The theories for radial basis functions (RBFs) as well as piecewise polynomial splines have reached a stage of relative maturity as is demonstrated by the recent publication of a number of monographs in either field. However, there remain a number of issues that deserve to be investigated further. For instance, it is well known that both splines and radial basis functions yield “optimal” interp...

The role of width of Gaussians in two types of computational models is investigated: Gaussian radial-basis-functions (RBFs) where both widths and centers vary and Gaussian kernel networks which have fixed widths but varying centers. The effect of width on functional equivalence, universal approximation property, and form of norms in reproducing kernel Hilbert spaces (RKHS) is explored. It is pr...

Ribosome biogenesis is fundamental for cellular life, but surprisingly little is known about the underlying pathway. In eukaryotes a comprehensive collection of experimentally verified ribosome biogenesis factors (RBFs) exists only for Saccharomyces cerevisiae. Far less is known for other fungi, animals or plants, and insights are even more limited for archaea. Starting from 255 yeast RBFs, we ...

A parametric geometric metamodel is built for a nonlinear magnetostatic problem, using proper orthogonal decomposition (POD) approach combined with radial basis functions (RBFs) interpolation. Furthermore, the geometrical variation of problem modeled an RBF interpolation smooth mesh deformation. The applied single-phase EI inductance, and aim to create precise flux cartographies based on few so...

Traditional finite difference (FD) methods are designed to be exact for low degree polynomials. They can be highly effective on Cartesian-type grids, but may fail for unstructured node layouts. Radial basis function-generated finite difference (RBF-FD) methods overcome this problem and, as a result, provide a much improved geometric flexibility. The calculation of RBF-FD weights involves a shap...

We discuss the solution of cornea curvature using a meshless method based on radial basis functions (RBFs). A full two-dimensional nonlinear thin membrane partial differential equation (PDE) model is introduced and solved using the multiquadratic (MQ) and inverse multiquadratic (IMQ) RBFs. This new approach does not rely on radial symmetry or other simplifying assumptions in respect of the corn...

We present a novel hierarchical spatial partitioning method for creating interpolating implicit surfaces using compactly supported radial basis functions (RBFs) from scattered surface data. From this hierarchy of functions we can create a range of models from coarse to fine, where a coarse model approximates and a fine model interpolates. Furthermore, our method elegantly handles irregularly sa...

Implicit representations have the potential to represent large volumes succinctly. In this paper we present a multiresolution and progressive implicit representation of scalar volumetric data using anisotropic Gaussian radial basis functions (RBFs) defined over an octree. Our representation lends itself well to progressive level-of-detail representations. Our RBF encoding algorithm based on a M...

In this paper, a previously defined hybrid multilogistic regression model is extended and applied to a precision agriculture problem. This model is based on a prediction function which is a combination of the initial covariates of the problem and the hidden neurons of an Artificial Neural Network (ANN). Several statistical and soft computing techniques have been applied for determining these mo...