Regular Structures Lectures in Pattern Theory Volume III
Main Author: | |
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Format: | eBook |
Language: | English |
Published: |
New York, NY
Springer New York
1981, 1981
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Edition: | 1st ed. 1981 |
Series: | Applied Mathematical Sciences
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Subjects: | |
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.