scholarly journals Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series

Entropy ◽  
2020 ◽  
Vol 22 (3) ◽  
pp. 315 ◽  
Author(s):  
Aurora Martins ◽  
Riccardo Pernice ◽  
Celestino Amado ◽  
Ana Paula Rocha ◽  
Maria Eduarda Silva ◽  
...  
Keyword(s):  
Time Series ◽  
Long Range ◽  
Time Scales ◽  
Multivariate Time Series ◽  
Multiscale Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Control Mechanisms ◽  
Long Range Correlations ◽  
Dynamical Complexity

Assessing the dynamical complexity of biological time series represents an important topic with potential applications ranging from the characterization of physiological states and pathological conditions to the calculation of diagnostic parameters. In particular, cardiovascular time series exhibit a variability produced by different physiological control mechanisms coupled with each other, which take into account several variables and operate across multiple time scales that result in the coexistence of short term dynamics and long-range correlations. The most widely employed technique to evaluate the dynamical complexity of a time series at different time scales, the so-called multiscale entropy (MSE), has been proven to be unsuitable in the presence of short multivariate time series to be analyzed at long time scales. This work aims at overcoming these issues via the introduction of a new method for the assessment of the multiscale complexity of multivariate time series. The method first exploits vector autoregressive fractionally integrated (VARFI) models to yield a linear parametric representation of vector stochastic processes characterized by short- and long-range correlations. Then, it provides an analytical formulation, within the theory of state-space models, of how the VARFI parameters change when the processes are observed across multiple time scales, which is finally exploited to derive MSE measures relevant to the overall multivariate process or to one constituent scalar process. The proposed approach is applied on cardiovascular and respiratory time series to assess the complexity of the heart period, systolic arterial pressure and respiration variability measured in a group of healthy subjects during conditions of postural and mental stress. Our results document that the proposed methodology can detect physiologically meaningful multiscale patterns of complexity documented previously, but can also capture significant variations in complexity which cannot be observed using standard methods that do not take into account long-range correlations.

scholarly journals Cardiovascular and Cardiorespiratory Signals Complexity Analysis Using Different Techniques

2021 ◽  
Author(s):  
Kirti Singh ◽  
Indu Saini ◽  
Neetu Sood
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Complexity Analysis ◽  
Multiscale Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Short Term ◽  
Dynamic Complexity ◽  
Long Range Correlations ◽  
Biological Time

In recent decades, the concept of complex physiological systems has become more and more popular. The evaluation of the biological time series' dynamic complexity is an essential subject with possible applications such as the characterization of physiological states i.e. HRV, BP, and RESP signals and pathological disorders to the measurement of diagnostic parameters. The convergence of several physiological regulation processes is the cause of heterogeneity in cardiovascular time series, that consider many factors and function over several time scales, resulting not only the presence of short-term dynamics but also the coexistence of long-range correlations in various physiological signals. The most popular approach to evaluating the dynamic complexity and irregularity of time series over multiple time scales is entropy based analysis. The most used approach is multiscale entropy (MSE) and refined MSE (RMSE). It is then added to the heart period time series, respiration time series, and blood pressure time series, measured in young subjects and old subjects under resting conditions. This research applies to short-term cardiovascular and cardiorespiratory variability documents that LMSE can better describe physiological processes' behavior causing biological oscillations at various time scales than RMSE.

scholarly journals Scale-dependent intrinsic entropies of complex time series

2016 ◽  
Vol 374 (2065) ◽  
pp. 20150204 ◽  
Author(s):  
Jia-Rong Yeh ◽  
Chung-Kang Peng ◽  
Norden E. Huang
Keyword(s):  
Time Series ◽  
Time Scales ◽  
Spatial Scales ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Complex Time ◽  
Multi Scale ◽  
Mode Decomposition ◽  
Simulated Time ◽  
Simulated Time Series

Multi-scale entropy (MSE) was developed as a measure of complexity for complex time series, and it has been applied widely in recent years. The MSE algorithm is based on the assumption that biological systems possess the ability to adapt and function in an ever-changing environment, and these systems need to operate across multiple temporal and spatial scales, such that their complexity is also multi-scale and hierarchical. Here, we present a systematic approach to apply the empirical mode decomposition algorithm, which can detrend time series on various time scales, prior to analysing a signal’s complexity by measuring the irregularity of its dynamics on multiple time scales. Simulated time series of fractal Gaussian noise and human heartbeat time series were used to study the performance of this new approach. We show that our method can successfully quantify the fractal properties of the simulated time series and can accurately distinguish modulations in human heartbeat time series in health and disease.

Molecular dynamics algorithm for multiple time scales: Systems with long range forces

1991 ◽  
Vol 94 (10) ◽  
pp. 6811-6815 ◽  
Author(s):  
Mark E. Tuckerman ◽  
Bruce J. Berne ◽  
Glenn J. Martyna
Keyword(s):  
Molecular Dynamics ◽  
Long Range ◽  
Time Scales ◽  
Multiple Time Scales ◽  
Multiple Time

Quantifying the dynamics of electroencephalographic (EEG) signals to distinguish alcoholic and non-alcoholic subjects using an MSE based K-d tree algorithm

2018 ◽  
Vol 63 (4) ◽  
pp. 481-490 ◽  
Author(s):  
Lal Hussain ◽  
Wajid Aziz ◽  
Sharjil Saeed ◽  
Saeed Arif Shah ◽  
Malik Sajjad A. Nadeem ◽  
...  
Keyword(s):  
Time Scales ◽  
Coarse Grained ◽  
Multiscale Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Operating Characteristics ◽  
Eeg Signals ◽  
Temporal Scales ◽  
Online Application ◽  
Time And Space Complexity

Abstract In this paper, we have employed K-d tree algorithmic based multiscale entropy analysis (MSE) to distinguish alcoholic subjects from non-alcoholic ones. Traditional MSE techniques have been used in many applications to quantify the dynamics of physiological time series at multiple temporal scales. However, this algorithm requires O(N2), i.e. exponential time and space complexity which is inefficient for long-term correlations and online application purposes. In the current study, we have employed a recently developed K-d tree approach to compute the entropy at multiple temporal scales. The probability function in the entropy term was converted into an orthogonal range. This study aims to quantify the dynamics of the electroencephalogram (EEG) signals to distinguish the alcoholic subjects from control subjects, by inspecting various coarse grained sequences formed at different time scales, using traditional MSE and comparing the results with fast MSE (fMSE). The performance was also measured in terms of specificity, sensitivity, total accuracy and receiver operating characteristics (ROC). Our findings show that fMSE, with a K-d tree algorithmic approach, improves the reliability of the entropy estimation in comparison with the traditional MSE. Moreover, this new technique is more promising to characterize the physiological changes having an affect at multiple time scales.

MULTIPLE TIME-SCALES NONLINEAR PREDICTION OF RIVER FLOW USING CHAOS APPROACH

2016 ◽  
Vol 78 (7) ◽  
Author(s):  
Nur Hamiza Adenan ◽  
Mohd Salmi Md Noorani
Keyword(s):  
Time Series ◽  
Time Scales ◽  
River Flow ◽  
Moving Average ◽  
Multiple Time Scales ◽  
Support Vector ◽  
Multiple Time ◽  
Nonlinear Prediction ◽  
Prediction Result ◽  
Flow Prediction

River flow prediction is important in determining the amount of water in certain areas to ensure sufficient water resources to meet the demand. Hence, an analysis and prediction of multiple time-scales data for daily, weekly and 10-day averaged time series were performed using chaos approach. An analysis was conducted at the Tanjung Tualang station, Malaysia. This method involved the reconstruction of a single variable in a multi-dimensional phase space. River flow prediction was performed using local linear approximation. The prediction result is close to agreement with a high correlation coefficient for each time scale. The analysis suggests that the presence of low dimensional chaos as an optimal embedding dimension exists when the inverse method is adopted. In addition, a comparison of the prediction performance of chaos approach, autoregressive integrated moving average (ARIMA), artificial neural network (ANN), support vector machine (SVM) and least squares support vector machines (LSSVM) were performed. The comparative analysis shows that all methods provide comparable predictions. However, chaos approach provides a simpler means of analysis since it only use a scalar time series (river flow data). Therefore, the relevant authorities may use this prediction result for the creation of a water management system for local benefit.

MULTISCALE ENTROPY ANALYSIS OF TRAFFIC TIME SERIES

2013 ◽  
Vol 24 (02) ◽  
pp. 1350006 ◽  
Author(s):  
JING WANG ◽  
PENGJIAN SHANG ◽  
XIAOJUN ZHAO ◽  
JIANAN XIA
Keyword(s):  
Time Series ◽  
Coarse Grained ◽  
Multiscale Entropy ◽  
Permutation Entropy ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Entropy Analysis ◽  
Traffic Time Series ◽  
Real World Datasets ◽  
Physiologic Time Series

There has been considerable interest in quantifying the complexity of different time series, such as physiologic time series, traffic time series. However, these traditional approaches fail to account for the multiple time scales inherent in time series, which have yielded contradictory findings when applied to real-world datasets. Then multi-scale entropy analysis (MSE) is introduced to solve this problem which has been widely used for physiologic time series. In this paper, we first apply the MSE method to different correlated series and obtain an interesting relationship between complexity and Hurst exponent. A modified MSE method called multiscale permutation entropy analysis (MSPE) is then introduced, which replaces the sample entropy (SampEn) with permutation entropy (PE) when measuring entropy for coarse-grained series. We employ the traditional MSE method and MSPE method to investigate complexities of different traffic series, and obtain that the complexity of weekend traffic time series differs from that of the workday time series, which helps to classify the series when making predictions.

scholarly journals Evaluation of Multi-Precipitation Products for Multi-Time Scales and Spatial Distribution During 2007-2015

2019 ◽  
Vol 5 (1) ◽  
pp. 255 ◽  
Author(s):  
Nguyen Tien Thanh
Keyword(s):  
Time Series ◽  
Spatial Distribution ◽  
Water Resources ◽  
Time Scales ◽  
Heavy Rain ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Precipitation Estimates ◽  
Rain Events ◽  
Trmm 3B42

Recently, several precipitation products are released with the improved algorithm to strengthen the performance of precipitation construction and monitoring. These data play a key role in a wide range of hydrological models, water resources modeling and environmental researches. Especially in developing countries like Vietnam, it is challenging to gather data for long-term time series at scales of daily and sub-daily due to the very coarse density of observation station. In order to overcome the problem of data scarcity, this study aims to evaluate the performance of newest multiple precipitation products including Tropical Rainfall Measuring Mission (TRMM 3B42 V7), Climate Prediction Center (CPC) MORPHing Version 1.0 (CMORPH_V1.0), European Centre for Medium-Range Weather Forecasts (ECMWF) reanalysis systems (ERA-Interim), Climate Research Unit Time series Version 4.0.1 (CRU TS 4.0.1) and Asian Precipitation-Highly-Resolved Observational Data Integration Towards Evaluation of Water Resources version 2 (APHRODITE) in comparison with measured precipitation for multiple time scales (daily, monthly, seasonal and annual), taking the VuGia-ThuBon (VG-TB) as a pilot basin where climate regime is complex. Seven continuous and four dichotomous statistics are applied to evaluate the precipitation estimates qualitatively at multiple time scales. In addition, specifically, evaluation of spatial distribution of multiple time scales is implemented. The results show lower precipitation estimates in areas of high elevation and higher precipitation estimates over the areas of plain and coastal in comparison with measured precipitation for all considered precipitation data. More importantly, ERA-Interim well captures rain events of heavy rain (50.0-100 mm/day). CMORHPH_V1.0 better reproduces the rain events with little overestimation of light rain (0.6-6 mm/day) than the others. For zero rain events (0-0.6 mm/day), TRMM 3B42 V7 gives the best performance. Furthermore, the cumulative distribution function of APHRODITE well matches the distribution of measured precipitation. All precipitation products completely fail to capture the rain events of extremely heavy rain. More importantly, a formula is proposed to scale and adjust the merged satellite precipitation at a sub-daily scale.

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