Search principle

Hobert H (1995) Library search - principles and applications. In Chemometrics in environmental chemistry - applications. Vol 2, part H (Vol ed J Einax), Springer, Berlin Heidelberg New York, p 1... 

Figure 5-3 The top part of the figure shows the isolines of the misfit functional map and the steepest descent path of the iterative solutions in the space of model parameters. The bottom part presents a magnified element of this map with just one iteration step shown, from iteration (n. — 1) to iteration number ti. According to the line search principle, the direction of the steepest ascent at iteration number n must be perpendicular to the misfit isoline at the minimum point along the previous direction of the steepest descent. Therefore, many steps may be required to reach the global minimum, because every subsequent steepest descent direction is perpendicular to the previous one, similar to the path of experienced slalom skiers.

When necessary, the searcher may break the rules. However, this should not be taken as a license to do so at whim. Searches vary in type, length, and requirements, so that occasionally one or more searching principles do not apply. 

Differences in the approach to searching in the various branches of science and technology lie not in searching principles but in (1) the nature of the material to be searched and the variations in the best methods of dealing with it, and (2) the objectives sought in making the search. 

Thorough Use of Searching Principles Saves Time. Searching principles were evolved for two reasons to produce better searches, and to produce them more quickly. Consequently, the more the searcher applies these principles, the less will he waste his energies. 

Similarity search appears as an extremely useful tool for computer-aided structure elucidation as well as for molecular design. Here the similarity property principle is involved. This may be stated as ... 

A molecular dynamics simulation samples the phase space of a molecule (defined by the position of the atoms and their velocities) by integrating Newton s equations of motion. Because MD accounts for thermal motion, the molecules simulated may possess enough thermal energy to overcome potential barriers, which makes the technique suitable in principle for conformational analysis of especially large molecules. In the case of small molecules, other techniques such as systematic, random. Genetic Algorithm-based, or Monte Carlo searches may be better suited for effectively sampling conformational space. 

Following the similar structure - similar property principle", high-ranked structures in a similarity search are likely to have similar physicochemical and biological properties to those of the target structure. Accordingly, similarity searches play a pivotal role in database searches related to drug design. Some frequently used distance and similarity measures are illustrated in Section 8.2.1. 

Figure 10.3-16. The principle of similarity searches. The query (target, precursor) as well as the catalog compound are transformed by the criterion maximum oxidation state". Since the transformation for both compounds results in the samie transformed structure, the catalog compound is presented to the user as a suitable starting material. The comparison of the structure is performed by a hashcode algorithm.

With many variables and constraints, linear and nonlinear programming may be applicable, as well as various numerical gradient search methods. Maximum principle and dynamic programming are laborious and have had only limited applications in this area. The various mathematical techniques are explained and illustrated, for instance, by Edgar and Himmelblau Optimization of Chemical Processes, McGraw-Hill, 1988). 

Physical modeling involves searching for the same or nearly the same similarity criteria for the model and the real process. The full-scale process is modeled on an increasing scale with the principal linear dimensions scaled-up in proportion, based on the similarity principle. For relatively simple systems, the similarity criteria and physical modeling are acceptable because the number of criteria involved is limited. For complex systems and processes involving a complex system of equations, a large set of similarity criteria is required, which are not simultaneously compatible and, as a consequence, cannot be realized. 

Gas turbines and power stations are particularly prone to generate NOx and the search for the low-NOx burner that will operate at high efficiency (i.e. with low hydrocarbon emissions) continues. The principle of the low-NOx burner is to slow the rate of combustion by dividing it into several stages by the gradual mixing of the combustion gases with the stoichiometric air volume. 

---