Random populations represented by stochastically scattered collections of real-valued points are abundant across many fields of science. Fractality, in the context of random populations, is conventionally associated with a Paretian distribution of the population's values.

Properties of low-variability periods in the time series are analysed. The theoretical approach is used to show the relationship between the multi-scaling of low-variability periods and multi-affinity of the time series. It is shown that this technically simple method is capable of revealing...

We present a thermodynamic formulation for scale-invariant systems based on the minimization with constraints of the Fisher information measure. In such a way a clear analogy between these systems’ thermal properties and those of gases and fluids is seen to emerge in a natural fashion. We...

This paper performs a fractal analysis of the galaxy distribution and presents evidence that it can be described as a fractal system within the redshift range of the FORS Deep Field (FDF) galaxy survey data. The fractal dimension D was derived by means of the galaxy number densities calculated...

In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We investigated quantitatively the calm-time intervals of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index in the 27-year period from...

We present a universal mechanism for the temporal generation of power-law distributions with arbitrary integer-valued exponents.

The unique scaling behavior of financial time series have attracted the research interest of physicists. Variables such as stock returns, share volume, and number of trades have been found to display distributions that are consistent with a power-law tail. We present an overview of recent...

Since the seminal work of the Italian economist Vilfredo Pareto, the study of wealth and income has been a topic of active scientific exploration engaging researches ranging from economics and political science to econophysics and complex systems. This paper investigates the intrinsic fractality...

We introduce and study a stochastic growth–collapse model. The growth process is a steady random inflow with stationary, independent, and non-negative increments. Crashes occur according to an arbitrary renewal process, they are geometric, and their magnitudes are random and are governed by an...

We introduce and study an analytic model for physical systems exhibiting growth-collapse and decay-surge evolutionary patterns. We consider a generic system undergoing a smooth deterministic growth/decay evolution, which is occasionally interrupted by abrupt stochastic collapse/surge...