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Large language models generate text through probabilistic sampling from high-dimensional distributions, yet how this process reshapes the structural statistical organization of language remains incompletely characterized. Here we show that…

Presented is an analytic microeconomic model of the temporal price dispersion of homogeneous goods in polypoly markets. This new approach is based on the idea that the price dispersion has its origin in the dynamics of the purchase process.…

This paper presents a reproducibility study examining how Large Language Models (LLMs) manage competing factual and counterfactual information, focusing on the role of attention heads in this process. We attempt to reproduce and reconcile…

We investigate the nature of written human language within the framework of complex network theory. In particular, we analyse the topology of Orwell's \textit{1984} focusing on the local properties of the network, such as the properties of…

We model and compute the probability distribution of the letters in random generated words in a language by using the theory of set partitions, Young tableaux and graph theoretical representation methods. This has been of interest for…

The goal of developing a firmer theoretical understanding of inhomogenous temporal processes -- in particular, the waiting times in some collective dynamical system -- is attracting significant interest among physicists. Quantifying the…

We describe a general strategy for sampling configurations from a given distribution, NOT based on the standard Metropolis (Markov chain) strategy. It uses the fact that nontrivial problems in statistical physics are high dimensional and…

We investigate the problem of wealth distribution from the viewpoint of asset exchange. Robust nature of Pareto's law across economies, ideologies and nations suggests that this could be an outcome of trading strategies. However, the simple…

The power law distribution is usually used to fit data in the upper tail of the distribution. However, commonly it is not valid to model data in all the range. In this paper, we present a new family of distributions, the so-called…

Reaction networks are often used to model interacting species in fields such as biochemistry and ecology. When the counts of the species are sufficiently large, the dynamics of their concentrations are typically modeled via a system of…

A language dynamics model on a square lattice, which is an extension of the one popularized by Abrams and Strogatz [1], is analyzed using ODE bifurcation theory. For this model we are interested in the existence and spectral stability of…

Starting from the model of continuous time random walk, we focus our interest on random walks in which the probability distributions of the waiting times and jumps have fat tails characterized by power laws with exponent between 0 and 1 for…

Analyzing relational data consisting of multiple samples or layers involves critical challenges: How many networks are required to capture the variety of structures in the data? And what are the structures of these representative networks?…

We introduce a simple agent-based model which allows us to analyze three stylized facts: a fat-tailed size distribution of companies, a `tent-shaped' growth rate distribution, the scaling relation of the growth rate variance with firm size,…

Some statements have one well-defined continuation (e.g., "the Eiffel Tower is in [Paris]"), whereas others have a natural distribution over multiple options (e.g., "the weighted coin flip was [Heads/Tails].") We argue that language model…

We investigate several geometric models of network which simultaneously have some nice global properties, that the small diameter property, the small-community phenomenon, which is defined to capture the common experience that (almost)…

In recent decades, it has been emphasized that the evolving structure of networks may be shaped by interaction principles that yield sparse graphs with a vertex degree distribution exhibiting an algebraic tail, and other structural traits…

Many large cities are found at locations with certain first nature advantages. Yet, those exogenous locational features may not be the most potent forces governing the spatial pattern of cities. In particular, population size, spacing and…

Interpretability research aims to bridge the gap between empirical success and our scientific understanding of the inner workings of large language models (LLMs). However, most existing research focuses on analyzing a single mechanism, such…

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…