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"This book synthesizes current methods used to quantify functional diversity, providing step-by-step examples for defining functional groups and estimating functional indices. The authors show how to compare communities, and how to analyze changes of diversity along environmental gradients, using real-life examples throughout. One section of the book demonstrates the selection of traits, and the standardization and characterization of ecosystem data. Another section presents methods used to quantify functional diversity, shows how to relate functional diversity with environmental variables and how to connect these to ecosystem services. The concluding section introduces FDiversity, a free program developed by the authors. The reader is guided through every step from software installation and basic functions, to sample and database design, to graphical projection methods, employing case study data to illustrate key concepts."

"In this paper a K-theoretic classification is given of the simple real rank zero C*-algebras that can be expressed as inductive limits of sequences of finite direct sums of matrix algebras over finite connected graphs (possibly with dimension drop). This class of C*-algebras provides torsion K1. The special case that the graphs are intervals is due to Elliott. "