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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.
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.
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
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.
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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