Inherent dimensionality,

Soft and topologically adaptable supramolecular modules that allow host lattices to achieve dense packing through low-energy deformations, while retaining their inherent dimensionality and supramolecular connectivity, can facilitate the systematic design of molecular inclusion compounds. This is demonstrated by the ability to predict and maintain architectural control in a series of lamellar host frameworks. 

The model diagnostic tools suggest the inherent dimensionality of this data set is 2. th two principal components, the percent variance described is 99.4% and the residuals appear reasonably random and are small in magnitude. The RMSECV PCA is not revealing, but also does not contradict this conclusion. 

Used to deteimine the number of relevant PCs (i.e., inherent dimensionality) and interpret the ( agnostics that follow. 

With problematic data the inherent dimensionality that is indicated is not consistent with what is expected. 

As the niunber of PCs used in the model approaches the inherent dimensionality the residuals decrease in magnitude and become more random. 

Measunment Residual Plot (Model, Sample, and Variable Diagnostic) Figure 4.3 c shows the residuals after using 1, 3, and 4 principal components, respctively. The residuals have been convened back from the autoscaled ui to the original measurement imits to facilitate comparisons. In this exampfe these plots do not definitively indicate the inherent dimensional-it> of the dan set. 

A common approach to cross-validation is called leave-one-out" cross-validation. Here one sample is left out, a PC model with given number of factors is calculated using the remaining samples, and then the residua of the sample left out is computed. This is repeated for each sample and for models with 1 to n PCs. The result is a set of cross-validation residuals for a given number of PCs. The residuals as a function of the number of PCs can be examined graphically as discussed above to determine the inherent dimensionality. In practice, the cross-validation residuals are summarized into a single number termed the Root Mean Squared Error of Cross Validation for PCA (RMSECV PCA), calculated as follows ... 

The RMSECV PCA values are plotted versus the number of PCs to determine the inherent dimensionality. Ideally, the RMSECV PCA will decrease quiddy and... 

The loadings plot is also examined for inherent dimensionality and unusual variables. No conclusions can be drawn because of the limited utility of this diagnostic when examining data sets comprised of discrete measurement variables. 

Numerous attempts to interpret the Stefan-Ostwald constant in terms of molecular models have been reviewed by Partington Some of the proposed equations contain, not surprisingly, or with the inherent dimensional problem of non-integer powers of numbers of moles. Others contain the latent heat of evaporation, or or both. By way of illustration Abdulnur found that... 

Polysulfone parts can be joined with aU the processes described in this chapter. Because of their inherent dimensional stability and creep resistance, polysulfone parts can be press fitted with ease. Generally, the amount of interference wUl be less than that required for other thermoplastics. Self-tapping screws and threaded inserts have also been used. 

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