A non-commutative time-frequency tomography

The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the time-frequency plane. The time-frequency distributions have difficult interpretation problems arising from negative and complex values or spurious components. In this paper, we get time-frequency information from the marginal distributions in rotated directions in the time-frequency plane. The rigorous probability interpretation of the marginal distributions is without any ambiguities. This time-frequency transformation is similar to the computerized axial tomography (CT or CAT) and is applied to signal analysis and signal detection and reveals a lot of advantages especially in the signal detection of the low signal/noise (S/N).     

Identification of the deposited layers in landslides reservoir and investigation of the sediment yields during the later sixteenth century on the Hill Loess Plateau,China

There are many sediment trapping reservoirs in the Hill Loess Plateau. The Huangtuwa small catchment is selected as a research field where samples were collected in a sediment deposit profile with a vertical length of 12.73 m. By the variation of fine particle content and pollen concentration, 54 flood couples were identified. Taking the freeze-thawing disturbed texture as the sign of the latest flood couple in a year, it is ascertained that those 54 floods should happen in 31 years. Using pyramid volume calculation formula, the sediment yields of flood ranged between 716-30376 t· km^-2, The average sediment yield was 7106 t· km^-2, The annual sediment yields varied between 968-55579 t· （km^2· a）^-1, and the average value is 12629 t· （km^2· a）^-1. Compared with the modern annual sediment discharge of the Huaining River, the erosion rate in the Huangtuwa region 450 years ago was similar to the modern erosion rate. In the period from the 27th year to the 31st year, the average annual sediment yield increased sharply to 31309 t· （km^2· a）^-1. It implied that re-reclamation of the abandoned land in the catchment since the landslide disaster, where vegetation had rehabilitated already, caused very severe soil erosion in the catchment.     

Multifractal mass exponent spectrum of complex physiological time series

Physiological signal belongs to the kind of nonstationary and time-variant ones. Thus, the nonlinear analysis methods may be better to disclose its characteristics and mechanisms. There have been plenty of evidences that physiological signal generated by complex self-regulated system may have a fractal structure. In this work, we introduce a new measure to characterize multifractality, the mass exponent spectrum curvature, which can disclose the complexity of fractal structure from total bending degree of the spectrum. This parameter represents the nonlinear superpositions of the discrepancies of fractal dimension from all adjacent points in the curve and therefore solves the problem of original parameters for not fully reflecting the information of entire subsets in the fractal structure. The evaluations of deterministic fractal system Cantor measure validate that it is completely effective in exploring the complexity of chaotic series, and is also not affected by nonstability of the signal as well as disturbances of the noises. We then apply it to the analysis of human heart rate variability (HRV) signals and sleep electroencephalogram (EEG) signals. The experimental results show that this method can be better to discriminate cohorts under different physiological and pathological conditions. Compared with the indicator of singularity spectrum width, there are some improvements both on the computing efficiency and accuracy. Such conclusion may provide some valuable information for clinical diagnoses.     

Multiscale analysis of heart beat interval increment series and its clinical significance

Analysis of multiscale entropy （MSE） and multiscale standard deviation （MSD） are performed for both the heart rate interval series and the interval increment series. For the interval series, it is found that, it is impractical to discriminate the diseases of atrial fibrillation （AF） and congestive heart failure （CHF） unambiguously from the healthy. A clear discrimination from the healthy, both young and old, however, can be made in the MSE analysis of the increment series where we find that both CHF and AF sufferers have significantly low MSE values in the whole range of time scales investigated, which reveals that there are common dynamic characteristics underlying these two different diseases. In addition, we propose the sample entropy （SE） corresponding to time scale factor 4 of increment series as a diagnosis index of both AF and CHF, and the reference threshold is recommended. Further indication that this index can help discriminate sensitively the mild heart failure （cardiac function classes 1 and 2） from the healthy gives a clue to early clinic diagnosis of CHF.     

Nonlinear short-term heart rate variability prediction of spontaneous ventricular tachyarrhythmia

As malign ventricular tachyarrhythmias triggering sudden cardiac death （SCD）, both ventricular tachycardla （VT） and ventricular fibrillation （VF） are major causes of mortality. The most efficient therapy for SCD prevention is implantable cardioverter defibrillators （ICD）. The ICD can accurately and effectively Identify the forthcoming of fatal ventricular tachyarrhythmlas and deliver a shock in order to restore patients＇ normal sinus rhythm. In this study, two nonlinear complexity measures based on entropy： approximate entropy （ApEn） and sample entropy （SampEn） as well as two time linear indices： the mean RR interval （the average of time intervals between consecutive R-waves） and the standard deviation of RR Intervals were used for short-term forecasting of VT-VF occurrence. The last small sections of interbeat Intervals preceding 135 VT-VF episodes from 78 patients stored by the ICD were analyzed and compared with individually acquired control time series （CON series） from the same patients, which are normally intrinsic sinus rhythms. The results demonstrate that in addition to an obvious increase in heart rates of the patients, the values of two entropy measures are significantly smaller for VT-VF episodes than those for CON series. Conclusions can be drawn that when a ventricular tachyarrhythmia approaches, the sympathetic tone of the patients is increased, and the complexity of their RR intervals immediately before the onset of VT-VF events is obviously lower than that of RR intervals recorded during sinus rhythms. For a better separation, the optimal range of threshold r is determined for two algorithms. ApEn and SampEn measures might be the suitable nonlinear parameters for shodterm prediction of life-threatening ventricular tachyarrhythmias in the application of the cardioversion and defibrillation.     

Sign series entropy analysis of short-term heart rate variability

Complexity and nonlinearity approaches can be used to study the temporal and structural order in heart rate variability （HRV） signal, which is helpful for understanding the underlying rule and physiological essence of cardiovascular regulation. For clinical applications, methods suitable for short-term HRV analysis are more valuable. In this paper, sign series entropy analysis （SSEA） is proposed to characterize the feature of direction variation of HRV. The results show that SSEA method can detect sensitively physiological and pathological changes from short-term HRV signals, and the method also shows its robustness to nonstationarity and noise. Thus, it is suggested as an efficient way for the analysis of clinical HRV and other complex physiological signals.