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See detailDe l’importance des échelles dyadiques dans les espaces Snu
Kleyntssens, Thomas ULg; Nicolay, Samuel ULg

Conference (2014, September 23)

Le but de l’analyse multifractale est de fournir une méthode permettant d’approximer le spectre de singularités d’une fonction. En 1985, Frisch et Parisi ont proposé un premier formalisme. D'autres ... [more ▼]

Le but de l’analyse multifractale est de fournir une méthode permettant d’approximer le spectre de singularités d’une fonction. En 1985, Frisch et Parisi ont proposé un premier formalisme. D'autres formalismes, basés sur les coefficients d'ondelettes, ont été introduits (ex WLM). Cependant, de part leurs natures, ces méthodes ne peuvent détecter que des spectres concaves. En 2004, Jaffard introduit les espaces Snu pour palier à ce problème. Ces espaces sont inclus dans une intersection d'espaces de Besov. Dans cet exposé, je présente une généralisation des espaces Snu. Ceux-ci sont mis en relation avec les espaces de Besov généralisés et une mise en pratique est présentée. [less ▲]

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See detailDetection of non concave and non increasing multifractal spectra using wavelet leaders (Part I)
Esser, Céline ULg; Kleyntssens, Thomas ULg; Bastin, Françoise ULg et al

Conference (2014, May 22)

Multifractal analysis is concerned with the study of very irregular signals. For such functions, the pointwise regularity may change widely from a point to another. Therefore, it is more interesting to ... [more ▼]

Multifractal analysis is concerned with the study of very irregular signals. For such functions, the pointwise regularity may change widely from a point to another. Therefore, it is more interesting to determine the spectrum of singularities of the signal, which is the Hausdor ff dimension of the set of points which have the same H ölder exponent. For real-life signals, the computation of the spectrum of singularities from its de finition is not feasible. Multifractal formalisms are used to approximate this spectrum. Currently, there exist several methods. In this talk, we present a new multifractal formalism based on the wavelet leaders of a signal which allows to detect non concave and non increasing spectra. [less ▲]

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See detailDetection of non concave and non increasing multifractal spectra using wavelet leaders (Part II)
Kleyntssens, Thomas ULg; Esser, Céline ULg; Nicolay, Samuel ULg

Conference (2014, May 22)

This talk follows "Detection of non concave and non increasing multifractal spectra using wavelet leaders (Part I)" given by Céline Esser. A multifractal formalism is a numerically computable formula that ... [more ▼]

This talk follows "Detection of non concave and non increasing multifractal spectra using wavelet leaders (Part I)" given by Céline Esser. A multifractal formalism is a numerically computable formula that approximates the spectrum of singularities of a function. A new multifractal formalism based on the wavelet leaders is presented as well as a comparison with other formalisms. Its main advantages are that it allows to detect non concave and non increasing spectra. An implementation is proposed. [less ▲]

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See detailA new multifractal formalism based on wavelet leaders : detection of non concave and non increasing spectra (Part I)
Esser, Céline ULg; Kleyntssens, Thomas ULg; Nicolay, Samuel ULg et al

Conference (2014, March 25)

Multifractal analysis is concerned with the study of very irregular signals. For such functions, the pointwise regularity may change widely from a point to another. Therefore, it is more interesting to ... [more ▼]

Multifractal analysis is concerned with the study of very irregular signals. For such functions, the pointwise regularity may change widely from a point to another. Therefore, it is more interesting to determine the spectrum of singularities of the signal, which is the Hausdorff dimension of the set of points which have the same Hölder exponent. The spectrum of singularities of many mathematical functions can be determined directly from its definition. However, for many real-life signals, the numerical determination of their Hölder regularity is not feasible. Therefore, one cannot expect to have a direct access to their spectrum of singularities and one has to find an indirect way to compute it. A multifractal formalism is a formula which is expected to yield the spectrum of singularities from quantities which are numerically computable. Several multifractal formalisms based on the wavelet coefficients of a signal have been proposed to estimate its spectrum. The most widespread of these formulas is the so-called thermodynamic multifractal formalism, based on the Frish-Parisi conjecture. This formalism presents two drawbacks: it can hold only for spectra that are concave and it can yield only the increasing part of the spectrum. This first problem can be avoided using Snu spaces. The second one can be avoided using a formalism based on wavelet leaders of the signal. In this talk, we propose a new multifractal formalism, based on a generalization of the Snu spaces using wavelet leaders. It allows to detect non concave and non increasing spectra. An implementation of this method is presented in the talk "A new multifractal formalism based on wavelet leaders: detection of non concave and non increasing spectra (Part II)" of T. Kleyntssens. [less ▲]

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See detailA new multifractal formalism based on wavelet leaders: detection of non concave and non increasing spectra (Part II)
Kleyntssens, Thomas ULg; Esser, Céline ULg; Nicolay, Samuel ULg

Conference (2014, March 25)

This talk follows "A new multifractal formalism based on wavelet leaders: detection of non concave and non increasing spectra (Part I)" given by Céline Esser. For real-life signals, it is impossible to ... [more ▼]

This talk follows "A new multifractal formalism based on wavelet leaders: detection of non concave and non increasing spectra (Part I)" given by Céline Esser. For real-life signals, it is impossible to compute the spectrum of singularities by using its definition. A multifractal formalism is used to approximate this spectrum. We present a new multifractal formalism for non concave and non increasing spectra based on wavelet leaders. In this talk, an implementation of this formalism is given and several numerical examples are presented. [less ▲]

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See detailSnu Spaces, from Theory to Practice
Kleyntssens, Thomas ULg; Nicolay, Samuel ULg

Poster (2013, October 29)

Computing the spectrum of singularities of a real-life signal by using the definition is impossible. One rather uses an indirect way to compute it: the multifractal formalism. The first multifractal ... [more ▼]

Computing the spectrum of singularities of a real-life signal by using the definition is impossible. One rather uses an indirect way to compute it: the multifractal formalism. The first multifractal formalism was introduced by Frisch and Parisi in the context of fully developped turbulence (1985). Its main default is that it always leads to a concave spectrum. For this reason, Stéphane Jaffard has introduced the Snu spaces (2004). They lead to a new multifractal formalism which can detect non concave spectra. In practice, one has to avoid the concept of limit and to deal with finite size effects. I present a method to determine the spectrum based on the Snu spaces and I illustrate it numerically on theoretical functions. [less ▲]

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See detailMise en oeuvre du formalisme multifractal sur les espaces Snu
Kleyntssens, Thomas ULg; Nicolay, Samuel ULg

Conference (2013, September 24)

When considering very irregular functions, it does not make sense to try to characterize the pointwise irregularity because it can change from one point to another. It is more interesting to compute the ... [more ▼]

When considering very irregular functions, it does not make sense to try to characterize the pointwise irregularity because it can change from one point to another. It is more interesting to compute the spectrum of singularities, ie "the size'' of the set of points which share the same pointwise irregularity; by size, one means the Hausdorff dimension. To compute the spectrum of singularities in practice, we use a multifractal formalism. In 1885, Frisch and Parisi have proposed a first formalism. Its main default is that it always leads to a concave spectrum. In 2004, Stéphane Jaffard has introduced the Snu spaces. They lead to a new multifractal formalism which can detect non concave spectra. In practice, one has to avoid the concept of limit and to deal with finite size effects (for example, one can only calculate a finite number of wavelet coefficients). I present a method to determine the spectrum based on the Snu spaces and I illustrate it numerically on theoretical functions. [less ▲]

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See detailImplementation of the Multifractal Formalism on Snu Spaces
Kleyntssens, Thomas ULg; Nicolay, Samuel ULg

Conference (2013, September 09)

A multifractal formalism is a formula, numerically computable, which approximate the spectrum of singularities of a function. The first multifractal formalism (Frisch and Parisi, 1985) has the main ... [more ▼]

A multifractal formalism is a formula, numerically computable, which approximate the spectrum of singularities of a function. The first multifractal formalism (Frisch and Parisi, 1985) has the main default is that it always leads to a concave spectrum. In 2004, Stéphane Jaffard has introduced a new multifractal formalism, based on the Snu spaces, which can detect non concave spectra. In practice, one has to avoid the concept of limit and to deal with finite size effects. In this talk, I present the first results of an implementation of the multifractal formalism on Snu spaces on several theoretical functions. [less ▲]

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See detailAutomatic Cargo Load Planning: Special shipments
Kleyntssens, Thomas ULg; Limbourg, Sabine ULg; Schyns, Michael ULg

in ILS 2012 Proceedings (2012, August 28)

The aircraft loading problem is a real-world combinatorial optimisation problem highly constrained. Indeed, loading the aircraft so the gross weight is less than the maximum allowable is not enough. This ... [more ▼]

The aircraft loading problem is a real-world combinatorial optimisation problem highly constrained. Indeed, loading the aircraft so the gross weight is less than the maximum allowable is not enough. This weight must be distributed to keep the centre of gravity within specified limits. Moreover, an aircraft has usually several cargo compartments with specific contours and structural limitations such as floor loading, combined load limits and cumulative load limitations. Finally, some shipments are particularly restrictive to transport, like dangerous goods, live animals and perishable goods. This paper is concerned with the incorporation of these latter constraints in a mixed integer linear program for the problem of loading a set of Unit Loading Devices and bulk into an aircraft. Experimental results show that our method achieves optimal solutions within only few seconds. [less ▲]

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See detailChargement de marchandises dans un avion cargo: le cas des marchandises nécessitant des précautions particulières
Schyns, Michael ULg; Limbourg, Sabine ULg; Kleyntssens, Thomas ULg

Conference (2012, April)

D'une part, les entreprises de transport aérien ont acheminé en 2010 plus d’un tiers de la valeur des exportations mondiales. D'autre part, le chargement des avions est une opération complexe soumise à de ... [more ▼]

D'une part, les entreprises de transport aérien ont acheminé en 2010 plus d’un tiers de la valeur des exportations mondiales. D'autre part, le chargement des avions est une opération complexe soumise à de nombreuses contraintes et peu d'outils sont disponibles pour aider les loadmasters à trouver la meilleure disposition des conteneurs dans les avions. Limbourg, Schyns et Laporte (2011) ont proposé un modèle à variables entières pour traiter les problèmes élémentaires. Notre travail est une extension de ces travaux. Nous considérons des chargements spéciaux qui impliquent des précautions particulières (produits dangereux, animaux, produits réfrigérés, aliments périssables, ...) ainsi que le transport de marchandises de plus grande taille. L’ajout de ces deux types de contraintes se justifie par la grande fréquence de ces situations dans des problèmes réels rencontrés par nos partenaires industriels. Le problème résultant est très complexe et nous proposons un outil pour le résoudre. [less ▲]

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See detailAn Integer Programming model for air transport of hazardous and special shipments
Kleyntssens, Thomas ULg; Limbourg, Sabine ULg; Schyns, Michael ULg

Conference (2012, February 02)

The aircraft loading problem is a real-world combinatorial optimisation problem highly constrained. This weight must be distributed to keep the centre of gravity within speci ed limits. Moreover, an ... [more ▼]

The aircraft loading problem is a real-world combinatorial optimisation problem highly constrained. This weight must be distributed to keep the centre of gravity within speci ed limits. Moreover, an aircraft has usually several cargo compart- ments with speci c contours and structural limitations such as oor loading, com- bined load limits and cumulative load limitations. Finally, some shipments are par- ticularly restrictive to transport, like dangerous goods, live animals and perishable goods. This paper is concerned with the incorporation of these latter constraints in a mixed integer linear program for the problem of loading a set of Unit Load- ing Devices and bulk into an aircraft. Experimental results show that our method achieves optimal solutions within only few seconds. [less ▲]

Detailed reference viewed: 96 (31 ULg)
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See detailChargement d’un avion cargo : le cas des marchandises nécessitant des précautions particulières
Kleyntssens, Thomas ULg; Limbourg, Sabine ULg; Schyns, Michael ULg

Conference (2011, December 15)

Le problème du chargement de marchandises dans un avion cargo est soumis à des contraintes strictes de sécurité. C’est un problème d’optimisation combinatoire d’une importance cruciale pour les compagnies ... [more ▼]

Le problème du chargement de marchandises dans un avion cargo est soumis à des contraintes strictes de sécurité. C’est un problème d’optimisation combinatoire d’une importance cruciale pour les compagnies aériennes. En effet, un mauvais chargement diminue l’efficacité d’un avion et impose des tensions importantes sur sa structure qui peuvent entraîner la destruction d’équipements de haute valeur, voire la perte de vies. De plus, certains colis spéciaux ont des contraintes très restrictives. C’est le cas notamment des produits dangereux, des animaux, des marchandises alimentaires et périssables. En plus des incompatibilités entre certains produits, il faut tenir compte des interactions possibles sur des équipements de l’avion. Par exemple, des produits émettant des émissions magnétiques doivent être placés de manière à ne pas avoir des effets néfastes avec les instruments de navigation. Dans cet article, nous proposons d’incorporer ces contraintes liées aux colis nécessitant des précautions particulières dans un programme d’optimisation linéaire mixte du problème de chargement d’un ensemble de Unit Loading Devices et de vrac dans un avion. Les résultats obtenus à partir de données réelles montrent que notre méthode permet d’obtenir des solutions optimales en seulement quelques secondes. [less ▲]

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See detailSur les ensembles paradoxaux : de Banach-Tarski à Dougherty-Foreman
Kleyntssens, Thomas ULg

Master's dissertation (2011)

Detailed reference viewed: 111 (21 ULg)