Choosing appropriate metrics

Chapter 4—Choosing Appropriate Metrics based on identified process safety goals and objectives... 

Having shown that NESC may be formulated as an unnormalized Foldy-Wouthuysen transformation, it appears natural to proceed to a normahzed Foldy-Wouthuysen transformation. The normalization must be defined on the appropriate metric, here denoted G", for which the positive-positive block must be S. As we are no longer concerned with the negative-energy states, we can choose the negativenegative block arbitrarily. The normalized transformation can then be expressed in terms of the unnormalized transformation by... 

This example shows that given a 10% final demand perturbation for both sectors, the resulting total inoperability for Sector 1 will be 19%, which is equivalent to a 190 loss in its total output. By the same token, the total inoperability for Sector 2 will be 13%, which is equivalent to a 260 loss in its total output. From this illustrative example, we have demonstrated that the ranking of key sectors may vary between the two metrics (i.e., economic loss vs. total inoperabiUty). A policymaker that puts more weight on inoperability will choose to prioritize Sector 1. On the other hand, the policymaker will opt to prioritize Sector 2 when economic loss is used as the sole criterion. Hence, a balanced approach that takes into consideration policymaker preferences across economic loss, inoperability, and other appropriate metrics will result in a more holistic method for key sector identification and prioritization. 

Consider a set of molecules A,B,C,... with electron densities p (r), pg(r), pc(r)> and level sets G (fl),Gg(fl),Gc(a),respectively, for each density threshold value a. By choosing an appropriate definition for fuzzy membership function describing the fuzzy assignment of points r of the three-dimensional space to each molecule, such as the membership function /x (r) = p. (r)/p of Eq. (20) or = 1 - exp(- rpj(r)) of Eq. (21), the density-scaled fuzzy Hausdorff-type metric f p(A,B) applies... 

Even if the metrics are collected, without appropriate resources, the data may not be analyzed and reported to management. If lull support for the plan is not achieved, the persons charged with implementation may choose to reduce the... 

It is probably correct to say that successful application of simulated annealing requires a clever definition ofndghborhoods in the configuration space (i.e., specification of individual "moves") and a ju dous variation of the control parameter p. In the case of metric spaces we would like to have a rationale for choosing an appropriate step size and for specifying a priori an effective cooling schedule. 

To see whether the condition (9-320) provides the added input that is required for determining 0o(VO hi the closed-streamline region, it is convenient to express it in terms of the independent variables f and rj (which we choose as lines orthogonal to cylindrical coordinates (r, < />). To do this, we need only introduce the appropriate scale or metric factors for the (coordinate system, h,/, and hri. The reader is reminded that these scale factors are defined such that the length of a differential line element, expressed in the (f, >]) system, takes the form... 

The interpretation of the response of an assembly of microelectrodes to a cyclic voltam-metric waveform is more complicated than in the case of chronoamperometry. When applied to microelectrode arrays, it is mainly used in the steady-state limit. From an elec-troanalytical point of view, the major issue is to choose an appropriate scan rate v to ensure steady-state diffusion at the array interface. If the scan rate is not properly chosen, a peakshaped voltammogram is observed whose characteristics can be derived only from simulations (188). Figure 10.18 shows simulated cyclic voltammograms obtained at an infinite number of microdisks (r = 10 pm) in a hexagonal array with d/r ranging from 3 to 100 and d ranging from 20 to 1000 pm. 

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