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Dihedral Fourier Analysis

Data-analytic Aspects and Applications

  • Marlos A. G. Viana
  • Vasudevan Lakshminarayanan

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Marlos A. G. Viana, Vasudevan Lakshminarayanan
    Pages 1-9
  3. Marlos A. G. Viana, Vasudevan Lakshminarayanan
    Pages 11-40
  4. Marlos A. G. Viana, Vasudevan Lakshminarayanan
    Pages 41-58
  5. Marlos A. G. Viana, Vasudevan Lakshminarayanan
    Pages 59-76
  6. Marlos A. G. Viana, Vasudevan Lakshminarayanan
    Pages 77-85
  7. Marlos A. G. Viana, Vasudevan Lakshminarayanan
    Pages 87-112
  8. Back Matter
    Pages 113-118

About this book

Introduction

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 statistics.

Keywords

Analysis Data Dihedral Fourier Analysis Orbit Display Refraction Data

Authors and affiliations

  • Marlos A. G. Viana
    • 1
  • Vasudevan Lakshminarayanan
    • 2
  1. 1.Chicago Eye CenterUniversity of Illinois, ChicagoChicagoUSA
  2. 2.School of OptometryUniversity of WaterlooWaterlooCanada

Bibliographic information