A theoretical and experimental study of the fragmentation of closed thin shells made of a disordered brittle material is presented. Experiments were performed on eggshells under two different loading conditions: fragmentation due to an impact with a hard wall and explosion by a combustion mixture giving rise to power law fragment size distributions. For the theoretical investigations a three-di...

Objective. To ascertain the existence of power-law distributions of inter-spike intervals (ISI) occurring during the progression of status epilepticus (SE), so that the emergence of critical states could be reasonably hypothesized as being part of the intrinsic nature of the SE. Methods. Status epilepticus was induced by pilocarpine administration in post-natal 21-day rats (n=8). For each anima...

The existence of power law distributions (also known as heavy-tailed distributions) in various natural and man-made scenarios has been demonstrated empirically over the years [6], and attracted a great deal of interest, resulting in models that would naturally predict such distributions. The areas in which power laws have been observed are very diverse, as evidenced by the following, not nearly...

The paper is written with the assumption that the purpose of a mathematical theory of citation is to explain bibliometric regularities at the level of mathematical formalism. A mathematical formalism is proposed for the appearance of power law distributions in social citation systems. The principal contributions of this paper are an axiomatic characterization of citation distributions in terms ...

Empirical studies on many social issues show that numerous statistical distributions follow power laws, such as stock-price fluctuations, the probability distribution of the population of cities, the degree distributions in many networks and distribution of income or wealth. In particular, the wealth distribution which is an old topic has recently been renewed by a small band of econophysicists...

We investigate scaling properties of human brain functional networks in the resting-state. Analyzing network degree distributions, we statistically test whether their tails scale as power-law or not. Initial studies, based on least-squares fitting, were shown to be inadequate for precise estimation of power-law distributions. Subsequently, methods based on maximum-likelihood estimators have bee...

Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits q-exponential or power law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele-Shaw flow as simulated by the Lattice Boltzmann method and find similar behavior from the analysis of velocity field measurements. For the trans...

Until now we have focused on “typical” outcomes for a random walk in the “central region” of the probability distribution, which contains all of its weight as the number of steps N tends to ∞. For any finite N , now matter how large, however, there is always some chance of finding the random walk outside the central region. Such “extreme events” are not controlled by the Central Limit Theorem, ...

It is sometimes claimed that different types of size data in biology follow a power law. Here, a formal statistical test of the power law for discrete size data is described. The test is based on embedding the power law in the nonparametric family of distributions for which frequency is nonincreasing with size. A parametric bootstrap is used to assess significance. The test is applied to four d...

In this paper the web is analyzed as a graph aggregated by host and pay-level domain (PLD). The web graph datasets, publicly available, have been released by the Common Crawl Foundation 1 and are based on a web crawl performed during the period May-June-July 2017. The host graph has ∼1.3 billion nodes and ∼5.3 billion arcs. The PLD graph has ∼91 million nodes and ∼1.1 billion arcs. We study the...