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ENCYCLOPEDIA OF MATHEMATICAL SCIENCES

MATHEMATICS: CONCEPTS AND FOUNDATIONS

A VIEW OF MATHEMATICS

The Unity of Mathematics

The concept of Space

Fundamental Tools

The input from Quantum Field Theory

MATHEMATICS THROUGH MILLENIA

The dawn of mathematics

The Greek heritage in mathematics

The golden period of the Hindus and the Arabs in mathematics

Mathematics in China

European mathematics in the Renaissance

Mathematics and the scientific revolution

The tools of calculus are developed and consolidated

Abstract mathematical structures emerges

Mathematics in the twentieth century

Mathematics forever

Introduction

MATHEMATICS ALIVE AND IN ACTION

Fundamental mathematical research

Theoretical computer science

Mathematical modeling

Mathematics in the physical sciences

Mathematics in the life sciences

Mathematics in the social sciences

Mathematics and the arts

Mathematics in industry

The impact of mathematics on society

ALGEBRA

Equivalence Relations

Grobner Bases

Homological Algebra

MATRICES, VECTORS, DETERMINANT AND LINEAR ALGEBRA

Matrices, Vectors and their Basic Operations

Determinants

Systems of Linear Equations

Symmetric Matrices and Quadratic Forms

Vector Spaces and Linear Algebra

GROUPS AND APPLICATIONS

Groups

Commutative Groups

Examples

Subgroups

Homomorphism

Quotient Groups

Homomorphism and Isomorphism Theorems

Cyclic Groups

Direct Products

Finitely Generated Abelian Groups

Group Actions and Symmetry

Solvable Groups

Representations of Finite Groups

RINGS AND MODULES

Definition of Rings

Basic Properties and Examples

Noetherian Rings

Completion

Localization and Local Rings

Modules

Integral Extensions

FIELDS AND ALGEBRAIC EQUATIONS

Basic Properties and Examples of Fields

Algebraic Equations

Algebraic Extensions

Separability

Galois Theory

Finite Fields

Cyclotomic Extensions

Kummer Extensions

Solvability

Ruler and Compass Constructions

NUMBER THEORY AND APPLICATIONS

The Additive Structure of Natural Numbers

The Multiplicative Structure of Natural Numbers

The Ring of Integers

Congruence

Analytic Methods in Number Theory

Arithmetic of Quadratic Fields

Cyclotomic Fields

Comments on Kronecker’s Dream in his Youth and Class Field Theory

ALGEBRAIC GEOMETRY AND APPLICATIONS

Affine Algebraic Varieties

Projective Algebraic Varieties

Sheaves and General Algebraic Varieties

Properties of Algebraic Varieties

Divisors

Algebraic Geometry over Algebraically Closed Fields

Schemes

Applications

GEOMETRY

BASIC NOTIONS OF GEOMETRY AND EUCLIDEAN GEOMETRY

Introduction

Basic Notions

Euclidean Space

Euclidean Group

Conic Sections

Discrete Groups of Isometries

AFFINE GEOMETRY, PROJECTIVE GEOMETRY, AND NON-EUCLIDEAN GEOMETRY

Affine Geometry

Projective Geometry

Geometries and Groups

Non-Euclidean Geometry

DIFFERENTIAL GEOMETRY

Curves in Euclidean Plane and Euclidean Space

Surfaces in Euclidean Space

Differentiable Manifolds

Tensor Fields and Differential Forms

Riemannian Manifolds

Geometric Structures on Manifolds

Variational Methods and PDE

TOPOLOGY

Introduction

Convergence of sequences, continuity of maps, general topology

Connectedness and homotopy theory

Simplicial complexes and homology theory

Applications for manifold theory

COMPLEX ANALYTIC GEOMETRY

Analytic Functions of One Complex Variable

Analytic Functions of Several Complex Variables

Germs of Holomorphic Functions

Complex manifolds and analytic varieties

Germs of Varieties

Vector Bundles

Vector Fields and Differential Forms

Chern Classes of Complex Vector Bundles

Divisors

Complete Intersections and Local Complete Intersections

Grothendieck Residues

Residues at an Isolated Zero

Examples

Sheaves and Cohomology

de Rham and Dolbeault Theorems

Poincaré and Kodaira-Serre dualities

Riemann-Roch theorem

MATHEMATICAL ANALYSIS

DIFFERENTIAL AND INTEGRAL CALCULUS

Historical survey

Convergence of Sequences

Continuous Functions

Differential Calculus

Integral Calculus

Differential Calculus of Functions of Many Variables

Multiple Integral

COMPLEX ANALYSIS

Complex number

Holomorphic functions

Residue and residue calculus

Analytic functions of several complex variables

Brief history

MEASURE AND PROBABILITY

Measure

Probability

Introduction

FUNCTIONAL ANALYSIS AND FUNCTION SPACES

Function Spaces and Some Examples

Basic Concepts in Functional Analysis

Some Advanced Concepts in Functional Analysis

Miscellaneous Function Spaces

Introduction

NUMERICAL ANALYSIS AND COMPUTATION

Linear Systems of Equations

An Example

Condition Number

Norms and Vector Spaces

Application to Error Analysis

Stable Algorithms and Stable Problems

Application to Numerical Solution of Linear Systems

Iterative Methods

Eigenvalue Problems

The Singular Value Decomposition

Software and Remarks

INFINITE ANALYSIS

Ising Model and Monodromy Preserving Deformation

Soliton Equations and Vertex Operators

Conformal Coinvariants and Vertex Operators

XXZ Model and Quantum Vertex Operators

Form Factor Bootstrap Approach in Sine-Gordon Model

Introduction

FOURIER ANALYSIS AND INTEGRAL TRANSFORMS

Fourier series

Wavelet expansion

Fourier transforms

Fourier analysis on locally compact Abelian groups

Finite Fourier Transform

Integral transforms

OPERATOR THEORY AND OPERATOR ALGEBRA

Hilbert space

Bounded linear operator

Operator theory

Operator algebra

FORMAL LOGIC

Cantor’s Set Theory

The Birth of First Order Logic

The Paradoxes

Axiomatic Set Theory

Mathematical Logic

Gödel’s First Incompleteness Theorem

Computability and Unsolvability

Recursion and Computation

MODEL THEORY

Classical Model Theory

Models of Tame Theories

Beyond First Order Logic

Model Theory for Mathematical Structures

Introduction

PROOF THEORY AND CONSTRUCTIVE MATHEMATICS

Intuitionistic Logic, I

Semantics of Intuitionistic Logic

Intuitionistic (Heyting) Arithmetic, HA

Constructive Mathematics

Proof Theory of First-order Logic

Proof Theory of Mathematical Theories

Introduction

COMPUTABILITY AND COMPLEXITY

Recursive and Recursively Enumerable Sets

Unsolvable Problems

Hilbert’s 10th Problem

Classifying Unsolvable Problems.

Complexity

Introduction

SET THEORY

Some Elementary Tools

Constructible Sets

Forcing

Descriptive Set Theory

Other Topics

Introduction

LOGIC AND COMPUTER SCIENCE

Complexity Classes and the P=NP problem

Propositional Logic and Complexity Classes

The Complexity of First-Order Logic and Richer Logics

Finite Model Theory

Logic and Databases

Introduction

MODAL LOGIC AND ITS APPLICATIONS

Language and Logic

Semantics

Soundness and Completeness for K

Some Other Systems

Some Other Results

Alternative Interpretations of ‘~ ’

Multimodal Logics

Non-standard Semantics

Modal Predicate Logic

Modality and Language

DIFFERENTIAL EQUATIONS OF MATHEMATICAL PHYSICS

A BASIC EXAMPLE OF NONLINEAR EQUATIONS: THE NAVIER-STOKES EQUATIONS

Scaling, hierarchies and formal derivations

Stabilities and instabilities of macroscopic solutions

Turbulence, weak convergence and Wigner measures

Some special properties of the dimension 2

CALCULUS OF VARIATIONS, PARTIAL DIFFERENTIAL EQUATIONS, AND GEOMETRY

An example: minimal surfaces

Phase transitions and interfaces

Introduction

LINEAR DIFFERENTIAL EQUATIONS

Linearity and Continuity

Examples

Methods

Introduction

DIFFERENTIAL EQUATIONS AND SYMPLECTIC GEOMETRY

Lagrangian Mechanics

Hamiltonian Systems and Symplectic Geometry

Nonlinear First order Partial Differential Equations

Oscillatory Integrals

Fourier Integral Operators

FROM THE ATOMIC HYPOTHESIS TO MICROLOCAL ANALYSIS

The Schrödinger Equation And Semiclassical Analysis

High Frequency Asymptotics and Microlocal Analysis

Introduction

DISCRETE MATHEMATICS

Bipartite Matchings

Discrete Convex Functions

GRAPH THEORY

Degrees and Distances

Connectivity

Operations

Trees

Factor Theory

Eulerian Circuits and Hamiltonian Cycles

Coloring

Planar Graph

Introduction

COMBINATORICS

Selected Topics in Combinatorics

Introduction

COMPUTATIONAL COMPLEXITY

Machine Models and Complexity Measures

Complexity Classes

Fundamental Results and Questions

Selected Topics

Introduction

OPTIMIZATION

Integer Programming

Enumerative Algorithms for Integer Programming

Solvable Cases of Integer Programming

Approximation Algorithms

Metaheuristics

MATHEMATICAL PHYSIOLOGY

MICROARRAY DATA ANALYSIS: ACQUIRING A SYSTEMIC VIEW IN BIOLOGY

Units and Variables: The Basic Nature of the Problem

The Pessimistic Way (The Curse of Dimensionality)

The Optimistic Way (The Blessing of Dimensionality)

Conclusion: Where We Go From Here

MODELING THE CELL CYCLE

Introduction

Physiology of the Cell Cycle

Molecular Mechanisms of the Cell Cycle Control

Mathematical Models of the Cell Cycle Regulation

Conclusion

CA2+ DYNAMICS, CA2+ WAVES AND THE TOPOGRAPHY OF THE CA2+ CONTROL SYSTEM

Introduction

The Minimal Ca2+ Signal Generating System

Ca2+ Signals are Transient

Ca2+ Carries Information via Diffusion

The Relationship between Molecular Geometry and Ca2+ Sensitivity

Ca2+ Signaling i Small Cells and Small Structures

Ca2+ Signaling i Large Cells

Ca2+ Oscillations

Conclusion

MATHEMATICAL MODELS OF EXCITABILITY IN BIOLOGICAL MEMBRANES, CELLS AND NETWORKS

Introduction

The Passive Properties of Biological Membranes

The Active Membrane

The Repertoire of Ionic Channels

Excitable Cells as Dynamical Systems

Synaptic Potentials

Excitation in Networks of Neurons

Stochastic Models of Excitability

Conclusions

MATHEMATICAL MODELING OF THE CARDIOVASCULAR SYSTEM AND ITS CONTROL MECHANISMS

Introduction

Cardiovascular Physiology

Modeling of the Cardiac Pumping Mechanism

Electrical Circuit Model of the Vascular System

Ventricular-Vascular Integration

Control Mechanism of the Cardiovascular System

Conclusion

MATHEMATICAL MODELING OF THE CIRCULATORY SYSTEM

Introduction

Circulatory System Organization and Physiology

Control Mechanisms

Connections to Other Physiological Systems

Clinical Issues Related to Cardiovascular System Function

Models

Model Application: Data Collection and Parameter Estimation

Current Key Questions

HEMODYNAMICS IN HUMANS: PHYSIOLOGY AND MATHEMATICAL MODELS

Introduction

Cardiovascular System and Hemodynamics

Models

Examples of Hemodynamic Modeling

Modeling Application: Hemodialysis

Current Key Questions in Hemodynamics

MATHEMATICAL MODELING OF HEMATOPOIESIS

How did Mathematical Models come to be used in Hematopoiesis?

The First Models

Hematopoiesis as a Control System: Feeback Loops, Robustness and Flexibility

Hematopoiesis as an Ecosystem: Cell Division, Mutations, Migration, Survival and Death

Other Approaches

MATHEMATICAL MODELING OF THE RESPIRATORY SYSTEM

Introduction

Respiratory physiology: key concepts and important clinical issues

Models

Model complexity

Clinical applications

Parameter estimation problem

Current issue and key questions

DELAY DIFFERENTIAL EQUATION MODELS IN DIABETES MODELING: A REVIEW

Introduction

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

Introduction

Anatomy and Physiology of the Kidney

Mathematical Models of the TGF Mechanism

Conclusion

POSTURE, EQUILIBRIUM, AND POSTURAL STABILIZATION

Introduction

Postural Adjustments and Stability

Mechanisms of Postural Stability

Use of Models in Postural Control Studies

Controller Models for Postural Movements

Conclusion

MODELING APPROACHES IN EMBRYO DEVELOPMENT

Introduction

Mechanisms of Pattern Formation in Development

Gradient-Based Patterning as a Paradigm

Boundaries in Development: Mathematical Approaches

Mechanical Interactions in Development

Conclusions

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

Introduction

PROBABILITY THEORY

Introduction: Chance Mechanisms

Early Concepts of Probability

The First Steps Towards a Theory of Probability

Earliest Applications

The Axiomatization of Probability Theory

Probability and Statistics in Life Support Systems

Water

Energy

Environment

Food

Agriculture

MATHEMATICAL FOUNDATIONS AND INTERPRETATIONS OF PROBABILITY

Finite Probability Spaces

Conditional Probability

Discrete Probability Spaces

Kolmogorov Triplets

RANDOM VARIABLES AND THEIR DISTRIBUTIONS

The distribution function of a random variable.

Classification of random variables.

Some special discrete probability distributions.

Some special continuous probability distributions.

Location characteristics of a real-valued random variable.

Dispersion characteristics of a real-valued random variable.

Joint distribution functions.

Independence of Random Variables

Random Variables in Statistics

The moments and the characteristic function of a random variable.

Conditional probability distributions

Probability Distributions Presented as Borel Measures

Introduction

LIMIT THEOREMS OF PROBABILITY THEORY

Introduction and Preliminaries

Laws of Large Numbers

Central Limit Theorem

Limit Theorems of Large Deviations

Classical Summation Theory

Local Limit Theorems

Limit Theorems for Extreme Values

ALTERNATIVE PROBABILISTIC SYSTEMS

Early developments

Capacities

The 1970s and 80s

From the 1990s on

Introduction

STOCHASTIC PROCESSES AND RANDOM FIELDS

Important Concepts and Methods

Types of Stochastic Processes

Random Fields

Introduction

CONSTRUCTION OF RANDOM FUNCTIONS AND PATH PROPERTIES

Examples

Definition of the Stochastic Process

Poisson Process

Brownian Motion

MARKOV PROCESSES

Discrete Markov Chains

Continuous Time Markov Chains

Examples of Markov Chains

Stopping Times and the Strong Markov Property

Path Properties and Continuity

Transition Operators

Examples of Markov Processes

Introduction

STOCHASTIC CALCULUS

Stochastic Integral

Ito Formula

Tanaka Formula

Differential of the Brownian Motion

STOCHASTIC DIFFERENTIAL EQUATIONS

Existence and Unicity

A Stochastic Chain Rule

A Property of the Solution of a Stochastic Differential Equation

STATIONARY PROCESSES

Spaces and operators related to stationary processes

The correlation function

Spectral representations

Prediction

Introduction

ERGODIC PROPERTIES OF STATIONARY, MARKOV, AND REGENERATIVE PROCESSES

Ergodic Theory for Stationary Processes

Ergodic Properties of Markov Processes

Regenerative Processes

Applications of Ergodic Theorems

Introduction

HOMOGENEOUS RANDOM FIELDS AND THEIR EVALUATION

Homogenous random fields and their spectral representation

Meteorological applications.

Approximation and positive definiteness of correlation functions.

Perturbation theory for improvement of positive definiteness

Computational algorithm

Results

Introduction

PROBABILISTIC MODELS AND METHODS

A Simple Probabilistic Model

Risk Management

Independence

Stochastic Processes

Processes with Independent Increments

Markov Processes

Stochastic Differential Equation

Martingale

Introduction

STATISTICAL SIMULATION AND NUMERICAL PROCEDURES

Random Number Generation

Non Uniform Random Variate Generation

The Use of Simulation in Statistics

Use of Simulation in Numerical Calculations

Introduction

INSURANCE MATHEMATICS

Non-life Insurance

Life Insurance

Introduction

MATHEMATICAL MODELS IN FINANCE

A Tutorial on Mathematical Finance without Formula

The Pricing of Financial Derivatives by Mathematical Means

Interest Rate Models

Financial Time Series Models

RELIABILITY AND MAINTAINABILITY

Some Reliability Concepts

System Reliability

Availability and Maintainability

Reliability Data Analysis

Towards the 21st Century

Introduction

INVENTORIES, WATER STORAGE AND QUEUES

Inventory Models

Models for Water Storage

The Queueing System GI /G /S

Queueing Networks

Introduction

INFORMATION THEORY AND COMMUNICATION

Information source

Source coding

Measures of information

Transmission channel

The practice of classical telecommunication

Mobile communication

Cryptology

Introduction

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

Introduction

PRELIMINARY DATA ANALYSIS

Univariate Data Sets

Bivariate Data Sets

Multivariate Data Sets

Concluding Remarks

STATISTICAL INFERENCE

Parametric and Nonparametric Inference

Sufficiency and Information

Classical Statistical Inference

Bayesian Inference

Data Quality and Statistical Inference

Statistical Inference and Decisions

Introduction

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

Introduction

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

Introduction

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

APPLIED STATISTICS

Foundations

Exploratory Data Analysis

Models

Statistical Inference

Design of Experiments

The Future of Applied Statistics

Introduction

CORRELATION ANALYSIS

Correlation Between Two Random Variables (Simple Correlation)

Partial Correlation

Multiple Correlation

Canonical Correlation

REGRESSION ANALYSIS

Simple Regression

Multiple Regression

Gauß-Markov Theorem

Unequal Variances

Quasi-linear Regression

Multivariate Regression

ANALYSIS OF VARIANCE AND ANALYSIS OF COVARIANCE

Analysis of Variance (ANOVA)

Analysis of Covariance

SAMPLE METHOD AND QUALITY CONTROL

Introduction: Quality Control and Statistical Quality Control

Concepts of Quality

Inspection and Prevention in Quality Control

Decision Making and its Statistical Tools in Quality Control

Statistical Lot Inspection Schemes

Statistical Process Inspection Schemes

Recent Trends and Outlook

TIME SERIES ANALYSIS

Finite-difference equations

Interpolation, approximation, and checking

Correlations

Introduction

Conclusion

STATISTICAL EXPERIMENTS AND OPTIMAL DESIGN

Linear models

How to measure the information obtained in an experiment modeled linearly

The design of experiments with uncorrelated observations and non-restricted replications

Optimal design in linear models under a given covariance structure

Design of nonlinear regression experiments

Perspectives and further developments

Introduction

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

Introduction

INTRODUCTION TO MATHEMATICAL MODELING

Physical and mathematical models

Mathematical modeling

Fundamental and applied models

Using computers in mathematical modeling

Mathematical methods in experimental studies

Computational experiment

Computational experiment in science and technology

Types of computational experiment: an example

Constructing mathematical models

Previous study of mathematical models

Numerical algorithms

Introduction

Conclusion

MATHEMATICAL MODELING OF LIFE SUPPORT SYSTEMS: CLASSIFICATION OF MODELS

Mathematical models

Some classes of mathematical models

Linear and nonlinear models

Well-and ill-posed problems

Point models

Distributed models

Discrete models

Imitation modeling

Introduction

Conclusion

MATHEMATICAL MODELS IN WATER SCIENCES

Mathematical Models in Hydrodynamics

Mathematical Models of Flows in Rivers, Lakes, and Coastal Waters

Mathematical Models of Circulation in Oceans and Seas

Mathematical Models of Water Waves

Mathematical Models for Water Resources Management

Introduction

Conclusion

MATHEMATICAL MODELS OF CIRCULATION IN OCEANS AND SEAS

Mathematical Modeling of Oceanic and Marine General Circulation

Solvability of Problems of the Ocean and Sea Dynamics

Alternative and Generalized Models of the General Circulation in Oceans and Seas

Numerical Methods

Forward and Adjoint Models

Introduction

MATHEMATICAL MODELS FOR WATER RESOURCES MANAGEMENT

Mathematical modeling in water resources planning

Models of regional agricultural development, location and water use with regard to non-point source pollution

Water resources management in the face of climatic/ hydrological uncertainties

Water quality management

Global model of decision-making support system functioning

Introduction

Conclusion

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

Introduction

Conclusion

MATHEMATICAL MODELS IN ENVIRONMENTAL SCIENCES

MATHEMATICAL MODELS AND SIMULATION IN ENVIRONMENT

Mathematical model for regional transport and transformations of gaseous pollutants and aerosols

Application of the combined model of atmospheric thermo-hydrodynamics and pollution transport to solving specific environmental problems

Numerical model of global transport and transformations of multicomponent gaseous pollutants and aerosols

Introduction

MATHEMATICAL MODELS FOR PREDICTION OF CLIMATE

Mathematics for climate modeling

Climatic models

Predictability of climate changes

Introduction

Conclusion

MATHEMATICAL MODELING IN METEOROLOGY AND WEATHER FORECASTING

Equation system used in the hydrodynamic atmospheric models

Hydrodynamical Modeling of large-scale weather-producing mechanisms

Atmospheric models based on the primitive hydrodynamic equations

Application of hydrodynamical models to forecasting of local weather patterns

Tropical cyclone modeling

Introduction

Conclusion

ENVIRONMENTAL POLLUTION AND DEGRADATION MODELS

Mathematical model for global transport of persistent organic pollutants in the Northern Hemisphere

Numerical results

Introduction

Conclusion

MATHEMATICAL MODELS IN FOOD AND AGRICULTURAL SCIENCES

FOOD PRODUCTION AND AGRICULTURAL MODELS: BASIC PRINCIPLES OF DEVELOPMENT

Classification of Agricultural Models

Typical Theoretical Models in Agriculture

Agroecosystem Productivity Models and Simulation Systems

The Use of Models

Experimental Support of Models and Experiment Planning

Introduction

MATHEMATICAL MODELS OF SOIL IRRIGATION AND SALTING

Balance models of calculation of the irrigation regime and crops productivity.

Simulation of water and salts transport in unsaturated-saturated soils.

The complex simulation models

Introduction

Conclusion

DETERMINISTIC MODELS OF PLANT ENVIRONMENT

Static models: empirical-statistical approach

Dynamical models: An approach oriented to process account

Deterministic models of energy and mass exchange for plant environment

Introduction

MATHEMATICAL MODELS OF AGRICULTURAL SUPPLY

Models and decision making in agriculture

Mathematical models of optimization and allocation of sown areas

Mathematical models of fertilization optimization

Complex optimization of resource allocation in crop growing

Economic-mathematical models of optimization of structure of herds and flocks

Economic-mathematical models of optimization of rations of cattle feeding

Economic-mathematical models of optimization of combination of several branches in a farm

Economic efficiency of precision agriculture farm application

Introduction

MATHEMATICAL MODELS IN BIOLOGICAL AND MEDICAL SCIENCES

MATHEMATICAL MODELS IN BIOPHYSICS

Specificity of mathematical modeling of living systems

Basic models in mathematical biophysics

Oscillations and rhythms in biological systems

Space-time self-organization of biological systems

Physical and mathematical models of biomacromolecules

Modeling of complex biological systems

Introduction

Conclusion

POPULATION MODELS

Construction of Mathematical Population Models and the Main Tasks of Their Study

Deterministic Models of Population Genetics

Stochastic Models of Population Genetics

Mathematical Models of Biological Populations and Communities

PATTERN FORMATION AND NEURAL MODELS

Mathematical models of autowave systems of the type “reaction-diffusion” or the models with local connections

Autowaves in homogeneous neuron-like systems

Introduction to the Pattern Formation Theory

MATHEMATICAL MODELS IN IMMUNOLOGY

Mathematical models of humoral immune response

Mathematical models of network interactions in the immune system

Mathematical models of lymphocyte circulation

Mathematical models of infectious diseases

Other models

Immune system and optimality

Introduction

Concluding Remarks

MATHEMATICAL MODELING IN MEDICINE

Physiological systems and processes

System of blood circulation

The respiratory system

Regulation of water and salts exchange

Thermoregulation

Regulation of blood sugar

Introduction

Conclusion

MATHEMATICAL MODELS IN GLOBAL PROCESSES AND DEVELOPMENT

MATHEMATICAL MODELS AND CONTROL OF CATASTROPHIC PROCESSES

Basic Notions and Examples

Singularity Theory

Singularities in Optimization problems

Introduction

Conclusion

MODELS AND METHODS OF ACTUARIAL MATHEMATICS

Empirical principles of determination of insurance premiums.

Classification of risk models

Collective risk model

Individual risk model

Introduction

Conclusion

MATHEMATICAL MODELING AND GLOBAL PROCESSES

Mathematical Modeling and the Control Theory in Examining Complex Processes

Numerical Modeling of the General Circulation of the Atmosphere and Oceans; Climate

Mathematical Modeling of Biospheric Processes

Control Theory and Controllable Dynamics

Scientific Problems for the Twenty-first Century

Introduction

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

Introduction

Introduction

FUNDAMENTALS OF OPERATIONS RESEARCH

Linear Programming

Discrete Optimization and Integer Programming

Nonlinear Programming

Implementation Aspects: Efficiency and Productivity

Introduction

THE ROLE OF MODELING

Modeling as a Mental Activity

Mathematical Modeling

Introduction: Morphology of Models

LINEAR PROGRAMMING

Linear Programming Problems

Primal and Dual Programs and Polyhedra

The Simplex Method

Polynomial Solution Methods for LPs

NONLINEAR PROGRAMMING

Optimality Conditions

Optimization Algorithms

Large Scale Optimization

Introduction

DYNAMIC PROGRAMMING

Preliminary Examples

Sequential Decision Processes

Decomposition of Objective Functions

Functional Equations

Policies

Algorithms

The Principle of Optimality

The Curse of Dimensionality

Generalizations

The Art of Dynamic Programming

Epilogue

Introduction

DISCRETE OPTIMIZATION

Modeling

Solution Methods

Introduction

THE ROLE OF SOFTWARE IN OPTIMIZATION AND OPERATIONS RESEACH

Historical Perspectives

Obtaining a Solution

Modeling

Computer-Assisted Analysis

Intelligent Mathematical Programming Systems

Beyond the Horizon

Introduction

ADVANCED DETERMINISTIC OPTIMIZATION

Foundations

Seminal Development-Discrete Optimization

COMBINATORIAL OPTIMIZATION AND INTEGER PROGRAMMING

Modeling

Mathematical Foundations

Algorithmic Approaches

Software

GRAPH AND NETWORK OPTIMIZATION

Preliminaries

Shortest Path Problem

The Maximum Flow Problem

The Minimum Cost Flow Problem

The Minimum Spanning Tree Problem

SCHEDULING

General Scheduling Models

Applications

Classification, Complexity and Solution Methods

ROUTING PROBLEMS

The Chinese Postman Problem

The Traveling Salesman Problem

Vehicle Routing Problems

Capacitated Arc Routing Problems

LARGE SCALE OPTIMIZATION

LP Relaxations

Lagrangian Relaxations

Decomposition Methods

Reformulations

Final Remarks

DUALITY THEORY

Convex Programming

Linear Programming

Integer Programming

General Mathematical Programming

NONSMOOTH OPTIMIZATION

The general problem and its motivation

Algorithms for convex optimization

Some illustrations

GLOBAL OPTIMIZATION AND META-HEURISTICS

Meta-Heuristic Features

Brief Description of Some Meta-Heuristics

Metaphors of Nature

APPROXIMATION ALGORITHMS

Combinatorial Optimization Problems

Design Techniques for Approximation Algorithms

Non-approximability results

Advanced Topics

OPTIMIZATION IN INFINITE DIMENSIONS

Infinite-Dimensional Optimization Problems

Convex Problems and Duality

Necessary Optimality Conditions

Optimal Control Problems

Calculus of Variations

Nonsmooth Problems

Optimal Shape Design

THE PRINCIPLES OF THE CALCULUS OF VARIATIONS

Classical Theory

Direct Methods

Unstable Critical Points

THE MAXIMUM PRINCIPLE OF PONTRYAGIN

The Maximum Principle

Structure of Optimal Controls

Relation to Dynamic Programming

Numerical Solution Based on the Maximum Principle

DYNAMIC PROGRAMMING AND BELLMAN'S PRINCIPLE

Optimal Control

Value Function and Bellman’s Principle

The Hamilton-Jacobi-Bellman Equation

Optimal Feedback Synthesis

OPTIMIZATION AND CONTROL OF DISTRIBUTED PROCESSES

Optimization Problems Governed by Distributed Processes

Existence and Characterization of Solutions

Discretization of the Problem

Optimization Algorithms

NONCONVEX VARIATIONAL PROBLEMS

The Direct Method of the Calculus of Variations

Relaxation theory

Vector Valued Problems

Problems with No Minimizer, Minimizing Sequences

GAME THEORY

Foundations of Non-cooperative Game Theory

NTU-Games

TU-Games

The Equivalence Principle

Mechanism Theory

Repeated Games

Evolution and Learning in Games

Experimental Games

FOUNDATIONS OF NON-COOPERATIVE GAMES

Chess-Like Games

Representations of Non-Cooperative Games

Two-Person Zero-Sum Games

Non-Zero-Sum Games

Games with Incomplete Information

NTU-GAMES

Basic Model and Definitions

The Core of an NTU-Game

The Bargaining Set

Values for NTU-Games

TU-GAMES

Characteristic Function Form Games

Solutions

Market Games

Voting Games

Other Applications

THE EQUIVALENCE PRINCIPLE

Notation and the Basic Model

Walrasian Equilibrium

Equivalencies in Atomless Economies

Approximations to Equivalence: Large Finite Economies

Strategic Behavior and Walrasian Equilibria

MECHANISM THEORY

A General Mechanism Design Setting

Dominant Strategy Mechanism Design

Bayesian Mechanism Design

Implementation

STOCHASTIC AND REPEATED GAMES

Supergames

Repeated Games with Incomplete Information

Stochastic Games

EVOLUTION AND LEARNING IN GAMES

Biological Contexts: A Static Approach

Biological Contexts: A Dynamic Approach

Social Contexts

Equilibrium Selection: Coordination Games

Equilibrium Selection: Oligopoly Games

EXPERIMENTAL GAME THEORY

One-Person Decision Making

Experimental Results in Strategic Games

Alternating Offer Bargaining

Characteristic Function Experiments

Quo Vadis Experimental Game Theory?

STOCHASTIC OPERATIONS RESEARCH

Markov Models

Markov Decision Processes

Stochastic Games

Queueing Systems

Inventory Models

Investment Models

Adaptive Dynamic Programming

MARKOV MODELS

Discrete-time Markov Chains

Continuous-Time Markov Chains

Further Models

MARKOV DECISION PROCESSES

Problem Definition and Examples

Finite Horizon Decision Problems

Infinite Horizon Markov Decision Problems

Continuous-time Markov Decision Processes

Further Topics

STOCHASTIC GAMES

Basic Definitions and Notations

Zero-Sum Stochastic Games

General-Sum Stochastic Games

Further Topics

QUEUEING SYSTEMS

Design of Queueing Systems

Performance Measures and Special Queues

Little’s Formula

Queueing Networks and Examples

INVENTORY MODELS

The Basic EOQ Model

The Dynamic Economic Lotsize Model

Periodic Review Stochastic Demand Models

Continuous Review Stochastic Demand Models

INVESTMENT MODELS

Mean-Variance Portfolio Selection

Portfolio Selection in Discrete Time

Portfolio Selection in Continuous Time

Further Models

ADAPTIVE DYNAMIC PROGRAMMING

Basic Models and Valuations

Adaptive Algorithms

Estimation Procedures

Remarks on Applications

Remarks on Related Concepts

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

THE DEVELOPMENT OF MATHEMATICS IN A HISTORICAL PERSPECTIVE

Introduction

Measure Theories and Probability

Invariant Measures

Ergodicity and Dynamical Systems

MATHEMATICS IN EGYPT AND MESOPOTAMIA

The beginnings: invention of script, numbers, and metrological systems

Mathematical Texts: education and mathematical practices

Beyond the School: Mathematics in Daily Life, Literature and Art

Egyptian And Mesopotamian Mathematics in the Graeco-Roman Periods

Summary: Egypt vs. Mesopotamia

HISTORY OF TRIGONOMETRY TO 1550

Precursors

Alexandrian Greece

India

Islam

The West to 1550

MATHEMATICS IN JAPAN

Introduction

The beginnings (seventh to sixteenth century)

Textbooks of Commercial arithmetic

The construction of a learned tradition

Wasan status : between art and science

Conclusion

THE MATHEMATIZATION OF THE PHYSICAL SCIENCES - DIFFERENTIAL EQUATIONS OF NATURE

Everything is number

Ancient Astronomy

Optics and statics

The middle ages and the renaissance

Mechanics of motion

Newtonian mechanics

Early differential equations

The Brachistochrone

Early Methods of Solution- Linear Differential Equations

Newton’s Second Law as a Differential Equation- The Method of Perturbations

The Vibrating String- Partial Differential Equations

The Vibrating String-Trigonometric Series

Potential Theory- Laplace’s equation

The Parsimonious Universe- Calculus of Variations

The Hamilton Formalism

Electrostatics- Poisson’s equation

Fourier on Heat Conduction and Fourier Series

Orthogonal Functions and Curvilinear Coordinates

Sturm-Liouville Theory- The Qualitative Theory

Continuum Mechanics- Elasticity

Hydrodynamics- The Navier-Stokes Equation

Electromagnetism- Maxwell’s Equations

Relativity

Quantum Mechanics- The Schrodinger Equation

Distributions- Generalized Solutions of Differential Equations

Concluding Remarks

A SHORT HISTORY OF DYNAMICAL SYSTEMS THEORY: 1885-2007

Introduction

The qualitative theory of dynamical systems

Central themes

Some recent extensions and applications of dynamical systems

Epilogue and further reading

MEASURE THEORIES AND ERGODICITY PROBLEMS

Introduction

Measure theories and probability

Invariant measures

Ergodicity and dynamical systems

THE NUMBER CONCEPT AND NUMBER SYSTEMS

Introduction

Arithmetic

Length and Area

Algebra and Geometry

Real Numbers

Imaginary numbers

Geometry of Complex Numbers

Algebra of complex numbers

Quaternions

Geometry of Quaternions

Octonions

Incidence Geometry

OPERATIONS RESEARCH AND MATHEMATICAL PROGRAMMING: FROM WAR TO ACADEMIA – A JOINT VENTURE

Introduction

Precursor of OR: Taylorism

The beginning of OR in Britain: The use of radar in anti-aircraft warfare

OR’s move to the US military: The mobilisation of civilian scientists

ASWORG: Philip Morse’s OR group

The Applied Mathematics Panel: OR training courses during Word War II

Game theory: The significance of John von Neumann

The origin of linear programming: Logistic planning in the Army Air Force

Mathematical programming in academia: ONR project and game theory

Operations research in academia: Societies, journals, and conferences

Classical OR problems

Operations research and linear programming outside academia: some examples

The role of mathematical programming and game theory in OR: Disputes

Conclusion

ELEMENTARY MATHEMATICS FROM AN ADVANCED STANDPOINT

Introduction: Klein's view of elementary mathematics

Arithmetic

Computation

Algebra

Geometry

Calculus

Computers and their influence

THE HISTORY AND CONCEPT OF MATHEMATICAL PROOF

Introduction

The Concept of Proof

What Does a Proof Consist Of?

The Purpose of Proof

The History of Mathematical Proof

The Middle Ages

The Golden Age of the Nineteenth Century

Hilbert and the Twentieth Century

Computer-Generated Proofs

Closing Thoughts

GEOMETRY IN THE 20TH CENTURY

Introduction

The Incredible Successive Enlargements of the Notions of Space and Of Point

Studying Subspaces: Classification, Measuring Them, Optimality

Some Geometric Spaces Which Are Surprising Extremely Rich Crossroads

Groups and Geometry: A Journey There And Back

Some concepts and tools useful in many places

Convexity

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

NUMERICAL ANALYSIS AND METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS

The solution of systems of linear equations

The solution of nonlinear equations and systems

Numerical integration

Interpolation and approximation of functions

Numerical differentiation

Two-sided methods and interval analysis

Numerical methods for ordinary differential equations

SOLUTION OF SYSTEMS OF LINEAR ALGEBRAIC EQUATIONS

An Unusable Formula

Direct methods

Iterative methods

The conjugate gradient method

Conjugate gradient method: general case

Domain decomposition methods

NUMERICAL INTEGRATION

Statements of Problems

Quadrature Formulae

Cubature Formulae

NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS AND DYNAMIC SYSTEMS

Dynamic Systems

Analytic Methods

One-step Methods

Stiff Systems

Linear Multistep Methods

Error Estimation

Delay Differential Equations

NUMERICAL METHODS AND ALGORITHMS IN MATHEMATICAL PHYSICS

FINITE ELEMENT METHOD

Other one-dimensional boundary problems

Higher order elements in one dimension

Two or Three-dimensional Elliptic Problems

Two-dimensional Lagrange Elements

Three-dimensional Elements

Isoparametric elements

Numerical Quadrature Formulas

Error analysis with numerical integration

Error analysis with exact integration

AN INTRODUCTION TO FINITE VOLUME METHODS

Advection equation and method of characteristics.

Finite volumes for linear hyperbolic systems.

Gas dynamics with the Roe method.

Second order and two space dimensions.

NUMERICAL METHODS FOR INTEGRAL EQUATIONS

Quadrature methods

Degenerate Kernels. Projection and Collocation Methods

Iterative methods for linear and nonlinear integral equations

Singular integral equations

NUMERICAL ALGORITHMS FOR INVERSE AND ILL-POSED PROBLEMS

Inverse Problems

Ill-Posed Problems

Numerical Algorithms for Solving Inverse and Ill-Posed Problems

COMPUTATIONAL METHODS AND ALGORITHMS IN CONTINUOUS MEDIUM PROBLEMS

SOLUTION OF ELECTROMAGNETISM THEORY PROBLEMS

Two-dimensional electrostatics problems

Three-dimensional electrostatics problems

Two-dimensional magnetostatics problems

Three-dimensional magnetostatics problems

Electroconductivity problems

Solutions harmonic with respect to time

Nonstationary solutions

COMPUTATIONAL METHODS IN ELASTICITY

Basic aspects of continuum mechanics

The three-dimensional linearized elasticity

The three-dimensional elastodynamics problem

A particular case of structures: plates

COMPUTATIONAL METHODS FOR COMPRESSIBLE FLOW PROBLEMS

A Brief Description of the Solutions

Numerical Schemes for 1-D Problems

Schemes for Multidimensional Problems

Numerical Examples

METHODS OF NONLINEAR KINETICS

The Boltzmann equation

Phenomenology and Quasi-chemical representation of the Boltzmann equation

Kinetic models

Methods of reduced description

Discrete velocity models

Direct simulation

Lattice Gas and Lattice Boltzmann models

Other kinetic equations

METHODS FOR MAGNETOSPHERE AND NEAR-SPACE PROBLEMS

MHD model of solar wind flow around the magnetosphere

Mathematical statement of the flow problem: Basic equations

Thermal anisotropy of the magnetosheath plasma

Reconnection problem

NUMERICAL MODELS AND SIMULATION OF GLOBAL PROBLEMS

NUMERICAL SIMULATION OF CLIMATE PROBLEMS

Climate, Climatic Variability and Climate Changes

Atmosphere & Ocean Circulation Models

Numerical Modeling of Climatic Variability and Climate Changes

NUMERICAL SIMULATION OF BIOSPHERE DYNAMICS

Models of Global Dynamics by Club of Rome

The Problem of the Earth's Biosphere Stability

Canadian Climate Change Model

Global Models of Biosphere Dynamics

Problems of Biosphere Dynamics Prediction

Numerical Simulation and Experimental Models of the Biosphere

Is Uncertainty of Global Models Principal?

Resume

NUMERICAL METHODS FOR WEATHER FORECASTING PROBLEMS

Data assimilation system.

Numerical data analysis and initialization.

Mathematical Models for Numerical Weather Prediction

Numerical Methods in Weather Forecast

Parameterization schemes.

Use of numerical weather forecasting products.

Resume.

MODERN BIOMETRY

History

Biometric Data Collection and Analysis

Biometry in Action

Mathematics in Biometry

Future

DATA COLLECTION AND ANALYSIS IN BIOMETRICS

Experimental Design

Sample Surveys

Clinical Trials and Case Control Studies

Longitudinal Studies and Time Series

Species Abundance

Data Collection

THE DESIGN OF EXPERIMENTS

Standard Factorial Designs

Split-Plot Designs

Repeated Measures Designs

Importance of Correct Design and Analysis

SAMPLE SURVEYS

What is a Survey?

Probability sampling

Common probability sampling designs

Survey estimates and standard errors

Nonsampling errors

Sampling rare populations

Issues in Survey Design

RESPONSE ADAPTIVE RANDOMIZATION IN CLINICAL TRIALS

The Design

Likelihood Based Inference

Nonparametric Inference

Regression Models

TIME SERIES MODELS

Standard Linear ARMA Models

Bilinear Models

Standard Space Time ARMA Models

Space Time Bilinear Models

Exponential Models

ESTIMATING SPECIES ABUNDANCE

Quadrat Sampling

Adaptive Cluster Sampling

Line and Point Transect Sampling

Nearest-Neighbour Distance Methods

Capture-Recapture Methods

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

COMPUTATION AND BIOMETRY

Computer Language and Systems Past, Present and Future

Changing Views of Statistical Computing

Statistical Computing in the Larger Context of Scientific Computing

Limitations of Coverage

Directions for Future Development

Chapters Included Under This Theme

STATISTICAL GRAPHICS

Graphs for models involving two or more variables

Graphs for models involving several covariates

Graphs for modelling data developing in time or space

Graphs for modelling survival data

Graphs for multivariate data

COMPUTER-INTENSIVE STATISTICAL METHODS

Resampling and Monte Carlo methods

Numerical optimization and integration

Density estimation and smoothing

Relaxing least-squares and linearity

STATISTICAL COMPUTING

Advances in Routines Used for Statistical Computation

Languages and Systems for Statistical Computing

Key Ideas for Statistical Systems

Desiderata for Statistical Systems

Large Data Bases - Data Mining

Connectivity

The Future of Statistical Computing

SPATIAL STATISTICAL MODELING IN BIOLOGY

Gaussian Random Process Models

Non-Gaussian Random Process Models

Multivariate Spatial Models

Spatiotemporal Models

Computation

Future Directions

BIOSTATISTICAL METHODS AND RESEARCH DESIGNS

Biostatistical Research Strategies

Study Designs

Statistical Models and Methods

Statistical Inference

EPIDEMIOLOGY METHODS

Types of Investigation

Measures of Association

Common Designs

Discussion

COMMUNICABLE DISEASES AND DATA ANALYSIS

Transmission probability

Basic reproductive number

The dependent happening relation

Population-level effects of intervention

Challenges for the future

NUTRITIONAL EPIDEMIOLOGY

Research Designs and Methods

Example of Dietary Fat and Post-Menopausal Breast Cancer

Future Directions, Research Needs and Opportunities

STATISTICAL METHODS IN LABORATORY AND BASIC SCIENCE RESEARCH

Theory: Universal Distributions

The Role of Statistics

Statistical Strategies

Case Studies

Closing Remarks

STATISTICAL METHODS FOR TOXICOLOGY

Applications of Biostatistics to Toxicology

General Methods in Dose-Response Modeling

Quantitative Risk Assessment

SELECTED TOPICS IN BIOMETRY

Inference

Design and analysis of experiments

Spatial analysis

Multivariate methods

Variation over time

Simulation

Statistical genetics

Bioinformatics

STATISTICAL METHODOLOGY IN AGRICULTURE AND HORTICULTURE

Current methodology

Future developments

STATISTICAL METHODOLOGY IN FORESTRY

Forest Inventory

Modeling Individual Tree Characteristics

Quantitative Characteristics of Forest Stands

Statistically Designed Experiments in Forestry

STATISTICAL ECOLOGY AND ENVIRONMENTAL STATISTICS

Simple Stories but Challenging Concerns

Ecological Sampling and Statistical Inference

Biodiversity Measurement and Comparison

Environmental Data and Cost-Effective Acquisition

Landscape Ecology and Multi-Scale Assessment

Echelon Analysis for Multispectral Environmental Change Detection

Statistics as an Instrument to Deal with Environmental and Ecological Crisis

Future Areas of Concern and Challenge

Looking Ahead

POPULATION GENETICS

Basic Principles

Explanations for Genetic Variation

STATISTICAL GENETICS

Basic Principles

Relatedness

Plant and Animal Breeding

Locus Mapping

Quantitative Trait Locus Mapping

BIOINFORMATICS: PAST, PRESENT AND FUTURE

Biological sequence analysis

Applications of hidden Markov models in bioinformatics

Evolutionary models and phylogenetic reconstruction

Gene expression analysis

Statistical methods in proteomics

Systems biology

Federated Data Integration and BioGrids

Discussion

ENVIRONMETRICS

STATISTICAL ANALYSIS OF ECOLOGICAL DIVERSITY

Defining and Measuring Ecological diversity

Abundance Estimation

Statistical Inference on Diversity

Ecological Diversity Ordering

Field Studies

DESCRIPTIVE MEASURES OF ECOLOGICAL DIVERSITY

Diversity, richness, evenness

General properties of diversity indices

Special indices and families of indices

SAMPLING DESIGNS FOR MONITORING ECOLOGICAL DIVERSITY

Unit sampling

Area sampling

Further developments: two-stage sampling

INFERENCE ON ECOLOGICAL DIVERSITY

Diversity index estimation

Species-abundance curve models

THE INVENTORY AND ESTIMATION OF PLANT SPECIES RICHNESS

Species Inventorying

Estimating and Comparing Species Richness through Samples

SPATIAL STATISTICS

Models

Exploring Spatial Structure

Estimation

Prediction

Future Directions

GEOSTATISTICS: PAST, PRESENT AND FUTURE

Distribution-Free Methodology

Likelihood-Based Modeling

Model Based Prediction

Discussion and Future Directions

SPATIAL DESIGN

A statistical framework

Single purpose spatial designs

Multipurpose spatial designs

Relationships among design criteria

STATISTICAL ANALYSIS OF SPATIAL COUNT DATA

Random Spatial Indices

Non-Random Spatial Indices

Spatial Epidemiology and Disease Mapping

SPATIAL DISEASE MAPPING

Reasons for spatial pattern in disease data

Types of spatial disease data

Analytic methods by data type

Future Trends

MULTIVARIATE DATA ANALYSIS

Multivariate Distributions

Parameter Estimation for a Multivariate Normal Population

Tests of Hypotheses for Mean Vectors and Covariance Matrices

The General Linear Hypothesis Model

Discriminant Analysis

Principal Components

Factor Analysis

THE ANALYSIS OF PUTATIVE SOURCES OF HEALTH HAZARD

Study Design

Problems of Inference

Modeling the Hazard Exposure Risk

Models for Case Event Data

Models for Count Data

SPATIO-TEMPORAL METHODS IN CLIMATOLOGY

Descriptive Statistical Methods

Future Directions

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

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 IN WATER SCIENCES

MATHEMATICAL MODELS IN HYDRODYNAMICS

Some fundamentals

Direct Numerical Simulation

Statistical turbulence modeling

Large Eddy simulation

MATHEMATICAL MODELING OF FLOW IN WATERSHEDS AND RIVERS

Flow in Watersheds and Channels

Laws of Science

Deterministic and Statistical Modeling

Deterministic Modeling of Flow in Watersheds

Deterministic Modeling of Flow in Channels

Statistical Modeling of Flow in Watersheds

Emerging Technologies for Flow Modeling

Uncertainty Analysis

Hydrologic Design

MATHEMATICAL MODELS OF CIRCULATIONS IN OCEANS AND SEAS

Areas of Model Application

Approximate Systems of Equations

Ocean Modeling Concepts

Numerical Aspects

The Quality of Model Results; Validation and Evaluation

Outlook

WAVE MODELING AT THE SERVICE OF SECURITY IN MARINE ENVIRONMENT

Physical principles of free surface waves

Forcing functions for wave modeling

Present applications of wave modeling

Outlook

MATHEMATICAL MODELING OF THE TRANSPORT OF POLLUTION IN WATER

Phemonenology

Experiments

A Short Introduction to Turbulence Theory

Mathematical Modelling of the Transport of Pollution

An Alternative Approach: Lagrangian Tracer Technique (LTT)

Examples

MATHEMATICAL MODELS IN ENERGY SCIENCES

MATHEMATICAL MODELS IN ELECTRIC POWER SYSTEMS

Basic Concepts

Elements of an Electric Power System

Power System Design, Operation and Control

Equipment Models

Modelling and Simulation of Power System Performance

MATHEMATICAL MODELS OF NUCLEAR ENERGY

Reactor Background.

Neutron Transport Equation

General Properties of Transport Equation

Methods of Solution

Optimization Models

Future: Prospective projects of nuclear power engineering

MATHEMATICAL MODELS IN CHEMICAL PHYSICS AND COMBUSTION THEORY

Chain Reactions

Link between Energy and Kinetics of Reaction

Length of Chains

Breaking of Chains

Breaking of Chains in a Volume and at the Surface

Development of Chains with Time

Combustion

Detonation Waves

Modeling the Temporal Evolution of a Reduced Combustion

A Model for Calculating Heat Release

MATHEMATICAL MODELING AND SIMULATION METHODS IN ENERGY SYSTEMS

Bottom-up versus top-down modeling

Simulation vs. optimization

Technology ranking

Issues in energy modeling

MATHEMATICAL MODELS OF CLIMATE AND GLOBAL CHANGE

MATHEMATICAL MODELS OF CLIMATE

Models Based upon Energy Balance

Atmospheric General Circulation Models

Oceanic GCMs

Coupled AOGCMs

Other Climate Components

Applications of Climate Models

Challenges for the Future

MATHEMATICAL MODELS IN METEOROLOGY AND WEATHER FORECASTING

History of Numerical Weather Prediction

Numerical Models

Data Assimilation

Ensemble Forecasting and Predictability

The Future

MATHEMATICAL MODELS OF HUMAN-INDUCED GLOBAL CHANGE

Historical Development

Current Methodology

Strengths and Weaknesses of Climate Models

Future Challenges

MATHEMATICAL MODELS IN AIR QUALITY PROBLEMS

A fundamental chemical kinetics system

Modeling of linear advection

Modeling of chemical ordinary differential equations

One example of the modeling of the air pollution problem: the CHIMERE software.

INFILTRATION AND PONDING

The Green and Ampt (1911) Model

Green and Ampt Model and Richards’ Equation

Richards’ Equation and Profile Analysis

Gravity effects

MATHEMATICAL EQUATIONS OF THE SPREAD OF POLLUTION IN SOILS

Convective-Diffusive Equation

Effects of Boundary Conditions

Chemical Reactions

Nonlinear Adsorption

Two Species Competition

Interaction of Surface Water and Chemical Transport in Soils

Column Flow

Transient Unsaturated Water and Solute Transport

Scale Dependent Solutions

Transient Solution Profiles

Source Solutions

Conclusion

MATHEMATICAL SOIL EROSION MODELLING

Surface Hydrology

Soil Erosion Processes

Steady State Solutions of the Rose - Hairsine Model

Dynamic Erosion - Time Dependence

Field Scale

MATHEMATICAL MODELS OF BIOLOGY

About modeling

Archetypical models of evolution and ecology

Conclusions

MATHEMATICAL MODELS OF MARINE ECOSYSTEMS

Introduction: Purposes of Mathematical Modeling in the study of Marine Ecosystems.

Processes and Fluxes in Marine Ecosystems

Various Approaches to Marine Ecosystems Modeling

More about Population-level Models

Parameter Estimation and Verification of Models

Some Open Problems

POPULATION MODELS

Continuous-Time Population Models

Discrete-Time Population Models

Stochastic Population Models

MODELS OF BIODIVERSITY

Description of the Biological Diversity

Dynamic Models of Diversity

Synthesis and Conclusion

MATHEMATICAL MODELS IN MEDICINE AND PUBLIC HEALTH

MATHEMATICAL MODELS IN EPIDEMIOLOGY

Models for Infectious Diseases

Models for Vector-Born Infections

Models for Parasite Populations

Models with Structure

MATHEMATICAL MODELS OF PUBLIC HEALTH POLICY

Posing the Question and Design of the Answer

Side Effects

Constraints of Actions

Alternative Actions

Policy Adoption and Implementation

Properties of Models

Simulations

Qualitative Models

Tailoring Models for Policy - the Intervener as Part of the System

MATHEMATICAL MODELING AND THE HUMAN GENOME

Modeling DNA

Modeling Genes

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

INTRODUCTION TO MATHEMATICAL ECONOMICS

The Origins of Mathematical Economics

Mid 20th Century

Econometrics

Mathematics Textbooks for Economists

Dynamics

Spatial Economics

Macroeconomics

Early Financial Economics

Outline of the History of Mathematics

MATHEMATICAL MODELS IN INPUT-OUTPUT ECONOMICS

The Basic Static Input-Output Model

Beyond the Basic Static Model

Major Model Extensions

Concluding Observations

ECONOMIC DYNAMICS

Introduction

Scalar Linear Equations and Their Applications to Economics

Scalar Nonlinear Equations and Their Applications to Economics

Planar Linear Equations and Their Applications to Economics

Two-dimensional Nonlinear Equations and Their Applications to Economics

Higher-Dimensional Linear Equations and Their Applications to Economics

Higher-Dimensional Nonlinear Equations And Their Applications to Economics

ECONOMETRIC METHODS

Least Squares Estimation

Maximum Likelihood

Generalized Method of Moments

Other Estimation Techniques

Time Series Models and Forecasting Techniques

Panel Data Models

Discrete and Limited Dependent Variables

GENERAL EQUILIBRIUM

Introduction

The classical model

Existence of equilibrium

Optimality properties of equilibrium

Uniqueness properties of equilibrium

Extensions of the classical model

Concluding remarks

LABOR MARKET ANALYSIS: ISSUES AND FACTS

Introduction

Rural Work Market

Urban Work Market

Recollecting Main Issues

HOUSEHOLD BEHAVIOR AND FAMILY ECONOMICS

Introduction

The Behavior of Single-Person Households

The Behavior of Multi-Person Households

Marxist and Feminist Perspectives

WELFARE THEORY: HISTORY AND MODERN RESULTS

Introduction

A Simple Walrasian General Equilibrium Model

Cost Benefit Analysis of Small Projects in General Equilibrium

The First and Second Welfare Theorem

Gains from Free Trade

Arrow’s Impossibility Theorem

Externalities

Public Goods

More on Mechanism Design

National Welfare Measures in Dynamic Economies

Final Comments and Short Summary

SOCIAL CHOICE

Introduction

Social Choice

Voting Rules

Conclusion

MATHEMATICAL MODELING IN AGRICULTURAL ECONOMICS

Simulation Models and Normative Modeling

Econometric Models and Positive Modeling

Theoretical Models

The Impact of Mathematical Models in Agricultural Economics

MODELS OF ECONOMIC GROWTH

Introduction

Stylized Facts

Exogenous Growth Models

Endogenous Growth Models

Conclusion

MATHEMATICAL MODELS OF ENVIRONMENTAL ECONOMICS

Externalities

Resources

Tragedy of the Commons – Global Warming

Uncertainty and irreversibility

Incentives

Further topics

Concluding Remarks

Bibliographical Notes

MONEY IN ECONOMIC ANALYSIS

Introduction

Money in Walrasian general equilibrium theory

Demand and supply of money in Keynesian Macroeconomics

Investment demand in Keynesian Macroeconomics

Analysis of monetary policy in an extended IS-LM model

Instability of Full Employment Equilibrium with Perfect Foresight: Paradoxical Dynamics in a Conventional Model

Concluding remarks

MODELS OF INTERNATIONAL ECONOMICS

Models of International Trade

Models of International Monetary Economics

GROWTH, DEVELOPMENT AND TECHNOLOGICAL CHANGE

Introduction

Horizontal Innovation

Vertical Innovations

R&D-based Growth with Horizontal and Vertical Differentiation

Conclusion

INNOVATION AND ECONOMIC DYNAMICS

Canonical Models

Scale Effects

Policy I: R&D Subsidies

Policy II: Patent Protection

Open Innovation

Introduction

Concluding Remarks

GROWTH AND DEVELOPMENT WITH INCOME AND WEALTH DISTRIBUTION

The Neoclassical Model of Economic Growth

Understanding Technical Progress: An Early Attempt

Technological Progress as a Conscious Economic Activity

Growth and Inequality

MATHEMATICAL MODELS OF TRANSPORTATION AND NETWORKS

Fundamental Decision-Making Concepts and Models

Models with Asymmetric Link Costs

Dynamics

A Transportation Network Efficiency Measure and the Importance of Network Components

MATHEMATICAL MODELS IN REGIONAL ECONOMICS

The Modeling Revolution in Economics

The Evolution of Models in Regional Economic Research

From Theory to Empirics

Trans-Disciplinary Advances in Regional Modeling

The Future of Regional-Economic Models

MATHEMATICAL MODELS OF RESOURCE AND ENERGY ECONOMICS

Introduction

Non-Renewable Resources

Renewable Resources

Investment in Energy-Efficiency

Conclusion

MATHEMATICAL MODELS IN SPATIAL ECONOMICS

Introduction

Market Areas and Competition in Continuous Space

The Development of Economic Models in Continuous Space

Land-Use Models

Imperfect Competition, Equilibrium and Dynamics

Remarks about Future Research