A measure of the unpredictability around a point in a complex signal. Based on local reconstruction around a point, singularity exponents can be evaluated in different ways and in different contexts (e.g. non-localized, through the consideration of moments and structure fonctions, leading to singularity spectra). In GEOSTAT we study approaches corresponding to *far from equilibrium* hypothesis (e.g. microcanonical) leading to geometrically localized singulariy exponents.

Local Predictability Exponent: another name for singularity exponents, that better underlines the relation with predictability.

Complex systems whose acquisitions can be reconstructed from the knowledge of the geometrical sets that maximize statistical information content. Study of complex signals' compact representations associated to unpredictability.

Microcanonical Multiscale Formalism.

The representation of a signal as a linear combination of elements taken in a dictionary, with the aim of finding the sparset possible one.

(OW). Wavelets whose associated multiresolution analysis optimizes inference along the scales in complex systems.

GEOSTAT is a research project in **nonlinear digital signal processing**, with the fundamental distinction that it considers the signals as the realizations of complex dynamic systems. The research in GEOSTAT encompasses nonlinear signal processing and the study of emergence in complex systems, with a strong emphasis on geometric approaches to complexity. Consequently, research in GEOSTAT is oriented towards the determination, in real signals, of quantities or phenomena that are known to play an important role both in the evolution of dynamical systems whose acquisitions are the signals under study, and in the compact representations of the signals themselves. Hence we first mention:

Singularity exponents, also called Local Predictability Exponents or LPEs,

how singularity exponents can be related to *sparse representations* with reconstruction formulae,

comparison with embedding techniques, such as the one provided by the classical theorem of Takens , .

Lyapunov exponents, how they are related to intermittency, large deviations and singularity exponents,

various forms of entropies,

multiresolution analysis, specifically when performed on the singularity exponents,

the cascading properties of associated random variables,

persistence along the scales, *optimal wavelets*,

the determination of subsets where statistical information is maximized, their relation to reconstruction and compact representation,

and, above all, **the ways that lead to effective numerical and high precision determination of nonlinear characteristics in real signals**. The MMF (Multiscale Microcanonical Formalism) is one of the ways to partly unlock this type of analysis, most notably w.r.t. LPEs and reconstructible systems . We presently concentrate our efforts on it, but GEOSTAT is intended to explore other ways .
Presently GEOSTAT explores new methods for analyzing and understanding complex signals in different applicative domains through the theoretical advances of the MMF, and the framework of **reconstructible systems** . Derived from ideas in Statistical Physics, the methods developped in GEOSTAT provide new ways to relate and evaluate quantitatively the *local irregularity* in complex signals and systems, the statistical concepts of *information content* and *most informative subset*. That latter notion is developed through the notion of *transition front* and *Most Singular Manifold*. As a result, GEOSTAT is aimed at providing *radically new approaches* to the study of signals acquired from different complex systems (their analysis, their classification, the study of their dynamical properties etc.). The common characteristic of these signals, as required by *universality classes* , being the existence of a *multiscale organization* of the systems. For instance, the classical notion of *edge* or *border*, which is of multiscale nature, and whose importance is well known in Computer Vision and Image Processing, receives profound and rigorous new definitions, in relation with the more physical notion of *transition* and fits adequately to the case of chaotic data. The description is analogous to the modeling of states far from equilibrium, that is to say, there is no stationarity assumption. From this formalism we derive methods able to determine geometrically the most informative part in a signal, which also defines its global properties and allows for *compact representation* in the wake of known problematics addressed, for instance, in *time-frequency analysis*. In this way, the MMF allows the reconstruction, at any prescribed quality threshold, of a signal from its most informative subset, and is able to quantitatively evaluate key features in complex signals (unavailable with classical methods in Image or Signal Processing). It appears that the notion of *transition front* in a signal is much more complex than previously expected and, most importantly, related to multiscale notions encountered in the study of nonlinearity . For instance, we give new insights to the computation of dynamical properties in complex signals, in particular in signals for which the classical tools for analyzing dynamics give poor results (such as, for example, correlation methods or optical flow for determining motion in turbulent datasets).
The problematics in GEOSTAT can be summarized in the following items:

the accurate determination in any n-dimensional complex signal of LPEs **at every point in the signal domain** .

The geometrical determination and organization of *singular manifolds* associated to various transition fronts in complex signals, the study of their geometrical arrangement, and the relation of that arrangement with statistical properties or other global quantities associated to the signal, e.g. *cascading properties* .

The study of the relationships between the dynamics in the signal and the distributions of LPEs .

The study of the relationships between the distributions of LPEs and other formalisms associated to *predictability* in complex signals and systems, such as cascading variables, large deviations and Lyapunov exponents.

The ability to compute *optimal wavelets* and relate such wavelets to the geometric arrangement of singular manifolds and cascading properties.

The translation of *recognition*, *analysis* and *classification problems* in complex signals to simpler and more accurate determinations involving new operators acting on singular manifolds using the framework of reconstructible systems.

GEOSTAT is studying complex signals under the point of view of *nonlinear* methods, in the sense of *nonlinear physics* i.e. the methodologies developed to study complex systems, with a strong emphasis on multiresolution analysis. Linear methods in signal processing refer to the standard point of view under which operators are expressed by simple convolutions with impulse responses. Linear methods in signal processing are widely used, from least-square deconvolution methods in adaptive optics to source-filter models in speech processing. Linear methods do not unlock the multiscale structures and cascading variables of primarily importance as previewed by the physics of the phenomena. This is the reason why new approaches, such as DFA (Detrented Fluctuation Analysis), Time-frequency analysis, variations on curvelets etc. have appeared during the last decades. One important result obtained in GEOSTAT is the effective use of multiresolution analysis associated to optimal inference along the scales of a complex system. The multiresolution analysis is performed on dimensionless quantities given by the *singularity exponents* which encode properly the geometrical structures associated to multiscale organization. This is applied successfully in the derivation of high resolution ocean dynamics, or the high resolution mapping of gazeous exchanges between the ocean and the atmosphere; the latter is of primary importance for a quantitative evaluation of global warming. Understanding the dynamics of complex systems is recognized as a new discipline, which makes use of theoretical and methodological foundations coming from nonlinear physics, the study of dynamical systems and many aspects of computer science. One of the challenges is related to the question of *emergence* in complex systems: large-scale effects measurable macroscopically from a system made of huge numbers of interactive agents , , , . Some quantities related to nonlinearity, such as Lyapunov exponents, Kolmogorov-Sinai entropy etc. can be computed at least in the phase space . Consequently, knowledge from acquisitions of complex systems (which include *complex signals*) could be obtained from information about the phase space. A result from F. Takens about strange attractors in turbulence has motivated the determination of discrete dynamical systems associated to time series , and consequently the theoretical determination of nonlinear characteristics associated to complex acquisitions. Emergence phenomena can also be traced inside complex signals themselves, by trying to localize information content geometrically. Fundamentally, in the nonlinear analysis of complex signals there are broadly two approaches: characterization by attractors (embedding and bifurcation) and time-frequency, multiscale/multiresolution approaches. Time-frequency analysis and multiscale/multiresolution are the subjects of intense research and are profoundly reshaping the analysis of complex signals by nonlinear approaches , .
In real situations, the phase space associated to the acquisition of a complex phenomenon is unknown. It is however possible to relate, inside the signal's domain, local predictability to local reconstruction and deduce from that singularity exponents (SEs) . The SEs are defined at any point in the signal's domain, they relate, but are different, to other kinds of exponents used in the nonlinear analysis of complex signals. We are working on their relation with:

properties in universality classses,

the geometric localization of multiscale properties in complex signals,

cascading characteristics of physical variables,

optimal wavelets and inference in multiresolution analysis.

The alternative approach taken in GEOSTAT is microscopical, or geometrical: the multiscale structures which have their "fingerprint" in complex signals are being isolated in a single realization of the complex system, i.e. using the data of the signal itself, as opposed to the consideration of grand ensembles or a wide set of realizations. This is much harder than the ergodic approaches, but it is possible because a reconstruction formula such as the one derived in is local and reconstruction in the signal's domain is related to predictability.

Nonlinear signal processing is making use of quantities related to predictability. For instance the first Lyapunov exponent

with

(

(

(

(*optimal wavelets*:

(**multiresolution analysis**. They are related to persistence along the scales and lead to multiresolution analysis whose coefficients verify

with

In a first example we give some insight about the collaboration with LEGOS Dynbio team

In a second example, we show in figure the highly promising results obtained in the application of nonlinear signal processing and multiscale techniques to the localization of heart fibrillation phenomenon acquired from a real patient and mapped over a reconstructed 3D surface of the heart. The notion of *source field*, defined in GEOSTAT from the computation of derivative measures related to the singularity exponents allows the localization of arythmic phenomena inside the heart .

Our last example is about speech. In speech analysis, we use the concept of the Most Singular Manifold (MSM) to localize critical events in domain of this signal. We show that in case of voiced speech signals, the MSM coincides with the instants of significant excitation of the vocal tract system. It is known that these major excitations occur when the glottis is closed, and hence, they are called the Glottal Closure Instants (GCI). We use the MSM to develop a reliable and noise robust GCI detection algorithm and we evaluate our algorithm using contemporaneous Electro-Glotto-Graph (EGG) recordings. See figure .

In GEOSTAT, the development of nonlinear methods for the study of complex systems and signals is conducted on four broad types of complex signals:

Ocean dynamics and ocean/atmosphere interactions: generation of high-resolution maps from cascading properties and the determination of optimal wavelets, geostrophic or non-geostrophic- complex oceanic dynamics, mixing phenomena.

Speech signal (analysis, recognition, classification).

Optimal wavelets for phase reconstruction in adaptive optics.

Heartbeat signals, in cooperation with IHU LIRYC and Professor M. Haissaguerre (INSERM EA 2668 Electrophysiology and Cardiac Stimulation) .

Denis Arrivault has joined the team for a complete refoundation, rewriting, generalization and diffusion of the FluidExponents software. FluidExponents is a software implementation of the MMF, presently written in Java, in a cooperative development mode on the Inria GForge, deposited at APP in 2010. The new software is presently in the phase of specification, and will be rewritten in C++, using existing libraries for data containers, mathematical computation and user interface. Denis Arrivault is recruited for a 24 month period on FluidExponents ADT.

During the new development, researchers still make use of the current version of the FluidExponents software written in Java, version number 0.8. Contact: denis.arrivault@inria.fr.

A

We perform a linear regression test:

with

We prove the feasibility of a reconstruction by computing the high resolution LPEs

The local singularity exponents of a signal are directly related to the distribution of information in it. This fact implies that accurate evaluation of such exponents opens the door to signal reconstruction and characterisation of the dynamical parameters of the process originating the signal. Many practical implications arise in a context of digital signal processing, since the information on singularity exponents is usable for compact encoding, reconstruction and inference. The evaluation of singularity exponents in a digital context is not straightforward and requires the calculation of the Unpredictable Point Manifold of the signal. In this work, we present an algorithm for estimating the values of singularity exponents at every point of a digital signal of any dimension. We show that the key ingredient for robust and accurate reconstructibility performance lies on the definition of multiscale measures in the sense that they encode the degree of singularity and the local predictability at the same time. See figure .

Related publication: .

The cardiac electrical activity is a complex system, for which nonlinear signal-processing is required to characterize it properly. In this context, an analysis in terms of singularity exponents is shown to provide compact and meaningful descriptors of the structure and dynamics. In particular, singularity components reconstruct the epicardial electric potential maps of human atria, inverse-mapped from surface potentials; such approach describe sinus-rhythm dynamics as well as atrial flutter and atrial fibrillation. See figure .

In this work, various notions of edges encountered in digital image processing are reviewed in terms of compact representation (or completion). We show that critical exponents defined in Statistical Physics lead to a much more coherent definition of edges, consistent across the scales in acquisitions of natural phenomena, such as high resolution natural images or turbulent acquisitions. Edges belong to the multiscale hierarchy of an underlying dynamics, they are understood from a statistical perspective well adapted to fit the case of natural images. Numerical computation methods for the evaluation of critical exponents in the non-ergodic case are recalled, which apply for the vast majority of natural images. We study the framework of reconstructible systems in a microcanonical formulation, show how it redefines edge completion, and how it can be used to evaluate and assess quantitatively the adequation of edges as candidates for compact representations. We study with particular attention the case of turbulent data, in which edges in the classical sense are particularly challenged. Tests are conducted and evaluated on a standard database for natural images. We test the newly introduced compact representation as an ideal candidate for evaluating turbulent cascading properties of complex images, and we show better reconstruction performance than the classical tested methods. See figure .

Turbulence in the Earth’s atmosphere leads to a distortion in the planar wavefront from outer space resulting in a phase error. This phase error is responsible for the refractive blurring of images accounting to the loss in spatial resolution power of ground based telescopes. The common mechanism used to remove phase error from incoming wavefront is Adaptive Optics (AO). In AO systems, an estimate of the phase error is obtained from the gradient measurements of the wavefront collected by a Hartmann-Shack (HS) sensor. The correction estimate is then passed through a servo-control loop to a deformable mirror which compensates for the loss in resolution power. In this work, we propose a new approach to reconstructing the phase error from the HS gradient measurements using the MMF. We also validate the results using standard validation techniques in Adaptive Optics (log power spectrum, structure functions). See figure .

We continued our work aiming at developing efficient versions of Large Margin Gaussian Mixture Models (LM-GMM) for speaker identification. We developed a new and efficient learning algorithm and evaluated it on NIST-SRE'2006 data. The results show that, combined with the channel compesentation technique SFA, this new algorithm outperforms the state-of-the-art discriminative method GMM-supervectors SVM combined with NAP compensatation.

Related publication: .

Development of a GCI detection algorithm (Vahid Khanagha, Khalid Daoudi, Hussein Yahia). According to the aerodynamic theory of voicing, the excitation source for voiced speech sounds is represented as glottal pulses, which to a first approximation, can be considered to occur at discrete instants of time. This major excitation usually coincides with the Glottal Closure Instants (the GCIs). The precise detection of GCIs has found many applications in speech technology: accurate estimation of vocal tract system, pitch marking of speech for pitch synchronous speech processing algorithms, conversion of pitch and duration of speech recordings, prosody modification and synthesis. We use the MMF for detection of these physically important instants. To do so, we study the correspondence of the Most Singular Manifold with the physical production mechanism of the speech signal and we show that this subset can be used for GCI detection. We show that, in clean speech, our algorithm has similar performance to recent methods and, in noisy speech, it significantly outperforms state-of-the-art methods. Indeed, as our algorithm is based on both time domain and inter-scale smoothings, it provides higher robustness against many types of noises. In the mean-time, the high geometrical resolution of singularity exponents prevents the accuracy to be compromised. Moreover, the algorithm extracts GCIs directly from the speech signal and does not rely on any model of the speech signal (such as the autoregressive model in linear predictive analysis). See figure .

Development of an efficient algorithm for sparse Linear Prediction Analysis (Vahid Khanagha, Khalid Daoudi). We address the problem of sparse Linear Prediction (LP) analysis, which involves the estimation of vocal tract model such that the corresponding LP residuals are as sparse as possible: for voiced sounds, one desires the residual to be zero all the time, except for few impulses at GCIs. Sparse Linear Prediction Analysis (LPA) problem has recently got much scientific attention and its classical solutions suffer from computational and algorithmic complexties. We introduce a simple closed-form solution in this chapter which is based on the minimization of weighted

Multi-pulse estimation of speech excitation source (Vahid Khanagha, Khalid Daoudi). In the GCI detector algorithm, the cardinality of MSM was restricted to one sample per pitch period. We then proceed to study the significance of MSMs of higher cardinalities, in the framework of multi-pulse estimation of voiced sound excitation source. Multi-pulse source coding has been widely used and studied within the framework of Linear Predictive Coding (LPC). It consists in finding a sparse representation of the excitation source (or residual) which yields a source-filter reconstruction with high perceptual quality. The MultiPulse Excitation (MPE) method is the first and one of the most popular techniques to achieve this goal. MPE provides a sparse excitation sequence through an iterative Analysis-by-Synthesis procedure to find the position and amplitudes of the excitation source in two stages: first the location of pulses are estimated one at a time by minimization of perceptually wieghted reconstruction error. In the second stage, the amplitude of these pulses are jointly re-optimized to find the optimal pulse values. Using the MSM, we propose a novel approach to find the locations of the multi-pulse sequence that approximates the speech source excitation. We consider locations of MSM points as the locations of excitation impulses and then, the amplitude of these impulses are computed using the second stage of the classical MPE coder by minimization of the spectrally weighted mean squared error of reconstruction. The multi pulse sequence is then fed to the classical LPC synthesizer to reconstruct speech. Our algorithm is more efficient than classical methods, while providing the same level of perceptual quality as the classical MPE method. See figure .

Speech representation based local singularity analysis (Vahid Khanagha, Khalid Daoudi, Hussein Yahia, Oriol Pont). Precise estimation of singularity exponents unlocks the determination a collection of points inside the complex signal which are considered as the least predictable points (the MSM). This leads to the associated compact representation and reconstruction. This work presents the very first steps in establishing the links between the MSM and the speech signal. To do so, we make slight modifications to the formalism so as to adapt it to the particularities of the speech signal. Indeed, the complex intertwining of different dynamics in speech (added to purely turbulent descriptions) suggests the definition of appropriate multi-scale functionals that might influence the evaluation of SEs, hence resulting in a more parsimonious MSM. We present a study that comforts these observations: we show that an alternative multi-scale functional does lead to a more parsimonious MSM from which the whole speech signal can be reconstructed with good perceptual quality. As MSM is composed of a collection of irregularly spaced samples, we use a classical method for the interpolation of irregularly spaced samples, called the Sauer-Allebach algorithm, to reconstruct the speech signal from its MSM. We show that by using this generic algorithm [and even by slight violation of its conditions] high quality speech reconstruction can still be achieved from a MSM of low cardinality. This shows that the MSM formed using the new multi-scale functional we define, indeed can give access to a subset of potentially interesting points in the domain of speech signal. Finally, in order to show the potential of this parsimonious representation in practical speech processing applications, we quantize and encode the MSM so as to develop a waveform coder. See figure .

Gradient-domain methods have become a standard for many computational photography applications including object cloning, panorama stitching and non-photorealistic rendering. Integration from a vector field is required to perform gradient-domain-based applications and this operation must be fast enough for interactive editing. The most popular way to perform this integration is known as the Poisson equation and requires solving a large linear system that becomes more costly as the region of interest becomes larger. We propose to use an FFT-based solution and the framework of reconstructible systems instead of performing interactive local/global editing in the gradient domain on the CPU/GPU for both images and videos. See figures , .

Related publication: .

OPTAD project. Title: *Méthodes multiéchelles pour l'optique adaptative et les données d'astronomie”*, with Conseil Régional Région Aquitaine. Duration: 2010-2013.

Convention CRA 20111602015 on speech processing, with Conseil Régional Région Aquitaine (2011-2014) (funding, equipement and Speech databases).

DIAFIL project, cofunded by Conseil Régional Région Aquitaine and IHU LYRIC. Title: *Méthodes non-linéaires pour le diagnostic et la prévention de la fibrillation ventriculaire*.

HIRESUBCOLOR, OSTST-CNES-NASA program. Partners: DYNBIO (LEGOS UMR CNRS 5565), LOCEAN, ICM-CSIC. Title: *Multiscale methods for the evaluation of high resolution ocean surface velocities and subsurface dynamics from ocean color, SST and altimetry*. We obtained a 1 year prolongation in 2012 from CNES. Coordinator: H. Yahia. Abstract: nonlinear signal processing methods for high resolution mapping of ocean dynamics. Duration: 2008-2012.

FIBAUR ARC: *Fibrillation auriculaire: approches nouvelles pour l'analyse des signaux complexes du rythme cardiaque*. Inria ARC, duration: 2011-2012. Partners: GEOSTAT, INSERM EA3668, SIGMA team (ESPCI).

CRSNG Canadian program. Title: *Profilage à partir des données hétérogènes du Web pour la cybercriminalité*. Partners: Concordia University, University of Sherbrooke, E-Profile Compagny, S. d. Quebec, GEOSTAT (Inria). Coordinator: Concordia University. Duration: 2011-2014. Abstract: use of various complex signals for cybersecurity.

OCEANFLUX project, ESA (European Space Agency), Program: Support to Sicence Element ESRIN/AO/1-6668/11/I-AM, fund: E/0029-01-L. Partners: IWR (University of Heidelberg, Germany), GEOSTAT (Inria, France) , KIT (Karlsruher Institu fur Technologie, Germany), LEGOS (CNRS DR14, France), IRD (France), University Paul Sabatier (France). Duration: 2011-2013. Abstract: Mapping at high spatial resolution of GHGs exchange flux between ocean and atmosphere using model outputs and nonlinear techniques in signal processing. Coordinator: C. Garbe, Interdiscplinary Center for Scientific Computing (IWR), University of Heidelberg.

PHC Volubilis. Title: *Study of upwelling in the Moroccan coast by satellite imaging*. Partners: GEOSTAT, Rabat University, CRTS. French coordinator: K. Daoudi. Abstract: multiscale methods for the characterization of coastal upwelling from remote sensing data. Duration: 2010-2012.

Max Little (MIT Media Lab Human Dynamics Group, Visiting Senior Research Associate, Oxford Complex Systems) has made one month visit at GEOSTAT. He made a presentation to Inria BSO: *A global functional minimization approach to nonlinear signal processing* on Thursday, April 5th.

Hicham Badri (from Mar 2012 until Aug 2012)

Subject: Computer graphics effects from the framework of reconstructible systems

Institution: Université Mohamed V Agdal - Faculté des Sciences de Rabat (Morocco)

Nicolas Vinuesa (from October 1st 2012 until April 31 2013)

Subject: Biologically realistic coding efficiency in auditory cortex vs wavelet analysis

Institution: Universidad Nacional de Rosario, Facultad de Ciencias Exactas, Agrimensura Y Ingineria, Rosaria, Argentina.

H. Yahia is a member of the editorial board of Elsevier's journal *Digital Signal Processing* (http://

H. Yahia is a member of the editorial board of *Frontiers in fractal physiology* (http://

H. Yahia is a member of CNU's section 61 (CNU: *Conseil National des Universités*).

Master : K. Daoudi was invited by the Moroccan CNRST within the FINCOME'2012 program (http://

PhD : R. Jourani, title: *reconnaissance automatique du locuteur par GMM à grande marge*, co-supervised between University Paul Sabatier (Toulouse, France) and Rabat-Agdal University (Morroco), defended September 6th, 2012, supervisors: K. Daoudi and R. André-Obrecht.

PhD in progress : V. Khanagha, title: *novel multiscale methods for nonlinear speech analysis using the Microcanonical Multiscale Formalism*, PhD started in 2009, supervisors: H. Yahia and K. Daoudi, to de defended on January 16th, 2013.

PhD in progress : S. Maji, title: *méthodes multiéchelles en traitement du signal pour l'optique adaptative*, PhD started in 2010, supervisor: H. Yahia.

PhD in progress : H. Badri , title: *sparse representation and gradient manipulation: application to multidimensional signals, natural and synthetic*, PhD started in 2012, supervisors: H. Yahia, D. Aboutajdine.

PhD in progress : A. Tamim , title: *image procesing for the segmentation and temporal evolution of moroccan upwelling*, PhD started in 2010, supervisors: K. Daoudi, D. Aboutajdine, H. Yahia.

H. Yahia was a member of Mr. Binbin Xu's PhD jury. The PhD was defended on July 11th, 2012, at Université de Bourgogne. Title: *étude de la dynamique des ondes spirales à l'échelle cellulaire par modèles expérimental et numérique*. The jury was composed of: Professor O. Meste, Dr. H. Yahia, Professors V. Kazantzev, M. Nadi, J.-M. Bilbault, S. Binczak, Dr. G. Laurent and Dr. S. Jaquir.

H. Yahia and K. Daoudi were members of H. Badri's master internship jury. The defence took place on October, 13th, 2012, at Rabat University, Morroco.

H. Yahia was an invited speaker at the EGU (European Geophysical Association) General Assembly, held in Vienna, Austria, from April 22th to April 27th, 2012. Session NP3.1 (“Nonlinear, scaling and Complex Physical and Biogeophysical Processes in the Atmosphere and Ocean”) .

K. Daoudi was invited from April 11th to April 22th, 2012, by Concordia University (Montreal, Canada), for a visit to Concordia and Sherbrooke universities. K. Daoudi has given a talk at Concordia on April 16th.

K. Daoudi was invited from September 13th to September 15th, 2012, by the Speech Group at Microsoft Research (Redmond, USA) and has given a talk on September 14th on the subject of nonlinear signal processing for speech.

H. Yahia participated to the CNU session held in Saint Malo, France, on January, 23th, 24th, 2012.

H. Yahia was invited by F. Schmidt, head of the LOG (Laboratoire d'Océanologie et de Géosciences, UMR CNRS 8187 and Université du Littoral), to make a lecture on the subject: *structure multiéchelle des signaux complexes et circulation océanique*, on June, 29th, 2012.