We consider the construction of least squares pyramids using shifted polynomial spline basis functions. We derive the pre and postfilters as a function of the degree n and the shift parameter . We show that the underlying projection operator is entirely specified by two transfer functions acting on the even and odd signal samples, respectively. We introduce a measure of shift invariance and sho...

Molecular dynamics (MD) is a valuable tool for the investigation of functional elements in biomolecules, providing information on dynamic properties and processes. Previous work by our group has characterized static geometric properties of the two MHC α-helices comprising the peptide binding region recognized by T cells. We build upon this work and used several spline models to approximate the ...

By the use of locally supported basis functions for spherical spline interpolation the applicability of this approximation method is spread out since the resulting interpolation matrix is sparse and thus eecient solvers can be used. In this paper we study locally supported kernels in detail. Investigations on the Legendre coeecients allow a characterization of the underlying Hilbert space struc...

We introduce the Neural Spline, that is a mathematical model built by combining a neural network and an associated Obreshkov polynomial. The neural spline has finite support and can be used as the basic element in constructing continuous modular neural-based models. These models are suitable for function approximation in partitioned domains and are also amenable to efficient parallel or distrib...

Spline quasi-interpolants are local approximating operators for functions or discrete data. We consider the construction of discrete and integral spline quasi-interpolants on uniform partitions of the real line having small infinite norms. We call them near minimally normed quasi-interpolants: they are exact on polynomial spaces and minimize a simple upper bound of their infinite norms. We give...

In this paper, we develop a new term structure model of interest rates with combinatorial optimization method based on four classical models: polynomial spline model, exponential spline model, Nelson-Siegel model and Svensson model. Genetic algorithms are employed to solve the combinatorial optimization model. Then, we make some empirical comparisons of five models using daily bond data from Sh...

We prove that a compactly supported spline function of degree k satisses the scaling equation (x) = P N n=0 c(n)(mx?n) for some integer m 2, if and only if (x) = P n p(n)B k (x?n) where p(n) are the coeecients of a polynomial P(z) such that the roots of P(z)(z ? 1) k+1 are mapped into themselves by the mapping z ! z m , and B k is the uniform B-spline of degree k. Furthermore, the shifts of for...

Refinable compactly supported bivariate C quartic and quintic spline function vectors on the four-directional mesh are introduced in this paper to generate matrix-valued templates for approximation and Hermite interpolatory surface subdivision schemes, respectively, for both the √ 2 and 1-to-4 split quadrilateral topological rules. These splines have their full local polynomial preservation ord...