Divide-and-conquer strategy

Fig. 7.2 Informative design - asking the right question The most efficient means for a player to guess the correct number from 1 to 16 is a divide and conquer" strategy. However, this requires that the player ask questions in sequence and wait for an answer before asking the next. Informative design asks specific questions so that when they are answered simultaneously, the player is led to the answer. In this example, the questions are compounds either possessing (denoted by 1) or lacking (denoted by 0) a specific pharmacophore. Once the compounds are assayed, a single outcome is found to be consistent with activities and the corresponding pharmacophore is found.

This multitude of scales provides a useful way to organize a divide-and-conquer strategy for the simulation of DPFs, with typical examples given in Konstandopoulos and Kostoglou (1999b) Konstandopoulos et al. (2001,... 

Ambrose Amin E, Welsh WJ (2001) Three-dimensional quantitative structure-activity relationship (3D-QSAR) models for a novel class of piperazine-based stromelysin-1 (MMP-3) inhibitors applying a divide and conquer strategy. J Med Chem 44 3849-3855... 

The cultural heterogeneity of class members may also be an obstacle to collective action. In 1.3.1 1 cited a passage on Ireland in which Marx implausibly suggests that the opposition between English and Irish workers was deliberately created, or at least artificially maintained by the English capitalists, as part of a "divide and conquer" strategy. More... 

Two years ago Yang developed a divide-and-conquer strategy to do the DFT computations [43], By projecting the Hamiltonian into subspaces, he was able to divide a large system into smaller subsystems, and solve a KS-like equation for each subsystem. Recently, Zhou has provided an alternative construction of the divide-and-conquer method by projecting the solutions of KS equations with different basis sets associated with each subsystem [44]. The divide-and-conquer method is shown to be as rigorous as the conventional KS method. As far as electron density and energy density are concerned the divide-and-conquer method is different from the conventional KS method only by the way in which the basis sets are truncated. The rest of this section will review the divide-and-conquer method and try to provide some reasons why the method should work. 

Three known facts are essentially important in the development of a divide-and-conquer strategy. First, the KS Hamiltonian is a single particle operator that depends only on the total density, not on individual orbitals. This enables one to project the energy density in real space in the same manner in which one projects the density (see below). Second, any complete basis set can solve the KS equation exactly no matter where the centers of the basis functions are. Thus, one has the freedom to select the centers. It is well known that for a finite basis set the basis functions can be tailored to better represent wavefunctions, and thus the density, of a particular region. The inclusion of basis functions at the midpoint of a chemical bond is the best known example. Finally, the atomic centered basis functions used in almost all quantum chemistry computations decay exponentially. Hence both the density and the energy density contributed by atomic centered basis functions also decrease rapidly. All these... 

If the basis set for each subsystem is complete, the KS solutions for all subsystems must be identical. The subsystem label becomes irrelevant. However, a practical calculation with the divide-and-conquer strategy will use finite, truncated basis sets. In this case the KS solutions from different subsystems will vary from one another. e , wiH fc>e a-dependent if x (r) is a-dependent. That is,... 

Why was G4 DNA not apparent in the cocrystals of telomeric DNA with ciliate TEBP complexes An explanation for this apparent paradox was provided by mutational analysis of TEBP (3, which showed that the basic C-terminal region of TEBPp is necessary to promote G4 DNA formation. Following the common divide and conquer strategy for structural analysis, this region had been truncated in the TEBPa/(3 heterodimer analyzed in the cocrystals. ... 

Our approach [8] consists in decomposing state sets, using a divide-and-conquer strategy, when, during traversal, they become too large to be repre-... 

To solve the problem [3, 12], we can, fortunately, apply a divide-and-conquer strategy. First we assume that variables with different names can never reference the same data. For instance, the variable ea j,i) and ec j - l,i) of Floyd can never cause flow dependence relations because they have different names. So, we sort the variables by name into sets of variables with equal names. Next, we divide each such set in a set of result variables and a set of... 

Localization transformations result in one application description suited for space-time mapping. However, the optimality of the architecture may heavily depend on how the localization was performed [20]. It is therefore necessary to couple the localization task with the space-time assignment. Due to complexity issues, we have found it impossible to perform the complete space-time assignment simultaneously with the localization task. A divide-and-conquer strategy that performs the two tasks sequentially, while monitoring the interaction be-... 

Logic algorithms designed by this basic divide-and-conquer strategy are covered by Schema 8-1, where R(TX,T ) stands for ai j R TXj,TYj), and j is a notation-variable. 

Some issues about the divide-and-conquer strategy need to be discussed in order to show its generality, and to clearly distinguish it from some other approaches. 

Also, we mentioned that step (1) of a divide-and-conquer strategy consists of dividing a problem into sub-problems, unless it can be trivially solved . We have here taken the option that the unless it can be trivially solved clause is applicable iff a minimal form of the domain of the induction parameter is attained. An alternative interpretation would be that the clause may be applicable in even other cases. A good illustration of this point of view is Sedgewick s enhancement of Hoare s original Quick-Sort algorithm it switches to Insertion-Sort once the unsorted list has less than, say, 15 elements. Such sophisticated design-choices are beyond the scope of our study. 

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