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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.
This book constitutes the refereed proceedings of the 17th International Symposium on Algorithms and Computation, ISAAC 2006, held in Kolkata, India, December 2006. The 73 revised full papers cover algorithms and data structures, online algorithms, approximation algorithm, computational geometry, computational complexity, optimization and biology, combinatorial optimization and quantum computing, as well as distributed computing and cryptography.
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
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 book constitutes the refereed proceedings of the 32nd International Colloquium on Automata, Languages and Programming, ICALP 2005, held in Lisbon, Portugal in July 2005.The 113 revised full papers presented together with abstracts of 5 invited talks were carefully reviewed and selected from 407 submissions. The papers address all current issues in theoretical computer science and are organized in topical sections on data structures, cryptography and complexity, cryptography and distributed systems, graph algorithms, security mechanisms, automata and formal languages, signature and message authentication, algorithmic game theory, automata and logic, computational algebra, cache-oblivious algorithms and algorithmic engineering, on-line algorithms, security protocols logic, random graphs, concurrency, encryption and related primitives, approximation algorithms, games, lower bounds, probability, algebraic computation and communication complexity, string matching and computational biology, quantum complexity, analysis and verification, geometry and load balancing, concrete complexity and codes, and model theory and model checking.

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