Visibility graphlet approach to chaotic time series

Stephen, Mutua; Gu, Changgui; Yang, Huijie

doi:10.1063/1.4951681

Cited by 37 publications

(18 citation statements)

References 53 publications

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“…By mapping a time series to a network one can extract the structural patterns at different scales [ 63 – 80 ]. By using a graph-let as the representative of a local state, we can monitor the evolutionary behavior of a complex system [ 81 , 82 ]. We hope our work stimulates an incorporation of the methods to enrich the knowledge of and to deepen the understanding on the novel of A Story of The Stone .…”

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

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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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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

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“…The structural stability test requires powerful new tools to detect scaling behaviors from short time series (see, for example, [ 34 – 41 ]). To reach further conclusions on the Chinese language, we will investigate more Chinese novels in the future.…”

Section: Discussionmentioning

confidence: 99%

Long-Range Correlations in Sentence Series from A Story of the Stone

Yang

2016

PLoS ONE

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A sentence is the natural unit of language. Patterns embedded in series of sentences can be used to model the formation and evolution of languages, and to solve practical problems such as evaluating linguistic ability. In this paper, we apply de-trended fluctuation analysis to detect long-range correlations embedded in sentence series from A Story of the Stone, one of the greatest masterpieces of Chinese literature. We identified a weak long-range correlation, with a Hurst exponent of 0.575±0.002 up to a scale of 104. We used the structural stability to confirm the behavior of the long-range correlation, and found that different parts of the series had almost identical Hurst exponents. We found that noisy records can lead to false results and conclusions, even if the noise covers a limited proportion of the total records (e.g., less than 1%). Thus, the structural stability test is an essential procedure for confirming the existence of long-range correlations, which has been widely neglected in previous studies. Furthermore, a combination of de-trended fluctuation analysis and diffusion entropy analysis demonstrated that the sentence series was generated by a fractional Brownian motion.

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“…The initial orbital elements of the planets are set to be those at the epoch of J2000 (JD 2451545.0), see Table A.2. in Murray & Dermott (2000).…”

Section: The Model Systemmentioning

confidence: 99%

Stability of exoplanetary systems retrieved from scalar time series

Kovács

2019

Monthly Notices of the Royal Astronomical Society

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We propose a novel method applied to extrasolar planetary dynamics to describe the system stability. The observations in this field serve the measurements mainly of radial velocity, transit time, and/or celestial position. These scalar time series are used to build up the high-dimensional phase space trajectory representing the dynamical evolution of planetary motion. The framework of nonlinear time series analysis and Poincaré recurrences allows us to transform the obtained univariate signals into complex networks whose topology carries the dynamical properties of the underlying system. The network-based analysis is able to distinguish the regular and chaotic behaviour not only for synthetic inputs but also for noisy and irregularly sampled real world observations. The proposed scheme does not require neither n-body integration nor best fitting planetary model to perform the stability investigation, therefore, the computation time can be reduced drastically compared to those of the standard numerical methods.

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Visibility graphlet approach to chaotic time series

Cited by 37 publications

References 53 publications

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

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

Long-Range Correlations in Sentence Series from A Story of the Stone

Stability of exoplanetary systems retrieved from scalar time series

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