2008/02/09 by Luciano da Fontoura Costa, Costa, Luciano da Fontoura
Business, Management and Accounting · Computer Science · Physics and Astronomy · #Business Process Modeling and Analysis #Complex Network Analysis Techniques #Computational Physics (physics.comp-ph) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Software System Performance and Reliability #cond-mat.dis-nn #physics.comp-ph #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.0802.1272
18 pages, 15 figures. A working manuscrip. Suggestions and comments welcomed
arxiv created 2008/02/09 · openalex publication_date 2008/02/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this work it is described how to enhance and generalize the equivalent model (arXiv:0802.0421) of integrate-and-fire dynamics in order to treat any complex neuronal networks, especially those exibiting modular structure. It has been shown that, though involving only a handful of equivalent neurons, the modular equivalent model was capable of providing impressive predictions about the non-linear integrate-and-fire dynamics in two hybrid modular networks. The reported approach has also allowed the identification of the causes of transient spiking confinement within the network communities, which correspond to the fact that the little activation sent from the source community to the others implies in long times for reaching the nearly-simultaneous activation of the concentric levels at the other communities and respective avalanches. Several other insights are reported in this work, including the smoothing of the spiking functions, the consideration of intra-ring connections and its effects, as well as the identification of how the weights in the equivalent model change for different source nodes. This work has paved the way for a number of promising developments, which are identified and discussed. Preliminary results are also described which reveal waves induced by the integrate-and-fire dynamics along the steady-state regime.