WINDOW FACTOR ANALYSIS:THEORETICAL DERIVATION AND APPLICATION TO FLOW INJECTION ANALYSIS DATA

Window factor analysis(WFA)is a self-modeling method for extracting the concentration profiles ofindividual components from evolutionary processes such as flow injection,chromatography,titrationsand reaction kinetics.The method takes advantage of the fact that each component lies in a specificregion along the evolutionary axis,called the‘window’.Theoretical equations are derived.The methodis used to extract the concentration profiles and spectra of seven bismuth species from data obtained byGemperline and Hamilton,who injected bismuth perchlorate into a flowing stream of hydrochloric acid.     

CONDITION NUMBERS, ITERATIVE REFINEMENT AND ERROR BOUNDS

Concentration estimates of components present in a sample mixture can be obtained using matrixmathematics. In the past, the condition number of the calibration matrix has been used to give anamplification factor by which uncertainties in data can work through to errors in the concentrationestimates. This paper explores an additional interpretation of condition numbers with regards tosignificant figures and rounding errors. A procedure is suggested which will always give the most accurateconcentration estimates provided the calibration matrix is not too ill-conditioned. Condition numbershave also been used by analytical chemists to discuss the error bounds for concentration estimates.Unfortunately, only one representative error bound can be approximated for all the components. Thispaper will show how to compute bounds for individual concentration estimates obtained as solutions to asystem of m equations and n unknowns. The procedure is appropriate when calibration data and sampleresponses are inaccurate.     

DETECTING AND ADJUSTING FOR NON-LINEARITIES IN CALIBRATION OF NEAR-INFRARED DATA USING PRINCIPAL COMPONENTS

A new regression method for non-linear near-infrared spectroscopic data is proposed.The technique isbased on a model which is linear in the principal components and simple functions(squares and products)of them.Added variable plots are used to determine which squares and products to incorporate into themodel.The regression coefficients are estimated by a Stein estimate which shrinks towards the estimatedetermined by the first several principal components and the selected non-linear terms.The technique isnot computationally intensive and is appropriate for routine predictions of chemical concentrations.Themethod is tested on three data sets and in all cases gives more accurate predictions than does linearprincipal components regression.     

RESIDUAL BILINEARIZATION.PART 1:THEORY AND ALGORITHMS

When using hyphenated methods in analytical chemistry,the data obtained for each sample are given asa matrix.When a regression equation is set up between an unknown sample (a matrix) and a calibrationset (a stack of matrices),the residual is a matrix R.The regression equation is usually solved by minimizing the sum of squares of R.If the sample containssome constituent not calibrated for,this approach is not valid.In this paper an algorithm is presentedwhich partitions R into one matrix of low rank corresponding to the unknown constituents,and onerandom noise matrix to which the least squares restrictions are applied.Properties and possibleapplications of the algorithm are also discussed.In Part 2 of this work an example from HPLC with diode array detection is presented and the resultsare compared with generalized rank annihilation factor analysis (GRAFA).     

VARIANCE-DECOMPOSITION OF PURE-COMPONENT SPECTRA AS A MEASURE OF SELECTIVITY

Care is required for multicomponent analysis if misleading results are to be avoided. The problem ofill-conditioned calibration matrices is of primary concern. This type of numerical instability isrepresented as spectral overlap of calibration spectra. Depending on the degree of spectral overlap, thesample concentration estimates can be severely affected. A practical statistical procedure is discussedwhich tests for the presence of spectral overlap among the pure-component spectra and simultaneouslyassesses the degree that concentration estimates may be degraded. Guidelines are developed to ascertainhow much departure from spectral orthogonality is acceptable.     

RESOLUTION OF STRONGLY OVERLAPPING TWO-WAY MULTICOMPONENT DATA BY MEANS OF HEURISTIC EVOLVING LATENT PROJECTIONS

High-performance liquid chromatography with diode array detection(HPLC-DAD)is used tocharacterize mixtures from chlorophyll α degradation experiments.Overlapping chromatographic peaksare resolved by means of the heuristic evolving latent projections(HELP)method.The HELP methodis a self-modelling curve resolution method.No assumptions are made about spectral and/orchromatographic peak shape.In the first step the method establishes the real noise level in the data byuse of the so-called zero-component regions.This information is used to reveal selective chromatographicinformation and the number of chemical species at every retention time in unresolved chromatographicpeaks.Utilising the selective chromatographic regions in combination with the zero-concentrationwindows,unique resolution into concentration profiles and spectra of the pure chemical species isaccomplished.HPLC-DAD data from six chlorophyll a degradation experiments were analysed.Consistent results were obtained even with very similar spectra for six or seven overlapping chemicalcomponents.     

A TEST OF SIGNIFICANCE FOR PARTIAL LEAST SQUARES REGRESSION

Partial least squares (PLS) regression is a commonly used statistical technique for performingmultivariate calibration, especially in situations where there are more variables than samples. Choosingthe number of factors to include in a model is a decision that all users of PLS must make, but iscomplicated by the large number of empirical tests available. In most instances predictive ability is themost desired property of a PLS model and so interest has centred on making this choice based on aninternal validation process. A popular approach is the calculation of a cross-validated r~2 to gauge howmuch variance in the dependent variable can be explained from leave-one-out predictions. Using MonteCarlo simulations for different sizes of data set, the influence of chance effects on the cross-validationprocess is investigated. The results are presented as tables of critical values which are compared againstthe values of cross-validated r~2 obtained from the user's own data set. This gives a formal test forpredictive ability of a PLS model with a given number of dimensions.     

DETERMINATION OF A MULTIVARIATE DETECTION LIMIT AND LOCAL CHEMICAL RANK BY DESIGNING A NON-PARAMETRIC TEST FROM THE ZERO-COMPONENT REGIONS

In this paper we redefine the term detection limit to embrace the inherent multivariate nature of samples,instrumental measurements and chemometrics resolution procedures. The so-called zero-componentregions, i.e. parts with no chemical components eluting, are used as repeated analytical blanks to estimatea statistical multivariate detection limit for determining the number of chemical species in local regionsof a single two-way chromatogram or a collection of synchronized one-way chromatograms. For two-waychromatography the detection limit is determined from the distribution of the first eigenvalues obtainedfrom all possible combinations of spectra in the zero-component regions. The number of spectra in eachcalculation should correspond to the number included in the later examination of the local retention timeregions. For one-way chromatography on a collection of samples with similar chemical components atvarying concentrations the same procedure is used, with the samples taking the role of the spectra intwo-way chromatography. The detection limit can be chosen at various confidence levels depending onwhether false positive or negative detection of minor components is most critical. The results obtainedfrom the zero-eigenvalue distribution are more robust than those obtained by a previously developedF-test.     

COMPARISON OF MEASUREMENT METHODS BASED ON A MODEL FOR THE ERROR STRUCTURE

Comparison of methods is a technique often used for investigation of systematic errors of measurementmethods.As concerns the design and analysis of such comparisons,much variety of opinion and practiceexists.In one approach a few specimens are measured several times by different operators in differentlaboratories(reproducibility conditions)and in another approach several specimens are measured on oneor a few occasions by one operator in the same laboratory(repeatability conditions).In this paper amodel for the error structure of measurements is formulated and it is emphasized that one has todistinguish between two types of systematic errors:the first type depends only on the level of themeasured quantity and the second type is specific for the separate specimens.On the basis of this modelthe information which can be obtained from the different designs of method comparisons is discussed.A new approach for the analysis of method comparisons with many specimens is also proposed.     

2000-2010年黄河上游流域植被年际变化及其对气候要素的响应(英文)

To understand the variations in vegetation and their correlation with climate factors in the upper catchments of the Yellow River, China, Normalized Difference Vegetation Index(NDVI) time series data from 2000 to 2010 were collected based on the MOD13Q1 product. The coefficient of variation, Theil–Sen median trend analysis and the Mann–Kendall test were combined to investigate the volatility characteristic and trend characteristic of the vegetation. Climate data sets were then used to analyze the correlation between variations in vegetation and climate change. In terms of the temporal variations, the vegetation in this study area improved slightly from 2000 to 2010, although the volatility characteristic was larger in 2000–2005 than in 2006–2010. In terms of the spatial variation, vegetation which is relatively stable and has a significantly increasing trend accounts for the largest part of the study area. Its spatial distribution is highly correlated with altitude, which ranges from about 2000 to 3000 m in this area. Highly fluctuating vegetation and vegetation which showed a significantly decreasing trend were mostly distributed around the reservoirs and in the reaches of the river with hydropower developments. Vegetation with a relatively stable and significantly decreasing trend and vegetation with a highly fluctuating and significantly increasing trend are widely dispersed. With respect to the response of vegetation to climate change, about 20–30% of the vegetation has a significant correlation with climatic factors and the correlations in most areas are positive: regions with precipitation as the key influencing factor account for more than 10% of the area; regions with temperature as the key influencing factor account for less than 10% of the area; and regions with precipitation and temperature as the key influencing factors together account for about 5% of the total area. More than 70% of the vegetation has an insignificant correlation with climatic factors.     

基于粗糙集理论的地学空间关系规则分析及其应用——以珠江三角洲为例

Spatial relations,reflecting the complex association between geographical phenomena and environments,are very important in the solution of geographical issues. Different spatial relations can be expressed by indicators which are useful for the analysis of geographical issues. Urbanization,an important geographical issue,is considered in this paper. The spatial relationship indicators concerning urbanization are expressed with a decision table. Thereafter,the spatial relationship indicator rules are extracted based on the application of rough set theory. The extraction process of spatial relationship indicator rules is illustrated with data from the urban and rural areas of Shenzhen and Hong Kong,located in the Pearl River Delta. Land use vector data of 1995 and 2000 are used. The extracted spatial relationship indicator rules of 1995 are used to identify the urban and rural areas in Zhongshan,Zhuhai and Macao. The identification accuracy is approximately 96.3%. Similar procedures are used to extract the spatial relationship indicator rules of 2000 for the urban and rural areas in Zhongshan,Zhuhai and Macao. An identification accuracy of about 83.6% is obtained.     

EFFECT OF ENVIRONMENTAL FACTORS ON POPULATION DYNAMECS OF DREPANOPUS BISPINOSUS IN BURTON LAKE, ANTARCTICA

The population dynamics of Drepanopus bispinosus (Calanoida: Copepoda) was studied throughout the year of December 1983-January 1985 in Burton Lake, a littoral saline lake on Vestfold Hills,Antarctica, and the environmental factors of the lake were observed simultaneously. D. bispinosus is univoltine. Its population life cycle could be in 20-21 months and reproduetive activity stays from winter to early summer. The adults (male and female) and nauplil mainly form the winter population. Adult females are instead of male and, copepodites are instead of nauplii in summer population. Then it consists of copepodites mainly in stages II-V from late summer through autumn. The density of population components considerably varies for their whole life time. Most of nauplii appearing in winter may not develop and transform into further stages under the restrictive conditions, such as low oxygen content and scarce food. Earlier stage copepodites of new generation appear largely in summer, when the lake is rich in o     

SHORT COMMUNICATION VARIATIONS IN ESSENTIAL OILS OF MANDARINE RELATED TO PROCESSING AND RIPENING

Mandarine essential oils are extracted from green unripened fruits as well as from red fruits at ripening,both oils having specific uses as natural additives in the food industry.Two processes of production,pressing and peeling,are currently adopted in their production.Capillary gas chromatography with flameionization detection has been suggested as a sensitive method for the fractionation of volatile componentsof the essential oils.Principal component analysis was proposed as an exploratory chemometric methodfor the differentiation of essential oils from fruits at different degrees of ripening,taking into accountthe processes of production.Product-moment correlations between variables(concentrations of 17components)were used as starting matrices and the explained variance was adopted as a criterion foreigenvalue selection.Bi-plots and three-dimensional plots of unrotated principal component scores weresystematically used as well as those of orthogonally rotated factor scores.The 17 variables were reducedto four principal components,which explained 87% of the total variance.Projection on the first threeeigenvectors of all data as unrotated component scores allowed for a tentative differentiation of 59 oilsaccording to their degree of ripening.The two processes of production were also differentiated in asample of 55 oils.     

PSEUDOINVERSE DETERMINATION OF THE CIRCULATION IN PRYDZ BAY AND ITS ADJACENT OPEN OCEAN, ANTARCTICA

An inverse model is used to infer the circulation in Prydz Bay and its adjacent open ocean using hydrographic data obtained by the cruise of the 7th Chinese National Antarctic Research Expedition (CHINARE-7), 1990/91. Barotropie components are found to be strong in the study area, esp. at the Antarctic Divergence, and from a whole view, the velocity is rather small. In the open ocean, the flow is quasizonal, but outside the bay it shows a tendency of pressing onto the shelf from surface to bottom, and a feature of intensification just east of Fram Bank. We suggest here be the most important place to detect the possibility of the Antarctic Bottom Water formation. The meridional profiles of the distribution indicate a strong (relative to the ambient) core and a slope-trapped part into the bargain. In the southeastern part of the bay, there seems to exist a strong coastal current flowing westward. The computed upwelling centers are mainly situated in the west of the study region, as agrees quite well with     

THE EFFECT OF MISLABELED SAMPLES ON THE PERFORMANCE OF THE LINEAR LEARNING MACHINE

Over the past 15 years the linear learning machine has been applied to a large number of chemicalproblems.The learning machine approach is conceptually simple and does not require knowledge aboutthe statistical distribution of the data.However,there are problems associated with this approach.Oneproblem which has not been investigated is the influence of mislabeled samples on the positioning of thehyerplane in feature space.If a few samples in a data set are incorrectly tagged prior to training(i.e.thesamples are labeled as members of class 2 even though they are actually members of class 1),it is stilIpossible using the linear learning machine to achieve a classification success rate of 100% for the trainingset.However,unfavorable results will be obtained for the prediction set.The magnitude of this effect andits potential implications regarding the proper use of the linear learning machine are discussed.     

LABORATORIO DI CHEMIOMETRIA,UNIVERSITY OF PERUGIA,ITALY

The Laboratory for Chemometrics at the University of Perugia is situated in the NaturalSciences Building,close to the centre of Perugia.Perugia is situated in Umbria,about 3 hoursnorth of Rome (by train).The old city centre is on a hilltop and has a well-preserved medievalcharacter,and also reminders from its Roman and Etruscan origin are abundant.Very closeto the Natural Sciences Building are the Via Appia and the Etruscan gate,and below the     

CORRESPONDENCE ANALYSIS AND ADSORBATE SELECTION FOR CHEMICAL SENSOR ARRAYS

Carey et al.utilized principal components analysis (PCA) to analyze frequency shift data obtained frompiezoelectric sensors formed by coating quartz crystals with 27 different GC stationary phases and testedusing 14 analytes.The objective of the analysis was to determine an optimal reduced set of coatings fordetection of the analytes.The results were correlated with those obtained from cluster analysis.In thispaper the data are re-analyzed using correspondence analysis (CA).The advantage of using CA includea symmetric treatment of sensor coatings and analytes and better identification of the representation ofthe analytes in terms of the detection components.The results obtained by the conjunctive use of PCA,a varimax rotation and cluster analysis were obtained by CA.     

THE EFFECT OF MEAN CENTERING ON PREDICTION IN MULTIVARIATE CALIBRATION

Traditionally,one form of preprocessing in multivariate calibration methods such as principal componentregression and partial least squares is mean centering the independent variables(responses)and thedependent variables(concentrations).However,upon examination of the statistical issue of errorpropagation in multivariate calibration,it was found that mean centering is not advised for some datastructures.In this paper it is shown that for response data which(i)vary linearly with concentration,(ii)have no baseline(when there is a component with a non-zero response that does not change inconcentration)and(iii)have no closure in the concentrations(for each sample the concentrations of allcomponents add to a constant,e.g.100%)it is better not to mean center the calibration data.That is,the prediction errors as evaluated by a root mean square error statistic will be smaller for a model madewith the raw data than a model made with mean-centered data.With simulated data relativeimprovements ranging from 1% to 13% were observed depending on the amount of error in thecalibration concentrations and responses.     

RAPID ESTIMATION OF THE NUMBER OF COELUTING COMPONENTS IN LIQUID CHROMATOGRAPHY BY FACTOR ANALYSIS

Evaluation of the results of factor analysis of sets of spectroscopically detected chromatograms is carriedout by examining the shapes of the abstract factors.This is done either by visual inspection or by analysisof the power density spectra produced from them.Owing to constraints imposed by the column functionand the spectroscopic instrument function,the information content of the chromatograms necessarilyoccurs at low spatial frequencies.As a consequence,it appears as relatively broad features in the abstractchromatograms and as a peak in the low-frequency region of the corresponding power density plot.Onthe basis of examination of the power density distribution,a well-defined distinction is made betweenprimary and secondary abstract factors.The major uncertainty encountered in determining the numberof chemical components appears to arise from effects of contaminants in reagents.