Biomathematics in 1980 (eBook)

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

eBook Download: PDF

1982 | 1. Auflage
296 Seiten
Elsevier Science (Verlag)
978-0-08-087169-1 (ISBN)

Infos

Biomathematics in 1980

Inhalt

Front Cover 1
Biomathematics in 1980 4
Copyright Page 5
Table of Contents 10
PREFACE 6
CHAPTER I: FEEDFORWARD CONTROL AND SENESCENCE 16
CHAPTER II: MATHEMATICAL METHODS OF SYNERGETICS FOR APPLICATIONS TO SELF-ORGANIZING SYSTEMS 24
1. Introduction 24
2. The general approach 26
3. Some generalizations 27
4. Instability hierarchies, chaos, and how to escape it 28
5. Conclusion 28
CHAPTER III: THE MATHEMATICS OF EXCITATION 30
1. Introduction 30
2. The phenomenology of excitation 30
3. The geometry of excitation 35
4. Numerical solutions of the H-H equations 35
5. The FitzHugh equations 41
6. The FitzHugh-Nagumo equations 43
7. The Hodgkin-Huxley membrane equations 44
8. Generalized excitation-propagation equations 46
9. Alternatives to the Hodgkin-Huxley equations 48
10. Other excitation equations 49
11. General membrane excitation equations 53
12. Conclusions 54
CHAPTER IV: NERVE PULSE INTERACTIONS 64
1. Introduction 64
2. Materials and methods 64
3. Measurement of velocity ratio 65
4. A simple theory 68
5. Comparison of experimental results with simple theory 73
6. Discussion 77
7. Conclusions 84
Appendix: Calculation of R/-R 84
CHAPTER V: MODELS FOR THE TRANSIENT AMACRINE CELLS IN THE RETINA 88
1. Introduction 88
2. Roles of horizontal cells and amacrine cells for the formation of direction-selective cells 88
3. Model for the transient amacrine cell in the catfish retina 92
CHAPTER VI: OPERATIONAL MODELS OF NEURAL ENCODING 102
1. Introduction 102
2. Phase-locking and leakage in the integration 103
3. Statistical properties of the neural discharge and neural models 106
CHAPTER VII: A STRATEGY FOR INVESTIGATING SOLUTIONS OF COUPLED NONLINEAR DIFFUSION EQUATIONS, WITH APPLICATIONS TO PATTERN FORMATION MODELS IN BIOLOGY 110
1. Introduction 110
2. Stability diagrams and varying diffusion coefficients 111
3. Numerical integration of coupled nonlinear diffusion equations 115
4. A model for pattern formation in biological systems 117
5. Conclusions 120
CHAPTER VIII: SOME RECENT TOPICS IN PATTERN FORMATION 126
1. Generalities 126
2. Space-dependent kinetics 127
CHAPTER IX: REGULATION OF CELL DIVISIONS IN THE SEA URCHIN EMBRY 132
1. Introduction 132
2. The pattern of cell divisions in the sea urchin egg 133
3. Coordination of the mitotic activity by periodic waves of chemical activity 136
4. Conclusion 139
CHAPTER X: OUTLINE OF A THEORY OF THE CEREBRAL CORTEX 142
1. Reflexive action of the cerebral cortex 142
2. Areas, columns, compartments 142
3. Types of neurons 143
4. Neuronal circuits 144
5. Connections between pyramidal cells 144
6. Pyramidal cells as elements of learning 145
7. Areal architectonics: knowledge 146
8. Orientation columns in the visual cortex 146
CHAPTER XI: MODELLING COGNITIVE PROCESSES IN SELF-ORGANIZING NEURAL NETWORKS, AN EXERCISE IN SCIENTIFIC REDUCTION 148
1. Introduction, formulation of the problem 148
2. Scientific reduction 150
3. Basic aspects of self-organization 151
4. Scientific reduction of psychological phenomena to neural processes 153
5. Example of a model of simple arithmetic in collective representation 155
CHAPTER XII: HOW USEFUL ARE ASSOCIATIVE MEMORIES ? 160
CHAPTER XIII: SEARCH FOR A FORMALISM DESCRIBING A GENERALIZED "ALOPEX" PROCESS 170
CHAPTER XIV: A MATHEMATICAL THEORY OF SELF-ORGANIZING NERVE SYSTEMS 174
1. Introduction 174
2. Equation of neural learning 174
3. Dynamics of neural excitations 181
4. Self-organization of neural systems 187
5. Conclusion 191
CHAPTER XV: EFFECTIVE EXTRACTION OF INFORMATION INCLUDED IN NETWORK DESCRIPTIONS AND NEURAL SPIKE RECORDS 194
1. Introduction 194
2. Axiomatic foundation of neuronal network theory 194
3. Neuronal network in relation to wiring 195
4. Hypothesis that neuronal language is necessary 195
5. Behaviour of formal neuronal networks 197
6. The quality of behaviour and the size of network 197
7. Synthesis of formal neuronal networks 200
8. Contents of formal network synthesis 200
9. Sufficient and necessary conditions for detection of movement with example of network synthesis and analysis 201
10. Solution of synthesis is not unique: The problem of network vulnerability 202
11. Point process model of spike records as a basis for network synthesis 202
12. What can be computed from neuronal spike sequences? 204
13. Method of design of a formal neuronal generating observed pattern 205
CHAPTER XVI: QUANTITATIVE OBJECTIVE STUDY OF HUMAN VISUAL PERCEPTION AND RECOGNITION 210
CHAPTER XVII: ON A CLASS OF DIFFERENCE EQUATIONS MODELING GROWTH PROCESSES 232
1. Introduction 232
2. Logistic and Gompertz equations 233
3. Dynamical behavior of a class of growth equations 234
4. Dynamics of the Gompertz process 247
Appendix 256
CHAPTER XVIII: A MATHEMATICAL MODEL OF DENSITY DEPENDENT DISPERSIVE MOTIONS 260
1. Introduction 260
2. Behavioural character of ant lions 261
3. Generalization 262
4. Application 264
CHAPTER XIX: AN APPLICATION OF PERIODIC OPTIMAL CONTROL TO A PROBLEM OF FISH HARVESTING 268
1. Introduction 268
2. The problem 268
3. Optimal steady states 270
4. A second variation analysis 271
5. Pulse fishing 277
CHAPTER XX: IDENTIFICATION AND SENSITIVITY ANALYSIS FOR THE PULMONARY CIRCUIT IN THE CARDIOVASCULAR SYSTEM 280
1. Introduction 280
2. Model construction 280
3. Model equations 283
4. Identification problem for the pulmonary system 284
5. Results of identification 290
6. Sensitivity analysis of the pulmonary subsystem model 290
7. Final remarks 293
AUTHOR'S ADDRESSES 296
AUTHOR INDEX 300
SUBJECT INDEX 308

Produkt-Details

• Erscheint lt. Verlag: 1.1.1982
• Mitarbeit: Herausgeber (Serie): Luigi Ricciardi, Alwyn Scott
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik
• ISBN-10: 0-08-087169-0 / 0080871690
• ISBN-13: 978-0-08-087169-1 / 9780080871691