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1. Full Text Complexity–entropy causality plane based on power spectral entropy for complex time series
by Dai, Yimei and Zhang, Hesheng and Mao, Xuegeng and Shang, Pengjian
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 11/2018, Volume 509, pp. 501 - 514
The complexity–entropy causality plane based on permutation entropy is a powerful tool to discriminate signals from different systems. In this paper, we... 
Fault diagnosis | Power spectral entropy | Complexity–entropy causality plane | Classification | DIAGNOSIS | Complexity-entropy causality plane | APPROXIMATE ENTROPY | PHYSICS, MULTIDISCIPLINARY | FAULT-DETECTION | Electrical engineering | Analysis
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2. Full Text Analysis of time series through complexity–entropy curves based on generalized fractional entropy
by Wang, Yuanyuan and Shang, Pengjian and Liu, Zhengli
Nonlinear Dynamics, ISSN 0924-090X, 4/2019, Volume 96, Issue 1, pp. 585 - 599
In this paper, we propose the complexity–entropy causality plane based on the generalized fractional entropy. When applying the proposed method into artificial... 
Engineering | Vibration, Dynamical Systems, Control | Complexity–entropy curves | Classical Mechanics | Automotive Engineering | Permutation entropy | Mechanical Engineering | Financial time series | Generalized fractional entropy | SYSTEM | MECHANICS | INFORMATION | Complexity-entropy curves | DYNAMICS | DERIVATIVES | ENGINEERING, MECHANICAL | Analysis | Financial markets | Entropy | Chaos theory | Empirical analysis | Time series | Complexity | Extreme values
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3. Full Text Entropy in Image Analysis
by Sparavigna, Amelia Carolina
2019, ISBN 3039210939
Image analysis is a fundamental task for extracting information from images acquired across a range of different devices. Since reliable quantitative results... 
keyframes | time-delay | whale optimization algorithm | multilevel thresholding | multi-exposure image fusion | additive manufacturing | patch structure decomposition | ultra-sound images | 3D scanning | Arimoto entropy | contrast enhancement | spatial filling factor | depth maps | image processing | 3D prints | differential evolution | field of experts | normalized divergence measure | image privacy | multiscale top-hat transform | q-exponential | texture information entropy | diffusion | hybrid algorithm | Weibull statistics | adaptive selection | nonextensive entropy | computer aided diagnostics | fatty liver | random forest | DNA encoding | low contrast | entropy | Minkowski island | fuzzy entropy | free-form deformations | person re-identification | chaotic system | DNA computing | pavement | information entropy | discrete entropy | Tsallis statistics | video skimming | prime-indexed primes | natural scene statistics (NSS) | Hénon map | q-sigmoid | image entropy | Shannon entropy | macrotexture | Shannon’s entropy | binary image | multi-feature fusion | image analysis | uncertainty assessment | non-rigid registration | hash layer | Cantor set | dynamic filtering | deep neural network | security analysis | multiple-image encryption | Hamming distance | blind image quality assessment (BIQA) | q-Gaussian | remote sensing | decay trend | chaotic cryptography | chaotic strategy | cross-entropy loss | random insertion | metabolic syndrome | sign languages | generalized entropies | relevance feedback | image retrieval | two-dimensional chaotic economic map | cryptanalysis | infrared images | 3D Latin cube | SHA-256 hash value | gradient distributions | structural entropy | discrete cosine transform (DCT) | chaotic map | hepatic steatosis | machine vision | electromagnetic field optimization | security | image segmentation | quantization loss | colonoscopy | video summarization | permutation | Kapur’s entropy | surface quality assessment | permutation-diffusion | Ramanujan primes | Rényi entropies | chosen-plaintext attack | image encryption | dynamic index | color image segmentation | ultrasound | Otsu method | sigmoid | reconstruction | image information entropy | 3-D digital imaging | positron emission tomography | medical imaging
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4. Full Text Classification of 5-S epileptic EEG recordings using distribution entropy and sample entropy
by Li, Peng and Karmakar, Chandan and Yan, Chang and Palaniswami, Marimuthu and Liu, Changchun
Frontiers in Physiology, ISSN 1664-042X, 04/2016, Volume 7, p. 136
Epilepsy is an electrophysiological disorder of the brain, the hallmark of which is recurrent and unprovoked seizures. Electroencephalogram (EEG) measures... 
Sample entropy (SampEn) | Electroencephalogram (EEG) | Distribution entropy (DistEn) | Epileptic seizure | Short-length EEG analysis | PERMUTATION ENTROPY | SEIZURE DETECTION | PHYSIOLOGY | SERIES | APEN | SIGNALS | epileptic seizure | sample entropy (SampEn) | electroencephalogram (EEG) | EXTREME LEARNING-MACHINE | ARTIFICIAL NEURAL-NETWORKS | APPROXIMATE ENTROPY | short-length EEG analysis | COMPLEXITY | distribution entropy (DistEn) | TRANSFORM | Measurement | Electroencephalography | Records and correspondence | Entropy (Information theory)
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5. Full Text Generalized entropy plane based on permutation entropy and distribution entropy analysis for complex time series
by Dai, Yimei and He, Jiayi and Wu, Yue and Chen, Shijian and Shang, Pengjian
Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, 04/2019, Volume 520, pp. 217 - 231
Entropy is an accessible way to work as a measure of the irregularity and the uncertainty between the predicting knowledge and the given time series.... 
Outlier detection | Permutation entropy | Generalized entropy plane | Permuted distribution entropy | APPROXIMATE ENTROPY | PHYSICS, MULTIDISCIPLINARY | CAUSALITY PLANE | Electrical engineering | Data mining | Analysis
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6. Full Text Bubble Entropy: An Entropy Almost Free of Parameters
by Manis, George and Aktaruzzaman, Md and Sassi, Roberto
IEEE Transactions on Biomedical Engineering, ISSN 0018-9294, 11/2017, Volume 64, Issue 11, pp. 2711 - 2718
Objective: A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new... 
Measurement | Estimation | conditional Rényi permutation entropy | Entropy | Electronic mail | permutation entropy | r parameter elimination">r parameter elimination | Sorting | HRV timeseries | Physiology | Bubble entropy | embedding dimension | Heart rate variability | entropy | ELECTROENCEPHALOGRAM | r parameter elimination | ENGINEERING, BIOMEDICAL | conditional Renyi permutation entropy | HEART-RATE-VARIABILITY | COMPLEXITY | HRV time-series | Algorithms | Computer Simulation | Humans | Middle Aged | Heart Failure - physiopathology | Electrocardiography | Heart Rate - physiology | Signal Processing, Computer-Assisted | Adult | Aged | Signal processing | Research | Permutations | Parameter estimation | Bubbles | Decoupling | Stability | Mathematical analysis | Data processing | Embedding | Critical point | Vectors (mathematics) | Sorting algorithms
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7. Full Text EEG entropy measures in anesthesia
by Liang, Zhenhu and Wang, Yinghua and Sun, Xue and Li, Duan and Voss, Logan J and Sleigh, Jamie W and Hagihira, Satoshi and Li, Xiaoli
Frontiers in Computational Neuroscience, ISSN 1662-5188, 02/2015, Volume 9, p. 16
Objective: Entropy algorithms have been widely used in analyzing EEG signals during anesthesia. However, a systematic comparison of these entropy algorithms in... 
Anesthesia | Entropy | Depth of anesthesia monitoring | EEG | Pharmacokinetic/pharmacodynamic modeling | PERMUTATION ENTROPY | TIME-SERIES ANALYSIS | QUANTIFICATION | pharmacokinetic/pharmacodynamic modeling | DETRENDED FLUCTUATION ANALYSIS | COMPLEXITY-MEASURES | NEUROSCIENCES | anesthesia | EMPIRICAL-MODE DECOMPOSITION | depth of anesthesia monitoring | SPECTRAL ENTROPY | entropy | APPROXIMATE ENTROPY | MATHEMATICAL & COMPUTATIONAL BIOLOGY | SAMPLE ENTROPY | DEPTH | Consciousness | Electroencephalography | Drug screening | Sevoflurane | Fuzzy sets | Algorithms | Researchers | Signal processing | Anesthesiology | Information theory
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8. Full Text Characterizing time series by extended complexity-entropy curves based on Tsallis, Rényi, and power spectral entropy
by Mao, Xuegeng and Shang, Pengjian and Wang, Jing and Ma, Yan
Chaos: An Interdisciplinary Journal of Nonlinear Science, ISSN 1054-1500, 11/2018, Volume 28, Issue 11, p. 113106
In this paper, we create three different entropy curves, Tsallis q-complexity-entropy curve, Rényi r-complexity-entropy curve, and Tsallis-Rényi entropy curve... 
MATHEMATICS, APPLIED | STATISTICAL MEASURE | PHYSICS, MATHEMATICAL | NONLINEARITY | CAUSALITY PLANE | Permutations | Sleep | Robustness (mathematics) | Computer simulation | Stochastic processes | Time series | Feature extraction | Entropy | Electroencephalography | Curvature | Complexity
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9. Full Text The equality of Kolmogorov–Sinai entropy and metric permutation entropy generalized
by Amigó, José M
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 04/2012, Volume 241, Issue 7, pp. 789 - 793
In a 2005 paper, the author and collaborators proposed an approach to permutation entropy based on symbolic dynamics. This approach allowed us to prove the... 
Discrete-time dynamical systems | Kolmogorov–Sinai entropy | Permutation entropy | KolmogorovSinai entropy | MATHEMATICS, APPLIED | Kolmogorov-Sinai entropy | INTERVAL MAPS | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Equality | Intervals | Nonlinear dynamics | Permutations | Nonlinear phenomena | Maps | Dynamics | Entropy | Ergodic processes
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10. Full Text Dynamic Cross-Entropy
by Aur, Dorian and Vila-Rodriguez, Fidel
Journal of Neuroscience Methods, ISSN 0165-0270, 01/2017, Volume 275, pp. 10 - 18
Complexity measures for time series have been used in many applications to quantify the regularity of one dimensional time series, however many dynamical... 
Chaos | Nonlinear dynamics | Brain synchrony | Entropy | Nonlinear resonance | Complexity | PERMUTATION ENTROPY | EEG | INFORMATION | BIOCHEMICAL RESEARCH METHODS | NEUROSCIENCES | SEVOFLURANE | TRANSITION | APPROXIMATE ENTROPY | SEIZURES | HEART-RATE-VARIABILITY | SAMPLE ENTROPY | Brain - physiopathology | Humans | Periodicity | Probability | Rats | Logistic Models | Epilepsy - physiopathology | Seizures - therapy | Brain - physiology | Electroencephalography - methods | Artifacts | Seizures - physiopathology | Algorithms | Animals | Time Factors | Signal Processing, Computer-Assisted | Electroconvulsive Therapy | Nonlinear Dynamics | Epilepsy - therapy | Disease Models, Animal
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11. Full Text On the relation of KS entropy and permutation entropy
by Keller, Karsten and Unakafov, Anton M and Unakafova, Valentina A
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 09/2012, Volume 241, Issue 18, pp. 1477 - 1481
Since Bandt et al. have shown that the permutation entropy and the Kolmogorov–Sinai entropy coincide for piecewise monotone interval maps, the relationship of... 
Kolmogorov–Sinai entropy | Ordinal patterns | Permutation entropy | Kolmogorov-Sinai entropy | MATHEMATICS, APPLIED | ORDINAL VIEWPOINT | PHYSICS, MULTIDISCIPLINARY | PHYSICS, MATHEMATICAL | Intervals | Permutations | Entropy | Maps | Nonlinear phenomena | Dynamical systems
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12. Full Text Time series analysis using composite multiscale entropy
by Wu, Shuen-De and Wu, Chiu-Wen and Lin, Shiou-Gwo and Wang, Chun-Chieh and Lee, Kung-Yen
Entropy, ISSN 1099-4300, 03/2013, Volume 15, Issue 3, pp. 1069 - 1084
Multiscale entropy (MSE) was recently developed to evaluate the complexity of time series over different time scales. Although the MSE algorithm has been... 
Fault diagnosis | Multiscale entropy | Composite multiscale entropy | PERMUTATION ENTROPY | fault diagnosis | PHYSICS, MULTIDISCIPLINARY | multiscale entropy | EEG | COMPLEXITY | DYNAMICS | SIGNALS | composite multiscale entropy
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13. Full Text Conditional entropy of ordinal patterns
by Unakafov, Anton M and Keller, Karsten
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 02/2014, Volume 269, pp. 94 - 102
In this paper we investigate a quantity called conditional entropy of ordinal patterns, akin to the permutation entropy. The conditional entropy of ordinal... 
Markov shift | Kolmogorov–Sinai entropy | Permutation entropy | Ordinal pattern | Conditional entropy | Complexity | Kolmogorov-Sinai entropy | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | TIME-SERIES | VIEWPOINT | PHYSICS, MATHEMATICAL | Permutations | Nonlinear phenomena | Computation | Dynamics | Mathematical analysis | Alphabets | Markov processes | Entropy
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14. Full Text Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics
by Xu, Kaixuan and Wang, Jun
Physics Letters A, ISSN 0375-9601, 02/2017, Volume 381, Issue 8, pp. 767 - 779
In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation... 
Potts random price model | Weighted fractional permutation entropy | Fractional calculus | Fractional sample entropy | Nonlinear complexity | SYSTEM | STATES | COMPLEXITY ANALYSIS | PRICE DYNAMICS | PHYSICS, MULTIDISCIPLINARY | BEHAVIOR | MODEL | HEART-RATE-VARIABILITY | FLUCTUATIONS | TIME-SERIES | Stock markets | Analysis | Numerical analysis
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15. Full Text A comparison of multiscale permutation entropy measures in on-line depth of anesthesia monitoring
by Su, Cui and Liang, Zhenhu and Li, Xiaoli and Li, Duan and Li, Yongwang and Ursino, Mauro
PLoS ONE, ISSN 1932-6203, 10/2016, Volume 11, Issue 10, p. e0164104
Objective Multiscale permutation entropy (MSPE) is becoming an interesting tool to explore neurophysiological mechanisms in recent years. In this study, six... 
ELECTROENCEPHALOGRAPHIC MEASURE | SPECTRAL ENTROPY | APPROXIMATE ENTROPY | FEEDBACK-CONTROL | CLOSED-LOOP CONTROL | TIME-SERIES ANALYSIS | PROPOFOL ANESTHESIA | MULTIDISCIPLINARY SCIENCES | QUANTITATIVE EEG-ANALYSIS | SEVOFLURANE | BISPECTRAL INDEX | Algorithms | Patient monitoring equipment | Anesthesia | Electroencephalography | Models | Comparative analysis | Neurophysiology | Neurosciences | Tracking | Balances (scales) | Noise | Correlation coefficients | Entropy | Decomposition | Surgery | Monitoring | Electrical engineering | Correlation coefficient | Permutations | Sensitivity analysis | Granulation | Unconsciousness | Computer simulation | EEG | Cortex | Time series | Noise measurement | Studies | Noise generation | Entropy (Information theory) | Multiscale analysis | Signal processing | Anesthesiology
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16. On entropy, entropy-like quantities, and applications
by Amigo, Jose M and Keller, Karsten and Unakafova, Valentina A
Discrete and Continuous Dynamical Systems - Series B, ISSN 1531-3492, 12/2015, Volume 20, Issue 10, pp. 3301 - 3343
This is a review on entropy in various fields of mathematics and science. Its scope is to convey a unified vision of the classical entropies and some newer,... 
Ergodic theory | Entropy | Applications | Dynamical systems | Entropy-like quantities | Information theory | PERMUTATION ENTROPY | MATHEMATICS, APPLIED | ergodic theory | STRANGE ATTRACTORS | entropy-like quantities applications | dynamical systems | MEASURE-PRESERVING TRANSFORMATIONS | APPROXIMATE ENTROPY | HEART-RATE-VARIABILITY | KOLMOGOROV-SINAI ENTROPY | TIME-SERIES | information theory | ORDINAL PATTERNS | TOPOLOGICAL-ENTROPY | TSALLIS ENTROPY
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17. Full Text Configurational entropy of polydisperse supercooled liquids
by Ozawa, Misaki and Parisi, Giorgio and Berthier, Ludovic
The Journal of Chemical Physics, ISSN 0021-9606, 10/2018, Volume 149, Issue 15, p. 154501
We propose a computational method to measure the configurational entropy in generic polydisperse glass-formers. In particular, our method resolves issues... 
STATISTICAL-MECHANICS | GLASS-TRANSITION | THERMODYNAMICS | BINARY-MIXTURE | PHYSICS, ATOMIC, MOLECULAR & CHEMICAL | CHEMISTRY, PHYSICAL | SYSTEMS | MONTE-CARLO METHOD | HARD | GIBBS | FREE-ENERGY | Problems | Permutations | Solid solutions | Polydispersity | Glass | Entropy | Free energy | Physics - Statistical Mechanics | Condensed Matter | Physics | Statistical Mechanics
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