We investigate equilibrium statistical properties of a disordered urn model. New types of urn models are proposed, in which quenched disorder parameters play an important role in generating power-law behavior. We evaluate the occupation probability P (k) with which an urn has k balls by using the concept of statistical physics of disordered systems. In our new disordered urn model, we find that...

On-line communities offer a great opportunity to investigate human dynamics, because much information about individuals is registered in databases. In this paper, based on data statistics of online comments on Blog posts, we first present an empirical study of a comment arrival-time interval distribution. We find that people interested in some subjects gradually disappear and the interval distr...

Models based on a power law are prevalent in many areas of study. When regression analysis is performed on data sets modeled by a power law, the traditional model uses a lead coefficient. However, the proposed model replaces the lead coefficient with a scaling parameter and reduces uncertainties in best-fit parameters for data sets with exponents close to 3. This study extends previous work by ...

Many populations live in environments subject to frequent biotic and abiotic changes. Nonetheless, it is interesting to ask whether an evolving population's mean fitness can increase indefinitely, and potentially without any limit, even in a constant environment. A recent study showed that fitness trajectories of Escherichia coli populations over 50 000 generations were better described by a po...

Portfolio optimization methods suffer from a catalogue of known problems, mainly due to the facts that pair correlations asset returns are unstable, and extremal risk measures such as maximum drawdown difficult predict non-Gaussianity portfolio returns. \\ In order look at optimal portfolios for arbitrary penalty functions, we construct shapes where is proportional moment $p>2$. The resulting c...

We propose a new model of the steep power law state of luminous black hole X-ray binaries. The model uses the fact that at high luminosities, radiation pressure dominated accretion discs become effectively optically thin. The gas temperature therefore rises sharply inwards, producing local saturated Compton spectra with rapidly increasing peak energy. These spectra sum together to form a steep ...

Sudden failure of a single transmission element in a power grid can induce a domino effect of cascading failures, which can lead to the isolation of a large number of consumers or even to the failure of the entire grid. Here we present results of the simulation of cascading failures in power grids, using an alternating current (AC) model. We first apply this model to a regular square grid topol...

Many empirically studied networks have approximately so-called power-law or scale-free degree distributions. In Section 1 we formally define such distributions and explore some of their properties. We also introduce and briefly compare two methods for constructing random networks with approximately power-law degree distributions: generic scale-free networks and the preferential attachment model...

The power law wave equation uses two different fractional derivative terms to model wave propagation with power law attenuation. This equation averages complex nonlinear dynamics into a convenient, tractable form with an explicit analytical solution. This paper develops a random walk model to explain the appearance and meaning of the fractional derivative terms in that equation, and discusses a...