A new concept, called the row-column visibility graph, is proposed to map two-dimensional landscapes to complex networks. A cluster coverage is introduced to describe the extensive property of node clusters on a Euclidean lattice. Graphs mapped from fractals generated with the probability redistribution model behave scale-free. They have pattern-induced hierarchical organizations and comparatively much more extensive structures. The scale-free exponent has a negative correlation with the Hurst exponent, however, there is no deterministic relation between them. Graphs for fractals generated with the midpoint displacement model are exponential networks. When the Hurst exponent is large enough （e.g., H 〉 0.5）, the degree distribution decays much more slowly, the average coverage becomes significant large, and the initially hierarchical structure at H 〈 0.5 is destroyed completely. Hence, the row-column visibility graph can be used to detect the pattern-related new characteristics of two-dimensional landscapes.
We investigate the impact of financial factors on daily volume recurrent time intervals in the developing Chinese stock markets. The tails of probability distribution functions（PDFs） of volume recurrent intervals behave as a power-law, and the scaling exponent decreases with the increase of stock lifetime, which are similar to those in the US stock markets, and they are typical representatives of developed markets. The difference is that the power-law exponent values remain almost the same with the changes of market capitalization, mean volume, and mean trading value, respectively. These findings enrich the results for event statistics for financial markets.
Adaption of circadian rhythms in behavioral and physiological activities to the external light–dark cycle is achieved through the main clock, i.e., the suprachiasmatic nucleus(SCN) of the brain in mammals. It has been found that the SCN neurons differ in the amplitude relaxation rate, which represents the rigidity of the neurons to the external amplitude disturbance. Thus far, the appearance of that difference has not been explained. In the present study, an alternative explanation based on the Poincare′ model is given which takes into account the effect of the difference in the entrainment range of the SCN. Both our simulation results and theoretical analyses show that the largest entrainment range is obtained with suitable difference in the case that only a part of SCN neurons are sensitive to the light information. Our findings may give an alternative explanation for the appearance of that difference(heterogeneity) and shed light on the effects of the heterogeneity in the neuronal properties on the collective behaviors of the SCN neurons.
