
Biomathematics in 1980
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- Front Cover
- Biomathematics in 1980
- Copyright Page
- Table of Contents
- PREFACE
- CHAPTER I: FEEDFORWARD CONTROL AND SENESCENCE
- CHAPTER II: MATHEMATICAL METHODS OF SYNERGETICS FOR APPLICATIONS TO SELF-ORGANIZING SYSTEMS
- 1. Introduction
- 2. The general approach
- 3. Some generalizations
- 4. Instability hierarchies, chaos, and how to escape it
- 5. Conclusion
- CHAPTER III: THE MATHEMATICS OF EXCITATION
- 1. Introduction
- 2. The phenomenology of excitation
- 3. The geometry of excitation
- 4. Numerical solutions of the H-H equations
- 5. The FitzHugh equations
- 6. The FitzHugh-Nagumo equations
- 7. The Hodgkin-Huxley membrane equations
- 8. Generalized excitation-propagation equations
- 9. Alternatives to the Hodgkin-Huxley equations
- 10. Other excitation equations
- 11. General membrane excitation equations
- 12. Conclusions
- CHAPTER IV: NERVE PULSE INTERACTIONS
- 1. Introduction
- 2. Materials and methods
- 3. Measurement of velocity ratio
- 4. A simple theory
- 5. Comparison of experimental results with simple theory
- 6. Discussion
- 7. Conclusions
- Appendix: Calculation of R/-R
- CHAPTER V: MODELS FOR THE TRANSIENT AMACRINE CELLS IN THE RETINA
- 1. Introduction
- 2. Roles of horizontal cells and amacrine cells for the formation of direction-selective cells
- 3. Model for the transient amacrine cell in the catfish retina
- CHAPTER VI: OPERATIONAL MODELS OF NEURAL ENCODING
- 1. Introduction
- 2. Phase-locking and leakage in the integration
- 3. Statistical properties of the neural discharge and neural models
- CHAPTER VII: A STRATEGY FOR INVESTIGATING SOLUTIONS OF COUPLED NONLINEAR DIFFUSION EQUATIONS, WITH APPLICATIONS TO PATTERN FORMATION MODELS IN BIOLOGY
- 1. Introduction
- 2. Stability diagrams and varying diffusion coefficients
- 3. Numerical integration of coupled nonlinear diffusion equations
- 4. A model for pattern formation in biological systems
- 5. Conclusions
- CHAPTER VIII: SOME RECENT TOPICS IN PATTERN FORMATION
- 1. Generalities
- 2. Space-dependent kinetics
- CHAPTER IX: REGULATION OF CELL DIVISIONS IN THE SEA URCHIN EMBRY
- 1. Introduction
- 2. The pattern of cell divisions in the sea urchin egg
- 3. Coordination of the mitotic activity by periodic waves of chemical activity
- 4. Conclusion
- CHAPTER X: OUTLINE OF A THEORY OF THE CEREBRAL CORTEX
- 1. Reflexive action of the cerebral cortex
- 2. Areas, columns, compartments
- 3. Types of neurons
- 4. Neuronal circuits
- 5. Connections between pyramidal cells
- 6. Pyramidal cells as elements of learning
- 7. Areal architectonics: knowledge
- 8. Orientation columns in the visual cortex
- CHAPTER XI: MODELLING COGNITIVE PROCESSES IN SELF-ORGANIZING NEURAL NETWORKS, AN EXERCISE IN SCIENTIFIC REDUCTION
- 1. Introduction, formulation of the problem
- 2. Scientific reduction
- 3. Basic aspects of self-organization
- 4. Scientific reduction of psychological phenomena to neural processes
- 5. Example of a model of simple arithmetic in collective representation
- CHAPTER XII: HOW USEFUL ARE ASSOCIATIVE MEMORIES ?
- CHAPTER XIII: SEARCH FOR A FORMALISM DESCRIBING A GENERALIZED "ALOPEX" PROCESS
- CHAPTER XIV: A MATHEMATICAL THEORY OF SELF-ORGANIZING NERVE SYSTEMS
- 1. Introduction
- 2. Equation of neural learning
- 3. Dynamics of neural excitations
- 4. Self-organization of neural systems
- 5. Conclusion
- CHAPTER XV: EFFECTIVE EXTRACTION OF INFORMATION INCLUDED IN NETWORK DESCRIPTIONS AND NEURAL SPIKE RECORDS
- 1. Introduction
- 2. Axiomatic foundation of neuronal network theory
- 3. Neuronal network in relation to wiring
- 4. Hypothesis that neuronal language is necessary
- 5. Behaviour of formal neuronal networks
- 6. The quality of behaviour and the size of network
- 7. Synthesis of formal neuronal networks
- 8. Contents of formal network synthesis
- 9. Sufficient and necessary conditions for detection of movement with example of network synthesis and analysis
- 10. Solution of synthesis is not unique: The problem of network vulnerability
- 11. Point process model of spike records as a basis for network synthesis
- 12. What can be computed from neuronal spike sequences?
- 13. Method of design of a formal neuronal generating observed pattern
- CHAPTER XVI: QUANTITATIVE OBJECTIVE STUDY OF HUMAN VISUAL PERCEPTION AND RECOGNITION
- CHAPTER XVII: ON A CLASS OF DIFFERENCE EQUATIONS MODELING GROWTH PROCESSES
- 1. Introduction
- 2. Logistic and Gompertz equations
- 3. Dynamical behavior of a class of growth equations
- 4. Dynamics of the Gompertz process
- Appendix
- CHAPTER XVIII: A MATHEMATICAL MODEL OF DENSITY DEPENDENT DISPERSIVE MOTIONS
- 1. Introduction
- 2. Behavioural character of ant lions
- 3. Generalization
- 4. Application
- CHAPTER XIX: AN APPLICATION OF PERIODIC OPTIMAL CONTROL TO A PROBLEM OF FISH HARVESTING
- 1. Introduction
- 2. The problem
- 3. Optimal steady states
- 4. A second variation analysis
- 5. Pulse fishing
- CHAPTER XX: IDENTIFICATION AND SENSITIVITY ANALYSIS FOR THE PULMONARY CIRCUIT IN THE CARDIOVASCULAR SYSTEM
- 1. Introduction
- 2. Model construction
- 3. Model equations
- 4. Identification problem for the pulmonary system
- 5. Results of identification
- 6. Sensitivity analysis of the pulmonary subsystem model
- 7. Final remarks
- AUTHOR'S ADDRESSES
- AUTHOR INDEX
- SUBJECT INDEX
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