Skip to main content

Skewed and Long-Tailed Distributions of Spiking Activity in Coupled Network Modules with Log-Normal Synaptic Weight Distribution

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11301))

Abstract

Recent studies with neuroimaging modalities have been elucidating a structure of a whole network of the brain and its functional activity. The characteristics of various functional neural activities and network structures exhibit skewed and long-tailed distributions. However, it remains unclear how heavy-tailed structural distribution affects functional distribution. In this study, we constructed spiking neural networks composed of two modules with excitatory post-synaptic potential (EPSP) following log-normal distribution. Through the evaluation of multi-scale entropy analysis and its surrogate data analysis, we reveal that the long-tailed synaptic weight distribution enhances the complexity of spiking activity at large temporal scales and emerges non-linear dynamics. Furthermore, we compared distribution of residence time in each spiking pattern between cases with/without large EPSPs. The results show that strong synapses are crucial in the heavy-tailed distribution of residence time.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. Bassett, D.S., Sporns, O.: Network neuroscience. Nat. Neurosci. 20(3), 353–364 (2017)

    Article  Google Scholar 

  2. Battaglia, F.P., Sutherland, G.R., Cowen, S.L., Mc Naughton, B.L., Harris, K.D.: Firing rate modulation: a simple statistical view of memory trace reactivation. Neural Netw. 18(9), 1280–1291 (2005)

    Article  Google Scholar 

  3. Blake, R., Logothetis, N.K.: Visual competition. Nat. Rev. Neurosci. 3(1), 13 (2002)

    Article  Google Scholar 

  4. Borsellino, A., De Marco, A., Allazetta, A., Rinesi, S., Bartolini, B.: Reversal time distribution in the perception of visual ambiguous stimuli. Kybernetik 10(3), 139–144 (1972)

    Article  Google Scholar 

  5. Bullmore, E., Sporns, O.: Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10(3), 186–198 (2009)

    Article  Google Scholar 

  6. Buzsáki, G., Mizuseki, K.: The log-dynamic brain: how skewed distributions affect network operations. Nat. Rev. Neurosci. 15(4), 264–278 (2014)

    Article  Google Scholar 

  7. Costa, M., Goldberger, A.L., Peng, C.K.: Multiscale entropy analysis of complex physiologic time series. Phys. Rev. Lett. 89(6), 068102 (2002)

    Article  Google Scholar 

  8. Eguiluz, V.M., Chialvo, D.R., Cecchi, G.A., Baliki, M., Apkarian, A.V.: Scale-free brain functional networks. Phys. Rev. Lett. 94(1), 018102 (2005)

    Article  Google Scholar 

  9. Fell, J., Kaplan, A., Darkhovsky, B., Röschke, J.: EEG analysis with nonlinear deterministic and stochastic methods: a combined strategy. Acta Neurobiol. Exp. 60(1), 87–108 (1999)

    Google Scholar 

  10. Glasser, M.F., et al.: A multi-modal parcellation of human cerebral cortex. Nature 536(7615), 171–178 (2016)

    Article  Google Scholar 

  11. Glasser, M.F., et al.: The human connectome project’s neuroimaging approach. Nat. Neurosci. 19(9), 1175–1187 (2016)

    Article  Google Scholar 

  12. Hagmann, P., et al.: Mapping the structural core of human cerebral cortex. PLoS Biol. 6(7), e159 (2008)

    Article  Google Scholar 

  13. Hagmann, P., et al.: Mapping human whole-brain structural networks with diffusion MRI. PloS One 2(7), e597 (2007)

    Article  Google Scholar 

  14. van den Heuvel, M., Mandl, R., Luigjes, J., Pol, H.H.: Microstructural organization of the cingulum tract and the level of default mode functional connectivity. J. Neurosci. 28(43), 10844–10851 (2008)

    Article  Google Scholar 

  15. van den Heuvel, M.P., Sporns, O.: Network hubs in the human brain. Trends Cogn. Sci. 17(12), 683–696 (2013)

    Article  Google Scholar 

  16. Hirase, H., Leinekugel, X., Czurkó, A., Csicsvari, J., Buzsáki, G.: Firing rates of hippocampal neurons are preserved during subsequent sleep episodes and modified by novel awake experience. Proc. Natl. Acad. Sci. 98(16), 9386–9390 (2001)

    Article  Google Scholar 

  17. Hromádka, T., DeWeese, M.R., Zador, A.M.: Sparse representation of sounds in the unanesthetized auditory cortex. PLoS Biol. 6(1), e16 (2008)

    Article  Google Scholar 

  18. Kanamaru, T.: Chaotic pattern alternations can reproduce properties of dominance durations in multistable perception. Neural Comput. 29(6), 1696–1720 (2017)

    Article  MathSciNet  Google Scholar 

  19. Lefort, S., Tomm, C., Sarria, J.C.F., Petersen, C.C.: The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron 61(2), 301–316 (2009)

    Article  Google Scholar 

  20. Lehky, S.R.: Binocular rivalry is not chaotic. Proc. R. Soc. Lond. B 259(1354), 71–76 (1995)

    Article  Google Scholar 

  21. Levelt, W.J.: Note on the distribution of dominance times in binocular rivalry. Br. J. Psychol. 58(1–2), 143–145 (1967)

    Article  Google Scholar 

  22. Mizuseki, K., Buzsáki, G.: Preconfigured, skewed distribution of firing rates in the hippocampus and entorhinal cortex. Cell Rep. 4(5), 1010–1021 (2013)

    Article  Google Scholar 

  23. Mizuseki, K., Buzsaki, G.: Theta oscillations decrease spike synchrony in the hippocampus and entorhinal cortex. Phil. Trans. R. Soc. B 369(1635), 20120530 (2014)

    Article  Google Scholar 

  24. Nagao, N., Nishimura, H., Matsui, N.: A neural chaos model of multistable perception. Neural Process. Lett. 12(3), 267–276 (2000)

    Article  Google Scholar 

  25. O’Connor, D.H., Peron, S.P., Huber, D., Svoboda, K.: Neural activity in barrel cortex underlying vibrissa-based object localization in mice. Neuron 67(6), 1048–1061 (2010)

    Article  Google Scholar 

  26. Peyrache, A., et al.: Spatiotemporal dynamics of neocortical excitation and inhibition during human sleep. Proc. Natl. Acad. Sci. 109(5), 1731–1736 (2012)

    Article  Google Scholar 

  27. Schreiber, T., Schmitz, A.: Improved surrogate data for nonlinearity tests. Phys. Rev. Lett. 77(4), 635 (1996)

    Article  Google Scholar 

  28. Shafi, M., Zhou, Y., Quintana, J., Chow, C., Fuster, J., Bodner, M.: Variability in neuronal activity in primate cortex during working memory tasks. Neuroscience 146(3), 1082–1108 (2007)

    Article  Google Scholar 

  29. She, Q., Chen, G., Chan, R.H.: Evaluating the small-world-ness of a sampled network: functional connectivity of entorhinal-hippocampal circuitry. Sci. Rep. 6, 21468 (2016)

    Article  Google Scholar 

  30. Song, S., Sjöström, P.J., Reigl, M., Nelson, S., Chklovskii, D.B.: Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol. 3(3), e68 (2005)

    Article  Google Scholar 

  31. Sporns, O.: Contributions and challenges for network models in cognitive neuroscience. Nat. Neurosci. 17(5), 652–660 (2014)

    Article  Google Scholar 

  32. Teramae, J.N., Tsubo, Y., Fukai, T.: Optimal spike-based communication in excitable networks with strong-sparse and weak-dense links. Sci. Rep. 2, 485 (2012)

    Article  Google Scholar 

  33. Walker, P.: Stochastic properties of binocular rivalry alternations. Percept. Psychophys. 18(6), 467–473 (1975)

    Article  Google Scholar 

Download references

Acknowledgment

This work was supported by JSPS KAKENHI for Early-Career Scientists (grant number: 18K18124).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Sou Nobukawa .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Nobukawa, S., Nishimura, H., Yamanishi, T. (2018). Skewed and Long-Tailed Distributions of Spiking Activity in Coupled Network Modules with Log-Normal Synaptic Weight Distribution. In: Cheng, L., Leung, A., Ozawa, S. (eds) Neural Information Processing. ICONIP 2018. Lecture Notes in Computer Science(), vol 11301. Springer, Cham. https://doi.org/10.1007/978-3-030-04167-0_48

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-04167-0_48

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-04166-3

  • Online ISBN: 978-3-030-04167-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics