Sparse partitioning

It is usual in developing a QSPR to spUt the database into two. One part is used for training the model, while the other part is used to validate the model. This goes to the predictability of the model the model is assumed to be predictive if it can predict the solubiUty of the validation set. Since the validation set is used intimately with the training set to refine the model, it is questionable if this partitioning is warranted [50]. This partitioning is particularly questionable where the available experimental data is sparse. 

Liquid/liquid partition constants within pharmaceutical chemistry have been of primary interest because of tlieir correlation with liquid/membrane partitioning behavior. A sufficiently fluid membrane may, in some sense, be regarded as a solvent. With such an outlook, tlie partitioning phenomenon may again be regarded as a liquid/liquid example, amenable to treatment with standard continuum techniques. Of course, accurate continuum solvation models typically rely on the availabihty of solvation free energies or bulk solvent properties in order to develop useful parameterizations, and such data may be sparse or non-existent for membranes. Some success, however, has been demonstrated for predicting such data either by intuitive or statistical analysis (see, for example. Chambers etal. 1999). 

The solution of a sparse system of equations can be carried out in three stages 1. Partitioning, 2. Reordering or "tearing", and 3. Numerical solution. Stages 1 and 2 contain only logical operations and their objective is to obtain a system which can be solved faster and/or with smaller round-off error propagated. 

The enthalpy and entropy of binding can be determined experimentally, as, for example, by isothermal titration calorimetry (46,471. These data, however, are still sparse and not always easy to interpret (48, 49). Substantial compensation between enthalpic and entropic contributions is observed (50-52) this phenomenon and its interpretations have recently been critically reexamined (53). Interestingly, the data also show that binding can be both enthalpy-driven (e.g., streptavidin-biotin, AG = -76.5 kJ/mol, AH = -134 kJ/mol) or entropy-driven (e.g., streptavidin-HABA, AG = -22.0 kJ/mol, AH = +7.1 kJ/mol) (54). However, because cf strong temperature dependencies, even this partitioning is a question of the temperature used for measuring. 

Conventional molecular beam reactive scattering studies have excelled in the determination of the angular and velocity distributions of reaction products, but direct information on the internal state distributions has been sparse. One of the most important of the non-beam methods for learning about the partitioning of reaction energy into the internal degrees of freedom of the products has been infra-red chemiluminescence studies. Unfortunately, this technique has hitherto been limited to hydride compounds, principally hydrogen halides. We present an alternative technique based on electronic fluorescence spectroscopy. 

Equation (29) can be used in conjunction with the lattice strain model to parametrize partition coefficients for ions of different charge and radius entering sites for which data are sparse. 

Problem size, as most process optimization problems have on the order of lO to 10 constraints and at least 10 to 100 decision variables. Generally, this is done with sparse matrix algorithms or by partitioning the problem to take advantage of the equation structure due to the unit equations and recycles. 

Group 14 elements (C, Si, Ge, Sn, Pb) have diverse speciation characteristics. C is partitioned dominantly between C032- and HC03-, while for both Si and Ge, uncharged forms are dominant (Si(OH)40 and Ge(OH)40) with lesser concentrations (< 15%) of SiO(OH)3- and GeO(OH)3-. The sparse data available for assessment of SnIV speciation indicate that Sn(OH)40 is dominant over a wide range of pH. The speciation of Pb is apparently unique among seawater constituents in that Pbll is partitioned between chloride complexes and carbonate complexes. [17] The latter are dominant above pH 7.85. 

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

The technique of paper-partition chromatography, which has been used so successfully in the analysis of reducing sugars and methylated derivatives, has been applied only very sparsely to the study of oxidation products A greater use of this method will undoubtedly lead to a better... 

---