Mathematical Technology of Networks: Bielefeld, December 2013 (Springer Proceedings in Mathematics & Statistics Book 128)

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. "Bringing together leading researchers in the fields of functional analysis, mathematical physics and graph theory, as well as natural scientists using networks as a tool in their own research fields, such as neuroscience and machine learning, this volume presents recent advances in functional, analytical, probabilistic, and spectral aspects in the study of graphs, quantum graphs, and complex networks. 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. All papers were presented at the conference "Mathematical Technology of Networks," held December 4-7, 2013 at the Zentrum für interdisziplinäre Forschung (ZiF) in Bielefeld, Germany, and are supplemented with detailed figures illustrating both abstract concepts as well as their real-world applications. 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 also increasingly attracting the attention of mathematicians and theoretical physicists interested in the fundamental phenomena (synchronization, phase transitions, etc.) that can be studied in the relatively simple framework of dynamical models of random graphs." -- Back cover Front Matter....Pages i-viii Lack of Ground State for NLSE on Bridge-Type Graphs....Pages 1-11 Instability of Stationary Solutions of Evolution Equations on Graphs Under Dynamical Node Transition....Pages 13-26 Statistical Characterization of a Small World Network Applied to Forest Fires....Pages 27-37 Network Dynamics as an Inverse Problem....Pages 39-48 Dynamics on a Graph as the Limit of the Dynamics on a “Fat Graph”....Pages 49-64 Spectral Inequalities for Quantum Graphs....Pages 65-80 Intrinsic Metrics on Graphs: A Survey....Pages 81-119 Spectral Gap for Complete Graphs: Upper and Lower Estimates....Pages 121-132 Sharp Spectral Estimates for Periodic Matrix-Valued Jacobi Operators....Pages 133-136 Identifying Key Nodes in Social Networks Using Multi-Criteria Decision-Making Tools....Pages 137-150 On Band-Gap Structure of Spectrum in Network Double-Porosity Models....Pages 151-174 Spectra, Energy and Laplacian Energy of Strong Double Graphs....Pages 175-189 System/Environment Duality of Nonequilibrium Network Observables....Pages 191-205