Imprecision

To nnderstand the internal molecnlar motions, we have placed great store in classical mechanics to obtain a picture of the dynamics of the molecnle and to predict associated patterns that can be observed in quantum spectra. Of course, the classical picture is at best an imprecise image, becanse the molecnlar dynamics are intrinsically quantum mechanical. Nonetheless, the classical metaphor mnst surely possess a large kernel of truth. The classical stnichire brought out by the bifiircation analysis has accounted for real patterns seen in wavefimctions and also for patterns observed in spectra, snch as the existence of local mode doublets, and the... 

Many expert systems also apply fnt zy logic (see Section 9.6) instead of strict Boolean logic and arc thus able to cope with rules which arc imprecise or incomplete. 

In the investigations described above, the measurements have been interpreted in terms of the parameters of a well-defined flux model. However, it is appropriate at this point to illustrate the dangers of an imprecise... 

The size of the error which can be introduced by imprecise interpretation of the data in terms of an "effective diffusion coefficient" can easily be estimated. Denoting by flux of substance 1 in the... 

In contrast, the method of Figure 7 is not only inaccurate and imprecise but it also over-estimates the true value. 

A particularly useful property of the PX monomer is its enthalpy of formation. Conventional means of obtaining this value, such as through its heat of combustion, are, of course, excluded by its reactivity. An experimental attempt was made to obtain this measure of chemical reactivity with the help of ion cyclotron resonance a value of 209 17 kJ/mol (50 4 kcal/mol) was obtained (10). Unfortunately, the technique suffers from lack of resolution in addition to experimental imprecision. It is perhaps better to rely on molecular orbital calculations for the formation enthalpy. Using a semiempirical molecular orbital technique, which is tuned to give good values for heat of formation on experimentally accessible compounds, the heat of formation of /5-xylylene has been computed to be 234.8 kj/mol (56.1 kcal/mol) (11). 

Potency of hGH preparations is quantitatively deterrnined, in terms of mass per vial, by one or more chromatographic procedures (50). Biopotency is calculated from the mass-based potency using a conversion factor, typically 3 lU/mg. Traditionally a bioactivity assay using hypophysectomized rats has been used to determine potency however, the imprecision of this assay has resulted in its use only as a semiquantitative indicator of bioactivity (1), sometimes referred to as a bioidentity test. 

Standard deviations from two to five or more. This means that the upper seventeenth percentile may be as much as from two to five times the mean. This variabihty is compounded by the problem of estimating the exposure of a group of workers having differing exposures to find the most exposed workers. Compared to this environmental variabihty, the variabihty introduced by the sampling and analytical error is smah, even for those methods such as asbestos counting, which are relatively imprecise. 

An a priori method for choosing a surfactant was attempted by several researchers (50) using the hydroph i1 e—1 ip oph i1 e balance or HLB system (51). In the HLB system a surfactant soluble in oil has a value of 1 and a surfactant soluble in water has a value of 20. Optimum HLB values have been reported for latices made from styrene, vinyl acetate, methyl methacrylate, ethyl acrylate, acrylonitrile, and their copolymers and range from 11 to 18. The HLB system has been criticized as being imprecise (52). 

The average value of the rephcates is reported along with the standard deviation, which reflects the variabihty in the measurement. Large standard deviations relative to the average measurement indicate the need for an action plan to improve measurement precision. This can be accomphshed through more rephcate measurements or the elimination of the source of variation, such as the imprecision of an instmment or poor temperature control during the measurement. 

Flow cytometer cell counts are much more precise and more accurate than hemocytometer counts. Hemocytometer cell counts are subject both to distributional (13) and sampling (14—16) errors. The distribution of cells across the surface of a hemocytometer is sensitive to the technique used to charge the hemocytometer, and nonuniform cell distribution causes counting errors. In contrast, flow cytometer counts are free of distributional errors. Statistically, count precision improves as the square root of the number of cells counted increases. Flow cytometer counts usually involve 100 times as many cells per sample as hemocytometer counts. Therefore, flow cytometry sampling imprecision is one-tenth that of hemocytometry. 

Randomization means that the sequence of preparing experimental units, assigning treatments, miming tests, taking measurements, and so forth, is randomly deterrnined, based, for example, on numbers selected from a random number table. The total effect of the uncontrolled variables is thus lumped together into experimental error as unaccounted variabiUty. The more influential the effect of such uncontrolled variables, the larger the resulting experimental error, and the more imprecise the evaluations of the effects of the primary variables. Sometimes, when the uncontrolled variables can be measured, their effect can be removed from experimental error statistically. 

Either of the two stable operating conditions can be selected by adjusting the positions of the curves so that only one intersection is obtained. In a plant, long-time unstable operation is unlikely because of imprecise temperature control. 

Permeability ( l), which is often used, albeit imprecisely, in referring to ferromagnetic substances, is the ratio of the magnetic-flux density to the magnetic-field density. 

A one-dimensional mesh through time (temporal mesh) is constructed as the calculation proceeds. The new time step is calculated from the solution at the end of the old time step. The size of the time step is governed by both accuracy and stability. Imprecisely speaking, the time step in an explicit code must be smaller than the minimum time it takes for a disturbance to travel across any element in the calculation by physical processes, such as shock propagation, material motion, or radiation transport [18], [19]. Additional limits based on accuracy may be added. For example, many codes limit the volume change of an element to prevent over-compressions or over-expansions. 

Computer simulation is an experimental science to the extent that calculated dynamic properties are subject to systematic and statistical errors. Sources of systematic error consist of size dependence, poor equilibration, non-bond interaction cutoff, etc. These should, of course, be estimated and eliminated where possible. It is also essential to obtain an estimate of the statistical significance of the results. Simulation averages are taken over runs of finite length, and this is the main cause of statistical imprecision in the mean values so obtained. 

Structure calculation algorithms in general assume that the experimental list of restraints is completely free of errors. This is usually true only in the final stages of a structure calculation, when all errors (e.g., in the assignment of chemical shifts or NOEs) have been identified, often in a laborious iterative process. Many effects can produce inconsistent or incorrect restraints, e.g., artifact peaks, imprecise peak positions, and insufficient error bounds to correct for spin diffusion. 

The well-known difficulties in calculating tliree-dimensional structures of macromolecules from NMR data mentioned above (sparseness of the data, imprecision of the restraints due to spin diffusion and internal dynamics) also make the validation of the structures a challenging task. The quality of the data [88] and the energy parameters used in the refinement [89] can be expected to influence the quality of structures. Several principles can be used to validate NMR structures. 

Data sources for Tables 5.5 and 5.6 were different. Thai the data do not always coincide is an indication of their imprecision. 

Cross-comparing the risks of various activities is difficult because of the lack of a common basis of comparison, however Cohen and Lee, 1979 provide such a comparison on the basis of loss of life expectancy. Solomon and Abraham, 1979 used an index of harm in a study of 6 occupational harms - three radiological and three nonradiological to bracket high and low estimates of radiological effects. The index of harm consists of a weighting factor for parametric study the lost time in an industry and the worker population at risk. The conclusions were that the data are too imprecise for firm conclusions but it is possible for a radiation worker under pessimistic health effects assumptions to have as high index of harm as the other industries compared. 

Thus, it seems inevitable that micromechanics predictions of properties will always be imprecise. 

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