Exhaustive search

Systematic searches exhaustively sample conformational space by sequentially incrementing the torsional angles of aU of the rotatable bonds in a given molecule. This conceptually simple approach is straightforward to implement, but scales exponentially with respect to the number of rotatable bonds. To control the exponential increase in the number of potential conformers obtained, systematic searches are usually combined with tree-based search techniques taken from computer science. Even the best implementations of systematic searches become impractical beyond several rotatable bonds (typically greater than 10). Stochastic searches are based on probabiHstic theories and are better suited to calculations... 

Variations of two exact algorithms (algorithms that will always find the optimal solution) are commonly used. The first is to search exhaustively through all possible tree topologies for the best solution(s). This method is computationally simple for 9 or fewer taxa (for which there are 135,135 labeled, unrooted, bifurcating trees) and is only moderately time-consuming for 10 or 11 taxa (2,027,025 and 34,459,425 trees, respectively).2 For 12 taxa, the evaluation becomes laborious (654,729,075 trees), and for 13 or more taxa (a 13,749,310,575 trees) the calculations are usually impractical. The chief advantages of exhaustive searches are (1) the optimal tree(s) is always found and (2) all other possibilities can be ranked with respect to the optimal solution(s). 

This paper does not intend to be a review rather comments and examples are given for some of the recent progress. The related literature is not searched exhaustively and the selection is rather arbitrary. Preliminary results of two new studies by the XD method are presented in order to demonstrate the capabilities of the method at new conditions. The reverse Monte Carlo (RMC) technique is also discussed in more detail to show a new perspective in the structural modelling of solutions. 

While the combinatorial approach attempts to search composition space broadly, an exhaustive search is usually not possible. It would take, for example, a library of 9 x 10 compounds to search a five-component system at a mole fraction resolution of 1%. Similarly, it would take a library of 20 " Ri 10 proteins to search exhaustively the space of all 100-amino acid protein domains. Clearly, a significant aspect to the design of a combinatorial chemistry experiment is the design of the library. The library members should be chosen so as to search the space of variables as effectively as possible, given the experimental constraints on the fibrary size. 

Heuristic searches usually guarantee neither a global optimal solution nor a bound on the error when computation stops because they make preemptive moves—moves for which there are viable alternatives that are not explored. In order to carry out a more exhaustive search, such moves must be taken as provisional. That is, a record must be retained of the alternatives not yet pursued, and search must backtrack to those alternatives, pursuing them until they prove incapable of producing an satisfactory solution. As the search encouters a particular partiM solution, it either terminates that solution, that is, finds it to admit no improving move, or branches it, that is, extends it by one applicable move. The best feasible solution encountered is recorded as the incumbent solution. Thus, if the search exhausts all open alternatives, the incumbent solution is a global optimum. 

If initial attempts are unsatisfactory, the chemist may enlarge his store of relevant knowledge, e.g. by reading the literature or talking to an expert or he may redefine the problem - i.e., find new keys so that more of his knowledge of reactions becomes relevant. In fact, chemists have been known to search exhaustively for a way to implement a preferred route, only to finally re analyze their problem and find an entirely different - and ultimately successful - one. 

Septanoses are relatively rare. Their conformations are either chairs or twist-chairs, or boats or twist-boats. Only a few of these structures have been modeled. All likely structures can be searched exhaustively for the furanoses and pyranoses if ample computing resources are available. 

Glide (Schrodinger) exhaustive search empirical score... 

Combinatorial. Combinatorial methods express the synthesis problem as a traditional optimization problem which can only be solved using powerful techniques that have been known for some time. These may use total network cost direcdy as an objective function but do not exploit the special characteristics of heat-exchange networks in obtaining a solution. Much of the early work in heat-exchange network synthesis was based on exhaustive search or combinatorial development of networks. This work has not proven useful because for only a typical ten-process-stream example problem the alternative sets of feasible matches are cal.55 x 10 without stream spHtting. 

Currently, there are about 197,500 entries in the National Institute of Standards and Technology (NIST) Crystal Data File. An exhaustive search takes about one minute. Unit cell parameters are very definitive. Usually only one or a few hits are found and the appropriate Hterature reference(s) are Hsted. If no hits are found, the stmcture has not been previously reported. 

Because fuel costs are high, the search is on for processes with higher thermal efficiency and for ways to improve efficiencies of existing processes. One process being emphasized for its high efficiency is the gas turbine combined cycle. The gas turbine exhaust heat makes steam in a waste heat boiler. The steam drives turbines, often used as lielper turbines. References 1, 2, and 3 treat this subject and mention alternate equipment hookups, some in conjunction with coal gasification plants. 

It is the purpose of the present review to examine in what wa the Hammett equation can be applied to heterocyclic systems, to give examples of such applications, and to examine the special problems which arise in the process. In view of the tremendous difficulties involved in systematically searching the literature for the type of data required, no attempt wiU be made at an exhaustive coverage of all available information. The different possible applications will be discussed and, where feasible, illustrated. If an unjustified number of such illustrations are taken from the authors work, this should be... 

What has been reported in the previous subsections does not amount to an exhaustive review of the existing literature on MO calculations for sulphones and sulphoxides— which is, anyway, not particularly rich. It must be said that the treatment of the S—O bond poses special problems, and is therefore less attractive for the theoretical chemist. A search was nevertheless conducted, and what follows provides nearly all the existing entry points to the theoretical literature of sulphone and sulphoxide compounds. 

However, if one lacks access to these, one may consult Chemical Titles and the keyword index (p. 1611) at the end of each issue of CA. In these cases, of course, it is necessary to know what name might be used for the compound. The name is not necessary for Index Chemicus (p. 1622) one consults the formula indexes. However, these methods are far from complete. Index Chemicus lists primarily new compounds, those which would not have been found in the earlier search. As for chemical Titles, the compound can be found only if it is mentioned in the title. The keyword indexes in CA are more complete, being based on internal subject matter as well as title, but they are by no means exhaustive. Furthermore, all three of these publications lag some distance behind the original journals. To locate all references to a compound after the period covered by the latest semiannual formula index of CA, it is necessary to use CAS-online. 

Environmental Applications Search for the Holy Grail for Diesel Exhaust Cleaning... 

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