Potential smoothing

To transform the potential smoothly and to avoid large perturbations, Aj has been increased in small steps from 0 to 1. To evaluate numerically AF(AES) with equations (43) and (44), we have used in each case the mapping potential Hm for which the most populated S subset is the one centred at AES. Following this procedure, each calculation converges very fast. 

Schematic representation of the mesenchymal and endothelial cascade of differentiation in a murine model (mice) and in humans (hum). All mesenchymal and endothelial cells are negative for the antigen CD45. Based on this, the dynamics of surface antigen expression along development of different mature cells derived from the mesenchymal and endothelial systems can be observed. Rounded arrows indicate selfrenewal potential. Smooth, thinner arrows indicate directions of cellular differentiation, and dotted arrows indicate possible hierarchies, but yet to be proved experimentally. The question marks indicate lack of data on the pathway or on cellular identity. The identification of CDs (clusters of differentiation) and other antigen cell markers can be found in the list of abbreviations LT-HSC, long-term hematopoietic stem cell EC, endothelial cell PDMPC, placental-derived mesenchymal progenitor cell MSC, mesenchymal stem cell MAPC, mesenchymal adult progenitor cell.

Tam, E.K., Franconi, G.M., Nadel, J.A. etal. (1990). Protease inhibitors potentiate smooth muscle relaxation induced by vasoactive intestinal peptide in isolated human bronchi. Am. J. Respir. Cell Mol. Biol. 2, 449-452. 

There are many other not so widely used norm-conserving pseudo-potentials [64,65,66,67,68]. Note that, in some cases, norm-conservation was abandoned in favor of increased pseudo-potential smoothness [69]. 

An important variation on the classical simulated annealing and potential smoothing methods is QMA. The system is represented quantum mechanically using wave packets," a variational wave function, or a diffusion MC approach" to solve the time-independent Schrddinger equation... 

A second approach has also been used in the ionie liquid/electrode context, in which the eleetrode surface is modeled as an equi-potential smooth surfaee with a net charge. Here, the entire electrode surface is effectively modeled as a metal foil separating the ions and a set of fixed charges located inside the electrode. The constant electrical potential is enforced on numerical grid points lying over the electrode surface by solving an auxiliary Laplace equation, following a method proposed in... 

Keywords Promolecular electron density distribution Poisson equation Coulomb potential Smoothing Molecular alignment Similarity index... 

Hart RK, Pappu RV, Ponder JW (2000) Exploring the similarities between potential smoothing and simulated annealing. J Comput Chem 21 531-552... 

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