Advances in Algorithms

However, error statistics confirm that the interpolating functions 

In fact, the function i fj [Eq. (11.40)] actually reduces the errors in GB solvation energies while simultaneously accelerating the calculations [45]. To wit, when quasi-perfect R6 radii [62], which can be computed cheaply, are used in place of the perfect radii that are only available in benchmark calculations, the mean absolute error in as compared to C-PCM benchmarks is reduced from 8.7 kcal/mol for the canonical GB operator q/StiH 5.1 kcal/mol for the interpolating function At the same time, use of reduces the cost by a factor of three relative to the canonical GB model based on [45]. The new interpolating function 

In this section we focus on technical rather than theoretical developments, but ones that are absolutely essential if PCMs are going to be brought to bear on macromolecules. 

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The unknown pressures are acquired by solving the system of algebraic equations, eqn. (8.144), after the boundary conditions are applied. With a known pressure field we can solve for the flow rates between the nodes and a the fill factor in the partially filled nodes can be updated using the smallest time step required to fill the next node. How to determine the appropriate time step is shown in Algorithm 3. The flow fronts are advanced in Algorithm 4. At that point, new boundary conditions are applied to the set of algebraic equations to solve for the new pressure and flow fields. This is repeated until all control volumes are full. 

Balcazar, J.L., Diaz, J., Gavald., R., Watanabe, O. Algorithms for learning finite automata from queries a unified view. In Du, D.Z., Ko, K.I. (eds.) Advances in Algorithms, Languages, and Complexity, pp. 73-91. Kluwer Academic Publishers, Dordrech (1997)... 

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