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Detection of non-concave and non-increasing spectra: Snu spaces revisited with wavelet leaders
http://hdl.handle.net/2268/172473
Title: Detection of non-concave and non-increasing spectra: Snu spaces revisited with wavelet leaders
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<br/>Author, co-author: Esser, Céline
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<br/>Abstract: Our objective is to study the pointwise regularity of functions via their multifractal spectrum. Computing the multifractal spectrum of a function using directly its definition is an unattainable goal in most of the practical cases, but there exist heuristic methods, called multifractal formalisms, which allow to estimate this spectrum and which give satisfactory results in many situations. The Frisch-Parisi conjecture, classically used and based on Besov spaces, presents two disadvantages: it can only hold for spectra that are concave and it can only yield the increasing part of spectra. Concerning the first problem, the use of S spaces allows to deal with non-concave
increasing spectra. Concerning the second problem, a generalization of the Frisch-Parisi conjecture obtained by replacing the role played by wavelet coefficients by wavelet leaders allows to recover the decreasing part of concave spectra. We present a combination of both approaches to define a new formalism derived from large deviations based on statistics of wavelet leaders. We also present the associated function space.Genericity and classes of ultradifferentiable functions
http://hdl.handle.net/2268/172472
Title: Genericity and classes of ultradifferentiable functions
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<br/>Author, co-author: Esser, Céline
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<br/>Abstract: As surprising as it may seem, there exist infinitely differentiable functions which are nowhere analytic. When such an unexpected object is found, a natural question is to ask whether many similar ones may exist. A classical technique is to use the Baire category theorem and the notion of residuality. This notion is purely topological and does not give any information about the measure of the set of objects satisfying such a property. In this purpose, the notion of prevalence has been introduced. Moreover, one could also wonder whether large algebraic structures of such objects can be constructed. This question is formalized by the notion of lineability.
The first objective of this talk is to go further into the study of nowhere analytic functions. It is known that the set of nowhere analytic functions is residual and lineable in C^infty([0, 1]). We prove that the set of nowhere analytic functions is also prevalent in this space. Those results of genericity are then generalized using Gevrey classes, which can be seen as intermediate between the space of analytic functions and the space of infinitely differentiable functions. We also study how far such results of genericity could be extended to spaces of ultradifferentiable functions, defined using weight sequences.De l’importance des échelles dyadiques dans les espaces Snu
http://hdl.handle.net/2268/172239
Title: De l’importance des échelles dyadiques dans les espaces Snu
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<br/>Author, co-author: Kleyntssens, Thomas; Nicolay, Samuel
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<br/>Abstract: 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.Fonction de Riemann généralisée
http://hdl.handle.net/2268/172189
Title: Fonction de Riemann généralisée
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<br/>Author, co-author: Simons, Laurent; Bastin, Françoise; Nicolay, Samuel
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<br/>Abstract: Dans cet exposé, nous étudions la régularité de la fonction de Riemann généralisée~$R_{\alpha,\beta}$ (avec $\alpha>1$ et $\beta>0$) définie par
\[
R_{\alpha,\beta}(x)=\sum_{n=1}^{+\infty}\frac{\sin(\pi n^\beta x)}{n^\alpha},\quad x\in\R.
\]
En particulier, nous déterminons son exposant de Hölder uniforme. Pour terminer, nous analysons le comportement de~$R_{\alpha,\beta}$ lorsque le paramètre $\alpha$ ou $\beta$ tend vers l'infini. Cet exposé est basé sur un travail en collaboration avec F. Bastin et S. Nicolay.Large-scale optimization for component analysis of fMRI resting brain data
http://hdl.handle.net/2268/172172
Title: Large-scale optimization for component analysis of fMRI resting brain data
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<br/>Author, co-author: Liegeois, RaphaëlNote on how cerebral functional connectivity encodes structural constraints of the human brain
http://hdl.handle.net/2268/172171
Title: Note on how cerebral functional connectivity encodes structural constraints of the human brain
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<br/>Author, co-author: Liegeois, RaphaëlAnalyse de la régularité hölderienne : De la théorie à l'application à des séries temporelles de températures
http://hdl.handle.net/2268/172055
Title: Analyse de la régularité hölderienne : De la théorie à l'application à des séries temporelles de températures
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<br/>Author, co-author: Deliège, Adrien
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<br/>Abstract: Part 1 is divided in 3 chapters. Chapter 1 is devoted to the definition of the notion of Hölder exponent and its properties. Chapter 2 introduces the Hausdorff measure and dimension and their properties. Chapter 3 is about multiresolution analysis and the wavelet leaders method, the multifractal formalism used in Part 2. Part 2 consists of applications of the wavelet leaders method to analyze the Hölder regularity of some well-known functions (Chapter 4) and of surface air temperature time series (Chapter 5).
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<br/>Commentary: Mémoire de fin d'études.A wavelet leaders-based climate classification of European surface air temperature signals
http://hdl.handle.net/2268/171961
Title: A wavelet leaders-based climate classification of European surface air temperature signals
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel
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<br/>Abstract: We explain the wavelet leaders method, a tool to study the pointwise regularity of signals, which is closely related to some functional spaces. We use the associated multifractal formalism to show that surface air temperature signals are monofractal, i.e. these climate time series
are regularly irregular. Then we use this result to establish a climate classification of weather stations in Europe which matches the Köppen-Geiger climate classification. This result could give rise to new criteria to determine the efficiency of current climatic models.A multifractal analysis of air temperature signals based on the wavelet leaders method
http://hdl.handle.net/2268/171956
Title: A multifractal analysis of air temperature signals based on the wavelet leaders method
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel
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<br/>Abstract: We present the wavelet leaders method (introduced by S. Jaffard) as a tool to study the Hölder regularity of signals, which is closely related to some functional spaces. We use the associated multifractal formalism to show that surface air temperature signals are monofractal, i.e. these are
regularly irregular. Then we use this result to establish a climate classification of weather stations in Europe which matches the Köppen-Geiger climate classification. This result could give rise to new criteria to determine the effectiveness of current climatic models.A wavelet leaders-based climate classification of European surface air temperature signals
http://hdl.handle.net/2268/171949
Title: A wavelet leaders-based climate classification of European surface air temperature signals
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel
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<br/>Abstract: We present the wavelet leaders method as a tool to study the pointwise regularity of signals, which is closely related to some functional spaces. We use the associated multifractal formalism to show that the surface air temperature signals are monofractal, i.e. these are regularly irregular. Then we use this result to establish a climate classification of weather stations in Europe which matches the Köppen-Geiger climate classification. This result could give rise to new criteria to determine the effectiveness of current climatic models.A wavelet-based analysis of surface air temperature regularity
http://hdl.handle.net/2268/171945
Title: A wavelet-based analysis of surface air temperature regularity
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel
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<br/>Abstract: The aim of the talk is to present the "wavelet transform microscope" and the wavelet leaders method to show that surface air temperature signals of weather stations selected in Europe are monofractal, i.e. all the points have the same Hölder (regularity) exponent. This study reveals that the information obtained in this way are richer than previous works studying long range correlations in meteorological stations. The approach presented here allows to bind the Hölder exponents with the pressure anomalies, and such a link does not exist with methods previously carried out. Moreover, this regularity is a signature of the type of climate the stations
are associated to: indeed, it is possible to establish a climate classification of weather stations in Europe which matches the Köppen-Geiger climate classification. A blind test is performed in order to confirm the results, which can be partly explained by the influence of the North Atlantic Oscillation. This result could give rise to new criteria to determine the efficiency of current climatic models.A wavelet-based analysis of surface air temperature variability
http://hdl.handle.net/2268/171943
Title: A wavelet-based analysis of surface air temperature variability
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<br/>Author, co-author: Deliège, Adrien; Nicolay, Samuel
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<br/>Abstract: We study the Hölder regularity of surface air temperature signals using the wavelet leaders method (WLM). This method has been successfully applied in several domains such as DNA analysis, fully developped turbulence analysis, internet data traffic analysis,... to name just a few, and we now use it in climatology. We first define the notions of Hölder exponent, monofractal functions and spectrum of singularities before explaining the WLM. Then we use it to study surface air temperature signals from weather stations spread across Western and Eastern Europe and show that they are monofractal, i.e. their irregularity (in the sense of variability) is regular. After, we show that the stations can be classified according to their Hölder exponent and that this classification matches with the worldwide used Köppen-Geiger climate classification. A blind test is performed in order to confirm the results, which can be partly explained by the influence of the North Atlantic Oscillation. Our results can be helpful to test the accuracy of current climatic models.Mathématiques convoquées par le registre graphique au sein du cours de physique
http://hdl.handle.net/2268/171813
Title: Mathématiques convoquées par le registre graphique au sein du cours de physique
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<br/>Author, co-author: Renkens, Céline; Henry, ValérieComparison of robust detection techniques for local outliers in multivariate spatial data
http://hdl.handle.net/2268/171721
Title: Comparison of robust detection techniques for local outliers in multivariate spatial data
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<br/>Author, co-author: Ernst, Marie; Haesbroeck, Gentiane
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<br/>Abstract: Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Spatial data may contain two types of atypical observations: global and/or local outliers. The attribute values of a global outlier are outlying with respect to the values taken by the majority of the data points while the attribute values of a local outlier are extreme when compared to those of its neighbors.
Usual outlier detection techniques may be used to find global outliers as the geographical positions of the data is not taken into account in this specific search. The detection of local outliers is more complex, especially when there are more than one non spatial attributes. This talk focuses on local detection with two main objectives.
First, we will shortly review some of the local detection techniques that seem to perform well in practice. Among these, one can find robust ``Mahalanobis-type'' detection techniques and a wheighted PCA approach. We suggest an adaptation to one of these to further develop its local characteristic.
Then, examples and simulations, based on linear model of co-regionalisation with Matern models, are reported and discussed in order to compare in an objective way the different detection techniques.Robust detection techniques for multivariate spatial data
http://hdl.handle.net/2268/171720
Title: Robust detection techniques for multivariate spatial data
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<br/>Author, co-author: Ernst, Marie; Haesbroeck, Gentiane
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<br/>Abstract: Spatial data are characterized by statistical units, with known geographical positions, on which non spatial attributes are measured. Two types of atypical observations can be defined: global and/or local outliers. The attribute values of a global outlier are outlying with respect to the values taken by the majority of the data points while the attribute values of a local outlier are extreme when compared to those of its neighbors. Classical outlier detection techniques may be used to find global outliers as the geographical positions of the data is not taken into account in this search. The detection of local outliers is more complex especially when there are more than one non spatial attribute. In this poster, two new procedures for local outliers detection are defined. The first approach is to adapt an existing technique using in particular a regularized estimator of the covariance matrix. The second technique measures outlyingness using depth function.Multi-Dimensional Vector Assignment Problems
http://hdl.handle.net/2268/171699
Title: Multi-Dimensional Vector Assignment Problems
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<br/>Author, co-author: Dokka, Trivikram; Crama, Yves; Spieksma, Frits C.R.
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<br/>Abstract: We consider a special class of axial multi-dimensional assignment problems called multi-
dimensional vector assignment (MVA) problems. An instance of the MVA problem is
defined by m disjoint sets, each of which contains the same number n of p-dimensional
vectors with nonnegative integral components, and a cost function defined on vectors.
The cost of an m-tuple of vectors is defined as the cost of their component-wise maximum.
The problem is now to partition the m sets of vectors into n m-tuples so that no two
vectors from the same set are in the same m-tuple and so that the sum of the costs of the m-tuples is minimized. The main motivation comes from a yield optimization problem
in semi-conductor manufacturing. We consider a particular class of polynomial-time
heuristics for MVA, namely the sequential heuristics, and we study their approximation
ratio. In particular, we show that when the cost function is monotone and subadditive,
sequential heuristics have a finite approximation ratio for every fixed m. Moreover, we
establish smaller approximation ratios when the cost function is submodular and, for a
specific sequential heuristic, when the cost function is additive. We provide examples to
illustrate the tightness of our analysis. Furthermore, we show that the MVA problem is
APX-hard even for the case m = 3 and for binary input vectors. Finally, we show that
the problem can be solved in polynomial time in the special case of binary vectors with
fixed dimension p.
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<br/>Commentary: A preliminary version of this paper, entitled "Approximation Algorithms for Multi-Dimensional Vector Assignment Problems", is available as a working paper at http://hdl.handle.net/2268/147977. This working paper contains a number of additional results which are only briefly mentioned in the article published in Discrete Optimization.ASSESSMENT OF THE PROPORTIONAL ODDS ASSUMPTION IN LONGITUDINAL STUDIES WITH MISSING ORDINAL OUTCOME DATA
http://hdl.handle.net/2268/171631
Title: ASSESSMENT OF THE PROPORTIONAL ODDS ASSUMPTION IN LONGITUDINAL STUDIES WITH MISSING ORDINAL OUTCOME DATA
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<br/>Author, co-author: Donneau, Anne-Françoise; Mauer, Murielle; Lambert, Philippe; Lesaffre, EmmanuelSIMULATION-BASED COMPARATIVE PERFORMANCE OF MULTIPLE IMPUTATION METHODS FOR INCOMPLETE LONGITUDINAL ORDINAL DATA
http://hdl.handle.net/2268/171630
Title: SIMULATION-BASED COMPARATIVE PERFORMANCE OF MULTIPLE IMPUTATION METHODS FOR INCOMPLETE LONGITUDINAL ORDINAL DATA
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<br/>Author, co-author: Donneau, Anne-Françoise; Mauer, Murielle; Lambert, Philippe; Molenberghs, GeertOlympiades mathématiques belges - Recueil de questions - Tome 8 (2011-2014)
http://hdl.handle.net/2268/171618
Title: Olympiades mathématiques belges - Recueil de questions - Tome 8 (2011-2014)
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<br/>Author, co-author: Dupont, Pascal; Sebille, MichelDouble sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem
http://hdl.handle.net/2268/171464
Title: Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem
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<br/>Author, co-author: Vion, Alexandre; Geuzaine, Christophe