Topology errors

After running balance with these data, the message about topology errors appears on the screen ... 

Also node T2 is affected by missing stream of steam from TO to T2. There is no topology error found (why ) but the significant imbalance is reported. The following message appears therefore on the screen. 

The topological error measure (t), in which the respective first and second BMUs of all the data samples, are determined If these are not adjacent on the map, then, this is considered an error. The total error is then normalized to a range from 0 to 1, where 0 means perfect topology preservation (Polzlbauer, 2004). The actual topological error of the trained SOM map is 0.05. 

The actual average quantization error q and the topological error of the trained map are calculated and equal to 0.09 and 0.02, respectively. 

The voltage feedbaek loop must be isolated from the input voltage line and the eontrol IC. An optoisolator must be used. To minimize the drift effeet of the optoisolator an error amplifier is desired on the seeondary side. A TT431CP does this job nieely. The topology of the feedbaek eireuitry is shown in Figure 3-70. 

The %HIA, on a scale between 0 and 100%, for the same dataset was modeled by Deconinck et al. with multivariate adaptive regression splines (MARS) and a derived method two-step MARS (TMARS) [38]. Among other Dragon descriptors, the TMARS model included the Tig E-state topological parameter [25], and MARS included the maximal E-state negative variation. The average prediction error, which is 15.4% for MARS and 20.03% for TMARS, shows that the MARS model is more robust in modeling %H1A. 

Flexible optimal descriptors have been defined as specific modifications of adjacency matrix, by means of utilization of nonzero diagonal elements (Randic and Basak, 1999, 2001 Randic and Pompe, 2001a, b). These nonzero values of matrix elements change vertex degrees and consequently the values of molecular descriptors. As a rule, these modifications are aimed to change topological indices. The values of these diagonal elements must provide minimum standard error of estimation for predictive model (that is based on the flexible descriptor) of property/activity of interest. 

The inset in Figure 5.7 shows that both the RMSBC and RMSBP reach a minimum when four neurons are considered in the hidden layer. This was verified running more tests and it was concluded that this should be an optimum topology for this particular example. The best RMSBP corresponded to an ANN which yielded a 0.49 pg ml error. In addition, it was tested whether a larger or smaller number of PC scores might improve the predictions. Two extreme situations were studied considering 5 and 15 scores per sample. Improvements were not observed and, as a consequence, the net was not changed further. 

The same is true for low-dimensional systems, d — 1 and 2. The point is not only that for such systems the better statistics could be achieved accompanied with reasonable computational time spent for it. Another circumstance is that we can expect here that the superposition approximation gives greater errors. For example, for one-dimensional contact recombination the so-called bus effect is known [17] given particles A and B can react only after particles separating them disappear during reaction. This topological effect is not foreseen by the superposition approximation but can affect considerably the reaction rate. 

Nelson and Jurs [41] have developed models for three sets of compounds (1) hydrocarbons, (2) halogenated hydrocarbons, and (3) alcohols and ethers. Each model correlates log[C (mol L-1)] with nine molecular descriptors that represent topological, geometrical, and electronic molecule properties. The standard error for the individual models is 0.17 log unit and for a fourth model that combines all three compound sets, the standard error is 0.37 log unit. 

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