Trains pull into a railroad station and must wait for each other before leaving again in order to let passengers change trains. How do mathematicians then calculate a railroad timetable that accurately reflects their comings and goings? One approach is to use max-plus algebra, a framework used to model Discrete Event Systems, which are well suited to describe the ordering and timing of events. This is the first textbook on max-plus algebra, providing a concise and self-contained introduction to the topic. Applications of max-plus algebra abound in the world around us. Traffic systems, computer communication systems, production lines, and flows in networks are all based on discrete even systems, and thus can be conveniently described and analyzed by means of max-plus algebra. The book consists of an introduction and thirteen chapters in three parts. Part One explores the introduction of max-plus algebra and of system descriptions based upon it. Part Two deals with a real application, namely the design of timetables for railway networks. Part Three examines various extensions, such as stochastic systems and min-max-plus systems. The text is suitable for last-year undergraduates in mathematics, and each chapter provides exercises, notes, and a reference section.

#1 NEW YORK TIMES BESTSELLER • ONE OF TIME MAGAZINE’S 100 BEST YA BOOKS OF ALL TIME The extraordinary, beloved novel about the ability of books to feed the soul even in the darkest of times. When Death has a story to tell, you listen. It is 1939. Nazi Germany. The country is holding its breath. Death has never been busier, and will become busier still. Liesel Meminger is a foster girl living outside of Munich, who scratches out a meager existence for herself by stealing when she encounters something she can’t resist–books. With the help of her accordion-playing foster father, she learns to read and shares her stolen books with her neighbors during bombing raids as well as with the Jewish man hidden in her basement. In superbly crafted writing that burns with intensity, award-winning author Markus Zusak, author of I Am the Messenger, has given us one of the most enduring stories of our time. “The kind of book that can be life-changing.” —The New York Times “Deserves a place on the same shelf with The Diary of a Young Girl by Anne Frank.” —USA Today DON’T MISS BRIDGE OF CLAY, MARKUS ZUSAK’S FIRST NOVEL SINCE THE BOOK THIEF.

Recent years have seen a significant rise of interest in max-linear theory and techniques. Specialised international conferences and seminars or special sessions devoted to max-algebra have been organised. This book aims to provide a first detailed and self-contained account of linear-algebraic aspects of max-algebra for general (that is both irreducible and reducible) matrices. Among the main features of the book is the presentation of the fundamental max-algebraic theory (Chapters 1-4), often scattered in research articles, reports and theses, in one place in a comprehensive and unified form. This presentation is made with all proofs and in full generality (that is for both irreducible and reducible matrices). Another feature is the presence of advanced material (Chapters 5-10), most of which has not appeared in a book before and in many cases has not been published at all. Intended for a wide-ranging readership, this book will be useful for anyone with basic mathematical knowledge (including undergraduate students) who wish to learn fundamental max-algebraic ideas and techniques. It will also be useful for researchers working in tropical geometry or idempotent analysis.

Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.

A number of different problems of interest to the operational researcher and the mathematical economist - for example, certain problems of optimization on graphs and networks, of machine-scheduling, of convex analysis and of approx imation theory - can be formulated in a convenient way using the algebraic structure (R,$,@) where we may think of R as the (extended) real-number system with the binary combining operations x$y, x®y defined to be max(x,y),(x+y) respectively. The use of this algebraic structure gives these problems the character of problems of linear algebra, or linear operator theory. This fact hB.s been independently discovered by a number of people working in various fields and in different notations, and the starting-point for the present Lecture Notes was the writer's persuasion that the time had arrived to present a unified account of the algebra of linear transformations of spaces of n-tuples over (R,$,®),to demonstrate its relevance to operational research and to give solutions to the standard linear-algebraic problems which arise - e.g. the solution of linear equations exactly or approximately, the eigenvector eigenvalue problem andso on.Some of this material contains results of hitherto unpublished research carried out by the writer during the years 1970-1977.

Learn everything you need to know to master your GoPro MAX 360 camera in this guide book from the #1 AMAZON BEST SELLING AUTHOR on how to use GoPro cameras. Written specifically for GoPro Max, this is the perfect guide book for anyone who wants to learn how to use the GoPro Max camera to capture unique 360 and traditional videos and photos. Packed with color images, this book provides clear, step-by-step lessons to get you out there using your GoPro MAX camera to document your life and your adventures. This book covers everything you need to know about using your GoPro MAX camera. The book teaches you: *how to operate your GoPro Max camera; *how to choose settings for full 360 spherical video; *how you can tap into the most powerful, often overlooked settings for traditional video; *tips for the best GoPro mounts to use with GoPro Max; *vital 360 photography/cinematography knowledge; *simple photo, video and time lapse editing techniques for 360 and traditional output and *the many ways to share your edited videos and photos. Through the SEVEN STEPS laid out in this book, you will understand your camera and learn how to use mostly FREE software to finally do something with your results. This book is perfect for beginners, but also provides in depth knowledge that will be useful for intermediate camera users. Written specifically for the GoPro MAX camera.

This book provides a long-overdue account of online technology and its impact on the work and lifestyles of professional employees. It moves between the offices and homes of workers in the knew "knowledge" economy to provide intimate insight into the personal, family, and wider social tensions emerging in today’s rapidly changing work environment. Drawing on her extensive research, Gregg shows that new media technologies encourage and exacerbate an older tendency among salaried professionals to put work at the heart of daily concerns, often at the expense of other sources of intimacy and fulfillment. New media technologies from mobile phones to laptops and tablet computers, have been marketed as devices that give us the freedom to work where we want, when we want, but little attention has been paid to the consequences of this shift, which has seen work move out of the office and into cafés, trains, living rooms, dining rooms, and bedrooms. This professional "presence bleed" leads to work concerns impinging on the personal lives of employees in new and unforseen ways. This groundbreaking book explores how aspiring and established professionals each try to cope with the unprecedented intimacy of technologically-mediated work, and how its seductions seem poised to triumph over the few remaining relationships that may stand in its way.

Stephen Jones is a shiny new hire at Zephyr Holdings. From the outside, Zephyr is just another bland corporate monolith, but behind its glass doors business is far from usual: the beautiful receptionist is paid twice as much as anybody else to do nothing, the sales reps use self help books as manuals, no one has seen the CEO, no one knows exactly what they are selling, and missing donuts are the cause of office intrigue. While Jones originally wanted to climb the corporate ladder, he now finds himself descending deeper into the irrational rationality of company policy. What he finds is hilarious, shocking, and utterly telling.

Static analysis is a research area aimed at developing principles and tools for veri?cation, certi?cation, semantics-based manipulation, and high-performance implementation of programming languages and systems. The series of Static Analysis symposia has served as the primary venue for presentation and disc- sion of theoretical, practical, and application advances in the area. This volume contains the papers accepted for presentation at the 15th Inter- tional Static Analysis Symposium (SAS 2008), which was held July 16–18, 2008, in Valencia, Spain. The previous SAS conferences were held in Kongens Lyngby, D- mark (2007), Seoul, South Korea (2006), London, UK (2005), Verona, Italy (2004), San Diego, USA (2003), Madrid, Spain (2002), Paris, France (2001), Santa B- bara, USA (2000), Venice, Italy (1999), Pisa, Italy (1998), Paris, France (1997), Aachen, Germany (1996), Glasgow, UK (1995), and Namur, Belgium (1994). In response to the call for papers, 63 contributions were submitted from 26 d- ferent countries. The Program Committee selected 22 papers, basing this choice on their scienti?c quality, originality, and relevance to the symposium. Each - per was reviewed by at least three Program Committee members or external r- erees. In addition to the contributed papers, this volume includes contributions by two outstanding invited speakers: Roberto Giacobazzi (Universit` a degli Studi di Verona) and Ben Liblit (University of Wisconsin-Madison). The resulting volume o?ers the reader a complete landscape of the research in this area.