Generic Structures Problems

Another searching capability is required by the need to find a partial structure or substructure in a database that includes generic structures. The ability to do a substructure search is standard in modem chemical structure information systems. The problem is more complicated when generic structures must be searched, yet even more necessary since the generic might represent millions of specific structures. The query in Fig. 8 is compared with the generic structure to find the set of specific structures. 

Interpretation of generic, or Markush, structures is a very useful but nontrivial task, and from the published work, it appears that so far, CLiDE is the only system among the various structure recognition systems introduced in Projects, above, that addresses the problem of generic structure interpretation. 

Certainly, complete generation of all structures is not the only way to solve the problem. A review of different methods can be found in [13], where in particular the evaluation of molecular descriptors for large libraries specified by generic structural formulas is described. In any case canonization of data and normal forms play a central role. Hence it is time to consider this problem and to describe a canonizer. 

Equation (6.1) is a highly generic and domain-independent system representation. Equation (6.2) is still generic, but is a domain-dependent representation. Only those things and their relationships are considered to exist in system instances W. Equation (6.2) is the system taxonomy formalism, where W is the supply chain domain. A detailed description of the taxonomy of a system in general can be found in Chandra et al. (2007). For each possible system instance w e IT, the intended structure of w according to S is the structure (problem classification in problem taxonomy)... 

To overcome these problems, the Extended Set of Smallest Rings (ESSR) was developed as part, of the research on the (Generic Structures Project at Sheffield University. The ESSR includes all simple-faces plus all primary and secondary cut-faces, as defined here it does not include regions or non-regions that are not simple-cycles, or non-regions that are classified as tertiary cut-faces. An algorithm to find the ESSR has been described. ... 

The concept of superatoms included in the SMD format permits a structured representation of (large) molecules and reactions. Furthermore we believe that this concept indicates a possible way of handling generic structures and Markush formulas. We do not have a final solution for these problems yet, but promising attempts are under investigation. 

The maximal rank of an (m x g) matrix having no specified structure is equal to min (m, g). The inclusion of the structure into the problem makes it possible for matrices to have less than full rank, independent of the values of the free parameters, as was shown by Schields and Pearson (1976). Therefore, a structured matrix B has full generic rank if, and only if, there exists an admissible matrix B with full rank. 

In the most generic case it is true that the derivative T / 0. The interior solution of Eqs. (6)-(9) can be obtained only numerically. In principle there is no problem to evaluate these equations, but the structure of them must be understood. 

Additives are often used to increase selectivity. They are paramount in chiral separations, but they are also frequently used in non-chiral separations, e.g., cyclodextrins (CDs). In our lab, BGEs with and without a cyclodextrin are part of our generic protocol. Figure 8 demonstrates that although one can more or less predict interaction with the additive from the chemical structures, it is still difficult to predict separation.Batch-to-batch variability and variability between suppliers can be a problem of (chiral) additives and a check of different batches has to be part of the robustness test (e.g., reference 56). If the additive is charged and has one or more pK s around the pH of the BGE, extra care should be taken to control the pH. Alternatively, better robustness might be obtained with another uncharged additive, even if this results in lower resolution. 

Application of the MORT technique is based on a predefined tree structure laid out vertically (top down) in eight interconnecting trees. The structure is quite complex, but contains 98 generic problem areas and up to 1500 possible causes. A user s manual 02) provides detailed instructions on how to use the tree. 

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