Complete enumeration

In this review we have concentrated on giving a picture of the main lines and some recent developments in the field of nucleophilic aromatic photosubstitution. A more complete enumeration of the many reactions discovered will be presented elsewhere (Cornelisse and Havinga, 1975). 

As a result, we would have to solve 2100 LP problems. Hence, such an approach that involves complete enumeration becomes prohibitive. 

They constructed the following example for which all integer feasible points need to be examined before finding the solution, that is, complete enumeration is required. 

A plethora of techniques has been employed to address the sampling problem, ranging from complete enumeration of the relative orientations of the rigid binding partners to methods based on effective energy gradients to determine new atomic positions. 

Meyer et al.49 Complete enumeration (FFT) Hydrogen-bond filtering and shape matching 6 ca. 1.5 A lh... 

Ritchie and Kemp51 Complete enumeration (polynomial expansion) Electrostatic and shape matching 6 Depends on degree of polynomial used ih... 

As an alternative to completely enumerating all relative orientations, Fischer et al.52 reported the development of a computer-vision-based technique called geometric hashing. This scheme is conceptually similar to that utilized in the DOCK program53,74 which tries to find matches in the internal distances between spheres74 or shape-based site-points,53 which represent the surface features of the proteins. 

For benzenoids with k = 12 the first data were published in 1988 as a result of a collaboration between He He and Trondheim (cf. Sect. 2.8 for a listing of the research centres). The number C l2 (for catacondensed benzenoids with h = 12) became available after the enumeration of the branched catacondensed h = 12 systems in Trondheim, while He He succeeded in a complete enumeration of benzenoids with this number of hexagons. Consistent h = 12 numbers were reported [69] as private communications from He He and from Cioslowski. 

Clinicians should be aware that specific recommendations, such as the AREDS formulation, may not be recognized as compounding doses of other over-the-counter supplements. An example would be accumulating a toxic dose of beta-carotene from using the AREDS formulation along with additional sources of beta-carotene. Other examples exist, and a complete enumeration of... 

Wood s views on the etiology of disease were even more opaque and diffused, and he stated that a complete enumeration of all the possible causes of disease would be an almost endless task. 32 He did outline five though (1) exterior influences and moral relations (2) bodily derangements and those governed by the will (3) noxious matters within the body (4) systemic, functional, or stmctural problems and (5) accidental injuries, which include not only trauma but also chemical causes such as aU stimulants [coffee, tea, alcohol. 

Exact results of combinatorial optimization of PWCs structure are presented in the Table. The data were obtained by different methods. For small and middle-size clusters (N < 28), we used a complete enumeration method. For large clusters (N = 36, 60), the data were obtained using symbolic calculations and max-plus algebra. Characteristics of two lowest energy levels for the SWEB model are presented. For water fullerene N = 60) on the base of SWEB model, the data obtained only for ground state level without isomorphism analysis. Values in italics correspond to ground sates of the SWB model. For example, the... 

This section will give a discussion of these open problems They are completely enumerated, ordered, and ranked according to their degree of severity. When discussing the problems, we are also discussing the results we have achieved so far. 

Often, problem solutions (complete or partial) are labeled with costs. Then, an optimal solution is represented by a path from the root to a leaf with optimal cost. In general, in order to find an optimal solution, the whole tree has to be enumerated. Complete enumeration can be avoided if we can provide for each node v inside the tree a lower bound (for minimization, upper bound for maximization) on the cost of all leaves that are contained in the subtree rooted at v. If this bound exceeds the cost of any solution that we have found before in the tree traversal, the whole subtree rooted at v can be disregarded. The sharper the lower bound the larger the regions of the tree that can be eliminated in this branch bound procedure. 

It is easy to see that this technique is more efficient than complete enumeration. Actually, one can reduce the amount of computation even more by using dominance rules or elimination criteria (see Emmons 1969), For the 1 27 the following dominance rule exists If there is a pair of jobs j and k such that pj s and dj d, then there exists an optimal sequence with job j appearing in the sequence before job k. This rule makes it possible to reduce the amount of computation since it is not necessary to evaluate any sequence where job k appears before job j. (However, it still is not possible to find a polynomial time algorithm for this problem, since it is known to be NP-hard.)... 

One very fast EFM enumeration method uses the binary nullspace implementation [20, 21] of the double description (DD) method [22]. This method has proven particularly useful for the complete enumeration of EFMs in metabolic networks [22]. 

Hunt, K.A., Folsom, J.P., Taflfe, R.L., and Carlson, R.P. (2014) Complete enumeration of elementary flux modes through scalable demand-based subnetwork definition. Bioinformatics, 30 (11), 1569-1578. 

In summary, then, the complexity of zeolitic structures is too great to allow a complete enumeration, so that this approach could not be used to identify all new zeolite structure types from a comparison of observed diffraction profiles and those predicted from energy minimisation. Nevertheless, for structures where the symmetry is quite high the method may find application in structure solution. Furthermore, novel hypothetical structures which are chemically feasible and which would possess important new properties if made would be attractive targets for synthesis via the methods of templating described elsewhere in this book. 

In the previous discussion of two important safety issues, design approaches to avoid accidents have been introduced. This section provides a more complete enumeration without discussing implementational details, which are covered by Growl and Louvar (1990). 

Complete enumeration of each type of subgraph becomes computationally intense as structure complexity increases. All the necessary computations are carried out by computer software along with calculations for many other quantities of interest in QSAR. ... 

Here, A is the antisymmetrizer and are the atomic basis functions that participate in the k-i structure. The spin function sm is constructed to make each structure an eigenfunction of and operators with quantum numbers S and M. VB theory has many variants that can be classified by their method of selection of structures for the calculation. A more complete enumeration of VB wave functions can be found in references [124] and [125]. 

BICLAIM, the chemical space of synthesizable combinatorial libraries described in Section 13.2.6, comprises about 10 virtual molecules. The enormous number of compounds precludes time consuming, systematic searches and reduces the repertoire of computational techniqnes to those tools that are explicitly optimized to handle combinatorial libraries. Complete enumeration of the entire compound set is impossible due to the time needed to perform complete enumeration and due to the storage size of the enumerated chemical space. However, even if the storage problem could be solved, there are no tools to perform a search in such a huge compound space within a satisfying time frame. Therefore, applicable tools are typically optimized to work within nn-ennmerated fragment spaces. 

A complete enumeration of IRRs and ORRs along with the corresponding IRs and ORs may, in principle, be achieved by considering all of the successive choices of q and q + 1 elementary reactions from a total of p. This method, however, is computationally laborious. We have developed a more effective alternate method of enumeration that will be discussed elsewhere. 

Exactly all the circular benzenoids 0 N S) with 5 > 18 can be perforated by a coronene hole to produce single coronoids 0(n 5). Then one has i T=n+6, 5=5 — 6. A detailed treatment on a complete enumeration of the isomers of the class 0 has been published (Cyvin BN, Brunvoll, Chen and Cyvin 1993). The smallest system of this class is kekulene. In the cited reference a coronoid with coronene hole(s) was referred to as "coronenic . We quote a nice sentence therefrom "A coronenic coronoid has a coronene corona hole. We shall not use the term "coronenic in the following, although it is analogous with our term "naphthalenic (Definition 3.3). A brief account on the title systems and their enumeration is given in the next two paragraphs. 

This is not the place for a complete enumeration of the activities of inspectorates but one more should be mentioned, namely intensive programs designed to improve compliance and reduce injuries in particular industries. The industries are often (not always) chosen on the basis of their high workers compensation costs. In view of... 

Thin-layer chromatography today is a dynamically developing modem analytic method. Areas of progress include increase of the spectrum of selectivity, improvement of efficiency, and in certain cases simplification of handling. The discussion of bulk sorbents and precoated layers above is not a complete enumeration of all possibilities e.g., the different carriers for the layers (glass plates, aluminum, or plastic sheets) are not shown explicitly. In addition, special plates with very restricted applicability are not discussed. 

For specific targets, a complete enumeration of conceivable scaffolds based on previous experience may open the door toward novel, highly potent core structures, as it has been achieved in the field of BACE-1 inhibitors [106]. 

Koide, T., Shinmori, S. Ishii, FI. 2002. An Efficient Complete Enumeration Method for Network Design Problems and Its Applications, Journal of the Operations Research Society of Japan 45(3) 299-316. 

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