Publications of W Garrett Mitchener    :chronological  alphabetical  combined listing:

%% Papers Published   
@article{fds40001,
   Author = {W. G. Mitchener},
   Title = {A Simulation of Language Change in the Presence of
             Non-Idealized Syntax},
   Year = {2005},
   Month = {June},
   url = {http://www.math.duke.edu/~wgm/WGM-MLCPNIS-Corrected.pdf},
   Abstract = {Both Middle English and Old French had a syntactic property
             called verb-second or V2 that disappeared. This paper
             describes a simulation being developed to shed light on the
             question of why V2 is stable in some languages, but not
             others. The simulation, based on a Markov chain, uses fuzzy
             grammars where speakers can use an arbitrary mixture of
             idealized grammars. Thus, it can mimic the variable syntax
             observed in Middle English manuscripts. The simulation
             supports the hypotheses that children use the topic of a
             sentence for word order acquisition, that acquisition takes
             into account the ambiguity of grammatical information
             available from sample sentences, and that speakers prefer to
             speak with more regularity than they observe in the primary
             linguistic data.},
   Key = {fds40001}
}

@article{fds42480,
   Author = {W. G. Mitchener},
   Title = {A Mathematical Model of the Loss of Verb-Second in Middle
             English},
   Booktitle = {Proceedings of the 13th International Conference on English
             Historical Linguistics},
   Year = {2005},
   Abstract = {Lightfoot (1999) proposes the following explanation for the
             loss of the verb-second rule in Middle English: There were
             two regional dialects of Middle English, a northern dialect
             influenced by Old Norse with a verb-second rule, and a
             southern dialect with a slightly different word order.
             Children acquire the verb-second rule based on hearing some
             critical fraction of cue sentences requiring such a rule. As
             the dialects experienced increased contact, northern
             children were less likely to hear enough cue sentences, and
             consequently acquired a different grammar, resulting in the
             extinction of the northern dialect. This hypothesis can be
             modeled with differential equations. By using dynamical
             systems methods, the catastrophe in question may be modeled
             by a mathematical event known as a saddle-node bifurcation.
             A key part of the model is the function q that gives the
             probability of learning the northern dialect given that a
             fraction of the local population uses it. Other model
             acquisition algorithms, such as memoryless learner (Niyogi &
             Berwick 1996), give the mysterious result that verb-second
             languages should be extremely stable, in contrast to the
             history of English. This new model provides an explanation
             for that behavior: Memoryless learners are more sensitive to
             noise, resulting in a differently shaped q function that
             does not allow the northern grammar to disappear. This model
             demonstrates how dynamical systems theory can be used to
             study language change and learning models.},
   Key = {fds42480}
}

@article{fds20941,
   Author = {W.G. Mitchener and Martin A. Nowak},
   Title = {Chaos and Language},
   Journal = {Proceedings of the Royal Society: Biological
             Sciences},
   Volume = {271},
   Number = {1540},
   Pages = {701--704},
   Year = {2004},
   Month = {April},
   url = {http://www.journals.royalsoc.ac.uk/openurl.asp?genre=article&id=doi:10.1098/rspb.2003.2643},
   Abstract = {Human language is a complex communication system with
             unlimited expressibility. Children spontaneously develop a
             native language by exposure to linguistic data from their
             speech community. Over historical time, languages change
             dramatically and unpredictably by accumulation of small
             changes and by interaction with other languages. We have
             previously developed a mathematical model for the
             acquisition and evolution of language in heterogeneous
             populations of speakers. This model is based on game
             dynamical equations with learning. Here we show that simple
             examples of such equations can display complex limit cycles
             and chaos. Hence, language dynamical equations mimic
             complicated and unpredictable changes of languages over
             time. In terms of evolutionary game theory, we note that
             imperfect learning can induce chaotic switching among strict
             Nash equilibria.},
   Key = {fds20941}
}

@article{fds15984,
   Author = {W.G. Mitchener},
   Title = {Bifurcation Analysis of the Fully Symmetric Language
             Dynamical Equation},
   Journal = {Journal of Mathematical Biology},
   Volume = {46},
   Number = {3},
   Pages = {265--285},
   Year = {2003},
   Month = {March},
   url = {http://dx.doi.org/10.1007/s00285-002-0172-8},
   Key = {fds15984}
}

@article{fds15983,
   Author = {W.G. Mitchener and Martin A. Nowak},
   Title = {Competitive exclusion and coexistence of universal
             grammars},
   Journal = {Bulletin of Mathematical Biology},
   Volume = {65},
   Number = {1},
   Pages = {67--93},
   Year = {2003},
   Month = {January},
   url = {http://dx.doi.org/10.1006/bulm.2002.0322},
   Key = {fds15983}
}


%% Papers Accepted   
@article{fds40002,
   Author = {Brian P. Tighe and Joshua E. S. Socolar and David G. Schaeffer and W.
             G. Mitchener and Mark Huber},
   Title = {Force distributions in a triangular lattice of rigid
             bars},
   Journal = {Physical Review E},
   Year = {2005},
   Key = {fds40002}
}