Approximation and compression of arbitrary time-series based on nonlinear dynamics

2002 ◽  
Author(s):  
M.J. Ogorzalek
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Arbitrary Time

Correlation in the heart rate data

1998 ◽  
Vol 2 ◽  
pp. 141-148
Author(s):  
J. Ulbikas ◽  
A. Čenys ◽  
D. Žemaitytė ◽  
G. Varoneckas
Keyword(s):  
Nonlinear Dynamics ◽  
Experimental Data ◽  
Heart Rate ◽  
Time Series ◽  
Cardiovascular Function ◽  
Statistical Properties ◽  
Rate Data ◽  
Heart Rate Data ◽  
Dynamical Nature ◽  
Analysis Of Time Series

Variety of methods of nonlinear dynamics have been used for possibility of an analysis of time series in experimental physiology. Dynamical nature of experimental data was checked using specific methods. Statistical properties of the heart rate have been investigated. Correlation between of cardiovascular function and statistical properties of both, heart rate and stroke volume, have been analyzed. Possibility to use a data from correlations in heart rate for monitoring of cardiovascular function was discussed.

Phenomenological Modelling

2018 ◽  
Author(s):  
Ray Huffaker ◽  
Marco Bittelli ◽  
Rodolfo Rosa
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Real World ◽  
Biological Diversity ◽  
False Positives ◽  
World Systems ◽  
Economic Activities ◽  
Essential Services ◽  
Low Dimension ◽  
Convergent Cross Mapping

Detecting causal interactions among climatic, environmental, and human forces in complex biophysical systems is essential for understanding how these systems function and how public policies can be devised that protect the flow of essential services to biological diversity, agriculture, and other core economic activities. Convergent Cross Mapping (CCM) detects causal networks in real-world systems diagnosed with deterministic, low-dimension, and nonlinear dynamics. If CCM detects correspondence between phase spaces reconstructed from observed time series variables, then the variables are determined to causally interact in the same dynamic system. CCM can give false positives by misconstruing synchronized variables as causally interactive. Extended (delayed) CCM screens for false positives among synchronized variables.

Characterization of Epileptic EEG Time Series (I): Gabor Transform and Nonlinear Dynamics Methods

1997 ◽  
pp. 179-226 ◽  
Author(s):  
Susana Blanco ◽  
Silvia Kochen ◽  
Rodrigo Quian Quiroga ◽  
Luis Riquelme ◽  
Osvaldo A. Rosso ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Gabor Transform

scholarly journals Permutation Entropy: Enhancing Discriminating Power by Using Relative Frequencies Vector of Ordinal Patterns Instead of Their Shannon Entropy

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1013 ◽  
Author(s):  
David Cuesta-Frau ◽  
Antonio Molina-Picó ◽  
Borja Vargas ◽  
Paula González
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Classification Accuracy ◽  
Markov Models ◽  
Hidden Markov ◽  
Permutation Entropy ◽  
Time Series Classification ◽  
Discriminating Power ◽  
Ordinal Patterns ◽  
Temperature Records

Many measures to quantify the nonlinear dynamics of a time series are based on estimating the probability of certain features from their relative frequencies. Once a normalised histogram of events is computed, a single result is usually derived. This process can be broadly viewed as a nonlinear I R n mapping into I R , where n is the number of bins in the histogram. However, this mapping might entail a loss of information that could be critical for time series classification purposes. In this respect, the present study assessed such impact using permutation entropy (PE) and a diverse set of time series. We first devised a method of generating synthetic sequences of ordinal patterns using hidden Markov models. This way, it was possible to control the histogram distribution and quantify its influence on classification results. Next, real body temperature records are also used to illustrate the same phenomenon. The experiments results confirmed the improved classification accuracy achieved using raw histogram data instead of the PE final values. Thus, this study can provide a very valuable guidance for the improvement of the discriminating capability not only of PE, but of many similar histogram-based measures.

scholarly journals Phase Entropy Analysis of Electrohysterographic Data at the Third Trimester of Human Pregnancy and Active Parturition

Entropy ◽  
2020 ◽  
Vol 22 (8) ◽  
pp. 798
Author(s):  
José Javier Reyes-Lagos ◽  
Adriana Cristina Pliego-Carrillo ◽  
Claudia Ivette Ledesma-Ramírez ◽  
Miguel Ángel Peña-Castillo ◽  
María Teresa García-González ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Coarse Graining ◽  
Entropy Analysis ◽  
Third Trimester ◽  
K Value ◽  
Order Difference ◽  
Robust Approach ◽  
The Third ◽  
Nonlinear Features

Phase Entropy (PhEn) was recently introduced for evaluating the nonlinear features of physiological time series. PhEn has been demonstrated to be a robust approach in comparison to other entropy-based methods to achieve this goal. In this context, the present study aimed to analyze the nonlinear features of raw electrohysterogram (EHG) time series collected from women at the third trimester of pregnancy (TT) and later during term active parturition (P) by PhEn. We collected 10-min longitudinal transabdominal recordings of 24 low-risk pregnant women at TT (from 35 to 38 weeks of pregnancy) and P (>39 weeks of pregnancy). We computed the second-order difference plots (SODPs) for the TT and P stages, and we evaluated the PhEn by modifying the k value, a coarse-graining parameter. Our results pointed out that PhEn in TT is characterized by a higher likelihood of manifesting nonlinear dynamics compared to the P condition. However, both conditions maintain percentages of nonlinear series higher than 66%. We conclude that the nonlinear features appear to be retained for both stages of pregnancy despite the uterine and cervical reorganization process that occurs in the transition from the third trimester to parturition.

Separation of Stochastic and Deterministic Information from Seismological Time Series with Nonlinear Dynamics and Maximum Entropy Methods

2007 ◽  
Author(s):  
Rafael M. Gutiérrez ◽  
Gina M. Useche ◽  
Elias Buitrago ◽  
Kevin H. Knuth ◽  
Ariel Caticha ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Maximum Entropy ◽  
Entropy Methods

State Space Reconstruction of Nonstationary Time-Series

2016 ◽  
Vol 12 (3) ◽  
Author(s):  
Hong-Guang Ma ◽  
Chun-Liang Zhang ◽  
Fu Li
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
State Space ◽  
Phase Angle ◽  
Analytical Form ◽  
Nonstationary Time Series ◽  
Original Time Series ◽  
State Space Reconstruction ◽  
Original Time ◽  
The Hilbert Transform

In this paper, a new method of state space reconstruction is proposed for the nonstationary time-series. The nonstationary time-series is first converted into its analytical form via the Hilbert transform, which retains both the nonstationarity and the nonlinear dynamics of the original time-series. The instantaneous phase angle θ is then extracted from the time-series. The first- and second-order derivatives θ˙, θ¨ of phase angle θ are calculated. It is mathematically proved that the vector field [θ,θ˙,θ¨] is the state space of the original time-series. The proposed method does not rely on the stationarity of the time-series, and it is available for both the stationary and nonstationary time-series. The simulation tests have been conducted on the stationary and nonstationary chaotic time-series, and a powerful tool, i.e., the scale-dependent Lyapunov exponent (SDLE), is introduced for the identification of nonstationarity and chaotic motion embedded in the time-series. The effectiveness of the proposed method is validated.

Observability of nonlinear dynamics: Normalized results and a time-series approach

2008 ◽  
Vol 18 (1) ◽  
pp. 013123 ◽  
Author(s):  
Luis A. Aguirre ◽  
Saulo B. Bastos ◽  
Marcela A. Alves ◽  
Christophe Letellier
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Time Series Approach

TIME SERIES ANALYSIS OF ECG: A POSSIBILITY OF THE INITIAL DIAGNOSTICS

2007 ◽  
Vol 17 (10) ◽  
pp. 3709-3713 ◽  
Author(s):  
ALEXANDER LOSKUTOV ◽  
OLGA MIRONYUK
Keyword(s):  
Nonlinear Dynamics ◽  
Time Series ◽  
Time Series Analysis ◽  
Initial Diagnosis ◽  
Rr Intervals ◽  
Advantages And Disadvantages ◽  
Series Analysis

The methods of nonlinear dynamics are applied to reveal the pathologies of patients with different heart failures. Our approach is based on the analysis of the correlation and embedding dimensions of the RR-intervals of ECGs. We demonstrate that these characteristics are quite convenient tools for the initial diagnosis. Advantages and disadvantages of the method are discussed.

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