Multifractal analysis of DNA walks and trails

Rosas, Alexandre; Nogueira, Eliane Maria de Souza; Fontanari, José F.

doi:10.1103/physreve.66.061906

Cited by 45 publications

(34 citation statements)

References 23 publications

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“…The generalization of the MF-DFA to two-or three-dimensional records is straightforward (Rosas et al 2002;Telesca et al 2007) as one needs only to change the basic equations (2.3) and (2.4), which are rewritten as a square fit of the series. Then, we determine the variance…”

Section: Methodsmentioning

confidence: 99%

Revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis: application to Bach's Sinfonias

Telesca

Lovallo²

2011

Proc. R. Soc. A.

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The one-, two-and three-dimensional multifractal detrended fluctuation analysis (MF-DFA) was applied to Bach's Sinfonias, which are characterized by the superposition of three different voices. Each voice, represented as a time series, can be considered as a component of a one-, two-or three-dimensional vector. The one-dimensional MF-DFA was applied to any single voice, while the two-and three-dimensional MF-DFA was applied to the couples of voices and to the triple, respectively. Each voice is characterized by a multifractal degree (MD), indicated by the range of the generalized Hurst exponents; the higher the MD, the larger the amount of heterogeneity and irregularity. Competitive scaling multifractal behaviours in Bach's Sinfonias were revealed; although one (or two) voices showed a relatively high MD, the other two voices, or voice, are characterized by a low MD. Nevertheless, the overall effect of the Sinfonia, measured by the MD of the triple, tends towards homogeneity, or at least to an average between the different competitive scaling behaviour shown by the different voices.

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Section: Methodsmentioning

confidence: 99%

Revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis: application to Bach's Sinfonias

Telesca

Lovallo²

2011

Proc. R. Soc. A.

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“…Multifractal structures were identified in systems from various areas such as physics [2][3][4][5], biology [6][7][8], chemistry [9,10], economics [11][12][13] and even music [14][15][16][17][18][19]. One of the most popular methods of the multifractal analysis is multifractal detrended correlation (MFDFA) [20][21][22] and cross-correlation analysis (MFCCA) [23,24].…”

Section: Methodsmentioning

confidence: 99%

Quantitative Characteristics of Correlations of Meteorological Data

Rak

Bwanakare

2016

Acta Phys. Pol. A

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This paper presents the quantitative characteristics of correlations (and cross-correlations) of plant main ecofactors i.e. the ground and over-ground temperature, the wind speed, and the humidity. The study is based upon hourly data statistical observations collected in the region of Lublin, in Poland for the period 2001.05. 07-2009.04.10. This paper indicates that plant growth conditions constitute an emergent response to the above direct eco-factors. Then, the dynamics properties of each eco-factor is first analyzed alone for its multifractal structure. We apply the multifractal detrended correlation analysis and multifractal detrended cross-correlation analysis. We show that the widest multifractal spectrum is for over-ground temperature and the strongest power-law cross-correlations exist between ground and over-ground temperature. Next, an impulse response analysis is carried out to measure dynamical inter causalities within all the considered variables. As far as cross-impact between different eco-variables is concerned, one observes that the wind speed, the ground temperature and the air humidity dynamics are the most influenced, in terms of memory length time, by external temperature.

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“…Existing algorithms used in such an analysis allow for determining generalized fractal dimensions or Hölder exponents based either on statistical properties of time series [9,10] or on time-frequency information [3,11]. Because of implementation simplicity and their utility, these algorithms have already been applied to characterize correlation structure of data in various areas of science like physics [12,13], biology [14][15][16], chemistry [17,18], geophysics [19,20], economics [21][22][23][24][25][26][27][28], hydrology [29], atmospheric physics [30], quantitative linguistics [31,32], music [33,34], and human communications [35]. As an important step towards quantifying complexity, in recent years algorithms designed for investigation of fractal cross-correlations were proposed [36,37] followed by the new statistical cross-correlation tests [38,39].…”

Section: Introductionmentioning

confidence: 99%

Detrended cross-correlation analysis consistently extended to multifractality

et al. 2014

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We propose an algorithm, multifractal cross-correlation analysis (MFCCA), which constitutes a consistent extension of the detrended cross-correlation analysis and is able to properly identify and quantify subtle characteristics of multifractal cross-correlations between two time series. Our motivation for introducing this algorithm is that the already existing methods, like multifractal extension, have at best serious limitations for most of the signals describing complex natural processes and often indicate multifractal cross-correlations when there are none. The principal component of the present extension is proper incorporation of the sign of fluctuations to their generalized moments. Furthermore, we present a broad analysis of the model fractal stochastic processes as well as of the real-world signals and show that MFCCA is a robust and selective tool at the same time and therefore allows for a reliable quantification of the cross-correlative structure of analyzed processes. In particular, it allows one to identify the boundaries of the multifractal scaling and to analyze a relation between the generalized Hurst exponent and the multifractal scaling parameter λ(q). This relation provides information about the character of potential multifractality in cross-correlations and thus enables a deeper insight into dynamics of the analyzed processes than allowed by any other related method available so far. By using examples of time series from the stock market, we show that financial fluctuations typically cross-correlate multifractally only for relatively large fluctuations, whereas small fluctuations remain mutually independent even at maximum of such cross-correlations. Finally, we indicate possible utility of MFCCA to study effects of the time-lagged cross-correlations.

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Multifractal analysis of DNA walks and trails

Cited by 45 publications

References 23 publications

Revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis: application to Bach's Sinfonias

Revealing competitive behaviours in music by means of the multifractal detrended fluctuation analysis: application to Bach's Sinfonias

Quantitative Characteristics of Correlations of Meteorological Data

Detrended cross-correlation analysis consistently extended to multifractality

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