{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,18]],"date-time":"2025-10-18T10:55:35Z","timestamp":1760784935829,"version":"build-2065373602"},"reference-count":70,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T00:00:00Z","timestamp":1607558400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","award":["DP190101248"],"award-info":[{"award-number":["DP190101248"]}],"id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Entropy profiling is a recently introduced approach that reduces parametric dependence in traditional Kolmogorov-Sinai (KS) entropy measurement algorithms. The choice of the threshold parameter r of vector distances in traditional entropy computations is crucial in deciding the accuracy of signal irregularity information retrieved by these methods. In addition to making parametric choices completely data-driven, entropy profiling generates a complete profile of entropy information as against a single entropy estimate (seen in traditional algorithms). The benefits of using \u201cprofiling\u201d instead of \u201cestimation\u201d are: (a) precursory methods such as approximate and sample entropy that have had the limitation of handling short-term signals (less than 1000 samples) are now made capable of the same; (b) the entropy measure can capture complexity information from short and long-term signals without multi-scaling; and (c) this new approach facilitates enhanced information retrieval from short-term HRV signals. The novel concept of entropy profiling has greatly equipped traditional algorithms to overcome existing limitations and broaden applicability in the field of short-term signal analysis. In this work, we present a review of KS-entropy methods and their limitations in the context of short-term heart rate variability analysis and elucidate the benefits of using entropy profiling as an alternative for the same.<\/jats:p>","DOI":"10.3390\/e22121396","type":"journal-article","created":{"date-parts":[[2020,12,10]],"date-time":"2020-12-10T08:59:34Z","timestamp":1607590774000},"page":"1396","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Entropy Profiling: A Reduced\u2014Parametric Measure of Kolmogorov\u2014Sinai Entropy from Short-Term HRV Signal"],"prefix":"10.3390","volume":"22","author":[{"given":"Chandan","family":"Karmakar","sequence":"first","affiliation":[{"name":"School of Information Technology, Deakin University, Geelong VIC 3216, Australia"}]},{"given":"Radhagayathri","family":"Udhayakumar","sequence":"additional","affiliation":[{"name":"School of Information Technology, Deakin University, Geelong VIC 3216, Australia"}]},{"given":"Marimuthu","family":"Palaniswami","sequence":"additional","affiliation":[{"name":"Department of Electrical &amp; Electronic Engineering, The University of Melbourne, Parkville VIC 3010, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2020,12,10]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"85","DOI":"10.5271\/sjweh.15","article-title":"Heart Rate Variability in Health and Disease","volume":"21","author":"Estela","year":"1995","journal-title":"Scand. J. Work Environ. Health"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1878","DOI":"10.1016\/S0735-1097(99)00468-4","article-title":"Measurement of heart rate variability: A clinical tool or a research toy?","volume":"34","author":"Huikuri","year":"1999","journal-title":"J. Am. Coll. Cardiol."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1016\/j.ijcard.2004.09.013","article-title":"Review: The reliability of short-term measurements of heart rate variability","volume":"103","author":"Sandercock","year":"2005","journal-title":"Int. J. Cardiol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1043","DOI":"10.1161\/01.CIR.93.5.1043","article-title":"Heart rate variability: Standards of measurement, physiological interpretation and clinical use. Task Force of the European Society of Cardiology and the North American Society of Pacing and Electrophysiology","volume":"93","author":"Malik","year":"1996","journal-title":"Circulation"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1111\/j.1749-6632.1987.tb48733.x","article-title":"Applications of nonlinear dynamics to clinical cardiology","volume":"504","author":"Goldberger","year":"1987","journal-title":"Ann. N. Y. Acad. Sci."},{"key":"ref_6","first-page":"277","article-title":"Methods Derived from Nonlinear Dynamics for Analysing Heart Rate Variability","volume":"367","author":"Voss","year":"2009","journal-title":"Philos. Trans. Math. Phys. Eng. Sci."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Voss, A., Schroeder, R., Heitmann, A., Peters, A., and Perz, S. (2015). Short Term Heart Rate Variability Influence of Gender and Age in Healthy Subjects. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0118308"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.medengphy.2008.04.005","article-title":"Measuring complexity using FuzzyEn, ApEn, and SampEn","volume":"31","author":"Chen","year":"2009","journal-title":"Med. Eng. Phys."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1966","DOI":"10.1109\/TBME.2008.919870","article-title":"Automatic Selection of the Threshold Value for Approximate Entropy","volume":"55","author":"Lu","year":"2008","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/s11517-014-1216-0","article-title":"Assessing the complexity of short-term heartbeat interval series by distribution entropy","volume":"53","author":"Li","year":"2015","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0167-2789(83)90298-1","article-title":"Measuring the strangeness of strange attractors","volume":"9","author":"Grassberger","year":"1983","journal-title":"Physica D"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1103\/RevModPhys.57.617","article-title":"Ergodic theory of chaos and strange attractors","volume":"57","author":"Eckmann","year":"1985","journal-title":"Rev. Mod. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1073\/pnas.88.6.2297","article-title":"Approximate entropy as a measure of system complexity","volume":"88","author":"Pincus","year":"1991","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"335","DOI":"10.1007\/BF01619355","article-title":"A regularity statistic for medical data analysis","volume":"7","author":"Pincus","year":"1991","journal-title":"J. Clin. Monit."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1900","DOI":"10.1109\/TBME.2006.889772","article-title":"Use of sample entropy approach to study heart rate variability in obstructive sleep apnea syndrome","volume":"54","author":"Sahakian","year":"2007","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_16","first-page":"H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"7140","DOI":"10.1016\/j.physleta.2008.10.049","article-title":"Measuring time series regularity using nonlinear similarity-based sample entropy","volume":"372","author":"Xie","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2871","DOI":"10.1016\/j.asoc.2010.11.020","article-title":"Complexity analysis of the biomedical signal using fuzzy entropy measurement","volume":"11","author":"Xie","year":"2011","journal-title":"Appl. Soft Comput. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"068102","DOI":"10.1103\/PhysRevLett.89.068102","article-title":"Multiscale entropy analysis of complex physiologic time series","volume":"89","author":"Costa","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"012405","DOI":"10.1103\/PhysRevE.100.012405","article-title":"Multiscale Entropy Profiling to Estimate Complexity of Heart Rate Dynamics","volume":"100","author":"Udhayakumar","year":"2019","journal-title":"Phys. Rev. E"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Udhayakumar, R., Karmakar, C., and Palaniswami, M. (2019, January 23\u201327). Cross Entropy Profiling to Test Pattern Synchrony in Short-Term Signals. Proceedings of the 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Berlin, Germany.","DOI":"10.1109\/EMBC.2019.8857272"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1016\/j.physd.2012.01.004","article-title":"The equality of Kolmogorov\u2013Sinai entropy and metric permutation entropy generalized","volume":"241","year":"2012","journal-title":"Phys. D Nonlinear Phenom."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0076-6879(00)21192-0","article-title":"Irregularity and asynchrony in biologic network signals","volume":"321","author":"Pincus","year":"2000","journal-title":"Methods Enzymol."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1088\/0967-3334\/32\/2\/002","article-title":"Comparison of different threshold values r for approximate entropy: Application to investigate the heart rate variability between heart failure and healthy control groups","volume":"32","author":"Liu","year":"2011","journal-title":"Physiol. Meas."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Mayer, C.C., Bachler, M., H\u00f6rtenhuber, M., Stocker, C., Holzinger, A., and Wassertheurer, S. (2014). Selection of entropy-measure parameters for knowledge discovery in heart rate variability data. BMC Bioinform., 15.","DOI":"10.1186\/1471-2105-15-S6-S2"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"349","DOI":"10.1007\/s10439-012-0668-3","article-title":"The appropriate use of approximate entropy and sample entropy with short data sets","volume":"41","author":"Yentes","year":"2013","journal-title":"Ann. Biomed. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"4785","DOI":"10.1016\/j.physa.2010.06.013","article-title":"Cross-sample entropy of foreign exchange time series","volume":"389","author":"Liu","year":"2010","journal-title":"Phys. A Stat. Mech. Its Appl."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Castiglioni, P., and Di Rienzo, M. (2008, January 14\u201317). How the threshold r influences approximate entropy analysis of heart-rate variability. Proceedings of the 2008 Computers in Cardiology, Bologna, Italy.","DOI":"10.1109\/CIC.2008.4749103"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"Castiglioni, P., Zurek, S., Piskorski, J., Kosmider, M., Guzik, P., Ce, E., Rampichini, S., and Merati, G. (2013, January 3\u20137). Assessing Sample Entropy of physiological signals by the norm component matrix algorithm: Application on muscular signals during isometric contraction. Proceedings of the 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Osaka, Japan.","DOI":"10.1109\/EMBC.2013.6610684"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Boskovic, A., Loncar-Turukalo, T., Japundzic-Zigon, N., and Bajic, D. (2011, January 8\u201310). The flip-flop effect in entropy estimation. Proceedings of the 2011 IEEE 9th International Symposium on Intelligent Systems & Informatics (SISY), Subotica, Serbia.","DOI":"10.1109\/SISY.2011.6034328"},{"key":"ref_31","first-page":"319","article-title":"Accurate estimation of entropy in very short physiological time series: The problem of atrial fibrillation detection in implanted ventricular devices","volume":"300","author":"Lake","year":"2011","journal-title":"Am. J. Physiol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"074002","DOI":"10.1088\/1361-6579\/aacc48","article-title":"A comparison of entropy approaches for AF discrimination","volume":"39","author":"Liu","year":"2018","journal-title":"Physiol. Meas."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"R368","DOI":"10.1152\/ajpregu.00161.2006","article-title":"Regular heartbeat dynamics are associated with cardiac health","volume":"292","author":"Cysarz","year":"2007","journal-title":"Am. J. Physiol. Regul. Integr. Comp. Physiol."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Kumar, M., Pachori, R.B., and Acharya, U.R. (2017). Use of Accumulated Entropies for Automated Detection of Congestive Heart Failure in Flexible Analytic Wavelet Transform Framework Based on Short-Term HRV Signals. Entropy, 19.","DOI":"10.3390\/e19030092"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1097\/00000542-199304000-00011","article-title":"Approximate entropy of heart rate as a correlate of postoperative ventricular dysfunction","volume":"78","author":"Fleisher","year":"1993","journal-title":"Anesthesiology"},{"key":"ref_36","unstructured":"Signorini, M.G. (2004, January 1\u20135). Nonlinear Analysis of Heart Rate Variability Signal: Physiological Knowledge and Diagnostic Indications. Proceedings of the Annual International Conference\u2014IEEE Engineering in Medicine and Biology Society, San Francisco, CA, USA."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"567","DOI":"10.1007\/s13246-014-0281-x","article-title":"Robustness evaluation of heart rate variability measures for age gender related autonomic changes in healthy volunteers","volume":"37","author":"Liu","year":"2014","journal-title":"Australas. Phys. Eng. Sci. Med."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1088\/0967-3334\/33\/8\/1289","article-title":"Short-term heart rate variability\u2013age dependence in healthy subjects","volume":"33","author":"Voss","year":"2012","journal-title":"Physiol. Meas."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Voss, A., Schroeder, R., Fischer, C., Heitmann, A., Peters, A., and Perz, S. (2013, January 3\u20137). Influence of age and gender on complexity measures for short term heart rate variability analysis in healthy subjects. Proceedings of the 2013 35th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Osaka, Japan.","DOI":"10.1109\/EMBC.2013.6610813"},{"key":"ref_40","first-page":"789","article-title":"Sample entropy analysis of neonatal heart rate variability","volume":"283","author":"Lake","year":"2002","journal-title":"Am. J. Physiol."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Xinnian, C., Solomon, I., and Chon, K. (2006, January 17\u201318). Comparison of the Use of Approximate Entropy and Sample Entropy: Applications to Neural Respiratory Signal. Proceedings of the 2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, Shanghai, China.","DOI":"10.1109\/IEMBS.2005.1615393"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/j.physa.2003.08.022","article-title":"Multiscale entropy analysis of human gait dynamics","volume":"330","author":"Costa","year":"2003","journal-title":"Physica A"},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"021906","DOI":"10.1103\/PhysRevE.71.021906","article-title":"Multiscale entropy analysis of biological signals","volume":"71","author":"Costa","year":"2005","journal-title":"Phys. Rev. E Stat. Nonlin. Soft Matter Phys."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s11517-006-0119-0","article-title":"Heart rate variability: A review","volume":"44","author":"Acharya","year":"2006","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1016\/j.physa.2005.10.008","article-title":"On multiscale entropy analysis for physiological data","volume":"366","author":"Thuraisingham","year":"2006","journal-title":"Physica A"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1016\/j.compbiomed.2012.11.005","article-title":"Analysis of heart rate variability using fuzzy measure entropy","volume":"43","author":"Liu","year":"2013","journal-title":"Comput. Biol. Med."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1186\/s12938-015-0063-z","article-title":"Analysis of short-term heart rate and diastolic period variability using a refined fuzzy entropy method","volume":"14","author":"Ji","year":"2015","journal-title":"Biomed. Eng. Online"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"975","DOI":"10.1016\/j.physa.2017.08.047","article-title":"Refined generalized multiscale entropy analysis for physiological signals","volume":"490","author":"Liu","year":"2018","journal-title":"Physica A"},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"2569","DOI":"10.1109\/TBME.2018.2808271","article-title":"Understanding Irregularity Characteristics of Short-term HRV Signals using Sample Entropy Profile","volume":"65","author":"Udhayakumar","year":"2018","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1007\/s11071-016-3278-z","article-title":"Approximate entropy profile: A novel approach to comprehend irregularity of short-term HRV signal","volume":"88","author":"Udhayakumar","year":"2016","journal-title":"Nonlinear Dyn."},{"key":"ref_51","first-page":"H1643","article-title":"Physiological time-series analysis: What does regularity quantify?","volume":"266","author":"Pincus","year":"1994","journal-title":"Am. J. Physiol."},{"key":"ref_52","first-page":"249","article-title":"Approximate entropy: A regularity measure for fetal heart rate analysis","volume":"79","author":"Pincus","year":"1992","journal-title":"Obstet. Addit. Gynecol."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1063\/1.166092","article-title":"Approximate entropy (ApEn) as a complexity measure","volume":"5","author":"Pincus","year":"1995","journal-title":"Chaos"},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"1700","DOI":"10.1016\/0735-1097(94)90177-5","article-title":"Gender- and age-related differences in heart rate dynamics: Are women more complex than men?","volume":"24","author":"Ryan","year":"1994","journal-title":"J. Am. Coll. Cardiol."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"1143","DOI":"10.1152\/japplphysiol.00293.2007","article-title":"Progressive decrease of heart period variability entropy-based complexity during graded head-up tilt","volume":"103","author":"Porta","year":"2007","journal-title":"J. Appl. Physiol."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/s10558-007-9049-1","article-title":"Multiscale Analysis of Heart Rate Dynamics: Entropy and Time Irreversibility Measures","volume":"8","author":"Madalena","year":"2008","journal-title":"Cardiovasc. Eng. Int. J."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"061918","DOI":"10.1103\/PhysRevE.84.061918","article-title":"Multivariate multiscale entropy: A tool for complexity analysis of multichannel data","volume":"84","author":"Ahmed","year":"2011","journal-title":"Phys. Rev. E Stat. Nonlin. Soft Matter Phys."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1109\/CIC.2002.1166726","article-title":"Multiscale entropy to distinguish physiologic and synthetic RR time series","volume":"29","author":"Costa","year":"2002","journal-title":"Comput. Cardiol."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1152\/physiologyonline.1991.6.2.87","article-title":"Is the normal heartbeat chaotic or homeostatic?","volume":"6","author":"Goldberger","year":"1991","journal-title":"Physiology"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"4032","DOI":"10.3390\/e16074032","article-title":"Application of a Modified Entropy Computational Method in Assessing the Complexity of Pulse Wave Velocity Signals in Healthy and Diabetic Subjects","volume":"16","author":"Chang","year":"2014","journal-title":"Entropy"},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"5865","DOI":"10.1016\/j.physa.2013.07.075","article-title":"Modified multiscale entropy for short-term time series analysis","volume":"392","author":"Wu","year":"2013","journal-title":"Physica A"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Udhayakumar, R., Karmakar, C., Li, P., Wang, X., and Palaniswami, M. (2020). Modified Distribution Entropy as a Complexity Measure of Heart Rate Variability (HRV) Signal. Entropy, 22.","DOI":"10.3390\/e22101077"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/BF01025868","article-title":"On the histogram as a density estimator:L2 theory","volume":"57","author":"Freedman","year":"1981","journal-title":"Z. Wahrscheinlichkeitstheorie Verwandte Geb."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Udhayakumar, R., Karmakar, C., and Palaniswami, M. (2017, January 11\u201315). Secondary measures of regularity from an entropy profile in detecting Arrhythmia. Proceedings of the 2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Seogwipo, Korea.","DOI":"10.1109\/EMBC.2017.8037607"},{"key":"ref_65","doi-asserted-by":"crossref","unstructured":"Udhayakumar, R., Karmakar, C., and Palaniswami, M. (2019, January 23\u201327). Entropy Profiling to Detect ST Change in Heart Rate Variability Signals. Proceedings of the 2019 41st Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), Berlin, Germany.","DOI":"10.1109\/EMBC.2019.8857297"},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"e215","DOI":"10.1161\/01.CIR.101.23.e215","article-title":"PhysioBank, PhysioToolkit, and PhysioNet: Components of a New Research Resource for Complex Physiologic Signals","volume":"101","author":"Goldberger","year":"2000","journal-title":"Circulation"},{"key":"ref_67","first-page":"1078","article-title":"Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics","volume":"271","author":"Iyengar","year":"1996","journal-title":"Am. J. Physiol."},{"key":"ref_68","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/51.932724","article-title":"The impact of the MIT-BIH arrhythmia database","volume":"20","author":"Moody","year":"2001","journal-title":"IEEE Eng. Med. Biol. Mag."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1016\/j.cmpb.2010.12.003","article-title":"Fast computation of sample entropy and approximate entropy in biomedicine","volume":"104","author":"Pan","year":"2011","journal-title":"Comput. Methods Programs Biomed."},{"key":"ref_70","doi-asserted-by":"crossref","first-page":"2309","DOI":"10.1007\/s00180-013-0408-7","article-title":"Statistical Analysis of Autoregressive Fractionally Integrated Moving Average Models in R","volume":"28","author":"Palma","year":"2013","journal-title":"Comput. Stat."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/12\/1396\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:43:27Z","timestamp":1760179407000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/12\/1396"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,10]]},"references-count":70,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2020,12]]}},"alternative-id":["e22121396"],"URL":"https:\/\/doi.org\/10.3390\/e22121396","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,12,10]]}}}