Applications of maximum likelihood principal component analysis: incomplete data sets and calibration transfer

The application of a new method to the multivariate analysis of incomplete data sets is described. The new method, called maximum likelihood principal component analysis (MLPCA), is analogous to conventional principal component analysis (PCA), but incorporates measurement error variance information in the decomposition of multivariate data. Missing measurements can be handled in a reliable and simple manner by assigning large measurement uncertainties to them. The problem of missing data is pervasive in chemistry, and MLPCA is applied to three sets of experimental data to illustrate its utility. For exploratory data analysis, a data set from the analysis of archeological artifacts is used to show that the principal components extracted by MLPCA retain much of the original information even when a significant number of measurements are missing. Maximum likelihood projections of censored data can often preserve original clusters among the samples and can, through the propagation of error, indicate which samples are likely to be projected erroneously. To demonstrate its utility in modeling applications, MLPCA is also applied in the development of a model for chromatographic retention based on a data set which is only 80% complete. MLPCA can predict missing values and assign error estimates to these points. Finally, the problem of calibration transfer between instruments can be regarded as a missing data problem in which entire spectra are missing on the ‘slave’ instrument. Using NIR spectra obtained from two instruments, it is shown that spectra on the slave instrument can be predicted from a small subset of calibration transfer samples even if a different wavelength range is employed. Concentration prediction errors obtained by this approach were comparable to cross-validation errors obtained for the slave instrument when all spectra were available.     

Simple correction for perturbations of peak amplitudes in statistical models of overlap

Summary The application of statistical models of overlap (SMOs) to saturated separations is made possible by theory that addresses variable peak amplitudes. These amplitudes cause peak widths to vary, and this variation can be modeled by a random variable whose effect on the probability of overlap is expressed by a convolution integral. Modified probabilities of overlap are derived for both homogeneous and nonhomogeneous one-dimensional separations, and the new probabilities are compared to results determined from published computer simulations. The new theory can describe overlap at saturations that are 3 to 4 times larger than before. Previously reported experimental chromatograms are reinterpreted to show the capabilities of theory. The theoretical extension is an important step towards making SMOs into practical tools for screening analytical separations.     

Fast folding and comparison of RNA secondary structures

Summary Computer codes for computation and comparison of RNA secondary structures, the Vienna RNA package, are presented, that are based on dynamic programming algorithms and aim at predictions of structures with minimum free energies as well as at computations of the equilibrium partition functions and base pairing probabilities.An efficient heuristic for the inverse folding problem of RNA is introduced. In addition we present compact and efficient programs for the comparison of RNA secondary structures based on tree editing and alignment.All computer codes are written in ANSI C. They include implementations of modified algorithms on parallel computers with distributed memory. Performance analysis carried out on an Intel Hypercube shows that parallel computing becomes gradually more and more efficient the longer the sequences are.

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Schnelle Faltung und Vergleich von Sekundärstrukturen von RNA

Zusammenfassung Die im Vienna RNA package enthaltenen Computer Programme für die Berechnung und den Vergleich von RNA Sekundärstrukturen werden präsentiert. Ihren Kern bilden Algorithmen zur Vorhersage von Strukturen minimaler Energie sowie zur Berechnung von Zustandssumme und Basenpaarungswahrscheinlichkeiten mittels dynamischer Programmierung.Ein effizienter heuristischer Algorithmus für das inverse Faltungsproblem wird vorgestellt. Darüberhinaus präsentieren wir kompakte und effiziente Programme zum Vergleich von RNA Sekundärstrukturen durch Baum-Editierung und Alignierung.Alle Programme sind in ANSI C geschrieben, darunter auch eine Implementation des Faltungs-algorithmus für Parallelrechner mit verteiltem Speicher. Wie Tests auf einem Intel Hypercube zeigen, wird das Parallelrechnen umso effizienter je länger die Sequenzen sind.

     

Chemometric data analysis of pollutants in wastewater—a case study

In this study, chemometric techniques such as cluster analysis (CA), discriminant analysis (DA), principal component analysis (PCA) and partial least squares (PLS) were used to analyse the wastewater dataset to identify the factors which affect the composition of sewage of domestic origin, spatial and temporal variations, similarity/dissimilarity among the wastewater characteristics of cis- and trans-drains and discriminating variables. Samples collected from 24 wastewater drains in Lucknow city and from three sites on Gomti river in the month of January/February, May, August and November during the period of 5 years (1994-1999) were characterized for 32 parameters. The multivariate techniques successfully described the similarities/dissimilarities among the sewage drains on the basis of their wastewater characteristics and sources signifying the effect of routine domestic/commercial activities in respective drainage areas. Spatial and seasonal variations in wastewater composition were also determined successfully. CA generated six groups of drains on the basis of similar wastewater characteristic. PCA provided information on seasonal influence and compositional differences in sewage generated by domestic and industrial waste dominated drains and showed that drains influenced by mixed industrial effluents have high organic pollution load. DA rendered six variables (TDS, alkalinity, F, TKN, Cd and Cr) discriminating between cis- and trans-drains. PLS-DA showed dominance of Cd, Cr, NO₃, PO₄ and F in cis-drains wastewater. The results suggest that biological-process based STPs could treat wastewater both from the cis- as well as trans-drains, however, prior removal of toxic metals will be required from the cis-drains sewage. Further, seasonal variations in wastewater composition and pollution load could be the guiding factor for determining the STPs design parameters. The information generated would be useful in selection of process type and in designing of the proposed sewage treatment plants (STPs) for safe disposal of wastewater.     

Oxidative addition of the ethane C-C bond to Pd. An ab initio benchmark and DFT validation study

We have computed a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the ethane C-C bond to the palladium atom and have used this to evaluate the performance of 24 popular density functionals, covering LDA, GGA, meta-GGA, and hybrid density functionals, for describing this reaction. The ab initio benchmark is obtained by exploring the PES using a hierarchical series of ab initio methods [HF, MP2, CCSD, CCSD(T)] in combination with a hierarchical series of five Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Our best estimate of kinetic and thermodynamic parameters is -10.8 (-11.3) kcal/mol for the formation of the reactant complex, 19.4 (17.1) kcal/mol for the activation energy relative to the separate reactants, and -4.5 (-6.8) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). Our work highlights the importance of sufficient higher angular momentum polarization functions for correctly describing metal-d-electron correlation. Best overall agreement with our ab initio benchmark is obtained by functionals from all three categories, GGA, meta-GGA, and hybrid DFT, with mean absolute errors of 1.5 to 2.5 kcal/mol and errors in activation energies ranging from -0.2 to -3.2 kcal/mol. Interestingly, the well-known BLYP functional compares very reasonably with a slight underestimation of the overall barrier by -0.9 kcal/mol. For comparison, with B3LYP we arrive at an overestimation of the overall barrier by 5.8 kcal/mol. On the other hand, B3LYP performs excellently for the central barrier (i.e., relative to the reactant complex) which it underestimates by only -0.1 kcal/mol.     

Trifluoromethyl‐Radical‐Mediated Carbonylation of Alkanes Leading to Ethynyl Ketones

The carbonylation of alkanes 1 under radical‐reaction conditions was examined by using ethynyl triflone A as the unimolecular chain‐transfer (UMCT) reagent. Good to moderate yields of ethynyl ketones 2 were prepared by means of this three‐component coupling reaction. Higher CO pressures as well as lower concentrations of triflone A improved the efficiency of the reaction over the direct addition, the latter leading to alkylated ethynes 3 . In contrast to the reaction with A , the reaction of cyclohexane ( 1a ) with allyl triflone B (= ethyl 2‐methylene‐3‐[(trifluoromethyl)sulfonyl]propanoate) in the presence of CO gave a mixture of carbonylation products, including 8a formed from two molecules each of cyclohexane, CO, and allyl triflone B .     

Chemometric analysis of groundwater quality data of alluvial aquifer of Gangetic plain, North India

Water quality data set from the alluvial region in the Gangetic plain in northern India, which is known for high fluoride levels in soil and groundwater, has been analysed by chemometric techniques, such as principal component analysis (PCA), discriminant analysis (DA) and partial least squares (PLS) in order to investigate the compositional differences between surface and groundwater samples, spatial variations in groundwater composition and influence of natural and anthropogenic factors. Trilinear plots of major ions showed that the groundwater in this region is mainly of Na/K-bicarbonate type. PCA performed on complete data matrix yielded six significant PCs explaining 65% of the data variance. Although, PCA rendered considerable data reduction, it could not clearly group and distinguish the sample types (dug well, hand-pump and surface water). However, a visible differentiation between the water samples pertaining to two watersheds (Khar and Loni) was obtained. DA identified six discriminating variables between surface and groundwater and also between different types of samples (dug well, hand pump and surface water). Distinct grouping of the surface and groundwater samples was achieved using the PLS technique. It further showed that the groundwater samples are dominated by variables having origin both in natural and anthropogenic sources in the region, whereas, variables of industrial origin dominate the surface water samples. It also suggested that the groundwater sources are contaminated with various industrial contaminants in the region.     

Study of gas-liquid partitioning of alkane solutes in several organic solvents by using principal component analysis and linear solvation energy relationships

Principal component analysis (PCA) was used to extract the number of factors which can describe the 737 gas-liquid partition coefficients of five linear, four branched, and two cyclic alkanes in 67 common solvents. Based on the reconstruction of partition coefficient data matrix, we concluded that the experimental dataset could readily be reduced to two relevant factors. Using only these two factors, there were no errors larger than 3%, 7 cases had errors larger than 2%, and in 34 cases, errors were between 1 and 2%. n-Hexane and ethylcyclohexane were chosen as the test factors, and all other partition coefficients were expressed in terms of these two test factors. Prediction of the logarithmic partition coefficient of these alkanes in seven chemically different solvents, which were originally excluded from the data matrix, was excellent: the root mean square error was 0.064, only in 11 cases the errors were larger than 1%, and only 3 had errors larger than 4%.Linear solvation energy relationships (LSERs) using both theoretical and empirical solvent parameters were used to explain the molecular interactions responsible for partition. Several combinations of parameters were tried but the standard deviations were not less than 0.31. This could be attributed to the model itself, imprecisions in the data matrix or in some of the LSER parameters. Solvent cohesive parameters and surface tension in combination with polarity-polarizability or dispersion parameters perform the best.Finally, the two principal component factors were rotated onto the most relevant physicochemical parameters that control the gas-liquid partitioning phenomena.