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Diffusion models have achieved great success in modeling continuous data modalities such as images, audio, and video, but have seen limited use in discrete domains such as language. Recent attempts to adapt diffusion to language have…
In order to analyze the dynamics of two languages in competition, one approach is to fit historical data on their numbers of speakers with a mathematical model in which the parameters are interpreted as the similarity between those…
We propose a model for the evolutionary ecology of words as one attempt to extend evolutionary game theory and agent-based models by utilizing the rich linguistic expressions of Large Language Models (LLMs). Our model enables the emergence…
The now classical replicator equation describes a wide variety of biological phenomena, including those in theoretical genetics, evolutionary game theory, or in the theories of the origin of life. Among other questions, the permanence of…
The historical and geographical spread from older to more modern languages has long been studied by examining textual changes and in terms of changes in phonetic transcriptions. However, it is more difficult to analyze language change from…
Motivated by the dramatic disappearance of endangered languages observed in recent years, a great deal of attention has been given to the modeling of language competition in order to understand the factors that promote the disappearance of…
We propose a stochastic model to study phonetic changes as an evolutionary process driven by social interactions between two groups of individuals with different phonological systems. Particularly, we focus on the changes in the place of…
Understanding the evolutionary dynamics of reinforcement learning under multi-agent settings has long remained an open problem. While previous works primarily focus on 2-player games, we consider population games, which model the strategic…
I propose a novel Ising-like model of language evolution. In a simple way, Ising-like models represent the countervailing tendencies towards convergence and change present in language evolution. In the ordinary Ising-model, a node on a…
We propose a threshold model of language competition which includes intermediate bilingual state. The model is based on the Minett-Wang model but through the introduction of thresholds in the language shift rates it incorporates the effects…
Empirical evidence shows that the rate of irregular usage of English verbs exhibits discontinuity as a function of their frequency: the most frequent verbs tend to be totally irregular. We aim to qualitatively understand the origin of this…
In this paper, a single population model with memory effect and the heterogeneity of the environment, equipped with the Neumann boundary, is considered. The global existence of a spatial nonhomogeneous steady state is proved by the method…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
Large Language Models have achieved remarkable performance on reasoning tasks, motivating research into how this ability evolves during training. Prior work has primarily analyzed this evolution via explicit generation outcomes, treating…
Word evolution refers to the changing meanings and associations of words throughout time, as a byproduct of human language evolution. By studying word evolution, we can infer social trends and language constructs over different periods of…
A system of two cubic reaction-diffusion equations for two independent gene frequencies arising in population dynamics is studied. Depending on values of coefficients, all possible Lie and $Q$-conditional (nonclassical) symmetries are…
To understand the effect of assortative mating on the genetic evolution of a population, we consider a finite population in which each individual has a type, determined by a sequence of n diallelic loci. We assume that the population…
We consider the problem of determining the time evolution of a trait distribution in a mathematical model of non-uniform populations with parametric heterogeneity. This means that we consider only heterogeneous populations in which…
We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the…
The evolution of dispersal is a classical question in evolutionary biology, and it has been studied in a wide range of mathematical models. A selection-mutation model, in which the population is structured by space and a phenotypic trait,…