In this study, synchronization observed in dynamical oscillatory networks with non-uniform coupling distributions is investigated. The coupling states (on/off) of all connections are stochastically determined at every certain time with the coupling probability. We focus on the heavy tail type of coupling distribution for the network. By using computer simulations, we confirm that the dynamical ...

We analyze the effect of disorder and notches on crack roughness in two dimensions. Our simulation results based on large system sizes and extensive statistical sampling indicate that the crack surface exhibits a universal local roughness of zeta(loc)=0.71 and is independent of the initial notch size and disorder in breaking thresholds. The global roughness exponent scales as zeta=0.87 and is a...

We present a simple explanation for the occurrence of power-law tails in statistical distributions by showing that if stochastic processes with exponential growth in expectation are killed (or observed) randomly, the distribution of the killed or observed state exhibits power-law behavior in one or both tails. This simple mechanism can explain power-law tails in the distributions of the sizes o...

In this paper, we study the fluctuations of sums of random variables with distribution defined as a mixture of light-tail and truncated heavy-tail distributions. We focus on the case when both the mixing coefficient and the truncation level depend on the number of summands. The aim of this research is to characterize the limiting distributions of the sums due to various relations between these ...

In many practical situations, we encounter Gaussian distributions, for which the distribution tails are light – in the sense that as the value increases, the corresponding probability density tends to 0 very fast. There are many theoretical explanations for the Gaussian distributions and for similar light-tail distributions. In practice, however, we often encounter heavy-tailed distributions, i...

Recent research in queuing focuses more on the impacts of heavy-tailed service times, neglecting the fact that stochastic inter-arrival times are often heavy-tailed as well. We investigate the impacts of heavy-tailed gamma inter-arrival time distributions on the waiting-time distribution of a GI/G/2 queue, and simulate the tail properties of waiting-time distribution using real data.

This paper suggests a simple method of deriving nonparametric lower bounds of the accuracy of statistical inference on heavy-tailed distributions. We present lower bounds of the mean squared error of the tail index, the tail constant, and extreme quantiles estimators. The results show that the normalizing sequences of robust estimators must depend in a specific way on the tail index and the tai...

Many complex networks in natural and social phenomena have often been characterized by heavy-tailed degree distributions. However, due to rapidly growing size of network data and concerns on privacy issues about using these data, it becomes more difficult to analyze complete data sets. Thus, it is crucial to devise effective and efficient estimation methods for heavy tails of degree distributio...

By exploiting an infinite-server-model lower bound, we show that the tails of the steadystate and transient waiting-time distributions in the M/GI/s queue with unlimited waiting room and the first-come first-served discipline are bounded below by tails of Poisson distributions. As a consequence, the tail of the steady-state waiting-time distribution is bounded below by a constant times the sth ...