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Discrete and Continuous Models in the Theory of Networks

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  • © 2020

Overview

Editors:
  1. Fatihcan M. Atay

    1. Department of Mathematics, Bilkent University, Ankara, Turkey

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  2. Pavel B. Kurasov

    1. Department of Mathematics, Stockholm University, Stockholm, Sweden

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    You can also search for this editor in PubMed   Google Scholar

  3. Delio Mugnolo

    1. Mathematik und Informatik, FernUniversität in Hagen, Hagen, Germany

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  • Covers current research in the areas of operator theory and dynamical systems on networks and their applications
  • Indicates possible future directions
  • Will be interesting to all researchers focusing on the mathematical theory of networks

Part of the book series: Operator Theory: Advances and Applications (OT, volume 281)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xx
    Download chapter PDF

  2. Stability Matters for Reaction–Diffusion–Equations on Metric Graphs Under the Anti-Kirchhoff Vertex Condition

    • Joachim von Below, José A. Lubary
    Pages 1-28

  3. Many-Particle Quantum Graphs: A Review

    • Jens Bolte, Joachim Kerner
    Pages 29-66

  4. Deterministic and Stochastic Mean-Field SIRS Models on Heterogeneous Networks

    • Stefano Bonaccorsi, Silvia Turri
    Pages 67-89

  5. Kreı̆n Formula and Convergence of Hamiltonians with Scaled Potentials in Dimension One

    • Claudio Cacciapuoti
    Pages 91-112

  6. Ground States of the L 2-Critical NLS Equation with Localized Nonlinearity on a Tadpole Graph

    • Simone Dovetta, Lorenzo Tentarelli
    Pages 113-125

  7. An Asymptotic Expansion of the Trace of the Heat Kernel of a Singular Two-particle Contact Interaction in One-dimension

    • Sebastian Egger
    Pages 127-152

  8. Modeling Dynamic Coupling in Social Interactions

    • Merle T. Fairhurst
    Pages 153-168

  9. A Note on Cheeger Inequalities for Piecewise Flat Surfaces

    • Huabin Ge, Bobo Hua, Aijin Lin
    Pages 169-177

  10. Unravelling Topological Determinants of Excitable Dynamics on Graphs Using Analytical Mean-field Approaches

    • Marc-Thorsten Hütt, Annick Lesne
    Pages 179-198

  11. Spectral Zeta Functions

    • Anders Karlsson
    Pages 199-211

  12. A Family of Diameter-Based Eigenvalue Bounds for Quantum Graphs

    • J. B. Kennedy
    Pages 213-239

  13. Missing-Level Statistics in Chaotic Microwave Networks Versus Level Statistics of Partially Chaotic Systems

    • Michał Ławniczak, Małgorzata Białous, Vitalii Yunko, Szymon Bauch, Leszek Sirko
    Pages 241-253

  14. Signatures, Lifts, and Eigenvalues of Graphs

    • Shiping Liu, Norbert Peyerimhoff, Alina Vdovina
    Pages 255-269

  15. Strong Isoperimetric Inequality for Tessellating Quantum Graphs

    • Noema Nicolussi
    Pages 271-290

  16. Spectral Monotonicity for Schrödinger Operators on Metric Graphs

    • Jonathan Rohleder, Christian Seifert
    Pages 291-310

  17. Random Graphs and Their Subgraphs

    • Klemens Taglieber, Uta Freiberg
    Pages 311-340

  18. Massive Modes for Quantum Graphs

    • H. A. Weidenmüller
    Pages 341-357
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Keywords

About this book

This book contains contributions from the participants of the research group hosted by the ZiF - Center for Interdisciplinary Research at the University of Bielefeld during the period 2013-2017 as well as from the conclusive conference organized at Bielefeld in December 2017. The contributions consist of original research papers: they mirror the scientific developments fostered by this research program or the state-of-the-art results presented during the conclusive conference.

The volume covers current research in the areas of operator theory and dynamical systems on networks and their applications, indicating possible future directions. The book will be interesting to researchers focusing on the mathematical theory of networks; it is unique as, for the first time, continuous network models - a subject that has been blooming in the last twenty years - are studied alongside more classical and discrete ones. Thus, instead of two different worlds often growing independently without much intercommunication, a new path is set, breaking with the tradition. The fruitful and beneficial exchange of ideas and results of both communities is reflected in this book.

Editors and Affiliations

  • Department of Mathematics, Bilkent University, Ankara, Turkey

    Fatihcan M. Atay

  • Department of Mathematics, Stockholm University, Stockholm, Sweden

    Pavel B. Kurasov

  • Mathematik und Informatik, FernUniversität in Hagen, Hagen, Germany

    Delio Mugnolo

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