matrix and setting up a multi-bilinear model. Then, a new method called vertex vector sequential projection (VVSP) is proposed to select pure variables and then the alternating least squares (ALS) procedure is used to iteratively improve the fit of the data to the multi-bilinear model. With a good estimate that is as close as possible to the pure variables, a fast convergence can be expected. Moreover, no prerequisite on the shifting is required and the multi-bilinear model provides a plausible manner to make use of the multi-sample information. An additional advantage is that the present fitting procedure is easier to adjust when constraints such as non-negativity, unimodality, etc., are to be imposed on the loading matrix. The proposed method is evaluated with simulated and real chemical data sets. Satisfactory resolution results are obtained, which demonstrates the performance of the proposed method.     

A fully robust PARAFAC method for analyzing fluorescence data

Parallel factor analysis (PARAFAC) is a widespread method for modeling fluorescence data by means of an alternating least squares procedure. Consequently, the PARAFAC estimates are highly influenced by outlying excitation–emission landscapes (EEM) and element‐wise outliers, like for example Raman and Rayleigh scatter. Recently, a robust PARAFAC method that circumvents the harmful effects of outlying samples has been developed. For removing the scatter effects on the final PARAFAC model, different techniques exist. Newly, an automated scatter identification tool has been constructed. However, there still exists no robust method for handling fluorescence data encountering both outlying EEM landscapes and scatter. In this paper, we present an iterative algorithm where the robust PARAFAC method and the scatter identification tool are alternately performed. A fully automated robust PARAFAC method is obtained in that way. The method is assessed by means of simulations and a laboratory‐made data set. Copyright © 2009 John Wiley & Sons, Ltd.     

A novel strategy for solving matrix effect in three-way data using parallel profiles with linear dependencies

This work presents a novel strategy for solving matrix effects using the second-order advantage and a new method called PARAllel profiles with LINear Dependencies (PARALIND). PARALIND is a generalization of parallel factor analysis (PARAFAC) and was developed to extend its use to problems with linearly dependent factors where normal PARAFAC analysis will fail to provide meaningful results. Such linearly dependent factors occur in standard addition with second-order data such as fluorescence excitation emission matrices (EEM). By successive standard addition of an analyte, the concentrations of the remaining components (interferences) remain constant and introduce linear dependency between interference concentrations in the samples. This theoretically leads to rank deficiency in the score matrix holding the relative concentrations when using PARAFAC for modeling. In practice, PARAFAC models of such data will mostly provide solutions where the score matrix is not rank deficient but a function of the noise in the data. This problem is shown to be solved by using PARALIND. In order to evaluate the applicability of the method a simulated as well as an experimental data set is tested. The results from experimental data relate to the direct determination of salicylic acid (SA), the main product of aspirin degradation, in undiluted human plasma by spectrofluorimetry.     

A robust,general automatic phase correction algorithm for high‐resolution NMR data

The trends towards rapid NMR data acquisition, automated NMR spectrum analysis, and data processing and analysis by more naïve users combine to place a higher burden on data processing software to automatically process these data. Downstream data analysis is compromised by poor processing, and the automated processing algorithms must therefore be robust and accurate. We describe a new algorithm for automatic phase correction of frequency‐domain, high‐resolution NMR spectra. We show this to be reliable for data derived from a wide variety of typical NMR usages. We therefore conclude that the method will have wide‐spread applicability and a positive impact on automated spectral processing and analysis. Copyright © 2017 John Wiley & Sons, Ltd.     

三维(二阶)算法在液相色谱分析中的应用

使用"垂线法"、"切线法"或"三角形法"等传统方法对液相色谱重叠峰分辨时经常会遇到误差过大的情况,而使用三维(二阶)算法对重叠和拖尾峰分辨可以最大限度地降低这种因几何分割而人为产生的误差。这样改进的色谱解析方法具有自动化程度高、抗干扰能力强、对重叠/拖尾峰定量准确等优点,甚至可以减少样品前处理和色谱条件优化。该方法的核心是基于化学计量学三维(二阶)算法抽取有效信息和建模的思想,三维色谱数据按照对三线性模型的符合程度有"三线性数据"和"非三线性数据"的区别,相应地将三维(二阶)算法分为"三线性算法"和"非三线性算法"。本文综述了近10年来国内外三维(二阶)算法在复杂体系液相色谱分析中的应用进展,侧重于样品前处理、辅助算法、校正算法间的联用和对比等问题。     

A new matching algorithm for high resolution mass spectra

We present a new matching algorithm designed to compare high-resolution spectra. Whereas existing methods are bound to compare fixed intervals of ion masses, the accurate mass spectrum (AMS) distance method presented here is independent of any alignment. Based on the Jeffreys-Matusitas (JM) distance, a difference between observed peaks across pairs of spectra can be calculated, and used to find a unique correspondence between the peaks. The method takes into account that there may be differences in resolution of the spectra. The algorithm is used for indexing in a database containing 80 accurate mass spectra from an analysis of extracts of 80 isolates representing the nine closely related species in the Penicillium series Viridicata. Using this algorithm we can obtain a retrieval performance of approximately 97-98% that is comparable with the best of the existing methods (e.g., the dot-product distance). Furthermore, the presented method is independent of any variable alignment procedures or binning.     

Study of the interactions of berberine and daunorubicin with DNA using alternating penalty trilinear decomposition algorithm combined with excitation-emission matrix fluorescence data

Studies of interactions between drugs and DNA are very interesting and significant not only in understanding the mechanism of interaction, but also for guiding the design of new drugs. However, until recently, mechanisms of interactions between drug molecules and DNA were still relatively little known. It is necessary to introduce more simple methods to investigate the mechanism of interaction. In this study, the interactions of daunorubicin (DNR) or berberine (BER) with DNA and the competitive interactions of DNR and BER with DNA have been studied by alternating penalty trilinear decomposition algorithm (APTLD) combined with excitation-emission matrix fluorescence data. The excitation and emission spectra as well as the relative concentrations of co-existing species in different reaction and equilibrium mixtures can be directly and conveniently obtained by the APTLD treatment. The results obtained are valuable for providing a deeper insight into the interaction mechanism of DNR and BER with DNA. It is proved that the fluorescence spectrum of complex DNR-DNA is different from that of DNR. Furthermore, the present method provides a new way to search for a new non-toxic, highly efficient fluorescent probe. For controversial interaction mechanism of the drugs and DNA, it can provide a helpful verification.     

Comparative molecular field analysis (CoMFA) for phosphodiesterase (PDE) IV inhibitors

A comparative molecular field analysis (CoMFA) for phosphodiesterase (PDE) IV inhibitors has been performed to correlate their chemical structures with their observed biological activity. In this study, CoMFA model based on docking mode for active site of PDE IV can describe the relative change in magnitude of the steric and electrostatic fields as a function of the compounds. Pyridine N-oxide and pyridine group of each compound are aligned toward the metal ion in S2-sub pocket of PDE IV. The study provided a statistically valid model with good correlation and predictive power, and consequently we identified some key features that may be used to design new derivatives.     

A two-dimensional immune algorithm for resolution of overlapping two-way chromatograms

A two-dimensional immune algorithm is proposed for resolving the multicomponent overlapping two-way data matrices. The method is a development of the one-dimensional immune algorithm proposed elsewhere. When the inner product of vectors is expanded to the similar operation on matrices, the 1D immune algorithm can be expanded to the 2D algorithm which is suitable for the analysis of two-way data matrices. Both simulated and experimental two-way data sets were investigated by the method, and the results prove that the 2D immune algorithm is an effective tool for resolving the overlapping two-way signals. The effect of noise on the recoveries is also discussed.     

A two-dimensional immune algorithm for resolution of overlapping two-way chromatograms

A two-dimensional immune algorithm is proposed for resolving the multicomponent overlapping two-way data matrices. The method is a development of the one-dimensional immune algorithm proposed elsewhere. When the inner product of vectors is expanded to the similar operation on matrices, the 1D immune algorithm can be expanded to the 2D algorithm which is suitable for the analysis of two-way data matrices. Both simulated and experimental two-way data sets were investigated by the method, and the results prove that the 2D immune algorithm is an effective tool for resolving the overlapping two-way signals. The effect of noise on the recoveries is also discussed.     

SCOUT: A new algorithm for the inference of pseudo-time trajectory using single-cell data

Single cell technology is a powerful tool to reveal intercellular heterogeneity and discover cellular developmental processes. When analyzing the complexity of cellular dynamics and variability, it is important to construct a pseudo-time trajectory using single-cell expression data to reflect the process of cellular development. Although a number of computational and statistical methods have been developed recently for single-cell analysis, more effective and efficient methods are still strongly needed. In this work we propose a new method named SCOUT for the inference of single-cell pseudo-time ordering with bifurcation trajectories. We first propose to use the fixed-radius near neighbors algorithms based on cell densities to find landmarks to represent the cell states, and employ the minimum spanning tree (MST) to determine the developmental branches. We then propose to use the projection of Apollonian circle or a weighted distance to determine the pseudo-time trajectories of single cells. The proposed algorithm is applied to one synthetic and two realistic single-cell datasets (including single-branching and multi-branching trajectories) and the cellular developmental dynamics is recovered successfully. Compared with other popular methods, numerical results show that our proposed method is able to generate more robust and accurate pseudo-time trajectories. The code of the method is implemented in Python and available at https://github.com/statway/SCOUT.     

Inner chromatogram projection (ICP) for resolution of GC-MS data with embedded chromatographic peaks

The chromatographic peak located inside another peak in the time direction is called an embedded or inner peak in contradistinction with the embedding peak, which is called an outer peak. The chemical components corresponding to inner and outer peaks are called inner and outer components, respectively. This special case of co-eluting chromatograms was investigated using chemometric approaches taking GC-MS as an example. A novel method, named inner chromatogram projection (ICP), for resolution of GC-MS data with embedded chromatographic peaks is derived. Orthogonal projection resolution is first utilized to obtain the chromatographic profile of the inner component. Projection of the two-way data matrix columnwise-normalized along the time direction to the normalized profile of the inner component found is subsequently performed to find the selective m/z points, if they exist, which represent the chromatogram of the outer component by itself. With the profiles obtained, the mass spectra can easily be found by means of a least-squares procedure. The results for both simulated data and real samples demonstrate that the proposed method is capable of achieving satisfactory resolution performance not affected by the shapes of chromatograms and the relative positions of the components involved.     

Dynamic kinetic resolution (DKR) using immobilized amine nucleophiles

The first example of a dynamic kinetic resolution (DKR) using immobilized amine nucleophiles is described. This approach utilizes a nucleophilic amine attached to a solid phase resin via an organic spacer. The optical purities of the N-substituted α-amino ester products are superior to the solution phase DKR with diastereomeric ratios ranging from 11:1 to 18:1 and chemical yields between 66% and 98%.     

Efficient algorithm for "on-the-fly" error analysis of local or distributed serially correlated data

We describe the Dynamic Distributable Decorrelation Algorithm (DDDA) which efficiently calculates the true statistical error of an expectation value obtained from serially correlated data "on-the-fly," as the calculation progresses. DDDA is an improvement on the Flyvbjerg-Petersen renormalization group blocking method (Flyvberg and Peterson, J Chem Phys 1989, 91, 461). This "on-the-fly" determination of statistical quantities allows dynamic termination of Monte Carlo calculations once a specified level of convergence is attained. This is highly desirable when the required precision might take days or months to compute, but cannot be accurately estimated prior to the calculation. Furthermore, DDDA allows for a parallel implementation which requires very low communication, O(log(2)N), and can also evaluate the variance of a calculation efficiently "on-the-fly." Quantum Monte Carlo calculations are presented to illustrate "on-the-fly" variance calculations for serial and massively parallel Monte Carlo calculations.     

Robustness of the extraction step when parallel factor analysis (PARAFAC) is used to quantify sulfonamides in kidney by high performance liquid chromatography-diode array detection (HPLC-DAD)

The robustness of a multiresidue method has been analysed for the extraction and quantification of sulfamethoxypyridazine, sulfamethoxazole and sulfadimethoxine in porcine kidney by HPLC-DAD through a Plackett-Burman design. Two experimental responses were examined, the mean recovery from three replicates (accuracy) and their standard deviation (precision). Three factors were tested: the volume of phosphoric acid (pH) added in the extraction step, the time used for passing the sample through the solid-phase extraction cartridge (flow rate) and methanol volume to elute the analytes from the cartridge. Due to the non-specificity of the chromatograms (unknown matrix interferences coelute with each sulfonamide) the PARAFAC model was employed to evaluate the concentration recovered in the experiments of the Plackett-Burman design as well as to identify the spectra of the substances according to the criteria set in the European Decision 2002/657/EC for the analysis of residues. The extraction step was concluded to be robust to the recovery and the standard deviation of all three analytes.     

A convenient synthesis of enantiomerically pure (R)-mexiletine using hydrolytic kinetic resolution method

Enantiopure (R)-mexiletine was prepared in a simple and practical way using hydrolytic kinetic resolution method of terminal epoxide by Jacobsen’s catalyst. High enantiomeric purity (98% ee) was achieved and the method is well amenable to industrial scale-up.     

Strategies for solving matrix effects in the analysis of sulfathiazole in honey samples using three-way photochemically induced fluorescence data

A widely employed compound for honey treatment, sulfathiazole (ST), was determined in commercial honey samples, employing a combination of photochemically induced fluorescence excitation-emission matrices (EEMs) and chemometric processing of the recorded second-order data. Parallel Factor Analysis (PARAFAC) and Self-Weighted Alternating Trilinear Decomposition (SWATLD) methods were used for calibration. An appropriately designed calibration with a set of standards composed of 18 samples, coupled to the use of the second-order advantage offered by the applied chemometric techniques, allowed quantitation of sulfathiazole in spiked commercial honey samples. No previous separation or sample pretreatment steps were required. The results were compared with other calibration methods such as N-PLS and PLS-1 that produced good results on synthetic samples but not on the investigated commercial honey samples.