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Mitchener, W. G. (2003) A Mathematical Model of Human Languages: The Interaction of Game Dynamics and Learning Processes. PhD thesis, Program in Applied and Computational Mathematics, Princeton University.

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[1] L. V. Ahlfors. Complex Analysis. McGraw-Hill, third edition, 1979.

Google

[2] J. Aitchinson. Words in the Mind: An Introduction to the Mental Lexicon. Basil Blackwell, Oxford, 1987.

Google

[3] A. A. Andronov, E. A. Leontovich, I. I. Gordon, and A. G. Maier. Theory of Bifurcations of Dynamic Systems on a Plane. Keter Press, Jerusalem, 1971.

Google

[4] D. Angluin. Learning regular sets from queries and counterexamples. Information and Computation, 75:87-106, 1987.

Google

[5] D. Angluin and M. Kharitonov. When won't membership queries help? Journal of Computer and System Sciences, 50(336-355), 1995.

Google

[6] P. Ashwin and J. W. Swift. The dynamics of n weakly coupled identical oscillators. Journal of Nonlinear Science, 2:69-108, 1992.

Google

[7] D. Bickerton. Roots of Language. Karoma Publishers, Inc., Ann Arbor, 1981.

Google UIUC

[8] D. Bickerton. Language and Species. University of Chicago Press, Chicago, 1990.

Google UIUC

[9] A. Cangelosi and D. Parisi. The emergence of a "language" in an evolving population of neural networks. Connection Science, 10(2):83-97, 1998.

Google UIUC

[10] A. Cangelosi and D. Parisi, editors. Simulating the Evolution of Language. Springer- Verlag, 2001.

Google UIUC

[11] N. Chomsky. Language and Mind. Harcourt Brace Jovanovich, New York, 1972.

Google

[12] N. Chomsky. Language and Problems of Knowledge. MIT Press, 1988.

Google

[13] T. Crowley. An Introduction to Historical Linguistics. Oxford Univeristy Press, third edition, 1998.

Google

[14] R. L. Devaney. An Introduction to Chaotic Dynamical Systems. Addison-Wesley, second edition, 1989.

Google

[15] M. Eigen. Selforganization of matter and the evolution of biological macromolecules. Naturwissenschaften, 58(10):465-523, 1971.

Google

[16] M. Eigen, J. McCaskill, and P. Schuster. The molecular quasi-species. In I. Prigogine and S. A. Rice, editors, Advances in Chemical Physics, volume 75, pages 149-263. John Wiley and Sons, New York, 1989.

Google

[17] M. Eigen and P. Schuster. The Hypercycle: A Principle of Natural Self-Organisation. Springer-Verlag, Berlin, 1979.

Google

[18] W. Enard, M. Przeworski, S. E. Fisher, C. S. L. Lai, V. Wiebe, T. Kitano, A. P. Monaco, and S. Pšašabo. Molecular evolution of FOXP2, a gene involved in speech and language. Nature, 418(6900):869-872, 2002.

Google UIUC

[19] R. Ferrer i Cancho and R. V. SolŽe. Two regimes in the frequency of words and the origin of complex lexicons: Zipf's law revisited. Journal of Quantitative Linguistics, 8:165-173, 2001.

Google UIUC

[20] M. J. Field and R. W. Richardson. Symmetry breaking and the maximal isotropy subgroup conjecture for reflection groups. Archive for Rational Mechanics and Analysis, 105:61-94, 1989.

Google

[21] S. A. Frank. Foundations of Social Evolution. Princeton University Press, Princeton, NJ, 1998.

Google

[22] A. A. Ghazanfar and M. D. Hauser. The neuroethology of primate vocal communication: substrates for the evolution of speech. Trends in Cognitive Sciences, 3(18):377- 384, 1999.

Google

[23] E. Gibson and K. Wexler. Triggers. Linguistic Inquiry, 25:407-454, 1994.

Google

[24] E. M. Gold. Language identification in the limit. Information and Control, 10:447-474, 1967.

Google UIUC

[25] N. Grassly, A. von Haesler, and D. C. Krakauer. Error, population structure and the origin of diverse sign systems. Journal of Theoretical Biology, 206:369-378, 2000.

Google UIUC

[26] J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, 1990.

Google

[27] M. D. Hauser. The Evolution of Communication. Harvard University Press, Cambridge, MA, 1996.

Google UIUC

[28] M. D. Hauser, N. Chomsky, and W. T. Fitch. The faculty of language: What is it, who has it, and how did it evolve? Science, 298(5598):1569-1579, 2002.

Google UIUC

[29] M. D. Hauser, E. L. Newport, and R. N. Aslin. Segmentation of the speech stream in a nonhuman primate: statistical learning in cotton-top tamarins. Cognition, 78(3):B53- B64, 2001.

Google

[30] M. Hirsch and S. Smale. Differential Equations, Dynamical Systems, and Linear Algebra. Academic Press, 1997.

Google

[31] J. Hofbauer and K. Sigmund. Evolutionary Games and Population Dynamics. Cambridge University Press, 1998.

Google

[32] J. R. Hurford, M. Studdert-Kennedy, and C. Knight, editors. Approaches to the Evolution of Language. Cambridge University Press, 1998.

Google UIUC

[33] R. Jackendoff. Possible stages in the evolution of the language capacity. Trends in Cognitive Sciences, 3:272-279, 1999.

Google UIUC

[34] R. Jackendoff. Foundations of Language. Oxford University Press, Oxford, 2002.

Google UIUC

[35] S. Kirby. Spontaneous evolution of linguistic structure: an iterated learning model of the emergence of regularity and irregularity. IEEE Transactions on Evolutionary Computation, 5(2):102-110, 2001.

Google UIUC

[36] N. L. Komarova, P. Niyogi, and M. A. Nowak. The evolutionary dynamics of grammar acquisition. Journal of Theoretical Biology, 209(1):43-59, 2001.

Google UIUC

[37] N. L. Komarova and M. A. Nowak. The evolutionary dynamics of the lexical matrix. Bulletin of Mathematical Biology, 63(3):451-485, 2001.

Google UIUC

[38] N. L. Komarova and M. A. Nowak. Natural selection of the critical period for language acquisition. Proceedings of the Royal Society of London, Series B, 268:1189-1196, 2001.

Google UIUC

[39] D. C. Krakauer. Kin imitation for a private sign system. Journal of Theoretical Biology, 213:145-157, 2001.

Google UIUC

[40] A. Kroch. Reflexes of grammar in patterns of language change. Language Variation and Change, 1:199-244, 1989.

Google UIUC

[41] M. Lachmann, S. Szamado, and C. T. Bergstrom. Cost and conflict in animal signals and human language. Proceedings of the National Academy of Sciences, USA, 98:13189- 94, 2001.

Google UIUC

[42] C. S. L. Lai, S. E. Fisher, J. A. Hurst, F. Vargha-Khadem, and A. P. Monaco. A forkhead-domain gene is mutated in a severe speech and language disorder. Nature, 413(6855):519-523, 2001.

Google UIUC

[43] P. Lieberman. The Biology and Evolution of Language. Harvard University Press, Cambridge, MA, 1984.

Google UIUC

[44] D. Lightfoot. How to Set Parameters: Arguments from Language Change. MIT Press, Cambridge, MA, 1991.

Google UIUC

[45] D. Lightfoot. The Development of Language: Acquisition, Changes and Evolution. Blackwell Publishers, 1999.

Google UIUC

[46] R. M. May. Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton, NJ, 2001.

Google

[47] J. Maynard Smith. Evolution and the Theory of Games. Cambridge University Press, 1982.

Google

[48] W. G. Mitchener. Bifurcation analysis of the fully symmetric language dynamical equation. Journal of Mathematical Biology, 46:265-285, 2003.

Google UIUC

[49] W. G. Mitchener and M. A. Nowak. Competitive exclusion and coexistence of universal grammars. Bulletin of Mathematical Biology, 65(1):67-93, 2003.

Google UIUC

[50] P. Niyogi. The Informational Complexity of Learning. Kluwer Academic Publishers, Boston, 1998.

Google

[51] P. Niyogi and R. C. Berwick. A language learning model for finite parameter spaces. Cognition, 61:161-193, 1996.

Google UIUC

[52] P. Niyogi and R. C. Berwick. Evolutionary consequences of language learning. Linguistics and Philosophy, 20:697-719, 1997.

Google UIUC

[53] M. Nowak and K. Sigmund. Chaos and the evolution of cooperation. Proceedings of the National Academy of Sciences, USA, 90:5091-5094, 1993.

Google

[54] M. A. Nowak and N. L. Komarova. Towards an evolutionary theory of language. Trends in Cognitive Sciences, 2001.

Google UIUC

[55] M. A. Nowak, N. L. Komarova, and P. Niyogi. Evolution of universal grammar. Science, 291(5501):114-118, 2001.

Google UIUC

[56] M. A. Nowak, N. L. Komarova, and P. Niyogi. Computational and evolutionary aspects of language. Nature, 417(6889):611-617, 2002.

Google UIUC

[57] M. A. Nowak and D. C. Krakauer. The evolution of language. Proceedings of the National Academy of Sciences, USA, 96:8028-8033, 1999.

Google UIUC

[58] M. A. Nowak, J. Plotkin, and V. A. A. Jansen. Evolution of syntactic communication. Nature, 404(6777):495-498, 2000.

Google UIUC

[59] M. A. Nowak, J. Plotkin, and D. C. Krakauer. The evolutionary language game. Journal of Theoretical Biology, 200:147-162, 1999.

Google UIUC

[60] K. M. Page and M. A. Nowak. Unifying evolutionary dynamics. Journal of Theoretical Biology, 219:93-98, 2002.

Google

[61] S. Pinker. The Language Instinct. W. Morrow and Company, New York, 1990.

Google UIUC

[62] S. Pinker and A. Bloom. Natural language and natural selection. Behavioral and Brain Sciences, 13:707-784, 1990.

Google UIUC

[63] J. Plotkin and M. A. Nowak. Language evolution and information theory. Journal of Theoretical Biology, 205:147-159, 2000.

Google UIUC

[64] G. R. Price. Extension of covariance mathematics. Annals of Human Genetics, 35:485- 490, 1972.

Google

[65] F. Ramus, M. D. Hauser, C. Miller, D. Morris, and J. Mehler. Language discrimination by human newborns and by cotton-top tamarin monkeys. Science, 288(5464):349-351, 2000.

Google

[66] W. Schnabel, P. F. Stadler, C. Forst, and P. Schuster. Full characterization of a strange attractor. Physica D, 48(1):65-90, 1991.

Google

[67] P. Schuster. Structure and dynamics of replication-mutation systems. Physica Scripta, 35(3):402-416, 1987.

Google

[68] A. Senghas and M. Coppola. Children creating language: How Nicaraguan sign language acquired a spatial grammar. Psychological Science, 12(4):323-328, 2001.

Google UIUC

[69] P. F. Stadler and P. Schuster. Mutation in autocatalytic reaction networks. Journal of Mathematical Biology, 30(6):597-632, 1992.

Google

[70] S. H. Strogatz. Nonlinear Dynamics and Chaos. Perseus Books, Reading, MA, 1994.

Google

[71] M. Studdert-Kennedy. Evolutionary implications of the particulate principle: Imitation and the dissociation of phonetic form from semantic function. In C. Knight, J. R. Hurford, and M. Studdert-Kennedy, editors, The Evolutionary Emergence of Language: Social Function and the Origins of Linguistic Form. Cambridge University Press, Cambridge, 2000.

Google UIUC

[72] B. Tesar and P. Smolensky. Learnability in Optimality Theory. MIT Press, 2000.

Google

[73] P. E. Trapa and M. A. Nowak. Nash equilibria for an evolutionary language game. Journal of Mathematical Biology, 41:172-1888, 2000.

Google UIUC

[74] R. L. Trask. Historical Linguistics. Arnold, London, 1996.

Google

[75] C. Tresser. About some theorems by L. P. Sil'nikov. Annales de l'Institute Henri PoincarŽe - Physique thŽeorique, 40(4):442-461, 1984.

Google

[76] J. Uriagereka. Rhyme and Reason: An Introduction to Minimalist Syntax. MIT Press, Cambridge, MA, 1998.

Google

[77] L. G. Valiant. A theory of the learnable. Communications of the ACM, 27:436-445, 1984.

Google

[78] V. Vapnik. The Nature of Statistical Learning Theory. Springer-Verlag, New York, 1995.

Google

[79] T. Warnow. Mathematical approaches to comparative linguistics. Proceedings of the National Academy of Sciences, USA, 94:6585-6590, 1997.

Google UIUC

[80] C. Watkins, editor. The American Heritage Dictionary of Indo-European Roots. Houghton Mifflin, second edition, 2000.

Google

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