Part of Cambridge Series in Statistical and Probabilistic Mathematics
Publication planned for: January 2017
availability: Not yet published - available from January 2017
format: Hardback
isbn: 9781107172876
This rigorous introduction to network science presents random graphs as models for real-world networks. Such networks have distinctive empirical properties and a wealth of new models have emerged to capture them. Classroom tested for over ten years, this text places recent advances in a unified framework to enable systematic study. Designed for a master's-level course, where students may only have a basic background in probability, the text covers such important preliminaries as convergence of random variables, probabilistic bounds, coupling, martingales, and branching processes. Building on this base - and motivated by many examples of real-world networks, including the Internet, collaboration networks, and the World Wide Web - it focuses on several important models for complex networks and investigates key properties, such as the connectivity of nodes. Numerous exercises allow students to develop intuition and experience in working with the models.
Classroom-tested over several years and written with students in mind
Details the empirical properties of networks through in-depth, real-world examples
Numerous exercises provide familiarity and experience with the theory and properties of network models
Preface
Course outline
1. Introduction
Part I. Preliminaries:
2. Probabilistics methods
3. Branching processes
Part II. Basic Models:
4. Phase transition for the Erdos-Renyi random graph
5. Erdos?Renyi random graph revisited
Part III. Models for Complex Networks:
6. Generalized random graphs
7. Configuration model
8. Preferential attachment models
Appendix
Glossary
References
Index.
A large range of symmetries in art is presented through clear and aesthetically
outstanding examples of historical ornaments. Compendious comments
illustrate the selected photographic material by addressing the interested and
specialist reader alike.
* Broad selection of symmetry in art.
* Composed by an internationally renowned specialist.
* Concise explanations in a scientific and yet understandable language.
Emil Makovicky, University of Copenhagen, Denmark.
Approx. x, 254 pages, 100 Figures (bw),50 Figures (c)
Hardcover:
ISBN 978-3-11-041705-0
Date of Publication: August 2016
Language of Publication: English
Arts, general
Crystallography
Geology and Mineralogy
History and Philosophy
The purpose of this book is to present results on the subject of weak
convergence to study invariance principles in statistical applications. Different
techniques, formerly only available in a broad range of literature, are for the first
time presented in a self-contained fashion.
Vidyadhar Mandrekar, Michigan State University, USA.
De Gruyter Textbook
Approx. xvi, 200 pages
Paperback:
ISBN 978-3-11-047542-5
Date of Publication: September 2016
Language of Publication: English
Probability and Statistics
This textbook is devoted to a compressed and self-contained exposition of two
important parts of contemporary mathematics: convex and set-valued analysis.
In the first part, properties of convex sets, the theory of separation, convex
functions, and properties of convex cones in infinite-dimensional spaces are
discussed. The second part covers set-valued analysis, describes the properties of
the Hausdorff metric and set-valued maps.
* Contains many illustrative examples.
* An introduction for mathematicians, but also useful in mathematical economics and engineering.
Aram Arutyunov, Moscow, Russia.
Valerii Obukhovskii, Voronezh, Russia.
De Gruyter Textbook
xii, 250 pages, 10 Figures (bw)
Paperback:
ISBN 978-3-11-046028-5
Date of Publication: November 2016
Language of Publication: English
Analysis
EMS Series of Lectures in Mathematics
ISBN print 978-3-03719-162-0
DOI 10.4171/162
June 2016, 332 pages, softcover, 17 x 24 cm.
Sub-Riemannian manifolds model media with constrained dynamics: motion at any point is only allowed along a limited set of directions, which are prescribed by the physical problem. From the theoretical point of view, sub-Riemannian geometry is the geometry underlying the theory of hypoelliptic operators and degenerate diffusions on manifolds.
In the last twenty years, sub-Riemannian geometry has emerged as an independent research domain, with extremely rich motivations and ramifications in several parts of pure and applied mathematics, such as geometric analysis, geometric measure theory, stochastic calculus and evolution equations together with applications in mechanics, optimal control and biology.
The aim of the lectures collected here is to present sub-Riemannian structures for the use of both researchers and graduate students.
Keywords: Sub-Riemannian geometry, hypoelliptic operators, non-holonomic constraints, optimal control, rough paths
ISBN print 978-3-03719-157-6,
DOI 10.4171/157
July 2016, 397 pages, hardcover, 17 x 24 cm.
It has been known for some time that geometries over finite fields, their automorphism groups and certain counting formulae involving these geometries have interesting guises when one lets the size of the field go to 1. On the other hand, the nonexistent field with one element, F1
, presents itself as a ghost candidate for an absolute basis in Algebraic Geometry to perform the Deninger?Manin program, which aims at solving the classical Riemann Hypothesis.
This book, which is the first of its kind in the F1-world, covers several areas in F1-theory, and is divided into four main parts Combinatorial Theory, Homological Algebra, Algebraic Geometry and Absolute Arithmetic.
Topics treated include the combinatorial theory and geometry behind F1, categorical foundations, the blend of different scheme theories over F1
which are presently available, motives and zeta functions, the Habiro topology, Witt vectors and total positivity, moduli operads, and at the end, even some arithmetic.
Each chapter is carefully written by experts, and besides elaborating on known results, brand new results, open problems and conjectures are also met along the way.
The diversity of the contents, together with the mystery surrounding the field with one element, should attract any mathematician, regardless of speciality.
Keywords: The field with one element, F1
-geometry, combinatorial F1-geometry, non-additive category, Deitmar scheme, graph, monoid, motive, zeta function, automorphism group, blueprint, Euler characteristic, K-theory, Grassmannian, Witt ring, noncommutative geometry, Witt vector, total positivity, moduli space of curves, operad, torificiation, Absolute Arithmetic, counting function, Weil conjectures, Riemann Hypothesis
A publication of the Societe Mathematique de France
In this memoir, the author studies quasiperiodic cocycles in semi-simple compact Lie groups. For most of his study, he focuses on one-frequency cocyles. He proves that C∞-reducible cocycles are dense in the C∞ - topology, for a full measure set of frequencies. Moreover, he shows that every cocycle (or an appropriate iterate of it, if homotopy appears as an obstruction) is almost torus-reducible (i.e. can be conjugated arbitrarily close to cocycles taking values in an abelian subgroup of G).
In the course of the proof, the author first defines two invariants of the dynamics, which he calls energy and degree and which give a preliminary distinction between (almost-)reducible and non-reducible cocycles. He then takes up the proof of the density theorem and shows that an algorithm of renormalization converges to perturbations of simple models, indexed by the degree. Finally, the author analyzes these perturbations using methods inspired by KAM theory. - See more at: http://bookstore.ams.org/smfmem-146/#sthash.GdWYh2X7.dpuf
Graduate students and research mathematicians interested in cocycles.