What is the "archetypal" image that comes to mind when one thinks of an infinite graph? What with a finite graph - when it is thought of as opposed to an infinite one? What structural elements are typical for either - by their presence or absence - yet provide a common ground for both? In planning the workshop on "Cycles and Rays" it had been intended from the outset to bring infinite graphs to the fore as much as possible. There never had been a graph theoretical meeting in which infinite graphs were more than "also rans", let alone one in which they were a central theme. In part, this is a matter of fashion, inasmuch as they are perceived as not readily lending themselves to applications, in part it is a matter of psychology stemming from the insecurity that many graph theorists feel in the face of set theory - on which infinite graph theory relies to a considerable extent. The result is that by and large, infinite graph theorists know what is happening in finite graphs but not conversely. Lack of knowledge about infinite graph theory can also be found in authoritative l sources. For example, a recent edition (1987) of a major mathematical encyclopaedia proposes to ". . . restrict [itself] to finite graphs, since only they give a typical theory". If anything, the reverse is true, and needless to say, the graph theoretical world knows better. One may wonder, however, by how much.

#1 New York Times Bestseller “Significant...The book is both instructive and surprisingly moving.” —The New York Times Ray Dalio, one of the world’s most successful investors and entrepreneurs, shares the unconventional principles that he’s developed, refined, and used over the past forty years to create unique results in both life and business—and which any person or organization can adopt to help achieve their goals. In 1975, Ray Dalio founded an investment firm, Bridgewater Associates, out of his two-bedroom apartment in New York City. Forty years later, Bridgewater has made more money for its clients than any other hedge fund in history and grown into the fifth most important private company in the United States, according to Fortune magazine. Dalio himself has been named to Time magazine’s list of the 100 most influential people in the world. Along the way, Dalio discovered a set of unique principles that have led to Bridgewater’s exceptionally effective culture, which he describes as “an idea meritocracy that strives to achieve meaningful work and meaningful relationships through radical transparency.” It is these principles, and not anything special about Dalio—who grew up an ordinary kid in a middle-class Long Island neighborhood—that he believes are the reason behind his success. In Principles, Dalio shares what he’s learned over the course of his remarkable career. He argues that life, management, economics, and investing can all be systemized into rules and understood like machines. The book’s hundreds of practical lessons, which are built around his cornerstones of “radical truth” and “radical transparency,” include Dalio laying out the most effective ways for individuals and organizations to make decisions, approach challenges, and build strong teams. He also describes the innovative tools the firm uses to bring an idea meritocracy to life, such as creating “baseball cards” for all employees that distill their strengths and weaknesses, and employing computerized decision-making systems to make believability-weighted decisions. While the book brims with novel ideas for organizations and institutions, Principles also offers a clear, straightforward approach to decision-making that Dalio believes anyone can apply, no matter what they’re seeking to achieve. Here, from a man who has been called both “the Steve Jobs of investing” and “the philosopher king of the financial universe” (CIO magazine), is a rare opportunity to gain proven advice unlike anything you’ll find in the conventional business press.

A NEW YORK TIMES, WALL STREET JOURNAL, AND USA TODAY BESTSELLER The legendary investor shows how to identify and master the cycles that govern the markets. We all know markets rise and fall, but when should you pull out, and when should you stay in? The answer is never black or white, but is best reached through a keen understanding of the reasons behind the rhythm of cycles. Confidence about where we are in a cycle comes when you learn the patterns of ups and downs that influence not just economics, markets, and companies, but also human psychology and the investing behaviors that result. If you study past cycles, understand their origins and remain alert for the next one, you will become keenly attuned to the investment environment as it changes. You’ll be aware and prepared while others get blindsided by unexpected events or fall victim to emotions like fear and greed. By following Marks’s insights—drawn in part from his iconic memos over the years to Oaktree’s clients—you can master these recurring patterns to have the opportunity to improve your results.