where the functions ƒ and <p are defined and continuous throughout some interval, say for 0 ^ t ^ 1, and are not both constant throughout that interval. It is sometimes an aid to the imagination to suppose that they are not simultaneously constant throughout any subinterval of their interval of definition. The question naturally arises, whether this implies a restriction on the curve itself, or...

The front-end used in many speaker recognition systems extracts, from the input speech signal, a set of coe cients based on a mel-cepstrum technique. This paper addresses the problem of e ciency of melcepstrum coe cients in a speaker recognition system and suggests a technique permitting an appropriate choice of these coe cients. It is shown, by the results obtained, that this technique can sig...

We present several models to obtain simple parametric representations of the fuzzy numbers or intervals, based on the use of piecewise monotonic functions of different forms. The representations have the advantage of allowing flexible and easy to control shapes of the fuzzy numbers (we use the standard -cuts setting, but also the membership functions are obtained immediately) and can be used di...

Direct implementation of extended arithmetic operators on fuzzy numbers is computationally complex. Implementation of the extension principle is equivalent to solving a nonlinear programming problem. To overcome this difficulty many applications limit the membership functions to certain shapes, usually either triangular fuzzy numbers (TFN) or trapezoidal fuzzy numbers (TrFN). Then calculation o...

Parameterisation of facial expressions on PDE surface representations of human faces are presented in this work. Taking advantage of the boundary-value approach inherent to Bloor-Wilson PDE method, facial expressions are achieved by manipulating the original boundary curves. Such curves are responsible for generating a surface representation of a human face in its neutral configuration, so that...

The aim of the study was to explore the possibilities of multi-parametric representations of voxel-wise quantitative MRI data to objectively discriminate pathological cerebral tissue in patients with brain disorders. For this purpose, we recruited 19 patients with Multiple Sclerosis (MS) as benchmark samples and 19 age and gender matched healthy subjects as a reference group. The subjects were ...

We compute a parametric description of the totally mixed Nash equilibria of a generic game in normal form with pre-fixed structure. Using this representation, we show conditions under which a game has the maximum possible number of this kind of equilibria. Then, we present a symbolic procedure that allows us to describe and estimate the number of isolated totally mixed Nash equilibria of an arb...

This paper describes an ongoing implementation of an open source library dealing with parametric representation of dynamic geometry constructions. We show how some current issues in standard dynamic geometry environments, such as computing envelopes of lines which are not primitive objects known by the geometric system, can be efficiently solved using the correspondence between geometry and alg...

We present a novel parametric 3D shape representation, Generalized sum of Gaussians (G-SoG), which is particularly suitable for pose estimation of articulated objects. Compared with the original sum-of-Gaussians (SoG), G-SoG can handle both isotropic and anisotropic Gaussians, leading to a more flexible and adaptable shape representation yet with much fewer anisotropic Gaussians involved. An ar...