ROBUST Project

Since variance is very sensitive to outliers, the classical PCA is non-robust. Instead, a more robust projective index V(z) is used in the PP PCA. 

Besides the measure of the dispersion of the one-dimensional projection i.e. the projective index, another distinction of PP PCA from the classical PCA is the procedure of computation. Since the projective index is the quadratic form of X as stated above, the extremal problem of Eqn. 1 can be turned into the problem of finding the eigenvalues and eigenvectors of the sample covariance matrix for which a lot of algorithms such as SVD, QR are available. Because of the adoption of the robust projective index in PP PCA, some nonlinear optimization approaches should be used. In order to guarantee the global optimum. Simulated annealing (SA) is adopted which is the main topic of this book. 

The classical PCA is non-robust and sensitive to deviations of error distribution from the normal assumption, the PC directions being influenced by the presence of outlier(s). In PP PCA, the PC directions are determinated by the the inherent structure of the main body of the data. Using some robust projective index, the influence of the outliers is thus substantially reduced. The distorted appearance or misrepresentation of the projected data structure in the PC subspace caused by the presence of outlier(s) could be eliminated in PP PCA. This characteristic feature of PP PCA is essential for obtaining reliable results for exploratory data analysis, calibration and resolution in analytical chemometrics where PCA is used for dimension reduction. 

Our interview data show, however, that these finance capabilities are lacking in many firms. One respondent in Zimbabwe remarked that the firms were afraid to approach international banks because they are not able to produce a robust project proposal and are afraid of being asked questions. Crafting a project proposal requires knowledge of the firms ... 

Another useful profitability indicator is the internal rate of return (IRR), already introduced in the last section. This shows what discount rate would be required to reduce the NPV to zero. The higher the IRR, the more robust the project is, i.e. the more risk it can withstand before the IRR is reduced to the screening value of discount rate. Screening values are discussed below. 

In order to test the economic performance of the project to variations in the base case estimates for the input data, sensitivity analysis is performed. This shows how robust the project is to variations in one or more parameters, and also highlights which of the inputs the project economics is more sensitive to. These inputs can then be addressed more specifically. For example if the project economics is highly sensitive to a delay in first production, then the scheduling should be more critically reviewed. 

Therefore, as it is mentioned in the AR4, climate projections for the end of the century depend on the scenario and the particular model used to develop them. Temperature changes, and especially precipitation changes, show, for such temporal horizon, a broad range of values. On the other hand, projections for the next 2-4-decades are quite robust, since they depend less on long-term feedbacks and also on future greenhouse gases emissions. In fact, the climate of the next few years is tightly determined by past and recent emissions (climate commitment). 

Successful management of a central HTS operation requires a discipline of process control that extends beyond the automation systems. The progression of HTS projects must be carefully guided and tracked through several milestones designed to ensure that a steady and predictable stream of robust assays are available for transfer to the automation platforms and that sufficient bulk reagents and consumable supplies will arrive in time to support the HTS campaigns. 

As such, an asymmetric synthesis of tarantabant had been demonstrated centered around a DKR as the key step to set both stereocenters in a single catalytic step. The synthesis proceeded in six steps and 40% yield from the ketone rac-13. This route was found to be robust and reliable and generated in excess of 70 kg of API in various campaigns from both preparative laboratories and pilot plant facilities, and provided support for the project through longer term toxicology and clinical studies [13]. 

Since most drug discovery projects deal with very sparingly soluble compounds, the usual CE sample concentration would lead to precipitation. The handling of real dmg candidate molecules is poorly developed in CE applications, in comparison to the most robust potentiometric method. 

In order to achieve flexibility, sensitivity, and robustness, I plot departures of the variables of interest from specified reference values. A bar projecting to the right of the middle of the panel indicates a value larger than the reference value. A bar projecting to the left indicates a smaller value. The length of the bar is proportional to... 

A 40-km x 40 km sample spacing for the North American project will provide soil geochemical and mineralogical data that will display coherent and robust regional to continental-scale patterns, as also demonstrated by Smith and Reimann (2008). 

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