07124nam 22008175 450 99620002900331620200704093911.03-319-16967-X10.1007/978-3-319-16967-5(CKB)3710000000416800(SSID)ssj0001501591(PQKBManifestationID)11896733(PQKBTitleCode)TC0001501591(PQKBWorkID)11447129(PQKB)11284463(DE-He213)978-3-319-16967-5(MiAaPQ)EBC6302139(MiAaPQ)EBC5591782(Au-PeEL)EBL5591782(OCoLC)910302521(PPN)258846771(PPN)186029527(EXLCZ)99371000000041680020150519d2015 u| 0engurnn|008mamaatxtccrMathematical Foundations of Complex Networked Information Systems[electronic resource] Politecnico di Torino, Verrès, Italy 2009 /by P.R. Kumar, Martin J. Wainwright, Riccardo Zecchina ; edited by Fabio Fagnani, Sophie M. Fosson, Chiara Ravazzi1st ed. 2015.Cham :Springer International Publishing :Imprint: Springer,2015.1 online resource (VII, 135 p. 34 illus., 24 illus. in color.) C.I.M.E. Foundation Subseries ;2141Bibliographic Level Mode of Issuance: Monograph3-319-16966-1 Includes bibliographical references.Intro -- Preface -- Contents -- Some Introductory Notes on Random Graphs -- 1 Introduction -- 2 Generalities on Graphs -- 2.1 Basic Definitions and Notation -- 2.2 Large Scale Networks -- 3 Erdős-Rényi Model -- 3.1 Connectivity and Giant Component -- 3.2 Branching Processes -- 3.3 Behavior at the Giant Component Threshold -- 4 Configuration Model -- 4.1 Connectivity and Giant Component -- 5 Random Geometric Graph -- 5.1 Connectivity -- 5.2 Giant Component -- References -- Statistical Physics and Network Optimization Problems -- 1 Statistical Physics and Optimization -- 2 Elements of Statistical Physics -- 3 Statistical Physics Approach to Percolation in Random Graphs -- 3.1 The Potts Model Representation -- 3.1.1 Symmetric Saddle-Point -- 3.1.2 Symmetry Broken Saddle-Point -- 4 Statistical Physics Methods for More Complex Problems -- 5 Bethe Approximation and Message Passing Algorithms -- 5.1 Belief Propagation -- 5.1.1 Marginals -- 5.1.2 Free Energy -- 5.1.3 Graphs with Loops -- 5.2 The β→∞ Limit: Minsum Algorithm -- 5.3 Finding a Solution: Decimation and Reinforcement Algorithms -- 5.3.1 Decimation -- 5.3.2 Reinforcement -- 5.4 Replica Symmetry Breaking and Higher Levels of BP -- References -- Graphical Models and Message-Passing Algorithms: Some Introductory Lectures -- 1 Introduction -- 2 Probability Distributions and Graphical Structure -- 2.1 Directed Graphical Models -- 2.1.1 Conditional Independence Properties for Directed Graphs -- 2.1.2 Equivalence of Representations -- 2.2 Undirected Graphical Models -- 2.2.1 Factorization for Undirected Models -- 2.2.2 Markov Property for Undirected Models -- 2.2.3 Hammersley-Clifford Equivalence -- 2.2.4 Factor Graphs -- 3 Exact Algorithms for Marginals, Likelihoods and Modes -- 3.1 Elimination Algorithm -- 3.1.1 Graph-Theoretic Versus Analytical Elimination -- 3.1.2 Complexity of Elimination.3.2 Message-Passing Algorithms on Trees -- 3.2.1 Sum-Product Algorithm -- 3.2.2 Sum-Product on General Factor Trees -- 3.2.3 Max-Product Algorithm -- 4 Junction Tree Framework -- 4.1 Clique Trees and Running Intersection -- 4.2 Triangulation and Junction Trees -- 4.3 Constructing the Junction Tree -- 5 Basics of Graph Estimation -- 5.1 Parameter Estimation for Directed Graphs -- 5.2 Parameter Estimation for Undirected Graphs -- 5.2.1 Maximum Likelihood for Undirected Trees -- 5.2.2 Maximum Likelihood on General Undirected Graphs -- 5.2.3 Iterative Proportional Scaling -- 5.3 Tree Selection and the Chow-Liu Algorithm -- 6 Bibliographic Details and Remarks -- Appendix: Triangulation and Equivalent Graph-Theoretic Properties -- References -- Bridging the Gap Between Information Theory and WirelessNetworking -- 1 Introduction -- 2 Shannon's Point to Point Results -- 3 The Multiple-Access and Gaussian Broadcast Channels -- 4 A Spatial Model of a Wireless Network -- 5 Multi-Hop Transport -- 6 The Transport Capacity -- 7 Best Case Transport Capacity and Scaling Laws -- 8 An Upper Bound on Transport Capacity -- 9 Implication of Square-Root Law for Transport Capacity -- 10 The Need for an Information-Theoretic Analysis -- 11 Wireless Network Information Theory -- 12 Information-Theoretic Definition of Transport Capacity -- 13 Information-Theoretic Bounds -- 14 Implication of Information-Theoretic Scaling Law -- 15 Extensions -- References -- Lecture Notes in Math ematics.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.C.I.M.E. Foundation Subseries ;2141System theoryGraph theoryMathematical physicsPhysicsComplex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/M13090Graph Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M29020Mathematical Applications in the Physical Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/M13120Applications of Graph Theory and Complex Networkshttps://scigraph.springernature.com/ontologies/product-market-codes/P33010System theory.Graph theory.Mathematical physics.Physics.Complex Systems.Graph Theory.Mathematical Applications in the Physical Sciences.Applications of Graph Theory and Complex Networks.511.5Kumar P.Rauthttp://id.loc.gov/vocabulary/relators/aut721404Wainwright Martin Jauthttp://id.loc.gov/vocabulary/relators/autZecchina Riccardoauthttp://id.loc.gov/vocabulary/relators/autFagnani Fabioedthttp://id.loc.gov/vocabulary/relators/edtFosson Sophie Medthttp://id.loc.gov/vocabulary/relators/edtRavazzi Chiaraedthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK996200029003316Mathematical Foundations of Complex Networked Information Systems2105556UNISA