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Entropy
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Sample Entropy: Theory and Application
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Sample Entropy: Theory and Application

A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Entropy and Biology".

Deadline for manuscript submissions: closed (21 August 2022) | Viewed by 9526

Special Issue Editors

Prof. Dr. J Randall Moorman

E-Mail Website
Guest Editor
Center for Advanced Medical Analytics, Department of Medicine, Division of Cardiology, University of Virginia, Charlottesville, VA 22908, USA
Interests: predictive analytics monitoring; early warning scores
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Joshua Richman

E-Mail Website
Guest Editor
Division of Gastrointestinal Surgery, Department of Surgery, University of Alabama at Birmingham, 619 19th St S, Birmingham, AL 35249, USA
Interests: surgical outcomes; epidemiology; biostatistics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Sample entropy has found widespread use as a robust metric for comparing the non-linear dynamical properties of time series. It is based solidly on fundamental ideas and constructs from thermodynamics, information theory, and non-linear dynamical systems, and the works of Boltzmann, Gibbs, Shannon, Kolmogorov, Sinai, Renyi, Grassberger, Procaccia, Eckmann, Ruelle, Pincus, Richman, Moorman, Lake, Costa, Chen, Goldberger and others.

Sample entropy has been successfully applied in many fields, particularly in clinical medicine. The family of members of the sample entropy family is growing, and includes multiscale entropy, quadratic entropy rate, coefficient of sample entropy, and others, all of them with advances in theoretical and application-specific features. New applications of information theory, including techniques of deep learning and recurrent neural networks utilize entropy-based measures, as well. As a result, we see a need to bring together new developments in the theory and application of sample entropy.

This Special Issue will accept unpublished original papers and comprehensive reviews that present new theories, bring insights to current and new applications and methods, or present new directions in the theory and application of sample entropy and its offspring.

Prof. Dr. Joshua Richman
Prof. Dr. J Randall Moorman
Guest Editors

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 submissions that pass pre-check are 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 2600 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

  • Shannon entropy
  • Kolmogorov–Sinai entropy
  • Information theory
  • Time series complexity
  • Cross-entropy

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Published Papers (4 papers)

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Research

26 pages, 3029 KiB  
Article
Cardio-Hypothalamic-Pituitary Coupling during Rest and in Response to Exercise
by Nathaniel T. Berry, Christopher K. Rhea and Laurie Wideman
Entropy 2022, 24(8), 1045; https://doi.org/10.3390/e24081045 - 29 Jul 2022
Cited by 4 | Viewed by 1763
Abstract
The objective of this study was to examine cardio hypothalamic-pituitary coupling and to better understand how the temporal relations between these systems are altered during rest and exercise conditions. An intensive within subjects study design was used. Seven adult males completed two visits, [...] Read more.
The objective of this study was to examine cardio hypothalamic-pituitary coupling and to better understand how the temporal relations between these systems are altered during rest and exercise conditions. An intensive within subjects study design was used. Seven adult males completed two visits, each consisting of either a 24 h period of complete rest or a 24 h period containing a high-intensity exercise bout. An intravenous catheter was used to collect serum samples every 10 min throughout the 24 h period (i.e., 145 samples/person/condition) to assess growth hormone (GH) dynamics throughout the 24 h period. Cardiac dynamics were also collected throughout the 24 h period and epoched into 3 min windows every 10 min, providing serial short-time measurements of heart rate variability (HRV) concurrent to the GH sampling. The standard deviation of the normal RR interval (SDNN), the root mean square of successive differences (rMSSD), and sample entropy (SampEn) was calculated for each epoch and used to create new profiles. The dynamics of these profiles were individually quantified using SampEn and recurrence quantification analysis (RQA). To address our central question, the coupling between these profiles with GH was assessed using cross-SampEn and cross-RQA (cRQA). A comparison between the epoched HRV profiles indicated a main effect between profiles for sample entropy (p < 0.001) and several measures from RQA. An interaction between profile and condition was observed for cross-SampEn (p = 0.04) and several measures from cRQA. These findings highlight the potential application of epoched HRV to assess changes in cardiac dynamics, with specific applications to assessing cardio hypothalamic-pituitary coupling. Full article
(This article belongs to the Special Issue Sample Entropy: Theory and Application)
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15 pages, 68201 KiB  
Article
Measurement of the Spectral Efficiency of a Heterogeneous Network Architecture of the NG-PON Type for a Quasilinear Propagation Regime
by Anyi Girón, Eliana Rivera and Gustavo Gómez
Entropy 2022, 24(4), 481; https://doi.org/10.3390/e24040481 - 30 Mar 2022
Cited by 2 | Viewed by 2194
Abstract
The objective of future optical fiber networks is to provide an efficient infrastructure capable of supporting an increasing and variable number of data traffic generated by the diversification of applications with different speed requirements that the current legacy Line Speed networks Single Line [...] Read more.
The objective of future optical fiber networks is to provide an efficient infrastructure capable of supporting an increasing and variable number of data traffic generated by the diversification of applications with different speed requirements that the current legacy Line Speed networks Single Line Rate (SLR), with predefined modulation formats, cannot supply, because they do not offer enough flexibility to meet the requirements of the demands with such a wide range of granularities. Therefore, next-generation optical networks will be highly heterogeneous in nature, incorporating mixed modulation formats and Mixed Line Rates (MLR). In this work, an analysis of the measurement of the spectral efficiency of a heterogeneous network architecture of the next-generation passive optical network (NG-PON) type is reported for a quasilinear propagation regime through the use of the equation adapted from Shannon’s information theory and developed by the group from the GNTT Research of the University of Cauca, where it was found that it is better to transmit channels of 10 Gbps and 40 Gbps with robust modulations in MLR networks to make an improvement in the spectral efficiency of the network, achieving the same amount of information in a smaller bandwidth or more information in the same bandwidth. Full article
(This article belongs to the Special Issue Sample Entropy: Theory and Application)
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15 pages, 1485 KiB  
Article
Monitoring the Evolution of Asynchrony between Mean Arterial Pressure and Mean Cerebral Blood Flow via Cross-Entropy Methods
by Alberto Porta, Francesca Gelpi, Vlasta Bari, Beatrice Cairo, Beatrice De Maria, Cora May Panzetti, Noemi Cornara, Enrico Giuseppe Bertoldo, Valentina Fiolo, Edward Callus, Carlo De Vincentiis, Marianna Volpe, Raffaella Molfetta, Valeria Pistuddi and Marco Ranucci
Entropy 2022, 24(1), 80; https://doi.org/10.3390/e24010080 - 2 Jan 2022
Cited by 13 | Viewed by 2653
Abstract
Cerebrovascular control is carried out by multiple nonlinear mechanisms imposing a certain degree of coupling between mean arterial pressure (MAP) and mean cerebral blood flow (MCBF). We explored the ability of two nonlinear tools in the information domain, namely cross-approximate entropy (CApEn) and [...] Read more.
Cerebrovascular control is carried out by multiple nonlinear mechanisms imposing a certain degree of coupling between mean arterial pressure (MAP) and mean cerebral blood flow (MCBF). We explored the ability of two nonlinear tools in the information domain, namely cross-approximate entropy (CApEn) and cross-sample entropy (CSampEn), to assess the degree of asynchrony between the spontaneous fluctuations of MAP and MCBF. CApEn and CSampEn were computed as a function of the translation time. The analysis was carried out in 23 subjects undergoing recordings at rest in supine position (REST) and during active standing (STAND), before and after surgical aortic valve replacement (SAVR). We found that at REST the degree of asynchrony raised, and the rate of increase in asynchrony with the translation time decreased after SAVR. These results are likely the consequence of the limited variability of MAP observed after surgery at REST, more than the consequence of a modified cerebrovascular control, given that the observed differences disappeared during STAND. CApEn and CSampEn can be utilized fruitfully in the context of the evaluation of cerebrovascular control via the noninvasive acquisition of the spontaneous MAP and MCBF variability. Full article
(This article belongs to the Special Issue Sample Entropy: Theory and Application)
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12 pages, 271 KiB  
Article
Alternative Entropy Measures and Generalized Khinchin–Shannon Inequalities
by Rubem P. Mondaini and Simão C. de Albuquerque Neto
Entropy 2021, 23(12), 1618; https://doi.org/10.3390/e23121618 - 1 Dec 2021
Cited by 5 | Viewed by 1715
Abstract
The Khinchin–Shannon generalized inequalities for entropy measures in Information Theory, are a paradigm which can be used to test the Synergy of the distributions of probabilities of occurrence in physical systems. The rich algebraic structure associated with the introduction of escort probabilities seems [...] Read more.
The Khinchin–Shannon generalized inequalities for entropy measures in Information Theory, are a paradigm which can be used to test the Synergy of the distributions of probabilities of occurrence in physical systems. The rich algebraic structure associated with the introduction of escort probabilities seems to be essential for deriving these inequalities for the two-parameter Sharma–Mittal set of entropy measures. We also emphasize the derivation of these inequalities for the special cases of one-parameter Havrda–Charvat’s, Rényi’s and Landsberg–Vedral’s entropy measures. Full article
(This article belongs to the Special Issue Sample Entropy: Theory and Application)
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