Details

Autor(en) / Beteiligte

• Kumar, P.R
• Wainwright, Martin J
• Zecchina, Riccardo
• Fagnani, Fabio[Herausgeber]
• Fosson, Sophie M[Herausgeber]
• Ravazzi, Chiara[Herausgeber]

Titel

Mathematical Foundations of Complex Networked Information Systems : Politecnico di Torino, Verrès, Italy 2009 [electronic resource]

Auflage

1st ed. 2015

Ort / Verlag

Cham : Springer International Publishing

Erscheinungsjahr

2015

Beschreibungen/Notizen

• Bibliographic Level Mode of Issuance: Monograph
• 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.
• English
• Description based on publisher supplied metadata and other sources.