{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,16]],"date-time":"2026-02-16T16:11:06Z","timestamp":1771258266458,"version":"3.50.1"},"reference-count":161,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2020,3,9]],"date-time":"2020-03-09T00:00:00Z","timestamp":1583712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100010661","name":"Horizon 2020","doi-asserted-by":"publisher","award":["689260"],"award-info":[{"award-number":["689260"]}],"id":[{"id":"10.13039\/100010661","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/EEA\/50014\/2019"],"award-info":[{"award-number":["UID\/EEA\/50014\/2019"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["SFRH\/BD\/138302\/2018"],"award-info":[{"award-number":["SFRH\/BD\/138302\/2018"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The heart-rate dynamics are one of the most analyzed physiological interactions. Many mathematical methods were proposed to evaluate heart-rate variability. These methods have been successfully applied in research to expand knowledge concerning the cardiovascular dynamics in healthy as well as in pathological conditions. Notwithstanding, they are still far from clinical practice. In this paper, we aim to review the nonlinear methods most used to assess heart-rate dynamics. We focused on methods based on concepts of chaos, fractality, and complexity: Poincar\u00e9 plot, recurrence plot analysis, fractal dimension (and the correlation dimension), detrended fluctuation analysis, Hurst exponent, Lyapunov exponent entropies (Shannon, conditional, approximate, sample entropy, and multiscale entropy), and symbolic dynamics. We present the description of the methods along with their most notable applications.<\/jats:p>","DOI":"10.3390\/e22030309","type":"journal-article","created":{"date-parts":[[2020,3,10]],"date-time":"2020-03-10T11:59:36Z","timestamp":1583841576000},"page":"309","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":133,"title":["Nonlinear Methods Most Applied to Heart-Rate Time Series: A Review"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4032-9594","authenticated-orcid":false,"given":"Teresa","family":"Henriques","sequence":"first","affiliation":[{"name":"Centre for Health Technology and Services Research (CINTESIS), Faculty of Medicine University of Porto, 4200-450 Porto, Portugal"},{"name":"Health Information and Decision Sciences Department-MEDCIDS, Faculty of Medicine, University of Porto, 4200-450 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4337-1920","authenticated-orcid":false,"given":"Maria","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"Institute for Systems and Computer Engineering, Technology and Science (INESC-TEC), 4200-465 Porto, Portugal"},{"name":"Computer Science Department, Faculty of Sciences, University of Porto, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1199-2220","authenticated-orcid":false,"given":"Andreia","family":"Teixeira","sequence":"additional","affiliation":[{"name":"Centre for Health Technology and Services Research (CINTESIS), Faculty of Medicine University of Porto, 4200-450 Porto, Portugal"},{"name":"Health Information and Decision Sciences Department-MEDCIDS, Faculty of Medicine, University of Porto, 4200-450 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1312-0154","authenticated-orcid":false,"given":"Lu\u00edsa","family":"Castro","sequence":"additional","affiliation":[{"name":"Centre for Health Technology and Services Research (CINTESIS), Faculty of Medicine University of Porto, 4200-450 Porto, Portugal"},{"name":"Institute for Systems and Computer Engineering, Technology and Science (INESC-TEC), 4200-465 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9988-594X","authenticated-orcid":false,"given":"Lu\u00eds","family":"Antunes","sequence":"additional","affiliation":[{"name":"Institute for Systems and Computer Engineering, Technology and Science (INESC-TEC), 4200-465 Porto, Portugal"},{"name":"Computer Science Department, Faculty of Sciences, University of Porto, 4169-007 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7109-1101","authenticated-orcid":false,"given":"Cristina","family":"Costa-Santos","sequence":"additional","affiliation":[{"name":"Centre for Health Technology and Services Research (CINTESIS), Faculty of Medicine University of Porto, 4200-450 Porto, Portugal"},{"name":"Health Information and Decision Sciences Department-MEDCIDS, Faculty of Medicine, University of Porto, 4200-450 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2020,3,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ott, E. (2002). Chaos in Dynamical Systems, Cambridge University Press.","DOI":"10.1017\/CBO9780511803260"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mandelbrot, B.B. (1979). Fractals: Form, Chance and Dimension, WH Freeman & Co.","DOI":"10.1063\/1.2995555"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_4","first-page":"3","article-title":"Three approaches to the definition of the concept \u201cquantity of information\u201d","volume":"1","author":"Kolmogorov","year":"1965","journal-title":"Problemy Peredachi Informatsii"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Li, M., and Vit\u00e1nyi, P. (2008). An Introduction to Kolmogorov Complexity and Its Applications, Springer.","DOI":"10.1007\/978-0-387-49820-1"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"062114","DOI":"10.1103\/PhysRevE.95.062114","article-title":"Entropy measures, entropy estimators, and their performance in quantifying complex dynamics: Effects of artifacts, nonstationarity, and long-range correlations","volume":"95","author":"Xiong","year":"2017","journal-title":"Phys. Rev. E"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1016\/S0008-6363(96)00009-0","article-title":"Linear and non-linear analyses of heart rate variability: A minireview","volume":"31","author":"Mansier","year":"1996","journal-title":"Cardiovasc. Res."},{"key":"ref_8","first-page":"277","article-title":"Methods derived from nonlinear dynamics for analysing heart rate variability","volume":"367","author":"Voss","year":"2008","journal-title":"Philos. Trans. R. Soc. Lond. Ser. A"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"528","DOI":"10.17554\/j.issn.2309-6861.2016.03.101-4","article-title":"Nonlinear analysis of heart rate variability: A comprehensive review","volume":"3","year":"2016","journal-title":"J. Cardiol. Ther."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Nayak, S.K., Bit, A., Dey, A., Mohapatra, B., and Pal, K. (2018). A review on the nonlinear dynamical system analysis of electrocardiogram signal. J. Healthcare Eng., 2018.","DOI":"10.1155\/2018\/6920420"},{"key":"ref_11","unstructured":"Garc\u00eda-Mart\u00ednez, B., Martinez-Rodrigo, A., Alcaraz, R., and Fern\u00e1ndez-Caballero, A. (2019). A review on nonlinear methods using electroencephalographic recordings for emotion recognition. IEEE Trans. Affective Comput."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1109\/TBME.1985.325532","article-title":"A real-time QRS detection algorithm","volume":"32","author":"Pan","year":"1985","journal-title":"IEEE Trans. Biomed. Eng"},{"key":"ref_13","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_14","doi-asserted-by":"crossref","first-page":"704","DOI":"10.1016\/0002-8703(92)90510-3","article-title":"Patterns of beat-to-beat heart rate variability in advanced heart failure","volume":"123","author":"Woo","year":"1992","journal-title":"Am. Heart J."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1042\/cs0910201","article-title":"Poincare plot of heart rate variability allows quantitative display of parasympathetic nervous activity in humans","volume":"91","author":"Kamen","year":"1996","journal-title":"Clin. Sci."},{"key":"ref_16","unstructured":"Brennan, M., Palaniswami, M., and Kamen, P. (2001, January 25\u201328). New insights into the relationship between Poincare plot geometry and linear measures of heart rate variability. Proceedings of the 2001 Conference Proceedings of the 23rd Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Istanbul, Turkey."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"H1873","DOI":"10.1152\/ajpheart.00405.2000","article-title":"Poincar\u00e9 plot interpretation using a physiological model of HRV based on a network of oscillators","volume":"283","author":"Brennan","year":"2002","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1111\/j.1445-5994.1995.tb00573.x","article-title":"Application of the Poincar\u00e9 plot to heart rate variability: A new measure of functional status in heart failure","volume":"25","author":"Kamen","year":"1995","journal-title":"Aust. N. Z. J. Med."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"H244","DOI":"10.1152\/ajpheart.1996.271.1.H244","article-title":"Quantitative beat-to-beat analysis of heart rate dynamics during exercise","volume":"271","author":"Tulppo","year":"1996","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1342","DOI":"10.1109\/10.959330","article-title":"Do existing measures of Poincare plot geometry reflect nonlinear features of heart rate variability?","volume":"48","author":"Brennan","year":"2001","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1109\/51.537065","article-title":"Applying continuous chaotic modeling to cardiac signal analysis","volume":"15","author":"Cohen","year":"1996","journal-title":"IEEE Eng. Med. Biol. Mag."},{"key":"ref_22","unstructured":"D\u2019Addio, G., Acanfora, D., Pinna, G.D., Maestri, R., Furgi, G., Picone, C., and Rengo, F. (1998, January 13\u201316). Reproducibility of short-and long-term poincare plot parameters compared with frequency-domain HRV indexes in congestive heart failure. Proceedings of the Computers in Cardiology 1998, Cleveland, OH, USA."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1836","DOI":"10.1161\/01.CIR.93.10.1836","article-title":"Abnormalities in beat-to-beat dynamics of heart rate before the spontaneous onset of life-threatening ventricular tachyarrhythmias in patients with prior myocardial infarction","volume":"93","author":"Huikuri","year":"1996","journal-title":"Circulation"},{"key":"ref_24","first-page":"H946","article-title":"Dynamic heart rate variability: A tool for exploring sympathovagal balance continuously during sleep in men","volume":"275","author":"Otzenberger","year":"1998","journal-title":"Am. J. Physiol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/S0022-0736(95)80020-4","article-title":"Numeric processing of Lorenz plots of RR intervals from long-term ECGs: Comparison with time-domain measures of heart rate variability for risk stratification after myocardial infarction","volume":"28","author":"Hnatkova","year":"1995","journal-title":"J. Electrocardiol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"887","DOI":"10.1249\/01.mss.0000218135.79476.9c","article-title":"Validity of the polar S810 heart rate monitor to measure RR intervals at rest","volume":"38","author":"Gamelin","year":"2006","journal-title":"Med. Sci. Sports Exercise"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1007\/BF00364139","article-title":"Is the normal heart a periodic oscillator?","volume":"58","author":"Babloyantz","year":"1988","journal-title":"Biol. Cybern."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"H424","DOI":"10.1152\/ajpheart.1998.274.2.H424","article-title":"Vagal modulation of heart rate during exercise: Effects of age and physical fitness","volume":"274","author":"Tulppo","year":"1998","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"973","DOI":"10.1209\/0295-5075\/4\/9\/004","article-title":"Recurrence plots of dynamical systems","volume":"4","author":"Eckmann","year":"1987","journal-title":"Europhys. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/j.physrep.2006.11.001","article-title":"Recurrence plots for the analysis of complex systems","volume":"438","author":"Marwan","year":"2007","journal-title":"Phys. Rep."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1016\/0167-2789(92)90111-Y","article-title":"Topological analysis and synthesis of chaotic time series","volume":"58","author":"Mindlin","year":"1992","journal-title":"Physica D"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1016\/0375-9601(92)90426-M","article-title":"Embeddings and delays as derived from quantification of recurrence plots","volume":"171","author":"Zbilut","year":"1992","journal-title":"Phys. Lett. A"},{"key":"ref_33","first-page":"361","article-title":"Use of recurrence plots in the analysis of time-series data","volume":"Volume 12","author":"Koebbe","year":"1994","journal-title":"SFI Studies in the Science of Complexity"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1016\/S0375-9601(02)00436-X","article-title":"Recurrence quantification based Liapunov exponents for monitoring divergence in experimental data","volume":"297","author":"Zbilut","year":"2002","journal-title":"Phys. Lett. A"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"138","DOI":"10.1016\/S0167-2789(02)00586-9","article-title":"Influence of observational noise on the recurrence quantification analysis","volume":"171","author":"Thiel","year":"2002","journal-title":"Physica D"},{"key":"ref_36","unstructured":"Webber, C.L., and Zbilut, J.P. (2005). Recurrence quantification analysis of nonlinear dynamical systems. Tutorials in Contemporary Nonlinear Methods for the Behavioral Sciences, National Science Foundation."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"026702","DOI":"10.1103\/PhysRevE.66.026702","article-title":"Recurrence-plot-based measures of complexity and their application to heart-rate-variability data","volume":"66","author":"Marwan","year":"2002","journal-title":"Phys. Rev. E"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1152\/jappl.1994.76.2.965","article-title":"Dynamical assessment of physiological systems and states using recurrence plot strategies","volume":"76","author":"Webber","year":"1994","journal-title":"J. Appl. Physiol."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1186\/1475-925X-10-96","article-title":"Nonlinear heart rate variability features for real-life stress detection. Case study: Students under stress due to university examination","volume":"10","author":"Melillo","year":"2011","journal-title":"Biomed. Eng. Online"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1016\/j.cmpb.2013.08.017","article-title":"Linear and nonlinear analysis of normal and CAD-affected heart rate signals","volume":"113","author":"Acharya","year":"2014","journal-title":"Comput. Methods Prog. Biomed."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"8514","DOI":"10.1073\/pnas.1016955108","article-title":"Synchronized arousal between performers and related spectators in a fire-walking ritual","volume":"108","author":"Konvalinka","year":"2011","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/S1350-4533(01)00112-6","article-title":"Recurrence quantification analysis as a tool for nonlinear exploration of nonstationary cardiac signals","volume":"24","author":"Zbilut","year":"2002","journal-title":"Med. Eng. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1114\/1.248","article-title":"Recurrent patterns of atrial depolarization during atrial fibrillation assessed by recurrence plot quantification","volume":"28","author":"Censi","year":"2000","journal-title":"Ann. Biomed. Eng."},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Barab\u00e1si, A.L. (1995). Fractal Concepts in Surface Growth, Cambridge University Press.","DOI":"10.1017\/CBO9780511599798"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/0010-4825(88)90041-8","article-title":"Fractals and the analysis of waveforms","volume":"18","author":"Katz","year":"1988","journal-title":"Comput. Biol. Med."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0167-2789(88)90081-4","article-title":"Approach to an irregular time series on the basis of the fractal theory","volume":"31","author":"Higuchi","year":"1988","journal-title":"Physica D"},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/0167-2789(90)90039-R","article-title":"Relationship between the fractal dimension and the power law index for a time series: A numerical investigation","volume":"46","author":"Higuchi","year":"1990","journal-title":"Physica D"},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"142","DOI":"10.1016\/S1566-0702(01)00280-6","article-title":"Analysis of heart rate variability with correlation dimension method in a normal population and in heart transplant patients","volume":"90","author":"Bogaert","year":"2001","journal-title":"Auton. Neurosci."},{"key":"ref_49","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/S0008-6363(95)00159-X","article-title":"Non-linear dynamics and chaotic indices in heart rate variability of normal subjects and heart-transplanted patients","volume":"31","author":"Guzzetti","year":"1996","journal-title":"Cardiovasc. Res."},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1103\/PhysRevLett.50.346","article-title":"Characterization of strange attractors","volume":"50","author":"Grassberger","year":"1983","journal-title":"Phys. Rev. Lett."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"404","DOI":"10.1016\/0167-2789(93)90103-8","article-title":"Estimating correlation dimension from a chaotic time series: When does plateau onset occur?","volume":"69","author":"Ding","year":"1993","journal-title":"Physica D"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.cmpb.2005.01.004","article-title":"Correlation dimension analysis of heart rate variability in patients with dilated cardiomyopathy","volume":"78","author":"Carvajal","year":"2005","journal-title":"Comput. Methods Prog. Biomed."},{"key":"ref_53","first-page":"105","article-title":"The Levenberg-Marquardt algorithm: Implementation and theory","volume":"630","year":"1978","journal-title":"Numer. Anal."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"H2560","DOI":"10.1152\/ajpheart.00903.2005","article-title":"Ageing and non-linear heart rate control in a healthy population","volume":"290","author":"Beckers","year":"2006","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1109\/TBME.2002.1010858","article-title":"Study of features based on nonlinear dynamical modeling in ECG arrhythmia detection and classification","volume":"49","author":"Owis","year":"2002","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"875","DOI":"10.1152\/jappl.1993.74.2.875","article-title":"Autonomic control of heart rate during physical exercise and fractal dimension of heart rate variability","volume":"74","author":"Nakamura","year":"1993","journal-title":"J. Appl. Physiol."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/0013-4694(94)00270-U","article-title":"Heart period variability in sleep","volume":"94","author":"Vaughn","year":"1995","journal-title":"Electroencephalogr. Clin. Neurophysiol."},{"key":"ref_58","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF02667355","article-title":"Fractal character of the electrocardiogram: Distinguishing heart-failure and normal patients","volume":"24","author":"Turcott","year":"1996","journal-title":"Ann. Biomed. Eng."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"1685","DOI":"10.1103\/PhysRevE.49.1685","article-title":"Mosaic organization of DNA nucleotides","volume":"49","author":"Peng","year":"1994","journal-title":"Phys. Rev. E"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/S0022-0736(95)80017-4","article-title":"Fractal mechanisms and heart rate dynamics: Long-range correlations and their breakdown with disease","volume":"28","author":"Peng","year":"1995","journal-title":"J. Electrocardiol."},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Peng, C.K., Hausdorff, J.M., and Goldberger, A. (2000). Fractal Mechanisms in Neuronal Control: Human Heartbeat and Gait Dynamics in Health and Disease, Cambridge University Press.","DOI":"10.1017\/CBO9780511535338.006"},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1063\/1.166141","article-title":"Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series","volume":"5","author":"Peng","year":"1995","journal-title":"Chaos Interdiscip. J. Nonlinear Sci."},{"key":"ref_63","first-page":"R1078","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_64","doi-asserted-by":"crossref","first-page":"842","DOI":"10.1161\/01.CIR.96.3.842","article-title":"Predicting survival in heart failure case and control subjects by use of fully automated methods for deriving nonlinear and conventional indices of heart rate dynamics","volume":"96","author":"Ho","year":"1997","journal-title":"Circulation"},{"key":"ref_65","doi-asserted-by":"crossref","first-page":"3736","DOI":"10.1103\/PhysRevLett.85.3736","article-title":"Correlated and uncorrelated regions in heart-rate fluctuations during sleep","volume":"85","author":"Bunde","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_66","doi-asserted-by":"crossref","first-page":"393","DOI":"10.1161\/01.CIR.100.4.393","article-title":"Cardiac interbeat interval dynamics from childhood to senescence: Comparison of conventional and new measures based on fractals and chaos theory","volume":"100","author":"Sourander","year":"1999","journal-title":"Circulation"},{"key":"ref_67","unstructured":"Hurst, H.E., Black, R.P., and Simaika, Y.M. (1965). Long-Term Storage: An Experimental Study, Constable."},{"key":"ref_68","first-page":"770","article-title":"Long-term storage capacity of reservoirs","volume":"116","author":"Hurst","year":"1951","journal-title":"Trans. Am. Soc. Eng."},{"key":"ref_69","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1109\/51.139038","article-title":"Four methods to estimate the fractal dimension from self-affine signals (medical application)","volume":"11","author":"Schepers","year":"1992","journal-title":"IEEE Eng. Med. Biol. Mag."},{"key":"ref_70","first-page":"13","article-title":"On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena","volume":"3","author":"Schuster","year":"1898","journal-title":"Terr. Magn."},{"key":"ref_71","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1038\/161686a0","article-title":"Smoothing periodograms from time series with continuous spectra","volume":"161","author":"Bartlett","year":"1948","journal-title":"Nature"},{"key":"ref_72","unstructured":"Engelberg, S. (2008). Digital Signal Processing: An Experimental Approach, Springer Publishing Company."},{"key":"ref_73","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/TAU.1967.1161901","article-title":"The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms","volume":"15","author":"Welch","year":"1967","journal-title":"IEEE Trans. Audio Electroacoust."},{"key":"ref_74","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1093\/biomet\/37.1-2.1","article-title":"Periodogram analysis and continuous spectra","volume":"37","author":"Bartlett","year":"1950","journal-title":"Biometrika"},{"key":"ref_75","unstructured":"Borg, F.G. (2005). Review of nonlinear methods and modelling. arXiv."},{"key":"ref_76","doi-asserted-by":"crossref","first-page":"1312","DOI":"10.1016\/S0140-6736(96)90948-4","article-title":"Non-linear dynamics for clinicians: Chaos theory, fractals, and complexity at the bedside","volume":"347","author":"Goldberger","year":"1996","journal-title":"Lancet"},{"key":"ref_77","first-page":"R830","article-title":"On the fractal nature of heart rate variability in humans: Effects of vagal blockade","volume":"269","author":"Yamamoto","year":"1995","journal-title":"Am. J. Physiol."},{"key":"ref_78","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.autneu.2013.05.004","article-title":"Poincar\u00e9 plot indexes of heart rate variability: Relationships with other nonlinear variables","volume":"177","author":"Hoshi","year":"2013","journal-title":"Auton. Neurosci."},{"key":"ref_79","doi-asserted-by":"crossref","first-page":"050901","DOI":"10.1103\/PhysRevE.70.050901","article-title":"1\/ f scaling in heart rate requires antagonistic autonomic control","volume":"70","author":"Struzik","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_80","doi-asserted-by":"crossref","first-page":"012903","DOI":"10.1103\/PhysRevE.70.012903","article-title":"Changes in the Hurst exponent of heartbeat intervals during physical activity","volume":"70","author":"Martinis","year":"2004","journal-title":"Phys. Rev. E"},{"key":"ref_81","doi-asserted-by":"crossref","first-page":"287","DOI":"10.1088\/0967-3334\/32\/3\/002","article-title":"Automated detection of sleep apnea from electrocardiogram signals using nonlinear parameters","volume":"32","author":"Acharya","year":"2011","journal-title":"Physiol. Meas."},{"key":"ref_82","doi-asserted-by":"crossref","first-page":"4971","DOI":"10.1103\/PhysRevA.34.4971","article-title":"Liapunov exponents from time series","volume":"34","author":"Eckmann","year":"1986","journal-title":"Phys. Rev. A"},{"key":"ref_83","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1103\/RevModPhys.65.1331","article-title":"The analysis of observed chaotic data in physical systems","volume":"65","author":"Abarbanel","year":"1993","journal-title":"Rev. Mod. Phys."},{"key":"ref_84","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1109\/5.362751","article-title":"Detection of signals in chaos","volume":"83","author":"Haykin","year":"1995","journal-title":"Proc. IEEE"},{"key":"ref_85","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1016\/0167-2789(85)90011-9","article-title":"Determining Lyapunov exponents from a time series","volume":"16","author":"Wolf","year":"1985","journal-title":"Physica D"},{"key":"ref_86","doi-asserted-by":"crossref","first-page":"24","DOI":"10.1186\/1475-925X-3-24","article-title":"Heart rate analysis in normal subjects of various age groups","volume":"3","author":"Acharya","year":"2004","journal-title":"Biomed. Eng. Online"},{"key":"ref_87","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.nonrwa.2003.07.002","article-title":"Measures of LLE of heart rate in different frequency bands: A possible measure of relative vagal and sympathetic activity","volume":"5","author":"Yeragani","year":"2004","journal-title":"Nonlinear Anal. Real World Appl."},{"key":"ref_88","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1016\/S0006-3223(01)01347-6","article-title":"Diminished chaos of heart rate time series in patients with major depression","volume":"51","author":"Yeragani","year":"2002","journal-title":"Biol. Psychiatry"},{"key":"ref_89","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/0375-9601(90)90841-B","article-title":"An improved method for estimating Liapunov exponents of chaotic time series","volume":"151","author":"Briggs","year":"1990","journal-title":"Phys. Lett. A"},{"key":"ref_90","doi-asserted-by":"crossref","first-page":"3962","DOI":"10.1103\/PhysRevE.47.3962","article-title":"Calculating Lyapunov exponents for short and\/or noisy data sets","volume":"47","author":"Brown","year":"1993","journal-title":"Phys. Rev. E"},{"key":"ref_91","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1016\/0167-2789(93)90009-P","article-title":"A practical method for calculating largest Lyapunov exponents from small data sets","volume":"65","author":"Rosenstein","year":"1993","journal-title":"Physica D"},{"key":"ref_92","doi-asserted-by":"crossref","first-page":"1082","DOI":"10.1103\/PhysRevLett.55.1082","article-title":"Measurement of the Lyapunov spectrum from a chaotic time series","volume":"55","author":"Sano","year":"1985","journal-title":"Phys. Rev. Lett."},{"key":"ref_93","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1143\/PTP.77.1","article-title":"Practical methods of measuring the generalized dimension and the largest Lyapunov exponent in high dimensional chaotic systems","volume":"77","author":"Sato","year":"1987","journal-title":"Prog. Theor. Phys."},{"key":"ref_94","doi-asserted-by":"crossref","first-page":"3229","DOI":"10.1103\/PhysRevLett.66.3229","article-title":"Estimating the Lyapunov-exponent spectrum from short time series of low precision","volume":"66","author":"Zeng","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_95","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/0375-9601(94)90072-8","article-title":"Resonance-like phenomena in Lyapunov calculations from data reconstructed by the time-delay method","volume":"190","author":"Fell","year":"1994","journal-title":"Phys. Lett. A"},{"key":"ref_96","doi-asserted-by":"crossref","first-page":"656","DOI":"10.1002\/j.1538-7305.1949.tb00928.x","article-title":"Communication Theory of Secrecy Systems*","volume":"28","author":"Shannon","year":"1949","journal-title":"Bell Syst. Tech. J."},{"key":"ref_97","doi-asserted-by":"crossref","unstructured":"Eckmann, J.P., and Ruelle, D. (1985). Ergodic theory of chaos and strange attractors. The Theory of Chaotic Attractors, Springer.","DOI":"10.1007\/978-0-387-21830-4_17"},{"key":"ref_98","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/s004220050414","article-title":"Measuring regularity by means of a corrected conditional entropy in sympathetic outflow","volume":"78","author":"Porta","year":"1998","journal-title":"Biol. Cybern."},{"key":"ref_99","doi-asserted-by":"crossref","unstructured":"Takens, F. (1981). Detecting strange attractors in turbulence. Dynamical Systems and Turbulence, Springer.","DOI":"10.1007\/BFb0091924"},{"key":"ref_100","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1007\/BF02344774","article-title":"Information domain analysis of cardiovascular variability signals: Evaluation of regularity, synchronisation and co-ordination","volume":"38","author":"Porta","year":"2000","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_101","doi-asserted-by":"crossref","first-page":"1282","DOI":"10.1109\/10.959324","article-title":"Entropy, entropy rate, and pattern classification as tools to typify complexity in short heart period variability series","volume":"48","author":"Porta","year":"2001","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_102","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_103","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_104","doi-asserted-by":"crossref","unstructured":"Marques de S\u00e1, J.P. (2005, January 25\u201328). Characterization of fetal heart rate using approximate entropy. Proceedings of the Computers in Cardiology, Lyon, France.","DOI":"10.1109\/CIC.2005.1588190"},{"key":"ref_105","unstructured":"Magalhaes, F., Marques de S\u00e1, J.P., Bernardes, J., and Ayres-de Campos, D. (2006, January 17\u201320). Characterization of fetal heart rate irregularity using approximate entropy and wavelet filtering. Proceedings of the 2006 Computers in Cardiology, Valencia, Spain."},{"key":"ref_106","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_107","doi-asserted-by":"crossref","first-page":"H2039","DOI":"10.1152\/ajpheart.2000.278.6.H2039","article-title":"Physiological time-series analysis using approximate entropy and sample entropy","volume":"278","author":"Richman","year":"2000","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_108","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_109","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"},{"key":"ref_110","first-page":"971","article-title":"Complexity and 1\/f noise. A phase space approach","volume":"1","author":"Zhang","year":"1991","journal-title":"J. Phys. I"},{"key":"ref_111","doi-asserted-by":"crossref","first-page":"1768264","DOI":"10.1155\/2017\/1768264","article-title":"Efficient computation of multiscale entropy over short biomedical time series based on linear state-space models","volume":"2017","author":"Faes","year":"2017","journal-title":"Complexity"},{"key":"ref_112","doi-asserted-by":"crossref","first-page":"2202","DOI":"10.1109\/TBME.2009.2021986","article-title":"Refined multiscale entropy: Application to 24-h holter recordings of heart period variability in healthy and aortic stenosis subjects","volume":"56","author":"Valencia","year":"2009","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_113","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"},{"key":"ref_114","doi-asserted-by":"crossref","first-page":"1369","DOI":"10.1016\/j.physleta.2014.03.034","article-title":"Analysis of complex time series using refined composite multiscale entropy","volume":"378","author":"Wu","year":"2014","journal-title":"Phys. Lett. A"},{"key":"ref_115","doi-asserted-by":"crossref","first-page":"3110","DOI":"10.3390\/e17053110","article-title":"The multiscale entropy algorithm and its variants: A review","volume":"17","year":"2015","journal-title":"Entropy"},{"key":"ref_116","doi-asserted-by":"crossref","first-page":"1701","DOI":"10.1007\/s10439-009-9740-z","article-title":"Automatic real time detection of atrial fibrillation","volume":"37","author":"Dash","year":"2009","journal-title":"Ann. Biomed. Eng."},{"key":"ref_117","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.hrthm.2012.12.001","article-title":"A novel application for the detection of an irregular pulse using an iPhone 4S in patients with atrial fibrillation","volume":"10","author":"McManus","year":"2013","journal-title":"Heart Rhythm"},{"key":"ref_118","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1109\/TBME.2012.2208112","article-title":"Atrial fibrillation detection using an iPhone 4S","volume":"60","author":"Lee","year":"2013","journal-title":"IEEE Trans. Biomed. Eng."},{"key":"ref_119","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1016\/j.clinph.2007.12.017","article-title":"Short-term heart rate complexity is reduced in patients with type 1 diabetes mellitus","volume":"119","author":"Javorka","year":"2008","journal-title":"Clin. Neurophysiol."},{"key":"ref_120","doi-asserted-by":"crossref","unstructured":"Porta, A., Gnecchi-Ruscone, T., Tobaldini, E., Guzzetti, S., Furlan, R., and Montano, N. (2007). Progressive decrease of heart period variability entropy-based complexity during graded head-up tilt. J. Appl. Physiol.","DOI":"10.1152\/japplphysiol.00293.2007"},{"key":"ref_121","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s004220050549","article-title":"Conditional entropy approach for the evaluation of the coupling strength","volume":"81","author":"Porta","year":"1999","journal-title":"Biol. Cybern."},{"key":"ref_122","first-page":"R378","article-title":"Causal relationships between heart period and systolic arterial pressure during graded head-up tilt","volume":"300","author":"Porta","year":"2010","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_123","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1016\/S1566-0702(00)00239-3","article-title":"Linear and non-linear 24 h heart rate variability in chronic heart failure","volume":"86","author":"Guzzetti","year":"2000","journal-title":"Auton. Neurosci."},{"key":"ref_124","first-page":"R789","article-title":"Sample entropy analysis of neonatal heart rate variability","volume":"283","author":"Lake","year":"2002","journal-title":"Am. J. Physiol."},{"key":"ref_125","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_126","doi-asserted-by":"crossref","first-page":"991","DOI":"10.1590\/S0100-879X2002000800018","article-title":"Heart rate recovery after exercise: Relations to heart rate variability and complexity","volume":"35","author":"Javorka","year":"2002","journal-title":"Braz. J. Med. Biol. Res."},{"key":"ref_127","doi-asserted-by":"crossref","first-page":"H319","DOI":"10.1152\/ajpheart.00561.2010","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":"2010","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_128","doi-asserted-by":"crossref","unstructured":"Ahmad, S., Ramsay, T., Huebsch, L., Flanagan, S., McDiarmid, S., Batkin, I., McIntyre, L., Sundaresan, S.R., Maziak, D.E., and Shamji, F.M. (2009). Continuous multi-parameter heart rate variability analysis heralds onset of sepsis in adults. PLoS ONE, 4.","DOI":"10.1371\/journal.pone.0006642"},{"key":"ref_129","unstructured":"Costa, M., Goldberger, A., and Peng, C.K. (2002, January 22\u201325). Multiscale entropy to distinguish physiologic and synthetic RR time series. Proceedings of the Computers in Cardiology, Memphis, TN, USA."},{"key":"ref_130","first-page":"27","article-title":"Les surfaces \u00e0 courbures oppos\u00e9es et leurs lignes g\u00e9od\u00e9sique","volume":"4","author":"Hadamard","year":"1898","journal-title":"Eur. J. Pure Appl. Math."},{"key":"ref_131","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1016\/S0008-6363(96)00008-9","article-title":"The application of methods of non-linear dynamics for the improved and predictive recognition of patients threatened by sudden cardiac death","volume":"31","author":"Voss","year":"1996","journal-title":"Cardiovasc. Res."},{"key":"ref_132","doi-asserted-by":"crossref","first-page":"186","DOI":"10.1111\/j.1540-8159.1998.tb01086.x","article-title":"Multiparametric analysis of heart rate variability used for risk stratification among survivors of acute myocardial infarction","volume":"21","author":"Voss","year":"1998","journal-title":"Pacing and Clin. Electrophysiol."},{"key":"ref_133","doi-asserted-by":"crossref","first-page":"H702","DOI":"10.1152\/ajpheart.00006.2007","article-title":"Assessment of cardiac autonomic modulation during graded head-up tilt by symbolic analysis of heart rate variability","volume":"293","author":"Porta","year":"2007","journal-title":"Am. J. Physiol.-Heart Circ. Physiol."},{"key":"ref_134","doi-asserted-by":"crossref","unstructured":"Voss, A., Schroeder, R., Heitmann, A., Peters, A., and Perz, S. (2015). Short-term heart rate variability\u2014influence of gender and age in healthy subjects. PLoS ONE, 10.","DOI":"10.1371\/journal.pone.0118308"},{"key":"ref_135","doi-asserted-by":"crossref","first-page":"733","DOI":"10.1103\/PhysRevE.61.733","article-title":"Short-term forecasting of life-threatening cardiac arrhythmias based on symbolic dynamics and finite-time growth rates","volume":"61","author":"Wessel","year":"2000","journal-title":"Phys. Rev. E"},{"key":"ref_136","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1111\/j.1540-8167.2007.00728.x","article-title":"Nonlinear indices of heart rate variability in chronic heart failure patients: Redundancy and comparative clinical value","volume":"18","author":"Maestri","year":"2007","journal-title":"J. Cardiovasc. Electrophysiol."},{"key":"ref_137","doi-asserted-by":"crossref","first-page":"2599","DOI":"10.1113\/JP277501","article-title":"CrossTalk opposing view: Heart rate variability as a measure of cardiac autonomic responsiveness is fundamentally flawed","volume":"597","author":"Boyett","year":"2019","journal-title":"J. Physiol."},{"key":"ref_138","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1016\/0002-9149(93)91070-X","article-title":"Components of heart rate variability-what they really mean and what we really measure","volume":"72","author":"Malik","year":"1993","journal-title":"Am. J. Cardiol."},{"key":"ref_139","doi-asserted-by":"crossref","first-page":"1341","DOI":"10.1093\/europace\/euv015","article-title":"Advances in heart rate variability signal analysis: Joint position statement by the e-Cardiology ESC Working Group and the European Heart Rhythm Association co-endorsed by the Asia Pacific Heart Rhythm Society","volume":"17","author":"Sassi","year":"2015","journal-title":"EP Europace"},{"key":"ref_140","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_141","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1007\/s11517-005-0015-z","article-title":"Permutation entropy improves fetal behavioural state classification based on heart rate analysis from biomagnetic recordings in near term fetuses","volume":"44","author":"Frank","year":"2006","journal-title":"Med. Biol. Eng. Comput."},{"key":"ref_142","doi-asserted-by":"crossref","first-page":"046103","DOI":"10.1103\/PhysRevE.80.046103","article-title":"Horizontal visibility graphs: Exact results for random time series","volume":"80","author":"Luque","year":"2009","journal-title":"Phys. Rev. E"},{"key":"ref_143","doi-asserted-by":"crossref","unstructured":"Madl, T. (2016, January 11\u201314). Network analysis of heart beat intervals using horizontal visibility graphs. Proceedings of the 2016 Computing in Cardiology Conference (CinC), Vancouver, BC, Canada.","DOI":"10.22489\/CinC.2016.213-510"},{"key":"ref_144","doi-asserted-by":"crossref","first-page":"786","DOI":"10.1016\/j.physa.2017.04.091","article-title":"Visibility graph analysis of heart rate time series and bio-marker of congestive heart failure","volume":"482","author":"Bhaduri","year":"2017","journal-title":"Physica A"},{"key":"ref_145","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.1111\/jep.12068","article-title":"Entropy and compression: Two measures of complexity","volume":"19","author":"Henriques","year":"2013","journal-title":"J. Eval. Clin. Pract."},{"key":"ref_146","unstructured":"Santos, C.C., Bernardes, J., Vit\u00e1nyi, P.M., and Antunes, L. (2006, January 22\u201323). Clustering fetal heart rate tracings by compression. Proceedings of the 19th IEEE Symposium on Computer-Based Medical Systems (CBMS\u201906), Salt Lake City, UT, USA."},{"key":"ref_147","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1109\/81.904882","article-title":"A comparison of waveform fractal dimension algorithms","volume":"48","author":"Esteller","year":"2001","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"ref_148","doi-asserted-by":"crossref","first-page":"3325","DOI":"10.1142\/S0218127407019093","article-title":"Nonlinear methods of cardiovascular physics and their clinical applicability","volume":"17","author":"Wessel","year":"2007","journal-title":"Int. J. Bifurcation Chaos"},{"key":"ref_149","doi-asserted-by":"crossref","first-page":"8715605","DOI":"10.1155\/2017\/8715605","article-title":"Advancing Shannon entropy for measuring diversity in systems","volume":"2017","author":"Rajaram","year":"2017","journal-title":"Complexity"},{"key":"ref_150","doi-asserted-by":"crossref","unstructured":"Faes, L., G\u00f2mez-Extremera, M., Pernice, R., Carpena, P., Nollo, G., Porta, A., and Bernaola-Galv\u00e0n, P. (2019). Comparison of methods for the assessment of nonlinearity in short-term heart rate variability under different physiopathological states. arXiv.","DOI":"10.1063\/1.5115506"},{"key":"ref_151","doi-asserted-by":"crossref","first-page":"3403","DOI":"10.1103\/PhysRevA.45.3403","article-title":"Determining embedding dimension for phase-space reconstruction using a geometrical construction","volume":"45","author":"Kennel","year":"1992","journal-title":"Phys. Rev. A"},{"key":"ref_152","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1016\/S0167-2789(97)00118-8","article-title":"Practical method for determining the minimum embedding dimension of a scalar time series","volume":"110","author":"Cao","year":"1997","journal-title":"Physica D"},{"key":"ref_153","doi-asserted-by":"crossref","first-page":"1134","DOI":"10.1103\/PhysRevA.33.1134","article-title":"Independent coordinates for strange attractors from mutual information","volume":"33","author":"Fraser","year":"1986","journal-title":"Phys. Rev. A"},{"key":"ref_154","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1142\/S0218127494000204","article-title":"The multifractal formalism revisited with wavelets","volume":"4","author":"Muzy","year":"1994","journal-title":"Int. J. Bifurcation Chaos"},{"key":"ref_155","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1038\/20924","article-title":"Multifractality in human heartbeat dynamics","volume":"399","author":"Ivanov","year":"1999","journal-title":"Nature"},{"key":"ref_156","doi-asserted-by":"crossref","first-page":"3515","DOI":"10.1103\/PhysRevLett.67.3515","article-title":"Wavelets and multifractal formalism for singular signals: Application to turbulence data","volume":"67","author":"Muzy","year":"1991","journal-title":"Phys. Rev. Lett."},{"key":"ref_157","doi-asserted-by":"crossref","first-page":"6026","DOI":"10.1103\/PhysRevLett.86.6026","article-title":"Behavioral-independent features of complex heartbeat dynamics","volume":"86","author":"Amaral","year":"2001","journal-title":"Phys. Rev. Lett."},{"key":"ref_158","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/S0378-4371(01)00144-3","article-title":"Detecting long-range correlations with detrended fluctuation analysis","volume":"295","author":"Kantelhardt","year":"2001","journal-title":"Physica A"},{"key":"ref_159","doi-asserted-by":"crossref","first-page":"87","DOI":"10.1016\/S0378-4371(02)01383-3","article-title":"Multifractal detrended fluctuation analysis of nonstationary time series","volume":"316","author":"Kantelhardt","year":"2002","journal-title":"Physica A"},{"key":"ref_160","doi-asserted-by":"crossref","first-page":"64","DOI":"10.1016\/S0006-3495(94)80455-2","article-title":"Correlation approach to identify coding regions in DNA sequences","volume":"67","author":"Ossadnik","year":"1994","journal-title":"Biophys. J."},{"key":"ref_161","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/S0378-4371(03)00008-6","article-title":"Magnitude and sign scaling in power-law correlated time series","volume":"323","author":"Ashkenazy","year":"2003","journal-title":"Physica A"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/3\/309\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T09:05:34Z","timestamp":1760173534000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/3\/309"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,3,9]]},"references-count":161,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2020,3]]}},"alternative-id":["e22030309"],"URL":"https:\/\/doi.org\/10.3390\/e22030309","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,3,9]]}}}