02073 a2200181 4500008004500000020001500045020001800060082001600078100002400094245008900118260004800207300001400255440007000269504044600339520099700785650004601782856006301828151104b2010 xxu||||| |||| 00| 0 eng d a0511755473 a9780511755477 a519.5bV4S9 aViana, Marlos A.G. aSymmetry studies: an introduction to the analysis of structured data in applications aCambridgebCambridge University Pressc2010 ax, 235 p. aCambridge Series in Statistical and Probabilistic Mathematics; 26 aTable of contents:
1 - Symmetry, Classification, and the Analysis of Structured Data
2 - Sorting the Labels: Group 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
aExperimental 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 many different data-analysis applications of symmetry.
aStatistical and probabilistic mathematics 3http://ebooks.cambridge.org/ebook.jsf?bid=CBO9780511755477