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Hearings and mishearings: decrypting the spoken word. (English) Zbl 07843123

Summary: We propose a model of the speech perception of individual words in the presence of mishearings. This phenomenological approach is based on concepts used in linguistics, and provides a formalism that is universal across languages. We put forward an efficient two-parameter form for the word length distribution, and introduce a simple representation of mishearings, which we use in our subsequent modeling of word recognition. In a context-free scenario, word recognition often occurs via anticipation when, part-way into a word, we can correctly guess its full form. We give a quantitative estimate of this anticipation threshold when no mishearings occur, in terms of model parameters. As might be expected, the whole anticipation effect disappears when there are sufficiently many mishearings. Our global approach to the problem of speech perception is in the spirit of an optimization problem. We show for instance that speech perception is easy when the word length is less than a threshold, to be identified with a static transition, and hard otherwise. We extend this to the dynamics of word recognition, proposing an intuitive approach highlighting the distinction between individual, isolated mishearings and clusters of contiguous mishearings. At least in some parameter range, a dynamical transition is manifest well before the static transition is reached, as is the case for many other examples of complex systems.

MSC:

91-XX Game theory, economics, finance, and other social and behavioral sciences

References:

[1] Abrahams, E. (ed.), 50 Years of Anderson Localization (World Scientific, Singapore, 2010). · Zbl 1207.81002
[2] Altmann, E. G. and Gerlach, M., Statistical laws in linguistics, Creativity and Universality in Language, Esposti, M. D., Altmann, E. G. and Pachet, F. (eds.) (Springer, Berlin, 2016).
[3] Baayen, R. H., Piepenbrock, R. and Gulikers, L., CELEX Database (Linguistic Data Consortium, Philadelphia, 1995).
[4] Baxter, R. J., Exactly Solved Models in Statistical Mechanics (Academic Press, London, 1982). · Zbl 0538.60093
[5] Binder, K. and Young, A. P., Spin glasses: Experimental facts, theoretical concepts, and open questions, Rev. Mod. Phys.58 (1986) 801-976.
[6] Blythe, R. A., Hierarchy of scales in language dynamics, Eur. Phys. J. B88 (2015) 295.
[7] Castellani, T. and Cavagna, A., Spin glass theory for pedestrians, J. Stat. Mech.P05012 (2005) P05012. · Zbl 1456.82490
[8] Corral, A. and Serra, I., The brevity law as a scaling law, and a possible origin of Zipf’s law for word frequencies, Entropy22 (2020) 224.
[9] Crisanti, A., Paladin, G. and Vulpiani, A., Products of Random Matrices in Statistical Physics, (Springer, Berlin, 1992). · Zbl 0784.58003
[10] Eckart, T. and Quasthoff, U., Statistical corpus and language comparison on comparable corpora, Building and Using Comparable Corpora (Springer, Berlin, 2013).
[11] Eroglu, S., Menzerath-Altmann law for distinct word distribution analysis in a large text, Physica A392 (2013) 2775-2780.
[12] Garey, M. R. and Johnson, D. S., Computers and Intractability: A Guide to the Theory of NP-Completeness (Freeman, New York, 1979). · Zbl 0411.68039
[13] Grzybek, P. (ed.), Contributions to the Science of Text and Language. Word Length Studies and Related Issues, (Springer, Berlin, 2007).
[14] Gussenhoven, C. and Jacobs, H., Understanding Phonology (Hodder Education, London, 2011).
[15] Havlin, S. and Ben-Avraham, D., Diffusion in disordered media, Adv. Phys.36 (1987) 695-798.
[16] Hayes, B., Introductory Phonology (Wiley-Blackwell, London, 2009).
[17] Kirkpatrick, T. R. and Thirumalai, D., p-spin-interaction spin-glass models: Connections with the structural glass problem, Phys. Rev. B36 (1987) 5388-5397.
[18] Klemm, K., Mehta, A. and Stadler, P. F., Landscape encodings enhance optimization, PLoS ONE7(4) (2012) e34780.
[19] Kramer, B. and MacKinnon, A., Localization: Theory and experiment, Rep. Prog. Phys.56 (1993) 1469-1564.
[20] Krzakala, F., Montanari, A., Ricci-Tersenghi, F., Semerjian, G. and Zdeborová, L., Gibbs states and the set of solutions of random constraint satisfaction problems, Proc. Nat. Acad. Sci. USA104 (2007) 10318-10323. · Zbl 1190.68031
[21] Kwapien, J. and Drozdz, S., Physical approach to complex systems, Phys. Rep.515 (2012) 115-226.
[22] Ladefoged, P. and Johnson, K., A Course in Phonetics (Wads-worth, Cengage Learning, Boston, 2011).
[23] Lahiri, A., Asymmetric phonological representations of words in the mental lexicon, The Oxford Handbook of Laboratory Phonology (Oxford University Press, Oxford, 2011).
[24] Lahiri, A. and Marslen-Wilson, W. D., The mental representation of lexical form: A phonological approach to the recognition lexicon, Cognition38 (1991) 245-294.
[25] Lahiri, A. and Reetz, H., Distinctive features: Phonological underspecification in representation and processing, J. Phonetics38 (2010) 44-59.
[26] Luck, J. M. and Mehta, A., in preparation.
[27] Marinari, E., Parisi, G. and Ritort, F., Replica field theory for deterministic models. II. A non-random spin glass with glassy behaviour, J. Phys. A27 (1994) 7647-7668. · Zbl 0843.60097
[28] Marslen-Wilson, W. D., Functional parallelism in spoken word-recognition, Cognition25 (1987) 71-102.
[29] Mehta, A., Barker, G. C. and Luck, J. M., Heterogeneities in granular dynamics, Proc. Nat. Acad. Sci. USA105 (2008) 8244-8249.
[30] Mézard, M., Parisi, G. and Virasoro, M. A., Spin Glass Theory and Beyond (World Scientific, Singapore, 1987). · Zbl 0992.82500
[31] Monasson, R., Zecchina, R., Kirkpatrick, S., Selman, B. and Troyansky, L., Determining computational complexity from characteristic ‘phase transitions’, Nature400 (1999) 133-137. · Zbl 1369.68244
[32] Paladin, G. and Vulpiani, A., Anomalous scaling laws in multifractal objects, Phys. Rep.156 (1987) 147-225.
[33] Ferrer i Cancho, R. and Solé, R. V., The small world of human language, Proc. Roy. Soc. B268 (2001) 2261-2265.
[34] Ruml, W., Ngo, J. T., Marks, J. and Shieber, S., Easily searched encodings for number partitioning, J. Optim. Theory Appl.89 (1996) 251-291. · Zbl 0853.90096
[35] Segev, M., Silberberg, Y. and Christodoulides, D. N., Anderson localization of light, Nature Photonics7 (2013) 197-204.
[36] Sigurd, B., Eeg-Olofsson, M. and van de Weijer, J., Word length, sentence length and frequency: Zipf’s law revisited, Studia Linguistica58 (2004) 37-52.
[37] Stanley, H. E. and Meakin, P., Multifractal phenomena in physics and chemistry, Nature335 (1988) 405-409.
[38] Stauffer, D. and Aharony, A., Introduction to Percolation Theory (Taylor and Francis, London, 1992). · Zbl 0862.60092
[39] van Rossum, M. C. W. and Nieuwenhuizen, T. M., Multiple scattering of classical waves: Microscopy, mesoscopy, and diffusion, Rev. Mod. Phys.71 (1999) 313-371.
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