Correlation function fingerprint

In many investigations dynamic-mechanical properties have been determined not so much to correlate mechanical properties as to study the influence of polymer structure on thermo-mechanical behaviour. For this purpose, complex moduli are determined as a function of temperature at a constant frequency. In every transition region (see Chap. 2) there is a certain fall of the moduli, in many cases accompanied by a definite peak of the loss tangent (Fig. 13.22). These phenomena are called dynamic transitions. The spectrum of these damping peaks is a characteristic fingerprint of a polymer. Fig. 13.23 shows this for a series of polymers. 

The spin-related section mle can be proved by elastic neutron scattering measurements. In order to establish the specific fingerprint of the spin correlation, the scattering functions for the linear harmonic oscillator, for the double-well minimum function, and for pairs of coupled oscillators have been calculated in Ref. 119. 

Fig. 3. Statistical models a Correlation between the product of sets sizes and the mean of the raw score. The fitted function typically corresponds to an equation of the formula = mxn + p with n = 1. b Correlation between the product of sets sizes and the standard deviation of the raw score. The fitted function typically corresponds to an equation of the formula ya=qxr+ s, with 0.6

How does this example apply to the use of multiple similarity methods Each of the similarity methods can be considered to be equivalent to an independent judge, since none of the values produced by the other methods have an explicit impact on the value produced by a given method. This may not always be the case, for example, if two methods use MACCS key fingerprints, but one uses the Tanimoto (Jacard) and the other a closely related similarity function (see Table 15.3). As shown by Gower [76], some molecular similarity functions are monotonically related. Thus, comparisons of these functions based on the same molecular representation will produced linear correlations of the values computed by the two functionally similarity functions. Hence, only one of the functions should be used. 

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