Why Is The Edge Called The Edge

Edge-Based Clausal Syntax

An argument that there are three kinds of English grammatical objects, each with different syntactic properties. In Edge-Based Clausal Syntax, Paul Postal rejects the notion that an English phrase of the form [V + DP] invariably involves a grammatical relation properly characterized as a direct object. He argues instead that at least three distinct relations occur in such a structure. The different syntactic properties of these three kinds of objects are shown by how they behave in passives, middles, -able forms, tough movement, wh-movement, Heavy NP Shift, Ride Node Raising, re-prefixation, and many other tests. This proposal renders Postal's position sharply different from that of Chomsky, who defined a direct object structurally as [NP, VP], and with the traditional linguistics text's definition of the direct object as the DP sister of V. According to Postal's framework, sentence structures are complex graph structures built on nodes (vertices) and edges (arcs). The node that heads a particular edge represents a constituent that bears the grammatical relation named by the edge label to its tail node. This approach allows two DPs that have very different grammatical properties to occupy what looks like identical structural positions. The contrasting behaviors of direct objects, which at first seem anomalous—even grammatically chaotic—emerge in Postal's account as nonanomalous, as symptoms of hitherto ungrasped structural regularity.

Graph and Network Theory

This textbook covers a diversity of topics in graph and network theory, both from a theoretical standpoint, and from an applied modelling point of view. Mathematica® is used to demonstrate much of the modelling aspects. Graph theory and model building tools are developed in tandem with effective techniques for solving practical problems via computer implementation. The book is designed with three primary readerships in mind. Individual syllabi or suggested sequences for study are provided for each of three student audiences: mathematics, applied mathematics/operations research, and computer science. In addition to the visual appeal of each page, the text contains an abundance of gems. Most chapters open with real-life problem descriptions which serve as motivation for the theoretical development of the subject matter. Each chapter concludes with three different sets of exercises. The first set of exercises are standard and geared toward the more mathematically inclined reader. Many of these are routine exercises, designed to test understanding of the material in the text, but some are more challenging. The second set of exercises is earmarked for the computer technologically savvy reader and offer computer exercises using Mathematica. The final set consists of larger projects aimed at equipping those readers with backgrounds in the applied sciences to apply the necessary skills learned in the chapter in the context of real-world problem solving. Additionally, each chapter offers biographical notes as well as pictures of graph theorists and mathematicians who have contributed significantly to the development of the results documented in the chapter. These notes are meant to bring the topics covered to life, allowing the reader to associate faces with some of the important discoveries and results presented. In total, approximately 100 biographical notes are presented throughout the book. The material in this book has been organized into three distinct parts, each with a different focus. The first part is devoted to topics in network optimization, with a focus on basic notions in algorithmic complexity and the computation of optimal paths, shortest spanning trees, maximum flows and minimum-cost flows in networks, as well as the solution of network location problems. The second part is devoted to a variety of classical problems in graph theory, including problems related to matchings, edge and vertex traversal, connectivity, planarity, edge and vertex coloring, and orientations of graphs. Finally, the focus in the third part is on modern areas of study in graph theory, covering graph domination, Ramsey theory, extremal graph theory, graph enumeration, and application of the probabilistic method.

Edge Corporation Branching, Foreign Bank Takeovers, and International Banking Facilities