Random Graphs, Geometry and Asymptotic Structure PDF Download
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Author: Michael Krivelevich
Publisher: Cambridge University Press
ISBN: 1107136571
Category : Mathematics
Languages : en
Pages : 129
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Book Description
A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.
Author: Michael Krivelevich
Publisher: Cambridge University Press
ISBN: 1107136571
Category : Mathematics
Languages : en
Pages : 129
Get Book Here
Book Description
A concise introduction, aimed at young researchers, to recent developments of a geometric and topological nature in random graphs.
Author: Michael Krivelevich
Publisher: Cambridge University Press
ISBN: 1316552942
Category : Mathematics
Languages : en
Pages : 129
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Book Description
The theory of random graphs is a vital part of the education of any researcher entering the fascinating world of combinatorics. However, due to their diverse nature, the geometric and structural aspects of the theory often remain an obscure part of the formative study of young combinatorialists and probabilists. Moreover, the theory itself, even in its most basic forms, is often considered too advanced to be part of undergraduate curricula, and those who are interested usually learn it mostly through self-study, covering a lot of its fundamentals but little of the more recent developments. This book provides a self-contained and concise introduction to recent developments and techniques for classical problems in the theory of random graphs. Moreover, it covers geometric and topological aspects of the theory and introduces the reader to the diversity and depth of the methods that have been devised in this context.
Author: Remco van der Hofstad
Publisher: Cambridge University Press
ISBN: 110717287X
Category : Computers
Languages : en
Pages : 341
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Book Description
This classroom-tested text is the definitive introduction to the mathematics of network science, featuring examples and numerous exercises.
Author: Jonny Evans
Publisher: Cambridge University Press
ISBN: 1009372629
Category : Mathematics
Languages : en
Pages : 241
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Book Description
Comprehensive and visual introduction to the geometry of 4-dimensional symplectic manifolds via 2-dimensional almost-toric diagrams.
Author: Amaury Freslon
Publisher: Cambridge University Press
ISBN: 1009345737
Category : Mathematics
Languages : en
Pages : 301
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Book Description
Author: Antonio Giorgilli
Publisher: Cambridge University Press
ISBN: 1009151142
Category : Science
Languages : en
Pages : 473
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Book Description
Introduces Hamiltonian dynamics from the very beginning, culminating in the most important recent results: Kolmogorov's and Nekhoroshev's.
Author: Daniel Sanz-Alonso
Publisher: Cambridge University Press
ISBN: 100941433X
Category : Computers
Languages : en
Pages : 228
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Book Description
This concise introduction provides an entry point to the world of inverse problems and data assimilation for advanced undergraduates and beginning graduate students in the mathematical sciences. It will also appeal to researchers in science and engineering who are interested in the systematic underpinnings of methodologies widely used in their disciplines. The authors examine inverse problems and data assimilation in turn, before exploring the use of data assimilation methods to solve generic inverse problems by introducing an artificial algorithmic time. Topics covered include maximum a posteriori estimation, (stochastic) gradient descent, variational Bayes, Monte Carlo, importance sampling and Markov chain Monte Carlo for inverse problems; and 3DVAR, 4DVAR, extended and ensemble Kalman filters, and particle filters for data assimilation. The book contains a wealth of examples and exercises, and can be used to accompany courses as well as for self-study.
Author: Patrick Dehornoy
Publisher: Cambridge University Press
ISBN: 1108843948
Category : Mathematics
Languages : en
Pages : 259
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Book Description
This introduction to braid groups keeps prerequisites to a minimum, while discussing their rich mathematical properties and applications.
Author: Eilon Solan
Publisher: Cambridge University Press
ISBN: 1316516334
Category : Business & Economics
Languages : en
Pages : 279
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Book Description
This book for beginning graduate students presents a course on stochastic games and the mathematical methods used in their analysis.
Author: Rick Durrett
Publisher: Cambridge University Press
ISBN: 1139460889
Category : Mathematics
Languages : en
Pages : 203
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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.
