Foundations of Mathematical Biology

Foundations of Mathematical Biology

Supercellular Systems

1st Edition - January 1, 1973

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  • Editor: Robert Rosen
  • eBook ISBN: 9781483271859

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Foundations of Mathematical Biology, Volume III, is devoted to the treatment of behavior of whole organisms and groups of organisms. The viewpoint taken throughout the book is a holistic, phenomenological one. That is, the integrated behavior of these organisms and groups of organisms is not, in general, referred back to specific structural properties of interacting subunits (as in a reductionist scheme), but is rather treated on its own terms without invoking the properties of lower levels of organization. The book begins with an overview of organization and control in physiological systems, with emphasis on the mathematical techniques involved in more detailed investigations of specific physiological mechanisms. Separate chapters cover the cardiovascular system, with particular reference to blood flow; gross problems of organic form; a relational overview of physics, biology, and sociology; the automata theory in the context of the central nervous system; and populations of interacting organisms. The final chapter discusses the material presented in the entire work, some of its philosophical presuppositions and implications, and the possibility of constructing a unified theory of mathematical biology.

Table of Contents

  • List of Contributors


    Contents of Other Volumes

    Chapter 1 Physiological Regulation and Control

    I. Introduction

    II. Mathematical Formulation of Systems

    A. Some General Definitions

    B. Assumptions

    C. Description of Linear Systems

    D. State Vector and State Equations

    E. The Transfer Function and Its Properties

    F. Vector Representation of Transfer Functions

    G. Example: Electrical Phenomena across Excitable Membranes

    III. Control Theory

    A. Structure and Dynamics of Control Systems

    B. Structure of Physiological Control

    IV. Stability and Oscillations

    A. Stability

    B. Oscillations and Stability in Physiological Systems

    V. Optimization

    A. An Evolutionary Basis for Design and Operating Optimization

    B. Hierarchical Aspects

    C. Performance Indices, Cost Functions

    D. Analytical Trade-off and Optimality Conditions

    E. The Respiratory-Cardiovascular System


    Chapter 2A Mathematical Aspects of Some Cardiovascular Phenomena

    I. Introduction and Scope

    II. Linear Case

    III. Some Applications of the Linear Case: A Two-Chamber Theory

    IV. Nonlinear Case

    V. Applications of the Nonlinear Theory

    VI. Volume Elasticity and the Elasticity of the Blood Vessel Wall:

    Propagation of Pulse Waves


    Chapter 2B The Principle of Adequate Design

    I. Models and General Principles in Biology

    II. Quantitative Description of a Form of an Organism

    III. Form of Plants

    IV. An Example of the Application to the External Shape of a Quadruped

    V. Application to the Size of the Aorta

    VI. Overall Design of the Circulatory System: Peripheral Resistance

    VII. The Overall Design of the Cardiovascular System and the Evaluation

    of Its Basic Parameters


    Chapter 2C A Unified Approach to Physics, Biology, and Sociology

    Chapter 3 Automata Theory in the Context of Theoretical Neurophysiology

    I. The Concept of State

    II. Finite-State Models of Neural Nets

    III. Complexity Theory for Pattern Recognition Networks

    IV. An Aside: Gödel's Incompleteness Theorem

    V. From External to Internal Descriptions

    VI. The Correction of Errors in Communication and Computation

    A. Reliable Brains from Unreliable Neurons

    B. Von Neumann's Multiplexing Scheme

    C. Shannon's Communication Theory

    D. Communication Theory and Automata

    E. The Cowan-Winograd Theory of Reliable Automata


    Chapter 4 The Deterministic Theory of Population Dynamics

    I. Introduction

    II. The Dynamics of an Isolated Species

    A. Malthus' Equation

    B. The Pearl-Verhulst Equation

    C. A General Logistics Growth Rate Function

    III. The Modes of Interaction between Two Species

    A. Competition and Volterra's Competitive Exclusion Principle: Two

    Species Competing for a Common Ecological Niche

    B. Two Species Living in a Predator-Prey Relationship

    C. Symbiosis

    D. Parasitism

    E. A General Qualitative Theory for the Interactions between Two


    IV. The Interactions between Three or More Species

    A. Competition Involving Several Species

    B. Predation Involving Several Species

    V. Incorporation of "Historical Actions"

    A. The System Equations for Predation

    B. Law of Conservation of the Means and Law of Perturbation of the

    Means for "Historical Actions"

    VI. Epilogue


    Chapter 5 Is There a Unified Mathematical Biology?

    Author Index

    Subject Index, Volume I

    Subject Index, Volume II

    Subject Index, Volume III

Product details

  • No. of pages: 430
  • Language: English
  • Copyright: © Academic Press 1973
  • Published: January 1, 1973
  • Imprint: Academic Press
  • eBook ISBN: 9781483271859

About the Editor

Robert Rosen

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