Biomathematics in 1980

Name: Biomathematics in 1980 | Papers presented at a workshop on biomathematics: current status and future perspective, Salerno, April 1980
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Papers presented at a workshop on biomathematics: current status and future perspective, Salerno, April 1980

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Published on 1. January 1982

296 pages

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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
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Biomathematics in 1980

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