In the paper we investigate power law for PageRank components for the Buckley-Osthus model for web graph. We compare different numerical methods for PageRank calculation. With the best method we do a lot of numerical experiments. These experiments confirm the hypothesis about power law. At the end we discuss real model of web-ranking based on the classical PageRank approach.

We study the dynamics of an intriguing crossover from a chaotic to a power-law state as a function of strain rate within the context of a recently introduced model that reproduces the crossover. While the chaotic regime has a small set of positive Lyapunov exponents, interestingly, the scaling regime has a power-law distribution of null exponents which also exhibits a power law. The slow-manifo...

A computational model of loose snow avalanches was studied as an example of Self-Organized Criticality (SOC). The distribution of the magnitudes of avalanches was measured for a stairstepped system with various critical relative differences and system slopes. Depending on the configuration, the model showed either power law behaviors or a Gaussian distribution. For configurations that displayed...

Empirical studies on the spatial structures in several real transport networks reveal that the distance distribution in these networks obeys power law. To discuss the influence of the power-law exponent on the network’s structure and function, a spatial network model is proposed. Based on a regular network and subject to a limited cost C, long range connections are added with power law distance...

Technological Innovation, Financial Fragility and Complex Dynamics In this paper we suggest a scaling approach to business cycles. We develop a heterogeneous interacting agents (HIAs) model that replicates well known industrial dynamics stylized facts, as the power law distribution of firms’ size and the Laplace distribution of firms’ growth rates. In particular, the power law is a persistent b...

Abstract. We report the results of extracting the hard X-ray continuum spectrum of Cas A SNR from RXTE/PCA Target of Opportunity observations (TOO) and CGRO/OSSE observations. The data can rule out the single thermal bremsstrahlung model for Cas A continuum between 2 and 150 keV. The single power law model gives a mediocre fit (∼5%) to the data with a power-law index, Γ = 2.94±0.02. A model wit...

Autoregressive conditional duration (ACD) processes, which have the potential to be applied to power law distributions of complex systems found in natural science, life science, and social science, are analyzed both numerically and theoretically. An ACD(1) process exhibits the singular second order moment, which suggests that its probability density function (PDF) has a power law tail. It is ve...

Email viruses constitute one of the major Internet security problems. In this paper we present an email virus model that accounts for the behaviors of email users, such as email checking frequency and the probability of opening an email attachment. Email viruses spread over a logical network defined by email address books. The topology of email network plays an important role in determining the...

The quadratic and power laws are two typical formulations that can be used to extend the Darcy law to non-Darcy flows through porous media. Both laws are reformulated in the dimensionless form in this study. They are then evaluated by fitting to experimental data with specified variations in seepage velocity, which were specifically collected for a simplified ordered porous model. The results s...

The Zipf power law and its connection with the inhomogeneity of the system is investigated. We describe the statistical distributions of the domain masses in the Potts model near the temperature-induced phase transition. We found that the statistical distribution near the critical point is described by the power law form with a long tail, while beyond the critical point the power law tail is su...