Bounds-smoothing technique

In the basic metric matrix implementation of the distance constraint technique [16] one starts by generating a distance bounds matrix. This is an A X y square matrix (N the number of atoms) in which the upper bounds occupy the upper diagonal and the lower bounds are placed in the lower diagonal. The matrix is Ailed by information based on the bond structure, experimental data, or a hypothesis. After smoothing the distance bounds matrix, a new distance matrix is generated by random selection of distances between the bounds. The distance matrix is converted back into a 3D confonnation after the distance matrix has been converted into a metric matrix and diagonalized. A new distance matrix... 

Continuous optimization problems are usually easier to solve because the smoothness of the functions makes it possible to use objective and constraint information at a particular point x to deduce information about the function s behavior at all points close to x. In discrete problems, by contrast, the behavior of the objective and constraints may change significantly as we move from one feasible point to another, even if the two points are close by some measure. The feasible sets for discrete optimization problems can be thought of as exhibiting an extreme form of non-convexity, as a convex combination of two feasible points is in general not feasible. Continuous optimization techniques often play an important role in solving discrete optimization problems. For instance, the branch-and-bound... 

Layer-by-layer (LbL) technique can be apphed to form the smooth multilayer films based on PDMS. Using this method the covalently bound, robust multilayer films of optical quality were obtained from 3-aminopropyl-terminated homobifunctional PDMS and poly(ethylene-alt-maleic anhydride) (PEMA) on silica surfaces [48]. Due to the differences in solubility of the polymers used, the polymer layers were deposited from different solvents PEMA layers were prepared from tetrahydrofuran solution, while the PDMS layers were deposited from toluene. The multilayer assemblies show a solvent memory for swelling and de-swelling when immersed in the corresponding solvent for each polymer. Films prepared under these conditions were smooth up to 60 nm of thickness, as demonstrated by small angle X-ray reflectometry, and do not visibly scatter the incident light. Thicker films showed very homogeneous... 

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