Lecture Notes in Statistics

Dihedral Fourier Analysis

Data-analytic Aspects and Applications

Authors: Viana, Marlos A. G., Lakshminarayanan, Vasudevan

  • Theory and applications of dihedral analysis presented in easy to read lecture notes
  • Color images, practice problems, data sets and examples appear throughout
  • Contains information useful for researchers and students
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About this book

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.

Reviews

From the book reviews:

“The book under review is aimed to describe a series of techniques in which experimental data is indexed by, or associated with, symmetry transformations such as rotations or reversals. … The book is enriched with various colored illustrations and numerical examples. It is intended for data analysts interested in both theoretical and applicative aspects.” (Dan Emanuel Popovici, Mathematical Reviews, May, 2014)

“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. … These lecture notes are very well written in a pedagogical and smooth way. We recommend them to graduate students and researchers in dihedral analysis and related areas.” (George Stoica, Zentralblatt MATH, Vol. 1257, 2013)

Table of contents (6 chapters)

  • Symmetry and Experimental Data

    Viana, Marlos A. G. (et al.)

    Pages 1-9

  • Algebraic and Data-Analytic Aspects

    Viana, Marlos A. G. (et al.)

    Pages 11-40

  • Curvature and Refraction Data

    Viana, Marlos A. G. (et al.)

    Pages 41-58

  • Symbolic Sequences

    Viana, Marlos A. G. (et al.)

    Pages 59-76

  • Symmetry Preference and Perception

    Viana, Marlos A. G. (et al.)

    Pages 77-85

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-1-4614-5562-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $129.00
price for USA
  • ISBN 978-1-4614-5561-5
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Dihedral Fourier Analysis
Book Subtitle
Data-analytic Aspects and Applications
Authors
Series Title
Lecture Notes in Statistics
Series Volume
1026
Copyright
2013
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4614-5562-2
DOI
10.1007/978-1-4614-5562-2
Softcover ISBN
978-1-4614-5561-5
Series ISSN
0930-0325
Edition Number
1
Number of Pages
XVI, 118
Number of Illustrations and Tables
2 b/w illustrations, 46 illustrations in colour
Topics