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Introduction to Transfer Entropy: Information Flow in Complex Systems 1st ed. 2016 [Kõva köide]

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  • Formaat: Hardback, 190 pages, kõrgus x laius: 235x155 mm, kaal: 4557 g, 21 Illustrations, color; 3 Illustrations, black and white; XXIX, 190 p. 24 illus., 21 illus. in color., 1 Hardback
  • Ilmumisaeg: 24-Nov-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319432214
  • ISBN-13: 9783319432212
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Introduction to Transfer Entropy: Information Flow in Complex Systems 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 190 pages, kõrgus x laius: 235x155 mm, kaal: 4557 g, 21 Illustrations, color; 3 Illustrations, black and white; XXIX, 190 p. 24 illus., 21 illus. in color., 1 Hardback
  • Ilmumisaeg: 24-Nov-2016
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319432214
  • ISBN-13: 9783319432212
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319432212.html
Märksõnad:
This book considers a relatively new metric in complex systems, transfer entropy, derived from a series of measurements, usually a time series. After a qualitative introduction and a chapter that explains the key ideas from statistics required to understand the text, the authors then present information theory and transfer entropy in depth. A key feature of the approach is the authors" work to show the relationship between information flow and complexity. The later chapters demonstrate information transfer in canonical systems, and applications, for example in neuroscience and in finance.The book will be of value to advanced undergraduate and graduate students and researchers in the areas of computer science, neuroscience, physics, and engineering.

Introduction.- Statistical Preliminaries.- Information Theory.- Transfer Entropy.- Information Transfer in Canonical Systems.- Information Transfer in Financial Markets.- Miscellaneous Applications of Transfer Entropy.- Concluding Remarks.
1 Introduction
1(10)
1.1 Information Theory
2(1)
1.2 Complex Systems
2(7)
1.2.1 Cellular Automata
3(1)
1.2.2 Spin Models
4(1)
1.2.3 Oscillators
5(1)
1.2.4 Complex Networks
5(2)
1.2.5 Random Boolean Networks
7(1)
1.2.6 Flocking Behaviour
7(2)
1.3 Information Flow and Causality
9(1)
1.4 Applications
10(1)
1.5 Overview
10(1)
2 Statistical Preliminaries
11(22)
2.1 Set Theory
12(1)
2.2 Discrete Probabilities
13(1)
2.3 Conditional, Independent and Joint Probabilities
14(6)
2.3.1 Conditional Probabilities
14(1)
2.3.2 Independent Probabilities
14(1)
2.3.3 Joint Probabilities
15(1)
2.3.4 Conditional Independence
16(1)
2.3.5 Time-Series Data and Embedding Dimensions
17(1)
2.3.6 Conditional Independence and Markov Processes
18(2)
2.3.7 Vector Autoregression
20(1)
2.4 Statistical Expectations, Moments and Correlations
20(2)
2.5 Probability Distributions
22(6)
2.5.1 Binomial Distribution
22(1)
2.5.2 Poisson Distribution
23(1)
2.5.3 Continuous Probabilities
24(1)
2.5.4 Gaussian Distribution
25(1)
2.5.5 Multivariate Gaussian Distribution
25(3)
2.6 Symmetry and Symmetry Breaking
28(5)
3 Information Theory
33(32)
3.1 Introduction
33(2)
3.2 Basic Ideas
35(16)
3.2.1 Entropy and Information
35(3)
3.2.2 Mutual Information
38(4)
3.2.3 Conditional Mutual Information
42(1)
3.2.4 Kullback--Leibler Divergence
43(2)
3.2.5 Entropy of Continuous Processes
45(5)
3.2.6 Entropy and Kolmogorov Complexity
50(1)
3.2.7 Historical Note: Mutual Information and Communication
50(1)
3.3 Mutual Information and Phase Transitions
51(1)
3.4 Numerical Challenges
52(13)
3.4.1 Calculating Entropy
53(6)
3.4.2 Calculating Mutual Information
59(4)
3.4.3 The Non-stationary Case
63(2)
4 Transfer Entropy
65(32)
4.1 Introduction
65(1)
4.2 Definition of Transfer Entropy
66(12)
4.2.1 Determination of History Lengths
69(3)
4.2.2 Computational Interpretation as Information Transfer
72(2)
4.2.3 Conditional Transfer Entropy
74(3)
4.2.4 Source--Target Lag
77(1)
4.2.5 Local Transfer Entropy
77(1)
4.3 Transfer Entropy Estimators
78(4)
4.3.1 KSG Estimation for Transfer Entropy
79(1)
4.3.2 Symbolic Transfer Entropy
80(1)
4.3.3 Open-Source Transfer Entropy Software
81(1)
4.4 Relationship with Wiener--Granger Causality
82(8)
4.4.1 Granger Causality Captures Causality as Predictive of Effect
83(1)
4.4.2 Definition of Granger Causality
83(3)
4.4.3 Maximum-Likelihood Estimation of Granger Causality
86(2)
4.4.4 Granger Causality Versus Transfer Entropy
88(2)
4.5 Comparing Transfer Entropy Values
90(2)
4.5.1 Statistical Significance
90(1)
4.5.2 Normalising Transfer Entropy
91(1)
4.6 Information Transfer Density and Phase Transitions
92(1)
4.7 Continuous-Time Processes
93(4)
5 Information Transfer in Canonical Systems
97(28)
5.1 Cellular Automata
98(6)
5.2 Spin Models
104(2)
5.3 Random Boolean Networks
106(5)
5.4 Small-World Networks
111(4)
5.5 Swarming Models
115(4)
5.6 Synchronisation Processes
119(3)
5.7 Summary
122(3)
6 Information Transfer in Financial Markets
125(14)
6.1 Introduction to Financial Markets
126(2)
6.2 Information Theory Applied to Financial Markets
128(2)
6.2.1 Entropy and Economic Diversity: an Early Ecology of Economics
128(1)
6.2.2 Maximum Entropy: Maximum Diversity?
129(1)
6.2.3 Mutual Information: Phase Transitions and Market Crashes
129(1)
6.3 Information Transferred from One Market Index to Another
130(3)
6.4 From Indices to Equities and from Equities to Indices
133(2)
6.4.1 Economics of Beauty Pageants
134(1)
6.5 The Internal Economy and Its Place in the Global Economy
135(4)
7 Miscellaneous Applications of Transfer Entropy
139(28)
7.1 Information Transfer in Physiological Data
139(4)
7.2 Effective Network Inference
143(6)
7.2.1 Standard Pairwise TE Approach for Effective Network Inference
144(1)
7.2.2 Addressing Redundancy and Synergy in the Data
145(3)
7.2.3 Applications of Effective Network Inference
148(1)
7.3 Applications in Neuroscience
149(4)
7.3.1 TE for Pulse Sequences
149(2)
7.3.2 Direct TE Estimation Between Spiking Neurons
151(1)
7.3.3 TE in Brain Imaging
152(1)
7.4 Information Transfer in Biochemical Networks
153(4)
7.5 Information Transfer in Embodied Cognitive Systems
157(5)
7.6 Information Transfer in Social Media
162(2)
7.7 Summary
164(3)
8 Concluding Remarks
167(20)
8.1 Estimation
167(2)
8.1.1 Non-parametric Estimation
167(1)
8.1.2 Parametric Estimation
168(1)
8.1.3 Non-stationary Systems
169(1)
8.2 Systems with Many Variables
169(1)
8.3 Touching the Void: the Link to Thermodynamics
170(17)
References
171(16)
Index 187