Power-law distributions have been observed in a wide variety of areas. To our knowledge however, there has been no systematic observation of power-law distributions in chemoinformatics. Here, we present several examples of power-law distributions arising from the features of small, organic molecules. The distributions of rigid segments and ring systems, the distributions of molecular paths and ...

BACKGROUND Despite the common experience that interrupted sleep has a negative impact on waking function, the features of human sleep-wake architecture that best distinguish sleep continuity versus fragmentation remain elusive. In this regard, there is growing interest in characterizing sleep architecture using models of the temporal dynamics of sleep-wake stage transitions. In humans and other...

Weblog is the fourth way of network exchange after Email, BBS and MSN. Most bloggers begin to write blogs with great interest, and then their interests gradually achieve a balance with the passage of time. In order to describe the phenomenon that people’s interest in something gradually decreases until it reaches a balance, we first propose the model that describes the attenuation of interest a...

Aaron Clauset, 2 Cosma Rohilla Shalizi, and M. E. J. Newman Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA Department of Computer Science, University of New Mexico, Albuquerque, NM 87131, USA Department of Statistics, Carnegie Mellon University, Pittsburgh, PA 15213, USA Department of Physics and Center for the Study of Complex Systems, University of Michigan, Ann Arbor, MI 48...

When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf’s law or the Pareto distribution. Power laws appear widely in physics, biology, earth and planetary sciences, economics and finance, computer science, demography and the social sciences. For instance, the distri...

Tail estimates are developed for power law probability distributions with exponential tempering using a conditional maximum likelihood approach based on the upper order statistics. The method is demonstrated on simulated data from a tempered stable distribution, and for several data sets from geophysics and finance that show a power law probability tail with some tempering.

Motivated by the fact that many physical systems display (i) power-law correlations together with (ii) an asymmetry in the probability distribution, we propose a stochastic process that can model both properties. The process depends on only two parameters, where one controls the scaling exponent of the power-law correlations, and the other controls the degree of asymmetry in the distributions l...

Understanding the properties of response time distributions is a long-standing problem in cognitive science. We provide a tutorial overview of several contemporary models that assume power law scaling is a plausible description of the skewed heavy tails that are typically expressed in response time distributions. We discuss several properties and markers of these distribution functions that hav...

We establish an explicit correspondence between ergodicity breaking in a system described by power-law tail distributions and the divergence of the moments of these distributions.

Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty ...