This book presents an introduction to the foundations, interpretations, and data-analytic applications of symmetry studies with an emphasis on applications in optical sciences. Symmetry studies connect group theoretic and statistical methods for data summary and inference. Readers should have an understanding of calculus and linear algebra as well as introductory statistics. The book reviews finite group theory in the introductory chapters. Computational tools used in the text are available for download in the form of Mathmaticaâ notebooks or R scripts. This book:
- Demonstrates the usefulness of a unified view of algebra and symmetry studies to address data-analytic questions in optics and vision science
- Offers a brief review of finite group theory and elements of multivariate analysis
- Includes various examples from diverse areas of optical science
Table of Contents
1. Symmetry Studies
2. Algebraic Aspects
3. Dihedral Decompositions
5. Dihedral Polynomials
6. Visual Perception of Symmetry
7. Cyclic Reduction of Symbolic Sequences
8. Symmetrically Dependent Observations
9. Additional Aspects and Applications
Marlos Viana, Ph.D., served on the faculty of the University of Illinois at Chicago for nearly 30 years, where he worked in the area of applications of algebraic methods to the analysis and interpretation of data associated with symmetry conditions, with particular emphasis in linear optics, corneal topography, polarimetry, molecular chirality, decompositions of entropy, and short symbolic sequences. Professor Viana has advised, taught, and collaborated with students at all graduate and undergraduate levels in a variety of theoretical and applied fields since 1978 when he first joined the faculty of the Federal University at Rio de Janeiro, Brazil. His research also includes the development of methods for combined statistical inference, the assessment of screening tests and instrumentation, the covariance structures of dependent order statistics, and in applications of Bayesian inference. Professor Viana is a member of several editorial boards and the co-editor of Volumes 287 and 516 of the American Mathematical Society’s Contemporary Mathematics series.
Vasudevan Lakshminarayanan is a professor of vision science, physics, electrical and computer engineering, and systems design engineering at the University of Waterloo. He was a KITP Scholar at the Kavli Institute for Theoretical Physics at UC Santa Barbara, and has held research, teaching and visiting professorship positions at UC Irvine, UC Berkeley, University of Michigan, the University of Missouri, Indian Institute of Technology, Delhi, Universita degli Studii di Brescia, among others. He is a founder of the UNESCO Active Learning in Optics and Photonics program and serves on optics advisory board of the International Center for Theoretical Physics (Trieste, Italy). He is a consultant to the ophthalmic medical devices group of the US FDA (Food and Drug Administration) and is a Fellow of the APS, AAAS, OSA, SPIE, Institute of Physics (United Kingdom), Optical Society of India, among others. He has published over 300 articles in areas ranging from optical physics and engineering, image and signal processing, cognitive neuroscience, quantum physics, ophthalmology, optometry, biomedical engineering, history of science as well as science policy. He is the coauthor/coeditor of 22 books. His numerous awards include the SPIE Optics Educator award (2011) and the Esther Hoffman Beller medal of OSA (2013).