Power-law distributions are essential in computational and statistical investigations of extreme events complex systems. The usual technique to generate power-law distributed data is first infer the scale exponent $\alpha$ using observed interest then sample from associated distribution. This approach has important limitations because it relies on a fixed (e.g., limited applicability testing {\...

We study a q-difference equation of a BCn type Jackson integral, which is a multiple q-series generalized from a q-analogue of Selberg’s integral. The equation is characterized by some new symmetric polynomials defined via the symplectic Schur functions. As an application of it, we give another proof of a product formula for the BCn type Jackson integral, which is equivalent to the so-called q-...

Many communication and social networks have power-law link distributions, containing a few nodes that have a very high degree and many with low degree. The high connectivity nodes play the important role of hubs in communication and networking, a fact that can be exploited when designing efficient search algorithms. We introduce a number of local search strategies that utilize high degree nodes...

A simple adjustment to parametric failure-time distributions, which allows for much greater flexibility in the shape of the hazard-rate function, is considered. Closed-form expressions for the distributions of the power-law adjusted Weibull, gamma, log-gamma, generalized gamma, lognormal and Pareto distributions are given. Most of these allow for bathtub shaped and other multi-modal forms of th...

In the practical work of websites popularization, analysis of their efficiency and downloading it is of key importance to take into account web-ratings data. The main indicators of website traffic include the number of unique hosts from which the analyzed website was addressed and the number of granted web pages (hits) per unit time (for example, day, month or year). As one of the hundreds of r...

We report the results of 1D particle-in-cell simulations of ultrarelativistic shock waves in proton-electron-positron plasmas. We consider magnetized shock waves, in which the upstream medium carries a large scale magnetic field, directed transverse to the flow. Relativistic cyclotron instability of each species as the incoming particles encounter the increasing magnetic field within the shock ...