With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines h...
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With the advent of digital computers more than half a century ago, - searchers working in a wide range of scienti?c disciplines have obtained an extremely powerful tool to pursue deep understanding of natural processes in physical, chemical, and biological systems. Computers pose a great ch- lenge to mathematical sciences, as the range of phenomena available for rigorous mathematical analysis has been enormously expanded, demanding the development of a new generation of mathematical tools. There is an explosive growth of new mathematical disciplines to satisfy this demand, in particular related to discrete mathematics. However, it can be argued that at large mathematics is yet to provide the essential breakthrough to meet the challenge. The required paradigm shift in our view should be compa- ble to the shift in scienti?c thinking provided by the Newtonian revolution over 300 years ago. Studies of large-scale random graphs and networks are critical for the progress, using methods of discrete mathematics, probabil- tic combinatorics, graph theory, and statistical physics. Recent advances in large scale random network studies are described in this handbook, which provides a signi?cant update and extension - yond the materials presented in the "Handbook of Graphs and Networks" published in 2003 by Wiley. The present volume puts special emphasis on large-scale networks and random processes, which deemed as crucial for - tureprogressinthe?eld. Theissuesrelatedtorandomgraphsandnetworks pose very di?cult mathematical questions.
This handbook describes advances in large scale network studies that have taken place in the past 5 years since the publication of the Handbook of Graphs and Networks in 2003. It covers all aspects of large-scale networks, including mathematical foundations and rigorous results of random graph theory, modeling and computational aspects of large-scale networks, as well as areas in physics, biology, neuroscience, sociology and technical areas. Applications range from microscopic to mesoscopic and macroscopic models. The book is based on the material of the NSF workshop on Large-scale Random Graphs held in Budapest in 2006, at the Alfréd Rényi Institute of Mathematics, organized jointly with the University of Memphis.
Inhalt Part I: Theoretical FoundationsChapter 1 Random graphs and branching processesBela Bollobas and Oliver Riordan (Cambridge University, UK)Chapter 2 Sentry Selection in wireless networksPaul Balister and Bela Bollobas (U of Memphis, TN, and Cambridge University, UK) Amites Sarkar and Mark WaltersChapter 3 Scaling properties of complex networks and spanning trees Reuven Cohen and Shlomo Havlin, (MIT, USA)Chapter 4 Random Tree Growth with Branching Processes a Survey Anna Rudas and Balint Toth ( Technical University, Budapest, Hungary)Part II. Large-scale networks in biological systemsChapter 5 Reaction-diffusion processes in scale-free networks Michele Catanzaro, Marian Boguna, and Romualdo Pastor-Satorras, (U Catalunya, Barcelona, Spain)Chapter 6 Toward Understanding the Structure and Function of Cellular Interaction Networks C. Christensen, J. Thakar and R. Albert (Penn State University, PA, USA)Chapter 7 Scale-Free Cortical Planar Networks Bela Bollobas (Cambridge University, UK), Walter J Freeman (UC Berkeley, CA), Robert Kozma (U of Memphis, TN, USA)Chapter 8 Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity Nepusz P., Bazso F, (KFKI, Hungarian Academy of Sciences), Negyessy L. (Semmelweis Medical University, Budapest, Hungary) Tusnady G. (Renyi Institute of Mathematics, Hungarian Academy of Sciences)Part III. Large-scale networks in physics, technology, and the societyChapter 9 k-clique percolation and clusteringGergely Palla1, Daniel Abel, Illes J. Farkas, Peter Pollner, Imre Derenyi Tamas Vicsek (Eotvos University, Budapest, Hungary)Chapter 10 The inverse problem of evolving networks with application to social netsGabor Csardi, Katherine J. Strandburg, Jan Tobochnik, and Peter Erdi, (KFKI, Hungarian Academy of Sciences, Budapest, Hungary and Kalamazoo College, Mi, USA)Chapter 11 Learning and Representation: From Compressive Sampling to Szemerédi's Regularity LemmaAndras Lorincz (Eotvos University, Budapest, Hungary)Chapter 12 Telephone Call Network Data Mining: A Survey with Experiments Andras A. Benczur, Karoly Csalogany, Miklos Kurucz, Andras Lukacs, Laszlo Lukacs, David Siklosi (Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, Hungary)