Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction.

Interacting dynamical systems abound in nature, with examples ranging from biology and population dynamics, through physics and chemistry, to communications and climate. Often their states, parameters and functions are time-varying, because such systems interact with other systems and the environment, exchanging information and matter. A common problem when analysing time-series data from dynamical systems is how to determine the length of the time window for the analysis. When one needs to follow the time-variability of the dynamics, or the dynamical parameters and functions, the time window needs to be resolved first. We tackled this problem by introducing a method for adaptive determination of the time window for interacting oscillators, as modeled and scaled for the cardiorespiratory interaction. By investigating a system of coupled phase oscillators and utilizing the Dynamical Bayesian Inference method, we propose a procedure to determine the time window and the propagation parameter of the covariance matrix. The optimal values are determined so that the inferred parameters follow the dynamics of the actual ones and at the same time the error of the inference represented by the covariance matrix is minimal. The effectiveness of the methodology is presented on a system of coupled limit-cycle oscillators and on the cardiorespiratory interaction. Three cases of cardiorespiratory interaction were considered-measurement with spontaneous free breathing, one with periodic sine breathing and one with a-periodic time-varying breathing. The results showed that the cardiorespiratory coupling strength and similarity of form of coupling functions have greater values for slower breathing, and this variability follows continuously the change of the breathing frequency. The method can be applied effectively to other time-varying oscillatory interactions and carries important implications for analysis of general dynamical systems.

Contribution to understanding of the molecular dynamics in liquids.

The dielectric relaxation spectroscopy is used for studying the orientational molecular dynamics in the isotropic (I) and nematic (N) phases of two mesogenic liquids composed of the molecules of similar structure and length, but of an essentially different polarity: n-heptylcyanobiphenyl, C(7)H(15)PhPhCN, 7CB (molecular dipole moment mu approximately 5D) and 4-(trans-4'-n-hexylcyclohexyl)isothiocyanatobenzene, C(6)H(13)CyHxPhNCS, 6CHBT (mu approximately 2.5D); advantageously, the temperatures of the I-N phase transition for the two compounds are very close to each other (T(NI) = 316.6 +/- 0.2 K). It is shown that regardless of the differences in polarity of 7CB and 6CHBT molecules and their abilities in dipolar aggregation, the values and temperature dependences of the relaxation time (corresponding to the rotational diffusion of the molecules around their short axis) are very close to each other, in both the isotropic and nematic phases of the liquids studied. Therefore, the data show that the dielectric relaxation processes occurring in dipolar liquids in the isotropic and nematic states lead through the rotational diffusion of individual molecules and the diffusion seems to be not influenced by the intermolecular interactions.

Pretransitional critical-like behavior of dielectric permittivity in mixtures of mesomorphic and nonmesomorphic compounds.

Static dielectric measurements are performed in the temperature range of the isotropic-nematic phase transition of binary mixtures of mesomorphic n-heptylcyanobiphenyl (7CB) and nonmesomorphic: (a) n-heptylcyanophenyl (7CP) and (b) carbon tetrachloride (CCl4) , the solutes of different molecular shape and polarity. In the whole studied range of the solutes mole fraction (x) (x(max) approximately equal to 0.17) , the critical-like temperature behavior of the permittivity in the vicinity of the transition from the isotropic phase to the two-phase (nematic+isotropic) region can be well described with a critical exponent close to 0.5, as in a pure 7CB, indicating the tricritical nature of the transitions. It seems to be important that the fitting-determined temperatures of the virtual second-order transition in the solutions, T*, i.e., the temperature limit of the thermodynamic stability of supercooled isotropic phase, correspond well to the experimentally observed low-temperature limits of the two-phase isotropic+nematic region.

Static and dynamic dielectric behavior of mesogenic compounds of different polarity in the vicinity of the isotropic to nematic phase transition.

Mesogenic compounds belonging to the two well-known -cyanophenyl, and -isothiocyanatophenyl homologous series, which distinctly differ in the molecular polarity (-C identical with N, 5D; -N=C=S, 2.5D), show an essential difference in the pretransitional dielectric behavior in the vicinity of the isotropic to nematic (I-N) phase transition. Taking into account the results presented in Phys. Rev. E 67, 041705 (2003), the features of the I-N transition observed for the less polar mesogens are characteristic for the first order phase transition, whereas in the case of the strongly polar ones, the I-N transition is undoubtedly close to the second order.