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＜電子ブック＞
Regular Structures : Lectures in Pattern Theory Volume III / by U. Grenander
(Applied Mathematical Sciences. ISSN:2196968X ; 33)

版	1st ed. 1981.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1981
本文言語	英語
大きさ	VIII, 570 p : online resource
冊子体	Regular structures / Ulf Grenander
著者標目	*Grenander, U author SpringerLink (Online service)
件　名	LCSH:Discrete mathematics FREE:Discrete Mathematics
一般注記	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. -- 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-5905-3

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