By Ulf Grenander (auth.)

This can be the 3rd and ultimate quantity of the Lectures in

Pattern thought. Its first chapters describe the 5cience-

theoretic rules on which trend idea rests. bankruptcy

3 is dedicated to the algebraic research of regularity whereas

Chapter five includes new leads to metric development conception.

Some short comments on topological snapshot algebras are available

in bankruptcy four.

Two chapters care for development synthesis: bankruptcy 6 on

scientific speculation formation and bankruptcy 7 on social

domination buildings. In bankruptcy eight we research taxonomic pat-

terns, either their synthesis and research, whereas within the final

chapter we examine a trend processor for doing semantic

abduction.

TABLE OF CONTENTS

INTRODUCTION . . . . .

CHAPTER I. styles: FROM CHAOS to reserve

The look for regularity

Some general constructions . . .

The mathematical learn of regularity.

CHAPTE R 2. A trend FORMALISM.

2.1. the main of atomism.

2.2. The combinatory precept

2.3. the primary of observabi1ity.

2.4. the primary of realism.

CHAPTER three. ALGEBRA of normal constructions,

Generator coordinates . . .

Configuration coordinates .

Connectors. . . . . . . . .

Configuration homomorphisms

Configuration different types. .

Set operations in 5f(9i'). .

Operations on pictures. . . . . . . . . . .

Homomorphisms for given international regularity

Representations by way of photograph isomorphisms

CHAPTER four, a few TOPOLOGY OF picture ALGEBRAS.

A topology for configurations

A topology for photos . .

Some examples . . . . . .

CHAPTER five. METRIC trend conception.

Regularity managed possibilities

Conditioning via regularity. . . . .

Frozen styles: finite G and n . . .

Frozen styles: countless G and finite n.

Quadratic power functionality . . . . . .

Frozen styles: countless G and n. .

Asymptotically minimal strength . . . . . .

Asymptotics for big configurations. . .

Spectral density matrix for E = LINEAR(y) . .

Factorization of the spectral density matrix.

Representation of the random configurations .

Spectral density matrix for E = LATTICE(y). .

Factorization of the spectral density matrix

in dimensions . . . . . . . . . . . . .

Representations of the random configurations

in the 2 dimensional case . . . . .

Laws of enormous numbers in trend thought . . .

Random dynamics for configurations. . . . . .

CHAPTER 6. styles OF clinical HYPOTHESES.

Hypotheses as commonplace constructions. . .

Patterns of statistical hypotheses. .

Generators for statistical hypotheses

Examples of configurations. .

Hypotheses as pictures. . . . . .

Image algebras of hypotheses. .

Conclusions . . . . . . . . . .

CHAPTER 7. SYNTHESIS OF SOCIAL styles OF DOMINATION 353

Patterns in mathematical sociology.

Domination regularity . . , . . .

Configuration dynamics. . . . . .

System in equilibrium . . , . . .

Large configurations - simulation effects

Large configurations - analytical effects

Further difficulties and extensions

Appendix. . . . . . .

CHAPTER eight. TAXONOMIC styles. . . . .

A good judgment for taxonomic styles. . . .

Logic of taxonomic affinity styles. . .

Synthesis of taxonomic affinity styles.

Analysis of affinity styles . . . .

CHAPTER nine. styles IN MATHEMATICAL SEMANTICS

Introduction. . . . . . . . . . . . .

Introducing mathematical semantics. . . .

Formalization via commonplace buildings.

Two detailed snapshot algebras.

The selection of language variety for the research

Semantic maps . . . .

Special semantic maps

Learning semantics. .

Abduction of semantic maps.

OUTLOOK.

APPENDIX

NOTES. .

BIBLIOGRAPHY

INDEX. . . .