This paper presents a general framework for the construction of piecewise-polynomial local interpolants with given smoothness and approximation order, defined on non-uniform knot partitions. We design such splines through a suitable combination of polynomial interpolants with either polynomial or rational, compactly supported blending functions. In particular, when the blending functions are ra...

Decision theory requires agents to assign probabilities states of the world and utilities possible outcomes different actions. When commit having and/or in a decision problem defined by objective features world, they may find themselves unable decide which actions maximize expected utility. has long recognized that work-around strategies are available special cases; this is where dominance reas...

We study unitary random matrix ensembles in the critical regime where a new cut arises away from the original spectrum. We perform a double scaling limit where the size of the matrices tends to infinity, but in such a way that only a bounded number of eigenvalues is expected in the newborn cut. It turns out that limits of the eigenvalue correlation kernel are given by Hermite kernels correspond...

We investigate periodic, aperiodic and scaling behaviour of eigenmodes, i.e. daily price fluctuation time-series derived from eigenvectors, of correlation matrices of shares listed on the Johannesburg Stock Exchange (JSE) from January 1993 to December 2002. Periodic, or calendar, components are investigated by spectral analysis. We demonstrate that calendar effects are limited to eigenmodes whi...

We present an explicit solver of the three-dimensional screened and unscreened Poisson's equation, which combines accuracy, computational efficiency, and versatility. The solver, based on a mixed plane-wave/interpolating scaling function representation, can deal with any kind of periodicity (along one, two, or three spatial axes) as well as with fully isolated boundary conditions. It can seamle...

A dilation equation is a functional equation of the form f(t) = ∑N k=0 ck f(2t − k), and any nonzero solution of such an equation is called a scaling function. Dilation equations play an important role in several fields, including interpolating subdivision schemes and wavelet theory. This paper obtains sharp bounds for the Hölder exponent of continuity of any continuous, compactly supported sca...

The Ising model with ferromagnetic couplings on the Hanoi networks is analyzed with an exact renormalization group. In particular, the fixed points are determined and the renormalization- flow for certain initial conditions is analyzed. Hanoi networks combine a one-dimensional lattice structure with a hierarchy of long-range bonds to create a mix of geometric and small-world properties. Generic...

Nearest-neighbor, linear, and various cubic interpolation functions are frequently used in image resampling. Quadratic functions have been disregarded largely because they have been thought to introduce phase distortions. This is shown not to be the case, and a family of quadratic functions is derived. The interpolating member of this family has visual quality close to that of the Catmull-Rom c...

Wavelets and radial basis functions (RBF) have ubiquitously proved very successful to solve different forms of partial differential equations (PDE) using shifted basis functions, and as with the other meshless methods, they have been extensively used in scattered data interpolation. The current paper proposes a framework that successfully reconciles RBF and adaptive wavelet method to solve the ...

We propose a new time-scale modi cation method for high quality audio signals. Our approach strives to preserve pitch and timbre. In our method, the signal is represented as the sum of sinusoidal components and a residual (edges and noise). The decomposition is computed via a combined harmonic and wavelet representation. Time-scaling is performed on the harmonic components and residual componen...