Related papers: Competition and fragmentation: a simple model gene…
Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization,…
Natural language data follows a power-law distribution, with most knowledge and skills appearing at very low frequency. While a common intuition suggests that reweighting or curating data towards a uniform distribution may help models…
Similar to biological evolution and speciation we define a language through a string of 8 or 16 bits. The parent gives its language to its children, apart from a random mutation from zero to one or from one to zero; initially all bits are…
This paper presents the results of the application of a bit-string model of languages (Schulze and Stauffer 2005) to problems of taxonomic patterns. The questions addressed include the following: (1) Which parameters are minimally ne eded…
We construct a model of wealth distribution, based on an interactive multiplicative stochastic process on static complex networks. Through numerical simulations we show that a decrease in the number of links discourages equality in wealth…
The upper tail of a claim size distribution of a property line of business is frequently modelled by Pareto distribution. However, the upper tail does not need to be Pareto distributed, extraordinary shapes are possible. Here, the…
Given the rapidly evolving landscape of linguistic prevalence, whereby a majority of the world's existing languages are dying out in favor of the adoption of a comparatively fewer set of languages, the factors behind this phenomenon has…
Statistical studies of languages have focused on the rank-frequency distribution of words. Instead, we introduce here a measure of how word ranks change in time and call this distribution \emph{rank diversity}. We calculate this diversity…
The time evolution of Earth with her cities, languages and countries is considered in terms of the multiplicative noise and the fragmentation- processes, where the related families, size distributions, lifetimes, bilinguals, etc. are…
We introduce a simple model of economy, where the time evolution is described by an equation capturing both exchange between individuals and random speculative trading, in such a way that the fundamental symmetry of the economy under an…
Many-body stochastic processes with weighted multiplicative interactions are investigated analytically and numerically. An interaction rate between particles with quantities $x, y$ is controlled by a homogeneous symmetric kernel $K(x, y)…
We show that an economic system populated by multiple agents generates an equilibrium distribution in the form of multiple scaling laws of conditional PDFs, which are sufficient for characterizing the probability distribution. The existence…
This paper revisits Menzerath's Law, also known as the Menzerath-Altmann Law, which models a relationship between the length of a linguistic construct and the average length of its constituents. Recent findings indicate that simple…
A dynamic model of the social relations between workers and capitalists is introduced. The model is deduced from the assumption that the law of value is an organising principle of modern economies. The model self-organises into a dynamic…
We present a minimum hypothesis model for an IMF that resembles a lognormal distribution at low masses but has a distinct power-law tail. Even if the central limit theorem ensures a lognormal distribution of condensation masses at birth, a…
Large Language Models (LLMs), such as GPT, are considered to learn the latent distributions within large-scale web-crawl datasets and accomplish natural language processing (NLP) tasks by predicting the next token. However, this mechanism…
Multiplicative random processes in (not necessaryly equilibrium or steady state) stochastic systems with many degrees of freedom lead to Boltzmann distributions when the dynamics is expressed in terms of the logarithm of the normalized…
Can one hear the 'sound' of a growing network? We address the problem of recognizing the topology of evolving biological or social networks. Starting from percolation theory, we analytically prove a linear inverse relationship between two…
The distribution of living languages is investigated and scaling relations are found for the diversity of languages as a function of the country area and population. These results are compared with data from Ecology and from computer…
Heavy-tailed distributions of meme popularity occur naturally in a model of meme diffusion on social networks. Competition between multiple memes for the limited resource of user attention is identified as the mechanism that poises the…