Catastrophe hierarchy

Tallon, J.L. A hierarchy of catastrophes as a succession of stability limits for the crystalline state. Nature 1989, 342, 658-660. 

At the end of a brief review of elementary catastrophes, in which we discussed Morse functions in one and two state variables (Aj), catastrophes of one state variable A2, A3, A4, and catastrophes of two state variables B4+, D4, it should be noted that elementary catastrophes form a certain hierarchy according to the diagram shown below... 

Alarm indications should be arranged by their hierarchy of information and alarm status so the operator does not become inundated with a multitude of alarm indications. If such an arrangement exists, he may not be able to immediately discriminate critical alarms fiom non-critical alarms. Operators sometimes have to make decisions under h hly stressful situations with conflicting or incomplete information. It is therefore imperative to keep major alarms for catastrophic incidents as simple and direct as possible. 

Table 3.25 When the second order distance difference is considered between the individual inter-modeling paths of Table 3.24 can nevertheless be considered through the further variations of paths of Table 3.24. Also, the QSAR-I and the fold (F) catastrophe model intervene in changing the influence on specific interactions from POL to H. Therefore, by counting the minimiun hierarchy of these paths, the distance ordering is obtained as follows ...

Somehow the influences of POL and H are reversed relative to the prescription by trial succession of Eq. (3.250), revealing hydrophobicity as the main influential factor. However, due to the fact that the predicted activities of POL in Table 3.27 are all in the opposite evolution direction with respect to the activities recorded in Table 3.21, i.e., they are all negative, the uni-parametric tests and their associated hierarchy (3.256) are discarded, and one looks toward the second class of QSAR and catastrophe algorithms. 

Remarkably, the hierarchy (3.257) starts with the QSAR model, which is revealed to be at the top of the validated catastrophe models with statistical performance even higher than through the predicted equation of Table 3.23 and the trial set of Table 3.21. Moreover, the QSAR-II model involves parameters (LogP H) that are followed by the hyperbolic umbilic (HU) model in terms of (LogP POL) parameters, in this way... 

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