A well-performing set of radial basis functions (RBFs) can emerge from genetic competition among individual RBFs. Genetic selection of the individual RBFs is based on credit sharing which localizes competition within orthogonal niches. These orthogonal niches are derived using singular value decomposition and are used to apportion credit for the overall performance of the RBF network among indi...

During the last decade, three main variations have been proposed for solving elliptic PDEs by means of collocation with radial basis functions (RBFs). In this study, we have implemented them for infinitely smooth RBFs, and then compared them across the full range of values for the shape parameter of the RBFs. This was made possible by a recently discovered numerical procedure that bypasses the ...

Abstract In this article, a meshless numerical technique based on radial basis functions (RBFs) is proposed for the solution of singular perturbed, obstacle, and second-order boundary value problems. First, unknown function their derivatives are approximated by RBFs which reduces given problem into system algebraic equations easy to solve. The shape parameter involved in chosen hit trial method...

Until now, only non-oscillatory radial basis functions (RBFs) have been considered in the literature. It has recently been shown that a certain family of oscillatory RBFs based on J Bessel functions give rise to non singular interpolation problems and seem to be the only class of functions not to diverge in the limit of flat basis functions for any node layout. This paper proves another interes...

Although most work to date on RBFs relates to scattered data approximation and in general to interpolation theory, there has recently been an increased interest in their use for solving partial differential equations (PDEs). This approach, which approximates the whole solution of the PDE directly using RBFs, is very attractive due to the fact that this is truly a mesh-free technique. Kansa [1] ...

We examine the ability of radial basis functions (RBFs) to generalize. We compare the performance of several types of RBFs. We use the inverse dynamics of an idealized two-joint arm as a test case. We find that without a proper choice of a norm for the inputs, RBFs have poor generalization properties. A simple global scaling of the input variables greatly improves performance. We suggest some e...

Ribosome biogenesis involves a large inventory of proteinaceous and RNA cofactors. More than 250 ribosome biogenesis factors (RBFs) have been described in yeast. These factors are involved in multiple aspects like rRNA processing, folding, and modification as well as in ribosomal protein (RP) assembly. Considering the importance of RBFs for particular developmental processes, we examined the co...

We introduce a class of matrix-valued radial basis functions (RBFs) of compact support that can be customized, e.g. chosen to be divergence-free. We then derive and discuss error estimates for interpolants and derivatives based on these matrixvalued RBFs.

Radial Basis Functions (RBFs) are widely used in science, engineering and finance for constructing nonlinear models of observed data. Most applications employ activation functions from a relatively small list, including Gaussians, multi-quadrics and thin plate splines. We introduce several new candidate compactly supported RBFs for approximating functions in L (R) via overdetermined least squar...

There are two major paradigms for linear-space heuristic search: iterative deepening (IDA*) and recursive best-first search (RBFS). While the node regeneration overhead of IDA* is easily characterized in terms of the heuristic branching factor, the overhead of RBFS depends on how widely the promising nodes are separated in the search tree, and is harder to anticipate. In this paper, we present ...