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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.
List of contents
Symmetry and Experimental Data.- Algebraic and Data-Analytic Aspects.- Curvature and Refraction Data.- Symbolic Sequences.- Symmetry Preference and Perception.- Other Applications.- Glossary.- Index.
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.
Additional text
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)
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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)
