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. GEOSTAT focuses on a microcanonical formulation.

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.

(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. Among these parameters, we can mention:

Singularity exponents, also called Local Predictability Exponents or LPEs,

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,

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 these quantities 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 fit 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.

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.

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

Speech signal (analysis, recognition, classification) .

Optimal wavelets for phase reconstruction in adaptive optics .

In the collaboration with the DynBio team of CNRS LEGOS at Toulouse (UMR 5566), and during the HIRESUBCOLOR contract which is ending in 2011, nonlinear methods for the generation of ocean dynamics from remote sensing have been introduced. They consist in evaluating the cascading properties of physical variables associated to turbulent flows through optimal wavelets and propagate information about the dynamics acquired at low resolution up to higher resolution. H. Yahia has been invited to the AGU (American Geophysical Union) Fall meeting in San Francisco to make a presentation of HIRESUBCOLOR results (December 5-9 2011), and to the EGU meeting to be held in Vienna in 2012. These methods are generic, and can be applied to the determination of high resolution information for ocean/atmosphere interaction. For that matter, the Oceanflux proposal has been submitted and accepted, starting November 1, 2011, and a new proposal called MULTICARO will be submitted to CNES-OSTST in 2012.

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. 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. Fundamentally, linear signal processing is deeply rooted in
*stationarity hypothesis*of the underlying processes, an hypothesis that is questioned in complex systems whose signals are the acquisitions. 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 etc. have appeared during the last decades. 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 can be computed at least in 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 Local Predictability
Exponents
. The LPEs 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...

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*:

(

with

To take an example, we give some insight about the collaboration with LEGOS Dynbio team about high-resolution ocean dynamics from microcanonical formulations in nonlinear complex signal analysis. LPEs relate to the geometric structures linked with the cascading properties of indefinitely divisible variables in turbulent flows. Cascading properties can be represented by optimal wavelets (OWs); this opens new and fascinating directions of research for the determination of ocean motion field at high spatial resolution. OWs in a microcanonical sense pave the way for the determination of the energy injection mechanisms between the scales. From this results a new method for the complete evaluation of oceanic motion field is introduced; it consists in propagating along the scales the norm and the orientation of ocean dynamics deduced at low spatial resolution (geostrophic from altimetry and a part of ageostrophic from wind stress products). Using this approach, there is no need to use several temporal occurrences as in Optical Flow, Maximum Cross Correlation or FSLE techniques. Instead, the proper determination of the turbulent cascading and energy injection mechanisms in oceanographic signals allows the determination of oceanic motion field at the SST or Ocean colour spatial resolution (pixel size: 4 kms) which often go beyond the results obtained with other models (e.g. SQG models). We use the Regional Ocean Modelling System (ROMS) to validate the results on simulated data and compare the motion fields obtained with other techniques. See figure .

The following application domains are investigated by the GEOSTAT team:

Complex signal acquired from remote sensing and earth observation, notably in Oceanography, and ocean/climate interaction.

Speech signal.

Astronomical imaging and turbulence (in collaboration with LATT and ONERA).

Analysis of heartbeat signals (in collaboration with M. Haissaguerre, head of team INSERM EA3668
*Electrophysiologie et Stimulation Cardiaque*, Bordeaux University, R. Dubois (ESPCI) and the CARMEN team).

FluidExponents: software implementation of the MMF, written in Java, in a cooperative development mode on the INRIA GForge, deposited at APP in 2010. Contact: hussein.yahia@inria.fr. FluidExponents implements nonlinear signal processing on various types of input data (including NETCDF).

Version: 0.8

This work is performed during the final year of the HIRESUBCOLOR contract with CNES/NASA. From a fundamental point of view, significant advances have been worked out in the application of complex systems methods for the derivation of new methods for computing ocean dynamics at high spatial resolution (high resolution Sea Surface Temperature, pixel size: 4 x 4 kms). No temporal information is used. Instead, the norms and orientations of low resolution vector fields derived from altimetry and scatterometers are propagated along the scales of turbulent signals. This year, specific study on the propagation of the norm of the vector field has been conducted, resulting in the complete mapping (norm and orientation) of ocean dynamics at the high resolution of Sea Surface Temperature data. Validation is performed by comparison with the output of the ROMS 3D simulation model, with excellent results, and buoy validation is under way. H. Yahia has been invited to the AGU (American Geophysical Union) Fall meeting in San Francisco to make a presentation of HIRESUBCOLOR results (December 5-9 2011) and also to the EGU meeting to be held in Vienna in 2012. In 2011 the complete method for the determination of ocean dynamics has been finalized and it includes:

the determination of both norm and orientation of the vector fields,

the propagation along the scale of both geostrophic and ageostrophic dynamics.

These methods are generic, and can be applied to the determination of high resolution information for ocean/atmosphere interaction. For that matter, the Oceanflux proposal has been submitted and accepted, starting November 1, 2011, and a new proposal called MULTICARO will be submitted to CNES-OSTST. Related publications: , .

Cardiac diseases are the main cause of morbidity and mortality in western countries. Both the pathogenic areas and the evolution of the condition are complex to detect and estimate in the case of arrhythmias, specially in atrial and ventricular fibrillation. In these cases, the dynamics of the cardiac potential behaves chaotically in a highly complex way that challenges its description. Under this context, we are working in the direction of the characterization of the heartbeat dynamics in a model-agnostic way. We have performed analysis of heartbeat dynamics through singularity spectrum, empirical analysis of LPEs for the deart-beat Dynamics, and a novel innovative method to distinguish arrthymic heartbeat with rythmic heartbeat has been studied.

Intracardial potential is measured by means of electrode catheters used during the radiofrequency ablation procedure for cases of atrial fibrillation. We have found that in the electric potential signal, a simple fast-changing three-state orientation signal can be sifted from its complex but slow-changing modulation. The fast dynamics experimentally fits a Markovian process which can be described in a simple and compact way and its parameters are robustly estimated. This shows a clear change of signature even with small statistics that can be used to detect transitions in the arrhythmia and identify different regimes in them.

Previously we had developed a novel phonetic segmentation method based on Microcanonical Multiscale Formalism (MMF). The algorithm was based on precise computation of Local Predictability Exponents (LPEs) at each point, and then using their integration over time axis (ACC) as a quantitative representative of changes in behavior of distribution of these exponents between neighboring phonemes. The piecewise linear estimation of ACC had provided very good segmentation precision. By performing error analysis of the original algorithm, we proposed a 2-step technique which better exploits LPEs to improve the segmentation accuracy. In the first step, we detect the boundaries of the original signal and of a low-pass filtered version, and we consider the union of all detected boundaries as candidates. In the second step, we use a hypothesis test over the local LPE distribution of the original signal to select the final boundaries. In summary following steps have been taken:

Detailed error analysis of the original method, which resulted in the realization of the fact that a high-pass filtering can help to detect some of the missed boundaries.

Development of the hypothesis test method, using the Log Likelihood Ratio Test for final decision over a list of candidates.

Evaluation of the overall 2-step algorithm on the whole
*train*part of the TIMIT database, to compare with the original method.

Evaluation on
*test*part of TIMIT database to compare with the state of the art methods.

We continued and improved the adaptation of speaker segmentation methods to develop new (nonlinear) techniques for phonetic segmentation. We succeeded in proposing simple and efficient new algorithms that outperform existing ones. Even with new approaches, our nonlinear approach was still competitive.

We have found new theoretical developments that link the optimal wavelet description with the information transfer that characterizes the singularity exponents in complex signals. This fact is particularly relevant when there exists a microcanonical cascade as an effective dynamics for the underlying complex system. The implication of this is that under a multiscale hierarchy, the unpredictable set of a signal can be described in terms of its optimal wavelet coefficients and the multiplicative cascade relations between them, easing the information inference or reconstructability between resolution levels.

A new method for the detection of the unpredictable points manifold has been developed, enhancing previous implementations. The algorithm exploits the basic signal symmetries that can be easily verified and has the advantage of not assuming any underlying model. That work is the result of the collaboration between our team and A. Turiel's team at Institute of Marine Sciences of Barcelona.

Additionally, we have developed a new algorithm that allows for the first time a very robust detection of the optimal wavelet in 2D signals. The main advantage of this new algorithm is that it optimizes the wavelet shape in a totally unconstrained way, therefore not restricting to specific wavelet families.

Most of the speaker recognition systems rely on generative learning of Gaussian Mixture Models (GMM). During the last decade, discriminative approaches have been an interesting and valuable alternative to address directly the classification problem. For instance, Support Vector Machines (SVM) combined with GMM supervectors are among state-of-the-art approaches in speaker recognition. Recently a new discriminative approach for multiway classification has been proposed, the Large Margin Gaussian mixture models (LM-GMM). These latter methods have the same advantage as SVM in term of the convexity of the optimization problem to solve. However they differ from SVM because they draw nonlinear class boundaries directly in the input space, and thus no kernel trick is required. We continued our work on investigating simplified versions of LM-GMM for speaker recognition that can handle large scale databases. We developed a new and efficient learning algorithm and evaluated it on NIST-SRE data. The results show that this new algorithm not only outperforms both the original LM-GMM and the traditional GMM, but also outperforms state-of-the-art discriminative methods such as GMM-supervectors SVM.

Atmospheric turbulence in Earth's atmosphere upper layers plays a fundamenbtal role in limiting the resolution of ground based instruments. These turbulent layers perturbate to a great extent incoming light from outer space. One of the best known solutions to overcome this hurdle is Adaptative Optics (AO). It provides real-time compensation by deforming a mirror through a servo-loop, according to phase measurements provided by a wavefront sensor (WFS). We propose and experiment with a new model for phase reconstruction from an acquired subimage of the perturbated phase: instead of reconstructing the phase gradient using conventional methods of AO, we propagate along the scales phase information, from the low resolution of the WFS to higher resolution, using specific wavelet projections that mimic inference along the scales associated to cascading properties of fully developed turbulence.

Related Publication: .

Local Predictability Exponents (LPEs) can be used to classify a given signal's samples according to their predictability. In particular, the Unpredictable Points Manifold, the subset of less predictable points can be formed as the ensemble of points having the least value of singularity exponents. We call these exponents the Local Predictability Exponents since they are are computed according to a procedure based on the evaluation of the degree of reconstruction at a given point. We demonstrate in the case of Speech signal that LPEs are key quantities related to predictability in the framework of reconstructible systems: it is possible to reconstruct the whole Speech signal by applying a reconstruction kernel to the UPM. This provides a strong indication of the importance of the UPM, already demonstrated for other types of complex signals. Experiments show that a UPM containing a small number of the points provides very good perceptual reconstruction quality. In summary following steps have been taken:

Using the LPEs to form the UPM for Speech signal and coping with the implementation issues in particular case of Speech signal.

Successful reconstruction of Speech signal from the UPM. The performance was measured using objective measures of reconstruction quality.

Detailed study of geometrical implications of the points in UPM, and proposition of a new multiscale measure, to be used in estimation procedure of exponents, which is more appropriate for speech analysis. In fact, the same quality of reconstruction is achieved with a quite smaller UPM.

Development of a very simple compression algorithm (8-bit differential nonuniform quantizer) which overperforms the traditional DPCM coding method.

Related Publication: .

We started the Volubilis project on the study of upwelling in the Moroccan coast by satellite imaging. A Ph.D. student, Ayoub Tamim, was recruited in January 2011. We organized the kick-off meeting of the project in Rabat from June 6 to June 10 with the presence of all partners (INRIA, LEGOS, FSR and CRTS). A. Tamim implemented a new version of the software CRTS is using to compute an upwelling index. He then joined GEOSTAT (from September 5 to December 15, 2011) where he first constituted a small validation database of SST and Chlorophyll images. He then implemented some algorithms such as Morand index and multiscale entropy. The goal being to define in a first step a coarse segmentation of upwelling regions.

Related publication: .

**Program: Support to Science Element, ESRIN/AO/1-6668/11/I-AM, Fund: E/0029-01-L**

Project acronym: Oceanflux

Project title: Oceanflux

Duration: November 2011 - May 2013

Coordinator: Dr. Christoph S. Garbe, Interdisciplinary Center for Scientic Computing (IWR), University of Heidelberg.

Other partners: INRIA, GEOSTAT (FRANCE); KIT, IKM-ASF (Allemagne); CNRS, LEGOS (France); IRD (France); Université Paul Sabatier, (France).

Abstract: Mapping at high spatial resolution of GHGs exchange flux between ocean and atmosphere using model outputs and nonlinear techniques in signal processing.

**Program: PHC**

Project acronym: Volubilis

Project title: Study of upwelling in the Moroccan coast by satellite imaging

Duration: November 2010 - October 2013

Coordinator: K. Daoudi, INRIA, GEOSTAT (France)

Other partners: Rabat University, CRTS.

Abstract: Multiscale methods for the characterization of coastal upwelling from remote sensing data.

**Program: OSTST CNES-NASA**

Project acronym: Hiresubcolor

Project title: Multiscale methods for the evaluation of high resolution ocean surface velocities and subsurface dynamics from ocean color, sst and altimetry

Duration: November 2008 - December 2011

Coordinator: H. Yahia, INRIA, GEOSTAT (France)

Other partners: CNRS LEGOS (France), ICM-CSIC (Spain), LOCEAN (France)

Abstract: nonlinear signal processing methods for high resolution mapping of ocean dynamics.

Region Aquitaine research call. Funding of the OPTAD project on adaptive optics.

Region Aquitaine research call. Funding for equipement in Speech databases and software.

GEOSTAT is funded by
*Conseil Région Aquitaine*for acquiring Speech databases and software.

Marie-Curie post doctoral grant with
*Conseil Région Aquitaine*on heartbeat dynamics.

ARC FIBAUR with INRIA, ESPCI and (INSERM EA 2668 Electrophysiology and Cardiac Stimulation).

Joshua Winebarger (from Apr 2011 until Sep 2011)

Subject: Fusion of different speech segmentation algorithms

Institution: Georgia Tech. (United States)

Program: Canadian CRSNG

Project acronym: Profilage à partir des données hétérogènes du Web pour la cybersécurité

Project title: Profilage à partir des données hétérogènes du Web pour la cybersécurité

Duration: March 2011 - February 2014

Coordinator: Concordia University

Other partners: University of Sherbrooke, E-Profile Company, S. d. Quebec, GEOSTAT (INRIA)

Abstract: Use of various complex signals for cybersecurity.

H. Yahia is now a member of Elsevier's Digital Signal Processing journal editorial board.

H. Yahia has been an invited speaker at AGU (American Geophysical Union) Fall Meeting (San Francisco, December 5-9 2011). Section: Nonlinear Geophysics. Title of
presentation:
*High-resolution ocean dynamics from microcanonical formulations in nonlinear complex signal analysis*.

H. Yahia has been an invited speaker for the Assyst
*Workshop on Mathematics in Network Science: Implications to Socially Coupled Systems*, organized by ISI foundation at Torino (Italy) on November 23-21 2011. Title:
*Local Predictability Exponents and universality classes in the framework of reconstructible complex systems*

H. Yahia has joined an official visit of INRIA CEO Michel Cosnard in India in September 2011, organized by INRIA Direction of International Relations. The mission in
India consisted first in accompanying the Direction of International Relations for official visits to: Chennai Mathematical Institute, Institute of Mathematical Sciences (Chennai),
International Institute of Information Technology (Hyderabad), University of Hyderabad (where a plaque has been inaugurated in the presence of M. Cosnard in the Institute of Sanskrit
Studies about the collaboration with G. Huet), IIT Mumbai, Tata Institute of Fundamental Research (Mumbai), Indian Institute of Science (Bangaluru), and second, to participate to the
Indo-French seminar
*Modelling and analysis of complex systems for communication, health and sustainable development*organized by INRIA and CEFIPRA in Bangaluru on September 26-28, 2011. Titles of
presentations:
*Multiscale methods in the analysis of heartbeat data. Application to Atrial Fibrilation*and
*nonlinear signal processing for Earth Observation. A case study for a physical approach to complex signals*.

H. Yahia has given a presentation at CRTS and FSR, Rabat, during the first PHC Volubilis meeting, June 7, 2011. Title:
*: Analysis of complex signals: new trends in nonlinear approaches to complexity, and their application to specific classes of signals*.

H. Yahia has given a presentation during a workshop organized by Meteofrance on October 18, at the Meteofrance centre in Toulouse. Title:
*Evaluation de la dynamique océanique à haute résolution satellitaire SST par fusion de données à différentes échelles spatiales*(joint work with LEGOS partners J. Sudre, V. Garçon,
and CNES partner C. Pottier).

H. Yahia has been selected to give a presentation of the GEOSTAT research thematics during info days at the European Commission in Brussels, October 12, 2011.

O. Pont gave a lecture at a meeting on CARDIOSENSE action, with ANUBIS team, GEOSTAT team, partners involved in CARDIOSENSE, and Prof. M Haissaguerre team. Title:
*Analyse non-linéaire multiéchelle des signaux cardiaques*. January 7, 2011, at Bordeaux University.

H. Yahia has given a presentation at CEA on November 15, 2001. Title:
*Méthodes non-linéaires en analyse des signaux complexes: évaluation de la dynamique océanique à haute résolution spatiale*.

O. Pont has given a presentation at CEA on November 15, 2001. Title:
*Nonlinear analysis of heartbeat dynamics*.

H. Yahia has presented the results of HIRESUBCOLOR contract and the presentation for a MULTICARO proposal at CNES DSP/LEGOS 2011 meeting on November 18 in Toulouse.
Title:
*Méthodes non-linéaires en analyse de la dynamique océanique et interaction océan/atmosphère: résultats de Hiresubcolor, perspectives de Multicaro et Oceanflux*

O. Pont gave a lecture at INRIA Bordeaux Sud-Ouest
*Unithé ou Café*on January 21, 2011. Title:
*L'ordre complexe qui émerge du chaos*.

M2 : K. Daoudi, 10 hours, Speech processing, Master2 InfoTelecom, University of Rabat, Morroco.

PhD in progress : V. Khanagha, Nonlinear methods for speech processing, beginning November 2009, supervisors: K. Daoudi, O. Pont , H. Yahia,

PhD in progress : S. Kumar Maji, Optimal wavelets for adaptive optics, beginning November 2010, supervisors: O. Pont , H. Yahia,

PhD in progress : A. Tamim, Coastal Upwelling, beginning October 2010, supervisors: H. Yahia, K. Daoudi, K. Minaoui, D. Aboutajdine.