Descriptive error propagation

Figure 4.11 Monte-Carlo simulation (100 trials) of error propagation for La/Yb fractionation in residual melts by clinopyroxene-garnet removal from a basaltic parent magma (see text for parameter description and distributions used). Top mineral-liquid partition coefficients for La and Yb. Bottom variations of the La/Yb ratio as a function of the fraction F of residual melt.

The description of an object in the sense of environmental investigation may be the determination of the gross composition of an environmental compartment, for example the mean state of a polluted area or particular location. If this is the purpose, the number of individual samples required and the required mass or size of these increments have to be determined. The relationship between the variance of sampling and that of analysis must be known and both have to be optimized. The origin of the variance of the samples can be investigated by the study of variance contribution of the different steps of the analytical process by means of the law of error propagation (Eq. 4-21) according to Section 4.3.4. 

This factor can be calculated for each specific combination of the natural (analyte) isotope and the enriched (spike) isotope abundances for the element of interest. The description of error propagation plots (see below) includes a number of examples showing how this factor varies as a function of the isotope amount ratios in the spiked sample. The isotope proportions in the unmixed natural and isotopically enriched materials heavily influence the shape of these plots. Thus for... 

Fig. 11 shows an example of how error propagation is visualized for an Offset fault model that was applied on the wheel rotation input signal of the BBW model. This block is marked yellow according to the description in Section 3.3. 

In following sections, the basis of the main components of a neuron, how it works and, finally, how a set of neurons are connected to yield an ANN are presented. A short description of the most common rules by which ANNs learn is also given (focused on the error back-propagation learning scheme). We also concentrate on how ANNs can be applied to perform regression tasks and, finally, a review of published papers dealing with applications to atomic spectrometry, most of them reported recently, is presented. 

Description of fault events such as propagation, error event. 

There is extension of AADL for fault description, such as error event and propagation. As discussed earlier, errors may be different types such as value error, out of range, and inconsistency. These errors may propagate from sensor to controller and then to the actuator. Error behavior may be classified as error related transition, use of error type and propagation rules. Major application area of AADL may be ... 

While this approach to estimating long-term performance is relatively straightforward, adequate description of the associated measurement error and its propagation through all of the calculations is complex. In practice one could repeat the experiment several times to quantify its variability, but this would be potentially costly and time consuming. This paper describes a statistical treatment to place confidence bounds on Arrhenius-based performance degradation predictions by way of a hypothetical example. 

Fig. 1. Descriptive Equation (7) or (8) for the expansion speed Vn (Oregonator space unit/time unit) of 66 helices is plotted against numerical observations. The ten helices in which coil-coil separation violated the Keener-T son proscription are excluded. The unit of speed is about 1/6 of wave propagation speed at the parameters used (s = 1/50, / = 1.6, equal diffusion coefficients), so the fastest dilations shown here (negative Vn) are only a few percent of propagation speed. This is by far the best fit found to date with polynomials in curvature and twist if the mathematics exactly described these numerical solutions of the reaction-diffusion equations, then all dots would fall on the line of unit slope through the origin. There is a strong tendency to do so, yet many helices still expand or contract several times faster or slower than predicted . A serious problem with all numerical experiments is that no error bars have been determined around the data points.

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