Multifractals embedded in short time series: An unbiased estimation of probability moment

Qiu, Lu; Yang, Tianguang; Yin, Yuan‐Qi; Gu, Changgui; Yang, Huijie

doi:10.1103/physreve.94.062201

Cited by 14 publications

(6 citation statements)

References 106 publications

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“…Some interesting works in literature on the same walk trials show that, in about one hour walk the dynamical mechanism of the motor nervous system (measured by the scale-invariant exponent of time series) can be separated into three stages with significantly different values of the Hurst exponent. [25][26][27][28] This finding is consistent with our findings in this study. Hence, it is reasonable to say that the evolutionary behavior of mode network is produced by the dynamical mechanism of walk.…”

Section: Conclusion and Discussionsupporting

confidence: 93%

Patterns of cross-correlation in time series: A case study of gait trails*

Song¹,

Weng²,

Gu³

et al. 2020

Chinese Phys. B

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A complex system contains generally many elements that are networked by their couplings. The time series of output records of the system’s dynamical process is subsequently a cooperative result of the couplings. Discovering the coupling structure stored in the time series is an essential task in time series analysis. However, in the currently used methods for time series analysis the structural information is merged completely by the procedure of statistical average. We propose a concept called mode network to preserve the structural information. Firstly, a time series is decomposed into intrinsic mode functions and residue by means of the empirical mode decomposition solution. The mode functions are employed to represent the contributions from different elements of the system. Each mode function is regarded as a mono-variate time series. All the mode functions form a multivariate time series. Secondly, the co-occurrences between all the mode functions are then used to construct a threshold network (mode network) to display the coupling structure. This method is illustrated by investigating gait time series. It is found that a walk trial can be separated into three stages. In the beginning stage, the residue component dominates the series, which is replaced by the mode function numbered M 14 with peaks covering ∼680 strides (∼12 min) in the second stage. In the final stage more and more mode functions join into the backbone. The changes of coupling structure are mainly induced by the co-occurrent strengths of the mode functions numbered as M 11, M 12, M 13, and M 14, with peaks covering 200–700 strides. Hence, the mode network can display the rich and dynamical patterns of the coupling structure. This approach can be extended to investigate other complex systems such as the oil price and the stock market price series.

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Section: Conclusion and Discussionsupporting

confidence: 93%

Patterns of cross-correlation in time series: A case study of gait trails*

Song¹,

Weng²,

Gu³

et al. 2020

Chinese Phys. B

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“…One way to characterize the stochastic features inherent to the raw data is by empirically estimating the probability distributions underlying a parameter commonly used in the literature of motor control to investigate the nature of the variability in biophysical data. Such data include motion biorhythms extracted from signals harnessed from heart rate (Peng et al, 1995b ) including local-scale of shorter time series (Castiglioni et al, 2007 ), gait (Hausdorff et al, 1997 ; Kaipust et al, 2013 ) including short time series (Qiu et al, 2016 ; Terrier, 2016 ), finger tapping (Botcharova et al, 2015 ), among others. The parameter of interest is the alpha exponent (explained in the methods) derived from Detrended Fluctuation Analyses (DFA) (Peng et al, 1995b ), a popular method to examine stochastic processes and gaining insights on the self-affinity / stationarity (or lack thereof) of biophysical time series data (Stanley et al, 1999 ).…”

Section: Introductionmentioning

confidence: 99%

Characterization of Noise Signatures of Involuntary Head Motion in the Autism Brain Imaging Data Exchange Repository

Caballero

Mistry

Vero

et al. 2018

Front. Integr. Neurosci.

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The variability inherently present in biophysical data is partly contributed by disparate sampling resolutions across instrumentations. This poses a potential problem for statistical inference using pooled data in open access repositories. Such repositories combine data collected from multiple research sites using variable sampling resolutions. One example is the Autism Brain Imaging Data Exchange repository containing thousands of imaging and demographic records from participants in the spectrum of autism and age-matched neurotypical controls. Further, statistical analyses of groups from different diagnoses and demographics may be challenging, owing to the disparate number of participants across different clinical subgroups. In this paper, we examine the noise signatures of head motion data extracted from resting state fMRI data harnessed under different sampling resolutions. We characterize the quality of the noise in the variability of the raw linear and angular speeds for different clinical phenotypes in relation to age-matched controls. Further, we use bootstrapping methods to ensure compatible group sizes for statistical comparison and report the ranges of physical involuntary head excursions of these groups. We conclude that different sampling rates do affect the quality of noise in the variability of head motion data and, consequently, the type of random process appropriate to characterize the time series data. Further, given a qualitative range of noise, from pink to brown noise, it is possible to characterize different clinical subtypes and distinguish them in relation to ranges of neurotypical controls. These results may be of relevance to the pre-processing stages of the pipeline of analyses of resting state fMRI data, whereby head motion enters the criteria to clean imaging data from motion artifacts.

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“…Recent years have witnessed a significant progress in detecting structural patterns of time series. For instance, the unbiased estimator of probability moments [ 62 ] can evaluate multi-fractals in very short time series (with a length of ∼ 10 2 ). By mapping a time series to a network one can extract the structural patterns at different scales [ 63 – 80 ].…”

Section: Discussionmentioning

confidence: 99%

Evolution of scaling behaviors embedded in sentence series from A Story of the Stone

Yang

Xiao

et al. 2017

PLoS ONE

Self Cite

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The novel entitled A Story of the Stone provides us precise details of life and social structure of the 18th century China. Its writing lasted a long duration of about 10 years, in which the author’s habit may change significantly. It had been published anonymously up to the beginning of the 20th century, which left a mystery of the author’s attribution. In the present work we focus our attention on scaling behavior embedded in the sentence series from this novel, hope to find how the ideas are organized from single sentences to the whole text. Especially we are interested in the evolution of scale invariance to monitor the changes of the author’s language habit and to find some clues on the author’s attribution. The sentence series are separated into a total of 69 non-overlapping segments with a length of 500 sentences each. The correlation dependent balanced estimation of diffusion entropy (cBEDE) is employed to evaluate the scaling behaviors embedded in the short segments. It is found that the total, the part attributed currently to Xueqin Cao (X-part), and the other part attributed to E Gao (E-part), display scale invariance in a large scale up to 103 sentences, while their scaling exponents are almost identical. All the segments behave scale invariant in considerable wide scales, most of which reach one third of the length. In the curve of scaling exponent versus segment number, the X-part has rich patterns with averagely larger values, while the E-part has a U-shape with a significant low bottom. This finding is a new clue to support the attribution of the E-part to E Gao.

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Multifractals embedded in short time series: An unbiased estimation of probability moment

Cited by 14 publications

References 106 publications

Patterns of cross-correlation in time series: A case study of gait trails*

Patterns of cross-correlation in time series: A case study of gait trails*

Characterization of Noise Signatures of Involuntary Head Motion in the Autism Brain Imaging Data Exchange Repository

Evolution of scaling behaviors embedded in sentence series from A Story of the Stone

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