Graphs vector graphics

The SIMCA method has been developed to overcome some of these limitations. The SIMCA model consists of a collection of PCA models with one for each class in the dataset. This is shown graphically in Figure 10. The four graphs show one model for each excipient. Note that these score plots have their origin at the center of the dataset, and the blue dashed line marks the 95% confidence limit calculated based upon the variability of the data. To use the SIMCA method, a PCA model is built for each class. These class models are built to optimize the description of a particular excipient. Thus, each model contains all the usual parts of a PCA model mean vector, scaling information, data preprocessing, etc., and they can have a different number of PCs, i.e., the number of PCs should be appropriate for the class dataset. In other words, each model is a fully independent PCA model. 

Analyze the following equations graphically. In each case, sketch the vector field on the real line, find all the fixed points, classify their stability, and sketch the graph of x(z) for different initial conditions. Then try for a few minutes to obtain the analytical solution for x(z) if you get stuck, don t try for too long since in several cases it s impossible to solve the equation in closed form ... 

The graphical representation of the Cl space is used to construct the sigma-vector. First the procedure for non-symmetry adapted graphs is given after which generalization to symmetry adapted Cl spaces is considered. 

CSs come in three flavors (1) coordinate based, (2) cell based, and (3) graph or network based. Multidimensional vectors with continuous, real-valued components define the positions of molecules in coordinate-based CSs. The value associated with each of the coordinates is obtained from one of a wide variety of property descriptors discussed in Sect 1.2.2.1. A simple 3-D example is given in Fig. 1.7a, but since these spaces are generally greater than dimension three, their graphic portrayal requires some type of reduction in the dimensionality of the space. Details of how this can be accomplished will be described in Sect 1.3.2. 

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