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Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems.

History of engineering & technology --- Khovanov homology --- braid link --- Jones polynomial --- drone deployment --- drone port --- traveling salesman --- facility location problem --- molecular arrays --- constrained optimization --- equivariant bifurcation theory --- generalized Lane–Emden systems --- Noether-like operator --- conservation laws --- barycentric coordinate system --- coordinate system --- hexagonal grid --- triangular grid --- tri-hexagonal grid --- transformations --- test for outliers --- order statistics --- extreme values --- confidence intervals --- Monte-Carlo simulation --- nonlinear equations --- systems --- derivative-free methods --- fast algorithms --- computational efficiency --- neutrosophic soft sets --- inconsistent information --- prospect theory --- stochastic multi-criteria group decision making --- lie symmetries --- invariants --- shallow water --- similarity solutions --- optimal system --- equal volume projection --- hierarchical grid --- iterative function --- multiple root --- composite method --- derivative-free method --- optimal convergence --- full-scale fire experiment --- compartment fire --- permutation entropy --- two length permutation entropy --- time series analysis --- parametric Jensen-Shannon statistical complexity --- symmetric duality --- alpha-power skew-t distribution --- skew-t distribution --- power-t distribution --- asymmetry --- Fisher information matrix --- maximum likelihood estimation --- iteration --- fixed points --- fractals

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Applied mathematics and symmetry work together as a powerful tool for problem reduction and solving. We are communicating applications in probability theory and statistics (A Test Detecting the Outliers for Continuous Distributions Based on the Cumulative Distribution Function of the Data Being Tested, The Asymmetric Alpha-Power Skew-t Distribution), fractals - geometry and alike (Khovanov Homology of Three-Strand Braid Links, Volume Preserving Maps Between p-Balls, Generation of Julia and Mandelbrot Sets via Fixed Points), supersymmetry - physics, nanostructures -chemistry, taxonomy - biology and alike (A Continuous Coordinate System for the Plane by Triangular Symmetry, One-Dimensional Optimal System for 2D Rotating Ideal Gas, Minimal Energy Configurations of Finite Molecular Arrays, Noether-Like Operators and First Integrals for Generalized Systems of Lane-Emden Equations), algorithms, programs and software analysis (Algorithm for Neutrosophic Soft Sets in Stochastic Multi-Criteria Group Decision Making Based on Prospect Theory, On a Reduced Cost Higher Order Traub-Steffensen-Like Method for Nonlinear Systems, On a Class of Optimal Fourth Order Multiple Root Solvers without Using Derivatives) to specific subjects (Facility Location Problem Approach for Distributed Drones, Parametric Jensen-Shannon Statistical Complexity and Its Applications on Full-Scale Compartment Fire Data). Diverse topics are thus combined to map out the mathematical core of practical problems.

Khovanov homology --- braid link --- Jones polynomial --- drone deployment --- drone port --- traveling salesman --- facility location problem --- molecular arrays --- constrained optimization --- equivariant bifurcation theory --- generalized Lane–Emden systems --- Noether-like operator --- conservation laws --- barycentric coordinate system --- coordinate system --- hexagonal grid --- triangular grid --- tri-hexagonal grid --- transformations --- test for outliers --- order statistics --- extreme values --- confidence intervals --- Monte-Carlo simulation --- nonlinear equations --- systems --- derivative-free methods --- fast algorithms --- computational efficiency --- neutrosophic soft sets --- inconsistent information --- prospect theory --- stochastic multi-criteria group decision making --- lie symmetries --- invariants --- shallow water --- similarity solutions --- optimal system --- equal volume projection --- hierarchical grid --- iterative function --- multiple root --- composite method --- derivative-free method --- optimal convergence --- full-scale fire experiment --- compartment fire --- permutation entropy --- two length permutation entropy --- time series analysis --- parametric Jensen-Shannon statistical complexity --- symmetric duality --- alpha-power skew-t distribution --- skew-t distribution --- power-t distribution --- asymmetry --- Fisher information matrix --- maximum likelihood estimation --- iteration --- fixed points --- fractals

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In the current age of information explosion, newly invented technological sensors and software are now tightly integrated with our everyday lives. Many sensor processing algorithms have incorporated some forms of computational intelligence as part of their core framework in problem-solving. These algorithms have the capacity to generalize and discover knowledge for themselves and to learn new information whenever unseen data are captured. The primary aim of sensor processing is to develop techniques to interpret, understand, and act on information contained in the data. The interest of this book is in developing intelligent signal processing in order to pave the way for smart sensors. This involves the mathematical advancement of nonlinear signal processing theory and its applications that extend far beyond traditional techniques. It bridges the boundary between theory and application, developing novel theoretically inspired methodologies targeting both longstanding and emergent signal processing applications. The topics range from phishing detection to integration of terrestrial laser scanning, and from fault diagnosis to bio-inspired filtering. The book will appeal to established practitioners, along with researchers and students in the emerging field of smart sensor signal processing.

History of engineering & technology --- geometric calibration --- long- and short-period errors --- equivalent bias angles --- sparse recovery --- linear array push-broom sensor --- deep learning --- signal detection --- modulation classification --- the single shot multibox detector networks --- the multi-inputs convolutional neural networks --- medical image registration --- similarity measure --- non-rigid transformation --- computational efficiency --- registration accuracy --- signal denoising --- singular value decomposition --- Akaike information criterion --- reaction wheel --- micro-vibration --- permutation entropy (PE) --- weighted-permutation entropy (W-PE) --- reverse permutation entropy (RPE) --- reverse dispersion entropy (RDE) --- time series analysis --- complexity --- sensor signal --- tensor principal component pursuit --- stable recovery --- tensor SVD --- ADMM --- kalman filter --- nonlinear autoregressive --- neural network --- noise filtering --- multiple-input multiple-output (MIMO) --- frequency-hopping code --- dual-function radar-communications --- information embedding --- mutual information (mi) --- waveform optimization --- spectroscopy --- compressed sensing --- inverse problems --- dictionary learning --- image registration --- large deformation --- weakly supervised --- high-order cumulant --- cyclic spectrum --- decision tree–support vector machine --- wind turbine --- gearbox fault --- cosine loss --- long short-term memory network --- indoor localization --- CSI --- fingerprinting --- Bayesian tracking --- image reconstruction --- computed tomography --- nonlocal total variation --- sparse-view CT --- low-dose CT --- proximal splitting --- row-action --- brain CT image --- audio signal processing --- sound event classification --- nonnegative matric factorization --- blind signal separation --- support vector machines --- brain-computer interface --- motor imagery --- machine learning --- internet of things --- pianists --- surface inspection --- aluminum ingot --- mask gradient response --- Difference of Gaussian --- inception-v3 --- EEG --- sleep stage --- wavelet packet --- state space model --- image captioning --- three-dimensional (3D) vision --- human-robot interaction --- Laplacian scores --- data reduction --- sensors --- Internet of Things (IoT) --- LoRaWAN --- n/a --- decision tree-support vector machine

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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

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• Reference Manager
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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