Networks based on basis set function expansions, such as the Radial Basis Function (RBF), or Separable Basis Function (SBF) networks, have non-linear parameters that are not trivial to optimize. Clustering techniques are frequently used to optimize positions for localized functions. Context-dependent fuzzy clustering techniques improve convergence of parameter optimization, leading to better ne...

There are multiple reasons why anisotropic basis functions may be needed or be more appropriate. The most obvious is that if the basis function is to be defined on Rn × T then there is no natural norm on this space that would reflect the unique properties of time. A second reason is that function being interpolated or approximated may incorporate a directional dependence. Thirdly, differentiabi...

The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can, however, lifted considering sets states. Here we introduce the concept set for characterizing systems in basis-independent way. We construct measures quantifying states as well measurements. These feature operational meaning terms discrimination games and ...

We show that there exists a bounded subset of $\mathbb{R}$ such no system exponentials can be Riesz basis for the corresponding Hilbert space. An additional result gives lower bound constant any putative two dimensional disk.

Intermolecular potential energy surface (IPS) for protein — protein has been examined using RHF, DFT-B3LYPand MP2 levels of theory with 6-31G, 6-31G* basis sets. A number of basis sets were used in order to evaluatethe basis set effects, at all three levels of theory, basis sets has significant effects on the calculated potentialenergy curves (including position, depth and width of the potentia...