A stochastic model for the evolution of a growing population is proposed, in order to explain empirical power-law distributions in the frequency of family names as a function of the family size. Preliminary results show that the predicted exponents are in good agreement with real data. The...

In this paper, we looked for evidence of log-periodicity in recent US corporate bond spreads.

A model of the self-similar process of relaxation is given, and a method of derivation of the kinetic equations for the total polarization based on the ideas of fractional kinetics is suggested. The derived kinetic equations contain integro-differential operators having non-integer order. They...

Log-periodic oscillations have been used to predict price trends and crashes on financial markets. So far two types of log-periodic oscillations have been associated with the real markets. The first type oscillations accompany a rising market and end in a crash. The second type oscillations,...

Escape rate in the low-to-intermediate damping connecting the low damping with the intermediate damping is established for the power-law distribution on the basis of flux over population theory. We extend the escape rate in the low damping to the low-to-intermediate damping, and get an...

We examine whether the principle of detailed balance holds for the power-law distributions that are generated from the well-known two-variable Langevin equation and the associated Fokker–Planck equations. With the detailed balance and the generalized fluctuation–dissipation relation, we...

Escort distributions are a well established but (for physicists) a relatively new concept that is rapidly gaining wide acceptance in world. In this work we wish to revisit the concept within the strictures of the celebrated semiclassical Husimi distributions (HDs) and thereby investigate the...

We study a large social network consisting of over 106 individuals, who form an Internet community and organize themselves in groups of different sizes. On the basis of the users’ list of friends and other data registered in the database we investigate the structure and time development of the...

We show that the tenure lengths for managers of sport teams follow a power law distribution with an exponent between 2 and 3. We develop a simple theoretical model which replicates this result. The model demonstrates that the empirical phenomenon can be understood as the macroscopic outcome of...

The collision theory for power-law distributions and the generalized reaction rate coefficient are studied when reactions take place in nonequilibrium systems with power-law distributions. We obtain the power-law reaction rate coefficient, and by numerical analyses we show a very strong...