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Special Issue "Symbolic Entropy Analysis and Its Applications"

A special issue of Entropy (ISSN 1099-4300).

Deadline for manuscript submissions: closed (31 October 2017)

Special Issue Editor

Guest Editor
Prof. Dr. Raúl Alcaraz Martínez

Biomedical Engineering Research Group, Department of Electronic, University of Castilla-La Mancha, Campus
Universitario, 16071 Cuenca, Spain
Website | E-Mail
Phone: 34969179100
Fax: +34 969 179 119
Interests: entropy; complexity; information theory; information geometry; fractals; source separation; nonlinear dynamics; computational mathematics and statistics in medicine; biomedical time series analysis; cardiac signal processing

Special Issue Information

Dear Colleagues,

Symbolic data analysis is a relatively recent methodology that has received a great deal of attention in the last few years. Indeed, this kind of analysis has been applied to a wide variety of scenarios, including astrophysics and geophysics, biology and medicine, fluid flow, chemistry, mechanical systems, artificial intelligence, communication systems, and, recently, data mining. Briefly, symbolic analysis involves transformation of the original time series into a series of discrete symbols that are processed to extract useful information about the state of the system generating the process. Numerous ways to characterize the resulting series of symbols have been proposed to date. Indeed, several entropy-based metrics have been used for this purpose, such as Shannon or Rényi entropies. Nonetheless, there remain opportunities for revealing novel and useful information by quantifying symbol sequence dynamics by information theory-based approaches. Hence, this Special Issue will try to provide a forum for summarizing the most recent applications within this context, as well as collecting new ways of computing symbolic dynamics from any kind of time series.

Prof. Dr. Raúl Alcaraz Martínez
Guest Editor

Manuscript Submission Information

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Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Entropy is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Symbolic data analysis
  • Symbolization approaches
  • Symbolic Entropy
  • Transfer Entropy
  • Permutation Entropy
  • Lempel-Ziv Complexity

Published Papers (18 papers)

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Editorial

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Open AccessEditorial
Symbolic Entropy Analysis and Its Applications
Entropy 2018, 20(8), 568; https://doi.org/10.3390/e20080568
Received: 23 July 2018 / Accepted: 23 July 2018 / Published: 31 July 2018
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Abstract
This editorial explains the scope of the special issue and provides a thematic introduction to the contributed papers. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)

Research

Jump to: Editorial

Open AccessArticle
An Operation Reduction Using Fast Computation of an Iteration-Based Simulation Method with Microsimulation-Semi-Symbolic Analysis
Entropy 2018, 20(1), 62; https://doi.org/10.3390/e20010062
Received: 24 October 2017 / Revised: 26 December 2017 / Accepted: 11 January 2018 / Published: 18 January 2018
Cited by 1 | PDF Full-text (8006 KB) | HTML Full-text | XML Full-text
Abstract
This paper presents a method for shortening the computation time and reducing the number of math operations required in complex calculations for the analysis, simulation, and design of processes and systems. The method is suitable for education and engineering applications. The efficacy of [...] Read more.
This paper presents a method for shortening the computation time and reducing the number of math operations required in complex calculations for the analysis, simulation, and design of processes and systems. The method is suitable for education and engineering applications. The efficacy of the method is illustrated with a case study of a complex wireless communication system. The computer algebra system (CAS) was applied to formulate hypotheses and define the joint probability density function of a certain modulation technique. This innovative method was used to prepare microsimulation-semi-symbolic analyses to fully specify the wireless system. The development of an iteration-based simulation method that provides closed form solutions is presented. Previously, expressions were solved using time-consuming numerical methods. Students can apply this method for performance analysis and to understand data transfer processes. Engineers and researchers may use the method to gain insight into the impact of the parameters necessary to properly transmit and detect information, unlike traditional numerical methods. This research contributes to this field by improving the ability to obtain closed form solutions of the probability density function, outage probability, and considerably improves time efficiency with shortened computation time and reducing the number of calculation operations. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
A General Symbolic Approach to Kolmogorov-Sinai Entropy
Entropy 2017, 19(12), 675; https://doi.org/10.3390/e19120675
Received: 31 October 2017 / Revised: 4 December 2017 / Accepted: 5 December 2017 / Published: 9 December 2017
Cited by 2 | PDF Full-text (390 KB) | HTML Full-text | XML Full-text
Abstract
It is popular to study a time-dependent nonlinear system by encoding outcomes of measurements into sequences of symbols following certain symbolization schemes. Mostly, symbolizations by threshold crossings or variants of it are applied, but also, the relatively new symbolic approach, which goes back [...] Read more.
It is popular to study a time-dependent nonlinear system by encoding outcomes of measurements into sequences of symbols following certain symbolization schemes. Mostly, symbolizations by threshold crossings or variants of it are applied, but also, the relatively new symbolic approach, which goes back to innovative works of Bandt and Pompe—ordinal symbolic dynamics—plays an increasing role. In this paper, we discuss both approaches novelly in one breath with respect to the theoretical determination of the Kolmogorov-Sinai entropy (KS entropy). For this purpose, we propose and investigate a unifying approach to formalize symbolizations. By doing so, we can emphasize the main advantage of the ordinal approach if no symbolization scheme can be found that characterizes KS entropy directly: the ordinal approach, as well as generalizations of it provide, under very natural conditions, a direct route to KS entropy by default. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Characterisation of the Effects of Sleep Deprivation on the Electroencephalogram Using Permutation Lempel–Ziv Complexity, a Non-Linear Analysis Tool
Entropy 2017, 19(12), 673; https://doi.org/10.3390/e19120673
Received: 30 October 2017 / Revised: 2 December 2017 / Accepted: 5 December 2017 / Published: 8 December 2017
Cited by 3 | PDF Full-text (6479 KB) | HTML Full-text | XML Full-text
Abstract
Specific patterns of brain activity during sleep and waking are recorded in the electroencephalogram (EEG). Time-frequency analysis methods have been widely used to analyse the EEG and identified characteristic oscillations for each vigilance state (VS), i.e., wakefulness, rapid-eye movement (REM) and non-rapid-eye movement [...] Read more.
Specific patterns of brain activity during sleep and waking are recorded in the electroencephalogram (EEG). Time-frequency analysis methods have been widely used to analyse the EEG and identified characteristic oscillations for each vigilance state (VS), i.e., wakefulness, rapid-eye movement (REM) and non-rapid-eye movement (NREM) sleep. However, other aspects such as change of patterns associated with brain dynamics may not be captured unless a non-linear-based analysis method is used. In this pilot study, Permutation Lempel–Ziv complexity (PLZC), a novel symbolic dynamics analysis method, was used to characterise the changes in the EEG in sleep and wakefulness during baseline and recovery from sleep deprivation (SD). The results obtained with PLZC were contrasted with a related non-linear method, Lempel–Ziv complexity (LZC). Both measure the emergence of new patterns. However, LZC is dependent on the absolute amplitude of the EEG, while PLZC is only dependent on the relative amplitude due to symbolisation procedure and thus, more resistant to noise. We showed that PLZC discriminates activated brain states associated with wakefulness and REM sleep, which both displayed higher complexity, compared to NREM sleep. Additionally, significantly lower PLZC values were measured in NREM sleep during the recovery period following SD compared to baseline, suggesting a reduced emergence of new activity patterns in the EEG. These findings were validated using PLZC on surrogate data. By contrast, LZC was merely reflecting changes in the spectral composition of the EEG. Overall, this study implies that PLZC is a robust non-linear complexity measure, which is not dependent on amplitude variations in the signal, and which may be useful to further assess EEG alterations induced by environmental or pharmacological manipulations. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Label-Driven Learning Framework: Towards More Accurate Bayesian Network Classifiers through Discrimination of High-Confidence Labels
Entropy 2017, 19(12), 661; https://doi.org/10.3390/e19120661
Received: 31 October 2017 / Revised: 26 November 2017 / Accepted: 30 November 2017 / Published: 3 December 2017
Cited by 1 | PDF Full-text (4016 KB) | HTML Full-text | XML Full-text
Abstract
Bayesian network classifiers (BNCs) have demonstrated competitive classification accuracy in a variety of real-world applications. However, it is error-prone for BNCs to discriminate among high-confidence labels. To address this issue, we propose the label-driven learning framework, which incorporates instance-based learning and ensemble learning. [...] Read more.
Bayesian network classifiers (BNCs) have demonstrated competitive classification accuracy in a variety of real-world applications. However, it is error-prone for BNCs to discriminate among high-confidence labels. To address this issue, we propose the label-driven learning framework, which incorporates instance-based learning and ensemble learning. For each testing instance, high-confidence labels are first selected by a generalist classifier, e.g., the tree-augmented naive Bayes (TAN) classifier. Then, by focusing on these labels, conditional mutual information is redefined to more precisely measure mutual dependence between attributes, thus leading to a refined generalist with a more reasonable network structure. To enable finer discrimination, an expert classifier is tailored for each high-confidence label. Finally, the predictions of the refined generalist and the experts are aggregated. We extend TAN to LTAN (Label-driven TAN) by applying the proposed framework. Extensive experimental results demonstrate that LTAN delivers superior classification accuracy to not only several state-of-the-art single-structure BNCs but also some established ensemble BNCs at the expense of reasonable computation overhead. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
K-Dependence Bayesian Classifier Ensemble
Entropy 2017, 19(12), 651; https://doi.org/10.3390/e19120651
Received: 6 September 2017 / Revised: 23 November 2017 / Accepted: 27 November 2017 / Published: 30 November 2017
Cited by 3 | PDF Full-text (4203 KB) | HTML Full-text | XML Full-text
Abstract
To maximize the benefit that can be derived from the information implicit in big data, ensemble methods generate multiple models with sufficient diversity through randomization or perturbation. A k-dependence Bayesian classifier (KDB) is a highly scalable learning algorithm with excellent time and [...] Read more.
To maximize the benefit that can be derived from the information implicit in big data, ensemble methods generate multiple models with sufficient diversity through randomization or perturbation. A k-dependence Bayesian classifier (KDB) is a highly scalable learning algorithm with excellent time and space complexity, along with high expressivity. This paper introduces a new ensemble approach of KDBs, a k-dependence forest (KDF), which induces a specific attribute order and conditional dependencies between attributes for each subclassifier. We demonstrate that these subclassifiers are diverse and complementary. Our extensive experimental evaluation on 40 datasets reveals that this ensemble method achieves better classification performance than state-of-the-art out-of-core ensemble learners such as the AODE (averaged one-dependence estimator) and averaged tree-augmented naive Bayes (ATAN). Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Multivariate Multiscale Symbolic Entropy Analysis of Human Gait Signals
Entropy 2017, 19(10), 557; https://doi.org/10.3390/e19100557
Received: 25 September 2017 / Revised: 13 October 2017 / Accepted: 17 October 2017 / Published: 19 October 2017
Cited by 3 | PDF Full-text (2294 KB) | HTML Full-text | XML Full-text
Abstract
The complexity quantification of human gait time series has received considerable interest for wearable healthcare. Symbolic entropy is one of the most prevalent algorithms used to measure the complexity of a time series, but it fails to account for the multiple time scales [...] Read more.
The complexity quantification of human gait time series has received considerable interest for wearable healthcare. Symbolic entropy is one of the most prevalent algorithms used to measure the complexity of a time series, but it fails to account for the multiple time scales and multi-channel statistical dependence inherent in such time series. To overcome this problem, multivariate multiscale symbolic entropy is proposed in this paper to distinguish the complexity of human gait signals in health and disease. The embedding dimension, time delay and quantization levels are appropriately designed to construct similarity of signals for calculating complexity of human gait. The proposed method can accurately detect healthy and pathologic group from realistic multivariate human gait time series on multiple scales. It strongly supports wearable healthcare with simplicity, robustness, and fast computation. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Bowen Lemma in the Countable Symbolic Space
Entropy 2017, 19(10), 532; https://doi.org/10.3390/e19100532
Received: 14 August 2017 / Revised: 27 September 2017 / Accepted: 30 September 2017 / Published: 11 October 2017
Cited by 1 | PDF Full-text (261 KB) | HTML Full-text | XML Full-text
Abstract
We consider the sets of quasi-regular points in the countable symbolic space. We measure the sizes of the sets by Billingsley-Hausdorff dimension defined by Gibbs measures. It is shown that the dimensions of those sets, always bounded from below by the convergence exponent [...] Read more.
We consider the sets of quasi-regular points in the countable symbolic space. We measure the sizes of the sets by Billingsley-Hausdorff dimension defined by Gibbs measures. It is shown that the dimensions of those sets, always bounded from below by the convergence exponent of the Gibbs measure, are given by a variational principle, which generalizes Li and Ma’s result and Bowen’s result. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
Open AccessArticle
A Formula of Packing Pressure of a Factor Map
Entropy 2017, 19(10), 526; https://doi.org/10.3390/e19100526
Received: 26 July 2017 / Revised: 28 September 2017 / Accepted: 30 September 2017 / Published: 4 October 2017
Cited by 1 | PDF Full-text (238 KB) | HTML Full-text | XML Full-text
Abstract
In this paper, using the notion of packing pressure, we show a formula of packing pressure of a factor map. We also give an application in conformal repellers. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Symbolic Analysis of Brain Dynamics Detects Negative Stress
Entropy 2017, 19(5), 196; https://doi.org/10.3390/e19050196
Received: 3 March 2017 / Revised: 23 April 2017 / Accepted: 26 April 2017 / Published: 28 April 2017
Cited by 7 | PDF Full-text (5023 KB) | HTML Full-text | XML Full-text
Abstract
The electroencephalogram (EEG) is the most common tool used to study mental disorders. In the last years, the use of this recording for recognition of negative stress has been receiving growing attention. However, precise identification of this emotional state is still an interesting [...] Read more.
The electroencephalogram (EEG) is the most common tool used to study mental disorders. In the last years, the use of this recording for recognition of negative stress has been receiving growing attention. However, precise identification of this emotional state is still an interesting unsolved challenge. Nowadays, stress presents a high prevalence in developed countries and, moreover, its chronic condition often leads to concomitant physical and mental health problems. Recently, a measure of time series irregularity, such as quadratic sample entropy (QSEn), has been suggested as a promising single index for discerning between emotions of calm and stress. Unfortunately, this index only considers repetitiveness of similar patterns and, hence, it is unable to quantify successfully dynamics associated with the data temporal structure. With the aim of extending QSEn ability for identification of stress from the EEG signal, permutation entropy (PEn) and its modification to be amplitude-aware (AAPEn) have been analyzed in the present work. These metrics assess repetitiveness of ordinal patterns, thus considering causal information within each one of them and obtaining improved estimates of predictability. Results have shown that PEn and AAPEn present a discriminant power between emotional states of calm and stress similar to QSEn, i.e., around 65%. Additionally, they have also revealed complementary dynamics to those quantified by QSEn, thus suggesting a synchronized behavior between frontal and parietal counterparts from both hemispheres of the brain. More precisely, increased stress levels have resulted in activation of the left frontal and right parietal regions and, simultaneously, in relaxing of the right frontal and left parietal areas. Taking advantage of this brain behavior, a discriminant model only based on AAPEn and QSEn computed from the EEG channels P3 and P4 has reached a diagnostic accuracy greater than 80%, which improves slightly the current state of the art. Moreover, because this classification system is notably easier than others previously proposed, it could be used for continuous monitoring of negative stress, as well as for its regulation towards more positive moods in controlled environments. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
A Study of the Transfer Entropy Networks on Industrial Electricity Consumption
Entropy 2017, 19(4), 159; https://doi.org/10.3390/e19040159
Received: 11 January 2017 / Revised: 29 March 2017 / Accepted: 3 April 2017 / Published: 13 April 2017
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Abstract
We study information transfer routes among cross-industry and cross-region electricity consumption data based on transfer entropy and the MST (Minimum Spanning Tree) model. First, we characterize the information transfer routes with transfer entropy matrixes, and find that the total entropy transfer of the [...] Read more.
We study information transfer routes among cross-industry and cross-region electricity consumption data based on transfer entropy and the MST (Minimum Spanning Tree) model. First, we characterize the information transfer routes with transfer entropy matrixes, and find that the total entropy transfer of the relatively developed Guangdong Province is lower than others, with significant industrial cluster within the province. Furthermore, using a reshuffling method, we find that driven industries contain much more information flows than driving industries, and are more influential on the degree of order of regional industries. Finally, based on the Chu-Liu-Edmonds MST algorithm, we extract the minimum spanning trees of provincial industries. Individual MSTs show that the MSTs follow a chain-like formation in developed provinces and star-like structures in developing provinces. Additionally, all MSTs with the root of minimal information outflow industrial sector are of chain-form. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Unsupervised Symbolization of Signal Time Series for Extraction of the Embedded Information
Entropy 2017, 19(4), 148; https://doi.org/10.3390/e19040148
Received: 20 January 2017 / Revised: 17 March 2017 / Accepted: 28 March 2017 / Published: 31 March 2017
Cited by 4 | PDF Full-text (1116 KB) | HTML Full-text | XML Full-text
Abstract
This paper formulates an unsupervised algorithm for symbolization of signal time series to capture the embedded dynamic behavior. The key idea is to convert time series of the digital signal into a string of (spatially discrete) symbols from which the embedded dynamic information [...] Read more.
This paper formulates an unsupervised algorithm for symbolization of signal time series to capture the embedded dynamic behavior. The key idea is to convert time series of the digital signal into a string of (spatially discrete) symbols from which the embedded dynamic information can be extracted in an unsupervised manner (i.e., no requirement for labeling of time series). The main challenges here are: (1) definition of the symbol assignment for the time series; (2) identification of the partitioning segment locations in the signal space of time series; and (3) construction of probabilistic finite-state automata (PFSA) from the symbol strings that contain temporal patterns. The reported work addresses these challenges by maximizing the mutual information measures between symbol strings and PFSA states. The proposed symbolization method has been validated by numerical simulation as well as by experimentation in a laboratory environment. Performance of the proposed algorithm has been compared to that of two commonly used algorithms of time series partitioning. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Permutation Entropy for the Characterisation of Brain Activity Recorded with Magnetoencephalograms in Healthy Ageing
Entropy 2017, 19(4), 141; https://doi.org/10.3390/e19040141
Received: 30 January 2017 / Revised: 14 March 2017 / Accepted: 22 March 2017 / Published: 25 March 2017
Cited by 6 | PDF Full-text (2443 KB) | HTML Full-text | XML Full-text
Abstract
The characterisation of healthy ageing of the brain could help create a fingerprint of normal ageing that might assist in the early diagnosis of neurodegenerative conditions. This study examined changes in resting state magnetoencephalogram (MEG) permutation entropy due to age and gender in [...] Read more.
The characterisation of healthy ageing of the brain could help create a fingerprint of normal ageing that might assist in the early diagnosis of neurodegenerative conditions. This study examined changes in resting state magnetoencephalogram (MEG) permutation entropy due to age and gender in a sample of 220 healthy participants (98 males and 122 females, ages ranging between 7 and 84). Entropy was quantified using normalised permutation entropy and modified permutation entropy, with an embedding dimension of 5 and a lag of 1 as the input parameters for both algorithms. Effects of age were observed over the five regions of the brain, i.e., anterior, central, posterior, and left and right lateral, with the anterior and central regions containing the highest permutation entropy. Statistically significant differences due to age were observed in the different brain regions for both genders, with the evolutions described using the fitting of polynomial regressions. Nevertheless, no significant differences between the genders were observed across all ages. These results suggest that the evolution of entropy in the background brain activity, quantified with permutation entropy algorithms, might be considered an alternative illustration of a ‘nominal’ physiological rhythm. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Distance-Based Lempel–Ziv Complexity for the Analysis of Electroencephalograms in Patients with Alzheimer’s Disease
Entropy 2017, 19(3), 129; https://doi.org/10.3390/e19030129
Received: 9 February 2017 / Revised: 13 March 2017 / Accepted: 15 March 2017 / Published: 17 March 2017
Cited by 4 | PDF Full-text (889 KB) | HTML Full-text | XML Full-text
Abstract
The analysis of electroencephalograms (EEGs) of patients with Alzheimer’s disease (AD) could contribute to the diagnosis of this dementia. In this study, a new non-linear signal processing metric, distance-based Lempel–Ziv complexity (dLZC), is introduced to characterise changes between pairs of electrodes in EEGs [...] Read more.
The analysis of electroencephalograms (EEGs) of patients with Alzheimer’s disease (AD) could contribute to the diagnosis of this dementia. In this study, a new non-linear signal processing metric, distance-based Lempel–Ziv complexity (dLZC), is introduced to characterise changes between pairs of electrodes in EEGs in AD. When complexity in each signal arises from different sub-sequences, dLZC would be greater than when similar sub-sequences are present in each signal. EEGs from 11 AD patients and 11 age-matched control subjects were analysed. The dLZC values for AD patients were lower than for control subjects for most electrode pairs, with statistically significant differences (p < 0.01, Student’s t-test) in 17 electrode pairs in the distant left, local posterior left, and interhemispheric regions. Maximum diagnostic accuracies with leave-one-out cross-validation were 77.27% for subject-based classification and 78.25% for epoch-based classification. These findings suggest not only that EEGs from AD patients are less complex than those from controls, but also that the richness of the information contained in pairs of EEGs from patients is also lower than in age-matched controls. The analysis of EEGs in AD with dLZC may increase the insight into brain dysfunction, providing complementary information to that obtained with other complexity and synchrony methods. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications
Entropy 2017, 19(3), 128; https://doi.org/10.3390/e19030128
Received: 31 January 2017 / Revised: 11 March 2017 / Accepted: 15 March 2017 / Published: 17 March 2017
Cited by 2 | PDF Full-text (890 KB) | HTML Full-text | XML Full-text
Abstract
In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in [...] Read more.
In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoretical model, such as the scale relativity theory or the extended scale relativity theory. Thus, using the last theory, fractal entropy through non-differentiable Lie groups was established and, moreover, the pairs generating mechanisms through fractal entanglement states were explained. Our model has implications in the dynamics of biological structures, in the form of the “chameleon-like” behavior of cholesterol. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Packer Detection for Multi-Layer Executables Using Entropy Analysis
Entropy 2017, 19(3), 125; https://doi.org/10.3390/e19030125
Received: 31 January 2017 / Revised: 9 March 2017 / Accepted: 13 March 2017 / Published: 16 March 2017
Cited by 6 | PDF Full-text (446 KB) | HTML Full-text | XML Full-text
Abstract
Packing algorithms are broadly used to avoid anti-malware systems, and the proportion of packed malware has been growing rapidly. However, just a few studies have been conducted on detection various types of packing algorithms in a systemic way. Following this understanding, we elaborate [...] Read more.
Packing algorithms are broadly used to avoid anti-malware systems, and the proportion of packed malware has been growing rapidly. However, just a few studies have been conducted on detection various types of packing algorithms in a systemic way. Following this understanding, we elaborate a method to classify packing algorithms of a given executable into three categories: single-layer packing, re-packing, or multi-layer packing. We convert entropy values of the executable file loaded into memory into symbolic representations, for which we used SAX (Symbolic Aggregate Approximation). Based on experiments of 2196 programs and 19 packing algorithms, we identify that precision (97.7%), accuracy (97.5%), and recall ( 96.8%) of our method are respectively high to confirm that entropy analysis is applicable in identifying packing algorithms. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Effects of Fatty Infiltration of the Liver on the Shannon Entropy of Ultrasound Backscattered Signals
Entropy 2016, 18(9), 341; https://doi.org/10.3390/e18090341
Received: 20 June 2016 / Revised: 7 September 2016 / Accepted: 19 September 2016 / Published: 21 September 2016
Cited by 9 | PDF Full-text (5802 KB) | HTML Full-text | XML Full-text
Abstract
This study explored the effects of fatty infiltration on the signal uncertainty of ultrasound backscattered echoes from the liver. Standard ultrasound examinations were performed on 107 volunteers. For each participant, raw ultrasound image data of the right lobe of liver were acquired using [...] Read more.
This study explored the effects of fatty infiltration on the signal uncertainty of ultrasound backscattered echoes from the liver. Standard ultrasound examinations were performed on 107 volunteers. For each participant, raw ultrasound image data of the right lobe of liver were acquired using a clinical scanner equipped with a 3.5-MHz convex transducer. An algorithmic scheme was proposed for ultrasound B-mode and entropy imaging. Fatty liver stage was evaluated using a sonographic scoring system. Entropy values constructed using the ultrasound radiofrequency (RF) and uncompressed envelope signals (denoted by HR and HE, respectively) as a function of fatty liver stage were analyzed using the Pearson correlation coefficient. Data were expressed as the median and interquartile range (IQR). Receiver operating characteristic (ROC) curve analysis with 95% confidence intervals (CIs) was performed to obtain the area under the ROC curve (AUC). The brightness of the entropy image typically increased as the fatty stage varied from mild to severe. The median value of HR monotonically increased from 4.69 (IQR: 4.60–4.79) to 4.90 (IQR: 4.87–4.92) as the severity of fatty liver increased (r = 0.63, p < 0.0001). Concurrently, the median value of HE increased from 4.80 (IQR: 4.69–4.89) to 5.05 (IQR: 5.02–5.07) (r = 0.69, p < 0.0001). In particular, the AUCs obtained using HE (95% CI) were 0.93 (0.87–0.99), 0.88 (0.82–0.94), and 0.76 (0.65–0.87) for fatty stages ≥mild, ≥moderate, and ≥severe, respectively. The sensitivity, specificity, and accuracy were 93.33%, 83.11%, and 86.00%, respectively (≥mild). Fatty infiltration increases the uncertainty of backscattered signals from livers. Ultrasound entropy imaging has potential for the routine examination of fatty liver disease. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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Open AccessArticle
Application of Entropy-Based Features to Predict Defibrillation Outcome in Cardiac Arrest
Entropy 2016, 18(9), 313; https://doi.org/10.3390/e18090313
Received: 19 July 2016 / Revised: 11 August 2016 / Accepted: 19 August 2016 / Published: 24 August 2016
Cited by 10 | PDF Full-text (968 KB) | HTML Full-text | XML Full-text
Abstract
Prediction of defibrillation success is of vital importance to guide therapy and improve the survival of patients suffering out-of-hospital cardiac arrest (OHCA). Currently, the most efficient methods to predict shock success are based on the analysis of the electrocardiogram (ECG) during ventricular fibrillation [...] Read more.
Prediction of defibrillation success is of vital importance to guide therapy and improve the survival of patients suffering out-of-hospital cardiac arrest (OHCA). Currently, the most efficient methods to predict shock success are based on the analysis of the electrocardiogram (ECG) during ventricular fibrillation (VF), and recent studies suggest the efficacy of waveform indices that characterize the underlying non-linear dynamics of VF. In this study we introduce, adapt and fully characterize six entropy indices for VF shock outcome prediction, based on the classical definitions of entropy to measure the regularity and predictability of a time series. Data from 163 OHCA patients comprising 419 shocks (107 successful) were used, and the performance of the entropy indices was characterized in terms of embedding dimension (m) and matching tolerance (r). Six classical predictors were also assessed as baseline prediction values. The best prediction results were obtained for fuzzy entropy (FuzzEn) with m = 3 and an amplitude-dependent tolerance of r = 80 μ V . This resulted in a balanced sensitivity/specificity of 80.4%/76.9%, which improved by over five points the results obtained for the best classical predictor. These results suggest that a FuzzEn approach for a joint quantification of VF amplitude and its non-linear dynamics may be a promising tool to optimize OHCA treatment. Full article
(This article belongs to the Special Issue Symbolic Entropy Analysis and Its Applications)
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