Correlation approach

A more sophisticated statistical method for the characterization of diversity is to examine how the individual descriptors for each compound correlate with the average set descriptor (ASD). In low diversity data sets, the correlation coefficients will tend to reach 1.0, and their distribution will be small. 

FIGURE 6.12 Distribution of the correlation coefficients between individual descriptors and the ASD for high-diversity data (185 arbitrarily chosen organic compounds) and low-diversity data (185 benzene derivatives). 

The mean and standard deviation of correlation coefficients seems to be a reliable diversity measure. However, as mentioned in the theoretical section, the reliability of the correlation coefficient itself depends on the symmetry of distribution within a descriptor skewness or kurtosis should be regarded if a data set has to be classified as similar or diverse. 

Due to the characteristic shape, almost any raw RDF descriptor is skewed It typically exhibits an asymmetric tailing and is leptokurtic (flatted in relation to the Ganssian distribntion knrtosis 0). Depending on the descriptor type, the size, and the symmetry of a molecule, the skewness or kurtosis of a raw RDF descriptor may also show asymmetric fronting or platykurtic behavior (peaked in relation to the Ganssian distribntion kurtosis 0). As the general behavior applies to most of the RDF descriptors, it is no fault to neglect this skewness and to assume a skewed standard distribntion within the descriptor set. 

Checking the skewness distribution for outliers provides a fast method to determine if few individual structures do not fit in the data set (Fignre 6.13). The three ontliers with a descriptor skewness of 4.0 and higher are (1) hydrazine (2) thionyl chloride and (3) ammonium chloride — three compounds that are not representative for the wide variation of organic strnctnres in the remaining data set. 

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This summary of correlating approaches is far from complete. The focus herein is primarily on pure components, although the phase equiHbrium... 

The essential weakness of the correlation approach is that it lacks a linkage to molecular events. A correlation is not a cause-effect relationship. Nevertheless, with sufficient weight of evidence it becomes reasonable to seek an underlying... 

Arnold, R. J. Reilly, J. P. Fingerprint matching of E. coli strains with matrix-assisted laser desorption/ionization time-of-flight mass spectrometry of whole cells using a modified correlation approach. Rapid Commun. Mass Spectrom. 1998,12,630-636. 

Encouraged by this spectral reproducibility, we focused our efforts on the particularly challenging problem of distinguishing bacterial strains by MALDI MS. We developed a modified correlation approach22 that relies on two fundamental qualities of bacterial mass spectra. First, because different bacterial strains of the same species have substantial, if not complete, genetic overlap, most of the protein masses observed with two different strains will be identical. This feature limits the value of the biomarker approach that is commonly used to differentiate bacteria species. Second, as just noted, closely controlled sample preparation and mass analysis procedures can result in highly reproducible results.22 The modified correlation approach takes advantage of subtle, yet reproducible, differences in mass spectra obtained from dif-... 

While this chapter has described two examples of our efforts in bacterial strain identification, a number of other groups have contributed to this research area. It remains to be seen whether mathematical algorithms such as the modified correlation approach described herein are always more effective for strain assignments than the simple use of distinctive biomarker peaks. Nilsson reported MALDI mass spectra of Helicobacter pylori with three different matrices and solvent conditions.59 She showed that some strains of this bacteria yield rather similar mass spectra while others are quite different. Nevertheless, each strain appears to exhibit some unique peaks that might be used for distinguishing strains. 

Prediction methods based on animal pharmacokinetic data can be categorized into three types (1) allometric scaling, (2) proportionality methods, and (3) correlative approaches. All three make a basic underlying assumption that the types... 

Schreiner CA, Holden HE Jr. 1983. Mutagens as teratogens A correlative approach. Handbook of Experimental Pharmacology 65 135-168. 

Unfortunately, most of the correlation efforts to date with IR dosage forms have been based on the correlation Level C approach, although there also have been some efforts employing statistical moment theory (Level B). Level A correlation approach is often difficult with IR dosage forms because of the need to sample intensively in the absorptive region of the in vivo study. Thus, Levels B and C are the most practical approaches for IR dosage forms, even though they are not as information-rich and therefore more limited in their application. 

The correlation presented in this paper can be very simply applied to phase-equilibrium calculations for concentrated electrolyte systems, however, care must be taken to remember that it is basically a correlational approach and not a molecular model for aqueous electrolyte solutions. 

In summary, it appears that the state correlation approach represents a physically more realistic representation of the factors governing the formation of reaction barriers than the corresponding configuration treatment utilized in the bulk of this review. However, its practical utility as a readily applied model is handicapped by its more complex structure and the fact that its two-curve basis does not readily lend itself to the consideration of mechanistic variations. 

In adsorption chromatography, the energy of the interaction of a certain substance X with the pore surface and the variation of retention volumes depending on the polarity of the mobile phase are commonly assessed using Snyder s correlative approach 64). According to this approach, the energy of the interaction of substance X with adsorbent surface A from solvent S can be written as... 

Fig. 16.4. Three methods of obtaining Raman-based estimates of biofluid concentrations in vivo, a Confocal isolation of a subsurface volume occupied by a blood vessel, enabling direct measurement of a blood spectrum, b Difference measurement between tissue in two states, one with more blood in the sampling volume (in this case, due to pressure modulation by the subject [6]). Computing the difference removes the bulk tissue contributions to the spectral measurement and emphasizes the contribution from blood, c Statistical correlation approach of measuring many volunteers tissue in a region where sufficient blood is present (e.g., the forearm as shown here) and obtaining a correlated reference value from a blood sample drawn at the same time. Multivariate calibration is then used to find correlations between the reference value and the spectral data vector. Unlike the previous two methods, this does not intrinsically isolate the blood chemicals Raman signatures from those of the surrounding tissue volume...

Comparing to the accelerated life test where only the life distribution under a given stress level is recorded, the accelerated degradation test keeps track of the evolution of a damage metric (Fr), which allows the experimental validation of the correlation approach if the selected damage metric is observable. For example, the projected life distribution under normal stress can sometime... 

Furthermore, the link of the shared asset capacity to the overall plant capacity has to be determined. If the equipment capacity is to be selected by the optimization model, an additional integer decision variable is required. Alternatively, a fixed capacity or a capacity correlated with overall plant capacity (e.g., 50% of total plant capacity or one unit for every two production lines) can be assumed. Additional restrictions are required if the correlation approach is to be combined with the modular capacity concept. The choice of the most appropriate variant depends on the characteristics of the equipment considered and the effects on overall model complexity. 

The usual correlation approach is then to determine the parameters A and B in the equation... 

The "correlative" multi-scale CFD, here, refers to CFD with meso-scale models derived from DNS, which is the way that we normally follow when modeling turbulent single-phase flows. That is, to start from the Navier-Stokes equations and perform DNS to provide the closure relations of eddy viscosity for LES, and thereon, to obtain the larger scale stress for RANS simulations (Pope, 2000). There are a lot of reports about this correlative multi-scale CFD for single-phase turbulent flows. Normally, clear scale separation should first be distinguished for the correlative approach, since the finer scale simulation need clear specification of its boundary. In this regard, the correlative multi-scale CFD may be viewed as a "multilevel" approach, in the sense that each span of modeled scales is at comparatively independent level and the finer level output is interlinked with the coarser level input in succession. 

Correlation approach Objective is to determine if there is a consistent relationship between the concentration of the suspected toxicant(s) and effluent toxicity. A wide range of toxicity responses with several samples must be obtained in order to provide an adequate range of effect concentrations for analysis. Two key problems associated with the correlation approach are 1) lack of additivity requires careful data analysis, and 2) analysis is difficult when matrix effects are present. 

This type of correlative approach is widespread, as only a few marine studies involving inducible defenses (and none with mobile invertebrates) have directly demonstrated that the induction results in a decrease in the susceptibility of the organism to predation.71,72 Statistically significant differences in shell thickness or concentrations of defensive chemicals may or may not meaningfully affect predator preferences in ecologically relevant field situations. For chemical defenses, compound dose-response relationships may be nonlinear, and threshold levels of defense could be sufficient to deter predators so that further induction has little additional benefit. Thus, future studies should focus on directly demonstrating whether an induced response reduces predation on prey organisms. 

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