Radial Basis Functions (RBF) interpolation theory is briefly introduced at the “application level” including some basic principles and computational issues. The RBF interpolation is convenient for un-ordered data sets in n-dimensional space, in general. This approach is convenient especially for a higher dimension N 2 conversion to ordered data set, e.g. using tessellation, is computationally v...

While it was noted by R. Hardy and proved in a famous paper by C. A. Micchelli that radial basis function interpolants s(x) = ∑ λjφ(‖x − xj‖) exist uniquely for the multiquadric radial function φ(r) = √ r2 + c2 as soon as the (at least two) centres are pairwise distinct, the error bounds for this interpolation problem always demanded an added constant to s. By using Pontryagin native spaces, we...

We have examined the role of the renal sympathetic nerves in the renal blood flow (RBF) response to hemorrhage in seven conscious rabbits. Hemorrhage was produced by blood withdrawal at 1.35 ml ⋅ min-1 ⋅ kg-1for 20 min while RBF and renal sympathetic nerve activity (RSNA) were simultaneously measured. Hemorrhage was associated with a gradual increase in RSNA and decrease in RBF from the 4th min...

During Drosophila eye development, cell proliferation is coordinated with differentiation. Immediately posterior to the morphogenetic furrow, cells enter a synchronous round of S phase called second mitotic wave. We have examined the role of RBF, the Drosophila RB family homolog, in cell cycle progression in the second mitotic wave. RBF-280, a mutant form of RBF that has four putative cdk phosp...

Interpolation or approximation of scattered data is very often task in engineering problems. The Radial Basis Functions (RBF) interpolation is convenient for scattered (un-ordered) data sets in k-dimensional space, in general. This approach is convenient especially for a higher dimension k > 2 as the conversion to an ordered data set, e.g. using tessellation, is computationally very expensive. ...

An effective technique for identifying nonlinear discrete-time systems using raisedcosine radial basis function (RBF) networks is presented. Raised-cosine RBF networks are bounded-input bounded-output stable systems, and the network output is a continuously differentiable function of the past input and the past output. The evaluation speed of an n-dimensional raised-cosine RBF network is high b...

Radial basis function(RBF) methods have been actively developed in the last decades. The advantages of RBF methods are that these methods are mesh-free and yield high order accuracy if the function is smooth enough. The RBF approximation for discontinuous problems, however, deteriorates its high order accuracy due to the Gibbs phenomenon. With the Gibbs phenomenon in the RBF approximation, the ...

We previously identified Rbf as an activator for biofilm formation on polystyrene surfaces in Staphylococcus aureus strain 8325-4. However, strain 8325-4 contains genetic mutations that may affect biofilm formation. To extend the observation to other strains, we used strain Newman, a weak biofilm producer, and strain UAMS-1, an osteomyelitis clinical strain, in this study. We found that mutatio...