Allometric growth is found in many tagging systems online. That is, the number of new tags (T ) is a power law function of the active population (P ), or T ∼ P γ (γ 6= 1). According to previous studies, it is the heterogeneity in individual tagging behavior that gives rise to allometric growth. These studies consider the power-law distribution model with an exponent β, regarding 1/β as an index...

In discrete contexts such as the degree distribution for a graph, scale-free has traditionally been defined to be power-law. We propose a reasonable interpretation of scale-free, namely, invariance under the transformation of p-thinning, followed by conditioning on being positive. For each β ∈ (1, 2), we show that there is a unique distribution which is a fixed point of this transformation; the...

The paper deals with a Doubly Fed Induction Machine (DFIM). It presents a study of an active power distribution law between stator and rotor sides. The DFIM is supplied by two voltages PWM inverters in stator and rotor. The power distribution law imposes a relation between rotoric and statoric pulsations. Due to this relation, a new variation structure of the DFIM speed control is presented. Th...

In this paper, the influence of the constituent volume fractions by changing the values of the power-law exponent with uniform pressure on the vibration frequencies of reinforced functionally graded cylindrical shells is studied. The FGM shell with ring is developed in accordance to the volume fraction law from two constituents namely stainless steel and nickel. These constituents are graded th...

A study on the behavior of off-site AC power failure recovery times at three nuclear plant sites is presented. It is shown, that power law is appropriate for the representation of failure frequency-duration correlation function of off-site power failure events, based on simple assumptions about component failure and repair rates. It is also found that the annual maxima of power failure duration...

Tail estimates are developed for power law probability distributions with exponential tempering, using a conditional maximum likelihood approach based on the upper order statistics. Tempered power law distributions are intermediate between heavy power-law tails and Laplace or exponential tails, and are sometimes called “semiheavy” tailed distributions. The estimation method is demonstrated on s...

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...

In this paper, we are analyzing the interactivity time, defined as the duration between two consecutive tasks such as sending emails, collecting friends and followers and writing comments in online social networks (OSNs). The distributions of these times are heavy tailed and often described by a power-law distribution. However, powerlaw distributions usually only fit the heavy tail of empirical...

This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood estimation (MLE) is far more robust. Finally, it presents a new table for performing the Kolmogorov-Smirnof test for goodness-of-fit tailored to power-law distributi...

Recently, Mike and Farmer have constructed a very powerful and realistic behavioral model to mimick the dynamic process of stock price formation based on the empirical regularities of order placement and cancelation in a purely order-driven market, which can successfully reproduce the whole distribution of returns, not only the well-known power-law tails, together with several other important s...