8-10 Novembre 2010 : Synchronization, control & Bio-dynamics (Besançon)

From control theory, to dynamics in biology and biomedicine, through delay effects

Monday November 8, afternoon

- 13h30 :
**Welcome coffee**

- 14h00 : Pierre Rouchon
(Ecole des Mines de Paris)
*Feedback generation of quantum Fock states by discrete QND measures*

A feedback scheme for preparation of photon number states in a microwave cavity is proposed. Quantum Non Demolition (QND) measurement of the cavity field provides information on its actual state. The control consists in injecting into the cavity mode a microwave pulse adjusted to increase the population of the desired target photon number. In the ideal case (perfect cavity and measures), we present the feedback scheme and its detailed convergence proof through stochastic Lyapunov techniques based on sub-martingales and other probabilistic arguments. Quantum Monte-Carlo simulations performed with experimental parameters illustrate convergence and robustness of such feedback scheme. This is a work with H. Amini (Mines-ParisTech), M. Mirrahimi (INRIA) and physicists from ENS, M. Brune, I. Dotsenko, S. Haroche and J.M. Raimond.

- 14h45 : Floriane Collin (ENSISA, Mulhouse) &
**Gilles Millérioux**(CRAN, Nancy)*Parameter Identifiability*

Very often, the equations of a model involve unknown parameters that must be estimated from experimental data. A fundamental problem is whether the value of these parameters can be uniquely determined from input/output measurements. This is known as the parameter identifiability problem. There exist a lot of definitions of identifiability for continuous and discrete-time systems. We will focus on some of them and the possible relation between them will be highlighted.

On the other hand, several approaches for testing the parameter identifiability have been proposed in the literature for controlled systems (input/output relation approach, output equality approach, local state isomorphism approach …). These approaches will be presented. Finally, a general formalism based on the parameter identifiability is proposed for the cryptanalysis of a chaotic cryptosystem. In such a cryptosystem, the security is based on the system parameters expected to act as a secret key. The problem of the possible reconstructibility of the parameters is addressed. In fact, this problem is related to the one of the parameter identifiability.

- 15h10 : Christophe Letellier &
**Luis. A. Aguirre**(CORIA - Université de Rouen & UFMG, Belo Horizonte, Brésil)*Interplay between synchronization, observability, and dynamics*

Synchronizing nonidentical chaotic oscillators is very often achieved by using various types of couplings. In the practice of synchronization the “right choice” of the coupling variable—*y*for the Rössler system,*x*for the Lorenz equations, and so on—is usually stated rather than explained or justified. Using the Rössler and Rucklidge system, in this paper, it is shown that such “optimal” choices are strongly related to observability properties which, in turn, can be quantified. It will also be shown that synchronizability does not only depend on the observability of the system but it is also a consequence of the dynamical regimes under study. Our aim is to provide insights into the critical problem of making the “right choice” when it comes to choosing the coupling variable in synchronization schemes.

- 15h35 :
**Madalin Frunzete**& Jean-Pierre Barbot (ENSEA, Cergy-Pontoise)*Observability index and observability quality index for chaotic systems*

Investigating Rosler chaotic system from the points of view of the observability index and observability quality index. Starting from the definition of observability index we defined the observability quality index : exemplification with respect to the continuous Rossler chaotic system. Calculating the observability index in the context of Rossler discrete chaotic map ; the results confirm the way of using such chaotic system in cryptographic application.

- 16h00 :
**Tea Time**

**Session Delay systems I**

- 16h20 :
**Yanhua Hong**, Min Won Lee**& K. Alan Shore***Study of the message decoding quality in optical chaos communications using external-cavity laser diodes*

The message extraction performance has been studied using chaotic laser diode transmitter-receiver pairs. The study shows that the conditions for the best decoding quality do not match to those for achieving maximum chaos synchronisation quality.

- 16h45 : Mourad NOURINE,
**Yanne K. CHEMBO, Michael PEIL & Laurent LARGER**(FEMTO-ST, Besançon)*Second generation electro-optic intensity chaos communications*

We report on an experimental setup intended to propose a second generation electro-optic intensity chaos generator, for secure optical chaos communications. The chaotic intensity fluctuations are generated via a double delayed feedback loop closed on a four-arms Mach-Zehnder modulator with dual modulation electrodes (also known as a QPSK modulator in optical communication systems). The integrated optic device opens the way to customized electro-optic modulator for secure chaos communications, involving a 2D-nonlinear feedback function and a multiple delay architecture. In this contribution we will report on experimental and numerical results on the obtained dynamical regime at the emitter (the chaos generator), and we will also propose and explore numerically a receiver architecture, with which a secure chaos communication link could be achieved, after a proper chaos synchronization with the emitter. Synchronization results, and high bit rate binary message transmission will be reported.

- 17h10 : S. Takougang Kingni,
**G. Van der Sande, L. Gelens, S. Beri & J. Danckaert***Chaos synchronization and communication in directly modulated semiconductor ring lasers*

We numerically investigate the synchronization characteristics and the communication performances of unidirectionally coupled directly modulated semiconductor ring lasers (SRLs). The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Although typical internal parameter mismatches of the SRLs are shown to influence the synchronization quality and communication performance, the system possesses a good robustness to such parameter mismatches. Moreover, the security of the encoded message can be ensured and the message is recovered easily without any filter.

- 17h35 :
**End of the session**

- 18h30 :
**Buffet dinatoire**

Tuesday November 9, Morning

- 9h00 : Jean-Pierre Richard
(Laboratoire d’Automatique, Génie Informatique et Signal - LAGIS FRE CNRS 3303, Lille)
*A delay, what does it change ?*

Time-delay systems are also called systems with after effect or dead-time, hereditary systems, equations with deviating argument or differential-difference equations. They belong to the class of functional differential equations which are infinite dimensional, as opposed to ordinary differential equations. In spite of their complexity, they however often appear as simple infinite-dimensional models in the very complex area of partial differential equations. After the presentation of some motivating examples, the talk will try to show main differences arising from the presence of deviating time-arguments in the dynamics, seen from different points of view : state, solutions, stability, identification...

- 9h45 : Yanne K. Chembo & Laurent Larger
*A technological application of time-delayed systems : ultra-pure microwave generation using optoelectronic generators*.

Time-delayed systems find an ever increasing number of applications in modern technology. In this communication, we present one of the most interesting applications in recent years, namely ultra-pure microwave generation using optoelectronic oscillators. In this system, the role of time-delay is to perform energy storage, in replacement of the traditional high-finesse microwave resonators. This architecture achieves very satisfying performances relatively to other competing oscillators in the GHz frequency range. The main focus of our contribution is to use the differential-delay equations approach to investigate its behavior, thereby unveiling new phenomena that cannot be predicted from heuristic approaches.

- 10h10 : David Sukow (IFISC, Universitat de les Illes Balears, Spain)

Square wave solutions in semiconductor lasers with delayed mutual rotated optical coupling

Two edge-emitting semiconductor lasers that are mutually coupled through selective polarization-rotated optical injection can exhibit self-modulated square waves. The coupling is mutual, but selectively allowed only from each laser’s dominant TE mode to the other laser’s TM mode. Experimental observations of the resulting square wave dynamics show that the TE and TM modes within each individual laser are always observed to be in antiphase, but the TE mode of one laser leads the TM mode of the other by the one-way time of flight between them. The duty cycles of the square waves are continuously tunable by adjustment of coupling strength or pump current, while the total period remains governed by the roundtrip time. We also discuss the mixed and pure polarization steady-states which play a role in the square wave solution.

- 10h40 :
**Coffeebreak**

- 11h10 : Laurent Larger,
**Miguel Cornelies, Lennert Appeltent, Jan Daenckert, Claudio Mirasso & Ingo Fischer**(FEMTO-ST, Besançon)*Electro-optic delay dynamics used as a reservoir for Liquid State Computing*

Reservoir Computing, Liquid State Machines, and Echo State Network, are novel computing approaches that are clearly distinct from the Turing machine principles. A rough description of their operation principles is that the computational power is extracted from the transient response of a nonlinear and high dimensional dynamical systems, when the latter is excited by the information flow to be processed or computed. These generic principles have been proposed by the brain research community, and the neural network computing community. They have been already tested successfully through numerical simulations, making use of complex models corresponding to the dynamics of a large network of neurons. It has been recently proposed in the frame of a European project PHOCUS, that the required high dimensional phase space of a complex neural network, could be replaced by the other high dimensional one, but also in terms of practical realization the much simpler one, of a nonlinear delay dynamical system. In this contribution, we propose to report on a slightly modified standard electro-optic nonlinear delay dynamics, in order to demonstrate the first photonic liquid state machine. First results on the computing power applied to the spoken digit recognition will be presented.

- 11h35 :
**Otti D’Huys, Jan Danckaert**(Vrije Universiteit Brussel)**Lionel Weicker**& Thomas Erneux (Université Libre de Bruxelles)*Coupled Optoelectronic Oscillators*

The chaotic synchronization properties of two delayed coupled opto-electronic oscillators have been studied experimentally by Peil*et al*and by Murphy*et al*. Here, we concentrate on the emergence of stable square-wave oscillations exhibiting different plateau lengths. A singular perturbation analysis of the evolution equations allow us to derive bifurcation equations for the plateau values and lengths. The analytical solution suggests a new type of bifurcation phenomenon different from a Hopf bifurcation. Asymptotic and numerical solutions agree quantitatively.

- 12h00 :
**Lunch**

- 14h00 : Christian Straus & Thomas Similowski
(ER 10 UPMC, Assistance Publique - Hôpitaux de Paris, Groupe Hospitalier Pitié-Salpêtrière)
*Source of non-linear ventilatory complexity and application to mechanical ventilatory assistance*

Intuitive thinking would suggest that human ventilation is a repetitive monotonous phenomenon. In fact it is not and breath-by-breath variability seems to characterize health. Beyond that, the trajectory of the human ventilatory flow at rest adopts a chaos-like dynamics with nonlinear behavior and decrease in predictability as time elapses. The physiological meaning of such a property is not yet clear. Experimental data suggest it may take its source at the level of the automatic, neurovegetative command of breathing located in the brainstem. Chemosensitive and vagal afferents may contribute to the chaos-like dynamics but they may not be necessary. Recent clinical data obtained in acute respiratory failure patients showed that the chaos-like behavior of the ventilatory flow signal increases with the amount of ventilatory assistance. In contrast, the chaos-like trajectory of the integrated diaphragmatic EMG was high and did not change with le level of ventilatory assistance. Therefore, ventilatory chaos-like complexity in severely ill patients receiving ventilatory assistance may reflect neuromechanical coupling and help adjusting the level of assistance.

- 14h45 : Elise Roulin,
**Ubiratan S. Freitas & Christophe Letellier**, (CORIA & EA 3830 - Université & CHU de Rouen)*Guidelines for improving detection of nonlinearity and noise titration*

Based on the comparison between one-step-ahead predictions provided by linear and nonlinear models, the results of the so called “noise titration technique” are dependent on the model structure, that is, on the number of polynomial terms and on the nonlinearity degree chosen to define the models. Thus, as for any modelling technique, the noise titration should be applied under a range of adequately chosen parameters, which avoid erroneous conclusions. However, no guidelines for choosing these parameters were provided, nor was detailed in the literature how the model structure was selected. Based on illustrative examples, we propose ranges for these modelling parameters to properly apply the technique. Even if the noise titration cannot be used as a valid test for chaos, it could still be applied to evidence a nonlinear behaviour within an experimental dynamics. As we further showed, the distribution of the noise limit values allows us to identify the different non-linearity qualities between the three variables of the Rössler system. It is thus possible to compare different time series to state which one is governed by the strongest nonlinearity. For instance, it is shown that, when there is a single nonlinear term in the equations describing the system, the variable on which it acts can be identified among the others.

- 15h10 : Oleksandr Popovych (Institute of Neuroscience and Medicine, Juelich, Germany)
*Macroscopic entrainment of neuronal ensembles with application in medicine*

We show that if a neuronal population receives an external rhythmic input, the population local field potential may be entrained by the input, whereas the individual neurons are phase desynchronized both mutually and with their field potential. The individual neurons can get entrained by a periodic driving only for much larger strength of the forcing. This property is used for the functional target localization during deep brain stimulation (DBS), which is a standard therapy for medically refractory movement disorders. We developed a stimulation technique that effectively evoke the tremor in a well-defined and quantifiable manner, which is phase locked to the stimulus. We show that a weak patterned low-frequency stimulation may cause low-amplitude, but strongly phase-locked tremor, which is also in accordance with our computational results.

- 15h55 :
**Tea Time**

- 16h30 : Dounia Bounoiare,
**A. Portmann, R. Naeck, U. S. Freitas, A. Cuvelier, J.-F. Muir & C. Letellier**(CORIA & EA 3830 - Université et CHU de Rouen)*Quantifying sleep fragmentation using a Shannon entropy*

Estimating sleep quality is relevant for instance for assessing the influence of a noninvasive mechanical ventilation (NIV) on sleep. It is known that sleep fragmentation is a signature of a bad quality of sleep. Such a fragmentation is related to the rate of micro-arousals which must be also scored to the neurologist. To avoid this additional scoring, a Sleep Fragmentation Index (SFI) was introduced. It is based on hypnogram as the sum of micro-arousals and the number of stage switchs. Unfortunately, our 35 patients under NIV, SFI was not correlated to the micro-arousals rate (r=0.009). We therefore introduced a Shannon entropy computed from recurrence plot built on the hypnogram to quantify sleep fragmentation. It was found to be correlated to the rate of micro-arousals (r=0.42, p<0.007) and, consequently, provides better results than the SFI.

- 16h55 :
**G. G. Rodrigues**, U. S. Freitas,**L. A. Aguirre, J.F. Muir & C. Letellier**(UFMG, Belo Horizonte, Brésil - CORIA UMR 6614 & GHRV EA 3830 - Université & CHU de Rouen)*Patient Volume and Leakage Estimation for Noninvasive Ventilation using Kalman filter*

One of the main advantages of noninvasive mechanical ventilation (NIV) is that it doesn’t involve tracheal intubation nor tracheotomy. On the other hand, this means that NIV will often face leakage, and leak flow measurement becomes an important subject. Since leak flow cannot be measured directly, it has to be estimated using the available measurements : total flow and airway pressure. In this work, we review a current leak estimation strategy and point out its failures. We then show how one may use dynamical information from the patient with the extended Kalman filter in order to estimate both the patient volume and leak flow. We illustrate our method with real patient data.

- 17h20 :
**End of the third session**

Wednesday November 10 morning

- 9h30 : Ingo Fischer
(Instituto de Física Interdisciplinar y Sistemas Complejos, Université des Baléares)
*Dynamics of Delay- Coupled Systems : From Lasers to the Brain*

Collective behaviour of systems composed of interacting elements is a paradigm in modern science. During recent years the importance of delays in the propagation of the coupling signals has been recognised in systems ranging from coupled lasers to the brain. Delays have been identified as inducer of complex behaviour, but also as ordering mechanism, giving rise to particular synchronization phenomena. One crucial question is, under which conditions and how distant lasers or neural assemblies can synchronize their dynamics, even at zero-lag, in the presence of non-negligible delays in the transfer of information between them.

In this talk, an overview of the behaviour of such systems will be given, comprising the onset and phenomenology of delay-induced laser dynamics, how zero-lag synchronization can be achieved, and how stable it is. It will be illustrated in how far the gained insights can be transferred to neuronal systems and in how far they might help to understand aspects of brain dynamics. Finally, based on this interdisciplinary view, the opportunities for novel photonic applications will be discussed.

- 10h15 :
**J. Wang, P.-E. Morant, Q. Thommen, F. Lemaire, C. Vandermoëre, B. Parent**, M. Lefranc (PhLAM Lille - LIFL Lille - UGSF Lille)*Oscillations in the expression of a self-repressed gene induced by a slow transcriptional dynamics*

Most mathematical models of genetic regulatory networks assume that gene activities react instantaneously to protein concentrations. However, some experiments have evidenced a slow transcriptional dynamics at time scales comparable to that of other biochemical processes. We have thus revisited the dynamics of a gene repressed by its own protein assuming that transcription rate has a finite response time playing the role of a delay, and have studied the interaction of this delay with nonlinearities in degradation processes.

Remarkably, the oscillation threshold of our model can be computed analytically, and depends only on normalized gene response time and degradation rates. Moreover, we find that when gene response time is equal to a characteristic time scale, oscillations can be induced by degradation mechanisms much less nonlinear than for infinitely fast regulation. Deterministic predictions are confirmed by stochastic simulations of this minimal genetic oscillator. We also studied a more detailed model where delays due to transport or transcription add to the gene response time, confirming the robustness of our analysis.

This work not only highlights the importance of taking into account transcriptional dynamics but also provides one of the first quantitative analyses of the relative roles of delay and nonlinear degradation in the onset of oscillations in a genetic circuit.

- 10h40 :
**Coffeebreak**

- 11h10 : Sylvia de Monte (ENS, Paris)
*Collective oscillations in microbial populations*

A growing number of experimental observations show that microrganism display out-of equilibrium intracellular dynamics. In this talk, I will address oscillatory behaviour, and in particular its population-level emergence through the synchronization of individual cells. After reviewing some exemples of oscillating microbial populations, I will focus on glycolytic oscillations in yeast. I will deal with two cases where experimental observations can be interpreted by means of mathematical models of reduced complexity, in spite of the fact that the biological system is intrinsically nonlinear and with a high number of degrees of freedom. First, I will talk about the density-dependence of collective oscillations, then, I will present some recent results on the population-level response to external periodic perturbations.

- 12h00 :
**Lunch**

**Lieu des journées**

Salle des Actes, UFR ST

16, route de Gray, F-25030 Besançon

Jean-Pierre BARBOT
•
Dounia BOUNOIARE
•
Yanne CHEMBO
•
Thomas ERNEUX

Ubiratan FREITAS • Laurent LARGER • Min Won LEE • Marc LEFRANC

Christophe LETELLIER • Gilles MILLERIOUX • Luc PASTUR • Elise ROULIN

Sifeu TAKOUGANG KINGI

11/09/2010

Ubiratan FREITAS • Laurent LARGER • Min Won LEE • Marc LEFRANC

Christophe LETELLIER • Gilles MILLERIOUX • Luc PASTUR • Elise ROULIN

Sifeu TAKOUGANG KINGI

11/09/2010

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