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It was observed that the number of cases and deaths for infectious diseases were associated with heavy-tailed power law distributions such as the Pareto distribution. While Pareto distribution was widely used to model the cases and deaths…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
In a recent paper by Cabrera et al (Chaos, Solitons and Fractals 2021 146 110876), a linearization of DRM differences equation, (Delayed Regulation Model), has been proposed as a scheme to explain transfer of energy through different scales…
The SI model is the most basic of all compartmental models used to describe the spreading of information through a population. Despite its apparent simplicity, the analytic solution of this model on networks is still lacking. We address…
As an alternative to the paradigmatic fragmentation problem of a single object crushed into a great number of pieces, we survey a large collection of identical bodies, each one randomly split into two fragments only. While some key features…
We propose a stochastic model of a fragmentation process, developed by taking into account fragment lifetime as a function of their size based on the Gibrat process. If lifetime is determined by a power function of fragment size, numerical…
Close examination of wealth distributions reveal the existence of two distinct power law regimes. The Pareto exponents of the super-rich, identified for example in rich lists such as provided by Forbes are smaller than the Pareto exponents…
Communicating using only a limited vocabulary is a common but challenging cognitive phenomenon, requiring an ideal communicator to plan carefully to optimize for intelligibility while circumventing a constrained lexicon. In this work, we…
Abstract Like electoral systems, decision-making methods are also vulnerable to manipulation by decision-makers. The ability to effectively defend against such threats can only come from thoroughly understanding the manipulation mechanisms.…
This paper introduces new methods based on exponential families for modeling the correlations between words in text and speech. While previous work assumed the effects of word co-occurrence statistics to be constant over a window of several…
We investigate statistical properties of trails formed by a random process incorporating aggregation, fragmentation, and diffusion. In this stochastic process, which takes place in one spatial dimension, two neighboring trails may combine…
Does a high dispersal rate provide a competitive advantage when risking competitive exclusion? To this day, the theoretical literature cannot answer this question in full generality. The present paper focuses on the simplest mathematical…
Many natural or human-made systems encompassing local reactions and diffusion processes exhibit spatially distributed patterns of some relevant dynamical variable. These interactions, through self-organization and critical phenomena, give…
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 aim of this work is to establish the personal income distribution from the elementary constituents of a free market; products of a representative good and agents forming the economic network. The economy is treated as a self-organized…
Word embeddings allow natural language processing systems to share statistical information across related words. These embeddings are typically based on distributional statistics, making it difficult for them to generalize to rare or unseen…
Power laws and distributions with heavy tails are common features of many experimentally studied complex systems, like the distribution of the sizes of earthquakes and solar flares, or the duration of neuronal avalanches in the brain.…
Taylors Law (TL) describes the scaling relationship between the mean and variance of populations as a power-law. TL is widely observed in ecological systems across space and time with exponents varying largely between 1 and 2. Many…
A dynamical model for the distribution of resources between competing agents is studied. While global competition leads to the accumulation of all the resources by a single agent, local competition allows for a wider resource distribution.…
Linear systems with many degrees of freedom containing multiplicative and additive noise are considered. The steady state probability distribution for equations of this kind is examined. With multiplicative white noise it is shown that…