Mathematical Technology of Networks

1. Front Matter

   Pages i-viii

   PDF

2. Lack of Ground State for NLSE on Bridge-Type Graphs

   • Riccardo Adami, Enrico Serra, Paolo Tilli

   Pages 1-11

3. Instability of Stationary Solutions of Evolution Equations on Graphs Under Dynamical Node Transition

   • Joachim von Below, Baptiste Vasseur

   Pages 13-26

4. Statistical Characterization of a Small World Network Applied to Forest Fires

   • Fatima Zahra Benzahra Belkacem, Noureddine Zekri, Mekki Terbeche

   Pages 27-37

5. Network Dynamics as an Inverse Problem

   • Jose Casadiego, Marc Timme

   Pages 39-48

6. Dynamics on a Graph as the Limit of the Dynamics on a “Fat Graph”

   • Gianfausto Dell’Antonio, Alessandro Michelangeli

   Pages 49-64

7. Spectral Inequalities for Quantum Graphs

   • Semra Demirel-Frank

   Pages 65-80

8. Intrinsic Metrics on Graphs: A Survey

   • Matthias Keller

   Pages 81-119

9. Spectral Gap for Complete Graphs: Upper and Lower Estimates

   • Pavel Kurasov

   Pages 121-132

10. Sharp Spectral Estimates for Periodic Matrix-Valued Jacobi Operators

    • Anton A. Kutsenko

    Pages 133-136

11. Identifying Key Nodes in Social Networks Using Multi-Criteria Decision-Making Tools

    • Iman Mesgari, Mehrdad Agha Mohammad Ali Kermani, Robert Hanneman, Alireza Aliahmadi

    Pages 137-150

12. On Band-Gap Structure of Spectrum in Network Double-Porosity Models

    • Svetlana E. Pastukhova

    Pages 151-174

13. Spectra, Energy and Laplacian Energy of Strong Double Graphs

    • Shariefuddin Pirzada, Hilal A. Ganie

    Pages 175-189

14. System/Environment Duality of Nonequilibrium Network Observables

    • Matteo Polettini

    Pages 191-205

Dynamical models on graphs or random graphs are increasingly used in applied sciences as mathematical tools to study complex systems whose exact structure is too complicated to be known in detail. Besides its importance in applied sciences, the field is increasingly attracting the interest of mathematicians and theoretical physicists also because of the fundamental phenomena (synchronization, phase transitions etc.) that can be studied in the relatively simple framework of dynamical models of random graphs. This volume was developed from the Mathematical Technology of Networks conference held in Bielefeld, Germany in December 2013. The conference was designed to bring together functional analysts, mathematical physicists, and experts in dynamical systems. The contributors to this volume explore the interplay between theoretical and applied aspects of discrete and continuous graphs.  Their work helps to close the gap between different avenues of research on graphs, including metric graphs and ramified structures.

• complex networks
• graphs
• mathematical analysis
• operator theory
• quantum graphs
• spectral theory

• Lehrgebiet Analysis, FernUniversität in Hagen, Hagen, Germany

  Delio Mugnolo

Delio Mugnolo is an assistant professor at the Institute of Applied Analysis at Ulm University. He completed his postdoctoral studies at the Department of Mathematics at the University of Bari, Italy, and earned his Ph.D. in Mathematics at the University of Tübingen, Germany. Since 2009, he has been a Fellow of the Young ZiF (Zentrum für interdisziplinäre Forschung) at Bielefeld University.

Policies and ethics