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Principles of Brain Functioning
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Table of Contents

Prologue.- I Foundations.- 1. Introduction.- 1.1 Biological Systems are Complex Systems.- 1.2 Goals of Synergetics.- 1.3 The Brain as a Complex System.- 1.4 Traditional Versus Synergetic Interpretations of Brain Functions.- 2. Exploring the Brain.- 2.1 The Black Box Approach.- 2.2 Opening the Black Box.- 2.3 Structure and Function at the Macroscopic Level.- 2.4 Noninvasive Methods.- 2.4.1 X-ray Tomography.- 2.4.2 Electro-encephalograms (EEG).- 2.4.3 Magneto-encephalograms (MEG).- 2.4.4 Positron Emission Tomography (PET).- 2.4.5 Magnetic Resonance Imaging (MRI).- 2.5 Structure and Function at the Microscopic Level.- 2.6 Learning and Memory.- 3. Modeling the Brain. A First Attempt: The Brain as a Dynamical System.- 3.1 What are Dynamical Systems?.- 3.2 The Brain as a Dynamical System.- 4. Basic Concepts of Synergetics I: Order Parameters and the Slaving Principle.- 4.1 Factors Determining Temporal Evolution.- 4.2 Strategy of Solution.- 4.2.1 Instability, Order Parameters, Slaving Principle.- 4.2.2 The Laser Paradigm or Boats on a Lake.- 4.2.3 The Slaving Principle.- 4.2.4 The Central Role of Order Parameters.- 4.3 Self-Organization and the Second Law of Thermodynamics.- 5. Dynamics of Order Parameters.- 5.1 One Order Parameter.- 5.2 Two Order Parameters.- 5.3 Three and More Order Parameters.- 5.4 Order Parameters and Normal Forms *.- II Behavior.- 6. Movement Coordination - Movement Patterns.- 6.1 The Coordination Problem.- 6.2 Phase Transitions in Finger Movement: Experiments and a Simple Model.- 6.3 An Alternative Model?.- 6.4 Fluctuations in Finger Movement: Theory *.- 6.5 Critical Fluctuations in Finger Movements: Experiments.- 6.5.1 The Experimental Set-Up.- 6.5.2 Experimental Results.- 6.6 Some Important Conclusions.- 7. More on Finger Movements.- 7.1 Movement of a Single Index Finger.- 7.2 Coupled Movement of Index Fingers.- 7.3 Phase Transitions in Human Hand Movements During Multifrequency Tapping Tasks.- 7.3.1 Experiment: Transitions in Multifrequency Tapping.- 7.4 A Model for Multifrequency Behavior *.- 7.5 The Basic Locking Equations and Their Solutions *.- 7.6 Summary of the Main Theoretical Results.- 7.7 Summary and Outlook.- 8. Learning.- 8.1 How Learning Changes Order Parameter Landscapes.- 8.2 How Learning Changes the Number of Order Parameters.- 8.3 How Learning Gives Rise to New Order Parameters.- 9. Animal Gaits and Their Transitions.- 9.1 Introductory Remarks.- 9.2 Symmetries and Groups.- 9.3 An Empirical Study of Quadruped Gaits.- 9.4 Phase Dynamics and Symmetries.- 9.5 Equations of Phase Dynamics.- 9.6 Stationary Solutions.- 9.7 Gait Dynamics of Lower Symmetry.- 9.8 Summary and Outlook.- 10. Basic Concepts of Synergetics II: Formation of Spatio-temporal Patterns.- 11. Analysis of Spatio-temporal Patterns *.- 11.1 Karhunen-Loeve Expansion, Singular Value Decomposition, Principal Component Analysis - Three Names for the Same Method.- 11.2 A Geometric Approach Based on Order Parameters. The Haken-Friedrich-Uhl Method.- 11.2.1 One Real Order Parameter.- 11.2.2 Oscillations Connected with One Complex Order Parameter.- 12. Movements on a Pedalo.- 12.1 The Task.- 12.2 Description of the Movement Pattern.- 12.3 Quantification of the Pedalo Movement.- 12.4 Analysis of the Movement Using the Karhunen-Loeve Expansion.- 12.5 A Detailed Analysis of the Movements of Arms and Legs.- 12.6 Haken-Priedrich-Uhl Order Parameter Analysis.- 12.7 Concluding Remarks on Part II.- III EEG and MEG.- 13. Chaos, Chaos, Chaos.- 14. Analysis of Electroencephalograms.- 14.1 Goals of the Analysis.- 14.2 Identification of Order Parameters and Spatial Modes.- 14.3 Results.- 15. Analysis of MEG Patterns.- 15.1 Experimental Results.- 15.2 Temporal and Spatial Analysis.- 15.2.1 Temporal Analysis.- 15.2.2 Spatio-temporal Analysis.- 15.3 Modeling the Dynamics.- 15.4 Modeling the Dynamics: Towards a Field Theory of Brain Activity.- 15.5 EEG and MEG Analysis Revisited.- IV Cognition.- 16. Visual Perception.- 16.1 A Model of Pattern Recognition.- 16.2 The Role of Attention Parameters. Ambiguous Figures.- 16.3 Influence of a Bias.- 16.4 The Role of Fluctuations of Attention Parameters.- 16.5 Learning Patterns.- 16.6 A Model for Stereo Vision.- 17. Decision Making as Pattern Recognition.- 18. The Brain as a Computer or Can Computers Think?.- 18.1 An Excursion: What is Thinking?.- 18.2 Computers.- 18.3 Artificial Intelligence.- 18.4 Neurocomputers and Connectionism.- 18.5 Can Computers Think?.- 19. Networks of Brains.- 19.1 A General Model of IRN in Terms of Synergetics.- 19.2 Collective Cognitive Processes.- 19.3 Iterations.- 19.4 Concluding Remarks.- 20. Synergetics of the Brain: Where Do We Stand? Where Do We Go from Here?.- 20.1 Looking Back.- 20.2 Mind and Matter - An Eternal Question.- 20.3 Some Open Problems.- Appendices.- A. Analysis of Time Series.- A.1 Time Series Analysis.- A.2 Definition of Dimensions.- A.3 Dimension of Attractors.- A.4 Some Conclusions.- B. Determination of Adjoint Vectors.- C. The Potentials Occurring in Sect. 16.5.- References and Further Reading.- About the Author.

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