Abstract
The brain is organized as neuron assemblies with hierarchies of complex network connectivity. In 1998, Watts and Strogatz conjectured that the structures of most complex networks in the real world have the so-called small-world properties of a small mean path between nodes and a high cluster value, regardless of whether they are artificial networks, such as the Internet, or natural networks, such as the brain. Here we explore the nature of a small-world network of neuron assemblies by simulating the network structural dependence of Izhikevich’s spiking neuron model. The synchronized rhythmical firing is estimated in terms of rewiring probabilities, and the structural dependence of the firing correlation coefficient is discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Sakamoto, K., et al.: Discharge Synchrony during the Transition of Behavioral Goal Representations Encoded by Discharge Rates of Prefrontal Neurons. Cerebral Cortex 18, 2036–2045 (2008)
Watts, D.J., Strogatz, S.H.: Collective dynamics of ’Small-world’ networks. Nature 393, 440–442 (1998)
Boccaletti, S., Latora, V., Chavez, M., Hwang, D.-U.: Complex networks: Structure and dynamics. Physics Reports 424, 175–308 (2006)
Arenas, A., Díaz-Guilera, A., Kurths, J., Moreno, Y., Zhou, C.: Synchronization in complex networks. Physics Reports 469, 93–153 (2008)
Bassett, D.S., Bullmore, E.: Small-World Brain Networks. The Neuroscientist 12, 512–523 (2006)
Zemanová, L., Zhou, C., Kurths, J.: Structural and functional clusters of complex brain networks. Physica D 224, 202–212 (2006)
Brette, R., et al.: Simulation of networks of spiking neurons: A review of tools and strategies. J. Comput. Neurosci. 23, 349–398 (2007)
Izhikevich, E.M.: Simple Model of Spiking Neurons. IEEE Trans. Neural Networks 14, 1569–1572 (2003)
Izhikevich, E.M.: Which Model to Use for Cortical Spiking Neurons? IEEE Trans. Neural Networks 15, 1063–1070 (2004)
Erdös, P., Renyi, A.: On random graphs. Publ. Math (Debrecen) 6, 290–297 (1959)
Barabási, A.-L., Albert, R.: Emergence of scaling in random networks. Science 286, 349–352 (1999)
Kanamaru, T., Aihara, K.: The effects of Watts-Strogatz’s rewiring to the synchronous firings in a pulse neural network with gap junctions. Technical Report of IEICE, vol. 107, pp. 175–180 (2008)
Kanamaru, T., Aihara, K.: Stochastic Synchrony of Chaos in a Pulse-Coupled Neural Network with Both Chemical and Electrical Synapses Among Inhibitory Neurons. Neural Computation 20, 1951–1972 (2008)
Kamiya, A., et al.: A schizophrenia-associated mutation of DISC1 perturbs cerebral cortex development. Nature Cell Biology 7, 1167–1178 (2005)
Miswiring the Brain: Breakthrough of the year. Science 310, 1880–1885 (2005)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer Tokyo
About this paper
Cite this paper
Yamanishi, T., Nishimura, H. (2010). Firing Correlation in Spiking Neurons with Watts–Strogatz Rewiring. In: Peper, F., Umeo, H., Matsui, N., Isokawa, T. (eds) Natural Computing. Proceedings in Information and Communications Technology, vol 2. Springer, Tokyo. https://doi.org/10.1007/978-4-431-53868-4_41
Download citation
DOI: https://doi.org/10.1007/978-4-431-53868-4_41
Publisher Name: Springer, Tokyo
Print ISBN: 978-4-431-53867-7
Online ISBN: 978-4-431-53868-4
eBook Packages: Computer ScienceComputer Science (R0)