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Regular Structures Lectures in Pattern Theory Volume III

Bibliographic Details
Main Author: Grenander, U.
Format: eBook
Language:English
Published: New York, NY Springer New York 1981, 1981
Edition:1st ed. 1981
Series:Applied Mathematical Sciences
Subjects:
Discrete Mathematics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 5.5. Quadratic energy function
  • 5.6. Frozen patterns: infinite G and n
  • 5.7. Asymptotically minimum energy
  • 5.8. Asymptotics for large configurations
  • 5.9. Spectral density matrix for ? = LINEAR(?)
  • 5.10. Factorization of the spectral density matrix
  • 5.11. Representation of the random configurations
  • 5.12. Spectral density matrix for ? = LATTICE(?)
  • 5.13. Factorization of the spectral density matrix in two dimensions
  • 5.14. Representations of the random configurations in the two dimensional case
  • 5.15. Laws of large numbers in pattern theory
  • 5.16. Random dynamics for configurations
  • 6. Patterns of Scientific Hypotheses
  • 6.1. Hypotheses as regular structures
  • 6.2. Patterns of statistical hypotheses
  • 6.3. Generators for statistical hypotheses
  • 6.4. Examples of configurations
  • 6.5. Hypotheses as images
  • 6.6. Imagealgebras of hypotheses
  • 6.7. Conclusions
  • 7. Synthesis of Social Patterns of Domination
  • 7.1. Patterns in mathematical sociology
  • 7.2. Domination regularity
  • 7.3. Configuration dynamics
  • 7.4. System in equilibrium
  • 7.5. Large configurations — simulation results
  • 7.6. Large configurations — analytical result
  • 7.7. Further problems and extensions
  • 7.8. Appendix
  • 8. Taxonomic Patterns
  • 8.1. A logic for taxonomic patterns
  • 8.2. Logic of taxonomic affinity patterns
  • 8.3. Synthesis of taxonomic affinity patterns
  • 8.4. Analysis of affinity patterns
  • 9. Patterns in Mathematical Semantics
  • 9.1. Introduction
  • 9.2. Introducing mathematical semantics
  • 9.3. Formalization through regular structures
  • 9.4. Two special image algebras
  • 9.5. The choice of language type for the study
  • 9.6. Semantic maps
  • 9.7. Special semantic maps
  • 9.8. Learning semantics
  • 9.9. Abduction of semantic maps
  • Outlook
  • Notes
  • 1. Patterns: From Chaos to Order
  • 1.1. The search for regularity
  • 1.2. Some regular structures
  • 1.3. The mathematical study of regularity
  • 2. A Pattern Formalism
  • 2.1. The principle of atomism
  • 2.2. The combinatory principle
  • 2.3. The principle of observability
  • 2.4. The principle of realism
  • 3. Algebra of Regular Structures
  • 3.1. Generator coordinates
  • 3.2. Configuration coordinates
  • 3.3. Connectors
  • 3.4. Configuration homomorphisms
  • 3.5. Configuration categories
  • 3.6. Set operations in C (R)
  • 3.7. Operations on images
  • 3.8. Homomorphisms for given global regularity
  • 3.9. Representations by image isomorphisms
  • 4. Some Topology of Image Algebras
  • 4.1. A topology for configurations
  • 4.2. A topology for images
  • 4.3. Some examples
  • 5. Metric Pattern Theory
  • 5.1. Regularity controlled probabilities
  • 5.2. Conditioning by regularity
  • 5.3. Frozen patterns: finite G and n
  • 5.4. Frozen patterns: infinite G and finite n.

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