Abstract
The question about the effect of the host (node) morphology on complex network characteristics and properties of dynamical processes defined on networks is addressed. The complex networks are formed by hosts represented by realistic neural cells of complex morphology. The neural cells of different types are randomly placed on a 3-dimensional cubic domain. The connections between nodes established according to overlaps between different nearest-neighbor hosts significantly depend on the host morphology and thus are also random. The influence of host morphology on the following network characteristics has been studied: edge density, clustering coefficient, giant component size, global efficiency, degree entropy, and assortative mixing. The zero-field Ising model has been used as a prototype model to study the effect of the host morphology on dynamical processes defined on the networks of hosts which can be in two states. The mean magnetization, internal energy and spin-cluster size as function of temperature have been numerically studied for several networks composed of hosts of different morphology.
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References
Anderson, K., Bones, B., Robinson, B., Hass, C., Lee, H., Ford, K., Roberts, T.A., Jacobs, B.: The morphology of supragranular pyramidal neurons in the human insular cortex: a quantitative Golgi study. Cereb. Cortex 19(9), 2131–2144 (2009)
Ascoli, G.A.: Mobilizing the base of neuroscience data: the case of neuronal morphologies. Nat. Rev. Neurosci. 7, 318–324 (2006)
Ascoli, G.A., Scorcioni, R.: Neuron and Network Modeling. In: Zaborszky, L., Wouterlood, F.G., Lanciego, J.L. (eds.) Neuroanatomical Tract-Tracing, vol. 3, pp. 604–630. Springer, New York (2006)
Boccaletti, S., Latora, V., Moreno, Y., Chavez, M., Hwang, D.-U.: Complex networks: structure and dynamics. Phys. Rep. 424, 175–308 (2006)
Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)
da Costa, L.F., Manoel, E.T.M.: A percolation approach to neural morphometry and connectivity. Neuroinform. 1 (1), 65–80 (2003)
da Costa, L.F., Coelho, R.C.: Growth-driven percolations: the dynamics of connectivity in neuronal systems. Eur. Phys. J. B 47, 571–581 (2005)
da Costa, L.F., Rodrigues, F.A., Travieso, G., Boas, P.R.V.: Characterization of complex networks: a survey of measurements. Adv. Phys. 56 (1), 167–242 (2007)
Eberhard, J.P., Wanner, A., Wittum, G.: NeuGen: A tool for the generation of realistic morphology of cortical neurons and neuronal networks in 3D. Neurocomputing 70(1-3), 327–342 (2006)
Gleeson, P., Steuber, V., Silver, R.: Neuroconstruct: a tool for modeling networks of neurons in 3D space. Neuron. 54, 219–235 (2007)
Hayes, T.L., Lewis, D.A.: Magnopyramidal neurons in the anterior motor speech region. Dendritic features and interhemispheric comparisons. Arch. Neurol. 53(12), 1277–1283 (1996)
Jacobs, B., Schall, M., Prather, M., Kapler, E., Driscoll, L., Baca, S., Jacobs, J., Ford, K., Wainwright, M., Treml, M.: Regional dendritic and spine variation in human cerebral cortex: a quantitative Golgi study. Cereb. Cortex 11(6), 558–571 (2001)
Koene, R.A., Tijms, B., van Hees, P., Postma, F., Ridder, A., Ramakers, G.J.A., van Pelt, J., van Ooyen, A.: NETMORPH: A framework for the stochastic generation of large scale neuronal networks with realistic neuron morphologies. Neuroinform. 7, 195–210 (2009)
Lago-Fernández, L.F., Huerta, R., Corbacho, F., Sigüenza, J.A.: Fast response and temporal coherent oscillations in small-world networks. Phys. Rev. Lett. 84, 2758–2761 (2000)
Latora, V., Marchiori, M.: Efficient behavior of small-world networks. Phys. Rev. Lett. 87, 198701 (2001)
Newman, M.E.J.: Assortative mixing in networks. Phys. Rev. Lett. 89, 208701 (2002)
Wang, B., Tang, H., Guo, C., Xiu, Z.: Entropy optimization of scale-free networks’ robustness to random failures. Phys. A 363(2), 591–596 (2005)
Watson, K.K., Jones, T.K., Allman, J.M.: Dendritic architecture of the von Economo neurons. Neurosci. 141(3), 1107–1112 (2006)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ’small-world’ networks. Nature 393, 440–442 (1998)
White, J.G., Southgate, E., Thomson, J.N., Brenner, S.: The structure of the nervous system of the nematode Caenorhabditis elegans. Phil. Trans. R. Soc. Lond. B 314, 1–340 (1986)
Yu, S., Huang, D., Singer, W., Nikolic, D.: A small world of neuronal synchrony. Cereb. Cortex 18, 2891–2901 (2008)
Zubler, F., Douglas, R.: A framework for modeling the growth and development of neurons and networks. Front. Comput. Neurosci. (2009), doi: 10.3389/neuro.10.025.2009
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da Silva, R.A.P., Palhares Viana, M., da Fontoura Costa, L. (2011). The Effect of Host Morphology on Network Characteristics and Thermodynamical Properties of Ising Model Defined on the Network of Human Pyramidal Neurons. In: da F. Costa, L., Evsukoff, A., Mangioni, G., Menezes, R. (eds) Complex Networks. Communications in Computer and Information Science, vol 116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25501-4_10
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DOI: https://doi.org/10.1007/978-3-642-25501-4_10
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