Computer potential improvements

During recent years there has been an increasing demand for better operation of wastewater treatment plants in order to guarantee satisfactory effluent quality at minimal cost. The renewed interest in instrumentation and control comes after a period of huge investments in sewer networks and treatment plants. Several factors have contributed to the potential for better operation and control, such as cheap computing power, improving sensors and better knowledge of process dynamics and control. 

Because the number of potential rules can be so huge, powerful computers and improved methods are required to help navigate through the large number of combinations of items that may need to be considered, and to develop heuristics. Here in review are the reasons why this arises when you think that it might not be the case. 

As an overall measure of the quality of the shape of the computed potentials, two of the co-authors introduced the above mentioned non-parallelism error (NPE) (34), which is defined as the difference between the maximal and minimal deviations from the exact FCI potential. Clearly, NPE=0 when the computed potential differs from the FCI one by a constant shift. The NPE s of the computed potentials, given in Tables 1-5, are summarized in Table 6. We see that the CCSD and AL-CCSD NPE s, as well as the RMR CCSD and AL-RMR CCSD ones, are very similar, implying a similar quality of the resulting potentials. The RMR CCSD or AL-RMR CCSD NPE s are usually one order of magnitude smaller than the CCSD or AL-CCSD ones. For the H4 and H8 models, which are essentially two-reference cases, we indeed obtain similar results with either RMR CCSD or AL-RMR CCSD when using the (2,2) reference space. In the case of the S4 model and of the symmetric stretching of H2O, the AL-RMR CCSD potentials are slightly inferior to those obtained with RMR CCSD. However, the quality of the AL-RMR CCSD potentials improves when we employ a (4,4) reference space. 

The discussion in Section II.A has shown that many of the currently accepted semiempirical methods for computing potential surfaces are based on the MNDO model. These methods differ mainly in their actual implementation and parametrization. Given the considerable effort that has gone into their development, we believe that further significant overall improvements in general-purpose semiempirical methods require improvements in the underlying theoretical model. In this spirit we describe two recent developments The extension of MNDO to d orbitals and the incorporation of orthogonalization corrections and related one-electron terms into MNDO-type methods. 

The steps in the design process were examined. Areas where currently available computing power and analytic capabilities offered promise for cost reductions were identified. The potential reductions in manufacturing costs by increases in design flexibility were identified. Areas where no potential improvements could be identified at this time where identified. 

V. Potential Improvements in the Computer Methodology for Lipoprotein Analysis... 

Much has been achieved in the last 10 years. However, there is still huge potential for Data Mining to develop as computer technology improves in capability and new applications become available. 

Let us rationalize, via a thought experiment, what occurs in the limiting case of infinitely many reactions. In what follows, as we continue to run batch experiments, compute the convex hull of the set of points, and then seek concave regions to start new batch experiments, we can envision that a state is attained where no further improvements are achieved. The concave sections of the resulting regions become smaller with each new batch, and therefore it is difficult to locate additional mixture concentrations (the x, s) that serve to operate additional batches from. On reflection, the existence of a concave region provides a visual indication of potential improvement—the actual improvement is found... 

As computational resources improved, force fields were introduced which are parameterized exclusively based on ab initio calculations [20-24]. Different analytical site-site potential functions are employed, e.g., the Tang and Toennies potential [25] ... 

The so-called graphically contracted function scheme (GCF) introduce a completely new parameterization of the CASSCF-CI space (based on the so-called Shavitt graphs) while maintaining key qualities of the CASSCF approach. The new approach is still in a vigorous development phase and suffers from problems of conceptual importance. For example, the GCF approach is not invariant to the order of the active orbitals. However, the method exhibits enormous development potential and does not only offer a reduced parameter space but also an efficient way in which matrix elements can be computed. Recent improvement of the recursive algorithm, used in GCF, presents CASSCF calculation correlating 156 electrons in 156... 

Another potential improvement is to prove the observed sufficient conditions for NANDs. Namely, compute the probability that there are intersecting paths of sufficiently short length from each input to the output. 

While simulations reach into larger time spans, the inaccuracies of force fields become more apparent on the one hand properties based on free energies, which were never used for parametrization, are computed more accurately and discrepancies show up on the other hand longer simulations, particularly of proteins, show more subtle discrepancies that only appear after nanoseconds. Thus force fields are under constant revision as far as their parameters are concerned, and this process will continue. Unfortunately the form of the potentials is hardly considered and the refinement leads to an increasing number of distinct atom types with a proliferating number of parameters and a severe detoriation of transferability. The increased use of quantum mechanics to derive potentials will not really improve this situation ab initio quantum mechanics is not reliable enough on the level of kT, and on-the-fly use of quantum methods to derive forces, as in the Car-Parrinello method, is not likely to be applicable to very large systems in the foreseeable future. 

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