Max-Olivier Hongler

The resonant retina: exploiting vibration noise to optimally detect edges in an image

We show that, far from being a drawback, the ubiquitous presence of random vibrations in vision systems operating from mobile devices can advantageously be used as a fundamental tool for edge detection. Directly inspired by biology, the concept of dynamic retina uses the random spatiotemporal path, traced by a moving receptor that samples the image over time, as the basis for the edge detection operation. We propose a simple mathematical formalization of the dynamic retina concept that shows that the relevant information needed for edge detection is contained in the modulation of the variance of the output signal delivered by the retina. Based on a sequence of observations, we then use a variance estimator to determine the presence of the image edges. Following again a biological inspiration, more specifically focusing on neuron dynamics, we introduce a threshold type estimator and use its local asymptotic normality to optimize, via the Cramer-Rao relation, the value of the threshold. The optimal threshold value coincides with a maximum of the associated Fisher information and the overall process can therefore be directly interpreted as a stochastic resonance. We end our contribution by reporting some simple experimental illustrations.

Hard mode stationary states generated by fluctuations

The influence of the fluctuations on the dynamics of open macroscopic systems is analysed for a class of two dimensional examples. The amplitudes of the fluctuations are themselves dependent on the macro-variables. It is shown that such random noises can generate temporal oscillations of the macro-variables. This behaviour need not be inherent to the associated deterministic equations.

On the variance of the production output of transfer lines

The variability factor, (i.e., the variance) of the cumulative production, /spl Sigma/(t), delivered by a line composed of failure prone machines is studied in the fluid modeling approach. In this context, the evolution of /spl Sigma/(t) is described by a stochastic differential equation in which the noise source describes the random failures of the machines. We calculate the fluctuations of the production for three different situations, namely for a single nonMarkovian machine, for unbuffered networks of Markovian machines and for production dipoles composed of two machines separated by one buffer. The dynamics of the production dipole is approached via the introduction of a random environment model. Thanks to this new model, we can explicitly take into account the buffer induced correlations phenomena which directly influence the variability of /spl Sigma/(t). The probabilistic properties of the random time needed to complete a batch of fixed size are also explicitly derived.

Exact solution for the diffusion in bistable potentials

We solve analytically the Fokker-Planck equation for a one-parameter family of symmetric, attractive, nonharmonic potentials which include double-well situations. The exact knowledge of the eigenfunctions and eigenvalues allows us to fully discuss the transient behavior of the probability density. In particular, for the bistable potentials, we can give analytical expressions for the probability current over the working barrier and for the onset time which characterizes the transition from uni- to bimodal probability densities.

Fluctuations of the production output of transfer lines

By using a fluid modeling approach, we study the fluctuations around the average throughput delivered by simple production system. A special attention is paid to the buffered production dipole for which an explicit estimation for an stationary variance of the throughput is calculated.

Decentralized self-selection of swarm trajectories: from dynamical systems theory to robotic implementation

In this paper, we present a distributed control strategy, enabling agents to converge onto and travel along a consensually selected curve among a class of closed planar curves. Individual agents identify the number of neighbors within a finite circular sensing range and obtain information from their neighbors through local communication. The information is then processed to update the control parameters and force the swarm to converge onto and circulate along the aforementioned planar curve. The proposed mathematical framework is based on stochastic differential equations driven by white Gaussian noise (diffusion processes). Using this framework, there is maximum probability that the swarm dynamics will be driven toward the consensual closed planar curve. In the simplest configuration where a circular consensual curve is obtained, we are able to derive an analytical expression that relates the radius of the circular formation to the agent’s interaction range. Such an intimate relation is also illustrated numerically for more general curves. The agent-based control strategy is then translated into a distributed Braitenberg-inspired one. The proposed robotic control strategy is then validated by numerical simulations and by implementation on an actual robotic swarm. It can be used in applications that involve large numbers of locally interacting agents, such as traffic control, deployment of communication networks in hostile environments, or environmental monitoring.

Exact results for the diffusion in a class of asymmetric bistable potentials

We solve the Fokker–Planck equations with drifts deriving from a class of asymmetric nonharmonic potentials which include bistable cases. An analytical expression for the probability current over the potential barrier is obtained. Finally, we compare our exact results with those obtained by Kramers’ approximation.

Exact solutions of a class of non-linear Fokker-Planck equations

Abstract We propose a class of non-linear Fokker-Planck equations (i.e. with nonconstant diffusion) which admit intrinsically non-gaussian time dependent solutions.

Mesoscopic derivation of a fundamental diagram of one-lane traffic

Keywords: Strategie de Production ; Nonlinear Boltzmann-equation ; Burgers-equation ; Fluid-dynamical theories of vehicular traffic Reference LPM-ARTICLE-2002-003View record in Web of Science Record created on 2006-06-22, modified on 2016-08-08

Cooperative flow dynamics in production lines with buffer level dependent production rates

We study, in the fluid flow framework, the cooperative dynamics of a buffered production line in which the production rate of each work-cell does depend on the content of its adjacent buffers. Such state dependent fluid queueing networks are typical for people based manufacturing systems where human operators adapt their working rates to the observed environment. We unveil a close analogy between the flows delivered by such manufacturing lines and cars in highway traffic where the driving speed is naturally adapted to the actual headway. This close analogy is thoroughly explored. In particular, by investigating the dynamic response of small perturbations around free flow stationary regimes, we can draw a “phase diagram”. This diagram exhibits two different flow patterns, namely the free and jamming production regimes. The transitions between these regimes are tuned by the production control parameters (i.e. the buffer capacities, the reaction sensitivity, the control sampling time, ...). We finally extract a dimensionless dynamic parameter directly relevant for design purposes.