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The PCA modeling forms the basis for several classi cation and regression methods. The underlying idea is to replace a complex multidimensional data set by a simpler version having fewer dimensions, but still tting the original data closely enough to be considered a good approximation. Extracting information from a data table consists of exploring variations between samples, that is, nding out what makes a sample different from, or similar to, another. Two samples can be described as similar if they have close values for most variables. From a geometric perspective, in the case of close coordinates in the multidimensional space of variables, the two points are located in the same area. Likewise, two samples can be described as different if their values differ greatly with respect to at least some variables. The two points have different coordinates and are located far away from each other in the multidimensional space. An illustration of this geometrical concept is proposed in Figure 19. The principle of PCA consists of nding the directions in space known as principal components (PCs) along which the data points are furthest apart. It requires linear combinations of the initial variables that contribute most to making the samples different from each other. PCs are computed iteratively, with the rst PC carrying the most information, that is, the most explained variance, and the second PC carrying most of the residual information not taken into account by the previous PC, and so on. This process can go on until as many PCs have been computed as there are potential variables in the data table. At that point, all between-sample variation has been accounted for, and the PCs form a new set of axes having two

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(1) ludicello, F. and Baseley, S. (1999) CFD modelling of the flow control valve in a hydraulic valve, Bath Workshop on Power Transmission and Motion Control (PTMC99). Sorensen, H. L. (1999) Numerical and experimental analysis of flow and fluid force characteristics for hydraulic seat valves with difference in shape, Bath Workshop on Power Transmission and Motion Control (PTMC99). Halworth, D. C., Maguire, J. M., Rhein, R., and El Tahry, S. H. (1996) Dynamic fluid flow analysis of oil pumps, SAE/960422. Kubota, A., Kato H., and Yamaguchi, H. (1992) A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section, J. Fluid Mech., 240, 59-96. STAR-CD Version 3.10 Methodology and User Guide 1999, Computational Dynamics Limited, London. Launder, B. and Spalding, D. B. The numerical computation of turbulent flows, Comp. Meth. Appl. Mech. Engng, 3, p. 269. Hirt, C. W. and Nichols, B. D. (1981) Volume of fluid (VOF) method for the dynamics of free boundaries, J. Comp. Mech., 39, 201-225. Ubbink, O. (1996) Numerical Prediction of Two Fluid Systems with Sharp Interfaces, PhD thesis, Imperial College of Science, Technology, and Medicine.

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Output Levels: Use these options to curtail the range of brightness levels in an image by lightening the darkest pixels and darkening the lightest pixels. You adjust the brightness of the darkest pixels those that correspond to the black Input Levels slider triangle by entering a number from 0 to 255 in the first option box or by dragging the black slider triangle. For example, if you raise the value to 55, no color can be darker than that brightness level (roughly 80 percent black), which lightens the image as shown in the first example of Figure 17-19. You adjust the brightness of the lightest pixels those that correspond to the white Input Levels slider triangle by entering a number from 0 to 255 in the second option box or by dragging the white slider triangle. If you lower the value to 200, no color can be lighter than that brightness level (roughly 20 percent black), darkening the image as shown in the second example of Figure 17-19. In the last example of the figure, I raised the first value and lowered the second value, thereby dramatically decreasing the amount of contrast in the image. You can fully or partially invert an image using the Output Levels slider triangles. Just drag the black triangle to the right and drag the white triangle to the left past the black triangle. The colors flip, whites mapping to dark colors and blacks mapping to light colors.

Everyone has a different idea of what security should be and what degree of risk is tolerable. However, a crucial point to remember when building an IT network is to define what security means to your corporation. A corporatelevel security policy is crucial to establishing an effective barrier to intruders. A security policy is a set of guidelines adopted by the corporation to protect users, systems, and data. It serves as the fountainhead for architecting the network, implementing security, and resolving conflicts.

Figure out what elds to add to represent the relationship between the Orders and OrderItems tables.

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