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Short and Long Edges in Random Graphs for Neuropil Modeling

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Cognitive Phase Transitions in the Cerebral Cortex - Enhancing the Neuron Doctrine by Modeling Neural Fields

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 39))

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Abstract

Graph theoretical approaches have been very successful in the past decade to describe functional and structural aspects of brain networks; see, for example Eguiluz et al., Phys Rev Lett 94(1):018102, 2005 [1], Reijneveld et al., Clin Neurophysiol 118(11):2317–2331, 2007 [2], Turova and Villa, Biosystems 89(1):280–286, 2007, [3], Tlusty and Eckmann, J Phys A Math Theor 42(20):205004, 2009, [4] and Gallos et al., Proc Natl Acad Sci 109(8):2825–2830, 2012 [5]. The existence of functional links between cortical nodes has been postulated in EEG, MEG, and fMRI data Sporns et al., PLOS Comp Biol 1(4):245–251, 2005 [6], Honey et al., Neuroimage 52(3):766–776, 2010 [7], Stam et al., Cereb Cortex 17:92–99, 2007 [8], Bonifazi et al., Science 326(5958):1419–1424, 2009 [9], Deco and Corbetta, Neuroscientist 17(1):107–123, 2011 [10] and Kim et al., NeuroImage Clin 2:414–423, 2013 [11].

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Authors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, TN, USA

    Robert Kozma

  2. Division of Neurobiology, University of California at Berkele, Berkeley, CA, USA

    Walter J. Freeman

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Correspondence to Robert Kozma .

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Kozma, R., Freeman, W.J. (2016). Short and Long Edges in Random Graphs for Neuropil Modeling. In: Cognitive Phase Transitions in the Cerebral Cortex - Enhancing the Neuron Doctrine by Modeling Neural Fields. Studies in Systems, Decision and Control, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-24406-8_4

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