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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

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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.

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

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Recent advances in electronics have led to sensors whose sizes and weights are such that they can be placed on living systems without impairing their natural motion and habits. They may be worn on the body as accessories or as part of the clothing and enable personalized mobile information processing. Wearable sensors open the way for a nonintrusive and continuous monitoring of body orientation, movements, and various physiological parameters during motor activities in real-life settings. Thus, they may become crucial tools not only for researchers, but also for clinicians, as they have the potential to improve diagnosis, better monitor disease development and thereby individualize treatment. Wearable sensors should obviously go unnoticed for the people wearing them and be intuitive in their installation. They should come with wireless connectivity and low-power consumption. Moreover, the electronics system should be self-calibrating and deliver correct information that is easy to interpret. Cross-platform interfaces that provide secure data storage and easy data analysis and visualization are needed.This book contains a selection of research papers presenting new results addressing the above challenges.

Medical equipment & techniques --- inertial measurement unit --- movement analysis --- long-track speed skating --- validity --- IMU --- principal component analysis --- wearable --- scoring --- carving --- balance assessment --- data augmentation --- gated recurrent unit --- human activity recognition --- one-dimensional convolutional neural network --- intermittent claudication --- vascular rehabilitation --- 6 min walking test --- functional walking --- TUG --- kinematics --- fall risk --- logistic regression --- elderly --- inertial sensor --- artificial intelligence --- supervised machine learning --- head rotation test --- neck pain --- cerebral palsy --- dystonia --- choreoathetosis --- machine learning --- home-based --- wearable device --- MLP --- gesture recognition --- flex sensor --- model search --- neural network --- inertial measurement unit—IMU --- movement complexity --- sample entropy --- trunk flexion --- low back pain --- lifting technique --- camera system --- ward clustering method --- K-means clustering method --- ensemble clustering method --- Bayesian neural network --- pain self-efficacy questionnaire --- n/a --- inertial measurement unit-IMU

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This volume deals with recent advances in and applications of computational intelligence and advanced machine learning methods in power systems, heating and cooling systems, and gas transportation systems. The optimal coordinated dispatch of the multi-energy microgrids with renewable generation and storage control using advanced numerical methods is discussed. Forecasting models are designed for electrical insulator faults, the health of the battery, electrical insulator faults, wind speed and power, PV output power and transformer oil test parameters. The loads balance algorithm for an offshore wind farm is proposed. The information security problems in the energy internet are analyzed and attacked using information transmission contemporary models, based on blockchain technology. This book will be of interest, not only to electrical engineers, but also to applied mathematicians who are looking for novel challenging problems to focus on.

History of engineering & technology --- vacuum tank degasser --- rule extraction --- extreme learning machine --- classification and regression trees --- wind power: wind speed: T–S fuzzy model: forecasting --- linearization --- machine learning --- photovoltaic output power forecasting --- hybrid interval forecasting --- relevance vector machine --- sample entropy --- ensemble empirical mode decomposition --- high permeability renewable energy --- blockchain technology --- energy router --- QoS index of energy flow --- MOPSO algorithm --- scheduling optimization --- Adaptive Neuro-Fuzzy Inference System --- insulator fault forecast --- wavelet packets --- time series forecasting --- power quality --- harmonic parameter --- harmonic responsibility --- monitoring data without phase angle --- parameter estimation --- blockchain --- energy internet --- information security --- forecasting --- clustering --- energy systems --- classification --- integrated energy system --- risk assessment --- component accident set --- vulnerability --- hybrid AC/DC power system --- stochastic optimization --- renewable energy source --- Volterra models --- wind turbine --- maintenance --- fatigue --- power control --- offshore wind farm --- Interfacial tension --- transformer oil parameters --- harmonic impedance --- traction network --- harmonic impedance identification --- linear regression model --- data evolution mechanism --- cast-resin transformers --- abnormal defects --- partial discharge --- pattern recognition --- hierarchical clustering --- decision tree --- industrial mathematics --- inverse problems --- intelligent control --- artificial intelligence --- energy management system --- smart microgrid --- optimization --- Volterra equations --- energy storage --- load leveling --- cyber-physical systems --- vacuum tank degasser --- rule extraction --- extreme learning machine --- classification and regression trees --- wind power: wind speed: T–S fuzzy model: forecasting --- linearization --- machine learning --- photovoltaic output power forecasting --- hybrid interval forecasting --- relevance vector machine --- sample entropy --- ensemble empirical mode decomposition --- high permeability renewable energy --- blockchain technology --- energy router --- QoS index of energy flow --- MOPSO algorithm --- scheduling optimization --- Adaptive Neuro-Fuzzy Inference System --- insulator fault forecast --- wavelet packets --- time series forecasting --- power quality --- harmonic parameter --- harmonic responsibility --- monitoring data without phase angle --- parameter estimation --- blockchain --- energy internet --- information security --- forecasting --- clustering --- energy systems --- classification --- integrated energy system --- risk assessment --- component accident set --- vulnerability --- hybrid AC/DC power system --- stochastic optimization --- renewable energy source --- Volterra models --- wind turbine --- maintenance --- fatigue --- power control --- offshore wind farm --- Interfacial tension --- transformer oil parameters --- harmonic impedance --- traction network --- harmonic impedance identification --- linear regression model --- data evolution mechanism --- cast-resin transformers --- abnormal defects --- partial discharge --- pattern recognition --- hierarchical clustering --- decision tree --- industrial mathematics --- inverse problems --- intelligent control --- artificial intelligence --- energy management system --- smart microgrid --- optimization --- Volterra equations --- energy storage --- load leveling --- cyber-physical systems

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Entropies and entropy-like quantities play an increasing role in modern non-linear data analysis. Fields that benefit from this application range from biosignal analysis to econophysics and engineering. This issue is a collection of papers touching on different aspects of entropy measures in data analysis, as well as theoretical and computational analyses. The relevant topics include the difficulty to achieve adequate application of entropy measures and the acceptable parameter choices for those entropy measures, entropy-based coupling, and similarity analysis, along with the utilization of entropy measures as features in automatic learning and classification. Various real data applications are given.

fault diagnosis --- empirical mode decomposition --- auditory attention --- Dempster-Shafer evidence theory --- simulation --- uncertainty of basic probability assignment --- center of pressure displacement --- particle size distribution --- multivariate analysis --- symbolic analysis --- permutation entropy --- short time records --- co-evolution --- plausibility transformation --- experiment of design --- cross-entropy method --- weighted Hartley entropy --- firefly algorithm --- embedded dimension --- entropy measure --- effective transfer entropy --- treadmill walking --- ordinal patterns --- complex fuzzy set --- entropy visualization --- belief entropy --- signal classification --- machine learning evaluation --- novelty detection --- selfsimilar measure --- Permutation entropy --- automatic learning --- cross wavelet transform --- cross-visibility graphs --- Kolmogorov-Sinai entropy --- distance --- Shannon-type relations --- Tsallis entropy --- market crash --- support vector machine (SVM) --- conditional entropy of ordinal patterns --- sample entropy --- learning --- electroencephalography (EEG) --- meta-heuristic --- entropy --- data transformation --- information entropy --- signal analysis --- synchronization analysis --- similarity indices --- data analysis --- geodesic distance --- auditory attention classifier --- entropy measures --- distance induced vague entropy --- analog circuit --- vague entropy --- complex vague soft set --- entropy balance equation --- parametric t-distributed stochastic neighbor embedding --- global optimization --- learning systems --- image entropy --- algorithmic complexity --- support vector machine --- system coupling --- relevance analysis --- Chinese stock sectors --- Shannon entropy --- linear discriminant analysis (LDA) --- information --- information transfer --- dual-tasking --- non-probabilistic entropy