Phase coupling in the cardiorespiratory interaction.

Markovian analysis is applied to derive nonlinear stochastic equations for the reconstruction of heart rate and respiration rate variability data. A model of their 'phase' interactions is obtained for the first time, thereby gaining new insights into the strength and direction of the cardiorespiratory phase coupling. The reconstructed model can reproduce synchronisation phenomena between the cardiac and the respiratory systems, including switches in synchronisation ratio. The technique is equally applicable to the extraction of the multi-dimensional couplings between many interacting subsystems

Quantum key distribution for d-level systems with generalized Bell states

Using the generalized Bell states and controlled not gates, we introduce an enatanglement-based quantum key distribution (QKD) of d-level states (qudits). In case of eavesdropping, Eve's information gain is zero and a quantum error rate of (d-1)/d is introduced in Bob's received qudits, so that for large d, comparison of only a tiny fraction of received qudits with the sent ones can detect the presence of Eve.Comment: 8 pages, 3 figures, REVTEX, references added, extensive revision, to appear in Phys. Rev.

Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with non-decaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in {\it any} dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.Comment: 5 pages, 4 figures, to appear in Phys. Rev. Let

Modeling high-order synchronisation epochs and transitions in the cardiovascular system

We study a system consisting of two coupled phase oscillators in the presence of noise. This system is used as a model for the cardiorespiratory interaction in wakefulness and anaesthesia. We show that long-range correlated noise produces transitions between epochs with different n:m synchronisation ratios, as observed in the cardiovascular system. Also, we see that, the smaller the noise (specially the one acting on the slower oscillator), the bigger the synchronisation time, exactly as happens in anaesthesia compared with wakefulness. The dependence of the synchronisation time on the couplings, in the presence of noise, is studied; such dependence is softened by low-frequency noise. We show that the coupling from the slow oscillator to the fast one (respiration to heart) plays a more important role in synchronisation. Finally, we see that the isolines with same synchronisation time seem to be a linear combination of the two couplings

Direction of coupling from phases of interacting oscillators: A permutation information approach.

We introduce a directionality index for a time series based on a comparison of neighboring values. It can distinguish unidirectional from bidirectional coupling, as well as reveal and quantify asymmetry in bidirectional coupling. It is tested on a numerical model of coupled van der Pol oscillators, and applied to cardiorespiratory data from healthy subjects. There is no need for preprocessing and fine-tuning the parameters, which makes the method very simple, computationally fast and robust