Let us declare that the most important devoir of any physical theory is to draw firm predictions for the outcome of laboratory experiments and astronomical observations. Unfortunately, the devoir is quite difficult to fulfill in the case of general relativity, essentially because of the complexity of the Einstein field equations, to which only few exact solutions are known. For instance, it is ...

This paper is concerned with the notion of a local factorization of a function where we are mostly interested in the special case that this function is a probability distribution. We introduce the notions of local independence and of the local Kullback-Leibler divergence. We introduce a specific approximate local factorization. The number of terms required in the approximation is linear in the ...

We investigate the geometry of that function in the plane or 3-space, which associates to each point the square of the shortest distance to a given curve or surface. Particular emphasis is put on second order Taylor approximants and other local quadratic approximants. Their key role in a variety of geometric optimization algorithms is illustrated at hand of registration in Computer Vision and s...

Full numerical simulations of three-dimensional flows of two or more immiscible fluids of different densities and viscosities separated by a sharp interface with finite surface tension are discussed. The method used is based on a finite difference approximation of the full Navier-Stokes equations and explicit tracking of the interface between the fluids. Preliminary simulations of the Rayleigh-...

Forensic facial approximation involves building a likeness of the head and face on the skull of an unidentified individual, with the aim that public broadcast of the likeness will trigger recognition in those who knew the person in life. This paper presents an overview of the collaborative practice between Ronn Taylor (Forensic Sculptor to the Victorian Institute of Forensic Medicine) and Detec...

This paper proposes a method to obtain optimal 2-order approximation preserving prefilters for a given orthogonal unbalanced multiwavelet basis. This procedure uses the prefilter construction introduced in [3]. The prefilter optimization scheme exploits the Taylor series expansion of the prefilter combined with the multiwavelet. Using the DGHM multiwavelet with the obtained optimal prefilter, w...

We present a novel approach for the fast approximation of the discrete Gauss transform in higher dimensions. The algorithm is based on the dual-tree technique and introduces a new Taylor series expansion. It compares favorably to existing methods especially when it comes to higher dimensions and a broad range of bandwidths. Numerical results with different datasets in up to 62 dimensions demons...

Approximations of the Sedov self-similar solution for a strong point explosion in a medium with the power-law density distribution ρ ∝ r−m are reviewed and their accuracies are analyzed. The Taylor approximation is extended to cases m / = 0 and spherical, cylindrical and plane geometry. Two approximations of the solution are presented in the Lagrangian coordinates for all types of geometry. The...

The Euclidean Algorithm is the often forgotten key to rational approximation techniques, including Taylor, Lagrange, Hermite, osculating, cubic spline, Chebyshev, Padé and other interpolation schemes. A unified view of these various interpolation techniques is eloquently expressed in terms of the concept of the spectral basis of a factor ring of polynomials. When these methods are applied to th...