Related papers: Fine structure and complex exponents in power law …

Since the analogy between laser oscillation and second-order phase transition was indicated in the 1970s, dynamical fluctuations on lasing threshold inherent in critical phenomena have gained significant interest. Here, we numerically and…

Sequential likelihood ratio testing is found to be most powerful in sequential studies with early stopping rules when grouped data come from the one-parameter exponential family. First, to obtain this elusive result, the probability measure…

The use of statistical methods for the description of complex quantum systems was primarily motivated by the failure of a line-by-line interpretation of atomic spectra. Such methods reveal regularities and trends in the distributions of…

We investigate the dynamic scaling properties of stochastic particle systems on a non-deterministic scale-free network. It has been known that the dynamic scaling behavior depends on the degree distribution exponent of the underlying…

The spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…

The presence of the power-law memory is a significant feature of many natural (biological, physical, etc.) and social systems. Continuous and discrete fractional calculus is the instrument to describe the behavior of systems with the…

Strong frequency dependence is unlikely in diffusive or over-damped systems. When exceptions do occur, such as in the case of stochastic resonance, it signals an interesting underlying phenomenon. We find that such a case appears in the…

The full family of discrete logistic maps has been widely studied both as a canonical example of the period-doubling route to chaos, and as a model of natural processes. In this paper we present a study of the stochastic process described…

We study fractal properties of systems of densely and randomly packed disks, obeying a power-law distribution of radii, which is generated by using various protocols: Delaunay triangulation (DT) and constant pressure (CP) protocols, and the…

Hierarchical models of scale free networks are introduced where numbers of nodes in clusters of a given hierarchy are stochastic variables. Our models show periodic oscillations of degree distribution P(k) in the log-log scale. Periods and…

The prime numbers have been a source of fascination for millenia and continue to surprise us. Motivated by the hyperuniformity concept, which has attracted recent attention in physics and materials science, we show that the prime numbers in…

Unlike the well-studied models of growing networks, where the dominant dynamics consist of insertions of new nodes and connections, and rewiring of existing links, we study {\em ad hoc} networks, where one also has to contend with rapid and…

The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…

Dielectric relaxation in disordered dielectric mixtures are presented by emphasizing the interfacial polarization. The obtained results coincide with and cause confusion with those of the low frequency dispersion behavior. The considered…

Power-law distributions are widely recognized in complex systems physics as indicative of underlying complexity in interaction networks and critical macroscopic behavior. Previous studies, notably those of Newman and others, have emphasized…

Simulations are reported on the Ising two-dimensional ferromagnet in the presence of a special kind of noise. The noise spectrum P(n) follows a power law, where P(n) is the probability of flipping randomly selected n spins at each timestep.…

The turbulent dynamics of nearby and extragalactic gas structures can be studied with the column density power spectrum, which is often described by a broken power-law.In an extragalactic context, the breaks in the power spectra have been…

[Takayasu et al., Phys. Rev.Lett. 79, 966 (1997)] revisited the question of stochastic processes with multiplicative noise, which have been studied in several different contexts over the past decades. We focus on the regime, found for a…

Turbulence is ubiquitous in plasmas, leading to rich dynamics characterized by irregularity, irreversibility, energy fluctuations across many scales, and energy transfer across many scales. Another fundamental and generic feature of…

It was experimentally observed that the majority of real-world networks follow power law degree distribution. The aim of this paper is to study the algorithmic complexity of such "typical" networks. The contribution of this work is twofold.…