Encyclopedia Of Mathematical Sciences - Table of Contents

MATHEMATICS: CONCEPTS AND FOUNDATIONS

MATHEMATICAL PHYSIOLOGY

SIGNAL TRANSMISSION IN NEURONS

Conductance-based models

Qualitative models

DELAY DIFFERENTIAL EQUATION MODELS IN DIABETES MODELING: A REVIEW

Models in the form of delay differential equations

Concluding remarks

MATHEMATICAL PHYSIOLOGY OF THE GASTROINTESTINAL SYSTEM - THE IMPORTANCE, THE PROBLEMS, THE SOLUTIONS

Gastrointestinal Physiology

Mathematical Models of the Gastrointestinal System

Summary and Future Directions

MATHEMATICAL MODELING OF THE TUBULOGLOMERULAR FEEDBACK MECHANISM IN THE KIDNEY

Anatomy and Physiology of the Kidney

Mathematical Models of the TGF Mechanism

THE IMMUNE SYSTEM AND ITS MATHEMATICAL MODELLING

Innate Immune System

Acquired (Adaptive) Immunity

Immunology and Mathematics

BONE TISSUE REMODELLING – THE LOCAL AND SYSTEMIC CONTROL AND MATHEMATICAL MODELLING

Bone remodelling

Regulatory Factors of bone remodelling

Mathematical Models of bone remodelling

PROBABILITY AND STATISTICS

Origin and History

Probability

Descriptive Statistics

Stochastic Models

Sequences of Stochastic Quantities

Stochastic Processes

From Stochastic Models to Statistical Inference

Classical Statistical Inference

Bayesian Statistical Inference

Information and Decision

Types of Uncertainty and Data Quality

Outlook

FOUNDATIONS OF STATISTICS

Statistical data

Uncertainty

Probability and philosophical foundations

Statistical populations and samples

Sampling from the normal distribution

Confidence statements and statistical tests

A-priori information

Sensitivity and robustness

Information and decisions

PRELIMINARY DATA ANALYSIS

Univariate Data Sets

Bivariate Data Sets

Multivariate Data Sets

STATISTICAL INFERENCE

Parametric and Nonparametric Inference

Sufficiency and Information

Classical Statistical Inference

Bayesian Inference

Data Quality and Statistical Inference

Statistical Inference and Decisions

STATISTICAL PARAMETER ESTIMATION

Fundamental Concepts

Optimality Properties

Methods of Parameter Estimation

Classical Confidence Regions

STATISTICAL TESTING OF HYPOTHESES

Statistical Hypothesis

Statistical Test

Errors of the First and the Second Kind

The Power Function, the Power and the Significance Level of the Test

Non-randomized Test

Randomized Test

Unbiased Test

Uniformly Most Powerful Test

Neyman-Pearson Lemma

Consistency

Neyman Structure

Likelihood Ratio Test

ROBUST STATISTICS

Motivation and Introduction

Basic Concepts

The Breakdown Value

Positive-Breakdown Regression

Multivariate Location and Scatter

Regression Diagnostics

Other Robust Methods

The Maxbias Curve

Perspective and Future Directions

BAYESIAN STATISTICS

Foundations

The Bayesian Paradigm

Inference Summaries

Reference Analysis

A Simplified Case Study

Discussion and Further Issues

STATISTICAL INFERENCE WITH IMPRECISE DATA

Imprecise data

Imprecise numbers and characterizing functions

Construction of characterizing functions

Multivariate data, imprecise vectors, and combination of imprecise samples

Functions and imprecision

Generalized inference procedures for imprecise samples

Classical statistical inference for imprecise data

Bayesian inference for imprecise data

MATHEMATICAL MODELS OF LIFE SUPPORT SYSTEMS

Basic Principles of Mathematical Modeling

Mathematical Models in Water Sciences

Mathematical Models of Atmosphere and Climate

Mathematical Models in Energy Sciences

Mathematical Models in Food and Agricultural Sciences

Mathematical Models in Biological, Health, and Medical Sciences

Mathematical Models in Human Social Relations and Global Biosphere Processes

MATHEMATICAL MODELS IN ENERGY SCIENCES AND CHEMICAL PHYSICS

MATHEMATICAL MODELS OF PLASMA PHYSICS

Kinetic models

Transport properties of plasmas

Magnetohydrodynamic models

Mathematical models of thermonuclear plasmas

MATHEMATICAL MODELS IN GLOBAL PROCESSES AND DEVELOPMENT

MATHEMATICAL MODELS AND CONTROL OF CATASTROPHIC PROCESSES

Basic Notions and Examples

Singularity Theory

Singularities in Optimization problems

MODELS AND METHODS OF ACTUARIAL MATHEMATICS

Empirical principles of determination of insurance premiums.

Classification of risk models

Collective risk model

Individual risk model

OPTIMIZATION AND OPERATIONS RESEARCH

Optimization and operations research: history and organizations

Optimization and operations research: impact and excellence

Operations research: scientific decision-making and the role of modeling

Optimization: the mathematical theory of models and algorithms

Optimization and computers: complexity and efficiency

Operations research and information systems: the implementation issue

Operations research and decision support systems: a case study

Selected WWW sites related to optimization and operations research

DECISION ANALYSIS

Examples

General Concepts

Decision Making Under Uncertainty

The Expected Utility Paradigm

The Risk-Value Approach

Graphical Representation of Decision Problems

EXPECTED UTILITY THEORY AND ALTERNATIVE APPROACHES

The General Framework

Expected Utility Theory

Non-Expected Utility Theory

RISK-DEFUSING BEHAVIOR

Decision Behavior: Are Lottery Tasks and Quasi-Realistic Tasks Comparable?

An Outline of the Decision Process in Quasi-Realistic Risky Decision Tasks

Risk-Defusing Behavior

The Role of Probability

Consequences for Decision Analysis

DECISION PROBLEMS AND DECISION MODELS

A Classification of Decision Problems

Theories and Models

Decision Trees and Influence Diagrams

MULTIPLE-CRITERIA DECISION MAKING

Value Function Approach

Vector Optimization

Final Remarks

DECISION TREES AND INFLUENCE DIAGRAMS

A Medical Diagnosis Problem

Decision Trees

Influence Diagrams

FRAMING EFFECTS IN THEORY AND IN PRACTICE

Framing Effects in Theory

Framing Effects in Practice

Moderators of Framing Effects

FUZZY DECISION THEORY

Classical Decision Model

Basic Definitions of the Fuzzy Set Theory

Modeling Fuzzy Values

Fuzzy Expected Values

Fuzzy Preference Orderings

The Use of Additional Information

Fuzzy Probabilities

MEASUREMENT OF RISK

Standardized Risk Measures

Luce’s Measures of Risk

Sarin’s Measures of Risk

Fishburn’s Measures of Pure Risk

Fishburn’s Measures of Speculative Risk

Risk Measurement Under Partial Probability Information

Final Remarks

FOUNDATIONS OF TARGET-BASED DECISION THEORY

Bentham and Utility-Based Decision Analysis

Hobbes and Decision Analysis

Target-Based Decision Analysis

Bounded Rationality and Target-Based Decision Analysis

Pedagogical Advantages

Improved Modeling of Individual Choice

Better Linkages with Finance

State-Dependent Utility Functions

Better Linkages with Practice

More Consistent with Psychological Evidence

HISTORY OF MATHEMATICS

BOURBAKI, AN EPIPHENOMENON IN THE HISTORY OF MATHEMATICS

Introduction

The Origins

The Impact

The Elaboration of the Volumes Constituting the Treatise

COMPUTATIONAL METHODS AND ALGORITHMS

Mathematical modelling

Discretization process

Combination of the discretization and solution process

Parallelizm and decomposition

Solution process

Implementation aspects

BASIC METHODS FOR SOLVING EQUATIONS OF MATHEMATICAL PHYSICS

Analytical methods for problems of mathematical physics

Approximate methods

METHODS OF POTENTIAL THEORY

Fundamentals of the Potential Theory

Application of the Potential Theory to the Classical Problems of Mathematical Physics

Other Applications of the Potential Method

EIGENVALUE PROBLEMS: METHODS OF EIGENFUNCTIONS

Eigenvalue problems

Special functions

The method of eigenfunctions

The method of eigenfunctions for some problems of the theory of electromagnetism

The method of eigenfunctions for the heat conductivity problem

The method of eigenfunctions for problems of the oscillation theory

METHODS OF INTEGRAL TRANSFORMS

Basic integral transforms

The application of integral transforms to problems of the oscillation theory

The application of integral transforms to heat conductivity problems

The application of integral transforms in the theory of neutron slow-down and diffusion

The application of integral transforms to problems of hydrodynamics

The application of integral transforms in the elasticity theory

The application of integral transforms in the coagulation kinetics

Brief instructions for the application of integral transforms

DISCRETIZATION METHODS FOR PROBLEMS OF MATHEMATICAL PHYSICS

Finite difference methods

Variational methods

Projection methods

VARIATIONAL FORMULATION OF PROBLEMS AND VARIATIONAL METHODS

The variational method

Applications of the Lax-Milgram theorem

Extensions of the variational theory

METHODS OF TRANSFORMATION GROUPS

Continuous Transformation Groups

Invariant Differential Equations

Tangential Transformations

Conservation Laws

Bäcklund Transformations

Sine-Gordon Equation

Korteweg de Vries Equation and Lax Pairs

Hirota Transformation and Penleve Property

Method of Inverse Scattering Problem

Schrodinger Equation

MODERN BIOMETRY

History

Biometric Data Collection and Analysis

Biometry in Action

Mathematics in Biometry

Future

STATISTICAL METHODOLOGY IN BIOMETRY

Linear Regression, Generalized Linear Models, Exponential Family and Logistic Regression

Hierarchical Data

Survival Analysis

LINEAR REGRESSION MODELS

Simple Linear Regression model

Diagnostics and Remedial Measures

Multiple Linear Regression Model

Model Adequacy and Diagnostics

Comments on Interpreting Regression Analysis

GENERALIZED LINEAR MODELING

A Corner Stone: the Exponential Family of Distributions

Generalized Linear Modelling

Estimation for Generalized Linear Models

Quasi-likelihood and Generalized Estimating Equations (GEE)

CATEGORICAL DATA ANALYSIS

Inference for a Single Proportion

Analysis of 2 × 2 Contingency Tables

Analysis of R x C Contingency Tables

Analysis of Sets of 2 × 2 Contingency Tables

Log-linear Models

Logistic Regression

Multinomial Regression Models

Poisson Regression

Clustered Categorical Data

SURVIVAL ANALYSIS

Basic concepts of survival analysis

The Kaplan-Meier Method and the Log-rank Test

The Cox proportional hazards model

Evaluating the proportional hazards assumption

The stratified Cox model

Extension of the Cox Proportional Hazards Model for Time-dependent Variables

MULTIVARIATE AND MULTIDIMENSIONAL ANALYSIS

Continuous Outcomes

Non-continuous Outcomes

Graphical Analysis

A Magician at Work?

REPEATED MEASURES AND MULTILEVEL MODELING

General Model

Some Models for Continuous Data

Models for Discrete Data

Generalized Estimating Equations

Discussion

META-ANALYSIS

Types of meta-analyses

Statistical principles of meta-analysis

Statistical models for meta-analysis

Example of a meta-analysis

Further topics in meta-analysis

ENVIRONMETRICS

ENVIRONMENTAL MONITORING

AREA PRECIPITATION MEASUREMENT

The Area Precipitation Measurement Problem

The Kalman Filter Approach

The Cokriging Approach

WATER-QUALITY MONITORING OF RIVERS

Design Considerations in Water-Quality Monitoring Networks

Case Studies from the United States

The Future of Water-Quality Monitoring Networks

STOCHASTIC MODELING IN LIFE SUPPORT SYSTEMS

The Concept of Stochastic Modelling

SM Metaphors and Reality Levels

Spatiotemporal Random Field Models

Towards a SM Program

Mathematical Forms of Natural Laws Considered in SM Applications

SM in Genetic Research, Carcinogenesis and Toxicokinetics applications

The Importance of Physical Geometry and Space/Time Scales

Knowledge Integration and the Epistemic Approach to Space/time

Decision Making, Geographical Information Systems, and Sampling Design

Physical Indicator Functions

Population Indicator Functions

Risk Assessment and Environmental Exposure-Health Effect Associations

ECONOMIC ASPECTS OF MONITORING ENVIRONMENTAL FACTORS: A COST-BENEFIT APPROACH

Setting Environmental Standards

Economic Implications of Adopting Environmental Standards

Environmental Valuation

Environmental Policy Regulations

TREND ANALYSIS FOR ENVIRONMENTAL FACTORS: TIME EFFECTS ON NITROUS OXIDE (N2O) LEVELS AT MACE HEAD, IRELAND

The Global Atmospheric Gases Experiment

Nitrous Oxide Levels at Mace Head

Identifying Trends

Trend Analysis for Variance Change

Change-Point Analysis of Nitrous Oxide Levels

RANK TESTS FOR INDEPENDENCE AND RANDOMNESS

Introduction

Rank Tests for Independence

Tests for Randomness against Trend

Contingency Tables

MATHEMATICAL MODELS

Why Do We Resort to Mathematical Modeling of Life Support Systems?

What Kinds of Life Support Systems Can Be Described by Mathematical Models?

How Is Mathematical Modeling Done?

Understanding Uncertainty Accompanying Mathematical Models

The Impact of the Information Technology "Revolution" on Both the Practice and Uses of Mathematical Modeling

BASIC PRINCIPLES OF MATHEMATICAL MODELING

The mathematical concept of dynamical system

Modeling in automatic control (Mathematical systems theory)

CLASSIFICATION OF MODELS

Discrete time models

Continuous-time Models

BASIC METHODS OF THE DEVELOPMENT AND ANALYSIS OF MATHEMATICAL MODELS

Discrete time models

Continuous time models

MEASUREMENTS IN MATHEMATICAL MODELING AND DATA PROCESSING

Hypothesis Testing

Sufficient Statistics

Signal Detection

Estimation Theory

CONTROLLABILITY, OBSERVABILITY AND STABILITY OF MATHEMATICAL MODELS

Controllability

Stability

Observability

Observers

IDENTIFICATION, ESTIMATION AND RESOLUTION OF MATHEMATICAL MODELS

Problem of identification

Identification procedure

Identification for several other classes of dynamic systems

Research problems

Software for identification

MATHEMATICAL THEORY OF DATA PROCESSING IN MODELS (DATA ASSIMILATION PROBLEMS)

Variational data assimilation

Kalman filtering

CHAOS AND CELLULAR AUTOMATA

Chaos

Cellular automata

MATHEMATICAL MODELS OF SOCIETY AND DEVELOPMENT: DEALING WITH THE COMPLEXITY OF MULTIPLE-SCALES AND THE SEMIOTIC PROCESS ASSOCIATED WITH DEVELOPMENT

Introduction and Overview of the Underlying Chapters

The Epistemological Predicament Associated with the Analysis of the Evolution of Systems Organized Across Multiple Scales

The Epistemological Roots of the Predicament faced when Modeling the Sustainability of Human Societies

MATHEMATICAL MODELS IN DEMOGRAPHY AND ACTUARIAL MATHEMATICS

Life Table Models

Stable Populations

Multistate Population Models

“Two-Sex” Population Models

Dynamic Population Models

MATHEMATICAL MODELS IN ECONOMICS

Mathematics, general equilibrium and dynamical system theory

Equilibrium and disequilibrium dynamics

Implicit dynamics, learning, evolution

ECOLOGICAL AND SOCIO-ECOLOGICAL ECONOMIC MODELS

Ecological-economic interaction models

Dynamic macro and micro simulation models

Optimization and control in simulation models

Game-theoretic models

Equilibrium and optimality in dynamic games

MATHEMATICAL MODELING IN SOCIAL AND BEHAVIORAL SCIENCE

Optimization Theory - Job Amenity and Moonlighting

Operations Research - The Job Assignment Problem

Game Theory - Political Competition

Differential Equations - Economic Consequences of Altruism

Chaos Theory - Population Dynamics

MATHEMATICAL MODELS OF MANAGEMENT OF THE ENVIRONMENT AND ITS NATURAL RESOURCES

Positive and Negative Externalities

Socially Optimum Provision of Environmental Bads

Mechanisms to Achieve the Optimal Level of an Environmental Bad

Socially Optimum Provision of Environmental Public Goods

A Unified Framework for the Optimal Management of Natural Resources

MATHEMATICAL MODELS OF GLOBAL TRENDS AND TECHNOLOGICAL CHANGE

Global Trends and Global Change

Modeling of Global Trends and Global Changes

Models of World Dynamics

Integrated Assessment Global Models

Models of Technological Change

SYSTEMS SCIENCE AND CYBERNETICS: THE LONG ROAD TO WORLD SOCIOSYSTEMICITY

The Essential Features of the Systemic Method

Types of Systems

The Universal Scope of Systems

Current Trends

The Social System Concept: Differential Characteristics

Social Synergy as a Rational Design

Content and Structure of Contributions to this Theme

Application of Systems Science and Cybernetics: Modeling Society

Does the System Change?

Needs and Values: the Reference Pattern of Values

System Outputs: Raison D tre of "Systems Science and Cybernetics"

An Axiological Model of the World Pseudosystem

A New Model for the World System?

SYSTEM THEORIES: SYNERGETICS

Review of Subject Articles

Definition of Synergetics

Goals and General Approaches

Some Typical Examples

Basic Concepts

Applications to Science

Applications to Technology

Applications to Humanities

Mathematical Tools

Relations to Other Approaches

HISTORY AND PHILOSOPHY OF THE SYSTEMS SCIENCES: THE ROAD TOWARD UNCERTAINTY

Medieval Universals

The Snake of Rational Curiosity in the Medieval Garden

The Slow Dawn of Technology in Medieval Europe

Descartes, the not very Systemic Systemist

The Expansion of the Universe of Knowledge

The Twilight of Scientific Simplicity: A can of Worms in 20th Century Science

In Search of a New Coherence

GENERAL SYSTEMS THEORY

Contributions of General System Theory to the Philosophy of Science

Reductionism versus Holism

The Second Industrial Revolution

The Planet as a System

LIVING SYSTEMS THEORY

Basic Concepts

Characteristics of Living Systems

The Principle of Fray-Out

Levels of Life

Critical Subsystems

Observable Structures and Processes

ENTROPY SYSTEMS THEORY

History

Criteria for Entropy Evaluation

Assessing the Past

Future Research

ACTOR-SYSTEM-DYNAMICS THEORY

Background and Foundations

Applications and Policy Implications: The Knowledge Problematique vis--vis Complex Systems

ETHICS AS EMERGENT PROPERTY OF THE BEHAVIOR OF LIVING SYSTEMS

Ethics

Systemic aspect of ethics

Ethics as Emergent Property of Social Systems

Interactions among Ethics

Some Metaphors

Effectiveness of an Ethics

Growth, Development, and Sustainable Development in Economic Systems: The Role of Ethics

Relationship between Ethics and Quality

Systemic View of Ethics to Detect, Improve, and Design Quality of Life

Introduction

Conclusions

AXIOLOGICAL SYSTEMS THEORY

Fundamental Principles of Axiological Systems Theory

John van Gigch’s Contribution

The Basic Transformation Model

The Solved Problems of Axiological Systems Theory

Some Practical Applications of Axiological Systems Theory

EVOLUTIONARY COMPLEX SYSTEMS

Conceptual Framework

Self-contained Conceptualization

Multiplicity of Evolutionary Complex Systems and Sustainability

Evolutionary Complex Systems and Knowledge

EPISTEMOLOGICAL ASPECTS OF SYSTEMS THEORY RELATED TO BIOLOGICAL EVOLUTION

Integrating Epistemology of Thermodynamics and of Biological Evolutionary Systems

Thermodynamics of Ecosystems and of Biological Evolution

Towards an Evolutionary Physics

SOCIO-TECHNICAL SYSTEMS: HISTORY AND STATE-OF-THE ART

The Role of Automation of Work Processes

The Requirement of Flexible Human Skills: Road to a Socio-Technical View

The Socio-Technical System Approach with Respect to Information- and Communication Technologies

THE GEOMETRY OF THINKING

Generalized Principles

Universe

System

Structure

Pattern Integrity

Tetrahedron

Tensegrity

Synergy

Precession

Design Science

Sustainability

Fundamental Laws of Systems Science

Modeling a System

SYSTEMS APPROACHES: A TECHNOLOGY FOR THEORY PRODUCTION

Review of Subject Articles

Epistemologies of Production

Genealogy of the System

Systems Theory as Technology

Epistemic Implications of Systems Approaches

THE SYSTEMS SCIENCES IN SERVICE OF HUMANITY

Transformations in Society

The Relevance of the Systems Sciences

Systems Sciences as a Field of Inquiry

The Breadth and Diversity of the Systems Sciences

The Social Dimension of Systems Thinking

Recent Trends in the Humanities and the Systems Sciences

A Bridge between Two Cultures and to the Future

GENERAL SYSTEMS WELTANSCHAUUNG

Simplistic Generalizations have Engendered Civilizations

Humans Survive Simplistically

An Organismic Biology Emerged from GSW

Behavioral and Social Sciences Urgently Need GSW

Holistic Medicine and Education Generated by Implicit GSW

GSW Prospects

METAMODELING

Models

Metamodels

Taxonomies

Models of Outputs

Models as Objects of Choice

Other Conceptual Metamodels

Hypermodeling

DESIGNING SOCIAL SYSTEMS

The Design Imperative

What is Social Systems Design?

Why do we Need Design Today?

When Should We Design?

What is the Product of Design?

What is the Process of Design?

Who Should be the Designers?

Building a Design Culture

What Values Can Design Add to our Society?

A Closing Thought

A SYSTEMS DESIGN OF THE FUTURE

Macrosocial Issues and Their Inherent Values and Morals

Utopianism and Ideals without Illusions

Social Enginnering: Piecemil and Systemic

Top-Down Planning

Systemic Democratic Planning

Growth and Development

Integral and Sustainable Development

The Future of Social Studies

SOFT SYSTEMS METHODOLOGY

Problemology

Soft Systems Methodology - SSM: A General View

SOCIAL PROBLEM DIAGNOSIS: A SOCIOPATHOLOGY IDENTIFICATION MODEL

Anatomy of Sociophysics

Pathology of Socioproblematics

Methodology of Sociodiagnostics

CRITICAL SYSTEMS THINKING

Introduction: The Role of Critical Systems Thinking within the Systems Movement

Origins: Opposition to the Hard Systems Approach, Improvement of Soft Approach

Confrontation: Different Approaches Compared

The Five Commitments of Critical Systems Thinking

A System of System Methodologies

Outlook

TOTAL SYSTEMS INTERVENTION

Total Systems Intervention (TSI 1)

Local Systemic Intervention (LSI/TSI 2)

Application

Future Challenges

INTEGRATIVE SYSTEMS METHODOLOGY

The State of Systemic Problem-solving

Outline of Integrative Systems Methodology

A Case Study

Reflection

WSR DECISIONS FOR A SUSTAINABLE FUTURE

Philosophy

Methodology

Application

PSYCHOLOGICAL AND CULTURAL DYNAMICS OF SUSTAINABLE HUMAN SYSTEMS

Dimensions of Human Life-support Systems and Sustainability

Consequences of Maladaptive Meaning

Can Ecological and Emotional Well-being go together?

THE DYNAMICS OF SOCIAL AND CULTURAL CHANGE

Systems Theory

Sociological Theory

FORMAL APPROACHES TO SYSTEMS

A Template to Analyze General Systems Approaches

Current General Systems Approaches

The Basic General Systems Concepts

Other Comparisons and Open Questions

An Eventual Unified Approach to General Systems

THE QUANTIFICATION OF SYSTEM DOMAINS

Quantification, Mathematization and Measurement

The Scientific Imperative and the Quantification Problem

Quantification Means Representation and Evaluation

Quantification. Formal Definition

Adequacy in the form of Quantification

Quantification of Attributes in Soft System Domains

The Formalization and Quantification of Complexity

The Failure in Modeling Large Scale Systems

Traditional Approaches to the Evaluation Problem. The Theory of Measurement

The Application of Qualitative and Quantitative Reasoning

Quantification Theory and Quantifiers in Logic

Implicit Quantification and Implicit Quantifiers

A [Not Quite] "New" Quantification Approach. Implicit Quantification

Implicit Quantifiers in a Hierarchy of Imperatives

A Simple Calculus of Quantifiers

CHAOS: BACK TO "PARADISE LOST": PREDICTABILITY. THE CENTURY OF THE EMERGENCE OF SYSTEMIC THOUGHT AND CHAOS THEORY

The 20th century: the difficult co-existence of Mechanicist Thought and Systemic Thought: emergence of chaos

Structure

A multi-stage modeling process to research on the detection and control of chaos dynamics in the evolution of biological and social systems.

An outstanding example of the chaotic dynamic system: the logistic map

Other important chaotic systems

TRANSDISCIPLINARY UNIFYING THEORY: ITS FORMAL ASPECTS

Rationales to Unifying Transdisciplinarily

External and Internal Constraints

Systemhood Unifying Theories

Unifying the Unifying Theories

Foreseeable Developments

GENERAL SYSTEMS PROBLEM SOLVER

Classification of Systems in GSPS

Systems Problem Solving

Methodological Outcome of the GSPS

CYBERNETICS: CYBERNETICS AND THE THEORY OF KNOWLEDGE

Review of Subject Articles

First-Order Cybernetics

Second-Order Cybernetics

Applications of Cybernetic Principles

HISTORY OF CYBERNETICS

Origins of Cybernetics

Basic Concepts

Links with Other Theories

Future of Cybernetics

EXISTING CYBERNETICS FOUNDATIONS

Organization

Modeling

Information

Control

SECOND ORDER CYBERNETICS

Introduction: What Second Order Cybernetics is, and What it Offers

Background—the Logical Basis for Second Order Cybernetics

Second Order Cybernetics—Historical Overview

Theory of Second Order Cybernetics

Praxis of Second Order Cybernetics

A Note on Second Order Cybernetics and Constructivism

Cybernetics, Second Order Cybernetics, and the Future

KNOWLEDGE AND SELF-PRODUCTION PROCESSES IN SOCIAL SYSTEMS

Social Systems

Autopoiesis (Self-Production) of Networks

Knowledge as Coordination of Action

Model of Autopoiesis

Autopoietic Social Systems

Individuals in Networks

CYBERNETICS AND THE INTEGRATION OF KNOWLEDGE

Cybernetic Explanation and the Concept of Mechanism

Cybernetic Epistemology

The First Order Study of Natural Systems

Approaches to the Study of Social Systems

Cybernetics and the Arts, Humanities and Vocational Disciplines

Cybernetics and Philosophy

CYBERNETICS AND COMMUNICATION

Methodology

Communication between Man and Machine

Cybernetics and Communication on a Biological Level (cybernetics b)

Cybernetics and Communication on a Social Level (cybernetics s)

BIPOLAR FEEDBACK

Bipolar Feedback in Natural Processes

Models of Bipolar Feedback

Biotic Patterns Generated by Bipolar Feedback in Natural and Human Processes

Creative Development Generated by Bipolar Feedback

Feedback Models in Biology, Economics, and Psychotherapy

COMPUTATIONAL INTELLIGENCE

Review of Subject Articles

Introduction

Computability, Decidability, and Complexity

Computational Intelligence and Knowledge-based Systems

Computational Intelligence and Neural Networks

Computational Life and Genetic Programming

Computational Intelligence and Life in the World Wide Web

GENERAL PRINCIPLES AND PURPOSES OF COMPUTATIONAL INTELLIGENCE

Definition and Understanding of Computational Intelligence

Goals of Computational Intelligence and their Accomplishment to date

Goals for Future Research

Other Views of Computational Intelligence

Soft Computing

Computational Intelligence and Soft Computing: Combinations of different Components

Research Outcome Statistics

NEURAL NETWORKS

Introduction: Nervous Systems and Neurons

Perceptrons and More General Models of Neurons

Multilayered Perceptrons and General Neural Networks

Radial Basis Function Networks

Probabilistic Neural Networks

Self-Organizing Maps

SIMULATED ANNEALING: FROM STATISTICAL THERMODYNAMICS TO COMBINATORY PROBLEMS SOLVING

Complexities of Problems and Algorithms

Introduction to Global Search Methods

Contribution of Statistical Physics and Thermodynamics

The Simulated Annealing Algorithm

Examples of Problems Solved Thanks to Simulated Annealing

Comparisons with Other Heuristics and SA Performance Improvements

ADAPTIVE SYSTEMS

Controllability

Fulfillment of Goals

Strategies of Decision

General Theory of Learning

Models of Probabilistic Learning

Dilemma of the Prisoner

Anticipatory Adaptation

A General Model of Social Evolution

BIOLOGICAL INTELLIGENCE AND COMPUTATIONAL INTELLIGENCE

Historical Concepts of Intelligence

The Neurobiological Bases of Intelligence

The Relationship between Intelligence as a Physiological Function and the Organization of the Nervous System

Biological Intelligence and Computational Intelligence

MATHEMATICAL MODELS IN ECONOMICS

Introduction

A Modern Treatment of Walras’ General Equilibrium Theory

A Generalization of Ricardo’s Economic Theory

A Generalization of Malthus’ Population Dynamics with Chaos

Von Thunen’s Spatial Economics and a Short-Run Dynamics of Land Prices

The Ramsey Growth Model and Neoclassical Growth Theory

Monetary Economic Growth and Business Cycles

A Growth Model with Solow’s and Schumpeter’s Growth Mechanism

Economic Growth with Arrow’s Learning by Doing and Uzawa’s Education

A Nonlinear Keynesian Economic Dynamics and Chaos

Traditional Trade Theories and the Core Trade Theorems

On Gneralization of Economic Theories