Minimal models search algorithm

The proposed detection method belongs to the class of state space simulations. At first, the system model graph is evaluated to find candidates of minimal path sets. This is achieved by an adapted depth-first search algorithm and establishing of unions of the found paths. Then, the system model is simulated only for the candidates to detect the actual minimal path sets. Figure 9 shows a flow chart of the detection method. Without the prior evaluation of the model graph, the number of simulations would be 2", nr being the number of system components. 

These models are nested the search starts with the simplest model and proceeds to the models of increasing degree of complexity (number of fitting parameters). An Ockham s razor principle is assumed here if more than one model is consistent with the data, the simplest model is preferred. For each model of motion, all parameters are determined from fitting, based on the simplex algorithm, to minimize the following target function ... 

This statistical method is used for the estimation of parameters of -> electrode reaction by fitting a theoretical relationship to experimentally obtained data. This is achieved by minimizing the sum of squared deviations of the observed values for the dependent variable from those predicted by the model. Nonlinear least-square estimations can not be performed algebraically and numerical search procedures are used [i]. The Mar-quardt algorithm is commonly applied in the calculations performed by commercially available computer programs [ii]. 

Figure 11. The combiBUILD algorithm (a) Starting point is a scaffold modeled into its target receptor. CombiBUILD goes over a database of possible reactants to add to the scaffold (b) CombiBUILD performs a systematic rotational search on each reactant (typically in 10-15 increments within the low energy minima for each torsion type), pruning for intramolecular clashes and bumps to make the search more efficient (c) CombiBUILD performs a rigid body minimization on each possible component conformation, scores it with a force-field scheme.

Multiparameter, multiresponse models call for digital optimization. Early workers minimized n(0) by search techniques, which were tedious and gave only a point estimate of 9. Newtonlike algorithms for minimization of i (0) and for interval estimation of 6, were given by Stewart and Sorensen (1976, 1981) and by Bates and Watts (1985, 1987). Corresponding algorithms for likelihood-based estimation were developed by Bard and Lapidus (1968) and Bard (1974), extended by Klaus and Rippin (1979) and Steiner, Blau, and Agin (1986). 

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