Models incorrect

M. Hendlich, P. Lackner, S. Weitckus, H. Floeckner, R. Froschauer, K. Gotts-bacher, G. Casari and M. J. Sippl, Identification of native protein folds amongst a large number of incorrect models, J. Mol. Biol. 216 (1990), 167-180. 

From a plot of the internalisation flux against the metal concentration in the bulk solution, it is possible to obtain a value of the Michaelis-Menten constant, Am and a maximum value of the internalisation flux, /max (equation (35)). Under the assumption that kd kml for a nonlimiting diffusive flux, the apparent stability constant for the adsorption at sensitive sites, As, can be calculated from the inverse of the Michaelis-Menten constant (i.e. A 1 = As = kf /kd). The use of thermodynamic constants from flux measurements can be problematic due to both practical and theoretical (see Chapter 4) limitations, including a bias in the values due to nonequilibrium conditions, difficulties in separating bound from free solute or the use of incorrect model assumptions [187,188],... 

Although Bohr s model fits the energy levels for hydrogen, it is a fundamentally incorrect model for the hydrogen atom. 

Most programs provide plots of observed and calculated data versus the independent variable x. On both linear or semilog axes, these should be similar, with the calculated line running close to the observed data. If the observed and calculated data appear to be going in different directions, incorrect model specification should be suspected. If the two lines have a similar shape but do not coincide, may be a parameter value limit is causing a problem. Alternately, the program may have fallen into a local minimum. Rerunning the analysis with better (different) initial estimates may help. This plot can be useful in the identification of incorrectly entered data or outliers. 

Interpretation of nOe results must be performed with caution because a number of difficulties, both technical, such as spin diffusion, and theoretical, such as the use of oversimplified or incorrect models can lead to incorrect interpretations. 

Accuracy Characterizes the difference between the result of a measurement and the true value of the measured data. It is difficult to estimate properly because the true value is most generally unknown. Computer experiments permit an easy estimate of the errors due to the use of incorrect models, but are unable to accoimt for instrumental bias. 

DST methods are particularly competitive for organic compounds, which are more resistant to the traditional approaches and whose structural models can be easily guessed. At present, the complexity of crystal structures solved by direct-space methods is essentially limited by the number of DOFs that can be handled by the global optimization algorithms within a reasonable amount of time. In prospect, improvement of both search algorithms and computer power may overcome this limitation. The major pitfalls for the use of DST are (a) they are time consuming (b) they are dependent on the existence of reliable prior structural information. Partially incorrect models may compromise the success of the procedure independent of the computer time spent (c) they are sensitive to the accuracy of the peak profile parameterization through peak-shape and peak-width functions. ... 

The failure of non-electrostatic model is not surprising in view of its physical incorrectness. The model curves in Figs. 5.2-5.20 are presented as a reference for the model curves calculated using different electrostatic models, and the non-electrostatic model itself is not recommended. A few examples of agreement between the model curves and experimental results can serve as an example that the experiment can be successfully simulated by a physically incorrect model. 

Fig. 7.8 Other examples of incorrect model drawings on acids and acidic solutions [4]...

It is always useful to look at the residuals, i.e., the differences between the data and the fitted function in the present example, the residuals are the differences y,— acalc xt. The reason for this is that use of an incorrect model (such as fitting to, say, a linear or quadratic relation rather than to a proportionality) often leads to a discernible trend in the residuals, whereas random deviations do not. Therefore plot the residuals y- ycaic = y-... 

One popular model of retention has been the solvophobic theory, which relates retention to the surface tension of the mobile-phase solvents (103). As important as the solvophobic theory has been to the development of modern LC, it is based on an incorrect model of the relevant solution processes. It supposes that retention can be modeled in terms of the association of two solute molecules in a single solvent rather than on the transfer of a solute from one solvent to another. Hence the solvophobic theory does not take cognizance of the interactions of the solute with the second solvent, the cavity in the stationary phase it takes into account only the cavity in the mobile phase. 

The economic and social implications of an incorrect model choice can be tremendous. Employing a "non-linear" model when in truth the response is "linear" can result in an unacceptably large risk to the exposed population. Employing a "linear" model when response is "non-linear" could result in unnecessarily restricting or banning the use of a potentially beneficial product. Thus, a major concern in quantitative risk assessment is to accurately... 

Cases in the Figure 10.18 correspond to a) adequate model with random distribution, b) inappropriate weighting, c) systematic deviations due to an incorrect model, d) poor experimental design incapable of supplying the information expected. 

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