Search

In this work, a simple and fast analytical method based on a self-weighted alternating trilinear decomposition (SWATLD) algorithm coupled with excitation-emission matrix (EEM) fluorescence was developed for the simultaneous determination of sulfamethoxazole (SMZ) and trimethoprim (TMP) illegally added to health products. With the second-order advantage, the proposed method obtained satisfactory results in the presence of peak overlap and unknown interferences. The analysis time for a single sample is only 0.8 minutes. The average spiked recoveries of SMZ and TMP in three health product spiked samples were in the range of 91.0-106.2% and 86.8-107.8%, respectively. The relative standard deviations (RSDs) were lower than 8.6%. In addition, verification parameters including sensitivity (SEN), selectivity (SEL), the limit of detection (LOD), the limit of quantification (LOQ), intra-day precision, and inter-day precision were calculated, and the results show that the proposed method is feasible. The quantitative results of the proposed method were further confirmed by the LC-MS/MS method, which proved that the proposed method was efficient and green for drug-abuse monitoring of SMZ and TMP in health products.

Polycyclic aromatic hydrocarbons (PAHs) are of worldwide environmental concern because of their properties of carcinogenicity, mutagenicity and teratogenicity. In the work, a smart combination of gel permeation chromatography-diode array detector and second-order calibration based on alternating trilinear decomposition (ATLD-GPC-DAD) is proposed for simultaneous targeted identification and quantification of 15 PAHs in atmospheric pollution sources such as flue-dust and greasy-dirt samples. No need of tedious sample pretreatment and specific PAHs separation column, severely overlapped chromatograph peaks are successfully resolved by the ATLD-GPC-DAD method even with only 3 s of difference in retention times. Accurate quantitative results of 15 PAHs are achieved by using the developed method even in the presence of unexpected interferents. The limits of detection range from 0.94 ng mL−1 to 48.86 ng mL−1, and the average recoveries are in the range of (81.2 ± 1.0)% to (108.9 ± 11.6)% for flue-dust samples and (89.7 ± 3.4)% to (107.5 ± 8.0)% for greasy-dirt samples. The sensitivity and selectivity of analytes is significantly improved with the aid of “mathematical separation” of the method. These results indicate that it opens a promising analytical strategy for control of PAHs emissions and management of urban air quality.

For the first time, alternating trilinear decomposition-assisted multivariate curve resolution (ATLD-MCR) was applied to analyse complex gas chromatography–mass spectrometric (GC-MS) data with severe baseline drifts, serious co-elution peaks and slight retention time shifts for the simultaneous identification and quantification of polycyclic aromatic hydrocarbons (PAHs) in aerosols. It was also compared with the classic multivariate curve resolution-alternating least-squares (MCR-ALS) and the GC-MS-based external standard method. In validation samples, average recoveries of five PAHs were within the range from (96.2 ± 6.8)% to (106.5 ± 4.1)% for ATLD-MCR, near to the results of MCR-ALS ((98.0 ± 1.5)% to (106.7 ± 4.3)%). In aerosol samples, the concentrations of pyrene provided by ATLD-MCR were not significantly different from those of MCR-ALS. The other four PAHs including chrysene, benzo[a]anthracene, fluoranthene and benzo[b]fluoranthene were not detected by ATLD-MCR and the GC-MS-based external standard method. The results of figures of merit further demonstrated that ATLD-MCR achieved high sensitivities (8.9 × 10 4 to 1.7 × 10 6 mAU ml µg −1 ) and low limits of detection (0.003 to 0.087 µg ml −1 ), which were better than or similar to MCR-ALS, presenting a great choice to deal with complex GC-MS data for the simultaneous determination of targeted PAHs in aerosols.

The quantification of preservatives in cosmetics has attracted great attentions for their controversial and widespread use. HPLC is a prevailing method for preservatives determination among various analytical methods. However, it takes long time to fully separate these compounds because of the complexity of cosmetic matrices. In this study, a fast and green HPLC-DAD strategy assisted with second-order multivariate calibration methods based on alternating trilinear decomposition (ATLD) and multivariate curve resolution-alternating least squares (MCR-ALS) was developed for the simultaneous determination of eight selected preservatives in complex facial mask samples. This appealing strategy proved to be a useful tool for eliminating unknown interferences in complex matrices without complete separation, which benefited from the “second-order advantages” and thus made the determination of the eight analytes in facial mask samples shorten to 8.2 min under a fast elution program. In particular, for the first time, we focused on the applicability of ATLD method for modeling of HPLC-DAD data with severe signal overlapping and slight time shifts. The spiked recovery values were in the range of 71.4–124.6%, and the RMSEP and REP values ranged from 0.07 to 2.4 μg mL−1 and 1.3–14.5%, respectively, indicating that the ATLD method could provide satisfactory prediction. The resolved spectral profiles and concentration values were compared with those obtained by the MCR-ALS method, an excellent tool for modeling of data deviating from trilinearity. Both qualitative and quantitative results from the two methods were consistent with each other, which evidenced the competence of ATLD method in handling HPLC-DAD data with severe signal overlapping and slight time shifts.

This paper proposes a flexible and novel strategy that alternating trilinear decomposition (ATLD) method combines with two-dimensional linear discriminant analysis (2D-LDA). The developed strategy was applied to three-way chemical data for the characterization and classification of samples. In order to confirm the methodology performances of characterization and classification, a series of simulated three-way data arrays and a real-life EEMs data set involving the characterization and classification of tea samples according to the tea varieties were subjected to ATLD-2DLDA analysis. Further, the obtained results were compared with those obtained by using LDA based on relative concentrations of ATLD (ATLD-LDA), discriminant analysis by N-way partial least square (N-PLS-DA) and 2D-LDA method. For the simulated data sets with respect to different levels of noise and class overlap as well as number of groups, the ATLD-2DLDA always obtains superior classification performances than the ATLD-LDA, 2D-LDA and N-PLS-DA methods. Regarding the real EEMs data set of tea samples, the proposed methodology not only could provide a chemically meaningful model of the data for characterizing the different tea varieties, but also achieved the best correct classification rate (100%) for the test samples, compared with the results of ATLD-LDA (83.9%), 2D-LDA (90.3%) and N-PLS-DA (90.3%). These results demonstrated that the proposed methodology was indeed a feasible and reliable tool for characterization and classification of three-way chemical data arrays in a flexible and accurate manner.

In the present study, a smart analytical strategy that combines liquid chromatography-full scan mass spectrometry with the second-order calibration method based on the alternating trilinear decomposition (ATLD) algorithm was developed for the simultaneous determination of seven estrogens in infant milk powders. The seven estrogens were rapidly eluted out within 7.0 min under a simple gradient condition and then, they were detected by mass spectrometry operated in the full scan mode. With the aid of the prominent “second-order advantage” of the algorithm, specific qualitative and quantitative information about the target analytes could be extracted from the complex system even in the presence of considerable peak overlaps, baseline drifts and unknown interferences. The proposed strategy avoided time-consuming and laborious sample pretreatment procedures, resulting in minimal loss of analytes, which improved the analytical accuracy. Average recoveries of the seven estrogens in two spiked infant milk powder samples were in the range of 91.2–104.2% with the relative standard deviations (RSDs) lower than 5.0% (with the exception for 17α-estradiol), and the limits of detection (LOD) ranged from 0.07 to 2.49 ng mL−1. Besides, to further confirm the feasibility and reliability of the proposed method, the same batch of samples was analyzed using the LC-MS/MS method, and the statistical tests showed that no significant difference existed between the two methods, which fully indicated that the proposed strategy could provide satisfactory prediction results in real infant milk powder samples as well as other actual chemical systems.

The present study compared six commonly used algorithms, namely, alternating trilinear decomposition (ATLD), self-weighted alternating trilinear decomposition (SWATLD), alternating coupled two unequal residual functions (ACTUF), parallel factor analysis (PARAFAC), damped Gauss-Newton (dGN) and algorithm combination methodology (ACM). Their performances with respect to the pre-estimated component number, convergence rate, collinearity, noise, small component and slight non-linearity (chromatographic peak drift) were considered. The results indicate that the difference in the performances of the algorithms arises from differences in the computational mode and the construction of loss functions. Among the six algorithms, ATLD, SWATLD, ACTUF and ACM were insensitive to excessive factors; the ability to overcome severe collinearity was in the order of ACM, ACTUF and dGN > SWATLD > ATLD and PARAFAC; PARAFAC, dGN and ACM showed a stronger ability to resist noise; PARAFAC was the most sensitive to a small component; and ATLD and SWATLD could overcome some effect of slight non-linearity (chromatographic peak drift). Additionally, ATLD was found to be the fastest algorithm, and dGN and ACM had faster convergence rates than PARAFAC. This study is helpful for understanding the essential difference in the performances of algorithms and can provide guidance for choosing suitable algorithms for the analysis of three-way data.

Multi-way data arrays contain missing values for several reasons, such as various malfunctions of instruments, responses being outside instrument ranges, irregular measurement intervals between samples and data postprocessing. In the present study, one new method, weighted alternating penalty trilinear decomposition (W-APTLD), based on the weighted trilinear model and the idea of alternative trilinear decomposition was given to analyze three-way data arrays containing missing values. In addition, one improved core consistency diagnostic method (W-CORCONDIA) was proposed to estimate the chemical ranks of three-way data arrays containing missing values. The results of one simulation and two real data sets demonstrate that the new method W-APTLD could be used to deal with missing values and reserves the second-order advantage. When meeting excessive factors, W-APTLD could give more accurate results than weighted PARAFAC (W-PARAFAC), PARAFAC with single imputation (PARAFAC-SI) and incomplete data PARAFAC (INDAFAC). The convergence rate of W-APTLD was much faster than W-PARAFAC and PARAFAC-SI but slower than INDAFAC. Better than W-PARAFAC and PARAFAC-SI, W-APTLD could overcome the problem due to severe collinearity. In addition, this new method could be extended to analyze higher-way data arrays containing missing values.

Determining the number of chemical components in mixtures is a crucial step in four-way data analysis. However, few works about true four-way component-determining method are developed to estimate the optimum number of components of four-way data arrays. In this paper, a new method is proposed for the determination of the number of chemical components of four-way data from complicated chemical systems, namely, alternating weighted quadrilinear decomposition incorporating Monte Carlo simulation (AWQLD-MCS), as an extension of self-weighted alternating trilinear decomposition incorporating Monte Carlo simulation. The performance of the newly developed method has been demonstrated by two simulated and two real four-way data arrays. The results show that the proposed method can accurately and quickly estimate the number of components to fit the quadrilinear model. Moreover, the newly suggested method is compared with the other three component-determining methods, i.e., the core consistency diagnostic (CORCONDIA) test, the ADD-ONE-UP truncating and fitting method (ADD-ONE-UP) and factor indicator function (IND). It is found that the new method has the fast analytical speed and the strong ability of anti-noise-interference and anticollinearity in practical application, indicating that it is a promising alternative for four-way component determination in quadrilinear decomposition.

CP decomposition of large third-order tensors can be computationally challenging. Parameters are typically estimated by means of the ALS procedure because it yields least-squares solutions and provides consistent outcomes. Nevertheless, ALS presents two major flaws which are particularly problematic for large-scale problems: slow convergence and sensitiveness to degeneracy conditions such as over-factoring, collinearity, bad initialization and local minima. More efficient algorithms have been proposed in the literature. They are, however, much less dependable than ALS in delivering stable results because the increased speed often comes at the expense of accuracy. In particular, the ATLD procedure is one of the fastest alternatives, but it is hardly employed because of the unreliable nature of its convergence. As a solution, multi-optimization is proposed. ATLD and ALS steps are concatenated in an integrated procedure with the purpose of increasing efficiency without a significant loss in precision. This methodology has been implemented and tested under realistic conditions on simulated data sets.

Alternating trilinear decomposition (ATLD) method enables the qualitative and quantitative analysis of excitation-emission matrix fluorescence (EEMF) data acquired from complex samples. However, the impact of diverse background interferences from different sample sources on the performances of ATLD method has never been lucubrated. In this work, simulated and real EEMF data sets from different sample sources with diverse background interferences were collected and subjected to ATLD analysis. The performances of ATLD modeling individual and global EEMF data sets were comprehensively compared in terms of the resolved spectral profiles and quantitative results. It was found that ATLD method can use the same set of calibration samples to resolve and quantify multiple components of interest in multiple complex systems with diverse background interferences, regardless of individual or global modeling. The results revealed that the qualitative and quantitative results provided by ATLD method were affected neither by diversity of background interferences nor by data merging as long as the acquired EEMF data sets conform to the trilinear component model. This property of ATLD method can enrich the “second-order advantage”, i.e. the term “unknown interferences” in the concept of “second-order advantage” refers to not only constant background interferences but also diverse background interferences, which will be certain to further expand the practicality of ATLD method in complex sample analysis, especially in the field of fluorescence spectroscopy.

BACKGROUND Sesamin and sesamolin are two typical and important lignans isolated from sesame oil. Various studies have shown the bioactivity, physiological activity, and potential health benefits of the two components. In this study, a rapid method for the simultaneous determination of sesamin and sesamolin in sesame oils was proposed. The excitation-emission fluorescence spectra of the oils were obtained after a simple pretreatment, then self-weighted alternating trilinear decomposition was used to extract the quantitative information from the very overlapping spectra. RESULTS It was found that reasonable quantification results could be obtained with the limits of detection for the two lignans. These limits were 0.05 mg/g and 0.24 mg/g, and the limits of quantitation were 0.14 mg/g and 0.74 mg/g, respectively. The average recoveries for sesamin and sesamolin were 99.05% and 94.97%. CONCLUSION The results indicate that, with simple sample pretreatment, the application for combining excitation-emission fluorescence spectra and self-weighted alternating trilinear decomposition can be a useful and sensitive tool for the determination of lignans in sesame oil. © 2020 Society of Chemical Industry.

This work proposes a modern approach in separation of voltammetric current components which applies a pattern recognition strategy. Application of the trilinear decomposition algorithm ASD was first time demonstrated for detection and modelling of faradaic and capacitive components, recorded as total signal in DPV experiments. Using calibration set of the model substance i.e. K4Fe(CN)6, sampled with the frequency of 1 kHz, the signal components were extracted, which shape was consistent with the theoretic relations. Fitting in the area of peak expressed by r was 0.9957 for faradaic current and 0.9916 for capacitive component. Also the successive stages of the redox process was identified and interpreted. Essential influence for the quantitative analysis was observed. DP voltammograms utilizing all faradaic current samples were characterized by zero baseline and improved calibration line parameters. A wide application list of this modern strategy was also proposed.

An adaptation of the PARAFAC-ALS algorithm is implemented with the purpose of providing accurate and efficient estimates of CANDECOMP/PARAFAC parameters without being influenced by data characteristics and model specifications. This is a dual-optimization procedure in which values are first estimated by SWATLD and then refined through standard ALS steps. The use of an additional optimization phase is suggested with the purpose of canceling out specific ALS inefficiencies such as slow convergence and occurrence of over-factoring degeneracies. A complex simulation study is then implemented in order to identify the most adequate transition point between the stages of the proposed methodology and to show its advantages with respect to standard ALS.

Methanol gasoline, known as a new energy, has a certain degree of damage to automobile. The aim of this work was to identify and quantify the methanol in methanol gasoline using three-dimensional fluorescence spectroscopy technique combined with second order chemometric methods. Parallel factor analysis (PARAFAC) and self-weighted alternating trilinear decomposition (SWATLD) methods were used to analyse artificial samples. However, the obtained results by PARAFAC were not satisfactory. On the other hand, excellent prediction results were obtained when SWATLD model was applied, with recovery rate between 98.7 and 102.8%, and between 97.4 and 101.9% for two and three factor respectively. In order to verify the accuracy of the method, four real samples were predicted using SWATLD model with RMSEP between 0.1 μg/mL and 0.23 μg/mL.

In this work, high-performance liquid chromatography with diode array detection was applied for the simultaneous determination of andrographolide and dehydroandrographolide in Andrographis paniculata and its preparations. As a result of the incomplete baseline separation caused by complex backgrounds, the classical univariate calibration method failed to determine accurate contents of the analytes. On this occasion, chemometric second-order calibration based on the well-known alternating trilinear decomposition algorithm was then explored to serve as a post-experimental remedial tool to solve this problem. By using the intelligent "mathematical separation" of alternating trilinear decomposition, the peak areas of the analytes do not need to be directly measured and the predictive results become accurate. The contents of andrographolide and dehydroandrographolide were determined to be (7.95 ± 0.15) and (1.85 ± 0.02) μg/mL for Andrographis paniculata, (1.34 ± 0.01) and (5.53 ± 0.04) μg/mL for its preparations, which was in agreement with those obtained by a reference liquid chromatography with mass spectrometry method. This study showed the superiority of second-order calibration method over classical univariate calibration method for simultaneous determination of multi-analytes in complex samples. It also proved that second-order calibration may be a good choice for remedying incomplete baseline separation problem, with the accompanied reduction of experimental burden and toxic organic solvents as well as analysis time and cost.

This work reports a chemometrics-assisted high performance liquid chromatography-diode array detection (HPLC-DAD) strategy to solve varying interfering patterns from different chromatographic columns and sample matrices for the rapid simultaneous determination of six synthetic colorants in five kinds of beverages with little sample pretreatment. The investigation was performed using two types of LC columns under the same elution conditions. Although analytes using different columns have different co-elution patterns that appear more seriously in complex backgrounds, all colorants were properly resolved by alternating trilinear decomposition (ATLD) method and accurate chromatographic elution profiles, spectral profiles as well as relative concentrations were obtained. The results were confirmed by those obtained from traditional HPLC-UV method at a particular wavelength and the results of both methods were consistent with each other. All results demonstrated that the proposed chemometrics-assisted HPLC-DAD method is accurate, economical and universal, and can be promisingly applied to solve varying interfering patterns from different chromatographic columns and sample matrices for the analysis of complex food samples.

We investigate the topic of two-dimensional direction of arrival (2D-DOA) estimation for rectangular array. This paper links angle estimation problem to compressive sensing trilinear model and derives a compressive sensing trilinear model-based angle estimation algorithm which can obtain the paired 2D-DOA estimation. The proposed algorithm not only requires no spectral peak searching but also has better angle estimation performance than estimation of signal parameters via rotational invariance techniques (ESPRIT) algorithm. Furthermore, the proposed algorithm has close angle estimation performance to trilinear decomposition. The proposed algorithm can be regarded as a combination of trilinear model and compressive sensing theory, and it brings much lower computational complexity and much smaller demand for storage capacity. Numerical simulations present the effectiveness of our approach.

In the previous work for joint Direction-Of-Arrival (DOA) and frequency estimation with sub-Nyquist sampling, algorithm JDFTD has a superior estimation performance. However, the computational burden increases with the snapshot for iterative operation. In this paper, singular value decomposition (SVD) is employed to eliminate the effect of snapshot and a new version of algorithm JDFTD based on SVD (SVD-JDFTD) is proposed. Numerical simulations verify that SVD-JDFTD reduces the computational burden without loss the superior estimation performance of JDFTD.

Three analytical methodologies for the generation of third-order liquid chromatography–excitation–emission fluorescence matrix (LC–EEM) data are presented. Instrumental requirements were evaluated considering equipment complexity, costs and accessibility. A descriptive analysis of the generated data was done along trilinearity concept and chemometric resolution. For trilinear decomposition, PARallel FACtor Analysis (PARAFAC) model was utilized. Hence, possible effects that are caused in the resolution due to loss of trilinearity are detailed. Then, several data pre-processing and processing alternatives are proposed in order to successfully overcome the drawbacks that can be present in the chemometric resolution. Additionally, a reported analytical method for the determination of three analytes is presented to showcase the potential of the methodology to generate third-order LC–EEM data with quantitative aims. For data modelling, Augmented PARAFAC (APARAFAC) and Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) were used. Both algorithms demonstrated to be able to bear non-quadrilinear data in a multi-set analysis. Fil: Montemurro, Milagros. Universidad Nacional del Litoral. Facultad de Bioquímica y Ciencias Biológicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina Fil: Siano, Gabriel German. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Bioquímica y Ciencias Biológicas; Argentina Fil: Alcaraz, Mirta Raquel. Universidad Nacional del Litoral. Facultad de Bioquímica y Ciencias Biológicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina Fil: Goicoechea, Hector Casimiro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe; Argentina. Universidad Nacional del Litoral. Facultad de Bioquímica y Ciencias Biológicas; Argentina

A new receptor model based on the alternating trilinear decomposition followed by a score matrix reconstruction (ATLD-SMR) was developed for the source apportionment of urban PM10 for the first time. First, simulated three-way data arrays of gas chromatography-mass spectrometry (GC-MS) were used to verify the feasibility of the ATLD-SMR method. Then, PM10 samples (receptor) at five locations and TSP samples of ten pollution sources were collected during July and August, 2018 in Loudi City, China. The collected samples were measured by GC-MS. PAHs were used as tracers and their concentrations were accurately obtained by the ATLD-SMR analysis of GC-MS data of these samples after the problems of GC-MS including baseline drift, retention-time shift and unexpected peaks overlapping were successfully resolved. The highest concentrations of individual PAH in these samples were for phenanthrene and benzo [a] pyrene (40.76 ng m-3 and 39.63 ng m-3 in Liangang steel-making workshop, respectively). Last, a relative contribution matrix of the source to the receptor was estimated by the ATLD-SMR method. The proposed method was employed to apportion the source contributions to PM10 particles at five locations and reasonable results were obtained, thus presenting a promising tool for source apportionment of complex ambient particulate matter.

This study presents an in-depth discussion of the differential properties of various iterative trilinear decomposition algorithms, including Parallel Factor Analysis-Alternating Least Squares (PARAFAC-ALS), Alternating Trilinear Decomposition (ATLD), Self-Weighted Alternating Trilinear Decomposition (SWATLD), and Alternating Penalty Trilinear Decomposition (APTLD). The shape of each algorithm's objective function (“convex” or “strictly convex”) is related to the algorithm's sensitivity to the estimated component number of the trilinear system. Different situations near the objective solution are analyzed both theoretically and numerically. The wall of perturbation generated by deviations in the iterative steps prevents the PARAFAC algorithm from achieving the objective solution when the component number is overestimated. This may explain, from a calculational perspective, why the PARAFAC algorithm could not obtain the objective solution or any equivalent thereto (although equivalents might still be chemically meaningful optimal solutions). The different effects of deviation and residual on the algorithms are demonstrated by numerical analysis in this paper. The convergence rate can be improved by the use of high-performance computing strategy of the specific algorithm. The concept of solution set discussed in this paper complements the theory of the uniqueness of trilinear decomposition. Copyright © 2014 John Wiley & Sons, Ltd.

The triazophos is a kind of organic phosphorus pesticide, the quantitative determination model based on three-dimensional fluorescence spectroscopy coupled with alternating trilinear decomposition (ATLD) was explored for realizing the rapid determination of triazophos content in duck meat. Firstly, three-dimensional fluorescence spectra of duck meat extract, triazophos standard solution and duck meat extract containing triazophos were explored, respectively. Secondly, the fluorescence quenching phenomenon of the triazophos in duck meat extract was analyzed. Lastly, the number of components for three linear decomposition of ATLD was set as 2 by using the core consistency diagnostic, and the calibration curve between the relative fluorescence intensity and the actual concentration of the triazophos was established by using ATLD. The experimental results showed that the determination coefficient (R2) and the root mean squared error of prediction (RMSEP) for the proposed model in this paper were 0.9741 and 0.764 respectively, and it was feasible to predict the triazophos content in duck meat combining with three-demensional fluorescence spectroscopy and ATLD.

In this paper, we make study on the compressed matrices in the compressed sensing trilinear model-based angle estimation algorithm, whose complexity is lower than conventional trilinear decomposition-based method, due to the use of compressed matrices. And we take the problem of angle estimation for bistatic multiple-input multiple-output (MIMO) radar as an example. Simulation results can provide reference for the choice of compressed matrices.

Four-way room-temperature phosphorescence (RTP) data recorded by following the kinetic evolution of excitation–emission phosphorescence matrices (EEPMs) have been analyzed for the first time by third-order calibration based on parallel factor analysis (PARAFAC), alternating weighted residue constraint quadrilinear decomposition (AWRCQLD) and alternating quadrilinear decomposition (AQLD) algorithms. The AQLD constructed in pseudo-fully stretched matrix forms of quadrilinear model was a new third-order calibration algorithm, which was developed as a direct extension of alternating trilinear decomposition for quadrilinear data. These methodologies were applied to investigate the hydrolysis kinetic of carbaryl even in the presence of an uncalibrated phosphorescence background and comparisons among them were done subsequently. Spectral background drift produced in measured dataset was overcome by means of modeling the drift as an additional component as well as the analyte of interest in the mathematical model. Satisfactory results were obtained for determination of carbaryl in spiked tap water samples. The spectral and kinetic time profiles resolved by these methodologies were in good agreement with experimental observations. The present work successfully faced the difficulty in investigating the hydrolysis kinetic of analyte with the RTP techniques, opening a new approach for third-order data generation and subsequent third-order calibration.

The present investigation attempts to separate the variation in time domain from steady-state fluorescence and to discuss quantitatively the state-switching of α-chymotrypsin (CHT). The activity of CHT is pH dependent (inactive at low pH, such as 2.2, but active at physiological pH, such as 8). ANS (1-anilinonaphthalene-8-sulfonate) has two states of fluorescence corresponding to different excitation and emission processes. Though a steady-state technique, Excitation–Emission Matrix fluorescence (EEM) can record all the excitation and emission signals for the ANS–CHT complex system. The trilinear decomposition of the constructed three-way data set (using EEM data of different samples) can provide excitation and emission spectra indicating specific excitation and emission processes, respectively, and a quantitative description for the time domain processes. Besides a detailed description of the excitation–emission processes of ANS, the quantitative investigation of state-switching by CHT is also possible because the fluorescence, due to the S1,ct state of ANS, is sensitive to the solvation environment, which is one of the indicators of CHT activity. Finally, the switching output curve of the ANS–CHT system over a wide pH range is obtained. This study proposes a convenient and economical protocol for investigating state-switching in proteins.

This paper discusses the signal detection problem with rectangular array, and links the detection problem to the compressed sensing trilinear model. Exploiting this link, we derive a compressed sensing trilinear decomposition-based signal detection algorithm, which can obtain the estimation of the signals from different directions. The proposed algorithm requires no spectral peak searching, and it has lower complexity than conventional trilinear decomposition-based method. Simulation results illustrate the performance of the algorithm.

This paper describes the use of second-order calibration for development of HPLC-DAD method to quantify nine polyphenols in five kinds of honey samples. The sample treatment procedure was simplified effectively relative to the traditional ways. Baselines drift was also overcome by means of regarding the drift as additional factor(s) as well as the analytes of interest in the mathematical model. The contents of polyphenols obtained by the alternating trilinear decomposition (ATLD) method have been successfully used to distinguish different types of honey. This method shows good linearity (r>0.99), rapidity (t