Jean-Marie Bilbault

Experimental study of electrical FitzHugh-Nagumo neurons with modified excitability

We present an electronical circuit modelling a FitzHugh-Nagumo neuron with a modified excitability. To characterize this basic cell, the bifurcation curves between stability with excitation threshold, bistability and oscillations are investigated. An electrical circuit is then proposed to realize a unidirectional coupling between two cells, mimicking an inter-neuron synaptic coupling. In such a master-slave configuration, we show experimentally how the coupling strength controls the dynamics of the slave neuron, leading to frequency locking, chaotic behavior and synchronization. These phenomena are then studied by phase map analysis. The architecture of a possible neural network is described introducing different kinds of coupling between neurons.

3-D shape reconstruction in an active stereo vision system using genetic algorithms

Abstract The recovery of 3-D shape information (depth) using stereo vision analysis is one of the major areas in computer vision and has given rise to a great deal of literature in the recent past. The widely known stereo vision methods are the passive stereo vision approaches that use two cameras. Obtaining 3-D information involves the identification of the corresponding 2-D points between left and right images. Most existing methods tackle this matching task from singular points, i.e. finding points in both image planes with more or less the same neighborhood characteristics. One key problem we have to solve is that we are on the first instance unable to know a priori whether a point in the first image has a correspondence or not due to surface occlusion or simply because it has been projected out of the scope of the second camera. This makes the matching process very difficult and imposes a need of an a posteriori stage to remove false matching. In this paper we are concerned with the active stereo vision systems which offer an alternative to the passive stereo vision systems. In our system, a light projector that illuminates objects to be analyzed by a pyramid-shaped laser beam replaces one of the two cameras. The projections of laser rays on the objects are detected as spots in the image. In this particular case, only one image needs to be treated, and the stereo matching problem boils down to associating the laser rays and their corresponding real spots in the 2-D image. We have expressed this problem as a minimization of a global function that we propose to perform using Genetic Algorithms (GAs). We have implemented two different algorithms: in the first, GAs are performed after a deterministic search. In the second, data is partitioned into clusters and GAs are independently applied in each cluster. In our second contribution in this paper, we have described an efficient system calibration method. Experimental results are presented to illustrate the feasibility of our approach. The proposed method yields high accuracy 3-D reconstruction even for complex objects. We conclude that GAs can effectively be applied to this matching problem.

Spiking dynamics of interacting oscillatory neurons

Spiking sequences emerging from dynamical interaction in a pair of oscillatory neurons are investigated theoretically and experimentally. The model comprises two unidirectionally coupled FitzHugh-Nagumo units with modified excitability (MFHN). The first (master) unit exhibits a periodic spike sequence with a certain frequency. The second (slave) unit is in its excitable mode and responds on the input signal with a complex (chaotic) spike trains. We analyze the dynamic mechanisms underlying different response behavior depending on interaction strength. Spiking phase maps describing the response dynamics are obtained. Complex phase locking and chaotic sequences are investigated. We show how the response spike trains can be effectively controlled by the interaction parameter and discuss the problem of neuronal information encoding.

Nonlinear Schro¨dinger models and modulational instability in real electrical lattices

Abstract In nonlinear dispersive media, the propagation of modulated waves, such as envelope (bright) solitions or hole (dark) solitons, has been the subject of considerable interest for many years, as for example in nonlinear optics [A.C. Newell and J.V. Moloney, Nonlinear Optics (Addison-Wesley, 1991)]. On the other hand, discrete electrical transmission lines are very convenient tools to study the wave propagation in 1 D nonlinear dispersive media [A.C. Scott (Wiley-Interscience, 1970)]. In the present paper, we study the generation of nonlinear modulated waves in real electrical lattices. In the continuum limit, our theoretical analysis based on the Nonlinear Schrodinger equation (NLS) predicts three frequency regions with different behavior concerning the Modulational Instability of a plane wave. These predictions are confirmed by our experiments which show that between two modulationally stable frequency bands where hole solitons can be generated, there is a third band where spontaneous or induced modulational instability occurs and where envelope solitons exist. When lattice effects are considered the dynamics of modulated waves can be modeled by a discrete nonlinear Schrodinger equation which interpolates between the Ablowitz-Ladik and Discrete-self-trapping equations.

Optical and electrical properties of Nb doped BaTiO3 single crystals grown either by the KF flux or the pulling method

Abstract Electrical and optical properties of two kinds of BaTiO3:Nb crystals are presented and discussed. Among the three pictures (band conduction, small polarons and random electronic effects) the present study supports the first mechanism with the same forbidden band for all the crystals, where optically inactive levels due to impurity and optical transitions inside the conduction band for crystals with Ti3+ ions play an important role.

DIGITAL INFORMATION RECEIVER BASED ON STOCHASTIC RESONANCE

An electronic receiver based on stochastic resonance is presented to rescue subthreshold modulated digital data. In real experiment, it is shown that a complete data restoration is achieved for both uniform and Gaussian white noise.

NOISE-ENHANCED PROPAGATION IN A DISSIPATIVE CHAIN OF TRIGGERS

We study the influence of spatiotemporal noise on the propagation of square waves in an electrical dissipative chain of triggers. By numerical simulation, we show that noise plays an active role in improving signal transmission. Using the Signal to Noise Ratio at each cell, we estimate the propagation length. It appears that there is an optimum amount of noise that maximizes this length. This specific case of stochastic resonance shows that noise enhances propagation.

INVESTIGATION OF MICRO SPIRAL WAVES AT CELLULAR LEVEL USING A MICROELECTRODE ARRAYS TECHNOLOGY

During cardiac arrhythmia, functional reentries may take the form of spiral waves. The purpose of this study was to induce spiral waves by an electrical stimulation of cultured neonatal rat cardiomyocytes using a microelectrode arrays technology. In basal conditions, cardiac muscle cells in monolayer culture displayed a planar wavefront propagation. External electrical impulse trains induced severe arrhythmia and spiral waves appeared. This in vitro generation of spiral wave opens a new way to test the anti-arrhythmic drugs and for strategies at microscopically scale.

PROPAGATION FAILURE INDUCED BY COUPLING INHOMOGENEITIES IN A NONLINEAR DIFFUSIVE MEDIUM

Kink propagation failure induced by coupling inhomogeneities in a Nagumo lattice is investigated. Considering the case of weak couplings, we define analytically and numerically the coupling conditions leading to the pinning of the kink.

Gap solitons in nonlinear electrical superlattices

We investigate the amplitude dependence of the gap transmission properties of nonlinear electrical superlattices of finite length, sandwiched between two linear electrical transmission lines. We show that once the amplitude of the incident sinusoidal wave, with a frequency which lies in the first linear gap, is greater than a certain threshold, the system switches to a transmitting state: the transmittance of the system which can become unity presents gap soliton‐mediated bistability and hysteresis. The voltage‐current characteristic also exhibits bistability. The transmittance curve calculated by using the characteristic matrix method is in good agreement with the results of our numerical simulations performed with conditions close to those of real experiments. The gap soliton envelope calculated analytically fits both the results obtained by the characteristic matrix method and those obtained by numerical simulations on the dynamics of the wave transmission inside the electrical superlattice, after subt...