LEADER 07124nam 22008175 450 001 996200029003316 005 20200704093911.0 010 $a3-319-16967-X 024 7 $a10.1007/978-3-319-16967-5 035 $a(CKB)3710000000416800 035 $a(SSID)ssj0001501591 035 $a(PQKBManifestationID)11896733 035 $a(PQKBTitleCode)TC0001501591 035 $a(PQKBWorkID)11447129 035 $a(PQKB)11284463 035 $a(DE-He213)978-3-319-16967-5 035 $a(MiAaPQ)EBC6302139 035 $a(MiAaPQ)EBC5591782 035 $a(Au-PeEL)EBL5591782 035 $a(OCoLC)910302521 035 $z(PPN)258846771 035 $a(PPN)186029527 035 $a(EXLCZ)993710000000416800 100 $a20150519d2015 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aMathematical Foundations of Complex Networked Information Systems$b[electronic resource] $ePolitecnico di Torino, Verrès, Italy 2009 /$fby P.R. Kumar, Martin J. Wainwright, Riccardo Zecchina ; edited by Fabio Fagnani, Sophie M. Fosson, Chiara Ravazzi 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (VII, 135 p. 34 illus., 24 illus. in color.) 225 1 $aC.I.M.E. Foundation Subseries ;$v2141 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-16966-1 320 $aIncludes bibliographical references. 327 $aIntro -- 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 Erdo?s-Re?nyi 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 ??? 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. 327 $a3.2 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. 330 $aIntroducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance. The book is self-contained, and requires only an undergraduate mathematical background. 410 0$aC.I.M.E. Foundation Subseries ;$v2141 606 $aSystem theory 606 $aGraph theory 606 $aMathematical physics 606 $aPhysics 606 $aComplex Systems$3https://scigraph.springernature.com/ontologies/product-market-codes/M13090 606 $aGraph Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M29020 606 $aMathematical Applications in the Physical Sciences$3https://scigraph.springernature.com/ontologies/product-market-codes/M13120 606 $aApplications of Graph Theory and Complex Networks$3https://scigraph.springernature.com/ontologies/product-market-codes/P33010 615 0$aSystem theory. 615 0$aGraph theory. 615 0$aMathematical physics. 615 0$aPhysics. 615 14$aComplex Systems. 615 24$aGraph Theory. 615 24$aMathematical Applications in the Physical Sciences. 615 24$aApplications of Graph Theory and Complex Networks. 676 $a511.5 700 $aKumar$b P.R$4aut$4http://id.loc.gov/vocabulary/relators/aut$0721404 702 $aWainwright$b Martin J$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aZecchina$b Riccardo$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aFagnani$b Fabio$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aFosson$b Sophie M$4edt$4http://id.loc.gov/vocabulary/relators/edt 702 $aRavazzi$b Chiara$4edt$4http://id.loc.gov/vocabulary/relators/edt 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996200029003316 996 $aMathematical Foundations of Complex Networked Information Systems$92105556 997 $aUNISA