Related papers: Dynamics of two languages competing on a network: …
Recent years have witnessed significant progress in developing effective training and fast sampling techniques for diffusion models. A remarkable advancement is the use of stochastic differential equations (SDEs) and their…
The inverse relationship between the length of a word and the frequency of its use, first identified by G.K. Zipf in 1935, is a classic empirical law that holds across a wide range of human languages. We demonstrate that length is one…
While language is a complex adaptive system, most work on syntactic variation observes a few individual constructions in isolation from the rest of the grammar. This means that the grammar, a network which connects thousands of structures…
The dynamics of pulse solutions in a bistable reaction-diffusion system are studied analytically by reducing partial differential equations (PDEs) to finite-dimensional ordinary differential equations (ODEs). For the reduction, we apply the…
Classical language dynamics explains language shift as a process in which speakers adopt a higher status language in lieu of a lower status language. This is well documented with English having out-competed languages such as Scottish…
In cases where the same real-world system can be modeled both by an ODE system $\bD$ and a Boolean system $\bB$ it is of interest to identify conditions under which the two systems will be consistent, that is, will make qualitatively…
Quantitative linguistics has been allowed, in the last few decades, within the admittedly blurry boundaries of the field of complex systems. A growing host of applied mathematicians and statistical physicists devote their efforts to…
We consider a diffusive Coupled Map Lattice (CML) for which the local map is piece-wise affine and has two stable fixed points. By introducing a spatio-temporal coding, we prove the one-to-one correspondence between the set of global orbits…
Many languages' inflectional morphological systems are replete with irregulars, i.e., words that do not seem to follow standard inflectional rules. In this work, we quantitatively investigate the conditions under which irregulars can…
A series of phenomena pertaining to economics, quantum physics, language, literary criticism, and especially architecture is studied from the standpoint of synergetics (the study of self-organizing complex systems). It turns out that 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…
Synchronisation and stability under periodic oscillatory driving are well-understood, but little is known about the effects of aperiodic driving, despite its abundance in nature. Here, we consider oscillators subject to driving with slowly…
Smoothed analysis is a framework suggested for mediating gaps between worst-case and average-case complexities. In a recent work, Dinitz et al.~[Distributed Computing, 2018] suggested to use smoothed analysis in order to study dynamic…
One of the ultimate goals for linguists is to find universal properties in human languages. Although words are generally considered as representing arbitrary mapping between linguistic forms and meanings, we propose a new universal law that…
Languages evolve over time in a process in which reproduction, mutation and extinction are all possible, similar to what happens to living organisms. Using this similarity it is possible, in principle, to build family trees which show the…
This paper presents a novel treebank-driven approach to comparing syntactic structures in speech and writing using dependency-parsed corpora. Adopting a fully inductive, bottom-up method, we define syntactic structures as delexicalized…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
Diffusion models offer appealing properties for language generation, such as parallel decoding and iterative refinement, but the discrete and highly structured nature of text challenges the direct application of diffusion principles. In…
We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics…
Languages are continuously undergoing changes, and the mechanisms that underlie these changes are still a matter of debate. In this work, we approach language evolution through the lens of causality in order to model not only how various…