Abstract A fundamental quantity in the calculation of rain attenuation statistics is the specific attenuation (attenuation per unit distance). The power-law form of rain specific attenuation is very convenient and is commonly used. It is expressed as α R k ⋅ , where k and α are the power-law parameters, and R is the rain rate in mm/h. Limited number of power-law parameters were available in the...

We propose new evolutionary stochastic models for the web graph and other massive networks, where edges are deleted over time and an edge is chosen to be deleted with probability inversely proportional to the in-degree of the destination. The degree distributions of graphs generated by our models follow a power law. A rigorous proof of power law degree distributions is given using martingales a...

The size distribution of neuronal avalanches in cortical networks has been reported to follow a power law distribution with exponent close to -1.5, which is a reflection of long-range spatial correlations in spontaneous neuronal activity. However, identifying power law scaling in empirical data can be difficult and sometimes controversial. In the present study, we tested the power law hypothesi...

Recently, I became interested in a current debate over whether file size distributions are best modelled by a power law distribution or a lognormal distribution. In trying to learn enough about these distributions to settle the question, I found a rich and long history, spanning many fields. Indeed, several recently proposed models from the computer science community have antecedents in work fr...

We introduce a family of robust design problems for complex systems in uncertain environments which are based on tradeoffs between resource allocations and losses. Optimized solutions yield the "robust, yet fragile" features of highly optimized tolerance and exhibit power law tails in the distributions of events for all but the special case of Shannon coding for data compression. In addition to...

We advocate the use of certain dimensionless metrics, depending on the ratio of RTT over distance, to measure the quality of Internet paths. We have analyzed several independent samples of Internet paths, finding that the statistical distributions of these metrics are quite simple and show power-law tails. Understanding the exponents of these tails is of special interest to model-building. We e...