Schlagwort(e):
Electronic books.
Beschreibung / Inhaltsverzeichnis:
This book presents an introduction to the foundations, interpretations, and data-analytic applications of symmetry studies with an emphasis on applications in optical sciences. Symmetry studies connect group theoretic and statistical methods for data summary and inference.
Materialart:
Online-Ressource
Seiten:
1 online resource (209 pages)
Ausgabe:
1st ed.
ISBN:
9781466583986
Serie:
Multidisciplinary and Applied Optics Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5986935
DDC:
535
Sprache:
Englisch
Anmerkung:
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Dedication -- Contents -- Preface -- Authors -- Chapter 1: Symmetry Studies -- 1.1. Introduction -- 1.2. Bilateral Quantities -- 1.3. Sampling -- 1.4. Joint Bilateral Quantities -- 1.5. Covariance Structures -- 1.6. Visual Fields -- 1.7. Snellen Charts -- 1.8. Nystagmus -- 1.9. Corneal Curvature -- 1.10. Refraction -- 1.11. Extreme Values -- 1.12. Summary -- Chapter 2: Algebraic Aspects -- 2.1. Introduction -- 2.2. Main Definitions -- 2.3. Group Representations -- 2.4. Canonical Projections -- 2.5. Fourier Transforms -- 2.6. Additional Aspects -- 2.7. Summary -- Chapter 3: Dihedral Decompositions -- 3.1. Introduction -- 3.2. The Stokes Coefficients -- 3.3. The Group Algebra of Compensators -- 3.4. Elementary Optical Instruments -- 3.5. Coherence Matrix Formalism -- 3.6. Data-Analytic Considerations -- 3.7. Summary -- Chapter 4: Refraction -- 4.1. Introduction -- 4.2. Algebraic Descriptions -- 4.3. Finite Approximations -- 4.4. Conformal Analysis -- 4.5. The Refraction Study -- 4.6. Summary -- Chapter 5: Dihedral Polynomials -- 5.1. Introduction -- 5.2. Dihedral Polynomials -- 5.3. Between-Class Relations -- 5.4. Applications -- 5.5. Summary -- Chapter 6: Visual Perception of Symmetry -- 6.1. Introduction -- 6.2. A Symmetry Perception Experiment -- 6.3. The Elementary Orbits -- 6.4. Entropy Invariants -- 6.5. Product Orbit -- 6.6. Summary -- Chapter 7: Cyclic Reduction of Symbolic Sequences -- 7.1. Introduction -- 7.2. Symbolic Sequences -- 7.3. Injective Sequences -- 7.4. Scalar Quantifications -- 7.5. Orbit Invariance -- 7.6. Invariant Reductions -- 7.7. Entropy Invariants -- 7.8. Dihedral Fourier Analysis -- 7.9. Summary -- Chapter 8: Symmetrically Dependent Observations -- 8.1. Introduction -- 8.2. Models and Assumptions -- 8.3. The Joint Covariance Structure.
,
8.4. Maximum Likelihood and Large-Sample Estimates -- 8.5. Visual Acuity Data Applications -- 8.6. Block-Equicorrelated Observations -- 8.7. Intraocular Pressure Data Applications -- 8.8. Linearizations of Ordered Symmetric Observations -- 8.9. Concomitants of Order Statistics -- 8.10. Bilateral Hemispherical Data Applications -- 8.11. Summary -- Chapter 9: Additional Aspects and Applications -- 9.1. Chromatic-Spatial Decompositions -- 9.2. Dihedral Summaries of Visual Field Data -- 9.3. Actions on Mappings -- 9.4. Local and Global Symmetries -- 9.5. Entropy and Symmetry -- 9.6. Matrix and Transformation Groups -- Appendix -- Bibliography -- Index.
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