Subset search

Table 3. Best fitting subsets of size 1-6, identified by all subsets search for the glucose experiment...

Bayesian methods for subset selection offer several advantages over other approaches the assignment of posterior probabilities to different subsets of active effects provides a way of characterizing uncertainty about effect activity prior distributions can incorporate principles of effect dependence, such as effect heredity the identification of promising models via Bayesian stochastic search techniques is faster than all subsets searches, and more comprehensive than stepwise methods. 

Thus, linear regression with best subset search seems to be well-suited for modeling BPs of decanes. 

A correct LOO cross-validation can be done by moving the delete-and-predict step inside the subset search loop. In other words, we take the sample of size n, remove one case, search for the best subset regression on the remaining n - cases, and apply this subset regression to predict the holdout case. Repeat for each of the cases in turn, gethng a true holdout prediction for each of the cases. Use these holdouts as a measure of the fit [38,39]. 

If the investigated material is composed of a large number of phases, then the identification process can be more complicated due to substantial overlap of the Bragg peaks related to the different phases. Chemical information on the compound of interest may in this case help in defining subsets of phases from the database containing particular chemical elements. Subsets search may be more successful than the search performed on the whole database, although it requires prior knowledge of information on the sample. 

If you have entered only one S, the system asks for the L-number. Subsequently a substructure sample search is performed. Besides the sample and full search range and subset-searches are viable. A range search refers to CAS Accession Numbers. The choice of subset restricts the search to a set of results, where you wish to continue the search. Structure searches are executed in two steps (Sect. 7.2.2) ... 

This rarity value is equated with the fraction of hits that would be returned by searching large database of diverse molecules with the full pharmacophore (all K features) or thi subset (with K—1 features) as appropriate. Labelling this fraction of hits as p(x) we nov define q x) as the fraction of the M active molecules (i.e. the molecules originally suppliet as input to the procedure) which match each of the K + possible classes. The overal configuration is scored using ... 

A flow chart showing the various phases leading to the final compound is reproduced ii Figure 12.35. The first step was a 3D database search of a subset of the Cambridge Structura Database. The pharmacophore for this search comprised two hydrophobic groups and i... 

Answers from aH of these searches contain CAS Registry Numbers. Answer sets may be combined, using the Boolean operators AND, OR, or NOT, with other answer sets or with text terms, such as names or molecular formulas. Any answer set also may be used to define subsets of the file for subsequent stmcture searching. Answer sets of up to 10,000 Registry Numbers from any type of search in this file may also be used as search terms in other files, such as the CA or CAOLD files (53). 

Subject-Based Retrieval Parameters. There are numerous means by which the subject content of a patent can be expressed, and which a searcher can use in developing a search strategy. Different databases offer differing subsets of these means. Effective strategies should in general not be limited to a single type of retrieval parameter rather, they should be built from different parameters and modified as needed to provide the strategy best fitted to the subject at hand. 

ENTER SCOPE OF SEARCH (SAMPLE), FULL, RANGE, OR SUBSET ... 

The previous sections have summarized the basic techniques available for searching chemical databases for specific types of query. Another important database application is compound selection, the ability to select a subset of a database for submission to a biological testing program. The selection procedure can be applied to in-house databases, to externally available compound collections, or to virtual libraries, that is, sets of compounds that could potentially be synthesized. 

Before starting the search for solutions, it is necessary to select among the M decision variables a subset of H variables, Xf, h- 1,..., W, which influence significantly the system performance, and thus will be used by S and included in the definition of the final set of hyperrectangles, X. For this preliminary choice of critical decision variables, other than his or her own specific process knowledge, the decisionmaker can count on a number of auxiliary techniques enumerated in Saraiva and Stephanopoulos (1992c). 

Having formally defined the branching structure, we must now make explicit the mechanisms by which we can eliminate subsets of the solution space from further consideration. Ibaraki (1978) has stated three major mechanisms for controlling the evolution of the branch-and-bound search algorithms, by eliminating potential solution through... 

As discussed above, it is impossible to solve equation (1-13) by searching through all acceptable N-electron wave functions. We need to define a suitable subset, which offers a physically reasonable approximation to the exact wave function without being unmanageable in practice. In the Hartree-Fock scheme the simplest, yet physically sound approximation to the complicated many-electron wave function is utilized. It consists of approximating the N-electron wave function by an antisymmetrized product4 of N one-electron wave functions (x ). This product is usually referred to as a Slater determinant, OSD ... 

In order to connect this variational principle to density functional theory we perform the search defined in equation (4-13) in two separate steps first, we search over the subset of all the infinitely many antisymmetric wave functions Px that upon quadrature yield a particular density px (under the constraint that the density integrates to the correct number of electrons). The result of this search is the wave function vFxin that yields the lowest... 

Rummey et al. [223] searched replacements for the pyrrolidine present in their DPP-IV inhibitor searching a 10,000-molecule subset of small primary aliphatic amines extracted from the available chemical directory and visually inspected the top 500 of them. Four were selected for testing and two of them were novel hits. 

In general, branch-and-bound [5] is an enumerative search space exploration technique that successively constructs a decision tree. In each node, the feasible region is divided into two or more disjoint subsets which are then assigned to child nodes. During the search space exploration for minimization problems, a lower bound of the objective function is computed in each node and compared against the lowest upper bound found so far. If the lower bound is greater than the upper bound, the corresponding branch is said to be fathomed and not explored anymore. The exploration terminates when a certain gap between the upper and the lower bound is reached or when the all possible subsets have been enumerated. 

If H0 is rejected, a two-stage procedure is initiated. First, a list of candidate biases and leaks is constructed by means of the recursive search scheme outlined by Romagnoli (1983). All possible combinations of gross errors (measurement biases and/or process leaks) from this subset are analyzed in the second stage. Gross error magnitudes are estimated simultaneously for each combination and chi-square test statistic calculations are performed to identify the suspicious combinations. We will now explain the stages of the procedure. 

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