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Author: Rick Durrett Publisher: Cambridge University Press ISBN: 1139460889 Category : Mathematics Languages : en Pages : 203
Book Description
The theory of random graphs began in the late 1950s in several papers by Erdos and Renyi. In the late twentieth century, the notion of six degrees of separation, meaning that any two people on the planet can be connected by a short chain of people who know each other, inspired Strogatz and Watts to define the small world random graph in which each site is connected to k close neighbors, but also has long-range connections. At a similar time, it was observed in human social and sexual networks and on the Internet that the number of neighbors of an individual or computer has a power law distribution. This inspired Barabasi and Albert to define the preferential attachment model, which has these properties. These two papers have led to an explosion of research. The purpose of this book is to use a wide variety of mathematical argument to obtain insights into the properties of these graphs. A unique feature is the interest in the dynamics of process taking place on the graph in addition to their geometric properties, such as connectedness and diameter.
Author: Remco van der Hofstad Publisher: Cambridge University Press ISBN: 110717287X Category : Computers Languages : en Pages : 341
Book Description
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Author: Anthony C. C. Coolen Publisher: Oxford University Press ISBN: 0198709897 Category : Computers Languages : en Pages : 325
Book Description
This book describes how to correctly and efficiently generate random networks based on certain constraints. Being able to test a hypothesis against a properly specified control case is at the heart of the 'scientific method'.
Author: Geoffrey Grimmett Publisher: Cambridge University Press ISBN: 1108542999 Category : Mathematics Languages : en Pages : 279
Book Description
This introduction to some of the principal models in the theory of disordered systems leads the reader through the basics, to the very edge of contemporary research, with the minimum of technical fuss. Topics covered include random walk, percolation, self-avoiding walk, interacting particle systems, uniform spanning tree, random graphs, as well as the Ising, Potts, and random-cluster models for ferromagnetism, and the Lorentz model for motion in a random medium. This new edition features accounts of major recent progress, including the exact value of the connective constant of the hexagonal lattice, and the critical point of the random-cluster model on the square lattice. The choice of topics is strongly motivated by modern applications, and focuses on areas that merit further research. Accessible to a wide audience of mathematicians and physicists, this book can be used as a graduate course text. Each chapter ends with a range of exercises.
Author: Dr. Jens Krause Publisher: Oxford University Press ISBN: 0199679045 Category : Science Languages : en Pages : 279
Book Description
The scientific study of networks - computer, social, and biological - has received an enormous amount of interest in recent years. However, the network approach has been applied to the field of animal behaviour relatively late compared to many other biological disciplines. Understanding social network structure is of great importance for biologists since the structural characteristics of any network will affect its constituent members and influence a range of diverse behaviours. These include finding and choosing a sexual partner, developing and maintaining cooperative relationships, and engaging in foraging and anti-predator behavior. This novel text provides an overview of the insights that network analysis has provided into major biological processes, and how it has enhanced our understanding of the social organisation of several important taxonomic groups. It brings together researchers from a wide range of disciplines with the aim of providing both an overview of the power of the network approach for understanding patterns and process in animal populations, as well as outlining how current methodological constraints and challenges can be overcome. Animal Social Networks is principally aimed at graduate level students and researchers in the fields of ecology, zoology, animal behaviour, and evolutionary biology but will also be of interest to social scientists.
Author: James Abello Publisher: Springer ISBN: 1461500052 Category : Computers Languages : en Pages : 1209
Book Description
The proliferation of massive data sets brings with it a series of special computational challenges. This "data avalanche" arises in a wide range of scientific and commercial applications. With advances in computer and information technologies, many of these challenges are beginning to be addressed by diverse inter-disciplinary groups, that indude computer scientists, mathematicians, statisticians and engineers, working in dose cooperation with application domain experts. High profile applications indude astrophysics, bio-technology, demographics, finance, geographi cal information systems, government, medicine, telecommunications, the environment and the internet. John R. Tucker of the Board on Mathe matical Seiences has stated: "My interest in this problern (Massive Data Sets) isthat I see it as the rnost irnportant cross-cutting problern for the rnathernatical sciences in practical problern solving for the next decade, because it is so pervasive. " The Handbook of Massive Data Sets is comprised of articles writ ten by experts on selected topics that deal with some major aspect of massive data sets. It contains chapters on information retrieval both in the internet and in the traditional sense, web crawlers, massive graphs, string processing, data compression, dustering methods, wavelets, op timization, external memory algorithms and data structures, the US national duster project, high performance computing, data warehouses, data cubes, semi-structured data, data squashing, data quality, billing in the large, fraud detection, and data processing in astrophysics, air pollution, biomolecular data, earth observation and the environment.
Author: Geoffrey R. Grimmett Publisher: Springer Science & Business Media ISBN: 3540328912 Category : Mathematics Languages : en Pages : 392
Book Description
The random-cluster model has emerged as a key tool in the mathematical study of ferromagnetism. It may be viewed as an extension of percolation to include Ising and Potts models, and its analysis is a mix of arguments from probability and geometry. The Random-Cluster Model contains accounts of the subcritical and supercritical phases, together with clear statements of important open problems. The book includes treatment of the first-order (discontinuous) phase transition.
Author: Alan Frieze
Author: Alan Frieze
Author: Rick Durrett
Author: Remco van der Hofstad
Author: Dean Lusher
Author: Anthony C. C. Coolen
Author: Geoffrey Grimmett
Author: Dr. Jens Krause
Author: James Abello
Author: Geoffrey R. Grimmett
Author: Béla Bollobás