Mathematics and Statistics

This book integrates the fundamentals of asymmetric multidimensional scaling, spectral graph theory, graph embedding theory, and various dynamical systems theories, that deal with the static and dynamic aspects of asymmetric phenomena.  In this way, it provides a comprehensive introduction to theories and methods for analyzing phenomena observed universally in social, behavioral, economical, geographical, biological, neural, chemical reaction and other networks.  The topics addressed in here include the notions of asymmetric similarity matrices, graph spectra, dimension reduction, and difference and differential equations to describe the dynamics of networks, bifurcation of vector fields, Mandelbrot sets, fractals and chaos, and Hilbert spaces.  Illustrated by carefully chosen examples and supported by extensive simulation studies, the book is highly recommended to readers who seek to discover static asymmetric structures among members or nodes.  It also appeals to those who want to understand the kinds of dynamics that are theoretically possible in their research domains.