IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v153y2021ip1s096007792100922x.html
   My bibliography  Save this article

A novel parameter for nonequilibrium analysis in reconstructed state spaces

Author

Listed:
  • Yao, Wenpo
  • Yao, Wenli
  • Wang, Jun

Abstract

Kernel methods are widely used for probability estimation by measuring the distribution of low-passed vector distances in reconstructed state spaces. However, the information conveyed by the vector distances that are greater than the threshold has received little attention. In this paper, we consider the probabilistic difference of the kernel transformation in reconstructed state spaces, and derive a novel nonequilibrium descriptor by measuring the fluctuations of the vector distance with respect to the tolerance. We verify the effectiveness of the proposed kernel probabilistic difference using three chaotic series (logistic, Henon, and Lorenz) and a first-order autoregressive series according to the surrogate theory, and we use the kernel parameter to analyze real-world heartbeat data. In the heartbeat analysis, the kernel probabilistic difference, particularly that based on the Kullback–Leibler divergence, effectively characterizes the physiological complexity loss related to reduced cardiac dynamics in the elderly and diseased heartbeats. Overall, the kernel probabilistic difference provides a novel method for the quantification of nonequilibria by characterizing the fluctuation theorem in reconstructed state spaces, and enables reliable detection of cardiac physiological and pathological information from heart rates.

Suggested Citation

  • Yao, Wenpo & Yao, Wenli & Wang, Jun, 2021. "A novel parameter for nonequilibrium analysis in reconstructed state spaces," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s096007792100922x
    DOI: 10.1016/j.chaos.2021.111568
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S096007792100922X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2021.111568?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Brechtl, Jamieson & Xie, Xie & Liaw, Peter K. & Zinkle, Steven J., 2018. "Complexity modeling and analysis of chaos and other fluctuating phenomena," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 166-175.
    2. Yao, Wenpo & Li, Jin & Hou, Fengzhen & Wang, Jun, 2019. "Probabilistic divergence of permutations for nonlinearity detection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 532(C).
    3. Colangeli, Matteo & Rondoni, Lamberto & Verderosa, Antonella, 2014. "Focus on some nonequilibrium issues," Chaos, Solitons & Fractals, Elsevier, vol. 64(C), pages 2-15.
    4. Isler, Yalcin & Narin, Ali & Ozer, Mahmut & Perc, Matjaž, 2019. "Multi-stage classification of congestive heart failure based on short-term heart rate variability," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 145-151.
    5. Cang, Shijian & Li, Yue & Kang, Zhijun & Wang, Zenghui, 2020. "Generating multicluster conservative chaotic flows from a generalized Sprott-A system," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    6. Cammarota, Camillo & Rogora, Enrico, 2007. "Time reversal, symbolic series and irreversibility of human heartbeat," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1649-1654.
    7. Plamen Ch. Ivanov & Luís A. Nunes Amaral & Ary L. Goldberger & Shlomo Havlin & Michael G. Rosenblum & Zbigniew R. Struzik & H. Eugene Stanley, 1999. "Multifractality in human heartbeat dynamics," Nature, Nature, vol. 399(6735), pages 461-465, June.
    8. Watt, Stuart J. & Politi, Antonio, 2019. "Permutation entropy revisited," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 95-99.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. repec:plo:pone00:0105379 is not listed on IDEAS
    2. Vitanov, Nikolay K. & Sakai, Kenshi & Dimitrova, Zlatinka I., 2008. "SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 187-202.
    3. Luis A. N. Amaral & P. Gopikrishnan & Kaushik Matia & Vasiliki Plerou & H. E. Stanley, 2001. "Application of statistical physics methods and conceptsto the study of science & technology systems," Scientometrics, Springer;Akadémiai Kiadó, vol. 51(1), pages 9-36, April.
    4. Zhang, Yin & Li, Jin & Wang, Jun, 2017. "Exploring stability of entropy analysis for signal with different trends," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 60-67.
    5. Li, Jin & Chen, Chen & Yao, Qin & Zhang, Peng & Wang, Jun & Hu, Jing & Feng, Feilong, 2018. "The effect of circadian rhythm on the correlation and multifractality of heart rate signals during exercise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 1207-1213.
    6. Stanley, H.Eugene, 2000. "Exotic statistical physics: Applications to biology, medicine, and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 285(1), pages 1-17.
    7. Yuxin Zhao & Shuai Chang & Chang Liu, 2015. "Multifractal theory with its applications in data management," Annals of Operations Research, Springer, vol. 234(1), pages 133-150, November.
    8. Wu, Yue & Shang, Pengjian & Chen, Shijian, 2019. "Modified multifractal large deviation spectrum based on CID for financial market system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1331-1342.
    9. Jovanovic, Tijana & Mejía, Alfonso & Gall, Heather & Gironás, Jorge, 2016. "Effect of urbanization on the long-term persistence of streamflow records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 208-221.
    10. Dudkowska, A. & Makowiec, D., 2004. "Sleep and wake phase of heart beat dynamics by artificial insymmetrised patterns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 336(1), pages 174-180.
    11. Rodriguez, Eduardo & Echeverria, Juan C. & Alvarez-Ramirez, Jose, 2009. "Fractality in electrocardiographic waveforms for healthy subjects and patients with ventricular fibrillation," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1046-1054.
    12. West, Bruce J. & Latka, Miroslaw & Glaubic-Latka, Marta & Latka, Dariusz, 2003. "Multifractality of cerebral blood flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 318(3), pages 453-460.
    13. Li, Jin & Hu, Jing & Zhang, Yinhong & Zhang, Xiaofeng, 2011. "Dynamical complexity changes during two forms of meditation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(12), pages 2381-2387.
    14. Rodriguez, Eduardo & Echeverria, Juan C. & Alvarez-Ramirez, Jose, 2007. "Detrended fluctuation analysis of heart intrabeat dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 429-438.
    15. Conlon, Thomas & Cotter, John & Gençay, Ramazan, 2018. "Long-run wavelet-based correlation for financial time series," European Journal of Operational Research, Elsevier, vol. 271(2), pages 676-696.
    16. Huang, Yong & Yang, Dongqing & Wang, Lei & Wang, Kehong, 2020. "Classifying of welding time series based on multi-scale time irreversibility analysis and extreme learning machine," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    17. Cang, Shijian & Wang, Luo & Zhang, Yapeng & Wang, Zenghui & Chen, Zengqiang, 2022. "Bifurcation and chaos in a smooth 3D dynamical system extended from Nosé-Hoover oscillator," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    18. Vitanov, Nikolay K. & Yankulova, Elka D., 2006. "Multifractal analysis of the long-range correlations in the cardiac dynamics of Drosophila melanogaster," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 768-775.
    19. Saeed Aligholi & Manoj Khandelwal, 2022. "Order of Intermittent Rock Fractured Surfaces," Sustainability, MDPI, vol. 15(1), pages 1-7, December.
    20. Xue Pan & Lei Hou & Mutua Stephen & Huijie Yang & Chenping Zhu, 2014. "Evaluation of Scaling Invariance Embedded in Short Time Series," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-27, December.
    21. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 182-198.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:153:y:2021:i:p1:s096007792100922x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.