Covariation Formations

If it is also recalled that alkali soluble material (humic acid) builds up much more slowly than acidity (and always markedly dependent on T and [O]), and that the distinctly acidic parent coal is effectively insoluble in alkali, it becomes evident that acidity and alkali solubility are not necessarily covariant, and that accepted definitions of humic acid are, chemically speaking entirely arbitrary. Under the conditions of this study the oxidation appears to involve two simultaneous but seemingly unrelated reactions which result in the development of acidity and in molecular (skeletal) breakdown, respectively, and this suggests that alkali solubility is mainly a consequence of degradation which is only coincidentally connected with the formation of acidic functional groups. Figure 20 illustrates this concept qualitatively and leads to the inference that the wide spread in molecular weights of humic acids reported... 

The covariate analysis identified weight, sex, creatinine clearance, body mass index (BMI), and age as having an influence on PK parameters of NS2330 and/or Ml, respectively. The overall clearance of NS2330 is reduced by 20.5% in females compared to males and the NS2330 clearance which accounted for any elimination pathways except the formation of Ml from NS2330 (CLnon.met/F) is reduced in patients with a creatinine clearance lower than 62.5 ml/min ( 1.2% reduction per 1 ml/min reduction). The volume of distribution of NS2330 is influenced by body... 

The Trial Simulator (Pharsight Corp., http //www.pharsight.com) is a comprehensive and powerful tool for the simulation of clinical trials. Population PK/PD models developed with tools mentioned in Section 17.10.3 can be implemented in a Trial Simulator. In addition, treatment protocols, inclusion criteria, and observations can be specified. Also covariate distribution models, compliance models, and drop-out models can be specified. All of these models can be implemented via a graphical user interface. For the analysis of simulation results a special version of S-Plus is implemented and results can also be exported in different formats, like SAS. 

Figure 17 Nd-Hf isotope ratios in rocks and Fe-Mn deposits. In mantle and continental rocks these two isotope ratios a positive covariation, reflecting correlated fractionations of Sm/Nd and Ln/Hf during mantle melting and continent formation over Earth history. Seafloor Fe-Mn deposits are distinct, and lie off the continent-mantle array, at high Hf isotope ratios for a given Nd isotope ratio. Possible explanations are given in the text. The figure is modified from van de Flierdt et al. (2002). The crust-mantle array is based on Vervoort et al. (1999). (Hf isotope data on Fe-Mn samples White et al., 1986 Godfrey et al., 1997 Alhare(c)de et al., 1998 Burton et al., 1999 ...

Variations in Mg, Fe, and Mn concentrations reflect zoning in some of the concretion calcites examined. Covariations between these minor and trace elements differ greatly both between formations and between samples within a single formation. From limited temporal information it appears that the availability of Mg and Fe was greatest relatively early in diagnesis, whereas Mn was mobilized in at least two distinct pulses, one early and one late. 

Transformation of the original data to a new coordinate system is another possibility of data pretreatment. The methods are based on principal component analysis (PCA) or factor analysis (FA). The first step for these transformations is the formation of a data matrix that is derived from the original data matrix and that reflects the relationships among the data. Such derived data matrices are the variance-covariance matrix and the correlation matrix. 

The two large-scale cormnercial vendors of spectrometer-independent NMR software currently offer covariance processing as a feature of their spectral manipulation and interpretation suites. The Spectrus platform by ADC/Labs and the MNova by Mestrelab Research provide stand-alone solutions that allow the import of all spectrometer data formats without the necessity of pre-processing. Covariance processing can be performed according to the direct, indirect, and generalized indirect formalism. The doubly indirect covariance transformation is formd in MNova. While... 

Spectrus ACD/Labs Data format independent direct, indirect, unsymmetrical and generalized indirect covariance processing http //WWW. acdlabs.com/ products/ spectrus/... 

Topspin 3.0 Bruker Biospin AG Bruker data format User http //www. program (au) for direct bruker.com and indirect covariance processing ... 

COLMAR Rafael Briischweiler, Florida State University and National High Magnetic Field Laboratory Metabolomics Web portal NMILPipe, Varian, Bruker data format direct and indirect covariance processing with optional water removal also available DemixC, query, TOCCATA query [55,56] http // spinportal. magnet.fsu.edu... 

Covariance Toolbox David Snyder MATLAB/GNU OCTAVE base NMRPipe data format direct, indirect, 4D, generalized indirect and Z-matrix processing [57] http //WWW. mathworks. com/ matlabcentral/ fileexchange/ 27264- covariance-nmr- toolbox... 

Nmrglue Data-independent format various processing feature can be used for data preparation for use with Covariance Toolbox [58] http //mnrglue. com... 

The cross-correlation plot shown in Eig. 5.4 between the mean summer and spring temperatures has a similar format to the previously considered autocorrelation plot. The confidence interval is, as was previously noted, the same as for the autocorrelation plot. The salient feature is the 4 largest lags at —20, —16, 3, and 4. At this point, it would be useful to comment briefly about the meaning of these values. Since the formula for computing the cross-covariance can be written as or equivalently yt = Xf we can see that positive values correspond to a relationship between past values of x (or in our case, the mean spring temperature)... 

As shown in Appendix 2, the covariance of muscovite and san-idine enthalpies reduces the overall standard error of the enthalpy of reaction from 960.6 cal. to 278.6 cal., but the standard error of the free energy of reaction is only reduced from 1116 cal. to (278.6 + 929 x 0.611 ) or 632.3 cal. and the temperature standard error is reduced from 59 C to 632.3/19.0 or 33°C. These numbers check very well with Monte Carlo simulations. The determination of the enthalpy of formation of corundum was by combustion calorimetry and not solution calorimetry, so its variance is independent of those of the other phases. 

---