Detecting dynamical changes in time series by using the Jensen Shannon divergence.

Most of the time series in nature are a mixture of signals with deterministic and random dynamics. Thus the distinction between these two characteristics becomes important. Distinguishing between chaotic and aleatory signals is difficult because they have a common wide band power spectrum, a delta like autocorrelation function, and share other features as well. In general, signals are presented as continuous records and require to be discretized for being analyzed. In this work, we introduce different schemes for discretizing and for detecting dynamical changes in time series. One of the main motivations is to detect transitions between the chaotic and random regime. The tools here used here originate from the Information Theory. The schemes proposed are applied to simulated and real life signals, showing in all cases a high proficiency for detecting changes in the dynamics of the associated time series.

Distinguishability notion based on Wootters statistical distance: Application to discrete maps.

We study the distinguishability notion given by Wootters for states represented by probability density functions. This presents the particularity that it can also be used for defining a statistical distance in chaotic unidimensional maps. Based on that definition, we provide a metric d¯ for an arbitrary discrete map. Moreover, from d¯, we associate a metric space with each invariant density of a given map, which results to be the set of all distinguished points when the number of iterations of the map tends to infinity. Also, we give a characterization of the wandering set of a map in terms of the metric d¯, which allows us to identify the dissipative regions in the phase space. We illustrate the results in the case of the logistic and the circle maps numerically and analytically, and we obtain d¯ and the wandering set for some characteristic values of their parameters. Finally, an extension of the metric space associated for arbitrary probability distributions (not necessarily invariant densities) is given along with some consequences. The statistical properties of distributions given by histograms are characterized in terms of the cardinal of the associated metric space. For two conjugate variables, the uncertainty principle is expressed in terms of the diameters of the associated metric space with those variables.

Comment on "Quantum Kaniadakis entropy under projective measurement".

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,ϕ) 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.

Effect of the microtubule-associated protein tau on dynamics of single-headed motor proteins KIF1A.

Intracellular transport based on molecular motors and its regulation are crucial to the functioning of cells. Filamentary tracks of the cells are abundantly decorated with nonmotile microtubule-associated proteins, such as tau. Motivated by experiments on kinesin-tau interactions [Dixit et al., Science 319, 1086 (2008)] we developed a stochastic model of interacting single-headed motor proteins KIF1A that also takes into account the interactions between motor proteins and tau molecules. Our model reproduces experimental observations and predicts significant effects of tau on bound time and run length which suggest an important role of tau in regulation of kinesin-based transport.

Shock detection in dynamics of single-headed motor proteins KIF1A via Jensen-Shannon divergence.

Information theoretic quantities are useful tools to characterize symbolic sequences. In this paper, we use the Jensen-Shannon divergence to study symbolic binary sequences that represent the stationary state of a lattice-gas model describing the traffic of monomeric kinesin KIF1A. More specifically, the constructed binary sequences represent the state of a microtubule protofilament at different adenosine triphosphate (ATP) and KIF1A motor concentrations in the cytosol. The model presents some stationary regimes with phase coexistence. By using the Jensen-Shannon divergence, we develop a method of analysis that allows us to identify cases in which phase coexistence occurs and, for these cases, to locate the position of the interphase that separates the regions with different phase.

Regularization of the displacement moments for asymmetric Lévy flights.

Although the second displacement moments for Lévy flights are not defined in their usual sense, a few years ago it was shown that nonextensive statistical mechanics can be used to define them for symmetric flights. Here it is shown that the displacement moments for long-jump asymmetric Lévy flights can also be regularized by calculating the averages in the form prescribed by nonextensive statistical mechanics. The dependence of the generalized diffusion coefficient on the asymmetry strength is investigated. It is also shown that no extremum q -entropy principle can be associated with the asymmetric Lévy attractors.

Observability of stochastic resonance in neutron scattering.

The observability of the stochastic resonance phenomenon in a neutron scattering experiment is investigated, considering that the scatterer can hop between two sites. Under stochastic resonance conditions scattered intensity is transferred from the quasielastic region to two inelastic peaks. The magnitude of the signal-to-noise ratio is shown to be similar to that arising in the corresponding power spectrum. Effects of potential asymmetry are discussed in detail. Asymmetry leads to a reduction of the signal-to-noise ratio by a factor of 1-xi(2), where xi is an asymmetry parameter which is zero for symmetric problems and equal to unity in a completely asymmetric case.