Random Geometric Graphs

Author: Mathew Penrose

Publisher: Oxford University Press

ISBN: 0198506260

Category: Mathematics

Page: 330

View: 6390

This monograph provides and explains the probability theory of geometric graphs. Applications of the theory include communications networks, classification, spatial statistics, epidemiology, astrophysics and neural networks.
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Mathematical Foundations of Complex Networked Information Systems

Politecnico di Torino, Verrès, Italy 2009

Author: P.R. Kumar,Martin J. Wainwright,Riccardo Zecchina

Publisher: Springer

ISBN: 331916967X

Category: Mathematics

Page: 135

View: 6100

Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance. The book is self-contained, and requires only an undergraduate mathematical background.
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Operator Calculus on Graphs

Theory and Applications in Computer Science

Author: René Schott,G Stacey Staples

Publisher: World Scientific

ISBN: 1908977574

Category: Mathematics

Page: 428

View: 2646

This pioneering book presents a study of the interrelationships among operator calculus, graph theory, and quantum probability in a unified manner, with significant emphasis on symbolic computations and an eye toward applications in computer science. Presented in this book are new methods, built on the algebraic framework of Clifford algebras, for tackling important real world problems related, but not limited to, wireless communications, neural networks, electrical circuits, transportation, and the world wide web. Examples are put forward in Mathematica throughout the book, together with packages for performing symbolic computations. Contents:Combinatorial Algebras and Their Properties:IntroductionCombinatorial AlgebraNorm Inequalities on Clifford AlgebrasCombinatorics and Graph Theory:Specialized Adjacency MatricesRandom GraphsGraph Theory and Quantum ProbabilityGeometric Graph ProcessesProbability on Algebraic Structures:Time-Homogeneous Random WalksDynamic Walks in Clifford AlgebrasIterated Stochastic IntegralsPartition-Dependent Stochastic MeasuresOperator Calculus:Appell Systems in Clifford AlgebrasOperator Homology and CohomologySymbolic Computations:Multivector-Level ComplexityBlade-Level ComplexityOperator Calculus Approach to Minimal Path ProblemsSymbolic Computations with Mathematica Readership: Graduate students and researchers in mathematics, physics and computer science. Keywords:Operator Calculus;Algebraic Combinatorics;Clifford Algebras;Algebraic Probability;Theoretical Computer ScienceKey Features:This book is the first to explore the boundaries among Clifford algebras, graph theory, quantum probability, and theoretical computer scienceThe combinatorial view of Clifford algebras is used to address problems in random graphs and graph processes with wide-ranging applications such as communication networks, electrical circuits, transportation, neural networks, and the world wide webThere is no competing literature along these lines
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NETWORKING 2011

10th International IFIP TC 6 Networking Conference, Valencia, Spain, May 9-13, 2011, Proceedings

Author: Jordi Domingo-Pascual,Pietro Manzoni,Sergio Palazzo,Ana Pont,Caterina Scoglio

Publisher: Springer Science & Business Media

ISBN: 3642207561

Category: Business & Economics

Page: 473

View: 316

Constitutes the refereed proceedings of the 10th International IFIP TC 6 Networking Conference held in Valencia, Spain, in May 2011. This title features the papers that are organized in topical sections on anomaly detection, content management, DTN and sensor networks, energy efficiency, mobility modeling, network science, and path diversity.
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Proceedings

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Electric circuits

Page: N.A

View: 9175

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Equations of Motion in General Relativity

Author: Hideki Asada,Toshifumi Futamase,Peter Hogan

Publisher: OUP Oxford

ISBN: 0199584109

Category: Science

Page: 168

View: 6740

Einstein's theory of general relativity describes the gravitational field of a system of stars and predicts their paths by providing the 'equations of motion' of each star. Extracting these equations from his field equations is a highly technical procedure described in this book. Observable quantities can then be calculated to test the theory.
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Spatial distributions

density-equalizing map projections, facility location, and two-dimensional networks

Author: Michael T. Gastner

Publisher: N.A

ISBN: N.A

Category:

Page: N.A

View: 827

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Proceedings of the Seventh Workshop on Algorithm Engineering and Experiments and the Second Workshop on Analytic Algorithmics and Combinatorics

Author: Camil Demetrescu,Robert Sedgewick,Roberto Tamassia

Publisher: Society for Industrial and Applied Mathematics (SIAM)

ISBN: 9780898715965

Category: Computers

Page: 273

View: 6770

Presents the aim of the annual ALENEX workshop, which is to provide a forum for the presentation of original research in the implementation and experimental evaluation of algorithms and data structures.
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Poisson Approximation

Author: A. D. Barbour,Lars Holst,Svante Janson

Publisher: Oxford University Press on Demand

ISBN: N.A

Category: Mathematics

Page: 277

View: 3260

Poisson Approximation provides an introduction to the Stein-Chen method, including a varied selection of examples of its application which illustrate the flexibility of this technique. More advanced material is also included which brings the reader to the boundaries of common knowledge.
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Analysis and Stochastics of Growth Processes and Interface Models

Author: Peter Mörters,Roger Moser,Mathew Penrose,Hartmut Schwetlick,Johannes Zimmer

Publisher: OUP Oxford

ISBN: 019155359X

Category: Mathematics

Page: 352

View: 4848

This book is a collection of topical survey articles by leading researchers in the fields of applied analysis and probability theory, working on the mathematical description of growth phenomena. Particular emphasis is on the interplay of the two fields, with articles by analysts being accessible for researchers in probability, and vice versa. Mathematical methods discussed in the book comprise large deviation theory, lace expansion, harmonic multi-scale techniques and homogenisation of partial differential equations. Models based on the physics of individual particles are discussed alongside models based on the continuum description of large collections of particles, and the mathematical theories are used to describe physical phenomena such as droplet formation, Bose-Einstein condensation, Anderson localization, Ostwald ripening, or the formation of the early universe. The combination of articles from the two fields of analysis and probability is highly unusual and makes this book an important resource for researchers working in all areas close to the interface of these fields.
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Lectures on the Poisson Process

Author: Günter Last,Mathew Penrose

Publisher: Cambridge University Press

ISBN: 1107088011

Category: Mathematics

Page: 308

View: 7720

A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
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High-Dimensional Probability

An Introduction with Applications in Data Science

Author: Roman Vershynin

Publisher: Cambridge University Press

ISBN: 1108415199

Category: Business & Economics

Page: 296

View: 8050

An integrated package of powerful probabilistic tools and key applications in modern mathematical data science.
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Generating Random Networks and Graphs

Author: Alessia Annibale,Ton Coolen,Ekaterina Roberts

Publisher: Oxford University Press

ISBN: 0198709897

Category:

Page: 310

View: 8623

Generating random networks efficiently and accurately is an important challenge for practical applications, and an interesting question for theoretical study. This book presents and discusses common methods of generating random graphs. It begins with approaches such as Exponential Random Graph Models, where the targeted probability of each network appearing in the ensemble is specified. This section also includes degree-preserving randomisation algorithms, where the aim is to generate networks with the correct number of links at each node, and care must be taken to avoid introducing a bias. Separately, it looks at growth style algorithms (e.g. preferential attachment) which aim to model a real process and then to analyse the resulting ensemble of graphs. It also covers how to generate special types of graphs including modular graphs, graphs with community structure and temporal graphs. The book is aimed at the graduate student or advanced undergraduate. It includes many worked examples and open questions making it suitable for use in teaching. Explicit pseudocode algorithms are included throughout the book to make the ideas straightforward to apply. With larger and larger datasets, it is crucial to have practical and well-understood tools. Being able to test a hypothesis against a properly specified control case is at the heart of the 'scientific method'. Hence, knowledge on how to generate controlled and unbiased random graph ensembles is vital for anybody wishing to apply network science in their research.
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Probability on Graphs

Random Processes on Graphs and Lattices

Author: Geoffrey Grimmett

Publisher: Cambridge University Press

ISBN: 1108542999

Category: Mathematics

Page: N.A

View: 2981

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.
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Handbook of Large-Scale Random Networks

Author: Bela Bollobas,Robert Kozma,Dezső Miklós

Publisher: Springer Science & Business Media

ISBN: 3540693955

Category: Mathematics

Page: 600

View: 2158

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.
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Introduction to Probability

Author: John E. Freund

Publisher: Courier Corporation

ISBN: 0486158438

Category: Mathematics

Page: 247

View: 4125

Featured topics include permutations and factorials, probabilities and odds, frequency interpretation, mathematical expectation, decision making, postulates of probability, rule of elimination, much more. Exercises with some solutions. Summary. 1973 edition.
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Poisson Processes

Author: J. F. C. Kingman

Publisher: Clarendon Press

ISBN: 0191591246

Category: Mathematics

Page: 112

View: 6683

In the theory of random processes there are two that are fundamental, and occur over and over again, often in surprising ways. There is a real sense in which the deepest results are concerned with their interplay. One, the Bachelier Wiener model of Brownian motion, has been the subject of many books. The other, the Poisson process, seems at first sight humbler and less worthy of study in its own right. Nearly every book mentions it, but most hurry past to more general point processes or Markov chains. This comparative neglect is ill judged, and stems from a lack of perception of the real importance of the Poisson process. This distortion partly comes about from a restriction to one dimension, while the theory becomes more natural in more general context. This book attempts to redress the balance. It records Kingman's fascination with the beauty and wide applicability of Poisson processes in one or more dimensions. The mathematical theory is powerful, and a few key results often produce surprising consequences.
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