Library sparse

The so-called sparse libraries are now the norm, designed by creating larger virtual combinatorial libraries and then removing the unattractive or undesirable... 

As illustrated by the examples in Table 15.30, diketopiperazines are amenable to many structural variations. These heterocycles thus seem to be well suited for the preparation of libraries for lead discovery, and have, for instance, been used for the identification of new enzyme inhibitors [368]. Libraries of diketopiperazines will, however, be sparsely diverse because the diketopiperazine ring itself is pharmacophore-rich , and will contribute significantly to the overall properties of all the members of the library (see Section 1.4). 

Due to its remarkable sparseness, the matrix H from Eq. (130) is easy to diagonalize even for higher dimensions. In this way, we have explicitly obtained very accurate eigenvalues [uk f=1 for K 1000 [38,39] via the NAG library [50]. However, the same library fails when we used its corresponding routine in an attempt to directly root polynomials of much lower degrees, K > 120. 

It is to be expected that the predictive performance of global models will detoriate over time as projects move on and produce new chemotypes not used in the generation of the model. Literature on time-dependent QSAR model behavior is stiU sparse. In a recent investigation this effect was shown for a human plasma protein binding (hPPB) model.A solution to this behavior is the use of correction libraries (see Section in.B.4.) and/or to update (rebuild) the model regularly. " An automated approach to this problem has been published and it is expected that this technology (autoQSAR) will become more widespread in the future. " ... 

For stiff differential equations, the backward difference algorithm should be preferred to the Adams-Moulton method. The well-known code LSODE with different options was published in 1980 s by Flindmarsh for the solution of stiff differential equations with linear multistep methods. The code is very efficient, and different variations of it have been developed, for instance, a version for sparse systems (LSODEs). In the international mathematical and statistical library, the code of Hindmarsh is called IVPAG and DIVPAG. 

A novel approach was recently introduced to the BzzMath library (Manenti et al., 2009). A new DAE solver was created for very sparse systems corrupted by a few unstructured elements, as they typically occur in the process control field. The implementation of this algorithm is now part of... 

In the BzzMath library, the BzzMatrixSparseSyinitietricLocked class can be used to collect a sparse symmetric matrix. 

The BzzMatrixCoefficientsExistence and BzzMatrixSparse-Locked classes in the BzzMath library allow to separate the variables into several groups to evaluate the Jacobian of a sparse matrix using the techniques proposed by Curtis et al. (1972). 

In the BzzMath library, the BzzQuadraticPrograrmning class uses LQ factorization for small-medium dense problems and Gauss factorization for medium-large sparse problems. 

Karypis, G., Schloegel, K. Kumar, V. 1998. ParMETIS Parallel Graph Partitioning and Sparse Matrix Ordering Library. University of Minnesota. 

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