Measuring the interactions among variables of functions over the unit hypercube

in Journal of Mathematical Analysis & Applications (2011), 380

By considering a least squares approximation of a given square integrable function f: [0,1]^n\to\R by a multilinear polynomial of a specified degree, we define an index which measures the overall ... [more ▼]

By considering a least squares approximation of a given square integrable function f: [0,1]^n\to\R by a multilinear polynomial of a specified degree, we define an index which measures the overall interaction among variables of f. This definition extends the concept of Banzhaf interaction index introduced in cooperative game theory. Our approach is partly inspired from multilinear regression analysis, where interactions among the independent variables are taken into consideration. We show that this interaction index has appealing properties which naturally generalize several properties of the Banzhaf interaction index. In particular, we interpret this index as an expected value of the difference quotients of f or, under certain natural conditions on f, as an expected value of the derivatives of f. Finally, we discuss a few applications of the interaction index in aggregation function theory. [less ▲]

Measuring the phase of the scattering amplitude with vortex beams

in Physical Review. D : Particles and Fields (2012), 85(7), 07600110

We show that colliding vortex beams instead of (approximate) plane waves can lead to a direct measurement of how the overall phase of the plane wave scattering amplitude changes with the scattering angle ... [more ▼]

We show that colliding vortex beams instead of (approximate) plane waves can lead to a direct measurement of how the overall phase of the plane wave scattering amplitude changes with the scattering angle. Since vortex beams are coherent superpositions of plane waves with different momenta, their scattering amplitude receives contributions from plane wave amplitudes with distinct kinematics. These contributions interfere, leading to the measurement of their phase difference. Although interference exists for any generic wave packet collision, we show that using vortex beams dramatically enhances sensitivity to the phase in comparison with nonvortex beams. Since the overall phase is inaccessible in a plane wave collision, this measurement would be of great importance for a number of topics in hadronic physics, for example, meson production in the resonance region, physics of nucleon resonances, and small angle elastic hadron scattering. [less ▲]

Measuring the swimming behaviour in fish with two different computerised video tracking systems: comparison of the EthoVision system and a new multi-tracking prototype system

Poster (2004, September)

Measuring Time Delays in Gravitational Lenses

Poster (2008, September)

Measuring Total Electron Content with GNSS: Investigation of Two Different Techniques

in The Institution of Engineering and Technology 11th International Conference on Ionospheric Radio Systems and Techniques (IRST 2009) (2009, April)

The ionosphere widely affects Global Navigation Satellite Systems (GNSS) applications, inducing among others a delay in GNSS measurements. This delay is closely linked to the Total Electron Content (TEC ... [more ▼]

The ionosphere widely affects Global Navigation Satellite Systems (GNSS) applications, inducing among others a delay in GNSS measurements. This delay is closely linked to the Total Electron Content (TEC) of the ionosphere, a major parameter which can hence be monitored using GNSS. To this extent, phase measurements are taken as a basis for their lower noise level. Levelling strategies have then to be defined for the phase measurements are obtained with an initial unknown number of cycles called ambiguity. The most common technique, referred to as carrier-to-code levelling, consists in using the differences between code and phase measurements and their average on a continuous set of epochs. This option, chosen at the Royal Meteorological Institute (RMI) of Belgium to compute TEC for Belgian GPS stations, requires code hardware delays estimation. Another has been proposed which takes benefit from Global Ionospheric Maps (GIMs) to compute a reference TEC used for ambiguity resolution. In order to understand the consequences of using one method or the other, we compare slant TEC data obtained from both techniques for a mid-latitude station (Brussels) during a high solar activity period (2002). We observed large differences (6.8 TECu on average) showing features apparently related to ionospheric and geomagnetic activity. We attribute these observations to a combination of effects originating in code delays estimation, multipath and noise as well as GIMs errors. We try to differentiate between these effects by focusing on several days and satellites. We concentrate for example on days presenting large TEC differences and geomagnetic disturbances simultaneously (or not) or on satellites displaying recurrent patterns on consecutive days. Finally we highlight the impact of the choice of GIMs involved in sTEC calibration. To this extent, we analyse vertical TEC statistics showing a general underestimation from RMI data. The highest bias (5.8 TECu) is obtained for the UPC GIMs used in the second levelling technique. [less ▲]

Meat quality in relation to breed (Belgian blue vs Holstein) and conformation (double muscled vs dual purpose type)

in Proceedings of the International Workshop on Proteolysis and Meat Quality (1993)

La mecanica respiratoria en terneros sanos respirando Helio-Oxigeno

in Proceedings of the XVIIIth Jordanas Uruguayas de Buiatria (1990)

Mécanique analytique (2ème partie)

Learning material (2000)

Mécanique des fluides

Learning material (2007)

La mécanique du détail. Approches transversales

Book published by Editions de l'Ecole Normale Supérieure de Lyon (2013)

Parce qu’elle a trait aux relations nouées entre les parties et l’ensemble qui les comprend, la question du détail s’investit d’enjeux considérables pour toute tentative de réflexion interdisciplinaire ... [more ▼]

Parce qu’elle a trait aux relations nouées entre les parties et l’ensemble qui les comprend, la question du détail s’investit d’enjeux considérables pour toute tentative de réflexion interdisciplinaire. En effet, dans les disciplines qui s’attachent à rendre un objet visible ou lisible, les théoriciens rencontrent à l’endroit du détail des problèmes voisins, sinon analogues, que nous voudrions ici aborder de front, dans une perspective forcément « rapprochée » et plus que jamais attentive à des objets singuliers, que ceux-ci relèvent de la littérature, du cinéma, de la photographie, de la bande dessinée, de la peinture, de la philosophie, etc. À confronter nos méthodes et les présupposés sur lesquels elles reposent, il nous a semblé possible de cerner plus finement le mode de fonctionnement propre au détail. Certes, chacun fera part ici de ses étonnements particuliers ; de même, chacun sera amené à faire rapport des découvertes enthousiasmantes ou perturbantes qui, dans son domaine spécifique, auront innervé le travail de réflexion. Pourtant, il aurait été inutile de vouloir dresser une simple liste de détails, recueillis au sein d’une compilation bariolée et forcément non exhaustive. Adoptant une perspective plus large, le présent ouvrage vise à une compréhension approfondie de la mécanique du détail (extrait de l'Avant-propos, L. Belloï & M. Hagelstein). [less ▲]