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- R. A. Blythe
- 2008

We consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model (among other things) biological transport and traffic flow. We begin with a broad overview of this class of driven diffusive systems—which includes exclusion processes—focusing on interesting physical properties,… (More)

- Kenny Smith, Andrew D. M. Smith, Richard A. Blythe
- Cognitive Science
- 2011

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)

- G J Baxter, R A Blythe, W Croft, A J McKane
- Physical review. E, Statistical, nonlinear, and…
- 2006

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)

- R. A. Blythe, A. J. McKane
- 2007

We give a overview of stochastic models of evolution that have found applications in genetics, ecology and linguistics for an audience of nonspecialists, especially statistical physicists. In particular, we focus mostly on neutral models in which no intrinsic advantage is ascribed to a particular type of the variable unit, for example a gene, appearing in… (More)

- Graces Group, Clay Beckner, +8 authors Tom Schoenemann
- 2009

- Kenny Smith, Andrew D. M. Smith, Richard A. Blythe, Paul Vogt
- EELC
- 2006

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)

- G J Baxter, R A Blythe, A J McKane
- Mathematical biosciences
- 2007

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)

- Richard A. Blythe, Kenny Smith, Andrew D. M. Smith
- Cognitive Science
- 2010

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)

- G J Baxter, R A Blythe, A J McKane
- Physical review letters
- 2008

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)