Learn More
Cross-situational learning is a mechanism for learning the meaning of words across multiple exposures, despite exposure-by-exposure uncertainty as to the word's true meaning. We present experimental evidence showing that humans learn words effectively using cross-situational learning, even at high levels of referential uncertainty. Both overall success(More)
We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences with the Fisher-Wright model of population genetics, but there are significant differences. The continuous time(More)
We study the partially asymmetric exclusion process with open boundaries. We generalise the matrix approach previously used to solve the special case of total asymmetry and derive exact expressions for the partition sum and currents valid for all values of the asymmetry parameter q. Due to the relationship between the matrix algebra and the q-deformed(More)
We present a mathematical model of cross-situational learning , in which we quantify the learnability of words and vocabularies. We find that high levels of uncertainty are not an impediment to learning single words or whole vocabulary systems, as long as the level of uncertainty is somewhat lower than the total number of meanings in the system. We further(More)
We give an exact solution to the Kolmogorov equation describing genetic drift for an arbitrary number of alleles at a given locus. This is achieved by finding a change of variable which makes the equation separable, and therefore reduces the problem with an arbitrary number of alleles to the solution of a set of equations that are essentially no more(More)
Cross-situational learning is a mechanism for learning the meaning of words across multiple exposures, despite exposure-by-exposure uncertainty as to a word's true meaning. Doubts have been expressed regarding the plausibility of cross-situational learning as a mechanism for learning human-scale lexicons in reasonable timescales under the levels of(More)
We investigate a set of stochastic models of biodiversity, population genetics, language evolution, and opinion dynamics on a network within a common framework. Each node has a state 0<x(i)<1 with interactions specified by strengths m(ij). For any set of m(ij), we derive an approximate expression for the mean time to reach fixation or consensus (all x(i)=0(More)