We present a generalized stochastic Cantor set by means of a simple cut and delete process and discuss the self-similar properties of the arising geometric structure. To increase the flexibility of the model, two free parameters, m and b, are introduced which tune the relative strength of the...

Using functional equations with self-similar properties, we have derived the exact analytical result for convolution of a smooth function with the normalized density of the Cantor set in the limit N→∞. We have proved that the self-similar kernel of this convolution cannot be reduced...

In this paper we address the problem of forecasting the target events of a time series given the distribution ξ of time gaps between target events. Strong earthquakes and stock market crashes are the two types of such events that we are focusing on. In the series of earthquakes, as McCann...

A measure of the correlation between two earthquakes is used to link events to their aftershocks, generating a growing network structure. In this framework one can quantify whether an aftershock is close or far, from main shocks of all magnitudes. We find that simple network motifs involving...

The Hurst exponent of very long birth time series in Romania has been extracted from official daily records, i.e. over 97 years between 1905 and 2001 included. The series result from distinguishing between families located in urban (U) or rural (R) areas, and belonging (Ox) or not (NOx) to the...

We present the results of an experiment with light microscopy performed to capture the trajectories of live Nitzschia sp. diatoms. The time series corresponding to the motility of this kind of cells along ninety-five circular-like trajectories have been obtained and analyzed with the scaling...

Long birth time series for Romania are investigated from Benford’s law point of view, distinguishing between families with a religious (Orthodox and Non-Orthodox) affiliation. The data extend from Jan. 01, 1905 till Dec. 31, 2001, i.e. over 97 years or 35 429 days. The results point to a...

This study aims to enhance the understanding of logarithmic asset returns. In particular, more emphasis is given to the long memory property of financial returns, a well documented stylized fact. However, in the presence of structural breaks other studies suggest that statistical tools such as...

This study introduces an approach to study the multiscale transmission characteristics of the correlation modes between bivariate time series. The correlation between the bivariate time series fluctuates over time. The transmission among the correlation modes exhibits a multiscale phenomenon,...

The objective of this paper is to demonstrate the influence of the blue-chips companies in the stock market. In this, we apply the detrended cross-correlation coefficient ρDCCA at the São Paulo stock market (Ibovespa, Brazil). Initially we found that there is a positive cross-correlation...