First applications of a formula for the error of finite sinc interpolation

In former articles we have given a formula for the error committed when interpolating a several times differentiable function by the sinc interpolant on a fixed finite interval. In the present work we demonstrate the relevance of the formula through several applications: correction of the interpolant through the insertion of derivatives to increase its order of convergence, improvement of the barycentric formula, rational sinc interpolants (with and without replacement of the (usually unknown) derivatives with finite differences), convergence acceleration through extrapolation and improvement of one-sided interpolant

A formula for the error of finite sinc-interpolation over a finite interval

Sinc-interpolation is a very efficient infinitely differentiable approximation scheme from equidistant data on the infinite line. It, however, requires that the interpolated function decreases rapidly or is periodic. We give an error formula for the case where neither of these conditions is satisfie

A formula for the error of finite sinc interpolation with an even number of nodes

Sinc interpolation is a very efficient infinitely differentiable approximation scheme from equidistant data on the infinite line. We give a formula for the error committed when the function neither decreases rapidly nor is periodic, so that the sinc series must be truncated for practical purposes. To do so, we first complete a previous result for an odd number of points, before deriving a formula for the more involved case of an even number of point

Excess-tuberculosis-mortality in young women: high accuracy exploration

In a general way at all ages and for almost all diseases, male death rates are higher than female death rates. Here we report a case in which the opposite holds, namely for tuberculosis (TB) mortality between the ages of 5 and 25, female death rates are about two times higher than male rates. What makes this observation of interest is that it occurs in all countries for which data are available (e.g. Britain, Switzerland and United States), and in all years from the end of the 19th century up to the time in the 1960s when TB became a very rare disease in all developed countries. The fact that this regularity holds despite a drastic reduction in the number of deaths is also noteworthy. What is the practical usefulness of this investigation? So far, the reason of this anomaly remains an open question but the effect is so accurate that it can be used for probing the reliability and accuracy of mortality records. This will be explained in the case of developing countries. For instance, it turns out that in South African TB death data as published (and revised) by the "World Health Organization", female deaths were certainly under-estimated by a factor of two.Comment: 13 pages, 4 figure

Deciphering infant mortality. Part 1: empirical evidence

This paper is not (or at least not only) about human infant mortality. In line with reliability theory, "infant" will refer here to the time interval following birth during which the mortality (or failure) rate decreases. This definition provides a systems science perspective in which birth constitutes a sudden transition which falls within the field of application of the "Transient Shock" (TS) conjecture put forward in Richmond et al. (2016c). This conjecture provides predictions about the timing and shape of the death rate peak. (i) It says that there will be a death rate spike whenever external conditions change abruptly and drastically. (ii) It predicts that after a steep rising there will be a much longer hyperbolic relaxation process. These predictions can be tested by considering living organisms for which birth is a multi-step process. Thus, for fish there are three states: egg, yolk-sac phase, young adult. The TS conjecture predicts a mortality spike at the end of the yolk-sac phase, and this timing is indeed confirmed by observation. Secondly, the hyperbolic nature of the relaxation process can be tested using high accuracy Swiss statistics which give postnatal death rates from one hour after birth up to the age of 10 years. It turns out that since the 19th century despite a great overall reduction in infant mortality, the shape of the age-specific death rate has remained basically unchanged. This hyperbolic pattern is not specific to humans. It can also be found in small primates as recorded in the archives of zoological gardens. Our ultimate objective is to set up a chain of cases which starts from simple systems and then moves up step by step to more complex organisms. The cases discussed here can be seen as initial landmarks.Comment: 46 pages, 14 figures, 4 table

Evaluating and combining digital video shot boundary detection algorithms

The development of standards for video encoding coupled with the increased power of computing mean that content-based manipulation of digital video information is now feasible. Shots are a basic structural building block of digital video and the boundaries between shots need to be determined automatically to allow for content-based manipulation. A shot can be thought of as continuous images from one camera at a time. In this paper we examine a variety of automatic techniques for shot boundary detection that we have implemented and evaluated on a baseline of 720,000 frames (8 hours) of broadcast television. This extends our previous work on evaluating a single technique based on comparing colour histograms. A description of each of our three methods currently working is given along with how they are evaluated. It is found that although the different methods have about the same order of magnitude in terms of effectiveness, different shot boundaries are detected by the different methods. We then look at combining the three shot boundary detection methods to produce one output result and the benefits in accuracy and performance that this brought to our system. Each of the methods were changed from using a static threshold value for three unconnected methods to one using three dynamic threshold values for one connected method. In a final summing up we look at the future directions for this work

Un modèle de RI basé sur des critères d'obligation et de certitude

International audienceIl existe un grand nombre de modèles de recherche d'information chacun ayant pour but de répondre au mieux aux attentes des utilisateurs. Le modèle que nous proposons se base sur une formulation précise de la requête reflétant le besoin de l'utilisateur : Chaque terme de la requête est augmenté par deux critères, l'un exprimant l'obligation ou non de l'apparition du terme dans les documents et l'autre exprimant la certitude de l'utilisateur quand au terme utilisé. Des expérimentations nous ont permis de vérifier qu'une telle formulation permet de gagner en précision

Modèle d'indexation de données peu symboliques dans des documents structurés : L'exemple du graphique dans un corpus de documents techniques

International audienceCet article s'intéresse à l'indexation des données ayant une sémantique pauvre dans des documents structurés. Le but est d'exploiter le contenu des données symboliques avoisinantes afin d'en extraire les fragments adéquats pour compléter l'indexation de la donnée non symbolique. Cette approche a été abordée dans le cadre concret d'une application dans un contexte professionnel : indexer les graphiques des documents techniques en exploitant le texte qui les accompagne. Cette indexation est articulée autour d'un modèle de représentation des graphiques tenant compte de la finalité de leur utilisation et du professionnalisme de leurs usagers, et d'un modèle d'extraction des termes d'indexation à partir du texte du document technique