According to the formulation of the Hough Transform, it is possible to extract any shape that can be represented by an analytic equation with a number of free parameters. Nevertheless, the extraction of arbitrary shapes has centered on nonanalytic representations based on a table which specifies the position of edge points relative to a fixed reference point. In this paper we develop a novel ap...

It was generally believed throughout the 20-th century that irreversibility is a purely classical event without operator counterpart. However, a classical irreversible system cannot be consistently decomposed into a finite number of reversible quantum particles (and, vice versa), thus establishing that the origin of irreversibility is basically unknown at the dawn of the 21-th century. To resol...

We use the analytic signal approach based on the Hilbert transform to compute the phase difference between two non-stationary signals and find out epochs of phase locking. In: Nonlinear Analysis of Physiological Data, Edited by H. Kantz, J. Kurths, and G. Mayer–Kress (Springer, Berlin, 1998), pp. 91-99

We derive a simplified representation for the pion mass to two loops in threeflavour chiral perturbation theory. For this purpose, we first determine the reduced expressions for the tensorial two-loop 2-point sunset integrals arising in chiral perturbation theory calculations. Making use of those relations, we obtain the expression for the pion mass in terms of the minimal set of master integra...

This paper presents methods for detection and localization of photon-limited objects in noise. As opposed to the correlation based or Fourier transform based techniques which exhibit sensitivity to object scaling, we propose a method based on the continuous wavelet transform with its ability to reject noise and to localize objects in space and time as well as in scale. An advantageous twist pre...

In the literature adaptive Fourier decomposition is abbreviated as AFD that addresses adaptive rational approximation, or alternatively adaptive Takenaka-Malmquist system approximation. The AFD type approximations may be characterized as adaptive approximations by linear combinations of parameterized Szegö and higher order Szegö kernels. This note proposes two kinds of such analytic approximati...

We derive the structural relations between nested harmonic sums and the corresponding Mellin transforms of Nielsen integrals and harmonic polylogarithms at weight w = 6. They emerge in the calculations of massless single–scale quantities in QED and QCD, such as anomalous dimensions and Wilson coefficients, to 3– and 4–loop order. We consider the set of the multiple harmonic sums at weight six w...

1 Introduction This research is motivated by the study of model-theoretical properties of classical 'analytic' structures, i.e. ones having natural analytic representation (see also [Z]). For example, the structure of complex numbers as a field with exponentiation C exp = (C, +, ·, exp). One of the questions we can ask is whether C exp is quasi-minimal, i.e. any definable subset of C exp is eit...

Cepstral features derived from power spectrum are widely used for automatic speech recognition. Very little work, if any, has been done in speech research to explore phase-based representations. In this paper, an attempt is made to investigate the use of phase function in the analytic signal of critical-band filtered speech for deriving a representation of frequencies present in the speech sign...

A novel dimensional synthesis technique for solving the mixed exact and approximate motion synthesis problem for spatial CC kinematic chains is presented. The methodology uses an analytic representation of the spatial CC dyad’s rigid body constraint equation in combination with an algebraic geometry formulation of the perpendicular screw bisector to yield designs that exactly reach the prescrib...