Mathematical Technology of Networks: Bielefeld, December by Delio Mugnolo

By Delio Mugnolo

Dynamical types on graphs or random graphs are more and more utilized in technologies as mathematical instruments to review advanced platforms whose targeted constitution is just too advanced to be identified intimately. along with its value in technologies, the sphere is more and more attracting the curiosity of mathematicians and theoretical physicists additionally as a result of the basic phenomena (synchronization, part transitions etc.) that may be studied within the particularly easy framework of dynamical types of random graphs. This quantity used to be constructed from the Mathematical expertise of Networks convention held in Bielefeld, Germany in December 2013. The convention used to be designed to compile practical analysts, mathematical physicists, and specialists in dynamical structures. The participants to this quantity discover the interaction among theoretical and utilized features of discrete and non-stop graphs. Their paintings is helping to shut the space among diversified avenues of study on graphs, together with metric graphs and ramified structures.

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Comput. Neurosci. 5, 3 (2011) 19. : Phys. D Nonlinear Phenom. 143(1–4), 1–20 (2000) 20. : Matrix Analysis and Applied Linear Algebra. Society for Industrial and Applied Mathematics, Philadelphia, PA (2000) 21. : Proc. Natl. Acad. Sci. A. 99(9), 6163–6168 (2002) 22. ; Phys. Rev. Lett. 98(22), 224101 (2007) 23. : New J. Phys. 13(1), 013004 (2011) 24. : Phys. Rev. E 48(5), 3470–3477 (1993) 25. : Science 330(6009), 1385–1389 (2010) Dynamics on a Graph as the Limit of the Dynamics on a “Fat Graph” Gianfausto Dell’Antonio and Alessandro Michelangeli Abstract We discuss how the vertex boundary conditions for the dynamics of a quantum particle constrained on a graph emerge in the limit of the dynamics of a particle in a tubular region around the graph (“fat graph”) when the transversal section of this region shrinks to zero.

I x/ D 0 for all x in state space. If interactions with i are strictly pairwise, (1), i becomes Œ i jj D 8 ˆ ˆ

4 Network variance for networks of N D 11 oscillators and sampling rate dependence. (a) Network variance in time for three different proposed network connectivities. (b) Mean network variance hNvit versus t with the best power-law fit. The inset shows same data on a logarithmic scale. (c) Topology A (regular network). (d) Topology B (heterogeneous network). (e) Topology C (random network) 4 Conclusions Here we proposed to view network dynamics as an inverse problem. We presented a method to find the set of all networks yielding a pre-defined dynamics.

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