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Special Issue "The 20th Anniversary of Entropy - Approximate and Sample Entropy"

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

Deadline for manuscript submissions: closed (15 January 2019)

Special Issue Editor

Guest Editor
Prof. Dr. Roberto Hornero

Biomedical Engineering Group, E.T.S.I. de Telecomunicación, Universidad de Valladolid, Paseo Belén 15, 47011 Valladolid, Spain
Website | E-Mail
Interests: entropy; complexity; biomedical signal processing; information theory; non-linear dynamics; neurodegenerative diseases; sleep disorders; neural signals

Special Issue Information

Dear Colleagues,

We are celebrating the 20th anniversary of the journal Entropy in 2018. The growth of Entropy has only been possible because authors, reviewers, editors, and all people working in some way for the journal have joined their efforts for years. Thank you for your confidence and your enthusiasm.

To mark that important milestone, a special issue entitled “Approximate and Sample Entropy” is being launched. Based on information theory, a number of entropy measures have been proposed since the 1990s to assess systems’ irregularity. S.M. Pincus (1991) introduced Approximate Entropy as a measure of the regularity of a process that is related to Shannon’s entropy but suitable for characterizing short and noisy physiological signals. J.S. Richman and J.R. Moorman (2000) modified this algorithm to create a more robust and less biased statistic: Sample Entropy. Both Approximate and Sample entropy have received a great deal of attention in the last few years, and have been successfully verified and applied to biomedical applications and many others.

The aim of this Special Issue is to encourage researchers to present original and recent developments on time series analysis using Approximate and Sample entropy. Papers presenting concepts or applications are welcome. Applications can include (but are not limited to) biomedical engineering, chemical engineering, hydrology, pharmaceutical sciences, financial analyses, neurosciences, industrial engineering, geosciences, information sciences, etc.

Prof. Dr. Roberto Hornero
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

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.

Published Papers (6 papers)

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Research

Open AccessArticle Using Multiscale Entropy to Assess the Efficacy of Local Cooling on Reactive Hyperemia in People with a Spinal Cord Injury
Entropy 2019, 21(1), 90; https://doi.org/10.3390/e21010090
Received: 8 December 2018 / Revised: 15 January 2019 / Accepted: 15 January 2019 / Published: 18 January 2019
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Abstract
Pressure ulcers are one of the most common complications of a spinal cord injury (SCI). Prolonged unrelieved pressure is thought to be the primary causative factor resulting in tissue ischemia and eventually pressure ulcers. Previous studies suggested that local cooling reduces skin ischemia
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Pressure ulcers are one of the most common complications of a spinal cord injury (SCI). Prolonged unrelieved pressure is thought to be the primary causative factor resulting in tissue ischemia and eventually pressure ulcers. Previous studies suggested that local cooling reduces skin ischemia of the compressed soft tissues based on smaller hyperemic responses. However, the effect of local cooling on nonlinear properties of skin blood flow (SBF) during hyperemia is unknown. In this study, 10 wheelchair users with SCI and 10 able-bodied (AB) controls underwent three experimental protocols, each of which included a 10-min period as baseline, a 20-min intervention period, and a 20-min period for recovering SBF. SBF was measured using a laser Doppler flowmetry. During the intervention period, a pressure of 60 mmHg was applied to the sacral skin, while three skin temperature settings were tested, including no temperature change, a decrease by 10 °C, and an increase by 10 °C, respectively. A multiscale entropy (MSE) method was employed to quantify the degree of regularity of blood flow oscillations (BFO) associated with the SBF control mechanisms during baseline and reactive hyperemia. The results showed that under pressure with cooling, skin BFO both in people with SCI and AB controls were more regular at multiple time scales during hyperemia compared to baseline, whereas under pressure with no temperature change and particularly pressure with heating, BFO were more irregular during hyperemia compared to baseline. Moreover, the results of surrogate tests indicated that changes in the degree of regularity of BFO from baseline to hyperemia were only partially attributed to changes in relative amplitudes of endothelial, neurogenic, and myogenic components of BFO. These findings support the use of MSE to assess the efficacy of local cooling on reactive hyperemia and assess the degree of skin ischemia in people with SCI. Full article
(This article belongs to the Special Issue The 20th Anniversary of Entropy - Approximate and Sample Entropy)
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Open AccessArticle BBS Posts Time Series Analysis based on Sample Entropy and Deep Neural Networks
Entropy 2019, 21(1), 57; https://doi.org/10.3390/e21010057
Received: 10 December 2018 / Revised: 4 January 2019 / Accepted: 8 January 2019 / Published: 12 January 2019
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Abstract
The modeling and forecasting of BBS (Bulletin Board System) posts time series is crucial for government agencies, corporations and website operators to monitor public opinion. Accurate prediction of the number of BBS posts will assist government agencies or corporations in making timely decisions
[...] Read more.
The modeling and forecasting of BBS (Bulletin Board System) posts time series is crucial for government agencies, corporations and website operators to monitor public opinion. Accurate prediction of the number of BBS posts will assist government agencies or corporations in making timely decisions and estimating the future number of BBS posts will help website operators to allocate resources to deal with the possible hot events pressure. By combining sample entropy (SampEn) and deep neural networks (DNN), an approach (SampEn-DNN) is proposed for BBS posts time series modeling and forecasting. The main idea of SampEn-DNN is to utilize SampEn to decide the input vectors of DNN with smallest complexity, and DNN to enhance the prediction performance of time series. Selecting Tianya Zatan new posts as the data source, the performances of SampEn-DNN were compared with auto-regressive integrated moving average (ARIMA), seasonal ARIMA, polynomial regression, neural networks, etc. approaches for prediction of the daily number of new posts. From the experimental results, it can be found that the proposed approach SampEn-DNN outperforms the state-of-the-art approaches for BBS posts time series modeling and forecasting. Full article
(This article belongs to the Special Issue The 20th Anniversary of Entropy - Approximate and Sample Entropy)
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Open AccessArticle Entropy Measures in Analysis of Head up Tilt Test Outcome for Diagnosing Vasovagal Syncope
Entropy 2018, 20(12), 976; https://doi.org/10.3390/e20120976
Received: 21 November 2018 / Revised: 11 December 2018 / Accepted: 12 December 2018 / Published: 16 December 2018
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Abstract
The paper presents possible applications of entropy measures in analysis of biosignals recorded during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised 80 patients who developed syncope during HUTT (57 in the passive phase of the
[...] Read more.
The paper presents possible applications of entropy measures in analysis of biosignals recorded during head up tilt testing (HUTT) in patients with suspected vasovagal syndrome. The study group comprised 80 patients who developed syncope during HUTT (57 in the passive phase of the test (HUTT(+) group) and 23 who had negative result of passive phase and developed syncope after provocation with nitroglycerine (HUTT(−) group)). The paper focuses on assessment of monitored signals’ complexity (heart rate expressed as R-R intervals (RRI), blood pressure (sBP, dBP) and stroke volume (SV)) using various types of entropy measures (Sample Entropy (SE), Fuzzy Entropy (FE), Shannon Entropy (Sh), Conditional Entropy (CE), Permutation Entropy (PE)). Assessment of the complexity of signals in supine position indicated presence of significant differences between HUTT(+) versus HUTT(−) patients only for Conditional Entropy (CE(RRI)). Values of CE(RRI) higher than 0.7 indicate likelihood of a positive result of HUTT already at the passive phase. During tilting, in the pre-syncope phase, significant differences were found for: (SE(sBP), SE(dBP), FE(RRI), FE(sBP), FE(dBP), FE(SV), Sh(sBP), Sh(SV), CE(sBP), CE(dBP)). HUTT(+) patients demonstrated significant changes in signals’ complexity more frequently than HUTT(−) patients. When comparing entropy measurements done in the supine position with those during tilting, SV assessed in HUTT(+) patients was the only parameter for which all tested measures of entropy (SE(SV), FE(SV), Sh(SV), CE(SV), PE(SV)) showed significant differences. Full article
(This article belongs to the Special Issue The 20th Anniversary of Entropy - Approximate and Sample Entropy)
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Open AccessArticle Characterization of Artifact Influence on the Classification of Glucose Time Series Using Sample Entropy Statistics
Entropy 2018, 20(11), 871; https://doi.org/10.3390/e20110871
Received: 8 October 2018 / Revised: 7 November 2018 / Accepted: 9 November 2018 / Published: 12 November 2018
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Abstract
This paper analyses the performance of SampEn and one of its derivatives, Fuzzy Entropy (FuzzyEn), in the context of artifacted blood glucose time series classification. This is a difficult and practically unexplored framework, where the availability of more sensitive and reliable measures could
[...] Read more.
This paper analyses the performance of SampEn and one of its derivatives, Fuzzy Entropy (FuzzyEn), in the context of artifacted blood glucose time series classification. This is a difficult and practically unexplored framework, where the availability of more sensitive and reliable measures could be of great clinical impact. Although the advent of new blood glucose monitoring technologies may reduce the incidence of the problems stated above, incorrect device or sensor manipulation, patient adherence, sensor detachment, time constraints, adoption barriers or affordability can still result in relatively short and artifacted records, as the ones analyzed in this paper or in other similar works. This study is aimed at characterizing the changes induced by such artifacts, enabling the arrangement of countermeasures in advance when possible. Despite the presence of these disturbances, results demonstrate that SampEn and FuzzyEn are sufficiently robust to achieve a significant classification performance, using records obtained from patients with duodenal-jejunal exclusion. The classification results, in terms of area under the ROC of up to 0.9, with several tests yielding AUC values also greater than 0.8, and in terms of a leave-one-out average classification accuracy of 80%, confirm the potential of these measures in this context despite the presence of artifacts, with SampEn having slightly better performance than FuzzyEn. Full article
(This article belongs to the Special Issue The 20th Anniversary of Entropy - Approximate and Sample Entropy)
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Open AccessArticle On the Calculation of Sample Entropy Using Continuous and Discrete Human Gait Data
Entropy 2018, 20(10), 764; https://doi.org/10.3390/e20100764
Received: 1 August 2018 / Revised: 24 September 2018 / Accepted: 26 September 2018 / Published: 5 October 2018
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Abstract
Sample entropy (SE) has relative consistency using biologically-derived, discrete data >500 data points. For certain populations, collecting this quantity is not feasible and continuous data has been used. The effect of using continuous versus discrete data on SE is unknown, nor are the
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Sample entropy (SE) has relative consistency using biologically-derived, discrete data >500 data points. For certain populations, collecting this quantity is not feasible and continuous data has been used. The effect of using continuous versus discrete data on SE is unknown, nor are the relative effects of sampling rate and input parameters m (comparison vector length) and r (tolerance). Eleven subjects walked for 10-minutes and continuous joint angles (480 Hz) were calculated for each lower-extremity joint. Data were downsampled (240, 120, 60 Hz) and discrete range-of-motion was calculated. SE was quantified for angles and range-of-motion at all sampling rates and multiple combinations of parameters. A differential relationship between joints was observed between range-of-motion and joint angles. Range-of-motion SE showed no difference; whereas, joint angle SE significantly decreased from ankle to knee to hip. To confirm findings from biological data, continuous signals with manipulations to frequency, amplitude, and both were generated and underwent similar analysis to the biological data. In general, changes to m, r, and sampling rate had a greater effect on continuous compared to discrete data. Discrete data was robust to sampling rate and m. It is recommended that different data types not be compared and discrete data be used for SE. Full article
(This article belongs to the Special Issue The 20th Anniversary of Entropy - Approximate and Sample Entropy)
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Open AccessArticle Combination of R-R Interval and Crest Time in Assessing Complexity Using Multiscale Cross-Approximate Entropy in Normal and Diabetic Subjects
Entropy 2018, 20(7), 497; https://doi.org/10.3390/e20070497
Received: 15 April 2018 / Revised: 16 June 2018 / Accepted: 22 June 2018 / Published: 27 June 2018
Cited by 2 | PDF Full-text (1391 KB) | HTML Full-text | XML Full-text
Abstract
The present study aimed at testing the hypothesis that application of multiscale cross-approximate entropy (MCAE) analysis in the study of nonlinear coupling behavior of two synchronized time series of different natures [i.e., R-R interval (RRI) and crest time (CT, the time interval from
[...] Read more.
The present study aimed at testing the hypothesis that application of multiscale cross-approximate entropy (MCAE) analysis in the study of nonlinear coupling behavior of two synchronized time series of different natures [i.e., R-R interval (RRI) and crest time (CT, the time interval from foot to peakof a pulse wave)] could yield information on complexity related to diabetes-associated vascular changes. Signals of a single waveform parameter (i.e., CT) from photoplethysmography and RRI from electrocardiogram were simultaneously acquired within a period of one thousand cardiac cycles for the computation of different multiscale entropy indices from healthy young adults (n = 22) (Group 1), upper-middle aged non-diabetic subjects (n = 34) (Group 2) and diabetic patients (n = 34) (Group 3). The demographic (i.e., age), anthropometric (i.e., body height, body weight, waist circumference, body-mass index), hemodynamic (i.e., systolic and diastolic blood pressures), and serum biochemical (i.e., high- and low-density lipoprotein cholesterol, total cholesterol, and triglyceride) parameters were compared with different multiscale entropy indices including small- and large-scale multiscale entropy indices for CT and RRI [MEISS(CT), MEILS(CT), MEISS(RRI), MEILS(RRI), respectively] as well as small- and large-scale multiscale cross-approximate entropy indices [MCEISS, MCEILS, respectively]. The results demonstrated that both MEILS(RRI) and MCEILS significantly differentiated between Group 2 and Group 3 (all p < 0.017). Multivariate linear regression analysis showed significant associations of MEILS(RRI) and MCEILS(RRI,CT) with age and glycated hemoglobin level (all p < 0.017). The findings highlight the successful application of a novel multiscale cross-approximate entropy index in non-invasively identifying diabetes-associated subtle changes in vascular functional integrity, which is of clinical importance in preventive medicine. Full article
(This article belongs to the Special Issue The 20th Anniversary of Entropy - Approximate and Sample Entropy)
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