Exhaustive enumeration

1) Exhaustive enumeration all atoms with the same atomic number are permuted and the permutation corresponding to the minimal chemical distance is taken. 

This criterion follows from the assumption, that in a reaction each atom will try to maintain as many spheres of neighbors as possible. 

ACS Symposium Series American Chemical Society Washington, DC, 1977. 

This method will be iterated until all spheres of neighbors correspond to each other as good as possible. 

In example III one can find the optimal assignment only by criterion (iii). 

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A related study was the exhaustive enumeration of the global minimum energy structure for all iP possible sequences of the HP model described in Section 10.3.1 [Li et al. 1996 Ihis showed that 4 75% of these sequences have a unique ground state (i.e. just on... 

Lonally, the templates were chosen by trial and error or exhaustive enumeration. A itafional method named ZEBEDDE (ZEolites By Evolutionary De novo DEsign) en developed to try to introduce some rationale into the selection of templates et al. 1996 Willock et al. 1997]. The templates are grown within the zeolite by an iterative inside-out approach, starting from a seed molecule. At each jn an action is randomly selected from a list that includes the addition of new (from a library of fragments), random translation or rotation, random bond rota-ing formation or energy minimisation of the template. A cost function based on erlap of van der Waals spheres is used to control the growth of the template ale ... 

The foregoing design questions are highly combinatorial so any exhaustive enumeration tedmique would be hopelessly complicated. A hit-and-miss or trial-and-error approach to conjecturing the solution is likely to fail because it cannot consider the overwhelming number of decisions to be made. Hence, the designer... 

To identify this set of final feasible solutions, X e 1, with low scores, we developed a greedy search procedure, S (Saraiva and Stephanopoulos, 1992c), that has resulted, within an acceptable computation time, in almost-optimal solutions for all the cases studied so far, while avoiding the combinatorial explosion with the number of (x, y) pairs of an exhaustive enumeration/evaluation of all feasible alternatives. The algorithm starts by partitioning the decision space into a number of isovolu-... 

Correlated mutation analysis does not yield a precise and exhaustive enumeration of all the interacting residues in a complex. Rather, tests have shown (177) that the result is a definition of the neighborhood of interacting regions. This makes the careful construction of explicit 3D models of GPCR homodimers, using the information derived... 

The concept of elementary flux modes has resulted in a vast number of applications to analyze and predict the functionality of metabolic networks [64, 65, 138, 241 243]. Software resources that allow for the computation of elementary flux modes are fisted in Table V [178, 224], It should be noted that, due to their definition as an exhaustive enumeration of possible flux distributions,... 

For x < 19, the enumeration was done by hand since it contains some sporadic cases. For other values of x, we first remark that the at and bi cannot be elementary components of extremal polycycles. Afterward, we undertake exhaustive enumeration of all possibilities. ... 

The same applies for ( 5,13, 3)-spheres. But, in this case, more than half of the vertices are in the ( 4,3 — v)-replacement set S. Hence, it is better, from the computational viewpoint, to do an exhaustive enumeration of their complements. 

Discussion of the subject matter centers primarily on such physicochemical properties as are deemed indicative of -electron mobility and the attendant development of aromatic or antiaromatic character. Although it is not entirely neglected, the description of synthetic procedure is limited for the most part to the crucial final step. It may also be well to note that, while a serious attempt has been made to provide as complete as possible coverage of the area, the main emphasis in this review is on proper representation rather than on exhaustive enumeration. Also, in order to achieve maximum effectiveness in the coverage of the literature, compounds belonging to a given size-class are described in terms of increasing molecular complexity rather than historical sequence. 

Remark 9 It is not efficient to solve the master problem (6.20) directly, since we need to know all feasible xk points which implies that we have to solve all the primal problems P(yk),y Y (i.e., exhaustive enumeration of 0-1 alternatives). Instead, Duran and Grossmann (1986a) proposed a relaxation of the master problem which will be discussed in the next section. 

A unique database is the GDB-13 database (49), which is an exhaustive enumeration of small-molecule structures containing up to 13 heavy atoms (restricted to C, H, N, O, S, P, and Cl). Although the database does not contain activity information associated with the structures, it can be used as a source of structures for virtual screening purposes (50). It is similar in nature to databases such as ZINC (51). The key difference is that the latter are all commercially available, whereas the former are completely virtual. This class of databases is useful primarily for virtual screening type methods, where the goal is to identify candidates for more in-depth study, rather than to explicitly understand SAR trends. 

Exhaustive enumeration of fragment-based chemical space with target-specific constraints... 

The original theorem was limited to molecules, but in 1939 Van Vleck, who had been acquainted with this theorem at the American Physical Society meeting in April 1936 extended it to ions in crystals Really no mathematical proof was given by Jahn and Teller, since they limited themselves to present a proof by exhaustion enumerating every... 

The availability of complete genomes/proteomes makes it possible to search systematically for the combination of amino acid residues, which is most important for protein themostability (41, 54). An exhaustive enumeration of all possible subsets of 20 amino acids is performed by representing sets of amino acids by vectors, where each component at of the vector takes the value of 1 if the amino acid of type i is presented in the set and 0 otherwise. Thus, 2 - 2 = 524,286 linearly independent nontrivial combinations exist. Given fP, the fraction of amino... 

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