Symmetry Studies
An Introduction to the Analysis of Structured Data in Applications

Combines algebra and statistics to explore the interplay between symmetry-related research questions and their statistical analysis.

Marlos A. G. Viana (Author)

9780521841030, Cambridge University Press

Hardback, published 9 June 2008

248 pages, 25 b/w illus. 146 tables 96 exercises
26 x 18 x 2 cm, 0.61 kg

"... useful for introducing these algebraic methods as tools in applied mathematics and statistics to relatively inexperienced students."
Seth Sullivant, Mathematical Reviews

Experimental data can often be associated with or indexed by certain symmetrically interesting structures or sets of labels that appear, for example, in the study of short symbolic sequences in molecular biology, in preference or voting data, in (corneal) curvature data, and in studies of the handedness and entropy of symbolic sequences and elementary images. The symmetry studies introduced in this book describe the interplay among symmetry transformations that are characteristic of these sets of labels, their resulting classification, the algebraic decomposition of the data indexed by them, and the statistical analysis of the invariants induced by those decompositions. The overall purpose is to facilitate and guide the statistical study of the structured data from both a descriptive and inferential perspective. The text combines notions of algebra and statistics and develops a systematic methodology to better explore the interplay between symmetry-related research questions and their statistical analysis.

1. Symmetry, classification and the analysis of structured data, 2. Sorting the labels: groups actions and orbits, 3. Connecting symmetries and data: linear representations, 4. Data reduction and inference: the canonical projections and their invariants, 5. Examples and techniques, 6. Symmetry studies of short symbolic sequences, 7. Symmetry studies of curvature data, 8. Symmetry studies of planar chirality.

Subject Areas: Probability & statistics [PBT], Algebra [PBF]