Dihedral Fourier Analysis: Data-analytic Aspects and Applications

✍ Scribed by Marlos A. G. Viana, Vasudevan Lakshminarayanan (auth.)

• Publisher: Springer-Verlag New York
• Year: 2013
• Tongue: English
• Leaves: 131
• Series: 1026
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xvi
Symmetry and Experimental Data....Pages 1-9
Algebraic and Data-Analytic Aspects....Pages 11-40
Curvature and Refraction Data....Pages 41-58
Symbolic Sequences....Pages 59-76
Symmetry Preference and Perception....Pages 77-85
Other Applications....Pages 87-112
Back Matter....Pages 113-118

✦ Subjects

Statistical Theory and Methods; Statistics, general