Abstract. Nonlinear methods and artificial neural network techniques are applied to the study of the regime and the possibility of short-term forecasting of discharges of the spring of Almyros, Iraklion, Crete. Questions regarding the nonlinearity and chaotic characteristics of the system necessitate the examination of dynamical properties. Toward this objective the time series of daily average discharges is analyzed in detail. First, the dimensionality of the dynamics in the reconstructed phase space is found to be quite low, -3-4. Then several tests are applied to examine the nonlinearity and the presence of noise in the data. Using the surrogate time series test, a high degree of nonlinearity and a deterministic nature are revealed, while the differentiation test showed that the presence of high-frequency noise in the series of the discharge is not dynamically important. These suggest that an attempt to forecast the short-term future behavior of this time series may turn out to be quite successful. Nonlinear methods, such as Farmer's algorithm and artificial neural networks, were employed and found to exhibit a very satisfactory predictive ability, with neural networks achieving a slightly better performance.
In recent years there has been an increasing number of papers in the literature, applying the methods and techniques of Nonlinear Dynamics to the time series of electrical activity in normal electrocardiograms (ECGs) of various human subjects. Most of these studies are based primarily on correlation dimension estimates, and conclude that the dynamics of the ECG signal is deterministic and occurs on a chaotic attractor, whose dimension can distinguish between healthy and severely malfunctioning cases. In this paper, we first demonstrate that correlation dimension calculations must be used with care, as they do not always yield reliable estimates of the attractor's "dimension." We then carry out a number of additional tests (time differencing, smoothing, principal component analysis, surrogate data analysis, etc.) on the ECGs of three "normal" subjects and three "heavy smokers" at rest and after mild exercising, whose cardiac rhythms look very similar. Our main conclusion is that no major dynamical differences are evident in these signals. A preliminary estimate of three to four basic variables governing the dynamics (based on correlation dimension calculations) is updated to five to six, when temporal correlations between points are removed. Finally, in almost all cases, the transition between resting and mild exercising seems to imply a small increase in the complexity of cardiac dynamics. (c) 1995 American Institute of Physics.
An advanced spectral analysis technique of good spectral resolution for short data records is introduced and is applied to Heart Rate Variability (HRV) signals. The method, based on an exponential model for the signal and on a new approach to the Prony's spectral method, calculates the power spectrum on a running temporal window. Power Spectrum Density (PSD) is hence obtained in each window of analysis, giving us the capability to follow the dynamics of the spectral parameters (high and low 9equency powers). This method was applied to data obtained during Autonomic Nervous System (ANS) blockade (propranolol and atropine administration). The results showed that we can track the time-varying spectral features of the signal and to monitor the influence of ANS blockade on the heart. IntroductionThe analysis of HRV in the frequency domain has been carried out either in non-parametric (based upon the FFT algorithm) or in parametric form (based on Autoregressive modelling), providing quantitative indices on the action of the ANS [ 1,2].The discrete series of RR intervals (the time interval between successive QRS complexes on the ECG) has been analyzed in the frequency domain since the early 1970's and its power spectrum has shown three principal components.' a very low frequency component (VLF) in a range between 0.0033 Hz to 0.03 Hz, which may represent the influence of the thermoregulatory, peripheral vasomotor or renin-angiotensin systems. 0 a low frequency Component (LF) in a range between 0.03 Hz and 0.15 Hz, which is modulated by both the sympathetic and parasympathetic nervous system. But on the basis of pharmacological and clinical experiments, it has been observed that its power increases for increased sympathetic tone. a high frequency component (HF) in a range between 0.18 Hz to 0.4 Hz, which represnts the modulation of vagal activity especially influenced by respiration. The power related to the LF and HF components and their ratio LFMF have been chosen as noninvasive measures of the sympatho-vagal interactions [3].In this study, the changes in the power related to the LF and HF components are used to reveal the influence of ANS blockade (propranolol and atropine administration) on the heart. In order to follow the dynamics of the LF and HF powers (reflected sympathetic and vagal influences on the heart) a method with good spectral resolution for short data records is proposed.The method uses an exponential model for the signal in a running window of analysis and a new approach to the Prony's spectral estimation method. This new approach is based on the overdetermined FonvardBackward technique and the Singular Value Decomposition (SVD) for enchancement and accurate identification of the actual components of the signal especially in short data records. MethodA series of N values {y( 1) ...y( N)} representing a series of RR intervals is approximated by the M-term complex exponential model:where T is the sample interval in seconds, Ai is the amplitude of the ith exponential ai is the damping factor in seconds',...
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