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Table of Contents
Intro
Contents
Part I Language as a Complex System
1 Introduction
1.1 Aims
1.2 Structure of This Book
1.3 Position of This Book
1.3.1 Statistical Universals as Computational Properties of Natural Language
1.3.2 A Holistic Approach to Language via Complex Systems Theory
1.4 Prospectus
2 Universals
2.1 Language Universals
2.2 Layers of Universals
2.3 Universal, Stylized Hypothesis, and Law
3 Language as a Complex System
3.1 Sequence and Corpus
3.1.1 Definition of Corpus
3.1.2 On Meaning
3.1.3 On Infinity
3.1.4 On Randomness
3.2 Power Functions
3.3 Scale-Free Property: Statistical Self-Similarity
3.4 Complex Systems
3.5 Two Basic Random Processes
Part II Property of Population
4 Relation Between Rank and Frequency
4.1 Zipf's Law
4.2 Scale-Free Property and Hapax Legomena
4.3 Monkey Text
4.4 Power Law of n-grams
4.5 Relative Rank-Frequency Distribution
5 Bias in Rank-Frequency Relation
5.1 Literary Texts
5.2 Speech, Music, Programs, and More
5.3 Deviations from Power Law
5.3.1 Scale
5.3.2 Speaker Maturity
5.3.3 Characters vs. Words
5.4 Nature of Deviations
6 Related Statistical Universals
6.1 Density Function
6.2 Vocabulary Growth
Part III Property of Sequences
7 Returns
7.1 Word Returns
7.2 Distribution of Return Interval Lengths
7.3 Exceedance Probability
7.4 Bias Underlying Return Intervals
7.5 Rare Words as a Set
7.6 Behavior of Rare Words
8 Long-Range Correlation
8.1 Long-Range Correlation Analysis
8.2 Mutual Information
8.3 Autocorrelation Function
8.4 Correlation of Word Intervals
8.5 Nonstationarity of Language
8.6 Weak Long-Range Correlation
9 Fluctuation
9.1 Fluctuation Analysis
9.2 Taylor Analysis
9.3 Differences Between the Two Fluctuation Analyses
9.4 Dimensions of Linguistic Fluctuation
9.5 Relations Among Methods
10 Complexity
10.1 Complexity of Sequence
10.2 Entropy Rate
10.3 Hilberg's Ansatz
10.4 Computing Entropy Rate of Human Language
10.5 Reconsidering the Question of Entropy Rate
Part IV Relation to Linguistic Elements and Structure
11 Articulation of Elements
11.1 Harris's Hypothesis
11.2 Information-Theoretic Reformulation
11.3 Accuracy of Articulation by Harris's Scheme
12 Word Meaning and Value
12.1 Meaning as Use and Distributional Semantics
12.2 Weber-Fechner Law
12.3 Word Frequency and Familiarity
12.4 Vector Representation of Words
12.5 Compositionality of Meaning
12.6 Statistical Universals and Meaning
13 Size and Frequency
13.1 Zipf Abbreviation of Words
13.2 Compound Length and Frequency
14 Grammatical Structure and Long Memory
14.1 Simple Grammatical Framework
14.2 Phrase Structure Grammar
14.3 Long-Range Dependence in Sentences
14.4 Grammatical Structure and Long-Range Correlation
14.5 Nature of Long Memory Underlying Language
Contents
Part I Language as a Complex System
1 Introduction
1.1 Aims
1.2 Structure of This Book
1.3 Position of This Book
1.3.1 Statistical Universals as Computational Properties of Natural Language
1.3.2 A Holistic Approach to Language via Complex Systems Theory
1.4 Prospectus
2 Universals
2.1 Language Universals
2.2 Layers of Universals
2.3 Universal, Stylized Hypothesis, and Law
3 Language as a Complex System
3.1 Sequence and Corpus
3.1.1 Definition of Corpus
3.1.2 On Meaning
3.1.3 On Infinity
3.1.4 On Randomness
3.2 Power Functions
3.3 Scale-Free Property: Statistical Self-Similarity
3.4 Complex Systems
3.5 Two Basic Random Processes
Part II Property of Population
4 Relation Between Rank and Frequency
4.1 Zipf's Law
4.2 Scale-Free Property and Hapax Legomena
4.3 Monkey Text
4.4 Power Law of n-grams
4.5 Relative Rank-Frequency Distribution
5 Bias in Rank-Frequency Relation
5.1 Literary Texts
5.2 Speech, Music, Programs, and More
5.3 Deviations from Power Law
5.3.1 Scale
5.3.2 Speaker Maturity
5.3.3 Characters vs. Words
5.4 Nature of Deviations
6 Related Statistical Universals
6.1 Density Function
6.2 Vocabulary Growth
Part III Property of Sequences
7 Returns
7.1 Word Returns
7.2 Distribution of Return Interval Lengths
7.3 Exceedance Probability
7.4 Bias Underlying Return Intervals
7.5 Rare Words as a Set
7.6 Behavior of Rare Words
8 Long-Range Correlation
8.1 Long-Range Correlation Analysis
8.2 Mutual Information
8.3 Autocorrelation Function
8.4 Correlation of Word Intervals
8.5 Nonstationarity of Language
8.6 Weak Long-Range Correlation
9 Fluctuation
9.1 Fluctuation Analysis
9.2 Taylor Analysis
9.3 Differences Between the Two Fluctuation Analyses
9.4 Dimensions of Linguistic Fluctuation
9.5 Relations Among Methods
10 Complexity
10.1 Complexity of Sequence
10.2 Entropy Rate
10.3 Hilberg's Ansatz
10.4 Computing Entropy Rate of Human Language
10.5 Reconsidering the Question of Entropy Rate
Part IV Relation to Linguistic Elements and Structure
11 Articulation of Elements
11.1 Harris's Hypothesis
11.2 Information-Theoretic Reformulation
11.3 Accuracy of Articulation by Harris's Scheme
12 Word Meaning and Value
12.1 Meaning as Use and Distributional Semantics
12.2 Weber-Fechner Law
12.3 Word Frequency and Familiarity
12.4 Vector Representation of Words
12.5 Compositionality of Meaning
12.6 Statistical Universals and Meaning
13 Size and Frequency
13.1 Zipf Abbreviation of Words
13.2 Compound Length and Frequency
14 Grammatical Structure and Long Memory
14.1 Simple Grammatical Framework
14.2 Phrase Structure Grammar
14.3 Long-Range Dependence in Sentences
14.4 Grammatical Structure and Long-Range Correlation
14.5 Nature of Long Memory Underlying Language