ENCYCLOPEDIA OF MATHEMATICAL SCIENCES - Table of Contents

MATHEMATICS: CONCEPTS AND FOUNDATIONS

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

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

FUNCTIONAL ANALYSIS AND FUNCTION SPACES

Function Spaces and Some Examples

Basic Concepts in Functional Analysis

Some Advanced Concepts in Functional Analysis

Miscellaneous Function Spaces

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

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

MODEL THEORY

Classical Model Theory

Models of Tame Theories

Beyond First Order Logic

Model Theory for Mathematical Structures

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

COMPUTABILITY AND COMPLEXITY

Recursive and Recursively Enumerable Sets

Unsolvable Problems

Hilbert’s 10th Problem

Classifying Unsolvable Problems.

Complexity

SET THEORY

Some Elementary Tools

Constructible Sets

Forcing

Descriptive Set Theory

Other Topics

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

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 MATHEMATICALS 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

LINEAR DIFFERENTIAL EQUATIONS

Linearity and Continuity

Examples

Methods

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

GRAPH THEORY

Degrees and Distances

Connectivity

Operations

Trees

Factor Theory

Eulerian Circuits and Hamiltonian Cycles

Coloring

Planar Graph

COMBINATORICS

Selected Topics in Combinatorics

Introduction

COMPUTATIONAL COMPLEXITY

Machine Models and Complexity Measures

Complexity Classes

Fundamental Results and Questions

Selected Topics

OPTIMIZATION

Integer Programming

Enumerative Algorithms for Integer Programming

Solvable Cases of Integer Programming

Approximation Algorithms

Metaheuristics

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

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

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

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

ERGODIC PROPERTIES OF STATIONARY, MARKOV, AND REGENERATIVE PROCESSES

Ergodic Theory for Stationary Processes

Ergodic Properties of Markov Processes

Regenerative Processes

Applications of Ergodic Theorems

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

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

INSURANCE MATHEMATICS

Non-life Insurance

Life Insurance

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

INVENTORIES, WATER STORAGE AND QUEUES

Inventory Models

Models for Water Storage

The Queueing System GI /G /S

Queueing Networks

INFORMATION THEORY AND COMMUNICATION

Information source

Source coding

Measures of information

Transmission channel

The practice of classical telecommunication

Mobile communication

Cryptology

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

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

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

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

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

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

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 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

MATHEMATICAL MODELS FOR PREDICTION OF CLIMATE

Mathematics for climate modeling

Climatic models

Predictability of climate changes

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

ENVIRONMENTAL POLLUTION AND DEGRADATION MODELS

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

Numerical results

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

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

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

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

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

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

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

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

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

THE ROLE OF MODELING

Modeling as a Mental Activity

Mathematical Modeling

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

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

DISCRETE OPTIMIZATION

Modeling

Solution Methods

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

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

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

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?

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

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

BOURBAKI, AN EPIPHENOMENON IN THE HISTORY OF MATHEMATICS

Introduction

The Origins

The Impact

The Elaboration of the Volumes Constituting the Treatise

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

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

EolssLogn/mss/C02/E6-04/E6-04-03/E6-04-03-01/E6-04-03-01-TXT-09.aspx#9._ 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.

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

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

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

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

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

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

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

RANK TESTS FOR INDEPENDENCE AND RANDOMNESS

Introduction

Rank Tests for Independence

Tests for Randomness against Trend

Contingency Tables

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.

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 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 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

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

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

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

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