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 thought rests. bankruptcy
3 is dedicated to the algebraic research of regularity whereas
Chapter five comprises new ends up in metric trend concept.
Some short feedback on topological photo algebras are available
in bankruptcy four.
Two chapters care for development synthesis: bankruptcy 6 on
scientific speculation formation and bankruptcy 7 on social
domination constructions. In bankruptcy eight we learn taxonomic pat-
terns, either their synthesis and research, whereas within the final
chapter we examine a trend processor for doing semantic
TABLE OF CONTENTS
INTRODUCTION . . . . .
CHAPTER I. styles: FROM CHAOS to reserve
The look for regularity
Some common buildings . . .
The mathematical examine of regularity.
CHAPTE R 2. A development FORMALISM.
2.1. the main of atomism.
2.2. The combinatory precept
2.3. the primary of observabi1ity.
2.4. the main of realism.
CHAPTER three. ALGEBRA of standard buildings,
Generator coordinates . . .
Configuration coordinates .
Connectors. . . . . . . . .
Configuration different types. .
Set operations in 5f(9i'). .
Operations on pictures. . . . . . . . . . .
Homomorphisms for given international regularity
Representations by means of picture isomorphisms
CHAPTER four, a few TOPOLOGY OF snapshot ALGEBRAS.
A topology for configurations
A topology for photographs . .
Some examples . . . . . .
CHAPTER five. METRIC trend concept.
Regularity managed chances
Conditioning via regularity. . . . .
Frozen styles: finite G and n . . .
Frozen styles: endless G and finite n.
Quadratic power functionality . . . . . .
Frozen styles: endless G and n. .
Asymptotically minimal power . . . . . .
Asymptotics for giant 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 huge numbers in development concept . . .
Random dynamics for configurations. . . . . .
CHAPTER 6. styles OF medical HYPOTHESES.
Hypotheses as typical 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 common sense 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 common buildings.
Two distinct picture algebras.
The number of language kind for the research
Semantic maps . . . .
Special semantic maps
Learning semantics. .
Abduction of semantic maps.
INDEX. . . .