Related papers: MetaZipf. (Re)producing knowledge about city size …
In this paper we combine statistical analysis of large text databases and simple stochastic models to explain the appearance of scaling laws in the statistics of word frequencies. Besides the sublinear scaling of the vocabulary size with…
We present a thermodynamic formulation for scale-invariant systems based on the principle of extreme information. We create an analogy between these systems and the well-known thermodynamics of gases and fluids, and study as a compelling…
In his pioneering research, G. K. Zipf observed that more frequent words tend to have more meanings, and showed that the number of meanings of a word grows as the square root of its frequency. He derived this relationship from two…
Urban development is shaped by historical, geographical, and economic factors, presenting challenges for planners in understanding urban form. This study models commute flows across multiple U.S. cities, uncovering consistent patterns in…
The moment analysis method and nuclear Zipf's law of fragment size distributions are reviewed to study nuclear disassembly. In this report, we present a compilation of both theoretical and experimental studies on moment analysis and Zipf…
Causal processes can give rise to distinctive distributions in the linguistic variables that they affect. Consequently, a secure understanding of a variable's distribution can hold a key to understanding the forces that have causally shaped…
In this commentary we discuss the validity of scaling laws and their relevance for understanding urban systems and helping policy makers. We show how the recent controversy about the scaling of CO2 transport-related emissions with…
In a language corpus, the probability that a word occurs $n$ times is often proportional to $1/n^2$. Assigning rank, $s$, to words according to their abundance, $\log s$ vs $\log n$ typically has a slope of minus one. That simple Zipf's law…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…
Urban morphology has presented significant intellectual challenges to mathematicians and physicists ever since the eighteenth century, when Euler first explored the famous Konigsberg bridges problem. Many important regularities and scaling…
Evidence is given for a systematic text-length dependence of the power-law index gamma of a single book. The estimated gamma values are consistent with a monotonic decrease from 2 to 1 with increasing length of a text. A direct connection…
The availability of large datasets requires an improved view on statistical laws in complex systems, such as Zipf's law of word frequencies, the Gutenberg-Richter law of earthquake magnitudes, or scale-free degree distribution in networks.…
We propose a dynamical toy model of agents which possess a quantity and have an interaction radius depending on the amount of the quantity. They exchange the quantity with agents existing within their interaction radii. It is shown in the…
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
The Zipf distribution is a probability distribution widely used by scientists from various disciplines due to its ubiquity. Some of these areas include linguistics, physics, genetics, and sociology, among others. In this paper, it is proved…
Pareto distributions, and power laws in general, have demonstrated to be very useful models to describe very different phenomena, from physics to finance. In recent years, the econophysical literature has proposed a large amount of papers…
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…
Understanding how size influences the internal characteristics of a system is a crucial concern across various fields. Concepts like scale invariance, universalities, and fractals are fundamental to this inquiry and find application in…
This qualification work studies methods of statistical analysis of global brands distributions and development process of information system which is represented by computer program. Algorithm of estimation of correspondance to distribution…