Partitioning method

The fifth and final chapter, on Parallel Force Field Evaluation, takes account of the fact that the bulk of CPU time spent in MD simulations is required for evaluation of the force field. In the first paper, BOARD and his coworkers present a comparison of the performance of various parallel implementations of Ewald and multipole summations together with recommendations for their application. The second paper, by Phillips et AL., addresses the special problems associated with the design of parallel MD programs. Conflicting issues that shape the design of such codes are identified and the use of features such as multiple threads and message-driven execution is described. The final paper, by Okunbor Murty, compares three force decomposition techniques (the checkerboard partitioning method. 

The partitioning method also furnishes an excellent tool for the numerical solution of secular equations of any order.18 In such a case, one chooses the subset (a) to consist of a single function and, since Ca is then simply a number, Eq. III.48 gives... 

In conclusion, we observe that the elementary partitioning method described in this section is of value not only for numerical purposes and for estimating the remainder but also for studying theoretical problems connected with conventional perturbation theory and with Brueckner s approximation for treating many-particle systems. 

In order to solve the secular equation, we will now use the partitioning method discussed in Section III.D(lc). Choosing the subset (a) to contain only the SCF-determinant and using Eq. III.49, we obtain... 

Second order transition, 119 Second virial coefficient, 107, 112 Secular equation partitioning method, 270, 271... 

The simplest and fastest techniques for grouping molecules are partitioning methods. Every molecule is represented by a point in an n-dimensional space, the axes of which are defined by the n components of the descriptor vector. The range of values for each component is then subdivided into a set of subranges (or bins). As a result, the entire multidimensional space is partitioned into a number of hypercubes (or cells) of fixed size, and every molecule (represented as a point in this space) falls into one of these cells [57]. 

Partitioning methods occasionally struggle to provide the accuracy associated with more powerful, albeit less informative techniques such as machine learning and statistical approaches. For this reason, there is a continuing need for the application of more accurate and informative classification techniques to QSAR analysis. The goal of a classifier is to produce a model that can separate new, untested compounds into classes with a training set of already classified compounds. 

Xue L, Stahura FL, Bajorath J. Cell-based partitioning. Methods Mol Biol 2004 275 279-90. 

Kiehl, M., Partitioning methods for the simulation of fast reactions, Zentralbl. Angew. Math. Mech. 78 (1998) 967-970. 

The partitioned method of solution as described in Sec. 2.1.4 is used as the basis of solution. 

Local methods, on the other hand, are characterized by input transformations that are approached using partition methods for cluster seeking. The overall thrust is to analyze input data and identify clusters of the data that have characteristics that are similar based on some criterion. The objective is to develop a description of these clusters so that plant behaviors can be compared and/or data can be interpreted. 

However, Olgin employed a somewhat unwieldy matrix partition method to locate the surplus value term in the output multiplier matrix. An alternative derivation is suggested by substituting (A2.4) into (A2.1) such that... 

Dissimilarity and clustering methods only describe the compounds that are in the input set voids in diversity space are not obvious, and if compounds are added then the set must be re-analyzed. Cell-based partitioning methods address these problems by dividing descriptor space into cells, and then populating those cells with compounds [67, 68]. The library is chosen to contain representatives from each cell. The use of a partition-based method with BCUT descriptors [69] to design an NMR screening library has recently been described [70]. 

Partitioning methods make a crisp or hard assignment of each object to exactly one cluster. In contrast, fuzzy clustering allows for a fuzzy assignment meaning that an observation is not assigned to exclusively one cluster but at some part to all clusters. This fuzzy assignment is expressed by membership coefficients m(/ for each... 

The most common technique for the radiochemical determination of complexing constants utilizes partition methods which are based on reactions between two phases under static or dynamic conditions (chromatography). Partition methods offer the advantages of simplicity and rapidity and are amenable to a broad selection of phase compositions and arrangements. One of the most reliable partition methods, especially useful for measuring 0 , is solvent extraction. It is best applied to systems which exhibit compound formation (11). 

For the very heavy elements which are not available in micro-or nanogram quantities or which are synthesized one atom at a time , partition methods are the only practical way of determining complexing constants. When the half-life of an element is short, dynamic rather than static procedures are used since they give the most rapid experimental results (12). 

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