Minimum, local

The back-propagation strategy is a steepest gradient method, a local optimization technique. Therefore, it also suffers from the major drawback of these methods, namely that it can become locked in a local optimum. Many variants have been developed to overcome this drawback [20-24]. None of these does however really solve the problem. 

A way to obtain an idea on the robustness of the obtained solution is to retrain the network with a different weight initialization. The results of the different training sessions can be used to define a range around the performance curve as shown in Fig. 44.17. This procedure can also be used to compare different networks [20]. 

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The camera model has a high number of parameters with a high correlation between several parameters. Therefore, the calibration problem is a difficult nonlinear optimization problem with the well known problems of instable behaviour and local minima. In out work, an approach to separate the calibration of the distortion parameters and the calibration of the projection parameters is used to solve this problem. 

Figure 8 shows a one-dimensional sketch of a small fraction of that energy landscape (bold line) including one conformational substate (minimum) as well as, to the right, one out of the typically huge number of barriers separating this local minimum from other ones. Keeping this picture in mind the conformational dynamics of a protein can be characterized as jumps between these local minima. At the MD time scale below nanoseconds only very low barriers can be overcome, so that the studied protein remains in or close to its initial conformational substate and no predictions of slower conformational transitions can be made. 

Abstract. A smooth empirical potential is constructed for use in off-lattice protein folding studies. Our potential is a function of the amino acid labels and of the distances between the Ca atoms of a protein. The potential is a sum of smooth surface potential terms that model solvent interactions and of pair potentials that are functions of a distance, with a smooth cutoff at 12 Angstrom. Techniques include the use of a fully automatic and reliable estimator for smooth densities, of cluster analysis to group together amino acid pairs with similar distance distributions, and of quadratic progrmnming to find appropriate weights with which the various terms enter the total potential. For nine small test proteins, the new potential has local minima within 1.3-4.7A of the PDB geometry, with one exception that has an error of S.SA. 

Otieriched dynam ics can trap structures in local minima. I o prevent this problem, you can cool the system slowly to room temperature or some appropriate lower temperature. I heu run room letTiperature m olecti lar dyn am ics sim ulation s to search for con formations that have lower energies, closer to the starting structure. Cooling a structure slowly is called simulated annealing. 

The stored output of a stochastic search, STOCHASTIC.MEM, for the various local minima of n-pentane using Program MM3 is accessed by the following four lines... 

J. Simons. A discussion of how local minima and transition states are loeated on eleetronie energy surfaees is provided in Chapter 20 of the present text. 

One of the most important questions for a conformational search strategy is, When have I found all of the energetically interesting con formers This is an area of active research and the ideal answer seems to be, When you find all of the local minima. However, this answer is not always reasonable, because medium to large molecules have a large number of minima (see Complexity of Potential Energy Surfaces on page 14). 

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