Fragmentation model, nonlinear

E-state indices, counts of atoms determined for E-state atom types, and fragment (SMF) descriptors. Individual structure-complexation property models obtained with nonlinear methods demonstrated a significantly better performance than the models built using MLR. However, the consensus models calculated by averaging several MLR models display a prediction performance as good as the most efficient nonlinear techniques. The use of SMF descriptors and E-state counts provided similar results, whereas E-state indices led to less significant models. For the best models, the RMSE of the log A- predictions is 1.3-1.6 for Ag+and 1.5-1.8 for Eu3+. 

Thus, multilinear models were introduced, and then a wide series of tools, such as nonlinear models, including artificial neural networks, fuzzy logic, Bayesian models, and expert systems. A number of reviews deal with the different techniques [4-6]. Mathematical techniques have also been used to keep into account the high number (up to several thousands) of chemical descriptors and fragments that can be used for modeling purposes, with the problem of increase in noise and lack of statistical robustness. Also in this case, linear and nonlinear methods have been used, such as principal component analysis (PCA) and genetic algorithms (GA) [6]. 

This is a positive situation. It is also positive that for the same endpoint, there are, even now, different models. This offers a more robust series of tools to the user, mainly if these tools are based on different assumptions and adopt different techniques, such as fragments of chemical descriptors, linear or nonlinear systems, etc. It is not ideal to search for the best model. It is preferable to have a battery of tools, which, together, are in general more robust toward errors. 

The original model [17] contained 35 structural fragments whose coefficients were developed by linear and nonlinear regression using an ex-... 

In a more recent paper. Ho and Drzal [94] used a three-phase nonlinear finite-element analysis to investigate the stress transfer phenomenon in the singlefiber fragmentation test. The effect of fiber properties, interphase properties and thickness on the stress distribution in the vicinity of the fiber break was evaluated. Also, the stress fields for various fiber-matrix interface debonding conditions and the effect of frictional stress transfer were investigated. In this model, the fiber was assumed to be a linear elastic transversely isotropic material, the interphase as an elastic material and the matrix as a nonlinear material. It was found that... 

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