Deriving the respiratory sinus arrhythmia from the heartbeat time series using Empirical Mode Decomposition

Heart rate variability (HRV) is a well-known phenomenon whose characteristics are of great clinical relevance in pathophysiologic investigations. In particular, respiration is a powerful modulator of HRV contributing to the oscillations at highest frequency. Like almost all natural phenomena, HRV is the result of many nonlinearly interacting processes; therefore any linear analysis has the potential risk of underestimating, or even missing, a great amount of information content. Recently the technique of Empirical Mode Decomposition (EMD) has been proposed as a new tool for the analysis of nonlinear and nonstationary data. We applied EMD analysis to decompose the heartbeat intervals series, derived from one electrocardiographic (ECG) signal of 13 subjects, into their components in order to identify the modes associated with breathing. After each decomposition the mode showing the highest frequency and the corresponding respiratory signal were Hilbert transformed and the instantaneous phases extracted were then compared. The results obtained indicate a synchronization of order 1:1 between the two series proving the existence of phase and frequency coupling between the component associated with breathing and the respiratory signal itself in all subjects.Comment: 12 pages, 6 figures. Will be published on "Chaos, Solitons and Fractals

Arbitrary-order Hilbert spectral analysis and intermittency in solar wind density fluctuations

The properties of inertial and kinetic range solar wind turbulence have been investigated with the arbitrary-order Hilbert spectral analysis method, applied to high-resolution density measurements. Due to the small sample size, and to the presence of strong non-stationary behavior and large-scale structures, the classical structure function analysis fails to detect power law behavior in the inertial range, and may underestimate the scaling exponents. However, the Hilbert spectral method provides an optimal estimation of the scaling exponents, which have been found to be close to those for velocity fluctuations in fully developed hydrodynamic turbulence. At smaller scales, below the proton gyroscale, the system loses its intermittent multiscaling properties, and converges to a monofractal process. The resulting scaling exponents, obtained at small scales, are in good agreement with those of classical fractional Brownian motion, indicating a long-term memory in the process, and the absence of correlations around the spectral break scale. These results provide important constraints on models of kinetic range turbulence in the solar wind

Separation between coherent and turbulent fluctuations. What can we learn from the Empirical Mode Decomposition?

The performances of a new data processing technique, namely the Empirical Mode Decomposition, are evaluated on a fully developed turbulent velocity signal perturbed by a numerical forcing which mimics a long-period flapping. First, we introduce a "resemblance" criterion to discriminate between the polluted and the unpolluted modes extracted from the perturbed velocity signal by means of the Empirical Mode Decomposition algorithm. A rejection procedure, playing, somehow, the role of a high-pass filter, is then designed in order to infer the original velocity signal from the perturbed one. The quality of this recovering procedure is extensively evaluated in the case of a "mono-component" perturbation (sine wave) by varying both the amplitude and the frequency of the perturbation. An excellent agreement between the recovered and the reference velocity signals is found, even though some discrepancies are observed when the perturbation frequency overlaps the frequency range corresponding to the energy-containing eddies as emphasized by both the energy spectrum and the structure functions. Finally, our recovering procedure is successfully performed on a time-dependent perturbation (linear chirp) covering a broad range of frequencies.Comment: 23 pages, 13 figures, submitted to Experiments in Fluid

Relationship between Remittances and Macroeconomic Variables in Times of Political and Social Upheaval: Evidence from Tunisia's Arab Spring

If Tunisia was hailed as a success story with its high rankings on economic, educational, and other indicators compared to other Arab countries, the 2011 popular uprisings demonstrate the need for political reforms but also major economic reforms. The Arab spring highlights the fragility of its main economic pillars including the tourism and the foreign direct investment. In such turbulent times, the paper examines the economic impact of migrant' remittances, expected to have a countercyclical behavior. Our results reveal that prior to the Arab Spring, the impacts of remittances on growth and consumption seem negative and positive respectively, while they varyingly influence local investment. These three relationships held in the short-run. By considering the period surrounding the 2011 uprisings, the investment effect of remittances becomes negative and weak in the short-and medium-run, whereas positive and strong remittances' impacts on growth and consumption are found in the long term.Comment: ERF 23rd Annual Conference , Mar 2017, Amman, Jorda

Phase Distribution and Phase Correlation of Financial Time Series

Scaling, phase distribution and phase correlation of financial time series are investigated based on the Dow Jones Industry Average (DJIA) and NASDAQ 10-minute intraday data for a period from Aug. 1 1997 to Dec. 31 2003. The returns of the two indices are shown to have nice scaling behaviors and belong to stable distributions according to the criterion of Levy's alpha stable distribution condition. A novel approach catching characteristic features of financial time series based on the concept of instantaneous phase is further proposed to study phase distribution and correlation. The analysis of phase distribution concludes return time series fall into a class which is different from other non-stationary time series. The correlation between returns of the two indices probed by the distribution of phase difference indicates there was a remarkable change of trading activities after the event of 911 attack, and this change persisted in later trading activities.Phase Distribution, High Frequency Data, Scaling Analysis, Levy Distribution, Stock Market, Frequency Variant