Search results for: Zipf’s law

Authors: Neda Lovričević, Đilda Pečarić, Josip Pečarić

Abstract:

The Jensen functional in its discrete form is brought in relation to the Csiszar divergence functional, this time via its monotonicity property. This approach presents a generalization of the previously obtained results that made use of interpolating Jensen-type inequalities. Thus the monotonicity property is integrated with the Zipf-Mandelbrot law and applied to f-divergences for probability distributions that originate from the Csiszar divergence functional: Kullback-Leibler divergence, Hellinger distance, Bhattacharyya distance, chi-square divergence, total variation distance. The Zipf-Mandelbrot and the Zipf law are widely used in various scientific fields and interdisciplinary and here the focus is on the aspect of the mathematical inequalities.

Keywords: Jensen functional, monotonicity, Csiszar divergence functional, f-divergences, Zipf-Mandelbrot law

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Authors: Ana Barbir, S. Ivelic Bradanovic, D. Pecaric, J. Pecaric

Abstract:

We proved a converse to Sherman's inequality. Using the concept of f-divergence we obtained some inequalities for the well-known entropies, such as Shannon entropies that have many applications in many applied sciences, for example, in information theory, biology and economics Zipf-Mandelbrot law gave improvement in account for the low-rankwords in corpus. Applications of Zipf-Mandelbrot law can be found in linguistics, information sciences and also mostly applicable in ecological eld studies. We also introduced an entropy by applying the Zipf-Mandelbrot law and derived some related inequalities.

Keywords: f-divergence, majorization inequality, Sherman inequality, Zipf-Mandelbrot entropy

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Authors: Douglas W. Scott

Abstract:

The Allemande from J. S. Bach's Partita for solo flute (BWV 1013) presents many unique challenges for any flautist, especially in terms of segmentation analysis required to select breathing places in the first half. Without claiming to identify a 'correct' solution to this problem, this paper analyzes the section in terms of a set of techniques based around a statistical property commonly (if not ubiquitously) found in music, namely Zipf’s law. Specifically, the paper considers violations of this expected profile at various levels of analysis, an approach which has yielded interesting insights in previous studies. The investigation is then grounded by considering four actual solutions to the problem found in recordings made by different flautists, which opens up the possibility of expanding Zipfian analysis to include a consideration of inter-onset-intervals (IOIs). It is found that significant deviations from the expected Zipfian distributions can reveal and highlight stylistic choices made by different performers.

Keywords: inter-onset-interval, Partita for solo flute, BWV 1013, segmentation analysis, Zipf’s law

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Authors: Aris R. Terzopoulos, Georgia Z. Niolaki, Lynne G. Duncan, Mark A. J. Wilson, Antonios Kyparissiadis, Jackie Masterson

Abstract:

As word databases for bilingual children are not available, researchers, educators and textbook writers must rely on monolingual databases. The aim of this study is thus to develop a bilingual word database, BiLex-kids, an online open access developmental word database for 5-13 year old bilingual children who learn Greek as a second language and have English as their dominant one. BiLex-kids is compiled from 120 Greek textbooks used in Greek-English bilingual education in the UK, USA and Australia, and provides word translations in the two languages, pronunciations in Greek, and psycholinguistic variables (e.g. Zipf, Frequency per million, Dispersion, Contextual Diversity, Neighbourhood size). After clearing the textbooks of non-relevant items (e.g. punctuation), algorithms were applied to extract the psycholinguistic indices for all words. As well as one total lexicon, the database produces values for all ages (one lexicon for each age) and for three age bands (one lexicon per age band: 5-8, 9-11, 12-13 years). BiLex-kids provides researchers with accurate figures for a wide range of psycholinguistic variables, making it a useful and reliable research tool for selecting stimuli to examine lexical processing among bilingual children. In addition, it offers children the opportunity to study word spelling, learn translations and listen to pronunciations in their second language. It further benefits educators in selecting age-appropriate words for teaching reading and spelling, while special educational needs teachers will have a resource to control the content of word lists when designing interventions for bilinguals with literacy difficulties.

Keywords: bilingual children, psycholinguistics, vocabulary development, word databases

Procedia PDF Downloads 283