Structure of the Algorithm

The most important question that remains open concerns the search for an appropriate approach to the study of states having some spin orbitals with occupation numbers close to 0.5. The structure of the algorithms is what causes the difficulty, since the leading terms of the 2-RDM involve products of the type 0.5 X 0.5 = 0.25, which is much too small. In consequence, the value of the unknown elements is of the same order and can no longer be considered a small error. This is the case of many excited states for which the results have not been satisfactory up to now. 

The structure of the algorithm for the developed software is presented in Fig. 15.4. It integrates biosensor signal processing together with pesticide quantification algorithms and includes ... 

Figure 8 Logical structure of the algorithm for the construction of the numerators in the intermediates FjJKAC...

With privately used schemes, this secret may be the whole algorithm used. However, it was soon discovered that if a scheme is intended for widespread use, or to be carried out by machines, one cannot hope to keep the structure of the algorithm or the construction of the machines secret for a long time. Thus one divides the schemes intd algorithms, which may be public, and certain parameters, called keys, which have to remain secret. (See, e.g., [DiHe76] for a brief sketch after [Kahn67].)... 

The structure of the algorithm is shown in Figure 3. Three main classes of generic reactions are used in a systematic manner and are illustrated in Table 1. 

For each of the five blocks corresponding algorithms and programmes are developed. They can be activated manually or automatically. All blocks have a similar structure of the algorithm ... 

The structure of the algorithm is a section of preliminary calculations followed by an iterative loop which calculates the measurement and the associated error for each vial. At the end of the loop, preliminary calculations are made to measure the contribution each vial makes to the weighted average and error for the sample. The last program segment calculates the weighted average and error (Cochran, 1954, Cochran and Carroll, 1953, Hinkley, 1979, James, 1956). 

Figure 5.3 General structure of the algorithm for the advanced control approach. Adapted from Hristu-Varsakelis D, Shao C. A bio-inspired pursuit strategy for optimal control with partially constrained final state. Automatica 2007 43(7) 1265—1273.

It is not difficult to solve the steady-state optimization problems with constraints represented by algebraic equations by using commercial software packages. We mainly explain the dynamic optimization methods used in this work. The basic structure of the algorithm employed in this paper is shown in Figure 10. 

The correspondence between the investigated situation St and the optimal structure of the algorithm Si -> At, is realized by the function... 

The time dependency of additional parameters can be considered by two different approaches. On the one hand, there is variant I, which needs to compute the uncertain analysis for each time step Tj e T. The result is an uncertain process of the resptMise variable. This concept is highly time-consuming. The structure of the algorithm for fp-r variables is shown in Fig. 8. 

The extension to higher DF QS measures not only becomes the straightforward task of adding two more do loops for one QS measure order, but because of this modular structure of the Algorithm TDQS, the nested do loop programming technique [49-51] can be applied for the purpose of generating such a code, which could be associated to any kind of QS computation level and becomes completely adapted to parallel machines. 

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