Related papers: Maximal Diversity and Zipf's Law
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…
Diversity is a fundamental feature of ecosystems, even when the concept of ecosystem is extended to sociology or economics. Diversity can be intended as the count of different items, animals, or, more generally, interactions. There are two…
The binary many-step Markov chain with the step-like memory function is considered as a model for the analysis of rank distributions of words in stochastic symbolic dynamical systems. We prove that the envelope curve for this distribution…
This paper presents an extensive survey of regular distributions in natural and social sciences. The survey includes studies from a wide scope of academic disciplines, in order to create an inventory of the different mathematical functions…
By employing exhaustive lists of large firms in European countries, we show that the upper-tail of the distribution of firm size can be fitted with a power-law (Pareto-Zipf law), and that in this region the growth rate of each firm is…
We consider a system composed of a fixed number of particles with total energy smaller or equal to some prescribed value. The particles are non-interacting, indistinguishable and distributed over fixed number of energy levels. The energy…
The formation of sentences is a highly structured and history-dependent process. The probability of using a specific word in a sentence strongly depends on the 'history' of word-usage earlier in that sentence. We study a simple…
Tokenization is a fundamental step in natural language processing (NLP) and other sequence modeling domains, where the choice of vocabulary size significantly impacts model performance. Despite its importance, selecting an optimal…
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…
Zipf's law of abbreviation, namely the tendency of more frequent words to be shorter, has been viewed as a manifestation of compression, i.e. the minimization of the length of forms -- a universal principle of natural communication.…
We use the formalism of 'Maximum Principle of Shannon's Entropy' to derive the general power law distribution function, using what seems to be a reasonable physical assumption, namely, the demand of a constant mean "internal order"…
In this overview, we discuss the connections between the observations of critical dynamics in neuronal networks and the maximum entropy models that are often used as statistical models of neural activity, focusing in particular on the…
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 set of data with positive values follows a Pareto distribution if the log-log plot of value versus rank is approximately a straight line. A Pareto distribution satisfies Zipf's law if the log-log plot has a slope of -1. Since many types…
Background: Zipf's discovery that word frequency distributions obey a power law established parallels between biological and physical processes, and language, laying the groundwork for a complex systems perspective on human communication.…
We apply the Principle of Maximum Entropy to the study of a general class of deterministic fractal sets. The scaling laws peculiar to these objects are accounted for by means of a constraint concerning the average content of information in…
The length of coding sequence series in microbial genomes were regarded as a fluctuating system and characterized by the methods of statistical physics. The distribution and the correlatin properties of 50 genomes including bacteria and…
Entropy, under a variety of names, has long been used as a measure of diversity in ecology, as well as in genetics, economics and other fields. There is a spectrum of viewpoints on diversity, indexed by a real parameter q giving greater or…
We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in…
Zipf's law is well known in linguistics: the frequency of a word is inversely proportional to its rank. This is a special case of a more general power law, a common phenomenon in many kinds of real-world statistical data. Here, it is shown…