Mathematical foundations and applications of graph entropy Edited by Matthias Dehmer [and four others]

• Pubblicazione: Weinheim, [Germany] : , : Wiley-VCH Verlag GmbH & Co. KGaA, , 2016; ©2016
• Descrizione fisica: 1 online resource (299 p.)
• Disciplina: 511.5
• Soggetto topico: Graph theory - Data processing
• Persona (resp. second.): DehmerMatthias
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Title Page; Copyright; Contents; List of Contributors; Preface; Chapter 1 Entropy and Renormalization in Chaotic Visibility Graphs; 1.1 Mapping Time Series to Networks; 1.1.1 Natural and Horizontal Visibility Algorithms; 1.1.2 A Brief Overview of Some Initial Applications; 1.1.2.1 Seismicity; 1.1.2.2 Hurricanes; 1.1.2.3 Turbulence; 1.1.2.4 Financial Applications; 1.1.2.5 Physiology; 1.2 Visibility Graphs and Entropy; 1.2.1 Definitions of Entropy in Visibility Graphs; 1.2.2 Pesin Theorem in Visibility Graphs; 1.2.3 Graph Entropy Optimization and Critical Points ; 1.3 Renormalization Group Transformations of Horizontal Visibility Graphs1.3.1 Tangent Bifurcation; 1.3.2 Period-Doubling Accumulation Point; 1.3.3 Quasi-Periodicity; 1.3.4 Entropy Extrema and RG Transformation; 1.3.4.1 Intermittency; 1.3.4.2 Period Doubling; 1.3.4.3 Quasi-periodicity; 1.4 Summary; 1.5 Acknowledgments; References; Chapter 2 Generalized Entropies of Complex and Random Networks; 2.1 Introduction; 2.2 Generalized Entropies; 2.3 Entropy of Networks: Definition and Properties; 2.4 Application of Generalized Entropy for Network Analysis; 2.5 Open Networks; 2.6 Summary; References ; Chapter 3 Information Flow and Entropy Production on Bayesian Networks3.1 Introduction; 3.1.1 Background; 3.1.2 Basic Ideas of Information Thermodynamics; 3.1.3 Outline of this Chapter; 3.2 Brief Review of Information Contents; 3.2.1 Shannon Entropy; 3.2.2 Relative Entropy; 3.2.3 Mutual Information; 3.2.4 Transfer Entropy; 3.3 Stochastic Thermodynamics for Markovian Dynamics; 3.3.1 Setup; 3.3.2 Energetics; 3.3.3 Entropy Production and Fluctuation Theorem; 3.4 Bayesian Networks; 3.5 Information Thermodynamics on Bayesian Networks; 3.5.1 Setup; 3.5.2 Information Contents on Bayesian Networks ; 3.5.3 Entropy Production3.5.4 Generalized Second Law; 3.6 Examples; 3.6.1 Example 1: Markov Chain; 3.6.2 Example 2: Feedback Control with a Single Measurement; 3.6.3 Example 3: Repeated Feedback Control with Multiple Measurements; 3.6.4 Example 4: Markovian Information Exchanges; 3.6.5 Example 5: Complex Dynamics; 3.7 Summary and Prospects; References; Chapter 4 Entropy, Counting, and Fractional Chromatic Number; 4.1 Entropy of a Random Variable; 4.2 Relative Entropy and Mutual Information; 4.3 Entropy and Counting; 4.4 Graph Entropy; 4.5 Entropy of a Convex Corner; 4.6 Entropy of a Graph ; 4.7 Basic Properties of Graph Entropy4.8 Entropy of Some Special Graphs; 4.9 Graph Entropy and Fractional Chromatic Number; 4.10 Symmetric Graphs with respect to Graph Entropy; 4.11 Conclusion; Appendix 4.A; References; Chapter 5 Graph Entropy: Recent Results and Perspectives; 5.1 Introduction; 5.2 Inequalities and Extremal Properties on (Generalized) Graph Entropies; 5.2.1 Inequalities for Classical Graph Entropies and Parametric Measures; 5.2.2 Graph Entropy Inequalities with Information Functions fV, fP and fC; 5.2.3 Information Theoretic Measures of UHG Graphs ; 5.2.4 Bounds for the Entropies of Rooted Trees and Generalized Trees
• Titolo autorizzato: Mathematical foundations and applications of graph entropy
• ISBN: 3-527-69325-4; 3-527-69322-X; 3-527-69324-6
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910829886303321
• Lo trovi qui: Univ. Federico II
• Serie: Quantitative and network biology ; ; Volume 6.