One-component model

Three-Dimensional One-Component Model for Distortive Phase Transitions. 

Fig. 28. Bivariate example of bayesian confidence ellipses and SIMCA one-component models in a case of complex distributions. The direction of SIMCA components is not the same as the main axes of the ellipses because of the separate scaling used in SIMCA...

A. Christofferson, The One-Component Model with Incomplete Data, Thesis, Univ. Uppsala, Sweden (1970). 

Figure 11. Experimental osmotic coefficient data (X) [41, 112] for bovine serum albumin (BSA) and the corresponding multicomponent model results (full line) at pH = 5.4. For pH = 7.3, experimental data are denoted by (+) and one-component model results by the dashed line.

Our analysis indicates no self-association of protein molecules for BSA solutions [112] at pH = 5.4 and 7.3 (Fig. 11). The fraction of dimers giving good agreement with experiment in this case is zero this holds true for both the one-component [41] and the multicomponent model. The results obtained by the two theoretical models for pH = 5.4, where experimental results are denoted by (x), practically coincide. Experimental data for pH=7.3, are denoted by (+) and one-component model results by the dashed line. In this case no IET results since the multicomponent model could be obtained for concentrations above 330 g/dm-3 and therefore only one-component calculations are shown. 

Belloni, L. Electrostatic interactions in colloidal solutions - comparison between primitive and one-component models. Journal of Chemical Physics, 1986, 85, No. 1, p. 519— 526. 

Kalyuzhnyi, Yu.V., Rescic, J., and Vlachy, V. Analysis of osmotic pressure data for aqueous protein solutions via a one-component model. Acta Chimica Slovenica, 1998, 45, No. 2, p. 194-208. 

There are a number of properties of water ice that make it an ideal one-component model... 

The modelling process constitutes a projection of the object points in each space down to PLS components. The projections are made so that the variations in the swarm of points are well described by the PLS components with the constraint that for each PLS dimension, j, the PLS scores of the Y block (denoted Wj) should have a maximum correlation to the scores of the X block (denoted Zj). The principles are illustrated by a one-component model in Fig. 17.3. 

A plot similar to a scree plot can be made for PARAFAC, by plotting the sum of squares of the individual components. However, in this case, cumulative plots cannot be made directly because the variances of the individual factors are not additive due to the obliqueness of the factors. Furthermore, the sum of squares of the one-component model may not equal the size of the largest component in a two-component model. Hence, the scree plot is not directly useful for PARAFAC models. The cumulative scree plot for PARAFAC models, on the other hand, can be constructed by plotting the explained or residual sum of squares for a one-component model, a two-component model, etc. This will provide similar information to the ordinary two-way cumulative scree plot, with the exception that the factors change for every model, since PARAFAC is not sequentially fit. The basic principle is retained though, as the appropriate number of components to use is chosen as the number of components for which the decrease in the residual variation levels off to a linear trend (see Example 7.3). 

It is clear from the graphical representation in Figure 10.15 that at four components, all four models provide similar results whereas this is not the case for other numbers of components. The only other case is the one-component model (not shown) which is not relevant for other reasons (low variance as evidenced in Figure 10.11). 

Campbell [83] proposed a model that uses the syllable as the fundamental unit of duration. In this a syllable duration is predicted from a set of linguistic features after which the individual phone durations within the syllable are then calculated. This approach has the attraction in that it is more modular, where we have one component modelling the prosodic part of the duration and another modelling the phonetic part. 

The E statistic compares a PLS model of i components with the model containing one component less and, in order to evaluate PRESS for the one component model, PRESS for the model containing no components is calculated by comparing predicted values with the mean. A critical value of 0.4 has been suggested for E (Wold 1978) and when this is exceeded, the PLS equation with i components is doing no better (or worse) in prediction than the model with i—1 latent variables. 

Schneider T, StoU E Molecular dynamics study of a three-dimensional one-component model for distortive phase transitions, Phys Rev B 17 1302—1322, 1978. 

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