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The Mathematical Theory of Information:
Table of Contents

  1. About Information
  2. The Law of Diminishing Information
  3. General Properties of Information
  4. Specific Information Measurements
  5. Selected Applications
  6. Infodynamics
  7. Statistical Information
  8. Algorithmic Information
  9. Continuous Systems
  10. Continuous Information
  11. Deterministic Dynamics
  12. Control and Communication
  13. Information Physics
  14. The Information Quantum

References
Symbols
Index
(Re)Search hints by Jan Hajek, The Netherlands

  1. ABOUT INFORMATION
    1. Introduction
    2. Information @about
    3. A Day at the Races
    4. Bits and Entropy
    5. Hits and Reliability
    6. The Sailor's Tale
    7. The Ideal Receiver
    8. The Law of Diminishing Information
    9. Shannon's Noisy Channel
    10. Noise and nonlinearities
    11. Chains of channels
    12. Bliss of ignorance

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  1. THE LAW OF DIMINISHING INFORMATION
    1. Discrete messages
    2. Exhaustive sets
    3. Probability
    4. The transfer function
    5. Matrix notation
    6. Statistical independence
    7. Chain conditions
    8. The Law for discrete finite systems
    9. The axioms
    10. The Races revisited
    11. One observation
    12. Martha and Math

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  1. GENERAL PROPERTIES OF INFORMATION
    1. Classification of properties
    2. Irrelevant information
    3. Byron's law
    4. Theory of Games
    5. Utility
    6. Fair odds
    7. Reliability
    8. Deterministic systems
    9. Formal logic
    10. Reversibility
    11. One-to-one correspondence
    12. Information content
    13. Khinchin's condition
    14. Ford's formula
    15. The information function
    16. Joint information
    17. Volatility
    18. Additivity vs. Colligation
    19. Apples + Pears
    20. Quality of information
    21. Intrinsic information

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  1. SPECIFIC INFORMATION MEASURES
    1. Elements of Information
    2. Probabilistic information
    3. The absolute criterion
    4. Conditional information
    5. The semantic cont measure
    6. Extreme values
    7. Parameter space
    8. Convexity
    9. Hölder-Jensen inequality
    10. Entropy encore
    11. The uniqueness theorem
    12. The f-family
    13. A Medical Test
    14. Double-check

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  1. SELECTED APPLICATIONS
    1. Law lessons
    2. The Logic of Research
    3. Corroboration
    4. Popper's Conjecture...
    5. ...and its Refutation
    6. Beyond Bayes
    7. The absolute determinant
    8. Rank
    9. Capacity
    10. Convexity vs. Colligation
    11. Amount of data
    12. A bit uncertain
    13. Measure for Measure

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  1. INFODYNAMICS
    1. Dynamic systems
    2. Markov chains
    3. Rigidity
    4. The Pearson family
    5. Perron's formula
    6. Gerschgorin's theorem
    7. Regular chains
    8. Jordan canonical form
    9. Information decay
    10. Biased information
    11. The Information Society
    12. The Law and the law
    13. McTaggart's ABC
    14. Information geometry
    15. Intrinsic time
    16. Dissipative systems
    17. Deterministic time
    18. Thermodynamic reversibility
    19. Bit Brillouin
    20. The Gamow kitchen
    21. Lost ORDER
    22. Condensing systems
    23. Cause and effect
    24. Uniformity of nature

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  1. STATISTICAL INFORMATION
    1. Shannon's theory
    2. Bernoulli sets
    3. The law of large numbers
    4. Ergodicity
    5. Markov-Bernoulli messages
    6. The encoding problem
    7. Basic Binary Bernoulli
    8. The duality of reliability
    9. Total reliability maximized
    10. Safety first
    11. Average reliability maximized
    12. Utility encoding
    13. Semantic aspects
    14. The Entropy story
    15. Coarse graining
    16. Gibbs' paradox
    17. Work for a Cause

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  1. ALGORITHMIC INFORMATION
    1. Complexity
    2. Squeezin' a sequence
    3. Algorithmic compression
    4. Chaitin complexity
    5. Infinite message sets
    6. The ideal computer
    7. Computability
    8. The weakness of Kraft
    9. Genetic information
    10. Algorithmic channels
    11. Diophantine channels
    12. Cipher-cypher
    13. The Chaitin channel
    14. In Quest of Knowledge
    15. Induction and Seduction
    16. Coin-o'-two-tails
    17. Cultural constraints
    18. Evolution vs. Creation
    19. Darwin's dictum
    20. Anthropocentric information

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  1. CONTINUOUS SYSTEMS
    1. The probability density
    2. A discrete hint
    3. The inversion problem
    4. Transformed Laplace
    5. Kernel eigenvalues
    6. Triangular transfer
    7. Fredholm equations
    8. Symmetric Pincherle-Goursat
    9. The Bell of Gauss
    10. Jacobians
    11. Deterministic density
    12. A parabolic example
    13. Fuzzy sets
    14. Multi-variables
    15. Uncertain probability

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  1. CONTINUOUS INFORMATION
    1. Analog signals
    2. Continuous entropy
    3. Calculus of variations
    4. Continuous capacity
    5. Transmission with tolerance
    6. The Law in continuous form
    7. Direct approach to entropy
    8. Reversibility criterion
    9. Statistics and Information Theory
    10. Correlation: no information measure
    11. Uncorrelated data
    12. Deterministic correlation
    13. Invariance: an information measure
    14. Accuracy
    15. Sensitivity
    16. Small sample statistics
    17. Information gain
    18. Hypotheses, hypotheses!
    19. Fisher information
    20. Galilean invariance
    21. A Galilean chain
    22. Frequency filters

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  1. DETERMINISTIC DYNAMICS
    1. The macroscopic observer
    2. Stability and Chaos
    3. The reversibility collapse
    4. Perturbations
    5. The square amplitude law
    6. Collapsing entropy
    7. Shrinking volume
    8. Liapunov stability
    9. Liapunov's method
    10. Liapunov and the entropy
    11. Chaos: Stretch-'n'-Fold
    12. Folding
    13. Transfinite information
    14. Stretching
    15. Topological information
    16. The triangular map
    17. Farey sequences
    18. Computing transformations
    19. Fragile indestructibility
    20. The teachings of Chaos
    21. Economic chaos
    22. The prophet's fallacy
    23. Breakdown of computer models
    24. Order from information loss

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  1. CONTROL AND COMMUNICATION
    1. Cybernetics
    2. Timeliness
    3. Time-lag
    4. Process control
    5. Byron on control
    6. Optimization & control
    7. Control quality
    8. Ziegler-Nichols
    9. Shower time
    10. Deadbeat control
    11. Deming's Demon
    12. The Källe regulator
    13. The S of Malthus
    14. Variation and Selection
    15. Biological chains
    16. Complexity and sex
    17. The nature of information
    18. Neural correlates
    19. Extended Darwin
    20. River Time

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  1. INFORMATION PHYSICS
    1. Race in space
    2. Spacetime
    3. Einstein causality
    4. Einstein-Podolsky-Rosen
    5. The locality condition
    6. The Freedman-Clauser experiment
    7. Bell's inequalities
    8. Linear consistency
    9. Ghost buster symmetry
    10. Cramer killed the cat
    11. Relative time
    12. Einstein's twins
    13. Relative space
    14. The particular relativity
    15. The topological interpretation
    16. Muon time
    17. Limits to light
    18. Advanced wave communication
    19. Thinner than vacuum
    20. The Scharnhorst effect

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  1. THE INFORMATION QUANTUM
    1. Knowledge and measurement
    2. The Heisenberg receiver
    3. The Heffner amplifier
    4. Schrödinger's wave equation
    5. A particle in a box
    6. Statistical Quantum Mechanics
    7. Quantum statistical information
    8. The second law of thermodynamics
    9. Irreversible processes
    10. Loschmidt's paradox
    11. In search of hidden order
    12. Order and disorder
    13. Phenomenologic thermodynamics
    14. The ideal gas thermometer
    15. Potential work
    16. Maxwell's demon
    17. Szilard's engine
    18. Kinetic equivalence
    19. Computation
    20. Objectivity!
    21. Epilogue

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