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Die jüngsten Entwicklungen zeigen, dass sich Wahrscheinlichkeitsverfahren zu einem sehr wirkungsvollen Werkzeug entwickelt haben, und das auf so unterschiedlichen Gebieten wie statistische Physik, dynamische Systeme, Riemann'sche Geometrie, Gruppentheorie, harmonische Analyse, Graphentheorie und Informatik.
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Introduction to Parallel Algorithms and Architectures: Arrays Trees Hypercubes provides an introduction to the expanding field of parallel algorithms and architectures. This book focuses on parallel computation involving the most popular network architectures, namely, arrays, trees, hypercubes, and some closely related networks. Organized into three chapters, this book begins with an overview of the simplest architectures of arrays and trees. This text then presents the structures and relationships between the dominant network architectures, as well as the most efficient parallel algorithms for a wide variety of problems. Other chapters focus on fundamental results and techniques and on rigorous analysis of algorithmic performance. This book discusses as well a hybrid of network architecture based on arrays and trees called the mesh of trees. The final chapter deals with the most important properties of hypercubes. This book is a valuable resource for readers with a general technical background.
This carefully edited volume contains selected refereed papers based on lectures presented by many distinguished speakers at the "Integers Conference 2005", an international conference in combinatorial number theory. The conference was held in celebration of the 70th birthday of Ronald Graham, a leader in several fields of mathematics.
"These papers were presented and developed as expository talks at a summer-long workshop on Stein's method at Stanford's Department of Statistics in 1998."--P. iii.
The Fourth Conference on Infinite Dimensional Harmonic Analysis brought together experts in harmonic analysis, operator algebras and probability theory. Most of the articles deal with the limit behavior of systems with many degrees of freedom in the presence of symmetry constraints. This volume gives new directions in research bringing together probability theory and representation theory.
Most probability problems involve random variables indexed by space and/or time. These problems almost always have a version in which space and/or time are taken to be discrete. This volume deals with areas in which the discrete version is more natural than the continuous one, perhaps even the only one than can be formulated without complicated constructions and machinery. The 5 papers of this volume discuss problems in which there has been significant progress in the last few years; they are motivated by, or have been developed in parallel with, statistical physics. They include questions about asymptotic shape for stochastic growth models and for random clusters; existence, location and properties of phase transitions; speed of convergence to equilibrium in Markov chains, and in particular for Markov chains based on models with a phase transition; cut-off phenomena for random walks. The articles can be read independently of each other. Their unifying theme is that of models built on discrete spaces or graphs. Such models are often easy to formulate. Correspondingly, the book requires comparatively little previous knowledge of the machinery of probability.
This book forms a valuable guide to the direction in which current numerical analysis research is heading. It will be of particular interest to graduate students and researchers concerned with the theoretical and practical issues associated with scientific computation. The main topics include ordinary and partial differential equations, fluid flow, optimization, linear algebra, and approximation theory. Two recurring themes are the need for adaptive and structure preserving numerical methods. The work presented here has a list of direct applications that include colliding black holes, molecular dynamics, blow-up problems, and card shuffling.
ISAAC 2007, the 18th International Symposium on Algorithms and Compu- tion took place in Sendai, Japan, December 17-19, 2007. In the past, it was held in Tokyo (1990), Taipei (1991), Nagoya (1992), Hong Kong (1993), Beijing (1994), Cairns (1995), Osaka (1996), Singapore (1997), Daejeon (1998), Ch- nai (1999), Taipei (2000), Christchurch(2001), Vancouver(2002), Kyoto (2003), Hong Kong (2004), Hainan (2005), and Kolkata(2006). The symposium provided a forum for researchers working in algorithms and the theory of computation from all over the world. In response to our call for papers we received 220 submissions from 40 countries. The task of selecting the papers in this volume was done by our Program Committee and many other external reviewers. After a thorough review process, the Committee selected 77 papers. We hope all accepted papers will eventually appear in scienti?c journals in a more polished form. Two special issues, one of Algorithmica and one of the International Journal of Computational Geometry and Applications, with selected papers from ISAAC 2007 are in preparation. The best paper awardwasgivenfor "IntegerRepresentationandCounting in the Bit Probe Model" to Mohammad Rhaman and Ian Munro. Selected from 27 submissionsauthoredbyonlystudents, thebeststudentpaperawardsweregiven for "On Mixing and Edge Expansion Properties in Randomized Broadcasting" to Thomas Sauerwald and for "Faster Combinatorial Algorithms for Deter- nant and Pfa?an" to Anna Urbanska. Two eminent invited speakers, Pankaj K. Agarwal, Duke University, USA, and Robin Thomas, Georgia Institute of Technology, USA, also contributed to this volume