Spectra of the Spike-Flow Graphs in Geometrically Embedded Neural Networks

  • Jarosław Piersa
  • Tomasz Schreiber
Conference paper

DOI: 10.1007/978-3-642-29347-4_17

Part of the Lecture Notes in Computer Science book series (LNCS, volume 7267)
Cite this paper as:
Piersa J., Schreiber T. (2012) Spectra of the Spike-Flow Graphs in Geometrically Embedded Neural Networks. In: Rutkowski L., Korytkowski M., Scherer R., Tadeusiewicz R., Zadeh L.A., Zurada J.M. (eds) Artificial Intelligence and Soft Computing. ICAISC 2012. Lecture Notes in Computer Science, vol 7267. Springer, Berlin, Heidelberg

Abstract

In this work we study a simplified model of a neural activity flow in networks, whose connectivity is based on geometrical embedding, rather than being lattices or fully connected graphs. We present numerical results showing that as the spectrum (set of eigenvalues of adjacency matrix) of the resulting activity-based network develops a scale-free dependency. Moreover it strengthens and becomes valid for a wider segment along with the simulation progress, which implies a highly organised structure of the analysed graph.

Keywords

geometric neural networks graph spectrum scale-freeness 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jarosław Piersa
    • 1
  • Tomasz Schreiber
    • 1
  1. 1.Faculty of Mathematics and Computer ScienceNicolaus Copernicus UniversityPoland

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