Multifractal Spectra as a Measure of Complexity in Human Posture

Shimizu, Yu; Thurner, Stefan; Ehrenberger, K.

doi:10.1142/s0218348x02001130

Cited by 227 publications

(132 citation statements)

References 26 publications

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“…In other words, the wider the range of α , the 343 "richer" is the process in structure. A signal with a high value of o α , a wide range of fractal 344 exponents and a right-skewed shape is more complex than a signal with the opposite 345 characteristics (Shimizu et al, 2002). Consequently, the fine-structure of physical mechanisms 346 governing a signal could be analyzed if its complexity is high.…”

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confidence: 99%

Complexity and predictability of the monthly Western Mediterranean Oscillation index

Lana

Burgueño

Martínez

et al. 2015

Intl Journal of Climatology

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19The complexity, predictability and predictive instability of the Western Mediterranean 20 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 The contents of the paper include a description of the WeMOi, its cumulative distribution 72 (Section 2), monofractal properties (Section 3) and multifractal characteristics derived from 73 the multifractal detrended fluctuaction analysis, MF-DFA, which is also succinctly described 74 (Section 4). A comparison of the mono-and multifractal properties for the WeMO, NAO and 75 AMO indices, and the validity of fGn series to simulate the WeMOi are presented in Section 5. 76Section 6 introduces results derived from the ARIMA process and the Conclusions Section 77 outlines the main WeMOi fractal features and reviews the autoregressive prediction results. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 P e e r R e v i e w O n l y The monthly Western Mediterranean Oscillation index, WeMOi 82The WeMOi was proposed by Martín-Vide and López-Bustins (2006) to detect atmospheric 83 circulation patterns related to rainfall shortage or excess affecting the eastern Iberian 84Peninsula López-Bustins et al., 2008; Gonzalez-Hidalgo et al., 2009), 85 being also used in other regional climatic applications (Azorín-Molina and Lopez-Bustins, 2008; 86 Sánchez-Lorenzo et al., 2009;Vicente-Serrano et al., 2009;Ouachani et al., 2013; El Kenawy et 87 al., 2013;Beranová and Kyselý, 2015;Ríos-Cornejo et al., 2015). (Figure 1b), strongly suggests that this decreasing tendency could be mainly 107 linked to the behaviour of WeMOi at spring and summer seasons. The cumulative distribution 108 of WeMOi (Figure 2) is Gaussian, the observations being kept within the 95% confidence bands 109 derived from the Kolmogorov-Smirnov test (Benjamin and Cornell, 1970;Press et al., 1992). 110 Figure 3 represents WeMOi for several return periods, given in months, compared with 111 theoretic return values for a Gaussian distribution. Empiric values are also quite well described 112 by a logarithmic law, by taking as argument the return period (months). Taking into account 113 the symmetry of the Gaussian distribution, similar results would be obtained for negative 114 WeMOi. 115 116On the other hand, it is well known that the Mediterranean climate is submitted to the NAO 117 (Trigo et al., 2002;Lionello et al., 2006; López-Moreno et al., 2011) region, NAO plays a significant role on decadal variance in precipitation, especially...

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confidence: 99%

Complexity and predictability of the monthly Western Mediterranean Oscillation index

Lana

Burgueño

Martínez

et al. 2015

Intl Journal of Climatology

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“…Multifractality in the sequences is found to be due to both the long-range persistence of memory and to the fat-tail probability density function, and the strength of multifractality in the sequences are much more stronger than what was obtained for the original series. We parametrize the corresponding multifractal patterns in terms of a set of complexity parameters [33,34] and find that the sequence series are more complex than the actual series from where the sequences are extracted. The complexity of the positive sequences is found to be higher than that of the negative sequences.…”

Section: Discussionmentioning

confidence: 99%

Long-range memory and multifractality in gold markets

Mali

Mukhopadhyay

2015

Phys. Scr.

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Abstract. Long-range correlation and fluctuation in the gold market time series of world's two leading gold consuming countries, namely China and India, are studied. For both the market series during the period 1985-2013 we observe a long-range persistence of memory in the sequences of maxima (minima) of returns in successive time windows of fixed length, but the series as a whole are found to be uncorrelated. Multifractal analysis for these series as well as for the sequences of maxima (minima) is carried out in terms of the multifractal detrended fluctuation analysis (MF-DFA) method. We observe a weak multifractal structure for the original series that is mainly originated from the fat-tailed probability distribution function of the values, and the multifractal nature of the original time series is enriched into their sequences of maximal (minimal) returns. A quantitative measure of multifractality is provided by using a set of "complexity parameters".

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“…the width of the spectrum denotes range of exponents. A quantitative characterization of the spectra can be done by leastsquares fitting it to quadratic function [96] around the position of maximum 0…”

Section: Datamentioning

confidence: 99%

Epileptic Seizure: A New Approach for Quantification of Autonomic Deregulation with Chaos Based Technique

Ghosh¹,

Dutta²,

Chakraborty³

et al. 2017

Transl Biomed

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Background: Epileptic seizures can lead to changes in autonomic function affecting the sympathetic, parasympathetic and enteric nervous systems. Changes in cardiac signals are potential biomarkers that may provide an extracerebral indicator of ictal onset in some patients. Patients suffering from epilepsy experience some significant cardiac changes during seizure, causing some serious cardiac malfunctions which may lead to sudden unexpected death (SUDEP). The fluctuations observed in the heart rate during the process are non-linear and extremely complex. Chaos based non-linear methodology has become a very powerful tool in recent years in analysing such complex systems. Although a few papers on effect of seizure have been reported where study was done to assess the dynamics of cardiac systems for post-ictal patients not using non-linear technique, this paper reports the analysis of ECG signals of post-ictal patients using a modern and rigorous non-linear technique.

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Multifractal Spectra as a Measure of Complexity in Human Posture

Cited by 227 publications

References 26 publications

Complexity and predictability of the monthly Western Mediterranean Oscillation index

Complexity and predictability of the monthly Western Mediterranean Oscillation index

Long-range memory and multifractality in gold markets

Epileptic Seizure: A New Approach for Quantification of Autonomic Deregulation with Chaos Based Technique

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