Theory of Zipf's Law and Beyond

Theory of Zipf's Law and Beyond

Author: Alexander I. Saichev

Publisher: Springer Science & Business Media

Published: 2009-11-04

Total Pages: 176

ISBN-13: 3642029469

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Zipf’s law is one of the few quantitative reproducible regularities found in e- nomics. It states that, for most countries, the size distributions of cities and of rms (with additional examples found in many other scienti c elds) are power laws with a speci c exponent: the number of cities and rms with a size greater thanS is inversely proportional toS. Most explanations start with Gibrat’s law of proportional growth but need to incorporate additional constraints and ingredients introducing deviations from it. Here, we present a general theoretical derivation of Zipf’s law, providing a synthesis and extension of previous approaches. First, we show that combining Gibrat’s law at all rm levels with random processes of rm’s births and deaths yield Zipf’s law under a “balance” condition between a rm’s growth and death rate. We nd that Gibrat’s law of proportionate growth does not need to be strictly satis ed. As long as the volatility of rms’ sizes increase asy- totically proportionally to the size of the rm and that the instantaneous growth rate increases not faster than the volatility, the distribution of rm sizes follows Zipf’s law. This suggests that the occurrence of very large rms in the distri- tion of rm sizes described by Zipf’s law is more a consequence of random growth than systematic returns: in particular, for large rms, volatility must dominate over the instantaneous growth rate.


Within Language, Beyond Theories (Volume III)

Within Language, Beyond Theories (Volume III)

Author: Wojciech Malec

Publisher: Cambridge Scholars Publishing

Published: 2015-09-04

Total Pages: 260

ISBN-13: 1443882070

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This is the third volume in the series Within Language, Beyond Theories, which focuses on current linguistic research that surpasses the limits of contemporary theoretical frameworks in order to gain new insights into the structure of the language system and to offer more explanatorily adequate accounts of linguistic phenomena taken from a number of the world’s languages. This book offers a collection of fourteen chapters organized into three parts and serves as a vehicle for the survey of new voices in discourse analysis, pragmatics and corpus-based studies. Part I addresses a panorama of topics related to different discourse types, such as talk show discourse, multimodal discourse, and everyday spoken discourse, as well as written academic discourse. Part II covers a range of highly controversial issues in pragmatics, including the status of ad-hoc concepts, linguistically encoded meaning, explicit content, and the lexicographic treatment of modality. Part III encompasses chapters which offer an overview of some of the recent phenomena covered in the area of corpus-based research, including the semantic functions of the temporal meanings of selected prepositions; the diffusion of gerundive complements; the institutionalization and de-institutionalization of neologisms; contextual factors in the placement of the adverb “well”; the behaviour of the verb “bake” in copular constructions; the syntactic flexibility of English idioms and their thematic composition; tendencies in the formation of nouns in tabloids; and the application of cluster analysis to the categorization of linguistic data. Drawing on recent advances in discourse analysis, pragmatics and corpus-based studies, the majority of the issues discussed here are approached and investigated from a dual perspective. While on the theoretical side, an array of different theoretical models is surveyed, in the analytical parts, the practical applications of the models examined are tested against data from English (both British and American), Estonian and Polish. The wide range of theoretical and empirical issues discussed in this book will help to provoke further academic discussion on the study of language in the areas of discourse analysis, pragmatics, and corpus-based research.


Human Behavior and the Principle of Least Effort

Human Behavior and the Principle of Least Effort

Author: George Kingsley Zipf

Publisher: Ravenio Books

Published: 2016-01-27

Total Pages: 637

ISBN-13:

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This classic is arranged as follows: Preface 1. The Question of Practical Application. 2. The Question of Natural Science. 1. Introduction and Orientation I. The Selection of a Path II. The “Singleness of the Superlative” III. The Principle of Least Effort IV. The Scope of the Principle: “Tools-and-Jobs” V. Previous Studies VI. Prospectus 2. On the Economy of Words I. In Medias Res: Vocabulary Usage, and the Forces of Unification and Diversification II. The Question of Vocabulary Balance III. The Orderly Distribution of Meanings IV. The Integrality of Frequencies V. The Integrality of Rank VI. The Length of Intervals Between Repetitions VII. The Problem of Spreading Work Over Time (The Even Distribution of Work Over Time) 3. Formal Semantic Balance and the Economy of Evolutionary Process I. The “Minimum Equation” Of Arrangement II. The Law of Abbreviation of Words III. The Law of Diminishing Returns of Tools IV. The Law of Diminishing Returns of Words 4. Children’s Verbalizations and the “Origin of Speech” I. The Problem II. Quantitative Data III. Theoretical Discussion of the “Origin” Of Speech IV. Summary 5. Language as Sensation and Mentation I. The Comparative Conservatism of Tools in the Risks and Opportunities of the Environment II. The Economy of Sensation III. Mentation: The Correlation of Sensory Data IV. A Mind as a Unit Semantic System V. Intellectual Rigidity and Death: Miscellanea V. Summary: The N Minimum 6. The Ego as the “Origin” Of a Frame of Reference I. A Definition of an Organism II. The Biosocial Population of Organisms III. The Economy of Procreation IV. The Synchrony of the Biosocial Continuum 7. Mind and the Economy of Symbolic Process: Sex, Culture, and Schizophrenia I. Human Sexual Activity II. The Economy of Symbolic Process (Substitution III. Culture, Society, and the Superego IV. Autism and the Confusion of Kinds of Reality V. On Schizophrenic Speech VI. Semantic Dynamics: Summary VI. Language and the Structure of the Personality 8. The Language of Dreams and of Art I. The Language of Dreams II. The Language of Art III. Language and the Structure of the Personality: Mary of Part One 9. The Economy of Geography I. A Lemma in Which a Number of Human Beings Becomes Increasingly More Organized II. The Hypothesis of the “Minimum Equation” III. Empiric Tests IV. Concluding Remarks 10. Intranational and International Cooperation and Conflict I. Canadian Data II. Unstable and Stable Intranational Conditions III. Stable and Unstable International Equilibria 11. The Distribution of Economic Power and Social Status I. Theoretical Considerations II. Empiric Data III. The Interaction Between Individuals: Dominance and Submission IV. Summary 12. Prestige Symbols and Cultural Vogues I. Theoretical Considerations II. Pioneer Empiric Data III. Musical Composers and Compositions IV. Samples of Congressional Action V. Summary


Statistical Universals of Language

Statistical Universals of Language

Author: Kumiko Tanaka-Ishii

Publisher: Springer Nature

Published: 2021-04-01

Total Pages: 230

ISBN-13: 3030593770

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This volume explores the universal mathematical properties underlying big language data and possible reasons why such properties exist, revealing how we may be unconsciously mathematical in our language use. These properties are statistical and thus different from linguistic universals that contribute to describing the variation of human languages, and they can only be identified over a large accumulation of usages. The book provides an overview of state-of-the art findings on these statistical universals and reconsiders the nature of language accordingly, with Zipf's law as a well-known example. The main focus of the book further lies in explaining the property of long memory, which was discovered and studied more recently by borrowing concepts from complex systems theory. The statistical universals not only possibly lie as the precursor of language system formation, but they also highlight the qualities of language that remain weak points in today's machine learning. In summary, this book provides an overview of language's global properties. It will be of interest to anyone engaged in fields related to language and computing or statistical analysis methods, with an emphasis on researchers and students in computational linguistics and natural language processing. While the book does apply mathematical concepts, all possible effort has been made to speak to a non-mathematical audience as well by communicating mathematical content intuitively, with concise examples taken from real texts.


Computational Economics: Heterogeneous Agent Modeling

Computational Economics: Heterogeneous Agent Modeling

Author: Cars Hommes

Publisher: Elsevier

Published: 2018-06-27

Total Pages: 836

ISBN-13: 0444641327

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Handbook of Computational Economics: Heterogeneous Agent Modeling, Volume Four, focuses on heterogeneous agent models, emphasizing recent advances in macroeconomics (including DSGE), finance, empirical validation and experiments, networks and related applications. Capturing the advances made since the publication of Volume Two (Tesfatsion & Judd, 2006), it provides high-level literature with sections devoted to Macroeconomics, Finance, Empirical Validation and Experiments, Networks, and other applications, including Innovation Diffusion in Heterogeneous Populations, Market Design and Electricity Markets, and a final section on Perspectives on Heterogeneity. Helps readers fully understand the dynamic properties of realistically rendered economic systems Emphasizes detailed specifications of structural conditions, institutional arrangements and behavioral dispositions Provides broad assessments that can lead researchers to recognize new synergies and opportunities


Information Theory and Language

Information Theory and Language

Author: Łukasz Dębowski

Publisher: MDPI

Published: 2020-12-15

Total Pages: 244

ISBN-13: 3039360264

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“Information Theory and Language” is a collection of 12 articles that appeared recently in Entropy as part of a Special Issue of the same title. These contributions represent state-of-the-art interdisciplinary research at the interface of information theory and language studies. They concern in particular: • Applications of information theoretic concepts such as Shannon and Rényi entropies, mutual information, and rate–distortion curves to the research of natural languages; • Mathematical work in information theory inspired by natural language phenomena, such as deriving moments of subword complexity or proving continuity of mutual information; • Empirical and theoretical investigation of quantitative laws of natural language such as Zipf’s law, Herdan’s law, and Menzerath–Altmann’s law; • Empirical and theoretical investigations of statistical language models, including recently developed neural language models, their entropies, and other parameters; • Standardizing language resources for statistical investigation of natural language; • Other topics concerning semantics, syntax, and critical phenomena. Whereas the traditional divide between probabilistic and formal approaches to human language, cultivated in the disjoint scholarships of natural sciences and humanities, has been blurred in recent years, this book can contribute to pointing out potential areas of future research cross-fertilization.


Statistics and Dynamics of Urban Populations

Statistics and Dynamics of Urban Populations

Author: Marc Barthelemy

Publisher: Oxford University Press

Published: 2024-03-21

Total Pages: 177

ISBN-13: 0192867547

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This book describes all aspects of quantitative approaches to urban population growth, ranging from measures and empirical results such as the famous Zipf law, to the mathematical description of their evolution.


Word Frequency Distributions

Word Frequency Distributions

Author: R. Harald Baayen

Publisher: Springer Science & Business Media

Published: 2002-09-30

Total Pages: 364

ISBN-13: 9781402009273

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This book is a comprehensive introduction to the statistical analysis of word frequency distributions, intended for computational linguists, corpus linguists, psycholinguists, and researchers in the field of quantitative stylistics. It aims to make these techniques more accessible for non-specialists, both theoretically, by means of a careful introduction to the underlying probabilistic and statistical concepts, and practically, by providing a program library implementing the main models for word frequency distributions.


Fractals and Multifractals in Ecology and Aquatic Science

Fractals and Multifractals in Ecology and Aquatic Science

Author: Laurent Seuront

Publisher: CRC Press

Published: 2009-10-12

Total Pages: 366

ISBN-13: 1420004247

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Ecologists sometimes have a less-than-rigorous background in quantitative methods, yet research within this broad field is becoming increasingly mathematical. Written in a step-by-step fashion, Fractals and Multifractals in Ecology and Aquatic Science provides scientists with a basic understanding of fractals and multifractals and the techniques fo


The Psycho-Biology Of Language

The Psycho-Biology Of Language

Author: George Kingsley Zipf

Publisher: Routledge

Published: 2013-11-05

Total Pages: 360

ISBN-13: 1136310533

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This is Volume XXI in a series of twenty-one on the Cognitive Psychology. Orignally published in 1936, this is a study on the introduction to Dynamic Philology.