Neuro-Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling

738 Pages·2007·13.266 MB·English

by  Vladimir G. Ivancevic, Tijana T. Ivancevic

VladimirG.Ivancevic,TijanaT.Ivancevic
Neuro-FuzzyAssociativeMachineryforComprehensive
BrainandCognitionModelling
StudiesinComputationalIntelligence,Volume45
Editor-in-chief
Prof.JanuszKacprzyk
SystemsResearchInstitute
PolishAcademyofSciences
ul.Newelska6
01-447Warsaw
Poland
E-mail:[email protected]
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Neuro-FuzzyAssociativeMachineryfor
Vol.35.KeChen,LipoWang(Eds.) ComprehensiveBrainandCognitionModelling,
TrendsinNeuralComputation,2007 2007
ISBN978-3-540-36121-3 ISBN978-3-540-47463-0
Vladimir G. Ivancevic
Tijana T. Ivancevic
Neuro-Fuzzy Associative
Machinery for
Comprehensive Brain
and Cognition Modelling
With 123 Figures and 4 Tables
123
Dr.VladimirG.Ivancevic
HumanSystemsIntegration
LandOperationsDivisionDefence
Science&TechnologyOrganisation
POBox1500
75Labs
EdinburghSA5111,Australia
E-mail:[email protected]
TijanaT.Ivancevic
TheUniversityofAdelaide
DepartmentofAppliedMathematics
SchoolofMathematicalSciences
SA5005,Australia
E-mail:[email protected]
LibraryofCongressControlNumber:2006935539
ISSNprintedition:1860-949X
ISSNelectronicedition:1860-9503
ISBN-10 3-540-47463-3SpringerBerlinHeidelbergNewYork
ISBN-13 978-3-540-47463-0SpringerBerlinHeidelbergNewYork
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Preface
Neuro–Fuzzy Associative Machinery for Comprehensive Brain and Cognition
Modeling is a graduate–level monographic textbook. It represents a compre-
hensive introduction into both conceptual and rigorous brain and cognition
modeling.Itisdevotedtounderstanding,predictionandcontrolofthefunda-
mental mechanisms of brain functioning. The objective of the monograph is
to provide a reader with a scientific tool that will enable him/her to actually
perform a competitive research in brain and cognition modeling.
This book has four Chapters and Appendix. The first Chapter gives an
introduction into brain anatomy, physiology and biophysics, as well as psy-
chology and engineering of cognition. It also introduces the functorial meta-
language, which is essential for global comprehension of brain and cognition.
The second Chapter reviews various approaches (or, functors) currently used
forbrainandcognitionmodeling,including:(i)nonlineardynamicsandchaos,
(ii) control and complex systems and networks, (iii) intelligent (BDI) agents,
(iv) neural networks, (v) cellular automata and genetic algorithms, (vi) fuzzy
logic, and (vii) synergetics. The third Chapter develops the neurodynamics,
neuro–synergetics and synchronization approach of brain and cognition mod-
eling. The fourth Chapter further develops fuzzy and neuro–fuzzy systems. It
alsogivesourneuro–fuzzymodelingapproachtoreal–lifegames.TheAppen-
dixhastwosections:(i)universallanguageofcategoriesandfunctors,and(ii)
glossary of frequent neurophysiological terms.
Target readership includes all researchers and students interested in brain
and cognition modeling (in computer science, engineering, mathematics,
physics, chemistry, biology, psychology, sociology, economics, medicine, etc.),
working both in industry (i.e., clinics) and academia.
Adelaide, V. Ivancevic, Defence Science & Technology Organisation,
Aug 2006 Australia, e-mail: [email protected]
T. Ivancevic, School of Mathematics, The University of Adelaide,
e-mail: [email protected]
Dedicated to Nitya, Atma and Kali
Acknowledgments
The authors wish to thank Land Operations Division, Defence Science &
TechnologyOrganisation,Australia,forthesupportindevelopingtheHuman
Biodynamics Engine (HBE)andalltheHBE–relatedtextinthismonograph.
We also express our gratitude to Springer book series Studies in Compu-
tational Intelligence andespeciallytotheEditor,ProfessorJanuszKacprzyk.
Contents
0.1 Glossary of Frequently Used Symbols ...................... 1
1 Introduction to Brain and Cognition....................... 3
1.1 Brain .................................................. 3
1.1.1 Basics of Brain Physiology.......................... 10
1.1.2 Modern 3D Brain Imaging.......................... 30
1.2 Cognition and Associative Memory ........................ 37
1.3 Categorical Language for Neuro–Cognition.................. 43
1.3.1 Categorical Patterns and Hierarchical Links .......... 44
1.3.2 A General Natural System.......................... 46
1.3.3 The Category of Neurons........................... 47
1.3.4 Memory Evolutive System.......................... 47
1.3.5 Neural System in a Category ....................... 49
1.4 Hierarchical Associative Machinery of n−Functors ........... 51
1.4.1 Preliminary Examples of Brain and Cognition
Functors ......................................... 56
2 Various Approaches (Functors) to Brain and Cognition
Modeling .................................................. 61
2.1 Nonlinear Dynamics and Chaos Approach .................. 61
2.1.1 Chaos Theory Basics .............................. 62
2.1.2 Chaos Control .................................... 81
2.1.3 Fractal Calculus and Chaos Control .................103
2.1.4 Josephson Junctions and Quantum Computing........106
2.1.5 Solitons ..........................................110
2.1.6 Chaos Field Theory................................116
2.1.7 Geometrical Nonlinear Dynamics ....................118
2.1.8 Dynamics of n−Functors ...........................120
2.2 Systems and Networks Approach ..........................122
2.2.1 MIMO Systems and Kalman Filtering................122
2.2.2 Nonlinear Control Systems .........................128
2.2.3 Complex Adaptive Systems.........................144
X Contents
2.2.4 Complex Networks and Synchronization Dynamics.....147
2.2.5 Small–Worlds and Social Networks ..................152
2.3 Intelligent (BDI) Agents Approach ........................155
2.3.1 Agents Environments ..............................161
2.3.2 Agents’ Reasoning and Learning ....................164
2.4 Neural–Networks Approach ...............................183
2.4.1 Biological Versus Artificial Neural Nets ..............184
2.4.2 Common Discrete ANNs ...........................185
2.4.3 Common Continuous ANNs ........................209
2.4.4 Support Vector Machines...........................217
2.4.5 Dynamical Nets for Thought Process Modeling........220
2.5 Cellular and Evolutionary Approach .......................228
2.5.1 Cellular Automata.................................229
2.5.2 Evolutionary Algorithms ...........................237
2.6 Fuzzy–Logic Approach ...................................246
2.6.1 The Concept of Fuzziness ..........................246
2.6.2 Fuzzy Inference Engine.............................255
2.6.3 Fuzzy Logic Control ...............................258
2.7 Synergetics Approach ....................................267
2.7.1 Phase Transitions .................................270
2.7.2 Hamiltonian Biodynamics ..........................271
2.7.3 Kick Dynamics and Dissipation–Fluctuation
Theorem .........................................273
2.7.4 Mezoscopic Derivation of Order Parameters...........276
2.7.5 Example: Synergetic Control of Biodynamics..........278
2.7.6 Example: Chaotic Psychodynamics of Perception ......280
3 Neuro–Dynamics, Synergetics and Synchronization ........285
3.1 Distinguished ANN Models ...............................285
3.1.1 Generalized Kohonen’s SOM........................285
3.1.2 Dynamics of Hopfield’s Associative Recurrent Nets ....289
3.1.3 A Self–Organizing Bidirectional Competitive Net ......296
3.1.4 Vector AM–Neural Nets............................297
3.1.5 Small–World AM–Neural Nets ......................307
3.2 Local Neurodynamics ....................................311
3.2.1 Microscopic Neurodynamics and Quantum Brain ......311
3.2.2 Macroscopic Neurodynamics ........................324
3.2.3 Darwinian Oscillatory Neural Net ...................345
3.2.4 Oscillatory Phase Synchronization
in Neurodynamics .................................347
3.2.5 Synchronization in Cellular Automata ...............355
3.2.6 Kuramoto–Type Dynamics of Complex Nets ..........360
3.2.7 Oscillator AM with Scattered Natural Frequencies.....363
3.2.8 AM Neural Nets with Self–Control ..................367
3.2.9 BAM and Statistical Neurodynamics.................375
3.2.10 Firing Correlation in Layered AM Neural Nets ........384
3.3 Synergetics of Recurrent and Attractor Neural Nets..........388