ABSTRACT
We comment on the main result given by Ourabah et al. [Phys. Rev. E 92, 032114 (2015)PLEEE81539-375510.1103/PhysRevE.92.032114], noting that it can be derived as a special case of the more general study that we have provided in [Quantum Inf Process 15, 3393 (2016)10.1007/s11128-016-1329-5]. Our proof of the nondecreasing character under projective measurements of so-called generalized (h,Ï) entropies (that comprise the Kaniadakis family as a particular case) has been based on majorization and Schur-concavity arguments. As a consequence, we have obtained that this property is obviously satisfied by Kaniadakis entropy but at the same time is fulfilled by all entropies preserving majorization. In addition, we have seen that our result holds for any bistochastic map, being a projective measurement a particular case. We argue here that looking at these facts from the point of view given in [Quantum Inf Process 15, 3393 (2016)10.1007/s11128-016-1329-5] not only simplifies the demonstrations but allows for a deeper understanding of the entropic properties involved.
ABSTRACT
We study the coordinate-velocity couple of the harmonic oscillator with α-stable noise. As previously shown by Sokolov et al., the distribution of this couple is bivariate α-stable. In this work, we determine explicitly its associated spectral measure, exhibiting directly both the non-independence and non-ellipticity of the coordinate-velocity couple. Knowledge of the spectral measure allows to analyze and quantify the deviation from ellipticity.
ABSTRACT
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.
ABSTRACT
This paper intends to show how the theory of stochastic cyclostationary processes can be used to study stochastic resonance in static nonlinearities. The statistic we use is the covariance function of the output. The covariance is a second-order cumulant and is not dependent on by the mean. Furthermore, this covariance is not averaged in time as is usually done in the stochastic resonance literature. A two-dimensional Fourier transform of the covariance gives the so-called spectral correlation. The spectral correlation depends on the usual harmonic frequency and on another frequency, called cycle frequency. The cyclostationarity of a signal makes the spectral correlation discrete in the cycle frequency. The zero cycle frequency corresponds to the usual "stationary power spectrum" used in the stochastic resonance literature. We thus exploit all the second-order statistical information. We first revisit classical stochastic resonance in threshold devices using the spectral correlation, showing that the effect is seen for nonzero cycle frequencies. The cases of additive and multiplicative noise are detailed. We then study stochastic resonance in threshold devices for communication signals. These signals are usually modeled as stochastic cyclostationary processes. We show that stochastic resonance occurs, and the phenomenon is quantified using the spectral correlation of the output: The amplitude of the spectral correlation at nonzero cycle frequencies presents a maximum as the power of the input noise is increased.
