Frieden / Gatenby Exploratory Data Analysis Using Fisher Information

1. Auflage 2010
ISBN: 978-1-84628-777-0
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 363 Seiten

This book uses a mathematical approach to deriving the laws of science and technology, based upon the concept of Fisher information. The approach that follows from these ideas is called the principle of Extreme Physical Information (EPI). The authors show how to use EPI to determine the theoretical input/output laws of unknown systems. Will benefit readers whose math skill is at the level of an undergraduate science or engineering degree.

Professor Emeritus - B. Roy Frieden: B.S., M.S., Ph.D., Professor of Optical Sciences, Univ. of Arizona 1966-2002; books 'Probability, Statistical Optics and Data Testing' (Springer-Verlag, 3rd ed., 2001), 'Physics from Fisher Information' (Cambridge Univ. Press, 1998), 'Science from Fisher Information' (Cambridge Univ. Press, 2004); inventor of principle of Extreme physical information (EPI) Dr. Robert A. Gatenby: BSE, Princeton Univ. MD, University of Pennsylvania.

Autoren/Hrsg.

Frieden, Roy

Gatenby, Robert A.

Inhaltsverzeichnis

1;Table of Contents
;5
2;Contributor Details;7
3;1 Introduction to Fisher Information: Its Origin, Uses, and Predictions
;14
3.1;1.1. Mathematical Tools;16
3.1.1;1.1.1. Partial Derivatives;16
3.1.2;1.1.2. Euler-Lagrange Equations;17
3.1.2.1;1.1.2.1. Extremum Problem;17
3.1.2.2;1.1.2.2. Solution;17
3.1.2.3;1.1.2.3. Nature of Extremum;18
3.1.2.4;1.1.2.4. Building in Constraints;18
3.1.2.5;1.1.2 .5. Example: MFI Lagrangian;19
3.1.3;1.1.3. Dirac Delta Function;19
3.1.4;1.1.4. Unitary Transformation;20
3.2;1.2. A Tutorial on Fisher Information;21
3.2.1;1.2.1. Definition and Basic Properties;21
3.2.1.1;1.2.1.1. Comparisonwith ShannonInformation;21
3.2.1.2;1.2.1.2. System Input-Output Law;22
3.2.1.3;1.2.1.3. UnbiasedEstimators;22
3.2.1.4;1.2.1.4. Use of Schwarz Inequality;23
3.2.1.5;1.2.1.5. Cramer-Rao Inequality;24
3.2.1.6;1.2.1.6. Fisher Coordinates;24
3.2.1.7;1.2.1.7. Efficient Estimation;25
3.2.1.8;1.2.1.8. Examples of Tests for Efficiency;25
3.2.2;1.2.2. Alternative Forms of Fisher Information I;26
3.2.2.1;1.2.2.1. Multiple Parameters and Data;26
3.2.2.2;1.2.2.2. Shift-InvariantCases;27
3.2.2.3;1.2.2.3. One-Dimensional Applications;28
3.2.2.4;1.2.2.4. No Shift-Invariance, Discrete Data;28
3.2.2.5;1.2.2.5. Amplitude q-Forms of I;29
3.2.2.6;1.2.2.6. Tensor Form of I;29
3.2.2.7;1.2.2.7. One-Dimensional q-Form of I;30
3.2.2.8;1.2.2.8. Complex Amplitude 1/J-Form of I;30
3.2.2.9;1.2.2.9. Principal Value Integrals;31
3.2.2.10;1.2.2.10. I in Curved Space
;31
3.2.2.11;1.2.2.11. I for Gluon Four-Position Measurement
;32
3.2.2.12;1.2.2.12. Local vs Global Measures of Disorder;34
3.3;1.3. Introduction to Source Fisher Information J;34
3.3.1;1.3.1. EPI Zero Principle;34
3.3.2;1.3.2. Efficiency Constant K;35
3.3.3;1.3.3. Fisher I -Theorem;35
3.3.3.1;1.3.3.1. I as a Montonic Measure of Time;36
3.3.3.2;1.3.3.2. Re-Expressing the Second Law;36
3.4;1.4. Extreme Physical Information (EPI);36
3.4.1;1.4.1. Relation to Anthropic Principle;37
3.4.2;1.4.2. Varieties of EPI Solution
;38
3.4.3;1.4.3. Data Information is Generic;38
3.4.4;1.4.4. Underpinnings: A "Participatory" Universe;39
3.4.5;1.4.5. A "Cooperative" Universe and Its Implications;40
3.4.6;1.4.6. EPI as an Autopoietic Process;44
3.4.7;1.4.7. Drawbacks of Classical "Action Principle";44
3.5;1.5. Getting the Source Information J for a Given Scenario;45
3.5.1;1.5.1. Exact, Unitary Scenarios: Type (A) Abduction;45
3.5.2;1.5.2. Exhaustivity Property ofEPI;45
3.5.3;1.5.3. Inexact, Classical Scenarios : Type (B) Deduction;46
3.5.4;1.5.4. Empirical Scenarios: Type (C) Induction;47
3.5.5;1.5.5. Summary;47
3.6;1.6. Information Game;47
3.6.1;1.6.1. Minimax Nature ofSolution;48
3.6.2;1.6.2. Saddlepoint Property;48
3.6.3;1.6.3. Game Aspect ofEPI Solution;49
3.6.4;1.6.4. Information Demon;49
3.6.5;1.6.5. Peirce Graphs;49
3.6.6;1.6.6. Game Corollary;50
3.6.7;1.6.7. Science Education;51
3.7;1.7. Predictions of the EPI Approach;51
4;2 Financial Economics from Fisher Information
;55
4.1;2.1. Constructing Probability Density Functions on Price Fluctuation
;55
4.1.1;2.1.1. Summary;55
4.1.2;2.1.2. Background;56
4.1.3;2.1.3. Variational Approaches to the Determination of PriceValuation Fluctuation
;56
4.1.4;2.1.4. Trade as a Measurement in EPI Process;57
4.1.5;2.1.5. Intrinsic vs Actual Data Values
;58
4.1.6;2.1.6. Incorporating Data Values into EPI;59
4.1.7;2.1.7. Information J and the "Technical" Approach to Valuation
;60
4.1.8;2.1.8. Net EPI Principle
;61
4.1.9;2.1.9. SWE Solutions;61
4.2;2.2. Yield Curve Statics and Dynamics;63
4.2.1;2.2.1. Summary;63
4.2.2;2.2.2. Background;63
4.2.3;2.2.3. PDFin the Term Structure ofInterest Rates, and Yield Curve Construction
;64
4.2.4;2.2.4. PDF for a Perpetual Annuity
;68
4.2.5;2.2.5. Yield Curve Dynamics;70
4.2.6;2.2.6. Relation to Nelson Siegel Approach and Dynamical Fokker-Planck Solution
;73
4.2.7;2.2.7. A Measure of Volatility;74
4.2.8;2.2.8. Equilibrium Distributions;76
4.2.9;2.2.9. Aoki Theory;76
4.2.10;2.2.10. Non-equilibrium Distributions;77
4.3;2.3. Information and Investment;77
4.3.1;2.3.1. Summary;77
4.3.2;2.3.2. Background;78
4.3.3;2.3.3. Information I;79
4.3.4;2.3.4. Information J;80
4.3.5;2.3.5. Phase Space;80
4.3.6;2.3.6. Optimized Information and q-Theory;82
4.3.7;2.3.7. Other Optimized Strategies;83
4.3.8;2.3.8. Investment Parameters;84
4.3.9;2.3.9. Uncertainty Principle on Capital and Investment Flow
;85
4.3.10;2.3.10. Market Efficiency;85
5;3 Growth Characteristics of Organisms
;87
5.1;3.1. Information in Living Systems: A Survey;87
5.1.1;3.1.1. Summary;87
5.1.2;3.1.2. Introduction;88
5.1.3;3.1.3. Ideal Requirements of Biological Information
;89
5.1.4;3.1.4. Some Alternative Information Types;91
5.1.5;3.1.5. Kullback-Leibler Information;91
5.1.6;3.1.6. Principle ofExtreme K-L Information;92
5.1.7;3.1.7. Bias Property;93
5.1.8;3.1.8. A Transition to the EPI Principle;93
5.1.9;3.1.9. Biological Interplay ofSystem and Reference Probabilities
;93
5.1.10;3.1.10. Application ofK-L Principle to Developmental Biology
;94
5.1.11;3.1.11. Shannon Information Types;94
5.1.12;3.1.12. Information as an Expenditure of Energy
;96
5.1.13;3.1.13. Some Problems with Biological Uses of Shannon Information
;96
5.1.14;3.1.14. Intracellular Information Dynamics;97
5.1.14.1;3.1.14.1. Bioinformatics and Network Analysis;97
5.1.14.2;3.1.14.2. Hub Dynamics;99
5.1.14.3;3.1.14.3. Dynamics of System Failures;100
5.1.15;3.1.15. Information and Cellular Fitness;100
5.1.16;3.1.16. Cellular Information Utilization;101
5.1.17;3.1.17. Potential Controversies-Is All Cellular Information Stored in the Genome and Transmitted by Proteins?
;102
5.1.18;3.1.18. Multicellular Information Dynamics;104
5.1.19;3.1.19. Information and Disease;105
5.1.20;3.1.20. Conclusions;107
5.2;3.2. Applications of IT and EPI to Carcinogenesis;107
5.2.1;3.2.1. Summary;107
5.2.2;3.2.2. Introduction;108
5.2.3;3.2.3. Bound and Free Intracellular Information;109
5.2.4;3.2.4. Information Dynamics Before and After Reproduction,With and Without Mutation;110
5.2.5;3.2.5. Limits ofInformation Degradation in Carcinogenesis;112
5.2.5.1;3.2.5.1. Mutation Rates for Various Gene Proliferation Types;113
5.2.5.2;3.2.5 .2. Angiogenesis;113
5.2.6;3.2.6. The Evolving Microenvironment and Resulting Mutation Rate
;114
5.2.7;3.2.7. Application of EPI to Tumor Growth
;115
5.2.7.1;3.2.7.1. Fisher vs Shannon Informations;116
5.2.7.2;3.2.7.2. Brief Review of EPI;116
5.2.8;3.2.8. Fisher Variable, Measurements;117
5.2.9;3.2.9. Implementation of EPI
;118
5.2.9.1;3.2.9.1. Recourse to Probability Amplitude;118
5.2.9.2;3.2.9.2. Self-Consistency Approach, General Considerations;118
5.2.10;3.2.10. EPI Solution: A Power Law;119
5.2.11;3.2.11. Determining the Power by Minimizing the Information
;119
5.2.12;3.2.12. Experimental Verification;120
5.2.13;3.2.13. Implications of Solution
;121
5.2.13.1;3.2.13.1. Efficiency K;121
5.2.13.2;3.2.13.2. Fibonacci Constant;122
5.2.13.3;3.2.13.3 . Uncertainty in Onset Time;123
5.2.14;3.2.14. Alternative Growth Model Using Monte Carlo Techniques
;124
5.2.15;3.2.15. Conclusions;125
5.3;3.3. Appendix A: Derivation of EPI Power Law Solution;128
5.3.1;3.3.1. General Solution;128
5.3.2;3.3.2. Boundary-Value Conditions;130
5.3.3;3.3.3. Error in the Estimated Duration of the Cancer;130
6;4 Information and Thermal Physics
;132
6.1;4.1. Connections Between Thermal and Information Physics;133
6.1.1;4.1.1. Summary;133
6.1.2;4.1.2. Introduction;133
6.1.3;4.1.3. A Scientific Theory's Structure;134
6.1.4;4.1.4. Fisher-Related Activity in Contemporary Physics;135
6.1.5;4.1.5. BriefPrimer on Fisher's Information Measure;136
6.2;4.2. Hamiltonian Systems;136
6.2.1;4.2.1. Summary;136
6.2.2;4.2.2. Classical Statistical Mechanics a la Fisher
;137
6.2.3;4.2.3. Canonical Example;140
6.2.4;4.2.4. General Quadratic Hamiltonians;140
6.2.5;4.2.5. Free Particle;141
6.2.6;4.2.6. N Harmonic Oscillators;142
6.2.7;4.2.7. A Nonlinear Problem: Paramagnetic System;142
6.2.8;4.2.8. Conclusions;143
6.3;4.3. The Place of A Fisher Thermal Physics;144
6.3.1;4.3.1. Summary;144
6.3.2;4.3.2. Preliminaries;144
6.3.3;4.3.3. The Standard Macroscopic Theory;144
6.3.3.1;4.3.3.1. Macroscopic Thermodynamics
;144
6.3.3.2;4.3 .3.2. Legendre Structure;145
6.3.4;4.3.4. Statistical Mechanics;146
6.3.5;4.3.5. Axioms ofInformation Theory;146
6.4;4.4. Modem Approaches to Statistical Mechanics;147
6.4.1;4.4.1. Summary;147
6.4.2;4.4.2. Jaynes' Reformulation;147
6.4.3;4.4.3. Legendre Structure in Jaynes' Formulation;148
6.4.4;4.4.4. Non-Shannon Information Measures;149
6.4.5;4.4.5. Legendre Structure Preserved by a ChangeofMeasure Is --> IT
;149
6.4.6;4.4.6. Still More General Measures;150
6.5;4.5. Fisher Thermodynamics;151
6.5.1;4.5.1. Summary;151
6.5.2;4.5.2. FIM Concavity and Second Law;152
6.5.3;4.5.3. Minimizing FIM Leads to a Schrodinger-Like Equation;152
6.5.4;4.5.4. FIM Legendre Transform Structure;154
6.5.5;4.5.5. Shannon's S vs Fisher's I;154
6.5.6;4.5.6. Discussion;155
6.6;4.6. The Grad Approach in Ten Steps;157
6.6.1;4.6.1. Summary;157
6.6.2;4.6.2. Steps ofthe Approach;157
6.7;4.7. Connecting Excited Solutions of the Fisher-SWE to Nonequilibrium Thermodynamics
;158
6.7.1;4.7.1. Summary;158
6.7.2;4.7.2. Establishing the Connection;158
6.7.3;4.7.3. Application: Viscosity;159
6.7.3.1;4.7.3.1. Boltzmann Equation in the Relaxation Approximation;159
6.7.3.2;4.7.3.2. Generalities on Viscosity;160
6.7.4;4.7.4. Comparison with the Grad Treatment;164
6.7.5;4.7.5. The Fisher Treatment of Viscosity;165
6.7.5.1;4.7.5.1. Ground State;165
6.7.5.2;4.7.5 .2. Admixture of Excited State s;166
7;5 Parallel Information Phenomena of Biology and Astrophysics
;168
7.1;5.1. Corresponding Quarter-Power Laws of Cosmology and Biology
;168
7.1.1;5.1.1. Summary;168
7.1.2;5.1.2. Introduction;169
7.1.3;5.1.3. Cosmological Attributes;171
7.1.3.1;5.1.3.1. Unitless Physical Constants;171
7.1.3.2;5.1.3.2. Dirac Hypothesis for the Cosmological Constants;172
7.1.4;5.1.4. Objectives;173
7.1.5;5.1.5. Biological Attributes;173
7.1.6;5.1.6. Corresponding Attributes ofBiology and Cosmology;176
7.1.7;5.1.7. Discussion;180
7.1.8;5.1.8. Concluding Remarks;184
7.2;5.2. Quantum Basis for Systems Exhibiting Population Growth
;185
7.2.1;5.2.1. Summary;185
7.2.2;5.2.2. Introduction;185
7.2.3;5.2.3. Hartree Approximation;186
7.2.4;5.2.4. Schrodinger Equation;186
7.2.5;5.2.5. Force-Free Medium;187
7.2.6;5.2.6. Case ofa Complex Potential;188
7.2.7;5.2.7. SWE Without Planck Constant;189
7.2.8;5.2.8. Growth Equation;189
7.2.9;5.2.9. How Could Such a System Be Realized?;190
7.2.10;5.2.10. Current Evidence for Nanolife;191
8;6 Encryption of Covert Information Through a Fisher Game
;194
8.1;6.1. Summary;194
8.1.1;6.1.1. Fisher Information and Extreme Physical Information;194
8.1.2;6.1.2. Fisher Game;195
8.1.3;6.1.3. Extreme Physical Information vs Minimum Fisher Information
;196
8.1.4;6.1.4. Time-Independent Schrodinger Equation
;196
8.1.5;6.1.5. Real Probability Amplitudes and Lagrangians;197
8.1.6;6.1.6. MFI Output and the Time-Independent Schrodinger-Like Equation
;198
8.1.7;6.1.7. Quantum Mechanical Methods in Pattern Recognition Problems
;198
8.1.8;6.1.8. Solutions of the TISE and TISLE
;198
8.1.9;6.1.9. Information Theory and Securing Covert Information;199
8.1.10;6.1.10. Rationale for Encrypting Covert Information in a Statistical Distribution
;201
8.1.11;6.1.11. Reconstruction Problem;202
8.1.12;6.1.12. Ill-Conditioned Nature of Encryption Problem
;202
8.1.13;6.1.13. Use ofthe Game Corollary;203
8.1.14;6.1.14. Objectives to be Accomplished;203
8.2;6.2. Embedding Covert Information in a Statistical Distribution
;204
8.2.1;6.2.1. Operators and the Dirae Notation;204
8.2.2;6.2.2. Eigenstructure of the Constraint Operator
;205
8.2.3;6.2.3. The Encryption and Decryption Operators;206
8.2.4;6.2.4. Generic Strategy for Encryption and Decryption;206
8.3;6.3. Inference of the Host Distribution Using Fisher Information
;207
8.3.1;6.3.1. Correspondence Between MFI and MaxEnt;208
8.3.2;6.3.2. Amplitudes and Pseudo-Potentials Satisfying MFI and MaxEnt
;208
8.3.3;6.3.3. Modified Game Corollary;209
8.3.4;6.3.4. Fisher Game vs MaxEnt;212
8.4;6.4. Implementation of Encryption and Decryption Procedures
;216
8.4.1;6.4.1. Encryption Process;219
8.4.2;6.4.2. Decryption;223
8.4.3;6.4.3. Summary of the Encryption-Decryption Strategy;224
8.4.4;6.4.4. Security Against Malicious Attacks;225
8.5;6.5. Extension of the Encryption Strategy;227
8.6;6.6. Summary of Concepts;228
9;7 Applications of Fisher Information to the Management of Sustainable Environmental Systems
;230
9.1;7.1. Summary;230
9.2;7.2. Introduction;231
9.3;7.3. Fisher Information Theory;232
9.3.1;7.3.1. Definition;232
9.3.2;7.3.2. Shift-Invariant Cases;233
9.3.3;7.3.3. Phase States s of Dynamic Systems
;234
9.4;7.4. Probability Law on State Variable s;235
9.5;7.5. Evaluating the Information;237
9.6;7.6. Dynamic Order;238
9.7;7.7. Dynamic Regimes and Fisher Information;239
9.8;7.8. Evaluation of Fisher Information;240
9.9;7.9. Applications to Model Systems;242
9.9.1;7.9.1. Two-Species Model System;242
9.9.2;7.9.2. Multispecies Model: Species and Trophic Levels;246
9.9.3;7.9.3. Ecosystems with Pseudo-Economies: Agriculture and Industry
;248
9.10;7.10. Applications to Real Systems;250
9.10.1;7.10.1. North Pacific Ocean;251
9.10.2;7.10.2. Global Climate;253
9.10.3;7.10.3. Sociopolitical Data;254
9.11;7.11. Summary;256
10;8 Fisher Information in Ecological Systems
;258
10.1;8.1. Predicting Susceptibility to Population Cataclysm;258
10.1.1;8.1.1. Summary;258
10.1.2;8.1.2. Introduction;259
10.1.3;8.1.3. A Biological Uncertainty Principle;259
10.1.4;8.1.4. Ramification of the Uncertainty Principle
;260
10.1.5;8.1.5. Necessary Condition for Cataclysm;261
10.1.6;8.1.6. Scenarios of Cataclysm from Fossil Record;262
10.1.7;8.1.7. Usefully Conservative Scenario;263
10.1.8;8.1.8. Resulting Changes in Population Occurrence Rates;263
10.1.9;8.1.9. Getting the Information;264
10.1.10;8.1.10. Square Root Decision Rule;265
10.1.11;8.1.11. Final Decision Rule, Conditions of Use;265
10.1.12;8.1.12. Ideally Breeding Rabbits;267
10.1.13;8.1.13. Homo Sapiens;268
10.2;8.2. Finding the Mass Occurrence Law For Living Creatures;269
10.2.1;8.2.1. Summary;269
10.2.2;8.2.2. Background;269
10.2.3;8.2.3. Cramer-Rao Inequality and Efficient Estimation;271
10.2.4;8.2.4. Efficiency Condition;272
10.2.5;8.2.5. Objectives;272
10.2.6;8.2.6. How Can the Efficiency Condition be Satisfied?;273
10.2.7;8.2.7. Power-Law Solution;274
10.2.8;8.2.8. Normalized Law;275
10.2.9;8.2.9. Unbiasedness Condition;275
10.2.10;8.2.10. Asymptotic Power b = 1+E, with E Small
;276
10.2.11;8.2.11. Discussion;278
10.2.12;8.2.12. Experimental Evidence for a l/x Law;279
10.3;8.3. Derivation of Power Laws of Nonliving and Living Systems
;280
10.3.1;8.3.1. Summary;280
10.3.1.1;8.3.1.1. General Allometric Laws;281
10.3.1.2;8.3.1.2. Biological Allometric Laws;281
10.3.1.3;8.3.1.3. On Models for Biological Allometry;282
10.3.2;8.3.2. PriorKnowledge Assumed;283
10.3.3;8.3.3. Measurement Channel for Problem;284
10.3.3.1;8.3.3.1. Measurement, System Function;284
10.3.3.2;8.3.3.2. Some Caveats to EPI Derivation;285
10.3.4;8.3.4. Data Information I;285
10.3.5;8.3.5. Source Information lea);286
10.3.5.1;8.3.5.1. Microlevel Contributions;286
10.3.5.2;8.3.5.2. Fourier Analysis;286
10.3.6;8.3.6. Net EPI Problem
;288
10.3.7;8.3.7. Synopsis of the Approach
;288
10.3.8;8.3.8. Primary Variation ofthe System Function Leads to a Family of Power Laws
;289
10.3.9;8.3.9. Variation of the Attribute Parameters Gives Powers a - an = n/4
;290
10.3.10;8.3.10. Secondary Extremization Through Choice of h(x)
;291
10.3.10.1;8.3.10.1. Special Form of Function h(x);292
10.3.10.2;8.3.10.2. Resulting variational principle in Base Function h(x);292
10.3.10.3;8.3.10.3. Secondary Variational Principle in Associated Function k(x );293
10.3.10.4;8.3.10.4 . Result k(x ) = 0, Giving Base Function hex ) Proportional to x;293
10.3.11;8.3.11. Final Allometric Laws;294
10.3.12;8.3.12. Alternative Model Su = L;295
10.3.13;8.3.13. Discussion;295
11;9 Sociohistory: An Information Theory of Social Change
;298
11.1;9.1. Summary;298
11.1.1;9.1.1. Philosophical Background;299
11.1.2;9.1.2. Boundary Considerations;300
11.1.3;9.1.3. Sociohistory: Historical Aspects;301
11.1.4;9.1.4. Kant's Notion of the Noumenon;302
11.1.5;9.1.5. Extreme Phenomenal Information;302
11.1.6;9.1.6. Complex Systems and Chaos;303
11.1.7;9.1.7. fin-Yang Nature of Sociohistory
;303
11.1.8;9.1.8. Dialectic Process;304
11.1.9;9.1.9. Hegelian Doctrine of the Dialectic
;304
11.1.10;9.1.10. Principle ofImmanent Change;305
11.2;9.2. Social Cybernetics;305
11.2.1;9.2.1. SVS Theory;306
11.2.2;9.2.2. Collective Mind;308
11.2.3;9.2.3. Global Noumenon;308
11.2.4;9.2.4. Relative Noumenon;309
11.3;9.3. Developing a Formal Theory of Sociohistory;309
11.3.1;9.3.1. The Ontological Basis for SVS Theory;309
11.3.2;9.3.2. Extreme Phenomenal Information;314
11.3.3;9.3.3. System Informations I, J;314
11.3.4;9.3.4. Information Channel;315
11.3.5;9.3.5. Information I;316
11.3.6;9.3.6. Fisher I as a Measure of the Arrow of Time
;317
11.3.7;9.3.7. EPI Zero Condition;317
11.3.8;9.3.8. I is General, J is Specific;318
11.3.9;9.3.9. EPI Extremum Principle;318
11.3.10;9.3.10. Knowledge Game;319
11.4;9.4. Sociocultural Dynamics;320
11.4.1;9.4.1. Cultural Driving Forces;320
11.4.2;9.4.2. Sensate and Ideational Aspects;321
11.5;9.5. The Paradigm of Sociohistory;322
11.5.1;9.5.1. The Propositional Base Through SVS;322
11.5.2;9.5.2. Dispersed Agents;322
11.5.3;9.5.3. Ideational vs Sensate Dispersed Agents;323
11.5.4;9.5.4. The Dynamics of Viable Holons;324
11.5.5;9.5.5. Emergent States and EPI;327
11.5.6;9.5.6. Sensate and Ideational Aspects ofthe Informations;329
11.5.7;9.5.7. Role of Efficiency Constant K
;330
11.5.8;9.5.8. Coefficients ofInformation;331
11.5.9;9.5.9. Role ofK in Defining States ofSociety;332
11.5.10;9.5.10. Emerging Balance Between Cultural Dispositions;333
11.6;9.6. Exploring the Dynamic of Cultural Disposition;334
11.6.1;9.6.1. Time Evolution of the Informations
;334
11.6.2;9.6.2. Consequences ofEnantiomer Imbalance;336
11.6.3;9.6.3. A Quantification Using Information Parameter K;336
11.7;9.7. The Sociocultural Propositions of EPI;338
11.8;9.8. An Illustrative Application of EPI to Sociocultural Dynamics
;338
11.8.1;9.8.1. General Problem of Population Growth and Motion
;339
11.8.2;9.8.2. Population Growth and Depletion Coefficients;340
11.8.3;9.8.3. EPI Solution;341
11.9;9.9. A Case Illustration: Postcolonial Iran;343
11.9.1;9.9.1. Sensate vs Ideational Mindsets;343
11.9.2;9.9.2. Cultural Instability;344
11.9.3;9.9.3. Quantitative Growth Effects;345
11.9.4;9.9.4. Manifestations in Political Power and Dominance;346
11.10;9.10. Overview;347
12;References;349
13;Index;369

Leseproben

"7 Applications of Fisher Information to the Management of Sustainable Environmental Systems (p. 217-218)

AUDREYL. MAYER, CHRISTOPHER W. PAWLOWSKI, BRIAN D. FATH, ANDHERIBERTOCABEZAS

All organisms alter their surroundings, and humans now have the ability to affect environments at increasingly larger temporal and spatial scales. Indeed , mechanical and engineering advances of the twentieth century greatly enhanced the scale of human activities. Among these are the use and redistribution of natural resources . Unfortunately, these activities can have unexpected and unintended consequences. Environmental systems often respond to these activities with diminished or lost capacity of natural function. Fortunately, environmental management can play an important role in ameliorating these negative effects.

The aim is to promote sustainable development, i.e., enrichment of the lives of the majority of people without seriously degrading the diversity and richness of the environment. However, the management tools themselves often fall prey to the same narrow levels of perspective that generated the negative conditions. The challenge is to develop a system-level index, one that indicates the organizati on and direction of ecological system dynamics. This index could detect when the system is changing its configuration to a new, perhaps less desirable, dynamic regime and may be incorporated into a sustainable management plan for the system. In this chapter, we demonstrate the use of Fisher information (FI) as such an environmental system index.

7.1. Summary

We derive an expression for FI based on sampling of the system trajectory as it evolves in the phase space defined by the state variables of the system. This FI index is derived as a measure ofsystem dynami c order; as defined by its speed and acceleration along periodic steady-state trajectories. We illustrate the concepts on data collected from both computer model simulations and real-world environmental systems. PI is found to provide a valuable tool to identify impending and in-progress shifts in regime, as distinguished from normal cycles, fluctuations , and noise in the systems.

7.2. Introduction

"Sustainability" is often used in a qualitative sense. However, there is at present a great need to quantitatively measure (and monitor) its many qualitative aspects in real systems. Real systems are regarded as sustainable if they can maintain their current, desirable productivity and character without creating unfavorable conditions elsewhere or in the future [1-4]. Sustainability therefore incorporates both concern for the future of the current system (temporal sustainability) and concern about the degree to which some areas and cultures of the planet are improved at the expense of other areas and cultures (spatial sustainability). That is, sustainability is to hold over both space and time."