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Handbook of Large-Scale Random Networks pp 325–368Cite as

Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 18))

Abstract

The problem of prediction of yet uncharted connections in the large scale network of the cerebral cortex is addressed. Our approach was determined by the fact that the cortical network is highly reciprocal although directed, i.e. the input and output connection patterns of vertices are slightly different. In order to solve the problem of predicting missing connections in the cerebral cortex, we propose a probabilistic method, where vertices are grouped into two clusters based on their outgoing and incoming edges, and the probability of a connection is determined by the cluster affiliations of the vertices involved. Our approach allows accounting for differences in the incoming and outgoing connections, and is free from assumptions about graph properties. The method is general and applicable to any network for which the connectional structure is mapped to a sufficient extent. Our method allows the reconstruction of the original visual cortical network with high accuracy, which was confirmed after comparisons with previous results. For the first time, the effect of extension of the visual cortex was also examined on graph reconstruction after complementing it with the subnetwork of the sensorimotor cortex. This additional connectional information further improved the graph reconstruction. One of our major findings is that knowledge of definitely nonexistent connections may significantly improve the quality of predictions regarding previously uncharted edges as well as the understanding of the large scale cortical organization.

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Authors and Affiliations

  1. KFKI Research Institute for Particle and Nuclear Physics of the Hungarian Academy of Sciences, H-1525, Budapest, P.O. Box 49, Hungary

    Tamás Nepusz & Fülöp Bazsó

  2. Department of Measurement and Information Systems, Budapest University of Technology and Economics, H-1521, Budapest, P.O. Box 91, Hungary

    Tamás Nepusz

  3. Neurobionics Research Group Hungarian Academy of Sciences — Péter Pázmány Catholic University, Semmelweis University, H-1094, Budapest, Tűzoltó u. 58, Hungary

    László Négyessy

  4. Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, 1053, Budapest, Hungary

    Gábor Tusnády

  5. Polytechnical Engineering College Subotica, Marka Oreškovića 16, 24000, Subotica, Serbia

    Fülöp Bazsó

Authors
  1. Tamás Nepusz
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  2. László Négyessy
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  3. Gábor Tusnády
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  4. Fülöp Bazsó
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Editor information

Editors and Affiliations

  1. Department of Pure Mathematics & Mathematical Statistics, University of Cambridge, Centre for Mathematical Sciences, Cambridge, CB3 0WB, UK

    Béla Bollobás

  2. Dept. Mathematical Sciences, University of Memphis, Memphis, TN, 38152, USA

    Béla Bollobás  & Robert Kozma  & 

  3. Alfréd Rényi Inst. of Mathematics, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Dezső Miklós

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Nepusz, T., Négyessy, L., Tusnády, G., Bazsó, F. (2008). Reconstructing Cortical Networks: Case of Directed Graphs with High Level of Reciprocity. In: Bollobás, B., Kozma, R., Miklós, D. (eds) Handbook of Large-Scale Random Networks. Bolyai Society Mathematical Studies, vol 18. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69395-6_8

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