Related papers: Zipf and Heaps laws from dependency structures in …
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.…
The heap is a basic data structure used in a wide variety of applications, including shortest path and minimum spanning tree algorithms. In this paper we explore the design space of comparison-based, amortized-efficient heap…
Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean.…
Conversation is a cornerstone of social connection and is linked to well-being outcomes. Conversations vary widely in type with some portion generating complex, dynamic stories. One approach to studying how conversations unfold in time is…
In this paper the Zipf-Mandelbrot law is revisited in the context of linguistics. Despite its widespread popularity the Zipf--Mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of…
Inverse power-law interaction forms, such as the inverse-square law, recur across a wide range of physical, social, and spatial systems. While traditionally derived from specific microscopic mechanisms, the ubiquity of these laws suggests a…
We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution p(k) of the elements k of a population can be approximated by the…
This paper studies the limits of language models' statistical learning in the context of Zipf's law. First, we demonstrate that Zipf-law token distribution emerges irrespective of the chosen tokenization. Second, we show that Zipf…
In physics we often use very simple models to describe systems with many degrees of freedom, but it is not clear why or how this success can be transferred to the more complex biological context. We consider models for the joint…
The prevailing maximum likelihood estimators for inferring power law models from rank-frequency data are biased. The source of this bias is an inappropriate likelihood function. The correct likelihood function is derived and shown to be…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
We perform a quantitative analysis of extensive chess databases and show that the frequencies of opening moves are distributed according to a power-law with an exponent that increases linearly with the game depth, whereas the pooled…
Power-law distributions with various exponents are studied. We first introduce a simple and generic model that reproduces Zipf's law. We can regard this model both as the time evolution of the population of cities and that of the asset…
Previous efforts in complex networks research focused mainly on the topological features of such networks, but now also encompass the dynamics. In this Letter we discuss the relationship between structure and dynamics, with an emphasis on…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
We study the relationship between vocabulary size and text length in a corpus of $75$ literary works in English, authored by six writers, distinguishing between the contributions of three grammatical classes (or ``tags,'' namely, {\it…
Symbolic sequences such as written language and genomic DNA display characteristic frequency distributions and long-range correlations extending over many symbols. In language, this takes the form of Zipf's law for word frequencies together…
Random matrix theory allows for the deduction of stability criteria for complex systems using only a summary knowledge of the statistics of the interactions between components. As such, results like the well-known elliptical law are…
Scientific cooperation on an international level has been well studied in the literature. However, much less is known about this cooperation on the intercontinental level. In this paper, we address this issue by creating a collection of…
When dealing with evolving or multi-dimensional complex systems, network theory provides with elegant ways of describing their constituting components, through respectively time-varying and multi-layer complex networks. Nevertheless, the…