Calculation, robust

Lastly, it is desirable that parameters are able to discriminate between positive and negative conditions in a variety of experimental conditions. In other words they should be robust and reproducible. For this purpose, the Pearson correlation coefficient between all experimental repeats using control wells is calculated. Robust parameters have high Pearson correlation coefficients (above 0.7) in pairwise comparisons of experimental repeats. For this analysis we have developed another R template in KNIME to calculate the Pearson correlation coefficient between experimental runs. 

Calculational procedure of all the dynamic variables appearing in the above expressions—namely, the dynamic structure factor F(q,t) and its inertial part, Fo(q,t), and the self-dynamic structure factor Fs(q,t) and its inertial part, Fq (q, t) —is similar to that in three-dimensional systems, simply because the expressions for these quantities remains the same except for the terms that include the dimensionality. Cv(t) is calculated so that it is fully consistent with the frequency-dependent friction. In order to calculate either VACF or diffusion coefficient, we need the two-particle direct correlation function, c(x), and the radial distribution function, g(x). Here x denotes the separation between the centers of two LJ rods. In order to make the calculations robust, we have used the g(x) obtained from simulations. 

The conductor-like screening model (COSMO) is a continuum method designed to be fast and robust. This method uses a simpler, more approximate equation for the electrostatic interaction between the solvent and solute. Line the SMx methods, it is based on a solvent accessible surface. Because of this, COSMO calculations require less CPU time than PCM calculations and are less likely to fail to converge. COSMO can be used with a variety of semiempirical, ah initio, and DFT methods. There is also some loss of accuracy as a result of this approximation. 

The semiempirical techniques available include EH, CNDO, INDO, MINDO/3, ZINDO, MNDO, AMI, and PM3. The ZINDO/S, MNDO/d, and PM3(TM) variations are also available. The semiempirical module seems to be rather robust in that it did well on some technically difficult test calculations. 

Q-Chem also has a number of methods for electronic excited-state calculations, such as CIS, RPA, XCIS, and CIS(D). It also includes attachment-detachment analysis of excited-state wave functions. The program was robust for both single point and geometry optimized excited-state calculations that we tried. 

The typical phase equiHbrium problem eacouatered ia distiHatioa is to calculate the boiling temperature and the vapor composition ia equiHbrium with a Hquid phase of specified composition at a givea pressure. If the Hquid phase separates, thea the problem is to calculate the boiling temperature and the compositions of the two equiHbrium Hquid phases plus the coexistiag vapor phase at the specified overall Hquid compositioa. Robust and practical numerical methods have been devised for solving this problem (95—97) and have become the recommended techniques (98,99). 

It does not calculate source emission rates. While it handles jets, it does so simply and docs not calculate the details of the jet motions and thermodynamics. It should not be used for strongly buoyant plumes. The error diagnostics are limited to checking the consistency of input parameters. Run time error diagnostics are missing but are rarely needed due to its robustness. 

Uncertainty Analysis determines the effects on the overall results from uncertaintic.s in the database, assumptions in modeling, and the completeness of the analysis. Sensitivity analyses determine the robustness of the results importance calculations are useful for identifying and prioritizing plant improvements. 

Using computer-aided numerical calculations, one can readily simulate and identify critical parameters for process validation. Thus, one can evaluate the robustness of the process during its design. To ensure performance, optimization of the process and evaluation of critical parameters can be determined before actual operating conditions. 

The most useful characteristic of the median is the small influence exerted on it by extreme values, that is, its robust nature. The median can thus serve as a check on the calculated mean. 

The standard deviation, Sj, is the most commonly used measure of dispersion. Theoretically, the parent population from which the n observations are drawn must meet the criteria set down for the normal distribution (see Section 1.2.1) in practice, the requirements are not as stringent, because the standard deviation is a relatively robust statistic. The almost universal implementation of the standard deviation algorithm in calculators and program packages certainly increases the danger of its misapplication, but this is counterbalanced by the observation that the consistent use of a somewhat inappropriate statistic can also lead to the right conclusions. 

A wholly different approach is that of Huber, who orders the values according to size, and determines the median (cf. Section 1.1.1) then the absolute deviations jx, - x l are calculated and also ordered, the median absolute deviation (MAD) being found. MAD is then used as is Sx earlier, the coefficient k being chosen to be between 3 and 5. This algorithm is much more robust than the ones described before. 

For this reason alone the tacit assumption of a normal distribution when contemplating analytical results is understandable, and excusable, if only because there is no practical alternative (alternative distribution models require more complex calculations, involve more stringent assumptions, or are more susceptible to violations of these basic assumptions than the relatively robust normal distribution). 

Considering all potential experimental and systematic errors of NOE/ROE crosspeak intensities, it is remarkable how robust the derived distance restraints still are. The reason Ues in the dependence of the cross-relaxation rate even if a cross-peak intensity is determined wrongly by a factor 2, the resulting distance restraint is only affected by the factor 1.12, which usually lies within the error range of distance restraints used in structure calculations. It should be further noted that the quaUty of a resulting structure is not so much determined by the... 

As described in Section 9.4, the determination and refinement of molecular conformations comprehends three main methods DG, MD and SA. Other techniques like Monte Carlo calculations have only a limited applicability in the field of structure elucidation. In principle, it is possible to exclusively make use of DG, MD or SA, but normally it is strongly suggested to combine these methods in order to obtain robust and reliable structural models. Only when the results of different methods match a 3D structure should be presented. There are various ways of combining the described techniques and the procedural methods may differ depending on what kind of molecules are investigated. However, with the flowchart in Fig. 9.13 we give an instruction on how to obtain a reliable structural model. 

Nevertheless, DFT has been shown over the past two decades to be a fairly robust theory that can be implemented with high efficiency which almost always surpasses HF theory in accuracy. Very many chemical and spectroscopic problems have been successfully investigated with DFT. Many trends in experimental data can be successfully explained in a qualitative and often also quantitative way and therefore much insight arises from analyzing DFT results. Due to its favorable price/performance ratio, it dominates present day computational chemistry and it has dominated theoretical solid state physics for a long time even before DFT conquered chemistry. However, there are also known failures of DFT and in particular in spectroscopic applications one should be careful with putting unlimited trust in the results of DFT calculations. 

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