Explicit enumeration

Representation. The solution space is composed of discrete combinatorial alternatives of batch production schedules. For example, in the permutation flowshop problem, where the batches are assumed to be executed in the same order on each unit, there are A number of solutions, where N is the number of batches. We must find a way to compactly represent this solution space, in such a way that significant portions of the space can be characterized with respect to our objective as either poor or good without explicitly enumerating them. 

Enumerate on-the-fly the sub-region(s) using the optimized sets of bona fide reactants identified in step 2. One can see that reduction in reactant set sizes makes explicit enumeration of product structures practical (for the same example used, m x n = 104 vs. M x N= 106 and both are the total size of PGVL). 

All Basis Products in the PGVL have been explicitly enumerated to support numerous molecular design, fragment-based design, and 2D and 3D methods they also provide here a rigorous basis for the fuzzy reaction retrieval in the LEAP2 method. 

Search a database of Basis Products using Asymmetric Similarity measure. Here this search is done using the query molecule against a database of 106 explicit enumerated Basis Products. The asymmetry similarity search in the BP database is implemented using MDL Keys finger print (24) with ISIS host technology (25). 

Recognizing the tendency to use more than one set of polarization functions in modem calculations, the standard nomenclature for the Pople basis sets now typically includes an explicit enumeration of those functions instead of die star nomenclature. Thus, 6-31G(d) is to be preferred over 6-3IG because the fonner obviously generalizes to allow names like 6-31G(3d2fg,2pd), which implies heavy atoms polarized by three sets of d functions, two sets of f functions, and a set of g functions, and hydrogen atoms by two sets of p functions and one of d (note that since this latter basis set is only valence double-C, it is somewhat unbalanced by having so many polarization functions). 

As it turns out though even the simplified VB-theoretic formulations giving rise to conjugated-circuit theory or even just Kekule-structure enumeration, may become challenging for sufficiently large (perhaps formally infinite) systems, or for non-Kekulean (i.e., radicaloid) systems. It might oft be convenient if explicit enumeration of Kekule structures could be avoided. Notably for such cases there are some few alternative sorts of means by which to obtain some partial information about the system, within a VB-theoretic context. 

It is not necessary to explicitly enumerate the cycles with sign exactly opposite to those listed in Equation (9.25). 

In the hospitals, the survivors were cut off from any communications with the outside and their relatives were not allowed to visit them. An incorrect list of hospitals for victims was released. The main problem was the lack of information about those dealing with the identification and characterization of the chemical used and the unavailability of known antidotes (e.g. naloxon) by medical staff treating the victims (Bajgar et al, 2007a). It appeared from this event that there were compounds not explicitly enumerated in the CWC and therefore not controlled by this Convention. Fentanyl can be considered as a nonlethal weapon (a group of so-called calmatives) and these chemicals can also be used to incapacitate animals of course, its use against humans is not excluded (Bajgar, 2006 Hess et al, 2005). 

Theoretical Predictions and Molecular Parameters. As previously emphasized (21, 22), a major and unique virtue of the simple zeroth-order theory is that it makes many experimentally testable predictions. More-sophisticated versions of the theory, which include physical effects such as rotational defect interactions, solvent-induced polymer swelling, and polydispersity, have been constructed (21). However, the basic features of the theory are not very sensitive to these complications (21, 22). This encourages us to believe that the predictions extracted from the simplest version of the theory may have wide validity. In this section, we explicitly enumerate and illustrate, with our polysilylene results, the various predictions. 

He first developed hb theory of emotion as act ion in Solomon (1973). In Solomon (1976), which t cite in the revised edition of Solomon (1993), he modified some of the more outrageous claims from the article while still upholding the central argument. An explicit enumeration of the theses from the article that are abandoned in the book appears In the appendix to Solomon (1980). a reprint of Solomon (1973). 

Various approaches to the enumeration of connectional isomers have been discussed folding and gluing of a planar lattice section in every possible way, the application of tiling mles,3i,32 the application of hexagon matrix rules, and oth-erg 12,38 appears to have been only one report giving explicit enumeration... 

Thus, to build a decision tree, one needs to explicitly enumerate all possible scenarios and the responses (decisions) to such scenarios. However, for some problems,. .., a combinatorial explosion of branches makes calculations cumbersome or impractical (Schuyler, 2001). One way that this problem is ameliorated (but not solved) is by introducing Monte Carlo simulations at each node of the decision tree. However, this does not address the problem of having to build the tree in the first place. In addition, trees are appropriate for the case where discrete decisions are made. Continuous decisions like for example the size of the investment, or more specifically, the size of a production plant, cannot be easily fit into decision trees without discretizing. 

It is worth noticing that decision trees are in fact a particular case of two-stage programming. In other words, one can code through rules (mathematical in this case) the same decisions one makes in the tree explicitly, but in two-stage programming, one can also add logical constraints, if-the-else rules, etc., so there is no need for explicit enumeration of all options. 

As full enumeration of large combinatorial libraries is impractical, several methods have been developed to avoid explicit enumeration of all library members. Many diversity- and similarity-based design strategies apply sampling approaches such as genetic algorithms, simulated anneal-... 

Due to the nature of the problem there is not a one to one match between separation tasks and columns that perform a given separation. Even more, a given feasible sequence of separation tasks can be performed by different sequences of thermodynamically equivalent columns. In this paper we present a task based superstructure with intermediate characteristics between the pure State Task Network (STN) (Yeomans and Grossmann, 1999) in which all the separation tasks are explicitly enumerated, and a superstructure in which equipment is previously determined. Figure 2 shows the superstructure for a mixture of 5 components. Although the picture by itself... 

Virtual chemistry is taken to mean the universe of compounds we could make but haven t. An example would be a combinatorial chemistry library, from which only a subset is synthesised. In principle, any other member of the library is also synthetically accessible. The size of the universe is the product of the numbers of R-groups and can quickly reach infeasibly large numbers. Workers at Pfizer estimate that this accessible universe just within Pfizer is 10 compounds, compared to the < 5 million compounds in the archive. It is impractical to explicitly enumerate all these compounds and to search them, so two methods have been developed to narrow down the search space. Lessel et describe further improvements to the colibri... 

Constitution was ratified by all thirteen states, although several did so on the condition that a bill of rights be added as soon as possible. The Bill of Rights - the first ten amendments to the new Constitution - drafted by Madison and adopted in 1791, explicitly enumerated the rights to freedom of speech, press, assembly, and other protections. Many other issues, however, remained unresolved. The most troubling of these were the questions of slavery and secession. 

In macromolecular fluids several interesting physical aspects and questions arise that have no analog in atomic and small-molecule systems. There are two broad issues worthy of explicit enumeration. 

There are few enough different informational representations used in connection tables that they can be explicitly enumerated this is the set of transfer variables. An encoding convention is selected for each one. The GEMINI transfer variables are shown in Table 1. 

In contrast to the numerical taxonomy quality function, the conceptual clustering quality function takes into account the utility of the concepts representing the clusters, as seen below, where the parameter CONCEPTS is the set domain of concepts which may be used to describe the clusters. In the context of conceptual clustering, a concept is a valid cluster description as specified within the cluster description language. Consequently, the set of possible concepts need not be explicitly enumerated. An important bias in this method is the use of the simplicity of a cluster description as a metric for the quality of clustering. 

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