Steeve Zozor

Study of unipolar electrogram morphology in a computer model of atrial fibrillation.

Introduction: Electrograms exhibit a wide variety of morphologies during atrial fibrillation (AF). The basis of these time courses, however, is not completely understood. In this study, data from computer models were studied to relate features of the signals to the underlying dynamics and tissue substrate.

On the use of stochastic resonance in sine detection

This paper deals with the use of stochastic resonance (SR) for detection purposes. The nonlinear physical phenomenon of SR generally occurs in dynamical bistable systems excited by a noisy sine: such systems are able to force cooperation between sine and noise such that the noise amplifies the sine. Because of this non-intuitive effect, the use of SR can be envisaged to detect small amplitude sines corrupted by additive noise. In this paper we recall some basics of detection and then show why SR can be used in sine detection context. After recalling some basics of SR in discrete time, we show how to use SR in a detection scheme.

Study of atrial arrhythmias in a computer model based on magnetic resonance images of human atria.

The maintenance of multiple wavelets appears to be a consistent feature of atrial fibrillation (AF). In this paper, we investigate possible mechanisms of initiation and perpetuation of multiple wavelets in a computer model of AF. We developed a simplified model of human atria that uses an ionic-based membrane model and whose geometry is derived from a segmented magnetic resonance imaging data set. The three-dimensional surface has a realistic size and includes obstacles corresponding to the location of major vessels and valves, but it does not take into account anisotropy. The main advantage of this approach is its ability to simulate long duration arrhythmias (up to 40 s). Clinically relevant initiation protocols, such as single-site burst pacing, were used. The dynamics of simulated AF were investigated in models with different action potential durations and restitution properties, controlled by the conductance of the slow inward current in a modified Luo-Rudy model. The simulation studies show that (1) single-site burst pacing protocol can be used to induce wave breaks even in tissue with uniform membrane properties, (2) the restitution-based wave breaks in an atrial model with realistic size and conduction velocities are transient, and (3) a significant reduction in action potential duration (even with apparently flat restitution) increases the duration of AF. (c) 2002 American Institute of Physics.

Stochastic resonance in locally optimal detectors

The aim of the paper is to show that the nonlinear effect known as stochastic resonance, which corresponds to the improvement of the processing of information by noise, occurs naturally in some detection problems. We illustrate this by studying the problem of detecting a small amplitude sinusoid in non-Gaussian noise. We show that in some cases, the nonlinearity that appears in locally optimal detectors can be viewed as a stochastic resonator. If the parameters of the locally optimal detector (LOD) are not well tuned, the performance can be improved by the addition of noise.

Stochastic resonance in discrete time nonlinear AR(1) models

This paper deals with stochastic resonance. This nonlinear physical phenomenon generally occurs in bistable systems excited by random input noise plus a sinusoid. Through its internal dynamics, such a system forces cooperation between the input noise and the input sine: provided the existence of fine tuning between the power noise and the dynamics, the system reacts periodically at the frequency of the sine. Of particular interest is the fact that the local output signal-to-noise ratio presents a maximum when plotted against the input noise power; the system resounds stochastically. Continuous-time systems have already been studied. We study the ability of intrinsically discrete-time systems [general nonlinear AR(1) models] to produce stochastic resonance. It is then suggested that such discrete systems can be used in signal processing.

A numerical scheme for modeling wavefront propagation on a monolayer of arbitrary geometry

The majority of models of wavefront propagation in cardiac tissue have assumed relatively simple geometries. Extensions to complicated three-dimensional (3-D) representations are computationally challenging due to issues related both to problem size and to the correct implementation of flux conservation. In this paper, we present a generalized finite difference scheme (GDFS) to simulate the reaction-diffusion system on a 3-D monolayer of arbitrary shape. GDFS is a vertex-centered variant of the finite-volume method that ensures local flux conservation. Owing to an effectively lower dimensionality, the overall computation time is reduced compared to full 3-D models at the same spatial resolution. We present the theoretical background to compute both the wavefront conduction and local electrograms using a matrix formulation. The same matrix is used for both these quantities. We then give some results of simulation for simple monolayers and complex monolayers resembling a human atria.

Some extensions of the uncertainty principle

We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [I. Bialynicki-Birula, Formulation of the uncertainty relations in terms of the Renyi entropies, Physical Review A 74 (5) (2006) 052101] and Zozor et al. [S. Zozor, C. Vignat, On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles, Physica A 375 (2) (2007) 499–517]. Those inequalities can be considered as generalizations of the Heisenberg uncertainty principle, since they measure the mutual uncertainty of a wave function and its Fourier transform through their associated Renyi entropies with conjugated indices. We consider here the general case where the entropic indices are not conjugated, in both cases where the state space is discrete and continuous: we discuss the existence of an uncertainty inequality depending on the location of the entropic indices α and β in the plane (α,β). Our results explain and extend a recent study by Luis [A. Luis, Quantum properties of exponential states, Physical Review A 75 (2007) 052115], where states with quantum fluctuations below the Gaussian case are discussed at the single point (2,2).

On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles

In this paper we revisit the Bialynicki-Birula and Mycielski uncertainty principle and its cases of equality. This Shannon entropic version of the well-known Heisenberg uncertainty principle can be used when dealing with variables that admit no variance. In this paper, we extend this uncertainty principle to Renyi entropies. We recall that in both Shannon and Renyi cases, and for a given dimension n, the only case of equality occurs for Gaussian random vectors. We show that as n grows, however, the bound is also asymptotically attained in the cases of n-dimensional Student-t and Student-r distributions. A complete analytical study is performed in a special case of a Student-t distribution. We also show numerically that this effect exists for the particular case of a n-dimensional Cauchy variable, whatever the Renyi entropy considered, extending the results of Abe and illustrating the analytical asymptotic study of the Student-t case. In the Student-r case, we show numerically that the same behavior occurs for uniformly distributed vectors. These particular cases and other ones investigated in this paper are interesting since they show that this asymptotic behavior cannot be considered as a “Gaussianization” of the vector when the dimension increases.

A Parametric Approach to Suboptimal Signal Detection in

This paper deals with the detection of a known deterministic signal embedded in alpha-stable noise. The implementation of the optimal receiver requires the explicit expression of the probability density function (pdf) of the noise. Unfortunately, since there exists no closed-form for the pdf of alpha-stable distributed random variables, numerical integrations are required. To avoid such numerical approximations, we suggest a low-complexity parametric suboptimal detector well matched to essential properties of alpha-stable noises. This receiver does not require the explicit expression of the noise pdf. In addition, parameter optimization is fast for several optimization criteria and the selected receiver allows retrieval of the optimal Gaussian detector (matched filter) as well as the locally optimal detector in the Cauchy context. The performance of the detector is studied and a comparison with the optimal solution along with a variety of classical detectors is given. The robustness of the detector against the signal amplitude and the stability index alpha of the noise is discussed

\alpha

We present a quantum version of the generalized