Dihedral Fourier analysis : data-analytic aspects and applications
QA403.5 .V53 2013
- Unknown QA403.5 .V53 2013
- Lakshminarayanan, Vasudevan.
- Includes bibliographical references and index.
- Symmetry and experimental data. Introduction ; The flag ranking data ; The orbit invariants as Fourier transforms ; The algebraic framework ; Inference ; Problems ; Appendix A : the flag preference data
- Algebraic and data-analytic aspects. Introduction ; The dihedral groups ; Dn conjugacy orbits ; Dihedral sets and modules ; Class functions ; Dihedral projections ; Fourier bases ; The center of CDn ; Group rings ; Multivariate normal data ; Selected dihedral bases ; Log-transformed multinomial data ; Additional remarks ; Problems
- Curvature and refraction data. Introduction ; Dihedral analysis of optical power; The spectral decomposition ; Dihedral analysis of wavefront aberration polynomials ; Dihedral spatial filters ; The algebraic structure of dioptric power matrices ; Problems
- Symbolic sequences. Introduction ; The dihedral orbit display ; A center of mass display ; Invariant displays ; A class of D4 orbit invariants ; Entropy displays ; Problems ; Appendix A : selected computational tools
- Symmetry preference and perception. Introduction ; The D2 orbit structure in S4 ; The dihedral D2 summaries ; The dihedral D3 summaries ; Problems
- Other applications. Normal modes ; Center of mass displacements ; Polarization states ; Decompositions of entropy ; Elementary algebraic surfaces ; Problems
- Publisher's Summary
- Dihedral Fourier Analysis introduces the theory and applications necessary to study experimental data indexed by, or associated with, the points in a dihedral symmetry orbit. This book looks at experimental data and analytical models indexed by certain dihedral rotations and reversals realized as vector fields. Its particular relevance as a research tool in areas such as optical and molecular biology statistics appears when formulated within the context of symmetry studies, which formally connects algebraic and statistical reasoning together in one methodology for data summary and inference. Chapter 1 presents an overview of the theory and methods of dihedral analysis. It introduces data sets and examples defining and connecting the algebraic notions of symmetry with those of statistical summaries and inference. Chapter 2 includes the required algebraic aspects and data-analytic results. Chapters 3-6 offer applications of the methods presented in the text. This book is intended for data analysts of both theoretical and applied interests.
(source: Nielsen Book Data)
- Publication date
- Marlos A.G. Viana, Vasudevan Lakshminarayanan.
- Lecture notes in statistics ; 206