Mathematical Technology of Networks

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.

Autorentext
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.

Zusammenfassung
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.

Inhalt
Lack of ground state for NLSE on bridge-type graphs.- Dynamics on a graph as the limit of the dynamics of a "fat graph".- Instability of stationary solutions of evolution.- Statistical characterization of a small world network applied to forest fires.- Network dynamics of an inverse problem.- Spectral inequalities for quantum graphs.- Intrinsic metrics on graphs - a survey.- Spectral gap for complete graphs: upper and lower estimates.- Sharp spectral estimates for periodic matrix-valued Jacobi operators.- Identifying key nodes in social networks using multi-criteria decision-making tools.- On band-gap structure of spectrum.- Spectra, energy and Laplacian energy of strong double graphs.- System/environment duality of nonequilibrium network observables.