Group-generation algorithm

A probabilistic polynomial-time algorithm gen, the group-generation algorithm, that, on input 1 with k e IN (the security parameter), outputs a prime q and a value desc (representing the description of a group Hq desc of order q). 

Different proposals for the group-generation algorithm gen have the following in common First, q is chosen as a random prime of a certain length, and then the values p -dq+ with factors d from a certain range are tested for primality. The proposals vary in the range of d. In some cases, e.g., if only d = 2 is used, the choice of q must also be repeated if none of the possible p s is prime. 

It is assumed that the group-generation algorithm gen generates q of length q 2 == k, and this is simplified by assuming I l2 = k. 

NAMD [7] was born of frustration with the maintainability of previous locally developed parallel molecular dynamics codes. The primary goal of being able to hand the program down to the next generation of developers is reflected in the acronym NAMD Not (just) Another Molecular Dynamics code. Specific design requirements for NAMD were to run in parallel on the group s then recently purchased workstation cluster [8] and to use the fast multipole algorithm [9] for efficient full electrostatics evaluation as implemented in DPMTA [10]. 

There are two problems to consider when calculating 3D pharmacophores. First, unless the molecules are all completely rigid, one must take account of their conformational properties The second problem is to determine which combinations of pharmacophoric groups are common to the molecules and can be positioned in a similar orientation in space. More than one pharmacophore may be possible indeed, some algorithms can generate hundreds of possible pharmacophores, which must then be evaluated to determine which best fits the data. It is important to realise that all of these approaches to finding 3D pharmacophores assume that all of the molecules bind in a common manner to the macromolecule. 

As computing capabiUty has improved, the need for automated methods of determining connectivity indexes, as well as group compositions and other stmctural parameters, for existing databases of chemical species has increased in importance. New naming techniques, such as SMILES, have been proposed which can be easily translated to these indexes and parameters by computer algorithms. Discussions of the more recent work in this area are available (281,282). SMILES has been used to input Contaminant stmctures into an expert system for aquatic toxicity prediction by generating LSER parameter values (243,258). 

Figure 26.50 Algorithm to provide initial grouping for generation recycling.

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