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Many complex systems are composed of disparate, interacting types of varying sizes: Species abundances in ecosystems, firm sizes in markets, city populations in countries, word counts in language, etc. A longstanding mystery of complex…
The analysis of financial markets using models inspired by statistical physics offers a fruitful approach to understand collective and extreme phenomena [3, 14, 15] In this paper, we present a study based on a 2D Ising network model where…
Single index financial market models cannot account for the empirically observed complex interactions between shares in a market. We describe a multi-share financial market model and compare characteristics of the volatility, that is the…
In this paper we quantify the statistical properties and dynamics of the frequency of hashtag use on Twitter. Hashtags are special words used in social media to attract attention and to organize content. Looking at the collection of all…
Here, we analyse the behaviour of the higher order standardised moments of financial time series when we truncate a large data set into smaller and smaller subsets, referred to below as time windows. We look at the effect of the economic…
We propose a stochastic model for the number of different words in a given database which incorporates the dependence on the database size and historical changes. The main feature of our model is the existence of two different classes of…
The spatial distribution of people exhibits clustering across a wide range of scales, from household ($\sim 10^{-2}$ km) to continental ($\sim 10^4$ km) scales. Empirical data indicates simple power-law scalings for the size distribution of…
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems and has been widely reported in a variety of natural language processing applications. However, the emergence of natural language…
Human language, the most powerful communication system in history, is closely associated with cognition. Written text is one of the fundamental manifestations of language, and the study of its universal regularities can give clues about how…
This paper studies the mechanisms, implications, and potential applications of the recently discovered class of Zero Determinant (ZD) strategies in iterated 2x2 games. These strategies were reported to successfully extort pure economic…
At the beginning of 2022, a simplistic word-guessing game took the world by storm and was further adapted to many languages beyond the original English version. In this paper, we examine the strategies of daily word-guessing game players…
The linearization of the meteorological equations around a specified reference state, usually applied in NWP to define the linear system of constant-coefficients semi-implicit schemes, is outlined as an unnecessarily restrictive approach…
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…
We introduce preferential behavior into the study on statistical mechanics of money circulation. The computer simulation results show that the preferential behavior can lead to power laws on distributions over both holding time and amount…
The article presents a new interpretation for Zipf-Mandelbrot's law in natural language which rests on two areas of information theory. Firstly, we construct a new class of grammar-based codes and, secondly, we investigate properties of…
We propose a new method (implemented in an R-program) to simulate long-range daily stock-price data. The program reproduces various stylized facts much better than various parametric models from the extended GARCH-family. In particular, the…
Complex natural and technological systems can be considered, on a coarse-grained level, as assemblies of elementary components: for example, genomes as sets of genes, or texts as sets of words. On one hand, the joint occurrence of…
We propose a new set of stylized facts quantifying the structure of financial markets. The key idea is to study the combined structure of both investment strategies and prices in order to open a qualitatively new level of understanding of…
Past work has established scaling laws that predict the performance of a neural language model (LM) as a function of its parameter count and the number of tokens it's trained on, enabling optimal allocation of a fixed compute budget. Are…
A money-based model for the power law distribution (PLD) of wealth in an economically interacting population is introduced. The basic feature of our model is concentrating on the capital movements and avoiding the complexity of micro…