This book focuses on linear time eigenvalue location algorithms for graphs. This subject relates to spectral graph theory, a field that combines tools and concepts of linear algebra and combinatorics, with applications ranging from image processing and data analysis to molecular descriptors and random walks. It has attracted a lot of attention and has since emerged as an area on its own. Studies in spectral graph theory seek to determine properties of a graph through matrices associated with it. It turns out that eigenvalues and eigenvectors have surprisingly many connections with the structure of a graph. This book approaches this subject under the perspective of eigenvalue location algorithms. These are algorithms that, given a symmetric graph matrix M and a real interval I, return the number of eigenvalues of M that lie in I. Since the algorithms described here are typically very fast, they allow one to quickly approximate the value of any eigenvalue, which is a basic step in most applications of spectral graph theory. Moreover, these algorithms are convenient theoretical tools for proving bounds on eigenvalues and their multiplicities, which was quite useful to solve longstanding open problems in the area. This book brings these algorithms together, revealing how similar they are in spirit, and presents some of their main applications. This work can be of special interest to graduate students and researchers in spectral graph theory, and to any mathematician who wishes to know more about eigenvalues associated with graphs. It can also serve as a compact textbook for short courses on the topic.

Nathaniel J. Cauliflower's distinguished afterlife role as Musing Department caretaker is thrust into detrimental jeopardy when a single inspiration is neglected and absconded by one of his muses, Jonas Rothchild. With the very nature of time fracturing apart, Nathaniel enlists the help of the division's nine greatest modern day muses to assist in its provisional repair. Among these encouraging leaders is previous antisocial motivator Annette Slocum. Much to Nathaniel's chagrin, Annette's presence in the office stirs a ferocious unraveling of his secret backstory. His unfolding is an epic tale of deceit and murder that sweeps from 19th century Paris to modern day, giving rise to an underlying malevolent agenda atop an expansive field of dandelions where three fateful, interweaving fortune-telling Sisters reside. When it is discovered that Jonas is stealing other inspirations, with the anonymous assistance from one of the department's own, Nathaniel's unsettling past vicariously forces him into the spotlight as the prime suspect. With time splintering further, Nathaniel must clear his name by taking ownership of his previous, darkest, soul-shattering affairs and fight to reclaim the hereafter agency that he, for so many centuries, has devotedly sought to protect.

Annette Slocum's tragically boring unfulfilled life truly begins when she is struck by a Cadillac in front of her local library. In the afterlife Annette is indoctrinated as a modern day muse. Annette travels backwards and forwards through time, by use of a Hasbro Lite-Brite, providing catalysts of inspiration to the living. Unfortunately for Annette, one single misstep in the proceedings could cause a chain reaction that might decimate the already fragile tapestry of the Universe. Severely antisocial, Annette must now commune with the world that terrifies her. She must overcome her own inner demons and personal insecurities if she is to effectively inspire. It doesn't help matters when Annette's childhood foe, now adult adversary, Jonas Rothchild, resurfaces in the life of her favorite client. Jonas' past involvement in tormenting her escalates to dangerous levels, forcing Annette to find the bravery to stand up to her infamous villain once and for all. Rhapsody is a novel about the living and the muses who inspire them, treacherous violet envelopes, the insurmountable search for strength and the enthralling quest to uncover the secrets of an elusive stranger named Nathaniel J. Cauliflower who holds the key to the entire operation.