Computers shortcomings

While computing VaR as a post-optimization measure of risk is a simple task and does not require any assumptions on the profit distribution, it poses some difficulties when one attempts to use it in design models that manage risk. Given its computational shortcomings, VaR is only convenient to use as a risk indicator because of its popularity in finance circles. 

To gain unambiguous mechanistic support despite the computational shortcomings outlined above, we turned to experiments. If the anionic palladium species were indeed reactive in a polar solvent in the presence of coordinating additives (such as KF or ArB(OH)2), then one should also be able to observe C-Cl addition in a polar solvent, in the absence of those additives, as Pd(0)L... 

Despite all the shortcomings listed above, full particle classical MD can be considered mature [84]. Even when all shortcomings will be overcome, we can now clearly delineate the limits for application. These are mainly in the size of the system and the length of the possible simulation. With the rapidly growing cheap computer memory shear size by itself is hardly a limitation several tens of thousands of particles can be handled routinely (for example, we report a simulation of a porin trimer protein embedded in a phospholipid membrane in aqueous environment with almost 70,000 particles [85] see also the contribution of K. Schulten in this symposium) and a million particles could be handled should that be desired. 

Fortunately, as shown by Lee, Handy, and Colwell, 1995, it seems that the consequences of this approximation with regard to the accuracy of the computed chemical shifts are rather modest and are of less significance than the general shortcomings inherent in the functionals used. Hence, from an application-oriented, pragmatic point of view one does not need to worry too much about using functionals which are formally inadequate because they neglect the required dependence on j(r). 

A few words concerning the results of our analyses in Illustrations 12.8 and 12.9 are in order. Obviously, better estimates of the catalyst requirements could be obtained by using smaller conversion increments. We have not attempted to fully optimize the reactor stages in terms of catalyst minimization. Furthermore, we have again neglected pressure drop in each stage. Further calculations would remedy each of the aforementioned shortcomings of the analysis. They are readily accomplished with the aid of machine computation. 

In Chapters 63-66 [1-4], we discussed shortcomings of current methods used to assess the presence of nonlinearity in data, and presented a new method that addresses those shortcomings. This new method is statistically sound, provides an objective means to determine if nonlinearity is present in the relationship between two sets of data, and is inherently suitable for implementation as a computer program. 

It is important to realize that each of the electronic-structure methods discussed above displays certain shortcomings in reproducing the correct band structure of the host crystal and consequently the positions of defect levels. Hartree-Fock methods severely overestimate the semiconductor band gap, sometimes by several electron volts (Estreicher, 1988). In semi-empirical methods, the situation is usually even worse, and the band structure may not be reliably represented (Deak and Snyder, 1987 Besson et al., 1988). Density-functional theory, on the other hand, provides a quite accurate description of the band structure, except for an underestimation of the band gap (by up to 50%). Indeed, density-functional theory predicts conduction bands and hence conduction-band-derived energy levels to be too low. This problem has been studied in great detail, and its origins are well understood (see, e.g., Hybertsen and Louie, 1986). To solve it, however, requires techniques of many-body theory and carrying out a quasi-particle calculation. Such calculational schemes are presently prohibitively complex and too computationally demanding to apply to defect calculations. 

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