Related papers: Zipf's and Taylor's Laws
Understanding the innovation process, that is the underlying mechanisms through which novelties emerge, diffuse and trigger further novelties is undoubtedly of fundamental importance in many areas (biology, linguistics, social science and…
Zipf's law states that sequential frequencies of words in a text correspond to a power function. Its probabilistic model is an infinite urn scheme with asymptotically power distribution. The exponent of this distribution must be estimated.…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
Records of the traded value f_i(t) of stocks display fluctuation scaling, a proportionality between the standard deviation sigma(i) and the average <f(i)>: sigma(i) ~ f(i)^alpha, with a strong time scale dependence alpha(dt). The…
Zipf's law of city-size distributions can be expressed by three types of mathematical models: one-parameter form, two-parameter form, and three-parameter form. The one-parameter and one of the two-parameter models are familiar to urban…
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq…
Background: Zipf's law and Heaps' law are two representatives of the scaling concepts, which play a significant role in the study of complexity science. The coexistence of the Zipf's law and the Heaps' law motivates different understandings…
In this paper we quantify the statistical properties and dynamics of the frequency of hashtag use on Twitter. Hashtags are special words used in social media to attract attention and to organize content. Looking at the collection of all…
Biological systems with many components often exhibit seemingly critical behaviors, characterized by atypically large correlated fluctuations. Yet the underlying causes remain unclear. Here we define and examine two types of criticality.…
We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts…
Statistical laws describe regular patterns observed in diverse scientific domains, ranging from the magnitude of earthquakes (Gutenberg-Richter law) and metabolic rates in organisms (Kleiber's law), to the frequency distribution of words in…
A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law. The same pow-like behavior is exhibited by some simple random citation models. The observed regularity indicates not so…
Natural languages are full of rules and exceptions. One of the most famous quantitative rules is Zipf's law which states that the frequency of occurrence of a word is approximately inversely proportional to its rank. Though this `law' of…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
History-dependent processes are ubiquitous in natural and social systems. Many such stochastic processes, especially those that are associated with complex systems, become more constrained as they unfold, meaning that their sample-space, or…
Taylor's law (TL), a power-law relationship between the mean and variance of a quantity, has been observed across diverse scientific disciplines. Despite its ubiquity, the underlying mechanisms responsible for TL are not yet fully…
Throughout history most young adults have chosen to live where their parents did while a smaller number moved away. This is sufficient, by proof and simulation, to account for the well-known power law distributions of city sizes. The model…
The structure of very complicated irregular "microscopic" (local) entropy fluctuations around a big separated "macroscopic" (global) fluctuation in the statistical equilibrium was studied in numerical experiments on a simple 2--freedom…
Stochastic equations constitute a major ingredient in many branches of science, from physics to biology and engineering. Not surprisingly, they appear in many quantitative studies of complex systems. In particular, this type of equation is…
It has been shown recently that a specific class of path-dependent stochastic processes, which reduce their sample space as they unfold, lead to exact scaling laws in frequency and rank distributions. Such Sample Space Reducing processes…