Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T01:33:14.072Z Has data issue: false hasContentIssue false
  • English
  • Français

Effects of limiting memory capacity on the behaviour of exemplar dynamics

Part of: Other social and behavioral sciences (mathematical treatment)

Published online by Cambridge University Press:  26 July 2018

B. Goodman  and
P. F. Tupper
B. Goodman*
Affiliation:
Simon Fraser University
P. F. Tupper*
Affiliation:
Simon Fraser University
*
* Postal address: Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC, V5A 1S6, Canada.
* Postal address: Department of Mathematics, Simon Fraser University, 8888 University Dr., Burnaby, BC, V5A 1S6, Canada.
Get access Rights & Permissions [Opens in a new window]

Abstract

Exemplar models are a popular class of models used to describe language change. Here we study how limiting the memory capacity of an individual in these models affects the system's behaviour. In particular, we demonstrate the effect this change has on the extinction of categories. Previous work in exemplar dynamics has not addressed this question. In order to investigate this, we will inspect a simplified exemplar model. We will prove for the simplified model that all the sound categories but one will always become extinct, whether memory storage is limited or not. However, computer simulations show that changing the number of stored memories alters how fast categories become extinct.

Keywords

Exemplar modellinguisticslanguage changeextinction

MSC classification

Primary: 91F20: Linguistics
Secondary: 70F99: None of the above, but in this section
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 2 , June 2018 , pp. 390 - 401
Copyright
Copyright © Applied Probability Trust 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Bhattacharya, R. and Waymire, E. C. (2007). A Basic Course in Probability Theory. Springer, New York. Google Scholar
[2]Billingsley, P. (1995). Probability and Measure, 3rd edn. John Wiley, New York. Google Scholar
[3]Bybee, J. (2002). Phonological evidence for exemplar storage of multiword sequences. Stud. Second Language Acquisition 24, 215–221. Google Scholar
[4]Jäger, G. (2008). Applications of game theory in linguistics. Language Linguistics Compass 2, 406–421. Google Scholar
[5]Johnson, K. (1997). Speech perception without speaker normalization: an exemplar model. In Talker Variability in Speech Processing, Academic Press, San Diego, CA, pp. 145–165. Google Scholar
[6]Luce, R. D. (2005). Individual Choice Behavior: A Theoretical Analysis. Dover, Mineola, NY. Google Scholar
[7]Michel, J. B.et al. (2011). Quantitative analysis of culture using millions of digitized books. Science 331, 176–182. Google Scholar
[8]Nosofsky, R. M. (1986). Attention, similarity, and the identification–categorization relationship. J. Experimental Psychology General 115, 39–57. Google Scholar
[9]Nosofsky, R. M. (1988). Similarity, frequency, and category representations. J. Experimental Psychology Learning Mem. Cognition 14, 54–65. Google Scholar
[10]Pierrehumbert, J. B. (2001). Exemplar dynamics: word frequency, lenition, and contrast. In Frequency and the Emergence of Linguistic Structure, John Benjamins, Amsterdam, pp. 137–157. Google Scholar
[11]Romano, J. P. and Siegel, A. F. (1986). Counterexamples in Probability and Statistics. Wadsworth and Brooks/Cole, Monterey, CA. Google Scholar
[12]Rosenthal, J. S. (2000). A First Look at Rigorous Probability Theory. World Scientific, River Edge, NJ. Google Scholar
[13]Rudin, W. (1987). Real and Complex Analysis, 3rd edn. McGraw-Hill, New York. Google Scholar
[14]Steel, M. (2015). Reflections on the extinction–explosion dichotomy. Theoret. Pop. Biol. 101, 61–66. Google Scholar
[15]Tupper, P. F. (2015). Exemplar dynamics and sound merger in language. SIAM J. Appl. Math. 75, 1469–1492. Google Scholar
[16]Wedel, A. (2012). Lexical contrast maintenance and the organization of sublexical contrast systems. Language Cognition 4, 319–355. Google Scholar
[17]Winter, B. and Wedel, A. (2016). The co-evolution of speech and the lexicon: the interaction of functional pressures, redundancy, and category variation. Topics Cognitive Sci. 8, 503–513. Google Scholar