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Cross-lingual alignment, the meaningful similarity of representations across languages in multilingual language models, has been an active field of research in recent years. We survey the literature of techniques to improve cross-lingual…
We propose a statistical model for natural language that begins by considering language as a monoid, then representing it in complex matrices with a compatible translation invariant probability measure. We interpret the probability measure…
Computational modelling with multi-agent systems is becoming an important technique of studying language evolution. We present a brief introduction into this rapidly developing field, as well as our own contributions that include an…
We consider an aggregation model for two interacting species. The coupling between the species is via their velocities, that incorporate self- and cross-interactions. Our main interest is categorizing the possible steady states of the…
While multilingual language models can improve NLP performance on low-resource languages by leveraging higher-resource languages, they also reduce average performance on all languages (the 'curse of multilinguality'). Here we show another…
Language models (LMs) are statistical models trained to assign probability to human-generated text. As such, it is reasonable to question whether they approximate linguistic variability exhibited by humans well. This form of statistical…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
We introduce a class of stochastic models for the dynamics of two linguistic variants that are competing to become the single, shared convention within an unstructured community of speakers. Different instances of the model are…
Classical dynamical laws are conventionally formulated as closed evolution equations defined on fixed geometric backgrounds and a global time parameter. We develop a formulation in which neither prescribed evolution laws nor an external…
We adopt an evolutionary view on language change in which cognitive factors (in addition to social ones) affect the fitness of words and their success in the linguistic ecosystem. Specifically, we propose a variety of psycholinguistic…
Shared and correlated Gamma frailty models are widely used in the literature to model the association in multivariate current status data. In this paper, we have proposed two other new Gamma frailty models, namely shared cause-specific and…
Computing the agreement between two continuous sequences is of great interest in statistics when comparing two instruments or one instrument with a gold standard. The probability of agreement (PA) quantifies the similarity between two…
A simple mathematical homogeneous model of competition is used to describe Neanderthal extinction in Europe. It considers two interacting species, Neanderthals and Early Modern Men, in the same ecological niche. Using paleontological data…
Lexical Semantic Change is the study of how the meaning of words evolves through time. Another related question is whether and how lexical relations over pairs of words, such as synonymy, change over time. There are currently two competing,…
We show that the mutual information between two symbols, as a function of the number of symbols between the two, decays exponentially in any probabilistic regular grammar, but can decay like a power law for a context-free grammar. This…
This paper investigates economic convergence in terms of real income per capita among the autonomous regions of Spain. In order to converge, the series should cointegrate. This necessary condition is checked using two testing strategies…
Large Language Models (LLMs) have become a key element of modern artificial intelligence, demonstrating the ability to address a wide range of language processing tasks at unprecedented levels of accuracy without the need of collecting…
In this paper we describe an algorithm for aligning sentences with their translations in a bilingual corpus using lexical information of the languages. Existing efficient algorithms ignore word identities and consider only the sentence…
The Swadesh approach for determining the temporal separation between two languages relies on the stochastic process of words replacement (when a complete new word emerges to represent a given concept). It is well known that the basic…
The time variation of the rank $k$ of words for six Indo-European languages is obtained using data from Google Books. For low ranks the distinct languages behave differently, maybe due to syntaxis rules, whereas for $k>50$ the law of large…