The present study proposes a modelbased, statistical approach to characterizing episode patterns in paroxysmal atrial fibrillation (AF). Thanks to the rapid advancement of noninvasive monitoring technology, the proposed approach should become increasingly relevant in clinical practice. Methods: History-dependent point process modeling is employed to characterize AF episode patterns, using a novel alternating, bivariate Hawkes self-exciting model. In addition, a modified version of a recently proposed statistical model to simulate AF progression throughout a lifetime is considered, involving non-Markovian rhythm switching and survival functions. For each model, the maximum likelihood estimator is derived and used to find the model parameters from observed data. Results: Using three databases with a total of 59 long-term ECG recordings, the goodness-of-fit analysis demonstrates that the proposed alternating, bivariate Hawkes model fits SR-to-AF transitions in 40 recordings and AF-to-SR transitions in 51; the corresponding numbers for the AF model with non-Markovian rhythm switching are 40 and 11, respectively. Moreover, the results indicate that the model parameters related to AF episode clustering, i.e., aggregation of temporal AF episodes, provide information complementary to the well-known clinical parameter AF burden. Conclusion:Point process modeling provides a detailed characterization of the occurrence pattern of AF episodes that may improve the understanding of arrhythmia progression.
State-resolved chemical reactions in CO 2 are studied by taking into account excitation of all vibrational modes and preferential reaction mechanisms. The effect of several parameters on the reaction rate coefficients is discussed; it is shown that the nonequilibrium factor in the expression for the rate coefficients of exchange reactions is much less sensitive to the number of accounted vibrational states and model parameters than that of dissociation. On the other hand, the choice of thermal equilibrium Arrhenius law parameters is crucial for the correct prediction of rate coefficients for both reactions. Developed models are implemented to the one-dimensional boundary layer code for coupled state-to-state simulations of nonequilibrium CO 2 flows under Mars entry conditions. Vibrational distributions, mixture composition, flow variables, and heat flux are studied for several kinetic schemes and different models of chemical reactions. Whereas including the exchange reactions weakly affects the flow, switching between the Park and McKenzie sets of parameters results in significant modification of the kinetic mechanisms; for the McKenzie model, recombination near the wall is a dominating reaction, whereas for the Park model, chemical reactions are frozen. Different contributions to the heat flux are evaluated and a satisfactory agreement with experiments is shown.
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