Programmed optimization criteria

Based on the optimization criterion, SpinPro can select the most appropriate rotor. For example, suppose the investigator has a relatively large sample volume, all of which needs to be processed as soon as possible. The "minimize cumulative run time" criterion would be the appropriate choice. SpinPro would then initiate the following rotor selection procedure SpinPro determines the total sample volume based on inputs of the sample volume, the current concentration of the sample, and a correction for any pre-run dilutions of the sample. Next, consideration is made for whether tubes or bottles will be used. The program then evaluates rotors for the number of tube positions and the amount of sample per tube. At this point, SpinPro will have estimated for each rotor the number of runs required to process the sample. SpinPro then estimates the run time for each rotor to perform a single run. Based on these estimates, SpinPro selects the rotor that will give the shortest total run time when the run time is summed over the total number of runs. Similarly, the investigator can select any of the optimization criteria and initiate a variety of precise rotor selection procedures. 

Figure 6.12a shows the resulting optimal chromatogram for the separation of a mixture of seven barbiturates by programmed solvent RPLC This figure was obtained with the following optimization criterion ... 

If the retention vs. composition plots of all solutes are known, then it is in principle possible to calculate the optimum program parameters for a simple, continuous gradient (figure 6.2a-d). In such a procedure an appropriate optimization criterion can be selected such that the distribution of all the peaks over the chromatogram, as well as the required analysis time, can be taken into account (see chapter 4). 

Typically, resolution diagrams in MLC are complex, with several local maxima, frequently denoting interaction between factors. For this reason, reliable optimal conditions require considering all factors simultaneously, by applying an interpretive optimization strategy (i.e., based on the description of the retention behavior and peak shape of solutes). In this task, the product of free peak areas or purities has proved to be the best optimization criterion. An interactive computer program is available to obtain the best separation conditions in... 

An alternative procedure is the dynamic programming method of Bellman (1957) which is based on the principle of optimality and the imbedding approach. The principle of optimality yields the Hamilton-Jacobi partial differential equation, whose solution results in an optimal control policy. Euler-Lagrange and Pontrya-gin s equations are applicable to systems with non-linear, time-varying state equations and non-quadratic, time varying performance criteria. The Hamilton-Jacobi equation is usually solved for the important and special case of the linear time-invariant plant with quadratic performance criterion (called the performance index), which takes the form of the matrix Riccati (1724) equation. This produces an optimal control law as a linear function of the state vector components which is always stable, providing the system is controllable. 

In an earlier section, we had alluded to the need to stop the reasoning process at some point. The operationality criterion is the formal statement of that need. In most problems we have some understanding of what properties are easy to determine. For example, a property such as the processing time of a batch is normally given to us and hence is determined by a simple database lookup. The optimal solution to a nonlinear program, on the other hand, is not a simple property, and hence we might look for a simpler explanation of why two solutions have equal objective function values. In the case of our branch-and-bound problem, the operationality criterion imposes two requirements ... 

Table 1 summarizes several of the experimental methods discussed in this chapter. A need exists for new or revised methods for transport experimentation, particularly for therapeutic proteins or peptides in polymeric systems. An important criterion for the new or revised methods includes in situ sampling using micro techniques which simultaneously sample, separate, and analyze the sample. For example, capillary zone electrophoresis provides a micro technique with high separation resolution and the potential to measure the mobilities and diffusion coefficients of the diffusant in the presence of a polymer. Combining the separation and analytical components adds considerable power and versatility to the method. In addition, up-to-date separation instrumentation is computer-driven, so that methods development is optimized, data are acquired according to a predetermined program, and data analysis is facilitated. 

These screening approaches require minimum information for the evaluation of pharmaceutically relevant properties. Compounds that do not meet a predetermined criterion are eliminated from further consideration. Guidance is obtained for further structure optimization via synthetic modification. Thus, pharmaceutical properties are assessed on the timescale of compound synthesis, resulting in an optimization while programs are still active. Therefore, unfavorable candidates are eliminated early and resources are focused on more promising drug candidates. 

As with programmed temperature GC, the application of the Simplex optimization procedure to programmed solvent LC is relatively straightforward. The same procedure can be used both for isocratic and for gradient optimization, as long as an appropriate criterion is selected for each case. ... 

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