Interpretable factors

The aim of factor analysis is to calculate a rotation matrix R which rotates the abstract factors (V) (principal components) into interpretable factors. The various algorithms for factor analysis differ in the criterion to calculate the rotation matrix R. Two classes of rotation methods can be distinguished (i) rotation procedures based on general criteria which are not specific for the domain of the data and (ii) rotation procedures which use specific properties of the factors (e.g. non-negativity). 

The rotation of the factor solution is a tool to assist the ability to interpret factor loadings. The factor structures computed as explained above often have a shape which assigns nearly all features to the first factor. Interpretation of the contribution of features to this factor is, therefore, usually not possible. Although rotation of the coordinate system of factors will not affect the position of the objects relative to each other, it can be used to simplify the factor structure. Now one has to decide between the possibilities for rotation - they are infinite. THURSTONE (1965) [WEBER, 1974] developed some criteria for the so-called simple structure ... 

The predictive ability of the resulting model is assessed by validation, using test sets of ligands and biopolymers. When its validity has been confirmed, the proteochemo-metric model can be used for predicting the activity of novel biopolymers and ligands and for interpreting factors that determine biopolymer-ligand interactions. 

The key to the ethics of such studies is informed consent from patients, efficient scientific design and review by an independent research ethics committee. The key interpretative factors in the analysis of trial results are calculations of confidence intervals and statistical significance.The potential clinical significance needs to be considered within the confines of controlled clinical crials.This is best expressed by stating not only the percentage differences, but also the absolute difference or its reciprocal, the number of patients who have to be treated to obtain one desired outcome.The outcome might include both efficacy and safety... 

Varimax rotation is a commonly used and widely available factor rotation technique, but other methods have been proposed for interpreting factors from analytical chemistry data. We could rotate the axes in order that they align directly with factors from expected components. These axes, referred to as test vectors, would be physically significant in terms of interpretation and the rotation procedure is referred to as target transformation. Target transformation factor analysis has proved to be a valuable technique in chemo-metrics. The number of components in mixture spectra can be identified and the rotated factor loadings in terms of test data relating to standard, known spectra, can be interpreted. 

To transform the abstract factors determined in the first step into interpretable factors, rotation methods are applied. If definite target vectors can be assumed to be contained in the data, for example, a spectrum under a spectrochromatogram, the rotation of data is performed by using a target. This technique is known as target-transform factor analysis TTFA, c Example 5.6). 

The kt data are for systems at low monomer conversion, the conditions at which most measurements are conducted. Significant scatter, as much as an order of magnitude, is found in the data contained in reference 5, as reflected in the vinyl acetate kt data. The uncertainty arises from a number of measurement and interpretation factors [11]. The rest of the data are based on PLP studies, and have a higher level of... 

Table 6.1 Rules of thumb" to use in interpreting factors governing oil well corrosion...

Values between these ranges are mere difficult to interpret. Factors such as equilibria between solvent-exposed and solvent-shielded conformers or hydrogen-bonded species, as well as noncoplanarity of intramolecular hydrogen bonds, may be invoked. 

The other parameters used in the calculation of STOMP and GIIP have been discussed in Section 5.4 (Data Interpretation). The formation volume factors (B and Bg) were introduced in Section 5.2 (Reservoir Fluids). We can therefore proceed to the quick and easy deterministic method most frequently used to obtain a volumetric estimate. It can be done on paper or by using available software. The latter is only reliable if the software is constrained by the geological reservoir model. 

Table 1 Influence of various factors on the use of AI techniques for NDT data interpretation.

For interpretation of measuring results, calibration characteristics obtained on the samples in advance is used in the above instruments. However, if number of impediment factors increases, the interpretation of the signals detected becomes more complicated in many times. This fact causes the position that the object thickness T and crack length I are not taken into consideration in the above-mentioned instruments. It is considered that measuring error in this case is not significant. 

The interpretation of MAS experiments on nuclei with spin / > Fin non-cubic enviromnents is more complex than for / = Fiuiclei since the effect of the quadnipolar interaction is to spread the i <-> (i - 1) transition over a frequency range (2m. - 1)Vq. This usually means that for non-integer nuclei only the - transition is observed since, to first order in tire quadnipolar interaction, it is unaffected. Flowever, usually second-order effects are important and the angular dependence of the - ytransition has both P2(cos 0) andP Ccos 9) terms, only the first of which is cancelled by MAS. As a result, the line is narrowed by only a factor of 3.6, and it is necessary to spin faster than the residual linewidth Avq where... 

The factor A has been measured for a variety of samples, indicating that the approximation can be applied up to quasi-atomic resolution. In the case of biological specimens typical values of are of the order of 5-7%, as detemiined from images with a resolution of better than 10 A [37,38]- For an easy interpretation of image contrast and a retrieval of the object infomiation from the contrast, such a combination of phase and amplitude hifomiation is necessary. 

He observed an f-factor of 3 and argued for the formation of the di-protonated acid. He interpreted the high electrical conductivity of these media in support of this. 

In a later paper Knowles and Norman compared more fully nitrations of benzylic compounds in acetyl nitrate and in mixed acid (table 5.9), and interpreted the results in terms of three factors nitronium ion nitration in both media some degree of protonation of the oxygen... 

You can interpret the stereochemistry and rates of many reactions involving soft electrophiles and nucleophiles—in particular pericyclic reactions—in terms of the properties of Frontier orbitals. This applies in particular to pericyclic reactions. Overlap between the HOMO and the LUMO is a governing factor in many reactions. HyperChem can show the forms of orbitals such as HOMO and LUMO in two ways a plot at a slice through the molecule and as values in a log file of the orbital coefficients for each atom. 

These data are typical of lasers and the sorts of samples examined. The actual numbers are not crucial, but they show how the stated energy in a laser can be interpreted as resultant heating in a solid sample. The resulting calculated temperature reached by the sample is certainly too large because of several factors, such as conductivity in the sample, much less than I00% efficiency in converting absorbed photon energy into kinetic energy of ablation, and much less than 100% efficiency in the actual numbers of photons absorbed by the sample from the beam. If the overall efficiency is 1-2%, the ablation temperature becomes about 4000 K. 

On the basis of both thermodynamic and kinetic evidence-both of which are interpretable in terms of the strain associated with rings of certain sizes or similar structural factors we see that only rings with five or six atoms have any significant stability. Accordingly, we conclude the following ... 

Since rather than

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