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Multiscale entropy (MSE) measures to evaluate the complexity of time series by taking into account the multiple time scales in physical systems were proposed in the early 2000s. Since then, these approaches have received a great deal of attention and have been used in a wide range of applications. Multivariate approaches have also been developed. The algorithms for an MSE approach are composed of two main steps: (i) a coarse-graining procedure to represent the system’s dynamics on different scales and (ii) the entropy computation for the original signal and for the coarse-grained time series to evaluate the irregularity for each scale. Moreover, different entropy measures have been associated with the coarse-graining approach, each one having its advantages and drawbacks. In this Special Issue, we gathered 24 papers focusing on either the theory or applications of MSE approaches. These papers can be divided into two groups: papers that propose new developments in entropy-based measures or improve the understanding of existing ones (9 papers) and papers that propose new applications of existing entropy-based measures (14 papers). Moreover, one paper presents a review of cross-entropy methods and their multiscale approaches.

History of engineering & technology --- electrocardiogram --- heart rate variability --- multiscale distribution entropy --- RR interval --- short-term inter-beat interval --- Alzheimer disease --- functional near infra-red spectroscopy --- signal complexity --- clock drawing test --- digit span test --- corsi block tapping test --- structural health monitoring --- multi-scale --- composite cross-sample entropy --- PD --- fault diagnosis --- variational mode decomposition --- multi-scale dispersion entropy --- HMSVM --- multiscale entropy --- embodied media --- tele-communication --- humanoid --- prefrontal cortex --- human behavior --- complexity --- page view --- sample entropy --- Wikipedia --- missing values --- physiological data --- medical information --- postural stability index --- stability states --- ensemble empirical mode decomposition --- gait --- Multiscale Permutation Entropy --- ordinal patterns --- estimator variance --- Cramér–Rao Lower Bound --- finite-length signals --- nonlinear dynamics --- multiscale indices --- cardiac risk stratification --- Holter --- long term monitoring --- multifractal spectrum --- multiscale time irreversibility --- predictability --- multiscale analysis --- entropy rate --- memory effect --- financial time series --- entropy --- cardiac autonomic neuropathy --- diabetes --- mental workload --- motif --- multi-scale entropy --- permutation entropy --- HRV --- SVM --- multivariate multiscale dispersion entropy --- multivariate time series --- electroencephalogram --- magnetoencephalogram --- CPD --- EEG --- sleep staging --- tensor decomposition --- preterm neonate --- bearing fault diagnosis --- weak fault --- multi-component signal --- local robust principal component analysis --- multi-scale permutation entropy --- brain complexity --- dynamic functional connectivity --- edge complexity --- fluid intelligence --- node complexity --- resting-state functional magnetic resonance imaging --- aging --- consolidation --- default mode network --- episodic memory --- fMRI --- network complexity --- resting state --- copula density --- dependency structures --- Voronoi decomposition --- ambient temperature --- telemetry --- systolic blood pressure --- pulse interval --- thermoregulation --- vasopressin --- center of pressure --- falls --- postural control --- cross-entropy --- multiscale cross-entropy --- asynchrony --- coupling --- cross-sample entropy --- cross-approximate entropy --- cross-distribution entropy --- cross-fuzzy entropy --- cross-conditional entropy --- eye movement events detection --- nonlinear analysis time series analysis --- approximate entropy --- fuzzy entropy --- multilevel entropy map --- time-scale decomposition --- heart sound --- ICEEMDAN --- RCMDE --- Fisher ratio --- biometric characterization --- multi-scale entropy (MSE) --- vector autoregressive fractionally integrated (VARFI) models --- heart rate variability (HRV) --- systolic arterial pressure (SAP) --- multivariate data --- electrocardiogram --- heart rate variability --- multiscale distribution entropy --- RR interval --- short-term inter-beat interval --- Alzheimer disease --- functional near infra-red spectroscopy --- signal complexity --- clock drawing test --- digit span test --- corsi block tapping test --- structural health monitoring --- multi-scale --- composite cross-sample entropy --- PD --- fault diagnosis --- variational mode decomposition --- multi-scale dispersion entropy --- HMSVM --- multiscale entropy --- embodied media --- tele-communication --- humanoid --- prefrontal cortex --- human behavior --- complexity --- page view --- sample entropy --- Wikipedia --- missing values --- physiological data --- medical information --- postural stability index --- stability states --- ensemble empirical mode decomposition --- gait --- Multiscale Permutation Entropy --- ordinal patterns --- estimator variance --- Cramér–Rao Lower Bound --- finite-length signals --- nonlinear dynamics --- multiscale indices --- cardiac risk stratification --- Holter --- long term monitoring --- multifractal spectrum --- multiscale time irreversibility --- predictability --- multiscale analysis --- entropy rate --- memory effect --- financial time series --- entropy --- cardiac autonomic neuropathy --- diabetes --- mental workload --- motif --- multi-scale entropy --- permutation entropy --- HRV --- SVM --- multivariate multiscale dispersion entropy --- multivariate time series --- electroencephalogram --- magnetoencephalogram --- CPD --- EEG --- sleep staging --- tensor decomposition --- preterm neonate --- bearing fault diagnosis --- weak fault --- multi-component signal --- local robust principal component analysis --- multi-scale permutation entropy --- brain complexity --- dynamic functional connectivity --- edge complexity --- fluid intelligence --- node complexity --- resting-state functional magnetic resonance imaging --- aging --- consolidation --- default mode network --- episodic memory --- fMRI --- network complexity --- resting state --- copula density --- dependency structures --- Voronoi decomposition --- ambient temperature --- telemetry --- systolic blood pressure --- pulse interval --- thermoregulation --- vasopressin --- center of pressure --- falls --- postural control --- cross-entropy --- multiscale cross-entropy --- asynchrony --- coupling --- cross-sample entropy --- cross-approximate entropy --- cross-distribution entropy --- cross-fuzzy entropy --- cross-conditional entropy --- eye movement events detection --- nonlinear analysis time series analysis --- approximate entropy --- fuzzy entropy --- multilevel entropy map --- time-scale decomposition --- heart sound --- ICEEMDAN --- RCMDE --- Fisher ratio --- biometric characterization --- multi-scale entropy (MSE) --- vector autoregressive fractionally integrated (VARFI) models --- heart rate variability (HRV) --- systolic arterial pressure (SAP) --- multivariate data

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Multiscale entropy (MSE) measures to evaluate the complexity of time series by taking into account the multiple time scales in physical systems were proposed in the early 2000s. Since then, these approaches have received a great deal of attention and have been used in a wide range of applications. Multivariate approaches have also been developed. The algorithms for an MSE approach are composed of two main steps: (i) a coarse-graining procedure to represent the system’s dynamics on different scales and (ii) the entropy computation for the original signal and for the coarse-grained time series to evaluate the irregularity for each scale. Moreover, different entropy measures have been associated with the coarse-graining approach, each one having its advantages and drawbacks. In this Special Issue, we gathered 24 papers focusing on either the theory or applications of MSE approaches. These papers can be divided into two groups: papers that propose new developments in entropy-based measures or improve the understanding of existing ones (9 papers) and papers that propose new applications of existing entropy-based measures (14 papers). Moreover, one paper presents a review of cross-entropy methods and their multiscale approaches.

electrocardiogram --- heart rate variability --- multiscale distribution entropy --- RR interval --- short-term inter-beat interval --- Alzheimer disease --- functional near infra-red spectroscopy --- signal complexity --- clock drawing test --- digit span test --- corsi block tapping test --- structural health monitoring --- multi-scale --- composite cross-sample entropy --- PD --- fault diagnosis --- variational mode decomposition --- multi-scale dispersion entropy --- HMSVM --- multiscale entropy --- embodied media --- tele-communication --- humanoid --- prefrontal cortex --- human behavior --- complexity --- page view --- sample entropy --- Wikipedia --- missing values --- physiological data --- medical information --- postural stability index --- stability states --- ensemble empirical mode decomposition --- gait --- Multiscale Permutation Entropy --- ordinal patterns --- estimator variance --- Cramér–Rao Lower Bound --- finite-length signals --- nonlinear dynamics --- multiscale indices --- cardiac risk stratification --- Holter --- long term monitoring --- multifractal spectrum --- multiscale time irreversibility --- predictability --- multiscale analysis --- entropy rate --- memory effect --- financial time series --- entropy --- cardiac autonomic neuropathy --- diabetes --- mental workload --- motif --- multi-scale entropy --- permutation entropy --- HRV --- SVM --- multivariate multiscale dispersion entropy --- multivariate time series --- electroencephalogram --- magnetoencephalogram --- CPD --- EEG --- sleep staging --- tensor decomposition --- preterm neonate --- bearing fault diagnosis --- weak fault --- multi-component signal --- local robust principal component analysis --- multi-scale permutation entropy --- brain complexity --- dynamic functional connectivity --- edge complexity --- fluid intelligence --- node complexity --- resting-state functional magnetic resonance imaging --- aging --- consolidation --- default mode network --- episodic memory --- fMRI --- network complexity --- resting state --- copula density --- dependency structures --- Voronoi decomposition --- ambient temperature --- telemetry --- systolic blood pressure --- pulse interval --- thermoregulation --- vasopressin --- center of pressure --- falls --- postural control --- cross-entropy --- multiscale cross-entropy --- asynchrony --- coupling --- cross-sample entropy --- cross-approximate entropy --- cross-distribution entropy --- cross-fuzzy entropy --- cross-conditional entropy --- eye movement events detection --- nonlinear analysis time series analysis --- approximate entropy --- fuzzy entropy --- multilevel entropy map --- time-scale decomposition --- heart sound --- ICEEMDAN --- RCMDE --- Fisher ratio --- biometric characterization --- multi-scale entropy (MSE) --- vector autoregressive fractionally integrated (VARFI) models --- heart rate variability (HRV) --- systolic arterial pressure (SAP) --- multivariate data