We present the modification of natural visibility graph (NVG) algorithm used for the mapping of the time series to the complex networks (graphs). We propose the parametric natural visibility graph (PNVG) algorithm. The PNVG consists of NVG links, which satisfy an additional constraint determined by a newly introduced continuous parameter -the view angle. The alteration of view angle modifies the PNVG and its properties such as the average node degree, average link length of the graph as well as cluster quantity of built graph etc. We calculated and analyzed different PNVG properties depending on the view angle for different types of the time series such as the random (uncorrelated, correlated and fractal) and cardiac rhythm time series for healthy and ill patients. Investigation of different PNVG properties shows that the view angle gives a new approach to characterize the structure of the time series that are invisible in the conventional version of the algorithm. It is also shown that the PNVG approach allows to distinguish, identify and describe in detail various time series.
We investigate time series by mapping them to the complex networks using a parametric natural visibility graph (PNVG) algorithm that generates graphs depending on arbitrary continuous parameter-the angle of view. We study the behavior of the relative number of clusters in PNVG near the critical value of the angle of view. Artificial and experimental time series of different nature are used for numerical PNVG investigations to find critical exponents above and below the critical point as well as the exponent in the finite size scaling regime. Altogether, they allow us to find the critical exponent of the correlation length for PNVG. The set of calculated critical exponents satisfies the basic Widom relation. The PNVG is found to demonstrate scaling behavior. Our results reveal the similarity between the behavior of the relative number of clusters in PNVG and the order parameter in the second-order phase transitions theory. We show that the PNVG is another example of a system (in addition to magnetic, percolation, superconductivity, etc.) with observed second-order phase transition.
We consider the effective properties of composite structure that includes nanocontacts between macrocrystallits of bulk material. The model of a such nanostructured composite is developed. In the mean-field approximation we calculate effective values of the thermopower, heat -and the electrical conductivity, thermoelectric figure of merit.
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