In this paper, we describe and illustrate a tool for analyzing and visualizing sequence and distance data, called the splits-graph. The construction of this graph is based upon the split-decomposition technique which is a procedure to decompose a given metric de ned on a nite set in a canonical way into a sum of simpler metrics. In a way, this technique is comparable to Fourier analysis which a...

Rotation Due to the rotation property of the two-dimensional Fourier transform rotation of f (x , y) through an angle & also rotates the spectrum by the same amount. It is also well known that the Fourier spectrum (modulus) is invariant to translation. Now, suppose that we scan the Fourier spectrum IF,(along a circle centered at the origin. If circular sampling of 1 F,I * is used, then by takin...

J. Vijande,* A. Valcarce, and J.-M. Richard Departamento de Fı́sica Teórica and IFIC, Universidad de Valencia CSIC, 46100 Burjassot, Valencia, Spain Departamento de Fı́sica Fundamental, Universidad de Salamanca, 37008 Salamanca, Spain Laboratoire de Physique Subatomique et Cosmologie, Université Joseph Fourier-INPG-IN2P3-CNRS, 53, Avenue des Martyrs, 38026 Grenoble, France (Received 26 July 2007;...

Group elements of SU(2) are expressed in closed form as finite polynomials of the Lie algebra generators, for all definite spin representations of the rotation group. The simple explicit result exhibits connections between group theory, combinatorics, and Fourier analysis, especially in the large spin limit. Salient intuitive features of the formula are illustrated and discussed.