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A mathematical description of Model 1 is given in sub-section 3, and its computer implementation - in sub-section 4. The ends of these sub-sections provide reasoning for the extension to Model 2 in terms of multicriteria minimization of the discrepancies as functions of binding attempt intensities.
Minimization of the discrepancy is performed using the Levenberg-Marquardt algorithm for solving nonlinear least squares problems.
Inverse analysis is carried out by a batch, deterministic approach, using conventional optimization algorithms for the minimization of the discrepancy function.
Typically, models are calibrated and model parameters are estimated by minimization of the discrepancy between model simulations characterizing the system and existing observations requiring a substantial number of model evaluations.
Our algorithm is distinguished from other orientation refinement methods (i) by the simultaneous update of the density map and orientation parameters resulting in a highly efficient computational scheme and (ii) by the high quality of the results produced by a direct minimization of the discrepancy between the 2-D data and the projected views of the reconstructed 3-D structure.
Comparative computational exercises are presented in order to point out the consequent significant reduction of computing times in test simulations and, hence, in the minimization of the discrepancy function by the Trust Region Algorithm, namely by a traditional first-order mathematical programming method.
Identification is performed in a non-parametric setting, trying to identify the optimal smooth fit in the frequency domain by minimization of an appropriate discrepancy criterion, between the actual measurements and the model outputs.
Various sources of discrepancies are discussed.
The number of discrepancies is very low.
Possible sources of discrepancies are elucidated.
Analysis of discrepancies in SNF3.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com