• Chaos, Fractals and non-linear studies
    In the mid 70’s when people were playing around with early versions of computers, a mathematician was plotting the results of an equation containing a complex number, in a reiterative manner. And to his surprise, the results were quite fascinating: the patterns that emerged were beautiful to look at; but more interestingly, when you zoom […] keyboard_arrow_right
  • Improved visibility graph – reducing the noise
    The key idea for improvement is based on the concept that each pattern and behavior in a fractal time series is repeated frequently in different scales. In a fractal time series in different scales shows similar patterns. That is a pattern in one small scale is expected to manifest in other larger scales with roughly […] keyboard_arrow_right
  • Multi-fractal Detrended Fluctuation Analysis
    Let us denote the input data series as $x(i)$ for $i = 1,2,\ldots,N$, with $N$ number of points. The mean values of this series is calculated as $\bar{x} = \frac{1}{N}\sum_{i=1}^{N} x(i)$. Then accumulated deviation series for $x(i)$ is calculated as per the below equation. \begin{eqnarray} X(i) \equiv \sum_{k=1}^{i} [x(k)-\bar{x}], i = 1,2,\ldots,N \nonumber \end{eqnarray} This […] keyboard_arrow_right
  • Multifractal Detrended Cross-correlation Analysis
    Zhao et al.[4] have introduced MF-DXA method based on the MF-DFA method[1],[2] and analysed the cross-correlation between two non-stationary series quantitatively. The steps for the MF-DXA method are as follows. Let $x(i)$ and $y(i)$ are two data series for $i = 1,2,\ldots,N$, of length $N$. The mean of these series is calculated as $\bar{x} = […] keyboard_arrow_right
  • Power of Scale-freeness of Visibility Graph
    1. Visibility Graph Algorithm Figure1. Visibility Graph for time series X Visibility Graph algorithm plots time series $X$ to its Visibility Graph. Lets assume the $i^th$ point of time series is $X_{i}$. In this graph two nodes or vertices($X_{m}$ and $X_{n}$) are supposed to be connected by a two-way edge if and only if the equation […] keyboard_arrow_right