Curve Resolution Methods Research Articles

Toward the authentication of wines of Itata valley denomination of origin through total reflection x-ray fluorescence (TXRF) method for testing adulteration. A novel valuable tool by using Compton/Rayleigh scattering signals in wines

The evaluation of wine adulteration is often a cumbersome process not exempt from multiple difficulties. In this work, a valuable methodology to rapidly assess wine adulteration was used. Harnessing the ratio of Compton and Rayleigh scattering signals obtained in TXRF (total reflection X-ray fluorescence). The Compton/Rayleigh signal ratio as a sensitive way to estimate the average effective atomic number (Zeff) of a sample was used. Thus, any addition made into the wine, would cause a change in its Zeff which could be detected by TXRF. Non-adulterated and adulterated wines were selected and its Zeff was estimated. The method was developed using X-ray excitation Molybdenum tube. Deconvolution of independent Compton and Rayleigh signals was performed by non-Gaussian and Gaussian curve resolution methods, and the area ratio was evaluated. A calibration curve for Compton/Rayleigh signal ratio versus Zeff was established and wine adulterated samples were tested in a Zeff range between 4.3 and 7.2. Wine adulteration was detected in all cases. The method is simple, fast, sensitive, precise and non-destructive. It procedure is usefulness as an important tool for wine industry and for the maintenance of origin and quality of wines.

On the factor ambiguity of MCR problems for blockwise incomplete data sets

Multivariate curve resolution (MCR) methods are sometimes faced with missing or erroneous data, e.g., due to sensor saturation. In some cases, an estimation of the missing data is possible, but often MCR works with the largest submatrix without missing entries. This ignores all rows and columns of the data matrix that contain missing values. A successful approach to deal with incomplete data multisets has been proposed by Alier and Tauler (2013), but it does not include a factor ambiguity analysis. Here, the missing data problem is addressed in combination with a factor ambiguity analysis. An approach is presented that minimizes the factor ambiguity by extracting a maximum of spectral information even from incomplete rows and columns of the spectral data matrix. The method requires a high signal-to-noise ratio. Applications are presented for UV/Vis and HSI data.

Chemometric Exploration of Photostability of Ornidazole in Aqueous Solution with Soft and Hard Modelling Multivariate Curve Resolution Method

The photodegradation study of ornidazole in an aqueous solution was performed by using the multivariate curve resolution-alternative least square technique. The sample solution was exposed to direct sunlight for 42 hours, and the spectroscopic data was obtained at predetermined intervals of wavelengths. MCR-ALS, which is a chemometric technique, was applied to the data set. Initially, soft modeling was used, followed by hard modeling. The results show that ornidazole undergoes photodegradation via a two-step process in an aqueous medium, with three species involved in the degradation process. The initial concentration of pure ornidazole decreases while the concentration of intermediate start increasing and the concentration of intermediate falls with the formation of a new product. Thus, we have got three pure spectra in the MCR-ALS process. The reaction kinetics was performed with the hard modeling technique using kinetic constrain and the rate constant of the reaction was found to be k1 = 0.0955 and k2 = 1.287, respectively.

Two‐ and Three‐Dimensional Strategies for Determining Consecutive Acidity Constants of Ciprofloxacin and Enrofloxacin Using Fluorescent Excitation‐Emission Measurements

AbstractMultidimensional analysis is getting more popular by the day thanks to technical improvements of analytical instruments and development of chemometric methods. Here, we describe the application of two different chemometric methods to the analysis of three‐dimensional spectrofluorimetric dataset for green determination of dissociation constants of ciprofloxacin and enrofloxacin with minimal use of consumables. Three‐dimensional spectrofluorimetric datasets of both drugs were obtained by recording excitation‐emission matrices of only six sample solutions having different pH values. Parallel factor analysis (PARAFAC) and multivariate curve resolution (MCR) methods with the use of three components were used to decompose three‐dimensional excitation‐emission‐pH arrays. The number of components support the presence of two pKa values. The individual profiles of H2A, HA− and A2− species in excitation, emission and pH modes were obtained by the application of PARAFAC and MCR. The intersection points in the pH modes were used to predict pKa values. pKa1 and pKa2 of ciprofloxacin was reported as 6.35, 9.15 and 6.42, 9.40 by PARAFAC and MCR‐ALS, respectively. For enrofloxacin, consecutive pKa values were predicted as 6.11 and 9.06 by PARAFAC and 6.10 and 9.10 by MCR. A detailed comparison to literature was done for the estimated pKa values.

Application of ultramicrotomy and infrared imaging to the forensic examination of automotive paint

AbstractIn several previously published studies, Lavine and coworkers have demonstrated that infrared (IR) spectra from all layers of an intact multilayered automotive paint chip can be collected in a single analysis by scanning across each layer of a cross sectioned paint chip using a Fourier transform IR imaging microscope. Applying alternating least squares to the spectral data, the IR spectrum of each layer of an original equipment manufacturer paint chip can be extracted from a line map of the spectral image. To further develop this imaging technique for automotive paint analysis, the capability to cross section “small” paint chips (1 mm or less) using an ultramicrotome has been incorporated into our current imaging methodology. An ultramicrotome does not require epoxy or other embedding media for the paint chip and will simplify the analysis. However, extracting the IR spectra for each layer of an original equipment manufacturer paint chip by alternating least squares can be problematic for thin peels (less than one micron thickness), necessitating the use of target testing factor analysis to determine whether a specific layer is present in the line map and modified alternating least squares to recover the IR spectrum of the layer. Using a new sample preparation technique and the appropriate multivariate curve resolution methods, high quality IR spectra of the layers of a modern automotive paint system can be obtained from paint fragments that are smaller than what is practical to analyze by conventional Fourier transform IR spectroscopy.

Investigating the High-Temperature Water/MgCl2 Interface through Ambient Pressure Soft X-ray Absorption Spectroscopy

Magnesium chloride is a prototypical deliquescent material whose surface properties, although central for Ziegler-Natta cataysis, have so far remained elusive to experimental characterization. In this work, we use surface-selective X-ray absorption spectroscopy (XAS) at ambient pressure in combination with multivariate curve resolution, molecular dynamics, and XAS theoretical methods to track in real time and accurately describe the interaction between water vapor and the MgCl2 surface. By exposing MgCl2 to water vapor at temperatures between 595 and 391 K, we show that water is preferentially adsorbed on five-coordinated Mg2+ sites in an octahedral configuration, confirming previous theoretical predictions, and find that MgCl2 is capable of retaining a significant amount of adsorbed water even under prolonged heating to 595 K. As a consequence, our work provides first experimental insights into the unique surface affinity of MgCl2 for atmospheric water. The developed technique is proven highly sensitive to the modifications induced by adsorbates on a given low-Z metal based surface and may be useful in the toolbox required to disentangle the mechanisms of interfacial chemical processes.

Regions of Interest Multivariate Curve Resolution Liquid Chromatography with Data-Independent Acquisition Tandem Mass Spectrometry

New data-independent acquisition (DIA) modes coupled to chromatographic separations are opening new perspectives in the processing of massive mass spectrometric (MS) data using chemometric methods. In this work, the application of the regions of interest multivariate curve resolution (ROIMCR) method is shown for the simultaneous analysis of MS1 and MS2 DIA raw data obtained by liquid chromatography coupled to quadrupole-time-of-flight MS analysis. The ROIMCR method proposed in this work relies on the intrinsic bilinear structure of the MS1 and MS2 experimental data which allows us for the fast direct resolution of the elution and spectral profiles of all sample constituents giving measurable MS signals, without needing any further data pretreatment such as peak matching, alignment, or modeling. Compound annotation and identification can be achieved directly by the comparison of the ROIMCR-resolved MS1 and MS2 spectra with those from standards or from mass spectral libraries. ROIMCR elution profiles of the resolved components can be used to build calibration curves for the prediction of their concentrations in complex unknown samples. The application of the proposed procedure is shown for the analysis of mixtures of per- and polyfluoroalkyl substances in standard mixtures, spiked hen eggs, and gull egg samples, where these compounds tend to accumulate.

An upgrade of MVC2, a MATLAB graphical user interface for second-order multivariate calibration: Beyond trilinear models

In the present report, an upgrade of a MATLAB graphical user interface (GUI) toolbox for implementing second-order multivariate calibration models is presented, named Multivariate Calibration 2 (MVC2). Due to the advances in the chemometric field, this software has undergone numerous changes since its last release in 2009. The new freely available MVC2 incorporates novel features and models that make it a very practical tool for data processing. Overall, the current version presents different types of algorithms, designed to provide specific degrees of model flexibility for different multi-way data scenarios: in addition to trilinear decomposition (TLD) and residual bilinearization (RBL) models, which were previously included in the 2009 version, parallel factor analysis 2 (PARAFAC2) and multivariate curve resolution (MCR) methods are now available. All these chemometric methodologies are integrated in the software for quantitative purposes, and if needed, they permit to exploit the so-called analytical second-order advantage. The program offers practical tools for data loading and visualization, model development and validation, and prediction in unknown samples. The software output also includes a comprehensive report on the analytical figures of merit (AFOMs) applicable to second-order calibration models. Specifically, a tool was incorporated for the diagnosis of the remaining rotational ambiguity in the MCR solutions. In the present report, the new features of MVC2 are illustrated through simulated examples and real calibration datasets.

Analysis of Milk Microstructure Using Raman Hyperspectral Imaging

Optical spectroscopic analysis of the chemical composition of milk in its natural state is complicated by a complex colloidal structure, represented by differently sized fat and protein particles. The classical techniques of molecular spectroscopy in the visible, near-, and mid-infrared ranges carry only bulk chemical information about a sample, which usually undergoes a destructive preparation stage. The combination of Raman spectroscopy with confocal microscopy provides a unique opportunity to obtain a vibrational spectrum at any single point of the sample volume. In this study, scanning confocal Raman microscopy was applied for the first time to investigate the chemical microstructure of milk using samples of various compositions. The obtained hyperspectral images of selected planes in milk samples are represented by three-dimensional data arrays. Chemometric data analysis, in particular the method of multivariate curve resolution, has been used to extract the chemical information from complex partially overlaid spectral responses. The results obtained show the spatial distribution of the main chemical components, i.e., fat, protein, and lactose, in the milk samples under study using intuitive graphical maps. The proposed experimental and data analysis method can be used in an advanced chemical analysis of natural milk and products on its basis.

Gas chromatography/mass spectrometry with chemometric methods for the determination of fatty acid profiles in herbal oils.

The conventional method for analyzing fatty acid is gas chromatography (GC) with polar capillary columns. However, owing to the high cost and the sensitivity of these columns to the presence of water and oxygen, these columns are not the best choice for separation. Also, analyzing long-chain acids (>C28) with polar columns is impossible. On the other hand, complete separation with nonpolar columns is not possible for some saturated, unsaturated and long-chain fatty acids. Therefore, in this study, with the help of chemometric methods, a method was developed using GC/mass spectrometry (MS) with a nonpolar column to resolve the peaks to completely separate and accurately identify and quantify fatty acids. Using this method, the fatty acid profiles of the seed oils of Sesamum indicum L, Nigella sativa, Pimpinella anisum, Linum asitatissimum L, Silybum marianum and Amygdalus communis L. var. Amara and var. Dulcis were identified. Through applying the multivariate curve resolution method after GC/MS, the C-18 fatty acids such as α-linolenic, linoleic, oleic and stearic acids were separated and quantified. Also, the total percentages of identified fatty acids increased by 1-6% after resolving overlapping peaks. Finally, the obtained percentages of saturated and unsaturated fatty acids were confirmed by reference reports.

Remembering Prof. Edmund R. Malinowski, 1932–2020 Professor of Chemistry, 1963–1997 Stevens Institute of Technology

One of the great pioneers of chemometrics, Prof. Edmund R. Malinowski, passed away in February 2020. Contributors to this special issue are proud to recognize and honor the pioneering work of Professor Malinowski. It is my special privilege to write this remembrance of him. Prof. Malinowski had an enormous impact on the field of chemometrics, having published over 70 papers and most notably the pioneering book “Factor Analysis in Chemistry” in 1980. The timely introduction of this topic and his clear writing style in a language that chemists could understand made this book a valuable educational tool for the budding chemometrics community. Prof. Malinowski's clear writing style can be observed throughout all his research publications. Further details about his career, his awards, and his impact on the field are well summarized in a 1999 editorial.1 His last PhD student, Kathleen Schostack, described Prof. Malinowski as “thoughtful and soft-spoken; very much old school, a gentleman and a gentle man.” I wholeheartedly concur. Prof. Malinowski was always quick to acknowledge and recognize the work of others, and I was one of the beneficiaries of this particular kindness of him. It is my pleasure to share some of my remembrances about Prof Malinowski and the impact he had on my career. In 1982, fresh out of my PhD, not having been trained in chemometrics, I discovered Prof. Malinowski's 1980 book, “Factor Analysis in Chemistry” and read it cover to cover. I was already interested in mathematical methods for resolving overlapping GC/MS or LC/UV-Vis peaks. The clear writing style and detailed attention to the mathematics of factor analysis in this book laid a great foundation for me, and by 1984, I had written a draft of my first chemometrics paper.2 Being very early in my career, the faculty at ECU asked me to organize a half-day symposium on the topic of chemometrics. I invited Tom Isenhour and Ed Malinowski, and to my great surprise, both agreed to come. I remember picking Ed up at the airport the night before the symposium and nervously handing him a draft of my first chemometrics paper. The next morning in his introductory remarks to the faculty at ECU he stated with amazement that “One of your very own faculty members gave me a draft paper yesterday that for the first time shows a curve resolution method using factor analysis to resolve three or more overlapping peaks, whereas until now it was believed that only two peaks could be resolved.” He continued to cite this work and the work of other early-career chemometricians in his conference presentations and publications. By using his name recognition and standing in the field, he generously promoted early-career chemometricians. In many ways, Prof. Edmund R. Malinowski was a Renaissance Man like others from this era. His retirement and later his death signified the end of an era, and we are all the poorer for it. The peer review history for this article is available at https://publons.com/publon/10.1002/cem.3466. N/A.

Kinetic Model of Diclofenac Degradation Developed Using Multivariate Curve Resolution Method.

This study presents the kinetic modeling of the natural long-term aging of the pharmaceutical substance as well as the intact tablets of Diclofenac. Datasets are collections of near-infrared spectra acquired from the intact tablets packed in plastic blisters and the spectra of the pure substance. Fresh samples and samples at different stages of degradation are analyzed. No methods of accelerated aging were applied. Multi-step application of MCR-ALS in its soft version followed by the kinetic modeling of the results helps to propose a generic degradation mechanism; which includes: a global kinetic model; approximations of the NIR spectra of the intermediate and product; rough estimates of rate constants. We study tablets in blister packs; exactly as they are presented in pharmacies; and this is important from a practical point of view.

The water structure around chloride ion investigated from D2O ↔ H2O substitution effect

The Raman spectra for (D2O + H2O) − NaCl solutions (nH2O/nD2O = 0/1, 1/4, 1/1, 4/1 and 1/0) were measured at temperatures from 293 to 573 K. We further discuss the water structure in the solutions based on the solute-correlated (SC) OD/OH stretch bands obtained from the Multivariate Curve Resolution method. The most prominent effect of H ↔ D substitution is raising the relative intensity of the high-wavenumber modes. The ∼ 2660 cm−1/∼3635 cm−1 mode can become the main peak when isotopic substitution ratio is 80 % at temperatures over 493 K. The spectral features suggest a flexible water structure in the Cl− hydration shell where most hydrating water molecules are engaged in hydrogen bonding configurations of single donor (SD) and single hydrogen-bond water (SHW). The increase of isotopic substitution ratio leads to the structural transition of SD → SHW → FW (free water) so that FW is greatly increased at isotopic substitution ratio of 80 % and temperatures over 493 K. Moreover, the estimated hydrogen bond number for hydrating water indicates a stronger D2O − Cl− interaction than H2O − Cl− interaction in the hydration shell.

An active constraint approach to identify essential spectral information in noisy data

Multivariate curve resolution (MCR) methods aim at extracting pure component profiles from mixed spectral data and can be applied to high-dimensional data, e.g., from process spectroscopy or hyperspectral imaging techniques. One often observes that some parts of this data, namely certain rows and columns of the data matrix, are considered essential for MCR outcomes, while other parts are of minor importance. Some methods for determining essential data are known, but all have different disadvantages concerning the application for noisy data. This work presents a new approach on how to detect the essential information for noisy, experimental spectral data. Active nonnegativity constraints in combination with duality arguments are the key ingredients for determining essential spectra and frequency channels. The new approach is conceptually simple, computationally cheap and stable with respect to noise. The algorithm is tested for noisy experimental Raman, UV–Vis and FTIR-SEC data.

Effects of sulfamethoxazole exposure on mussels (Mytilus galloprovincialis) metabolome using retrospective non-target high-resolution mass spectrometry and chemometric tools

In this work, the Regions of Interest-Multivariate Curve Resolution (ROIMCR) method is proposed for the analysis of non-target metabolomics data. Samples from marine mussels (Mytilus galloprovincialis) exposed to a sublethal concentration (10 μg/L) of sulfamethoxazole (SMX) during 4 days in different seasonal conditions (summer and winter) were analyzed by High-Performance Liquid Chromatography – High-Resolution Mass Spectrometry (HPLC-HRMS) to study the effect of their exposure to SMX and the different seasonal conditions. The Regions of Interest (ROI) procedure has been applied for data filtering, compression, preprocessing and storage steps. Multivariate Curve Resolution-Alternating Least Squares (MCR-ALS) is then applied to the previously MS ROI preprocessed data sets to resolve the elution profiles and spectral fingerprints of the chemical constituents of the analyzed samples. The peak areas of the elution profiles of the chemical constituents resolved by the combined ROIMCR procedure were analyzed by Principal Component Analysis (PCA) and samples were clustered according to their experimental seasonal and SMX exposure. The effects of the two investigated factors and of their interaction on the concentrations of the metabolites were statistically assessed by ANOVA simultaneous component analysis (ASCA). Both types of analyses, PCA clustering and ASCA, confirmed that the seasonal conditions (summer versus winter) produced larger effects than those produced by the exposure to SMX and by the interaction of these two factors. The concentration changes of 16 identified endogenous metabolites were validated individually using a Wilcoxon statistical test, which confirmed the presence of significant disturbances in the levels of some of these metabolites (free fatty acids, amino acids and nucleic acids), and indicated the possible alteration of six different biological pathways, affected by the investigated seasonal and SMX exposure factors.

A temperature‐dependent hydrating structure around SO42− investigated from Raman spectroscopy

AbstractThe Raman spectra of H2O/D2O−Na2SO4 solutions are measured at temperatures (T) up to 573 K. The hydrating structure of SO42− is investigated based on the solute‐correlated (SC) OD/OH stretch bands obtained by the multivariate curve resolution method. Remaining a nearly constant wavenumber of the main peak with increasing temperature, the SC OD/OH bands are narrowed first due to the reduced relative intensity of the shoulder at 2395/~3245 cm−1 when T < ~473 K/~513 K but then because the OD/OH bands get sunken around 2610/3580 cm−1 above ~473/~513 K (letting the ~2660/~3635 cm−1 mode be more prominent and even a separate peak). These spectral features incline to support a temperature‐dependent water structure in the SO42− hydration shell balanced by the SO42−···H2O(D2O) and O–H(D)···O hydrogen bonds (those with D are stronger) as well as the electrostatics. Most hydrating water molecules are engaged in hydrogen bonding configurations of single donor (SD) and single hydrogen‐bond water (SHW). As temperature rises, the average number of hydrogen bonds per hydrating water molecule decreases below ~373 K because of the SD → SHW transition and increases afterward owning to the rapid increase of the ion pairs, and SO42− changes its role from structure breaker to structure maker above ~453 K. The temperature‐dependent solubility behavior of Na2SO4 in H2O can be rationalized by the ion pairing effect and temperature‐dependent structure details in SO42− hydration shell.

Spotlight on mass spectrometric non-target screening analysis: Advanced data processing methods recently communicated for extracting, prioritizing and quantifying features.

Non-target screening of trace organic compounds complements routine monitoring of water bodies. So-called features need to be extracted from the raw data that preferably represent a chemical compound. Relevant features need to be prioritized and further be interpreted, for instance by identifying them. Finally, quantitative data is required to assess the risks of a detected compound. This review presents recent and noteworthy contributions to the processing of non-target screening (NTS) data, prioritization of features as well as (semi-) quantitative methods that do not require analytical standards. The focus lies on environmental water samples measured by liquid chromatography, electrospray ionization and high-resolution mass spectrometry. Examples for fully-integrated data processing workflows are given with options for parameter optimization and choosing between different feature extraction algorithms to increase feature coverage. The regions of interest-multivariate curve resolution method is reviewed which combines a data compression alternative with chemometric feature extraction. Furthermore, prioritization strategies based on a confined chemical space for annotation, guidance by targeted analysis and signal intensity are presented. Exploiting the retention time (RT) as diagnostic evidence for NTS investigations is highlighted by discussing RT indexing and prediction using quantitative structure-retention relationship models. Finally, a seminal technology for quantitative NTS is discussed without the need for analytical standards based on predicting ionization efficiencies.

Predicting the uniqueness of single non-negative profiles estimated by multivariate curve resolution methods

In many kinds of chemical data, one or more species are unknown and the only efficient way to identify and/or quantify them is by mathematical resolution of the mixture spectra. The major problem with such mathematical decompositions is the possibility of obtaining a range of feasible solutions instead of a unique solution due to insufficient prior information about the system under study. However, even with the minimal non-negativity assumptions, there may be some levels of uniqueness, i.e., full/partial/fractional, in the results of the bilinear decomposition of chemical data which is very important to detect. In this study, a procedure is proposed to predict the uniqueness of the resolved non-negative profiles obtained by MCR-ALS (or analogous methods like NMF, EFA, SIMPLISMA, ITTFA, HELP, etc.). This uniqueness prediction is based on the data-based uniqueness (DBU) theorem and the general rule of uniqueness (GRU) presented in previous studies. The proposed procedure is easy to implement, has no additional computational cost, and is general for different systems with any number of components. Several simulated and experimental datasets containing different numbers of components were used to examine and evaluate the proposed procedure.

Analytical performance of Compton/Rayleigh signal ratio by total reflection X‐ray fluorescence (TXRF): A potential methodological tool for sample differentiation

AbstractThe high sensitivity Compton and Rayleigh X‐ray scattering signals can be used to gain valuable information on the chemical composition of various matrices, by exploiting the ratio of those signals as a function of the effective atomic number (Zeff). Neither total reflection X‐ray fluorescence (TXRF) nor the effect of the experimental setup, including sample preparation, X‐ray excitation source selection, and band deconvolution procedure, has been assessed in this kind of approach. Here, a Compton/Rayleigh ratio and Zeff‐based TXRF method was set up and tested as an analytical tool for milk samples differentiation. The method was developed using a 90° scattering angle and assessed using different X‐ray excitation sources: a molybdenum tube (Mo Kα 17.5 KeV) and a tungsten tube (W Lα 8.5 KeV and W‐Brems 35 KeV). The evaluation of independent Compton and Rayleigh signals was performed by non‐Gaussian and Gaussian curve resolution methods, and both height and area‐based calculations were evaluated. Different sample preparation conditions were assessed. By using 11 standard materials, a calibration curve for Compton/Rayleigh ratio versus Zeff was established. The method was tested to determine the Zeff of milk samples, which enabled its use as a parameter to differentiate them. Good precisions were obtained with the Mo excitation source and the area‐based calculations, which allowed to differentiate undiluted milk samples by species, treatment, and fat content according to their Compton/Rayleigh ratio. This simple and rapid method has the potential to be used for the differentiation of various types of samples, including liquids, solids, and aerosols.

Understanding temporal and spatial changes of O3 or NO2 concentrations combining multivariate data analysis methods and air quality transport models

The application of the multivariate curve resolution method to the analysis of temporal and spatial data variability of hourly measured O3 and NO2 concentrations at nineteen air quality monitoring stations across Catalonia, Spain, during 2015 is shown. Data analyzed included ground-based experimental measurements and predicted concentrations by the CALIOPE air quality modelling system at three horizontal resolutions (Europe at 12 × 12 km2, Iberian Peninsula at 4 × 4 km2 and Catalonia at 1 × 1 km2). Results obtained in the analysis of these different data sets allowed a better understanding of O3 and NO2 concentration changes as a sum of a small number of different contributions related to daily sunlight radiation, seasonal dynamics, traffic emission patterns, and local station environments (urban, suburban and rural). The evaluation of O3 and NO2 concentrations predicted by the CALIOPE system revealed some differences among data sets at different spatial resolutions. NO2 predictions, showed in general a better performance than O3 predictions for the three model resolutions, specially at urban stations. Our results confirmed that the application of the trilinearity constraint during the multivariate curve resolution factor analysis decomposition of the analyzed data sets is a useful tool to facilitate the understanding of the resolved variability sources.