Usual techniques for electroencephalographic (EEG) data analysis lack some of the important properties essential for quantitative assessment of the progress of the dysfunction of the human brain. EEG data are essentially nonlinear and this nonlinear time series has been identified as multi-fractal in nature. We need rigorous techniques for such analysis. In this article, we present the visibility graph as the latest, rigorous technique that can assess the degree of multifractality accurately and reliably. Moreover, it has also been found that this technique can give reliable results with test data of comparatively short length. In this work, the visibility graph algorithm has been used for mapping a time series-EEG signals-to a graph to study complexity and fractality of the time series through investigation of its complexity. The power of scale-freeness of visibility graph has been used as an effective method for measuring fractality in the EEG signal. The scale-freeness of the visibility graph has also been observed after averaging the statistically independent samples of the signal. Scale-freeness of the visibility graph has been calculated for 5 sets of EEG data patterns varying from normal eye closed to epileptic. The change in the values is analyzed further, and it has been observed that it reduces uniformly from normal eye closed to epileptic.
Multiplicity fluctuation provides enough information concerning the dynamics of particle production process and even signature of phase transition from hadronic to QGP phase expected in ultrarelativistic nuclear collision. Numerous analyses reported on the fluctuation pattern of pions have been studied from theoretical and phenomenological approaches. Also the fractal properties have been explored to characterize quantitative degree of fluctuation. The present work reports a study of pion fluctuation from a radically different perspective, using science of complexity. For this we have taken two different interactions — one hadron–nucleus and other nucleus–nucleus, namely [Formula: see text]-AgBr (350 GeV) and [Formula: see text]S-AgBr (200 A[Formula: see text]GeV). We have analyzed both data in the light of complex network analysis, viz. visibility graph method. The data reveal that power of the scale-freeness in visibility graph (PSVG), a quantitative parameter related to Hurst exponent, may provide information on the degree of fluctuation. Further, in a recent work, it was shown that phase transition can also be studied using the same methodology. Based on the result of the present study we further propose to use this methodology, where critical phenomena are to be assessed — even in case of pion fluctuation, for obtaining the QGP like phase transition.
Chaos and complex-network based study is performed to look for signature of phase transition in Pb-Pb collision data sample at 2.76T eV per nucleon pair from ALICE Collaboration. The analysis is done on the pseudorapidity(η) values extracted from the data of AL-ICE experiment and the methods used are Multifractal-Detrended-Fluctuation-Analysis(MF-DFA), and a rigorous chaos-based, complex-network based method -Visibility-Graph(VG) analysis.The fractal behavior of pionisation process is studied by utilizing MF-DFA method for extracting the Hurst exponent and Multifractal-spectrum-width to analyze the scale-freeness and fractality inherent in the fluctuation pattern of η. Then VG method is used to analyze the fluctuation from a completely different perspective of complex network. This algorithm's scale-freeness detection mechanism to extract the Power-of-Scale-freeness-of-Visibility-Graph(PSVG), re-establishes the scale-freeness and fractality. Earlier, it has been shown that the scaling behavior is different from one hadron-nucleus(π − -AgBr(350 GeV)) to one nucleus-nucleus( 32 S-AgBr(200 A GeV)) interaction which is of comparatively higher total energy [1]. In this work, we have compared the fluctuation pattern in terms of 3 rigorous parameters -Multifractalspectrum-width, Hurst exponent and PSVG, between Pb-Pb(2.76T eV per nucleon pair) data and either of π − -AgBr(350 GeV) or 32 S-AgBr(200 A GeV) data, where both the interaction data are of significantly less energy than the ALICE data. We found that the values of the 3 parameters are substantially different for ALICE data compared to the other two interaction data. As remarkably different value of long-range-correlation indicates phase-transition, similar change in the fluctuation pattern in terms of these parameters can be attributed to a phase-transition and also the onset of QGP.
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